Login to your account

If you don't remember your password, you can reset it by entering your email address and clicking the Reset Password button. You will then receive an email that contains a secure link for resetting your password

If the address matches a valid account an email will be sent to __email__ with instructions for resetting your password

Please enter a term before submitting your search.

New articles

Please select at least one article in order to proceed.

March 9, 2023

Neural knowledge assembly in humans and neural networks

Neural knowledge assembly in humans and neural networks

The neural architecture of theory-based reinforcement learning

The neural architecture of theory-based reinforcement learning

March 8, 2023

Choroid plexus-targeted NKCC1 overexpression to treat post-hemorrhagic hydrocephalus

Choroid plexus-targeted NKCC1 overexpression to treat post-hemorrhagic hydrocephalus

Glutamatergic and GABAergic neurons in pontine central gray mediate opposing valence-specific behaviors through a global network

Glutamatergic and GABAergic neurons in pontine central gray mediate opposing valence-specific behaviors through a global network

March 7, 2023

Communication dynamics in the human connectome shape the cortex-wide propagation of direct electrical stimulation

Communication dynamics in the human connectome shape the cortex-wide propagation of direct electrical stimulation

Transcriptional control of nucleus accumbens neuronal excitability by retinoid X receptor alpha tunes sensitivity to drug rewards

Transcriptional control of nucleus accumbens neuronal excitability by retinoid X receptor alpha tunes sensitivity to drug rewards

March 2, 2023

Molecular and cellular mechanisms of the first social relationship: A conserved role of 5-HT from mice to monkeys, upstream of oxytocin

Molecular and cellular mechanisms of the first social relationship: A conserved role of 5-HT from mice to monkeys, upstream of oxytocin

March 1, 2023

A spinal muscular atrophy modifier implicates the SMN protein in SNARE complex assembly at neuromuscular synapses

A spinal muscular atrophy modifier implicates the SMN protein in SNARE complex assembly at neuromuscular synapses

February 24, 2023

Hidden behavioral fingerprints in epilepsy

Hidden behavioral fingerprints in epilepsy

February 23, 2023

EndophilinA-dependent coupling between activity-induced calcium influx and synaptic autophagy is disrupted by a Parkinson-risk mutation

EndophilinA-dependent coupling between activity-induced calcium influx and synaptic autophagy is disrupted by a Parkinson-risk mutation

February 22, 2023

DNA-initiated epigenetic cascades driven by C9orf72 hexanucleotide repeat

DNA-initiated epigenetic cascades driven by C9orf72 hexanucleotide repeat

February 17, 2023

Development of top-down cortical propagations in youth

Development of top-down cortical propagations in youth

February 15, 2023

Centrosomal microtubule nucleation regulates radial migration of projection neurons independently of polarization in the developing brain

Centrosomal microtubule nucleation regulates radial migration of projection neurons independently of polarization in the developing brain

February 13, 2023

Neurodegeneration cell per cell

Neurodegeneration cell per cell

Cannabidiol modulates excitatory-inhibitory ratio to counter hippocampal hyperactivity

Cannabidiol modulates excitatory-inhibitory ratio to counter hippocampal hyperactivity

Brief synaptic inhibition persistently interrupts firing of fast-spiking interneurons

Brief synaptic inhibition persistently interrupts firing of fast-spiking interneurons

Social deprivation induces astrocytic TRPA1-GABA suppression of hippocampal circuits

Social deprivation induces astrocytic TRPA1-GABA suppression of hippocampal circuits

February 9, 2023

Large-scale differentiation of iPSC-derived motor neurons from ALS and control subjects

Large-scale differentiation of iPSC-derived motor neurons from ALS and control subjects

February 1, 2023

A neural substrate for negative affect dictates female parental behavior

A neural substrate for negative affect dictates female parental behavior

Agency affects pain inference through prior shift as opposed to likelihood precision modulation in a Bayesian pain model

Agency affects pain inference through prior shift as opposed to likelihood precision modulation in a Bayesian pain model

January 27, 2023

Oxytocin receptor is not required for social attachment in prairie voles

Oxytocin receptor is not required for social attachment in prairie voles

January 26, 2023

Local 5-HT signaling bi-directionally regulates the coincidence time window for associative learning

Local 5-HT signaling bi-directionally regulates the coincidence time window for associative learning

January 20, 2023

Ventral tegmental area astrocytes modulate cocaine reward by tonically releasing GABA

Ventral tegmental area astrocytes modulate cocaine reward by tonically releasing GABA

Causal role of a neural system for separating and selecting multidimensional social cognitive information

Causal role of a neural system for separating and selecting multidimensional social cognitive information

January 19, 2023

Virus exposure and neurodegenerative disease risk across national biobanks

Virus exposure and neurodegenerative disease risk across national biobanks

January 13, 2023

Machine learning dissection of human accelerated regions in primate neurodevelopment

Machine learning dissection of human accelerated regions in primate neurodevelopment

Humidity sensors that alert mosquitoes to nearby hosts and egg-laying sites

Humidity sensors that alert mosquitoes to nearby hosts and egg-laying sites

January 12, 2023

Dorsomedial prefrontal hypoexcitability underlies lost empathy in frontotemporal dementia

Dorsomedial prefrontal hypoexcitability underlies lost empathy in frontotemporal dementia

January 10, 2023

Temporal continuity shapes visual responses of macaque face patch neurons

Temporal continuity shapes visual responses of macaque face patch neurons

January 9, 2023

Human cortical interneurons optimized for grafting specifically integrate, abort seizures, and display prolonged efficacy without over-inhibition

Human cortical interneurons optimized for grafting specifically integrate, abort seizures, and display prolonged efficacy without over-inhibition

January 6, 2023

Evolutionarily conserved regulators of tau identify targets for new therapies

Evolutionarily conserved regulators of tau identify targets for new therapies

January 5, 2023

Extrinsic control of the early postnatal CA1 hippocampal circuits

Extrinsic control of the early postnatal CA1 hippocampal circuits

The content on this site is intended for healthcare professionals and researchers across all fields of science.


U.S. flag

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Logo of plosone

Invisible Brain: Knowledge in Research Works and Neuron Activity

1 Graduate School of Knowledge Service Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, 305-701, South Korea

2 School of Computing, KAIST, 291 Daehak-ro, Yuseong-gu, 305-701, South Korea

Dorothy Curtis

3 CSAIL, MIT, 32 Vassar St, Cambridge, MA, 02139, United States of America

Sukhwan Jung

Suhyun chae.

Conceived and designed the experiments: AS DC SJ. Performed the experiments: AS SC SJ. Analyzed the data: AS DC SC SJ. Contributed reagents/materials/analysis tools: AS DC SC SJ. Wrote the paper: AS.

Associated Data

All relevant data are within the paper and its Supporting Information files.

If the market has an invisible hand, does knowledge creation and representation have an “invisible brain”? While knowledge is viewed as a product of neuron activity in the brain, can we identify knowledge that is outside the brain but reflects the activity of neurons in the brain? This work suggests that the patterns of neuron activity in the brain can be seen in the representation of knowledge-related activity. Here we show that the neuron activity mechanism seems to represent much of the knowledge learned in the past decades based on published articles, in what can be viewed as an “invisible brain” or collective hidden neural networks. Similar results appear when analyzing knowledge activity in patents. Our work also tries to characterize knowledge increase as neuron network activity growth. The results propose that knowledge-related activity can be seen outside of the neuron activity mechanism. Consequently, knowledge might exist as an independent mechanism.


Neuron activity has been researched extensively in the area of knowledge representation. Previous work suggested that there is another layer between neuron activity and knowledge representation in brain activity [ 1 , 2 ]. In economics, the invisible hand of the market is a metaphor to describe the self-regulating behavior of the marketplace [ 3 ]. Our work shows that the neuron-like behavior appears in knowledge systems outside of the brain, therefore suggesting that knowledge can be represented directly by patterns of neuron activity as an “invisible brain”. Thus we suggest that biological neuron behaviors are a good tool for the representation of knowledge activity and might appear in multiple areas of life.

The biological neuron model describes the mathematical neuron spiking process. Neurons are viewed as cells specialized for communication with other neurons or cell types. Biological neuron communication is performed through synapses, which are electrical or electrochemical signal junctions. We conceptualize knowledge in research as spiking neuron communication and compare the research publication activity to real neuron behavior.

The method is based on identifying similarity between brain neuron behavior and research publication activity over time, which can be considered a representation of knowledge. We analyze 9,799,239 research publications as well as patents in different domains according to topics such as anaphylaxis, jet turbine, and game theory and identify the research areas over 45 years. We extract the communication activity between different research topics according to keyword frequency correlation appearing in published articles. Then we map all research topic activity to keyword frequency correlation and compare the resulting correlation to biological neuron activity simulations. The communication is monitored over time for spiking activity as in collective hidden neural networks. Similar communication in patents is analyzed to check whether the knowledge activity appears in other areas.

Knowledge and Brain

The topic of knowledge and brain activity has been researched ever since Plato stated that “knowledge is perception” [ 4 ] and speculated that knowledge is contained in the brain [ 5 ]. The hypothesis that the functional unit of the brain is the neuron was formed based on the development of a staining procedure by Golgi that used silver chromate salt to reveal the intricate structures of a single neuron. Cajal’s use of the technique led to the formation of the neuron doctrine, the hypothesis that the functional unit of the brain is the neuron [ 6 ].

Currently the neuron doctrine views the brain as a network [ 7 ]. There are many structure-function relationships in a brain. One can view a set of regions as a set of nodes while a relationship between two regions is mapped to a link between corresponding nodes. How we can determine each region is an issue which corresponds to building nodes in a network.

Previous work in graph theory employed a clustering coefficient as a measure of the degree to which nodes in a graph tend to cluster together. Evidence indicated that in most real-world networks, and especially in social networks, nodes tend to form tightly knit groups marked by a relatively high density of ties which tends to be greater than the average probability of a tie randomly established between two nodes [ 8 , 9 ].

The structure of a dynamic network, or evolving network, can alter as time passes. In some cases, we separate a period of time into several time slots, and we can view a dynamic network as a sequence of networks, where each network represents a snapshot of the dynamic network at each time slot [ 10 , 11 ].

For a given complex system, there are actuators of the system and there are interactions, interconnections, or relationships among them. Examples include social networks [ 9 ], collaboration networks [ 12 ], the Internet [ 13 ], the World Wide Web [ 14 ], and biological networks [ 15 ]. Many complex networks for real-world systems have the same properties, such as small world phenomena and power-law distribution; two nodes in a network are likely connected through a short path (a sequence of nodes of a network), and the degree (the number of neighbors of a node) follows a power-law distribution so that there exist some hub nodes which have many more connections than others.

Many methods have been developed for the analysis of homogeneous networks. But the analysis of heterogeneous networks is not simple, for links across entities can have several types. The Internet of Things is an example of a heterogeneous network [ 16 ]. The approach uses a variety of things or objects which can be represented as nodes. The nodes can be connected by their relations. Another approach is the network of networks, which can be viewed as a system of coupled networks, where the networks have different nodes or multilayer networks and networks can be layered when each layer contains the same type of edges in the presence of multiple types of edges [ 17 ].

Another problem is how to build a network for a given complex system. The problem is closely related to the problem of graph drawing or network visualization [ 18 ], where there is a suitable node-link diagram that describes a network. However, the graph drawing problem usually assumes that a set of nodes and a set of edges are given together and tries to find a set of positions of the nodes in a space. Other work addressed the problem of building a complex system by merging one network that contains the link structure and another network that contains the content information [ 19 ].

Evolutionary clustering deals with the problem of processing time stamped data to produce a sequence of clustering for each time step of the data arriving to the detecting system [ 20 ]. In analyzing dynamic networks such as social networks, node characteristics and behavior are often correlated with influence and homophily [ 21 ].

Optical [ 22 , 23 , 24 ] and electrophysiological [ 25 , 26 ] techniques exist for recording activity from many neurons. The field of recording a large number of neurons is still in its infancy. Current techniques allow recording only a small number of neurons for imaging. The current techniques are limited compared to the number of neurons existing in the brain of most animals analyzed today. The analysis of only a small number of neurons is limited in the isolation of the boundary of neural network behavior [ 27 , 28 ].

To analyze neuron network connectivity behavior, the electrical activity between the neurons can be sampled. When sampling neurons, both the spatial resolution and the time resolution should be considered. Previous research has sampled neuron activity extending from milliseconds to months. Regarding the neuron network area covered, the area sampled ranges from a small number of microns to centimeters [ 29 , 30 ].

Although it is known that neurons are connected by a network structure, how this network works and achieves the results attributed to the brain as a whole is far from being clear. The analysis of the change of fluorescence can assist in the understanding of the activity of neural events and the neural network spiking connectivity. Neural reconstruction can facilitate viewing how large networks of neurons spike and how different spiking areas in the network are associated. The idea behind it is that when the neural network spiking is over-excitable one neuron can trigger a large number of neurons which are not directly connected to it [ 31 ]. Previous work has also analyzed neuron spiking relative to background activity [ 32 , 33 ].

The idea that the connectivity of a neuron system can be generalized across systems in different animals based on existing knowledge of small circuits has been previously suggested [ 34 ]. Similarly, previous work suggested clustering knowledge according to passing messages by identifying a subset of processing sensory signal examples and detecting patterns in the data [ 35 ].

In the past Hopfield [ 36 ] suggested to build collective systems having a large number of simple elements similar in their activity to neurons used by biological organisms. The idea was expanded as a conceptual framework to understand the computational processing in the neural circuit model, where circuits consist of neurons organized in networks with effective synaptic connections [ 37 ].

The organization of large populations of interacting elements has been researched extensively in areas of physical, biological, chemical, and social systems. The problem of organization synchronization included the approach of modeling each member of the population as a phase oscillator [ 38 ]. Spiking neural systems are viewed as a class of distributed parallel computing devices motivated by the way neurons communicate by means of spikes. Asynchronous systems are non-synchronized systems, where the use of spiking rules is not mandatory [ 39 ].

One method used for simulating a large number of neurons was based on video viewing of neuron activity [ 40 ]. The method was based on taking snapshots of neuron networks through optical imaging. The video acquired from the time series snapshots allowed the measurement of large networks of neurons. Based on the neuron activity in the video, the structure of the neuron network could be reconstructed. The snapshots of the neuron calcium inflow assist in estimating the resulting actions of the individual spiking neurons. The implemented method analyzed the changing fluorescence values, which measured reactions between fluorescent molecules and calcium ions.

The method used here is based on a simulation that aims at inferring the connectivity of neuron networks from calcium fluorescence imaging of their network signals. The simulation method used [ 41 ] is based on analyzing cause and effect of neuron behavior over time. The problem is represented as a graph with nodes, neurons, and edges connecting to other nodes, synapses. The graph is directed where all edges are from one node to another. Therefore, edges can be viewed as either excitatory or inhibitory. The neurons are arranged in a two-dimension “square petri dish”. The coordinate location of the neurons is predetermined and used for both data sets including the neurons and the research activity. The simulation also includes light scattering effects due to overlapping signals.

The data simulation [ 41 ] used is based on real neuron behavior. The neuron network structure uses topology connectivity models. The simulation is based on neuron distance and estimates neuron clustering based on real biological data. The method incorporates NEST simulator models [ 42 , 43 ] for leaky integrate-and-fire models. These models provide a more accurate simulation of experimentally observed neuron spiking recordings. The fluorescence is modeled using time averaging of calcium fluorescence spiking and light scattering. The fluorescence emitted from neurons is compared to the “fluorescence” emitted from knowledge based on the analysis of research publications and patents to view the activity of the “invisible brain”.

Research Publication Activity

Research publication activity is analyzed by the number of publications on each topic (node) and correlation between topics (node connectivity or “synapses”). The activity on a specific topic can be viewed by the number of article or patent publications on a specific topic analyzed by keyword occurrences. The keyword set used to define each publication can be supplied by the author, the publication journal, or patent classifications based on a predefined set of keywords or extracted from the title or the abstract. The basic time frame for evaluating topic publication activity was set at one year. Smaller time frames were analyzed but seemed less significant due to the periodic timeline of research activity.

Evaluating connectivity, or communication, between research topics is based on identifying first the related topics. This is done by classifying multiple topics which appear in the same research article or patent, as identified by the selected keywords. Once two topics are marked as related, we analyze the degree of correlation of the topics’ activity over the whole time period viewed. Then we can select the top n highly correlated nodes to be compared to n simulated connected brain neurons and observe the “fluorescence” created by both activities.

PubMed and Web of Science provide access to multiple databases of references and abstracts on life sciences and biomedical topics. The United States Patent and Trademark Office provides information about all patents and intellectual property in the US. To analyze research publication activity, articles and patents were extracted from all three data sources according to general topic keywords such as anaphylaxis , Doppler effect , yellow fever , and diphtheria .

The research topic analysis method includes the following steps outlined in Fig 1 :

An external file that holds a picture, illustration, etc.
Object name is pone.0158590.g001.jpg

Neuron versus Research Activity

Analysis was performed on 9,799,239 research articles and on patents from 24 different topics in medicine and 9 topics related to physics and game theory in over 45 years. The data topic description is displayed in Table 1 . Data sets from PubMed, Web of Science (WoS), and United States Patent and Trademark Office (USPTO) were used in the experiments. The number of keywords which can be used ranges from a single term per article or patent to all possible words in the abstract. Two keyword search field tags were used from each data source. Web of Science has WC (Web of Science Category) and SC (Subject Category). PubMed has MH (MeSH—Medical Subject Headings Terms) and OT (Other Term). USPTO has CPC (Cooperative Patent Classifications) and ICL (International Classification). The total number of article or patent records used ranged from 182 ( quantum electro dynamics ) to 471,641 ( diabetes ). Except for topics such as epidemiology, microbiology, oncology, and genetics, which were too big, the input data can be found in the Supporting Information [ S1 – S9 Files]. Preprocessing was performed to remove duplications. The results were organized by descending correlation.

Simulated Neuron Activity

The simulated neuron data is based on a realistic simulator of real neurons and a model of calcium fluorescence recording. The data used in the simulation was based on the ChaLearn Connectomics Challenges ( http://connectomics.chalearn.org/ ). The data used was generated by a simulator described in [ 41 ] and detailed in the Methods Section. The motivation behind the simulation is to be able to isolate a predetermined number of neurons and allow them to interact in a “square petri dish”. While creating the option of isolating neurons and supplying the correct input is difficult due their connectivity to other neurons, the simulation allows tools to provide a controlled environment closely resembling real neurons. The simulation is based on a network of neurons interacting with one another. Each neuron spike is based on input received from nearby connected neurons. In the case of real neuron simulation, the spike or firing of a neuron depends on the chemical / electrical signal received from nearby connected neurons. In the case of research activity, the signal is based on information transfer between topics of research representing a neuron node. The visual aspects of the simulation are based on imaging the calcium florescence emitted by the interaction between neurons. The simulation is built on spiking based on interaction between neurons instead of separate neurons spiking at random times independently. The simulation also considers light effects based on multiple nearby neurons or light simulation based on multiple emitting sources.

The data used for the neuron activity simulation included files from the ChaLearn Connectomics Challenges ( https://www.kaggle.com/c/connectomics/data ). Two types of files were used. The first type of files describes the neural fluorescence activity. These files represent a time series of each neuron activity every 20ms. The neurons are ordered by rows and columns. The second type of files includes a list of X and Y position of each neuron in the “square petri dish”. The simulation represents neurons in an area of 1mm 2 . The files used for simulation included small networks of 100 neurons and normal networks of 1,000 neurons. In addition, a high rate of spiking neurons and a normal rate of spiking neurons with low signal noise were also analyzed.

Research Topic Activity

For the analysis of research records, the time series activity used was every year. The comparison was made using the same number of top 100 or 1,000 keywords in each of the topics. The location of each of the keywords was based on the neuron positions in the “square petri dish” and was randomly picked from the existing set of neuron positions appearing in the file.

To extract publications in medicine and physics, each of the topics appearing in Table 1 was used in the Web of Science, PubMed, or USPTO. All of the records were used for each topic. For each topic all possible keywords describing the publications were counted each year. For every pair of keywords that appeared at least once in the same publication, the correlation was analyzed over the whole time period. The keywords were organized in descending order of correlation followed by number of appearances. To compare research topic activity to neuron simulation, the top 100 or 1000 ranking keyword correlations were used. The simulated neuron activity data and the research topic activity data can be found in the Supporting Information [ S1 – S9 Files].

Image Comparison

Earth Mover's Distance (EMD) is used for image similarity comparison. EMD is a true metric if the ground distance is metric and if the total weights of two signatures are equal. This allows use of image spaces with a metric structure. EMD matches perceptual similarity better than other measures, when the ground distance is perceptually meaningful. This was shown by [ 44 ] for color- and texture-based image retrieval.

Fig 2 displays neuron activity change versus research activity on the topic of anaphylaxis . In this case, 100 neuron activity nodes were selected and compared to 100 high ranking correlated activity topics. The locations of the nodes of the research activity topics were randomly selected from the set of existing locations of the neuron nodes. The time line compares peaks in activity and the time scale is obviously not identical since the neuron activity is sampled at 20ms intervals and the publication activity in years. The neurons span a 1mm 2 square area. The activity was calibrated to show similar color shades for maximum and minimum activity. The EMD indicates the size of difference between each of the two images.

An external file that holds a picture, illustration, etc.
Object name is pone.0158590.g002.jpg

When the activity peaks, the similarity between the neuron activity and the research activity becomes visible. The similarity extends to both location and intensity of a specific node area. Prior to the peak, the activity seems considerably different and the neurons are not very active. The peak appears and disappears suddenly within a few seconds of neuron brain activity and similarly within a few years of publication. The assumption of continued similarity of activity in the future makes future extrapolations possible. Analysis of the peak activity and view of the next “frame” of the movie in neuron activity might provide some information on the future decrease in activity in a research topic such as anaphylaxis .

Fig 3 presents a more detailed perspective using 1000 nodes of neuron activity versus research activity on the topic of in vitro fertilization . Comparison of the results shows again that, as the activity increases, the similarity between the communication of the nodes becomes more visible. However, assuming the activity similarity will continue, the peak of research in the area of in vitro fertilization has not yet been achieved, as seen in the last neuron activity frame.

An external file that holds a picture, illustration, etc.
Object name is pone.0158590.g003.jpg

Fig 4(a) compares medical-based research activity with physics research activity over time. The medical domain includes five randomly selected topics: anaphylaxis , irritable bowel syndrome , diphtheria , yellow fever , and gastritis . Similarly the physics domain includes four topics: bubble chamber , jet turbine , uncertainty principle , and Doppler effect . An additional topic of game theory was added to represent a topic that spreads over multiple domains, including economics, political science, biology, and computer science. The Y-axis displays the EMD value based on comparing each image activity to a baseline image representing no activity, where higher values represent more research activity, while the X-axis represents the change in years from 1970.

An external file that holds a picture, illustration, etc.
Object name is pone.0158590.g004.jpg

The results show similarity between the activity of the different domains. Some topics represent a slow decrease and then fast growing research activity in areas such as Doppler effect , yellow fever , and diphtheria . Other topics show increased interest over time, such as irritable bowel syndrome and uncertainty principle . Game theory , representing a collection of research disciplines, is portrayed as a more stable research activity. Overall, no difference between the research domain activities and research domain areas is visible.

Fig 4(b) compares using EMD on two data sources, Web of Science and PubMed, to no activity baseline image based on the previous five medical topics. The sudden peaks in topics such as anaphylaxis and diphtheria can be attributed to the response to concerns about vaccine safety at the end of the 1980s. The Web of Science data source shows much more research activity than PubMed although topics are related to medical terms. This could be explained by the number of terms, or keywords, associated with each article. Web of Science has considerably fewer terms associated with each article, making each term more unique and making it easier to identify increase in specific research activity. This shows that different data sets of “similar knowledge” can be interpreted differently.

Fig 5 presents activity of anaphylaxis , irritable bowel syndrome , bubble chamber , diphtheria , and game theory research topics on a similar timeline. The small empty frames represent the time gap between the research activities analyzed over a period of 45 years. Although all research topics seem to be currently active, diphtheria displays decreased researched activity compared to previous years. Game theory seems to display a comeback from the early 70s, when in the 80s and 90s it seems to have “departed” from research activity. Many of the topics display a cycle of recurring peaking sudden research activity which also resembles the neuron activity.

An external file that holds a picture, illustration, etc.
Object name is pone.0158590.g005.jpg

Patents were analyzed to examine whether knowledge activity similar to neuron behavior also appears in other areas. The results show that knowledge processing activity similar to neuron behavior can be seen in patents as well as in research publications. Fig 6 displays similarity between article research activity and patent activity on the topics of bubble chamber and game theory . The activity of the two topics is presented in two timelines. The results show that for a long duration there is no activity in patents while the article research publication is active. In both topics there appears a small fluctuation in the patents, shortly followed by a sharp peak of activity in the patents, which becomes more active than the article research activity in that time duration.

An external file that holds a picture, illustration, etc.
Object name is pone.0158590.g006.jpg

The results show that neuron-like knowledge activity is not limited only to the area of article research and can be viewed also in patents. The research activity based on articles can be viewed as representing expanding knowledge, while the patents activity can be viewed as representing business activity or possibility of expanding economic activity in the topic field. One perspective is viewing the activity peak as knowledge transfer from research to patents for a short duration. Another perspective is that in comparison to neuron activity the patents also display a sudden short peak or excitation of activity due to an external stimulator, the article research activity. In both perspectives the result is similar to neuron activity—long durations of very little to no activity followed by short durations of extreme activity.

The goal of the paper is to show similarity between the knowledge activities. Based on this similarity it might be possible to view knowledge as independent of neurons. The minimum short term similarity presented is a year. Longer similarity, and possible knowledge explosion, can be analyzed based on rising activities detected in previous cases of similarity between knowledge publication topic activity and neuron activity. Pairs of similarities can be generated and stored based on a large number of cases. When a new topic is analyzed, it can be compared to previously known pairs and the case with highest similarity can be identified. Furthermore, groups of topics can be analyzed together to check if a combination of them yields a higher chance of knowledge explosion.

The method is used based on past knowledge activities. However, full cycles of neuron activities can be analyzed and compared showing peaks and lower points of the topic activity. New keywords are hard to simulate since the content of the possible label of keywords is harder to extract. However, previous work suggested that analyzing papers by clusters of topics can assist in identifying possible labels of new clusters [ 45 ].

Words are currently the most common method of storing knowledge. The keywords analyzed in this work can be viewed as concepts representing the main issues researched in each of the topics. Other tools of storing knowledge can be considered such as voice, music, or movies. In these cases the relations between each of the instances would have to be defined.

We show knowledge-related activity by observing similarity in behavior of brain neurons and research publication activity. This similarity is viewed as peaks in communication between neuron cells or alternatively communication between research topic areas. The results may allow us to examine knowledge according to neuron behavior patterns and to infer future knowledge behavior according to these patterns in different fields such as research, social behavior, or natural biological systems. In addition, the behavior of knowledge systems may allow us to infer neuron behavior.

Publication Correlation Analysis

To analyze correlation between publication topics over time, we employed the Pearson product-moment correlation coefficient. The Pearson correlation analyzes dependence between topic nodes, when dependence can be viewed as activity between neurons. The correlation is obtained by dividing the covariance of the two variables by the product of their standard deviation.

The correlation coefficient ρ X,Y between two random variables X and Y with expected value μ X and μ Y and standard deviation σ X and σ Y is defined as:

where E is the expected value operator, cov means covariance, and corr for the correlation coefficient. The correlation coefficient is symmetric.

The Pearson correlation reaches a maximum of 1 in the case of a perfect direct (increasing) linear relationship (correlation) and a minimum of −1 in the case of a perfect decreasing (inverse) linear relationship (anticorrelation) [ 46 ]. All other values between −1 and 1 indicate the linear dependence degree between the variables. The closer the values are to 0, the less correlated the variables are, which can be viewed as having less relationship between them. A Pearson correlation coefficient of 0 means the variables are totally independent.

For a given series of n measured variables of X and Y, x i and y i where i = 1, 2, …, n, the sample correlation coefficient can represent the population Pearson correlation r between X and Y.

The sample correlation coefficient is defined as:

where x and y are the sample means of X and Y, and S x and S y are the standard deviations of X and Y.

Simulation of Neural Network Activity

The changing activity of the neuron networks was generated using the NEST simulator [ 42 , 43 ].

The neurons simulation was modeled as leaky integrate-and-fire neurons. The membrane potential V i ( t ) of a neuron i defined by:

where g 1 = 50pS is the leak conductance and τ m = 20ms is the membrane time-constant. The time-dependent input current that derives from recurrent synaptic connections is defined by I syn .

The membrane potential was set to decrease exponentially and remain at zero when there are no synaptic inputs. Inputs from other neurons increase the membrane potential stimulation. When the membrane potential reaches a threshold of V thr = 20mV an action potential is obtained, defined as neuron firing or neuron spiking. The spiking is followed by resetting the membrane voltage to zero for a time period of t ref = 2ms.

The result of the membrane potential activates post-synaptic neurons connected to the spiking neuron. The total synaptic currents are defined by

where A is the adjacency matrix, and τ s = 2ms represents a synaptic time constant. The outcome is described as excitatory post-synaptic potentials (EPSPs) and has a standard difference-of-exponentials time-course [ 47 ].

There is a limited amount of synaptic resources, and therefore neuron connection with synapses includes short term depression [ 48 ]. To simulate the conditions where the inhibitory transmission is fully blocked, fully excitatory networks were created. For each reoccurring input of given neuron i , the set { t j k } represents times of spikes created by the presynaptic neuron j , where t d represents a delay of t d = 2 ms . The synaptic weights of the recurrent connections are defined as homogeneous by α int . The recurrent time dependent strength α int E ji ( t ) is defined by using the network firing history as:

where E ji ( t ) is the portion of neuron transmitting in what is viewed as the “effective state”, similarly R ji ( t ) represents the “recovered state”, while I ji ( t ) = 1 − R ji − E ji represents the “inactive state” [ 48 , 49 ]. Similar to the synaptic current, the recovered state is set to U = 0.3 of neuron transmitters after the presynaptic action potential is reached. The portion decreases exponentially to the inactive state with values of time scale τ inact = 3 ms . The recovery time scale is set to τ rec = 500 ms .

Random neuron networks with depressing synapses generate synchronous activity of integrating and spiking neuron behavior [ 49 ]. On the other hand, all or none activity behavior is observed in cultured networks [ 50 , 51 ]. The weight of the synaptic connections was set in all networks to represent a network bursting of 0.1 ± 0.01 Hz which is viewed as a realistic bursting rate [ 51 ]. Each neuron network was created and simulated for 200 seconds of network activity to evaluate the bursting rate average with an initial value of α int = 5.0 pA . Each time it was bigger than the target bursting rate the synaptic weight α int was decreased by 10% and vice versa for smaller values. Linear extrapolation was used to iteratively adjust until the result was smaller than 0.01 Hz to the target value.

Simulating Neural Network Calcium Fluorescence Spiking Signals

Neuron spiking activity was used to model the calcium fluorescence signals and simulate the experiments of fluorescence signal measured. Based on [ 52 ], a simulation model was used which performs rapid increase of fluorescence after activation. The rapid increase is followed by a gradual decay of   τ C a = 1 s . The model includes the concentration of calcium located between the neurons that match to the fluorescence experimental values. The concentration is changed for each action potential that the neuron evokes for a time step t by a fixed amount of   A C a = 50 μ , which causes fast changes of the concentration defined by

where n t is the total number of action potentials.

For a given neuron i the fluorescence level F is reached by performing saturating static non-linearity on the calcium concentration, followed by adding noise η t using Gaussian distribution with zero mean represented as:

The noise in the simulations was with a standard deviation of 0.03 and a set simulation saturation concentration of K d = 300 μM .

Simulation of Light Scattering

The simulation included light scattering around the neuron cells based on a predefined area between them. The distance between each two neurons i and j is defined by d ij . The scattering length scale is based on the normal light deviation for such optical devices and instruments and set to λ sc = 0.15mm. For a given neuron F i , t s c the fluorescence extent is defined by:

Where the scattering effect overall capacity in the simulation is determined by A sc . The value of the scaling factor is small, A sc = 0.15 to represent the continuing effect on the simulation.

Simulation of Generalized Entropy for Neuron Signal

The Transfer Entropy ( TE ) from two discrete Markov processes X and Y of order k is defined by [ 53 ]:

where n represents each time period measured, x n ( k ) is a vector of size k with measurements of X in time periods n , n −1, …, n − k . For all values of x n + 1 , x n ( k ) and y n ( k ) the total value is calculated.

According to Kullback-Leibler divergence [ 54 ], TE represents the distance based on probability of the space between a neuron node transition matrix P ( x n + 1 | x n ( k ) ) and two neuron node transition matrices P ( x n + 1 | x n ( k ) , y n ( k ) ) . If the two transition matrices are identical, then the distance measure, TE , is defined as zero and vice versa. Signaling dependence of the transition dynamics of X on Y occurs only if transitions of X are not dependent on existing values of Y and are greater than zero.

To analyze directed functional connectivity between different neuron network nodes, the Transfer Entropy was applied. To isolate potential spike events, a discrete differentiation operator was used on the calcium fluorescence time series   F x , t s c . For a neuron network node x ,   x n =   F x , n + 1 s c − F x , n s c . This is performed as pre-processing in order to improve the signal-to-noise ratio. The preprocessing creates for a limited number of data points more accurate probability distributions.

Evaluating Similarity with Earth Mover's Distance

The Earth Mover’s Distance (EMD) is a method for image comparison based on measuring two signatures in color space. Each image is represented by color histograms, and the distance between the two distributions can be viewed as a given ground distance .

The problem can be viewed as two given distributions, the mass of earth spread in space and collection of holes in space. The EMD calculates the least amount of work needed to move the earth to cover the holes with earth. The unit of work relates to transporting a unit of earth by a unit of ground distance.

A signature is defined as a set of clusters or modes of a distribution. Each cluster is represented by a single point representing the cluster center and a weight representing the cluster size.

EMD can be formalized as a linear programming problem: Let P = { ( p 1 , w p 1 ) , … , ( p m , w p m ) } be the first signature with m clusters, where p i is the cluster representative and w pi is the weight of the cluster; Q =   { ( q 1 , w q 1 ) , … , ( q n , w q n ) } the second signature with n clusters; and D = [ d ij ] the ground distance matrix where d ij is the ground distance between clusters p i and q j .

The goal is to find a flow = [ f ij ], with f ij the flow between p i and q j , that minimizes the overall cost

subject to the following constraints:

The first constraint allows moving “earth” from P to Q and not the opposite way. The following two constraints restrict the amount of earth that can be moved by the clusters in P to their weights and the clusters in Q to receive no more earth than their weights. The last constraint forces the movement of the maximum amount of earth possible. This amount is defined as the total flow . After the transportation problem is solved, and the optimal flow F has been found, the earth mover's distance is defined as the work normalized by the total flow:

EMD is used to analyze the differences between the neuron brain activity and the research-related “invisible brain” activity images. The EMD is also used to compare a set of images, which can be viewed as a movie, each set representing a research topic over time.

The activities of the research topics are compared between the domain of medicine and the domain of physics according to the subject category identified by Web of Science field tags. In addition, an analysis is performed to compare research activity based on data extracted from different sources, including Web of Science subject category, PubMed registry number representing concept records, and USPTO representing patent classifications.

Supporting Information

Funding statement.

This work was supported by the IT R&D program of MSIP/KEIT [10044494, WiseKB: Big data based self-evolving knowledge base and reasoning platform]. It was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) 2016R1A2B4011694.

Data Availability

Go to journal home page - Neuron

About the journal

Aims & scope.

Neuron has established itself as one of the most influential and relied upon journals in the field of neuroscience. The editors embrace interdisciplinary strategies which integrate biophysical, cellular, developmental, and molecular approaches with a systems approach to sensory, motor, and …

Latest published

Articles in press, most downloaded, most popular, the costs and benefits of psychedelics on cognition and mood, the centrality of population-level factors to network computation is demonstrated by a versatile approach for training spiking networks, mrna transport, translation, and decay in adult mammalian central nervous system axons, spinal vglut3 lineage neurons drive visceral mechanical allodynia but not sensitized visceromotor reflexes, glioma epileptiform activity and progression are driven by igsf3-mediated potassium dysregulation, microglia drive transient insult-induced brain injury by chemotactic recruitment of cd8 + t lymphocytes, brainstem serotonin neurons selectively gate retinal information flow to thalamus, inhibitory top-down projections from zona incerta mediate neocortical memory.

Copyright © 2023 Elsevier Inc. All rights reserved

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Similar articles being viewed by others

Slider with three articles shown per slide. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide.

research articles about neurons

Optimal responsiveness and information flow in networks of heterogeneous neurons

02 September 2021

Matteo Di Volo & Alain Destexhe

research articles about neurons

Cortical reliability amid noise and chaos

22 August 2019

Max Nolte, Michael W. Reimann, … Eilif B. Muller

research articles about neurons

Single neurons may encode simultaneous stimuli by switching between activity patterns

13 July 2018

Valeria C. Caruso, Jeff T. Mohl, … Jennifer M. Groh

research articles about neurons

Inhibition increases response variability and reduces stimulus discrimination in random networks of cortical neurons

21 March 2019

Netta Haroush & Shimon Marom

research articles about neurons

Computational models link cellular mechanisms of neuromodulation to large-scale neural dynamics

06 May 2021

James M. Shine, Eli J. Müller, … Michael Breakspear

research articles about neurons

The structures and functions of correlations in neural population codes

22 June 2022

Stefano Panzeri, Monica Moroni, … Christopher D. Harvey

research articles about neurons

Clustering and control for adaptation uncovers time-warped spike time patterns in cortical networks in vivo

29 July 2021

James B. Isbister, Vicente Reyes-Puerta, … Heiko J. Luhmann

research articles about neurons

Multiregion neuronal activity: the forest and the trees

03 October 2022

Timothy A. Machado, Isaac V. Kauvar & Karl Deisseroth

research articles about neurons

Scaling of sensory information in large neural populations shows signatures of information-limiting correlations

20 January 2021

MohammadMehdi Kafashan, Anna W. Jaffe, … Jan Drugowitsch

New Types of Experiments Reveal that a Neuron Functions as Multiple Independent Threshold Units

Scientific Reports volume  7 , Article number:  18036 ( 2017 ) Cite this article

55k Accesses

36 Citations

531 Altmetric

Metrics details

Neurons are the computational elements that compose the brain and their fundamental principles of activity are known for decades. According to the long-lasting computational scheme, each neuron sums the incoming electrical signals via its dendrites and when the membrane potential reaches a certain threshold the neuron typically generates a spike to its axon. Here we present three types of experiments, using neuronal cultures, indicating that each neuron functions as a collection of independent threshold units. The neuron is anisotropically activated following the origin of the arriving signals to the membrane, via its dendritic trees. The first type of experiments demonstrates that a single neuron’s spike waveform typically varies as a function of the stimulation location. The second type reveals that spatial summation is absent for extracellular stimulations from different directions. The third type indicates that spatial summation and subtraction are not achieved when combining intra- and extra- cellular stimulations, as well as for nonlocal time interference, where the precise timings of the stimulations are irrelevant. Results call to re-examine neuronal functionalities beyond the traditional framework, and the advanced computational capabilities and dynamical properties of such complex systems.


A neuron is composed of three main elements, a cell body (soma), dendritic trees and an axon. The dendritic trees are responsible for collecting the incoming electrical signals to the soma. Their number is typically greater than one and can exceed hundreds, while a single axon transmits the signal from the soma to the synapses of connected neurons. The diameter of the soma is a few tens of micrometers and is negligible comparing to the length of the dendrites and the axon, which can exceed millimeters, however, the soma is considered a crucial nonlinear computational element in the dynamics of the brain.

The long-lasting computational scheme, based on decades of experimental evidences 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , is that a neuron functions similar to a single electrical excitable threshold unit (Fig.  1A ). Additionally, it is well accepted that neurons sum the incoming electrical signals via their dendritic trees, and typically generate a spike to their axon if the membrane potential reaches a certain threshold, which varies among neurons (Fig.  1C , model I). According to this scheme the waveform of the spikes, e.g. rise time, peaks’ values, depolarization period and decay time to a resting potential, is consistently reproducible with high fidelity by the neuron, but varies among neurons 23 , 24 , 25 , 26 , 27 , 28 , 29 .

figure 1

Models for a Neuron Functioning as an Excitable Threshold Element. ( A ) A threshold unit is represented by a spring and the load on the spring represents the incoming signal to the threshold unit. If the load is sufficient, the spring stretches and crosses the threshold, Th, represented by the dashed horizontal line, which results in an evoked spike. ( B ) A scheme demonstrating a discontinuous transmission function of the incoming signal, W. The transmission is zero below the threshold, Th, where it jumps discontinuously and follows a nonlinear function represented by f(W). ( C ) A table showing three possible neuronal computation models and their corresponding neuronal activation equations. (Model I) A neuron (represented by the gray sphere) consists of a unique centralized excitable mechanism, represented by the central spring. The load of the spring consists of a linear sum of the incoming signals from all the dendrites connected to the neuron (three colored dendrites and corresponding three colored weights in this illustration). The incoming (loaded) signals, represented by the three colored arrows and weights, stretch the spring and if a threshold crossing occurs (stretching beyond the dashed horizontal line) an evoked spike is generated. The quantitative function of the input-output relation of the neuron is presented in the right column, where W i (t) stands for the accumulated input at time t of the i th dendrite (or a bunch of dendrites, see text), which is a weighted function, W i,j (t − t i,j ), of all the spikes, j, from the presynaptic neurons at preceding times, t i,j . (Model II) Similar to the first model, a neuron consists of a unique centralized excitable mechanism, represented by the central spring, however, there is also a spring associated with each dendrite, indicating that a dendrite transmits its signal to the central spring in a nonlinear manner only if a threshold crossing occurs (yellow and green dendrites, but not the pink one). The spring associated with each dendrite is characterized by its own threshold, Th i , and a nonlinear transfer function above Th i , f i (W i (t)), represented by modified weights on the central spring. The functioning of the central excitable spring is identical to the first model (see neuronal equation on the right column and (B)). Note that the spring associated with each dendrite represents a threshold element for the signal transferring, but does not generate a spike as the central excitable spring. (Model III) There is no central excitable spring, but rather independent excitable springs associated with each dendrite, each one with its own threshold, Th i . If the incoming signal to a dendrite (or a bunch of coupled dendrites, see text) is above its threshold, an evoked spike is generated (yellow spike associated with the yellow dendrite).

A variety of theoretical models, based on the abovementioned scheme, were introduced during the last decades in order to describe the neuron as an excitable element. They vary between formal spiking neuronal models such as the leaky integrate-and-fire model 30 , 31 , 32 , 33 , and experimental evidence-based models such as the Hodgkin-Huxley model 34 , 35 , 36 , 37 , which were followed by many combined variant models. Most of these models fairly capture the structure of observed biological spikes, but have difficulties in incorporating biological features, such as neuronal response failures in the intermittent phase 38 and dynamical changes in the neuronal response latency 39 , 40 , both mainly attributed to the dendrites. In addition, these standard neuronal models do not incorporate many nonlinear computations 41 , 42 , 43 , 44 , 45 , 46 , 47 which are done in parallel processing and locally in each dendrite and its branches, including amplification of the synaptic inputs, local dendritic spike and coincidence detection. This new variety of dendritic computations leads to model a neuron similarly to a feedforward two-layer network with nonlinear hidden units, however, the output unit is typically a threshold unit, representing a single spiking element which transmits its signal along the axon. One can fairly conclude that the long-lasting computation scheme for a biological neuron consists of a single centralized excitable mechanism which linearly sums its entire incoming signals (Fig.  1C , model I).

In this work we present advanced scenarios for the computation scheme of a neuron, based on nonlinear and discontinuous responses by the dendrites and/or the neurons. The formulation of these scenarios requires to introduce the following three parameters: Th, W and f(W) (Fig.  1B ); the parameter Th stands for a threshold for the generation of an evoked response in the neuron or its dendrite, the transmission function, f(W), of the incoming signal to the neuron, W, when W >Th, stands for a general continuous or discontinuous function (Fig.  1B , red lines).

The second scenario presented here is based on advanced dendritic computations, where the neuron sums its signals in a nonlinear manner. A signal from a dendrite is added to the summation only if it crosses a certain threshold, Th i , which varies among dendrites (Fig.  1C , model II). In both models (I and II in Fig.  1C ) the neuron consists of a unique single central excitable mechanism. Based on new types of experiments we question this common scheme, and suggest that a neuron functions as an anisotropic threshold unit 48 . More precisely, the neuron contains many independent excitable sites, each functioning as an independent threshold unit which sums up the incoming signals from a given limited spatial direction, most probably by a dendrite or a bunch of dendrites (Fig.  1C , model III). These anisotropic excitable sites are not identical and are characterized by different spike waveforms and different summation specifications. The neuron is a more complex and structured computational element than expected, and the implications on the functionality of neural networks are stimulating.

The mission of the proposed work demands the formation of a suitable experimental strategy which is based on the following fundamental steps and requirements. It initially demands stimulation of the neuron from several spatial directions, either independently or simultaneously. Indirect anisotropic stimulations of the neuron simultaneously require tunable stimulation timings on a sub-millisecond time scale. In addition, such stimulations schedule has to remain stable over timescales of many minutes while the neuronal responses have to be continuously recorded intracellularly . The achievements of all these requirements led us to implement anisotropic extracellular stimulations, which in addition have to be synchronized with the intracellular recording and stimulations. We indeed found some evident signatures in the responses of the neuron, which clearly differentiate between multiple stimulations from anisotropic sources and stimulations from a unique location. We have developed accordingly a set of experiments to reveal and to support the new proposed neuronal computational scheme.

Experimental Setup

Our experimental results are based on a new available versatile setup 49 , enabling complex multiple extracellular stimulations and recordings from a micro-electrode array (MEA), simultaneously with a patch-clamp stimulation and recording of a single neuron, selected from a cultured neural network (Figs  2A and B and Methods). Specifically, the in-vitro apparatus measurement (Fig.  2A ) consists of an array of 60-electrodes with a diameter of 30 μm each, typically separated by 200 μm from each other 38 , 50 (in a limited number of cultures separated by 500 μm, see Methods) and cover an area of (1.4 mm) X (1.4 mm) (Fig.  2A 2 ) of the entire ~5 cm 2 cortical tissue culture (gray circle in Fig.  2A 1 ). The spontaneous spiking activity 51 of the patched neuron as well as the nearby culture, sampled by the MEA, was typically silenced by the addition of synaptic blockers (Methods). Synchronized bursts activity 49 was measured in the neuronal cultures before the addition of synaptic blockers. After the addition of synaptic blockers, no intra- or extra-cellular activity were observed over tens of minutes. In addition, repeated extracellular stimulations to the culture did not provoke cascades of neuronal responses (recorded extra- or intra- cellular). The stability of the neuronal response latency (Fig.  2E ), much below a variance of a millisecond, also strongly excluded the possibility of leftover sparse connectivity in the culture. The stimulations and the recording of the intra- and the extra- cellular signals were done by two independent systems (Fig.  2B and Methods), and required a careful synchronization of their clocks. A sustained 20 μs matching between the two clocks was achieved using careful analysis of the relative drift of the two clocks and by using leader-laggard triggers for synchronization (Fig.  2B and Supplementary Fig.  S1 ).

figure 2

The Experimental Setup and Principles of Measurements. ( A ) A micro-electrode array (MEA) consisting of 60 electrodes (see Methods for details). (A 1 ) The gray circle with a diameter of ~2.2 cm represents the tissue culture area of ~1.3 million cortical neurons (Methods). (A 2 ) Zoom-in of the blue square in (A 1 ) showing the arrangement of the 60 extracellular electrodes, separated by 200 µm. A patched neuron, indicated by a yellow intracellular electrode, and two nearby extracellular electrodes (pink and green) are demonstrated. (A 3 ) A snapshot of a section of a neuronal culture with an intracellular patch electrode and four extracellular electrodes, similar to (A 2 ), allowing simultaneously recording and multiple stimulations. (A 4 ) A reconstruction of a fluorescence image (Methods) of a patched neuron and its dendrites (red), growing to different directions. The typical distance to the nearest extracellular electrode (black circles) is much less than 100 µm. ( B ) A simplified scheme of the experimental setup according to A 2 (see Methods and Supplementary Fig.  S1 for more details). The extracellular and the intracellular electrodes are capable of recording and stimulating simultaneously in a time resolution of 20 μs using their controlled unit (color-coded). A trigger from the extracellular electrodes to the control unit of the intracellular electrode is used to synchronize their clocks. ( C ) An example of the developed experimental method for finding a subset of extracellular electrodes which reliably generate evoked spikes measured by the intracellular electrode. The 60 extracellular electrodes are stimulated serially at 2 Hz and above-threshold, where each electrode is stimulated several times (twice in this demonstration) and the voltage of the first 30 ms after each stimulation is presented. Red electrodes in the raster plot indicate electrodes which result in reliable evoked spikes. ( D ) A zoom-in of the green area in (C), presenting evoked spikes originated from 2 different extracellular stimulating electrodes. The neuronal response latency (NRL), measuring the time-lag between the extracellular stimulation and the intracellularly recorded evoked spike (measured following threshold crossing, see Methods), is exemplified. The NRL of the same neuron varies among extracellular stimulating electrodes; however, for a given stimulating electrode it is reproducible (for low stimulation frequencies), as can be qualitatively seen in (C). ( E ) The stability of the NRL is quantitatively demonstrated for 40 consecutive stimulations from a given electrode at 1 Hz. The orange dashed line represents the average NRL, and the orange bar (and light-orange area) represents the standard deviation, ~0.1 ms. See also Supplementary Fig.  S1 .

The dense cultured MEA enables the possibility for effective stimulations from different spatial directions with resulted evoked spikes recorded intracellularly from a patched neuron (Fig.  2 ). An example of a reconstructed fluorescence image of a patched neuron and its dendrites (Fig.  2A 4 ) illustrates dendrites growing to different directions, where the distance to the nearest extracellular electrode (black circles) is much less than 100 µm, as expected in the case of 200 µm between electrodes. An efficient and fast procedure was developed to identify the subset of extracellular electrodes which can reliably evoke spikes recorded intracellularly (Fig.  2C and Methods). In this procedure, a stimulation is given by an extracellular electrode and repeated several times at 2 Hz (twice in Fig.  2C ), and then proceeds to the next extracellular electrode until all the 60 electrodes are stimulated. For convenience, time-slots of the first 30 ms after stimulations are demonstrated (Fig.  2C ). The time-lag between the extracellular stimulation and the intracellular recorded evoked spike is defined as the neuronal response latency (NRL) for a given stimulating electrode, and typically ranges between 1–15 ms, and varies between neurons and stimulating electrodes for a given neuron (Fig.  2C and D ). Nevertheless, at low stimulation frequencies, e.g. 2 Hz, the duration of the NRL is reproducible for a given neuron and stimulating electrode (Fig.  2C ), with fluctuations that can be scaled down much below a millisecond (Fig.  2E ). This subset of electrodes reproducing reliably intracellularly recorded evoked spikes with a stable NRL is a necessary prior demand for the implementation of the following three types of experiments. In each experiment we have verified that there were no changes, before and after performing the experiment, in the properties and the environmental conditions of the patched neuron (e.g., NRL and intra- and extra-cellular thresholds).

There are several phenomena which strongly support the assumption that the extracellular stimulations in blocked cultures (see Methods) affect the membrane potential via dendrites and not directly the soma or via the axon. The first evidence is the stretching of the NRL by several milliseconds as the stimulating frequency is enhanced (Supplementary Fig.  S4 ). Moreover, the absolute value of the NRL can exceed 10 ms. These phenomena do not exist when stimulating the soma or antidromic the axon. In addition, the appearance of neuronal response failures at low stimulating frequencies, e.g. 1–10 Hz, occur exclusively via dendritic stimulations.

First Type of Experiments – Variability in the Spike Waveforms

The first type of experiments consists of alternating stimulations of a patched neuron by two extracellular electrodes (green and pink as illustrated in Fig.  2A 2 ) which were detected to reliably generate evoked spikes (Fig.  2C ). We select a very low stimulating frequency, 0.5 Hz, of alternating stimulations (Fig.  3A ) to ensure that there are no accumulative effects along the sequence of stimulations, as indicated for instance by the time-independent recovered resting potential (Fig.  3B ). In addition, the alternating stimulations scheduling excludes the possibility that some changes in the measured neuron occurred during the transition from a sequence of stimulations by the first electrode to the second one. The symmetry between the pair of stimulating electrodes is preserved, including the resting periods before and after stimulations.

figure 3

Variability in the Spike Waveform as a function of the Stimulation Location. ( A ) The alternating stimulation scheduling for this type of experiments. The patch neuron is alternatingly stimulated by two extracellular electrodes (green and pink, see also Fig.  2A 2 ) at a low frequency, 0.5 Hz. Each colored rectangle represents a stimulation by the corresponding extracellular electrode (the width is arbitrary, see Methods for details), similar to the realization illustrated in Fig.  2A 2 . ( B ) An example of intracellular recording from a patch neuron stimulated alternatingly, as in (A), showing two different well-separated spike waveforms. The voltage is presented from 5 milliseconds prior to the threshold crossing, which is defined at -50 mV. ( C ) An illustration of a neuron stimulated above-threshold either via the green dendrite (C 1 ) or via the pink dendrite (C 2 ), where each one generates a different waveform for the spike (colored coded). The suitable neuronal model for the presented experimental results is model III in Fig.  1C , where when the green weight crosses its spring threshold a “green” spike is evoked, while when the pink weight crosses its spring threshold a “pink” spike is evoked. ( D ) Examples of different spike waveforms recorded intracellularly and generated by two extracellular stimulating electrodes (pink and green) with reliable evoked spikes (Fig.  2C ). Each one of the eight panels is associated with a different neuron, and for each two electrodes two evoked spikes are plotted to illustrate the reproducibility of the spike waveform.

The waveforms of the spikes, plotted 5 ms prior to the first time the membrane potential crosses -50 mV (Fig.  3B ), lead to the following conclusions. The shape of the spikes originated from stimulations from either the green or the pink extracellular electrode have a well define reproducible waveform (see also Fig.  2D ). However, the two stimulating electrodes generate two distinguishable sets of waveforms. The differences between the bunch of the green and the pink waveforms are evident in the rise shape, the values and the timings of the maximal membrane potential and in the shape of the decay of the voltage after the spike. It is clear that the two distinguishable sets of spike waveforms (green and pink) cannot become identical under either translation or rescaling of the voltage of one of the sets. We note that the waveform of spikes is robust to changes in the amplitude and the duration of the stimulations, as long as it is above the relative threshold of each one of the stimulating electrodes, hence the different waveforms cannot be attributed to the precise stimulation shape, i.e. duration with time-dependent amplitudes. Results clearly indicate (see Statistical analysis in Methods) that for a given neuron the waveform of a spike is not independent of the origin of the stimulation (Fig.  2A 4 ) and its relative direction (as illustrated in Fig.  3C and D ). It is evident that the outcome of this type of experiments is in contradiction with the scheme of a unique central excitable mechanism within the neuron; therefore, it can hardly fit with the scheme of model I and model II (Fig.  1C ). However, this observation and conclusions, based on the stimulation of a neuron from several directions independently, require an additional support and especially to include scenarios where the neuron is stimulated simultaneously from several directions.

Second Type of Experiments – the Absence of Anisotropic Spatial Summation

Spatial summation 52 , 53 , 54 , 55 , 56 , 57 is one of the eminent mechanisms to control and to maintain the activity of neural networks, since most of the synapses are much below a neuronal threshold. A neuron receives many sub-threshold electrical inputs via its dendrites and the possibility to generate a spike relies on the fact that the neuron integrates the incoming signals using a time-dependent weighted function. Consequently, threshold crossings occur with non-negligible probability. The current assumption is that the neuron integrates the incoming signals in an isotropic manner, independent of their arriving routes to the soma.

Following the observation in the above-mentioned first type of experiments, that the spike waveform depends on the origin of the stimulation, we designed a second type of experiments in order to explore whether the spatial summation is implemented isotropically or anisotropically by the neuron (Fig.  4A ). The designed experiments consist of two extracellular electrodes (green and pink as illustrated in Fig.  2A 2 ) which were detected to reliably generate evoked spikes recorded intracellularly (Fig.  4B ), with preferably different spike waveforms (Figs  4C and 2C ). In the first step of the experiment, the NRL was estimated for each one of the two electrodes (Fig.  4B ) as well as the threshold amplitude for 2 ms stimulation durations (Fig.  4D and Methods). In the second step, based on the prior measured NRLs of the two electrodes, the neuron was repeatedly stimulated by the two extracellular electrodes, where the arrival time-lag of the two stimulations to the soma was tuned (Fig.  4E and Methods). Results indicate (see Statistical analysis in Methods) that the neuron does not generate evoke spikes even in the most favored scenario, where the two stimulations (green and pink) arrive simultaneously to the soma from two different directions, and their amplitude sum significantly exceed the threshold. We note that the properties of the patched neuron, i.e. the threshold of each one of the two electrodes, are practically unchanged for stimulation duration of 1–2 ms (Methods), hence even a partial overlap between the arrivals of the two stimulations is expected to be sufficient to exceed the threshold. In addition, since the NRL of each electrode is different, a pair of stimulations for the two electrodes were typically given in different timings, reducing the possibility of some electrical reciprocal influence between them. Results clearly exclude model I (Fig.  1C ) and might fit model II where the thresholds to transmit the incoming signals from the dendrite to the soma (e.g. Th 1 and Th 2 for the green and pink dendrites, respectively) typically exceed a half of the threshold to generate an evoked spike from each electrode separately. The feasibility of model II seems somehow artificial, since such a powerful dendritic barrier, exceeding 0.7 of the threshold to generate an evoked spike (Fig.  4E ) was repeatedly observed in all experiments, and practically excluded efficient spatial summation (in the formulation of the neuronal equation of model II (Fig.  2C ), the dendritic thresholds always obey Th i >0.7·Th). In addition, model II also consists of a unique centralized excitable mechanism which does not fit to the anisotropic spike waveforms as observed in the first type of experiments. We turn now to the third type of experiments to further support model III over model II.

figure 4

The Absence of Spatial Summation in Simultaneous Stimulations from Two Different Sources. ( A ) Possible scenarios for a neuronal computational model, where the neuron is simultaneously stimulated by two sub-threshold stimulations arriving from two extracellular electrodes. The amplitude of each sub-threshold stimulation is significantly above one half of its threshold. Left scenario demonstrates the lack of spatial summation, where each dendrite is coupled to an independent threshold mechanism. Although the sum of the two signals is above-threshold an evoked spike is absent (Model III in Fig.  1C ). The right scenario presents a spike generated by the central threshold mechanism which sums all incoming signals (Model I or II in Fig.  1C) . ( B ) The measured NRL for the two extracellular electrodes (green/pink in B 1 /B 2 ), showing the stability of the NRLs around a different value for each one of the extracellular electrodes. ( C ) Intracellular recordings of the spike waveforms for the green and the pink extracellular electrodes (similar to Fig.  2A 2 ) when stimulated above-threshold. The distinct different spike waveforms are visible. ( D ) The threshold of each one of the two electrodes was estimated using stimulation pattern of 2 ms duration and varied amplitudes (see Methods). For both electrodes reliable evoked spikes were observed at an amplitude of 800 mV, where at an amplitude of 500 mV no evoked spikes were observed. Hence, the threshold is in the range of (500, 800) mV and a stimulation of 500 mV is significantly above a half of the threshold. ( E ) The neuron is stimulated by the two extracellular electrodes, using a stimulation patterns of 2 ms as in (D) and 550 mV (~0.8 of the threshold, Th, of each electrode), and recorded intracellularly. Based on the prior knowledge of the NRLs in (B), the time-lags between the two stimulations were dynamically adjusted by relatively shifting the stimulation timings of the green electrode (see Methods). Specifically, the green stimulation was adjusted from a partial overlap with the pink stimulation, to a complete overlap and finally to non-overlapping timings (left). All scenarios did not result in evoked spikes, but in a negligible local depolarization independent of the relative timings between the two extracellular stimulations (right).

Third Type of Experiments – the Absence of Intra- and Extra- Summation and Subtraction

The second type of experiments indicated that spatial summation is most probably performed anisotropically. We examine now this feature from a different perspective, where the neuron is stimulated by two sub-threshold stimulations, extracellular and intracellular, which their arithmetic sum is above-threshold (Fig.  5A ). We expect that if the neuron functions as a centralized excitable mechanism (models I and II in Fig.  1C ), an evoked spikes will be generated, otherwise the feasibility of model III is most likely (Fig.  1C ).

figure 5

The Absence of Spatial Summation in Simultaneous Intracellular and Extracellular Stimulations. ( A ) Possible scenarios for a neuronal computational model, where the neuron is simultaneously stimulated by two sub-threshold stimulations, one arriving from an extracellular electrode (green) and the second from an intracellular electrode (orange). The sum of the two sub-threshold stimulations is significantly above the threshold. Left scenario demonstrates the lack of spatial summation, where each dendrite is coupled to an independent threshold mechanism (Model III in Fig.  1C ). The right scenario presents a spike (combined colors) generated by the central threshold mechanism which sums all incoming signals (Model I or II in Fig.  1C ). ( B ) The scheme of the performed experiment. Orange and green rectangles represent the stimulations from the intracellular electrode, 3 ms duration, and the extracellular electrode, 2 ms duration, respectively. Both stimulations are sub-threshold, ~75% of their threshold, as demonstrated by their relative amplitude in comparison to their threshold (dashed orange and green lines). The stimulation scheduling of the intracellular stimulation (orange) was shifted successively by 0.5 ms relative to the timing of the extracellular stimulation (where the NRL is omitted, green). Three possible scenarios between the two stimulations (partial overlapping, overlapping or non-overlapping) are illustrated. ( C ) The intracellular recorded voltage from the neuron according to the three scenarios in (B). All three scenarios exemplify similar shallow local depolarization and without an evoked spike, indicating the absence of summation of the intra- and the extra- cellular stimulations. ( D ) The scheme of the performed experiment, similar to (C), but the duration of the extracellular stimulation is 0.2 ms, since the patched neuron was close to the stimulating electrode (see Methods). Nevertheless, the stimulation was extracellular, since as the stimulation frequency was enhanced an increase in the NRL and in its fluctuations around an average value were observed (Supplementary Fig.  S4 ). ( E ) A rare counter example, where the intracellular and the extracellular stimulations are summing up, both spatially and temporally. This behavior represents rare events, following our experimental evidence, and probably requires that the intra- and the extra- cellular spike waveforms will be identical (Supplementary Fig.  S3 ), i.e. generated by the same local threshold mechanism. See also Supplementary Figs.  S2 – S4 .

The added value of this type of experiments is twofold. The timing of the intracellular stimulation is precisely known and is independent of the NRL, hence fluctuations in the relative timings of the stimulations are reduced. In addition, the direct intracellular stimulation of the soma is expected to be more accurate and to fluctuate less than an indirect extracellular stimulation. We selected long durations for the intracellular stimulations (3 ms) and for the extracellular stimulations (2 ms) (Fig.  5B ) in order to precisely control the overlap in time of the two stimulations, and for each stimulation the threshold was measured (see Methods). In addition, the NRL of the extracellular stimulation was carefully estimated in order to control the relative timings of the stimulations of the soma. The time-lag between the extracellular stimulation (green) and the intracellular stimulation (orange) was tuned by intervals of 0.5 ms, and for each interval several pairs of intra- and extra- cellular stimulations were given. Almost all experiments of this type were found to be in agreement with the second type of experiments and with model III (Fig.  1C ). For all relative timings and stimulations no evoked spikes were observed (Fig.  5C ), although both the extracellular and the intracellular stimulations exceed 75% of their thresholds, indicating the lack of summation between the intra- and the extra- cellular stimulations. Nevertheless, in rare experiments (less than one out of ten) a spike was observed even when there was a time-lag of several ms between the intra- and the extra- cellular stimulations (Fig.  5D and E ). The duration of the extracellular stimulation in this case was reduced to 0.2 ms to avoid artifacts in the spike waveform, as the extracellular electrode was only several dozens of μm away from the patched neuron and the NRL was less than 2 ms (see Methods). A similar result was observed also for a larger NRL and 2 ms duration of the extracellular stimulation (Supplementary Fig.  S2 ). These rare results indicate that a spatial summation between extra- and intra- cellular stimulations can occur under some circumstances, probably the excitation of the same threshold element within the neuron, and present a benchmark to support the correctness of our experimental design.

The lack of summation between the intracellular and the extracellular stimulation (Fig.  5 and Statistical analysis in Methods), hints that a subtraction between the stimulations is also ineffective. The subtraction is implemented by stimulation with a negative amplitude for the intracellular electrode, resulting in a temporary drop in the membrane voltage for several ms (Fig.  6A ). We now simultaneously stimulate the neuron by an extracellular stimulation which is slightly above the threshold and by an intracellular stimulation which is slightly above the minus threshold amplitude (Fig.  6B ). The relative timings between these two stimulations, with the exclusion of the NRL, were carefully tuned (Fig.  6B and Methods). These two stimulations almost annihilate each other arithmetically (Fig.  6B ), however, an evoked spike was observed even when they completely overlapped (Fig.  6B , middle panel). A prior prolonged hyperpolarizing pre-pulse just before the depolarizing pulse might enhance the excitability of the neuron and reduce temporarily the threshold. However, in the presented experiments the pulse is short and the lack of evoked spike is observed even when the intra- and the extra- cellular stimulations are given simultaneously, indicating that a subtraction between the two stimulations does not occur.

figure 6

The Absence of Spatial Subtraction in Simultaneous Intracellular and Extracellular Stimulations. ( A ) Left: The intracellular threshold amplitude is represented by the upper dashed horizontal orange line and correspondingly the minus threshold amplitude, the lower dashed orange line. An intracellular stimulation with a duration of 0.5 ms and an amplitude of approximately -90% of the threshold amplitude is represented. Right: A temporary drop of several ms in the membrane voltage by such a short pulse with a negative amplitude (left) is presented. ( B ) Left: A neuron is simultaneously stimulated by a slightly above-threshold extracellular stimulation, a duration of 0.5 ms and an amplitude of 110% of the threshold (green), and by a negative intracellular amplitude slightly above the minus amplitude of the threshold as in (A) (orange). The relative timing between these two stimulations was tuned by shifting the timing of the intracellular stimulation by 0.5 ms every three pairs of such intra- and extra- cellular stimulations (see Methods). Three possible scenarios are presented (upper/middle/lower panels), where the extracellular stimulation, with the exclusion of the NRL, is slightly before/ at the same time/ after the intracellular stimulation. Right: An evoked spike is recorded for all three scenarios, indicating that there is no subtraction between the two stimulations.

Nonlocal Time Interference between the Intra- and Extra- Cellular Spiking Activities

The lack of additivity of two stimulations arriving at a neuron from two different stimulation locations is the main evidence so far for multiple independent threshold elements composing the computation dynamics of a neuron. These experiments require a careful tuning and dynamical maintenance of the arrival timings of the stimulating signals at the neuron almost simultaneously. We present below another supplemental type of experiments, where the precise timings of the stimulations and their NRLs are irrelevant.

The following experiment (see Statistical analysis in Methods) consists of a neuron with two extracellular stimulating electrodes reproducing reliably evoked spikes recorded intracellularly, each at 2 Hz (as in Fig.  2C ), and for a much longer period of alternating stimulations between the two extracellular electrodes (Fig.  7A ), resulting at 1 Hz stimulation frequency for each electrode. A comparison between the typical spike waveforms generated by each one of these two electrodes (green and pink) and the intracellular one (orange) (Fig.  7B ) leads to the following conclusions. The spike waveforms generated by the two extracellular electrodes are different (green and pink), where one of them (green) has a very similar waveform as the one generated by an intracellular stimulation (orange). This observation suggests that the following two scenarios are most likely (Fig.  7C ). Either each one of the three stimulation sources generates an independent spike (Fig.  7C 1 ) or the generation of spikes by the two sources with similar spike waveforms (green and orange) are coupled (Fig.  7C 2 ). This coupling is illustrated by two springs pulling in parallel the same threshold element and are capable to generate combined colored spike. waveforms will be identical (Supplementary Fig.  S3 ), i.e. generated by the same local threshold mechanism. See also Supplementary Figs  S2 – S4 .

figure 7

Non-Overlapping Time-Dependent Extra- and Intra- Cellular Stimulations Induce Interference in the Spiking Activity. ( A ) Intracellular recordings of a neuron stimulated alternately at 2 Hz by two extracellular electrodes (green and pink) with reliable evoked spikes. ( B ) The spike waveforms generated by the stimulations of the two extracellular electrodes (green and pink) and by an intracellular stimulation (orange). It is evident that the green and the orange waveforms are very similar, whereas the pink waveform is different. ( C ) Two possible scenarios for the spike generation. (C 1 ): The neuron consists of three threshold elements associated with intracellular stimulations and with each one of the two extracellular stimulation locations, represented by different spike colors. (C 2 ): The intracellular stimulation and the green extracellular stimulation activate the same sub-neuronal threshold element, represented by the two springs connected to the threshold spring and by a two-color spike. ( D ) Recorded spike train with the stimulating scheduling. The pink extracellular electrode was stimulated every 1 s and in between 8 intracellular stimulations were given separated by ~100 ms. The spike color is associated with the origin of the corresponding type of the stimulation. The duration/amplitude was 2 ms/800 mV for an extracellular stimulation and 3 ms/600 pA for an intracellular stimulation. ( E ) Similar to (D), but with the stimulation of the green extracellular electrode results in response failures. See also Supplementary Figs  S5 , S6 .

The differentiation between these two scenarios is examined by the following experiment, where an extracellular stimulation is given from one electrode every 1 s (pink in Fig.  7D and green in Fig.  7E ), where between every pair of consecutive extracellular stimulations the neuron is stimulated intracellularly eight times, separated by around 100 ms (Methods). Consequently, the entire stimulation frequency of the neuron is 9 Hz where around 8 Hz is attributed to the intracellular stimulations. The maximal firing frequency of a neuron, when stimulated solely intracellularly, is far beyond 10 Hz and can exceed 100 Hz (Supplementary Fig.  S5 ). In contrast, high extracellular stimulation frequency results in neuronal response failures (Supplementary Fig.  S4 ) which limit the neuronal maximal firing frequency, typically in the limit of sub-Hertz or several Hertz. The increase of the neuronal stimulation frequency to around 10 Hz (Fig.  7D ) when the spike waveforms of the intracellular and the extracellular stimulations differ (pink and orange), does not generate response failures. However, when the spike waveforms of the extra- and the intra- cellular stimulations are similar (green and orange, Fig.  7E ), the neuronal response probability for extracellular stimulations almost vanishes. In other words, the response probability for extracellular stimulations takes into account the intracellular stimulations. Results strongly support the scenario (Fig.  7C 2 ) where the mechanisms to generate extra- (pink) and intra- (orange) cellular stimulations could be uncoupled and the neuron consists of at least two independent threshold elements. One cannot exclude the scenario that at much higher stimulation frequencies a coupling will emerge (in the uncoupled case, Fig.  7E ), but this scenario is very unlikely. In addition, high-frequency extracellular stimulations typically lead to unstable responses of a neuron which are time-dependent and include an overshoot period 58 , hence a significant inference from such experiments will be very difficult.

The common viewpoint that a neuron consists of a unique and centralized excitable element which sums all incoming signals was questioned through the proposed new types of experiments. A new realization for the computational scheme of a neuron was presented, indicating that a neuron consists of several independent threshold units. Each sub-cellular threshold unit sums the incoming signals from a given confined direction with its given threshold. Hence, a neuron consists of a set of anisotropic threshold elements , transferring the incoming signals to its connected neuron via a single axon. These anisotropic threshold elements have to be distinguished from the pre-processing associated with the dendritic computations, which are done in parallel processing and locally in each dendrite and its branches.

Each threshold unit within the neuron collects its own anisotropic incoming signals; hence there is no direct spatial summation between incoming signals to different threshold units, as indicated by the presented experiments. Nevertheless, the resolution of the anisotropy of the neuron cannot be deduced from our experiments, as well as whether each sub-cellular threshold unit is coupled to a dendrite or to a bunch of adjacent dendrites (Fig.  2A 4 ). It is reasonable that the number of sub-cellular threshold units follows the number of main anisotropic directions of the neuronal dendrites, e.g. two, three or several. The scenario that the number of threshold units composing a neuron is independent of the number of dendrites is also possible and might be a new feature to classify neurons, i.e. following their computational capabilities and their spatial resolution to incoming signals. In addition, we restricted our study to examine pyramidal neurons which are commonly encountered in cortical cultures (Methods). Hence, it will be interesting to expand our investigation to other types of neurons. A far-reaching viewpoint of the presented mechanism might lead to a classification and hierarchy of the properties and the computational capabilities among neurons in different areas of the brain or different species.

The achievement of progress in the quantitative understanding of the proposed mechanism requires more deliberation and advanced controlled experiments. It requires to systematically and reproducibly excite neurons at low frequencies from several sources for long periods, first independently and then simultaneously, while measuring several local thresholds, spatial summations and intracellular recording. Since stimulation of each dendrite has its own latency, which might be unstable, a careful time-dependent adaptive maintenance of synchronization among different stimulating and recording timings is required. Moreover, the net duration of such experiments has to be extended over many tens of minutes and the parameters of the measured neuron have to be consistently preserved and in a controlled manner. The implementation of such experiments is conceptually and technologically intriguing, but seems to be realistic in the near future. In addition, the study of subcellular, microbiological, mechanisms for the initiation of spikes through the dendrites requires spatial and temporal high-resolution controlled experiments, with the ability of conditional multiple stimulation and recording sites, which are beyond the scope of this work.

Revision of the dynamical functionality of a neuron has broader impacts on the computational capabilities of the brain. In particular, the slow learning process between connected neurons has to be reexamined based on the new proposed neuronal activation scheme. The currently acknowledged learning processes, like spike-time-dependent-plasticity, STDP, are based on a spatial summation to a unique and centralized excitable unit. Specifically, the changes in the synaptic strengths are according to the relative arrival timing of the current from a synapse to the neuron in comparison to the spike timing. The incompatibility of this type of learning processes to the presented results is in question, since the proposed anisotropic computational scheme of a neuron consists of several independent threshold elements and it barely fits the current scheme of synaptic plasticity. It might be possible that a refined version of such learning processes, e.g. STDP, will be sufficient, where the traditional learning rules refer only to a subset of synapses associated with the stimulation of one of the sub-cellular threshold elements. Alternatively, a new learning rule has to be revealed. Answering this stimulating enigma requires more advanced and controlled experiments both on the proposed neuronal mechanism and on the dynamics of synaptic plasticity and dendritic computation.

The result that a neuron generates a variety of spike waveforms associated, most probably, to its sub-neuronal anisotropic threshold elements questions the current usefulness and accuracy of the spike sorting method. This method represents a class of techniques that was mainly invented to overcome the technological barrier to measure the activity of many neurons simultaneously. The assumption of these techniques is that each neuron tends to fire spikes of a particular waveform which serves as its own electrical signature. Under this assumption, an extracellular multi-electrode array, in the form of micro-wires, is inserted into a brain and is used to record the spiking activity of several surrounding neurons per electrode. Our results indicate that several spike waveforms can be associated with one neuron, hence the number of actually recorded neurons could be reduced and accordingly the complexity of each neuronal spike train is expected to be enhanced. In addition, the variability in the spike waveforms of each neuron reduces the efficiency of the spike sorting technique and enhanced the uncertainty of the results and their possible outcomes.

The mechanism behind the variability in the spike waveforms of a neuron as a function of the stimulation direction is unclear and definitely cannot be deduced from our experiments. Nevertheless, this variability together with a typical lack of spatial summation between simultaneous extracellular stimulations from two directions or between extra- and intra- cellular stimulations hint the following two factors which might qualitatively support such a phenomenon. The current flow via the membrane, inside and outside, is anisotropic since, for instance, the conductance of dendrites might vary from one to another as well as the concentration of ionic channels and their properties along the membrane. Indeed, results of the Hodgkin-Huxley model indicate that changing the concentration and properties of the potassium and sodium channels affect the threshold and the spike waveform. In addition, the cell shape is anisotropic, particularly as a result of the dendrites, and their ionic channels may be responsible for the anisotropic activity of the cell 59 , 60 , 61 , 62 . Hence, adding a charge at a location close to one of the dendrites does not instantaneously induce isotopically an equal voltage difference across the membrane. The dynamic of such processes and their time-scales might be relevant to understanding our findings and deserve further theoretical as well as careful high spatial and temporal experimental investigations.

Our experiments indicate some positive correlation between the spike waveforms and their tendency to form effective spatial or temporal interference. Specifically, two extracellular stimulations generating similar spike waveforms are more likely to generate effective spatial summation (Supplementary Fig.  S3 ). Similarly, an extracellular stimulation and an intracellular stimulation with similar waveforms are more likely to form constructive or destructive interference (Figs  6 and 7 ). These tendencies hint a mechanism of spike generation by multiple localized sites. Nevertheless, this tendency is not very significant in our experiments and in addition the measure of similarity among waveforms is subjective and its verification challenges future research.

The presented phenomena were reproduced tens of times using many cultures and were observed in a variety of scenarios, where the conductance time from a stimulation to a measured response, the neuronal-response latency, ranged from 1 to 15 ms. Nevertheless, more controlled experiments are expected to reveal more details regarding the neurophysiological origins of our results, in particular, experiments which take into consideration the pre-evaluated high-resolution morphology of the dendrites of a given measured neuron and the capability of high-resolution multiple temporal and spatial stimulation sites.

The proposed new computational scheme for a neuron is also expected to affect the theoretical efforts to explore the computational capability of neural networks. Initially one might conclude that the only effect of the proposed neuronal scheme is that a neuron has to be split into several independent traditional neurons, according to the number of threshold units composing the neuron. Each threshold element has fewer inputs than the entire neuron and possibly a different threshold, and accordingly, the spatial summation has to be modified. However, the dynamics of the threshold units are coupled, since they share the same axon and also may share a common refractory period, a question which will probably be answered experimentally. In addition, some multiplexing in the activity of the sub-cellular threshold elements cannot be excluded. The presented new computational scheme for neurons calls to explore its computational capability on a network level in comparison to the current scheme.

All procedures were in accordance with the National Institutes of Health Guide for the Care and Use of Laboratory Animals and Bar-Ilan University Guidelines for the Use and Care of Laboratory Animals in Research and were approved and supervised by the Bar-Ilan University Animal Care and Use Committee.

Culture preparation

Cortical neurons were obtained from newborn rats (Sprague-Dawley) within 48 h after birth using mechanical and enzymatic procedures. The cortical tissue was digested enzymatically with 0.05% trypsin solution in phosphate-buffered saline (Dulbecco’s PBS) free of calcium and magnesium, and supplemented with 20 mM glucose, at 37  ◦ C. Enzyme treatment was terminated using heat-inactivated horse serum, and cells were then mechanically dissociated mostly by trituration. The neurons were plated directly onto substrate-integrated multi-electrode arrays (MEAs) and allowed to develop functionally and structurally mature networks over a time period of 2–4 weeks in vitro , prior to the experiments. The number of plated neurons in a typical network was in the order of 1,300,000, covering an area of about ~5 cm 2 . The preparations were bathed in minimal essential medium (MEM-Earle, Earle’s Salt Base without L-Glutamine) supplemented with heat-inactivated horse serum (5%), B27 supplement (2%), glutamine (0.5 mM), glucose (20 mM), and gentamicin (10 g/ml), and maintained in an atmosphere of 37  ◦ C, 5% CO 2 and 95% air in an incubator.

Synaptic blockers

Experiments were conducted on cultured cortical neurons that were functionally isolated from their network by a pharmacological block of glutamatergic and GABAergic synapses. For each culture 4–20 μl of a cocktail of synaptic blockers were used, consisting of 10 μM CNQX (6-cyano-7-nitroquinoxaline-2,3-dione), 80 μM APV (DL-2-amino-5-phosphonovaleric acid) and 5 μΜ Bicuculline methiodide. This minimal cocktail did not necessarily block completely the spontaneous network activity, but rather made it sparse. Blockers were added until no spontaneous activity was observed both in the MEA and in the patch clamp recording. In addition, repeated extracellular stimulations did not provoke the slightest cascades of neuronal responses.

Stimulation and recording – MEA

An array of 60 Ti/Au/TiN extracellular electrodes, 30 μm in diameter, and spaced 200 or 500 μm from each other (Multi-Channel Systems, Reutlingen, Germany) was used. The insulation layer (silicon nitride) was pre-treated with polyethyleneimine (0.01% in 0.1 M Borate buffer solution). A commercial setup (MEA2100-60-headstage, MEA2100-interface board, MCS, Reutlingen, Germany) for recording and analyzing data from 60-electrode MEAs was used, with integrated data acquisition from 60 MEA electrodes and 4 additional analog channels, integrated filter amplifier and 3-channel current or voltage stimulus generator. Each channel was sampled at a frequency of 50k samples/s, thus the recorded action potentials and the changes in the neuronal response latency were measured at a resolution of 20 μs. Mono-phasic square voltage pulses were used, in the range of [−900, −100] mV and [100, 2000] μs.

Stimulation and recording – Patch Clamp

The Electrophysiological recordings were performed in whole cell configuration utilizing a Multiclamp 700B patch clamp amplifier (Molecular Devices, Foster City, CA). The cells were constantly perfused with the slow flow of extracellular solution consisting of (mM): NaCl 140, KCl 3, CaCl2 2, MgCl2 1, HEPES 10 (Sigma-Aldrich Corp. Rehovot, Israel), supplemented with 2 mg/ml glucose (Sigma-Aldrich Corp. Rehovot, Israel), pH 7.3, osmolarity adjusted to 300–305 mOsm. The patch pipettes had resistances of 3–5 MOhm after filling with a solution containing (in mM): KCl 135, HEPES 10, glucose 5, MgATP 2, GTP 0.5 (Sigma-Aldrich Corp. Rehovot, Israel), pH 7.3, osmolarity adjusted to 285–290 mOsm. In cases were fluorescence was performed, 2 mM Lucifer Yellow CH dipotassium salt (Sigma-Aldrich Corp. Rehovot, Israel) was added to the internal solution. After obtaining the giga-ohm seal, the membrane was ruptured and the cells were subjected to fast current clamp by injecting an appropriate amount of current in order to adjust the membrane potential to about −70 mV. The changes in neuronal membrane potential were acquired through a Digidata 1550 analog/digital converter using pClamp 10 electrophysiological software (Molecular Devices, Foster City, CA). The acquisition started upon receiving the TTL trigger from MEA setup. The signals were filtered at 10 kHz and digitized at 50 kHz. The cultures mainly consisted of pyramidal cells, as a result of the enzymatic and mechanical dissociation. For patch clamp recordings, pyramidal neurons were intentionally selected based on their morphological properties.

MEA and Patch Clamp synchronization

The experimental setup combines multi-electrode array, MEA 2100, and patch clamp. The multi-electrode array is controlled by the MEA interface boarded and a computer. The Patch clamp sub-system consists of several microstar manipulators, an upright microscope (Slicescope-pro-6000, Sceintifica), and a camera. Stimulations and recordings are implemented using multiclamp 700B and Digidata 1550 A and are controlled by a second computer. The recorded MEA/patch data is saved on the computers respectively. The time of the MEA system is controlled by a clock placed in the MEA interface board and the time of the patch subsystem is controlled by a clock placed in the Digidata 1550 A. The relative timings are controlled by triggers sent from the MEA interface board to the Digidata using leader-laggard configuration.

Extracellular electrode selection

For the extracellular stimulations in the performed experiments an extracellular electrode out of the 60 electrodes was chosen by the following procedure. While recording intracellularly, all 60 extracellular electrodes were stimulated serially at 2 Hz and above-threshold, where each electrode is stimulated several times. The electrodes that evoked well-isolated, well-formed spikes were used in the experiments.

Extracellular threshold estimation

After choosing an extracellular electrode, its threshold for stimulation was estimated. Stimulations at 0.5 Hz with duration of 2 ms and different values of voltage were given, until a response failure occurred. The threshold was defined between the stimulation voltage that resulted in a response failure to the closest value of stimulation voltage that resulted in an evoked spike. For patched neurons that were significantly close to an extracellular electrode (several micrometers) shorter stimulation durations were used in order to avoid the stimulation artifact in the voltage recordings.

Intracellular threshold estimation

In order to find a threshold for the intracellular stimulation, several stimulations at 1 Hz were given. The duration of the stimulations was set to 3 milliseconds, and the intensity ranged from 100 pA and increased by 50 pA every stimulation until an evoked spike occurred.

First type of experiments

Two extracellular electrodes were selected according to the procedure mentioned above. The electrodes were stimulated alternatively above-threshold at 0.5 Hz. The voltage recorded was then analyzed to detect evoked spikes by threshold crossing. The voltage of the evoked spike is presented from 5 ms prior to a threshold crossing, defined at −50 mV.

Second type of experiments

Two extracellular electrodes were selected according to the procedure mentioned above, and were stimulated above threshold several times in order to calculate the NRL for each electrode. The threshold of each one of the two electrodes was estimated. The patched neuron was stimulated by the two extracellular electrodes, using a stimulation pattern of 2 ms and a voltage of ~85% of their estimated threshold, and recorded intracellularly. According to the difference in the electrode’s NRLs, the time-lags between the two stimulations were dynamically adjusted by relatively shifting the stimulation timings of the shorter-NRL electrode, while the timings of the longer-NRL electrode were set. Specifically, the shorter-NRL electrode stimulation was adjusted from a partial overlap with the longer-NRL electrode stimulation, to a complete overlap and finally to non-overlapping timings.

Third type of experiments

One extracellular electrode was selected according to the procedure mentioned above and its threshold was estimated. The intracellular stimulation threshold was estimated as well. While recorded intracellularly, the patched neuron was stimulated by the extracellular and the intracellular electrodes, using a stimulation pattern of 2 ms for the extracellular electrode and 3 ms for the intracellular electrode, and both with a voltage of ~75% of their estimated threshold. The stimulation scheduling of the intracellular stimulation was shifted successively by 0.5 ms relative to the timing of the extracellular stimulation, covering the three possible scenarios between the two stimulations (partial overlapping, overlapping and non-overlapping). This type of experiment was performed also with a negative current stimulation from the intracellular electrode at ~-85% of their estimated threshold. In a different type of experiments the patched neuron was stimulated extracellularly above-threshold at 1 Hz, with 8–9 additional intracellular above-threshold stimulations at 10 Hz between each extracellular stimulation.

Statistical analysis

The reported results were confirmed based on at least twenty experiments for each type of experiment, using different patched neurons and several neural cultures.

Data analysis

Analyses were performed in a Matlab environment (MathWorks, Natwick, MA, USA). The recorded data from the MEA (voltage) was filtered by convolution with a Gaussian that has a standard deviation (STD) of 0.1 ms. Evoked spikes were detected by threshold crossing, typically -40 mV, using a detection window of 0.5–30 ms following the beginning of an electrical stimulation. In order to calculate the neuronal response latency, defined as the time-lag between the stimulation and its corresponding evoked spike, the evoked spikes times were extracted from the recorded voltage.

Anderson, J., Binzegger, T., Kahana, O., Martin, K. & Segev, I. Dendritic asymmetry cannot account for directional responses of neurons in visual cortex. Nature neuroscience 2 , 820–824 (1999).

Article   CAS   PubMed   Google Scholar  

Euler, T., Detwiler, P. B. & Denk, W. Directionally selective calcium signals in dendrites of starburst amacrine cells. Nature 418 , 845–852 (2002).

Article   ADS   CAS   PubMed   Google Scholar  

Gasparini, S., Migliore, M. & Magee, J. C. On the initiation and propagation of dendritic spikes in CA1 pyramidal neurons. Journal of Neuroscience 24 , 11046–11056 (2004).

Cai, X. et al . Unique roles of SK and Kv4. 2 potassium channels in dendritic integration. Neuron 44 , 351–364 (2004).

Branco, T. & Häusser, M. The single dendritic branch as a fundamental functional unit in the nervous system. Current opinion in neurobiology 20 , 494–502 (2010).

Smith, S. L., Smith, I. T., Branco, T. & Häusser, M. Dendritic spikes enhance stimulus selectivity in cortical neurons in vivo . Nature 503 , 115–120 (2013).

Larkum, M. E. & Nevian, T. Synaptic clustering by dendritic signalling mechanisms. Current opinion in neurobiology 18 , 321–331 (2008).

Liu, G. Local structural balance and functional interaction of excitatory and inhibitory synapses in hippocampal dendrites. Nature neuroscience 7 , 373–379 (2004).

London, M. & Häusser, M. Dendritic computation. Annu. Rev. Neurosci. 28 , 503–532 (2005).

Chklovskii, D. B., Mel, B. & Svoboda, K. Cortical rewiring and information storage. Nature 431 , 782–788 (2004).

Chklovskii, D. B. Synaptic connectivity and neuronal morphology: two sides of the same coin. Neuron 43 , 609–617 (2004).

CAS   PubMed   Google Scholar  

Poirazi, P. & Mel, B. W. Impact of active dendrites and structural plasticity on the memory capacity of neural tissue. Neuron 29 , 779–796 (2001).

Polsky, A., Mel, B. W. & Schiller, J. Computational subunits in thin dendrites of pyramidal cells. Nature neuroscience 7 , 621–627 (2004).

Schiller, J., Schiller, Y., Stuart, G. & Sakmann, B. Calcium action potentials restricted to distal apical dendrites of rat neocortical pyramidal neurons. The Journal of physiology 505 , 605–616 (1997).

Article   CAS   PubMed   PubMed Central   Google Scholar  

Taylor, W. R., He, S., Levick, W. R. & Vaney, D. I. Dendritic computation of direction selectivity by retinal ganglion cells. Science 289 , 2347–2350 (2000).

Gollo, L. L., Kinouchi, O. & Copelli, M. Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation. Physical Review E 85 , 011911 (2012).

Article   ADS   Google Scholar  

Kim, Y.-T., Goldenfeld, N. & Dantzig, J. Computation of dendritic microstructures using a level set method. Physical Review E 62 , 2471 (2000).

Article   ADS   CAS   Google Scholar  

Yuste, R. & Denk, W. Dendritic spines as basic functional units of neuronal integration. Nature 375 , 682 (1995).

Single, S., Haag, J. & Borst, A. Dendritic computation of direction selectivity and gain control in visual interneurons. Journal of Neuroscience 17 , 6023–6030 (1997).

George, S., Hasler, J., Koziol, S., Nease, S. & Ramakrishnan, S. Low power dendritic computation for wordspotting. Journal of Low Power Electronics and Applications 3 , 73–98 (2013).

Article   Google Scholar  

Hoekstra, J., Rouw, E. & Dubois, D. M. In AIP Conference Proceedings . 308–322 (AIP).

Vlasits, A. L. et al . A role for synaptic input distribution in a dendritic computation of motion direction in the retina. Neuron 89 , 1317–1330 (2016).

Guillory, K. & Normann, R. A 100-channel system for real time detection and storage of extracellular spike waveforms. Journal of neuroscience methods 91 , 21–29 (1999).

Fee, M. S., Mitra, P. P. & Kleinfeld, D. Variability of extracellular spike waveforms of cortical neurons. Journal of neurophysiology 76 , 3823–3833 (1996).

Aksenova, T. I. et al . An unsupervised automatic method for sorting neuronal spike waveforms in awake and freely moving animals. Methods 30 , 178–187 (2003).

Wood, F., Black, M. J., Vargas-Irwin, C., Fellows, M. & Donoghue, J. P. On the variability of manual spike sorting. IEEE Transactions on Biomedical Engineering 51 , 912–918 (2004).

Article   PubMed   Google Scholar  

Takahashi, S., Anzai, Y. & Sakurai, Y. A new approach to spike sorting for multi-neuronal activities recorded with a tetrode—how ICA can be practical. Neuroscience research 46 , 265–272 (2003).

Lewicki, M. S. A review of methods for spike sorting: the detection and classification of neural action potentials. Network: Computation in Neural Systems 9 , R53–R78 (1998).

Article   CAS   MATH   Google Scholar  

Harris, K. D., Henze, D. A., Csicsvari, J., Hirase, H. & Buzsáki, G. Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements. Journal of neurophysiology 84 , 401–414 (2000).

Brette, R. & Gerstner, W. Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of neurophysiology 94 , 3637–3642 (2005).

Naud, R., Marcille, N., Clopath, C. & Gerstner, W. Firing patterns in the adaptive exponential integrate-and-fire model. Biological cybernetics 99 , 335 (2008).

Article   MathSciNet   PubMed   PubMed Central   MATH   Google Scholar  

Burkitt, A. N. A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biological cybernetics 95 , 1–19 (2006).

Article   MathSciNet   CAS   PubMed   MATH   Google Scholar  

Liu, Y.-H. & Wang, X.-J. Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron. Journal of computational neuroscience 10 , 25–45 (2001).

Hodgkin, A. L. & Huxley, A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology 117 , 500 (1952).

Noble, D. Applications of Hodgkin-Huxley equations to excitable tissues. Physiological Reviews 46 , 1–50 (1966).

Hodgkin, A. L. & Huxley, A. F. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. The Journal of physiology 116 , 449 (1952).

Kistler, W. M., Gerstner, W. & van Hemmen, J. L. Reduction of the Hodgkin-Huxley equations to a single-variable threshold model. Neural computation 9 , 1015–1045 (1997).

Vardi, R. et al . Neuronal Response Impedance Mechanism Implementing Cooperative Networks with Low Firing Rates and Microseconds Precision. Front. Neural Circuits 9 , 29 (2015).

Spors, H., Wachowiak, M., Cohen, L. B. & Friedrich, R. W. Temporal dynamics and latency patterns of receptor neuron input to the olfactory bulb. Journal of Neuroscience 26 , 1247–1259 (2006).

Marmari, H., Vardi, R. & Kanter, I. Chaotic and non-chaotic phases in experimental responses of a single neuron. EPL (Europhysics Letters) 106 , 46002 (2014).

Xu, N.-l et al . Nonlinear dendritic integration of sensory and motor input during an active sensing task. Nature 492 , 247–251 (2012).

Branco, T., Clark, B. A. & Häusser, M. Dendritic discrimination of temporal input sequences in cortical neurons. Science 329 , 1671–1675 (2010).

Shepherd, G. M. & Brayton, R. K. Logic operations are properties of computer-simulated interactions between excitable dendritic spines. Neuroscience 21 , 151–165 (1987).

Lavzin, M., Rapoport, S., Polsky, A., Garion, L. & Schiller, J. Nonlinear dendritic processing determines angular tuning of barrel cortex neurons in vivo . Nature 490 , 397–401 (2012).

Legenstein, R. & Maass, W. Branch-specific plasticity enables self-organization of nonlinear computation in single neurons. Journal of Neuroscience 31 , 10787–10802 (2011).

Zador, A. M., Claiborne, B. J., Brown, T. H. & Clairborne, B. Nonlinear pattern separation in single hippocampal neurons with active dendritic membrane. Advances in neural information processing systems , 51–51 (1993).

Naud, R., Payeur, A. & Longtin, A. Noise Gated by Dendrosomatic Interactions Increases Information Transmission. Physical Review X 7 , 031045 (2017).

Vardi, R., Goldental, A., Sheinin, A., Sardi, S. & Kanter, I. Fast reversible learning based on neurons functioning as anisotropic multiplex hubs. EPL (Europhysics Letters) 118 , 46002 (2017).

Vardi, R., Goldental, A., Sardi, S., Sheinin, A. & Kanter, I. Simultaneous multi-patch-clamp and extracellular-array recordings: Single neuron reflects network activity. Scientific reports 6 (2016).

Vincent, K., Tauskela, J. S. & Thivierge, J.-P. Extracting functionally feedforward networks from a population of spiking neurons. Frontiers in computational neuroscience 6 (2012).

Sanseverino, E. R., Agnati, L., Maioli, M. & Galletti, C. Maintained activity of single neurons in striate and non-striate areas of the cat visual cortex. Brain research 54 , 225–242 (1973).

Movshon, J. A., Thompson, I. D. & Tolhurst, D. J. Spatial summation in the receptive fields of simple cells in the cat’s striate cortex. The Journal of physiology 283 , 53 (1978).

Barlow, H. Temporal and spatial summation in human vision at different background intensities. The Journal of physiology 141 , 337 (1958).

Sceniak, M. P., Ringach, D. L., Hawken, M. J. & Shapley, R. Contrast’s effect on spatial summation by macaque V1 neurons. Nature neuroscience 2 , 733–739 (1999).

Hardy, J. D., Wolff, H. G. & Goodell, H. Studies on pain. A new method for measuring pain threshold: observations on spatial summation of pain. Journal of Clinical Investigation 19 , 649 (1940).

Kapadia, M. K., Westheimer, G. & Gilbert, C. D. Dynamics of spatial summation in primary visual cortex of alert monkeys. Proceedings of the National Academy of Sciences 96 , 12073–12078 (1999).

Enroth-Cugell, C., Robson, J., Schweitzer-Tong, D. & Watson, A. Spatio-temporal interactions in cat retinal ganglion cells showing linear spatial summation. The Journal of Physiology 341 , 279 (1983).

Sardi, S., Goldental, A., Amir, H., Vardi, R. & Kanter, I. Vitality of Neural Networks under Reoccurring Catastrophic Failures. Scientific reports 6 (2016).

Huguenard, J. R., Hamill, O. P. & Prince, D. A. Sodium channels in dendrites of rat cortical pyramidal neurons. Proceedings of the National Academy of Sciences 86 , 2473–2477 (1989).

Regehr, W. G., Konnerth, A. & Armstrong, C. M. Sodium action potentials in the dendrites of cerebellar Purkinje cells. Proceedings of the National Academy of Sciences 89 , 5492–5496 (1992).

Lai, H. C. & Jan, L. Y. The distribution and targeting of neuronal voltage-gated ion channels. Nature Reviews Neuroscience 7 , 548–562 (2006).

Safronov, B. V., Wolff, M. & Vogel, W. Functional distribution of three types of Na+channel on soma and processes of dorsal horn neurones of rat spinal cord. The Journal of Physiology 503 , 371–385 (1997).

Download references


We thank Moshe Abeles and Herut Uzan for stimulating discussions. Invaluable technical assistance by Hana Arnon is acknowledged. This research was supported by the TELEM grant of the Council for Higher Education of Israel.

Author information

Shira Sardi and Roni Vardi contributed equally to this work.

Authors and Affiliations

Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel

Shira Sardi, Roni Vardi, Amir Goldental & Ido Kanter

Gonda Interdisciplinary Brain Research Center and the Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan, 52900, Israel

Roni Vardi & Ido Kanter

Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, 69978, Israel

Anton Sheinin

You can also search for this author in PubMed   Google Scholar


S.S. and R.V. prepared the tissue cultures and performed the experiments. A.G. developed the software of the proposed online experiments using the combined MEA and patch setups and the numerical package to analyze the data with the help of S.S., R.V. and A.S., S.S., R.V. and A.G. analyzed the data. I.K. initiated the study and developed the theoretical concepts with the authors and supervised all aspects of the work. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Ido Kanter .

Ethics declarations

Competing interests.

The authors declare that they have no competing interests.

Additional information

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Supplementary information, rights and permissions.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ .

Reprints and Permissions

About this article

Cite this article.

Sardi, S., Vardi, R., Sheinin, A. et al. New Types of Experiments Reveal that a Neuron Functions as Multiple Independent Threshold Units. Sci Rep 7 , 18036 (2017). https://doi.org/10.1038/s41598-017-18363-1

Download citation

Received : 19 July 2017

Accepted : 11 December 2017

Published : 21 December 2017

DOI : https://doi.org/10.1038/s41598-017-18363-1

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

Brain inspired neuronal silencing mechanism to enable reliable sequence identification.

Scientific Reports (2022)

Brain experiments imply adaptation mechanisms which outperform common AI learning algorithms

Scientific Reports (2020)

Fibrinogen and Neuroinflammation During Traumatic Brain Injury

Molecular Neurobiology (2020)

The missing G

AI & SOCIETY (2020)

Anisotropy Properties of Tissues: A Basis for Fabrication of Biomimetic Anisotropic Scaffolds for Tissue Engineering

Journal of Bionic Engineering (2019)

By submitting a comment you agree to abide by our Terms and Community Guidelines . If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Quick links

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

research articles about neurons

Articles on Neurons

Displaying 1 - 20 of 79 articles.

research articles about neurons

Electricity flow in the human brain can be predicted using the simple maths of networks, new study reveals

Caio Seguin , Indiana University and Andrew Zalesky , The University of Melbourne

research articles about neurons

How does RNA know where to go in the city of the cell? Using cellular ZIP codes and postal carrier routes

Matthew Taliaferro , University of Colorado Anschutz Medical Campus

research articles about neurons

Imagination makes us human – this unique ability to envision what doesn’t exist has a long evolutionary history

Andrey Vyshedskiy , Boston University

research articles about neurons

Why does the Alzheimer’s brain become insulin-resistant ?

Frederic Calon , Université Laval ; Manon Leclerc , Université Laval , and Vincent Emond , Université Laval

research articles about neurons

Epilepsy: gene therapy technique targeting overactive brain cells shows promise in treating drug-resistant form of the condition

Gabriele Lignani , UCL and Dimitri Kullmann , UCL

research articles about neurons

Axolotls can regenerate their brains – these adorable salamanders are helping unlock the mysteries of brain evolution and regeneration

Ashley Maynard , Swiss Federal Institute of Technology Zurich

research articles about neurons

Illuminating the brain one neuron and synapse at a time – 5 essential reads about how researchers are using new tools to map its structure and function

Vivian Lam , The Conversation

research articles about neurons

What epilepsy teaches us about diversity and resilience

Jérémie Lefebvre , L’Université d’Ottawa/University of Ottawa and Taufik A. Valiante , University of Toronto

research articles about neurons

Game of Thrones star Emilia Clarke is missing ‘quite a bit’ of her brain. How can people survive and thrive after brain injury?

Anthony Hannan , Florey Institute of Neuroscience and Mental Health

research articles about neurons

Lab-grown mini-brains could help find treatments for Alzheimer’s and other diseases

Étienne Aumont , Université du Québec à Montréal (UQAM)

research articles about neurons

Where our thoughts come from: How microemotions affect spontaneous thought

Francois Richer , Université du Québec à Montréal (UQAM)

research articles about neurons

Brain wrinkles and folds matter – researchers are studying the mechanics of how they form

Mir Jalil Razavi , Binghamton University, State University of New York and Weiying Dai , Binghamton University, State University of New York

research articles about neurons

Mapping how the 100 billion cells in the brain all fit together is the brave new world of neuroscience

Yongsoo Kim , Penn State

research articles about neurons

The 2021 Nobel Prize for medicine helps unravel mysteries about how the body senses temperature and pressure

Steven D. Munger , University of Florida

research articles about neurons

Swimming gives your brain a boost – but scientists don’t know yet why it’s better than other aerobic activities

Seena Mathew , University of Mary Hardin-Baylor

research articles about neurons

MDMA may help treat PTSD – but beware of claims that Ecstasy is a magic bullet

Arash Javanbakht , Wayne State University

research articles about neurons

How lobed brain corals are helping solve the mystery of what general anaesthesia does to the brain

Adam David Hines , The University of Queensland and Bruno van Swinderen , The University of Queensland

research articles about neurons

Astrocyte cells in the fruit fly brain are an on-off switch that controls when neurons can change and grow

Sarah DeGenova Ackerman , University of Oregon

research articles about neurons

Alzheimer’s: new research shows a leap forward in identifying neurons vulnerable to the disease

Eleftheria Kodosaki , Cardiff University

research articles about neurons

How does your brain wake up from sleep?

Hilary A. Marusak , Wayne State University and Aneesh Hehr , Wayne State University

Related Topics

Top contributors

research articles about neurons

Professeur agrégé de neurosciences computationnelles et neurophysiologie, L’Université d’Ottawa/University of Ottawa

research articles about neurons

Chancellor's Professor of Medicine, Liberal Arts, and Philanthropy, Indiana University

research articles about neurons

Postdoctoral Researcher in Cognitive Neurosciences, The University of Queensland

research articles about neurons

Professor of Electrical Engineering and Bioengineering, Tau Beta Pi Eminent Engineer, University of South Florida

research articles about neurons

Associate Professor of Neural and Behavioral Sciences, Penn State

research articles about neurons

Assistant Professor of Mechanical Engineering, Binghamton University, State University of New York

research articles about neurons

Assistant Professor of Computer Science, Binghamton University, State University of New York

research articles about neurons

Head of Developmental Psychobiology Lab, Deakin University

research articles about neurons

Professor and Head of Epigenetics and Neural Plasticity, Florey Institute of Neuroscience and Mental Health

research articles about neurons

Cultural Geographer, Royal Holloway University of London

research articles about neurons

Director of the Institute of Behavioural Neuroscience, UCL

research articles about neurons

Postdoctoral Research Fellow, The University of Queensland

research articles about neurons

Professor in Neuroscience, The Open University

research articles about neurons

Assistant Professor of Neurobiology, Northwestern University

research articles about neurons

Professor of Cognition, Lancaster University

research articles about neurons

Unlimited Science, 40% off!

The Adult Brain Does Grow New Neurons After All, Study Says

Study points toward lifelong neuron formation in the human brain’s hippocampus, with implications for memory and disease

The Adult Brain Does Grow New Neurons After All, Study Says

If the memory center of the human brain can grow new cells, it might help people recover from depression and post-traumatic stress disorder (PTSD), delay the onset of Alzheimer’s, deepen our understanding of epilepsy and offer new insights into memory and learning. If not, well then, it’s just one other way people are different from rodents and birds.

For decades, scientists have debated whether the birth of new neurons—called neurogenesis—was possible in an area of the brain that is responsible for learning, memory and mood regulation. A growing body of research suggested they could, but then a Nature paper last year raised doubts.

Now, a new study published in March in another of the Nature family of journals— Nature Medicine —tips the balance back toward “yes.” In light of the new study, “I would say that there is an overwhelming case for the neurogenesis throughout life in humans,” Jonas Frisén, a professor at the Karolinska Institute in Sweden, said in an e-mail. Frisén, who was not involved in the new research, wrote a News and Views about the study in the March issue of Nature Medicine .

Not everyone was convinced. Arturo Alvarez-Buylla was the senior author on last year’s Nature paper, which questioned the existence of neurogenesis. Alvarez-Buylla, a professor of neurological surgery at the University of California, San Francisco, says he still doubts that new neurons develop in the brain’s hippocampus after toddlerhood.

“I don’t think this at all settles things out,” he says. “I’ve been studying adult neurogenesis all my life. I wish I could find a place [in humans] where it does happen convincingly.”

For decades, some researchers have thought that the brain circuits of primates—including humans—would be too disrupted by the growth of substantial numbers of new neurons. Alvarez-Buylla says he thinks the scientific debate over the existence of neurogenesis should continue. “Basic knowledge is fundamental. Just knowing whether adult neurons get replaced is a fascinating basic problem,” he says.

New technologies that can locate cells in the living brain and measure the cells’ individual activity, none of which were used in the Nature Medicine study, may eventually put to rest any lingering questions.

A number of researchers praised the new study as thoughtful and carefully conducted. It’s a “technical tour de force,” and addresses the concerns raised by last year’s paper, says Michael Bonaguidi, an assistant professor at the University of Southern California Keck School of Medicine.

The researchers, from Spain, tested a variety of methods of preserving brain tissue from 58 newly deceased people. They found that different methods of preservation led to different conclusions about whether new neurons could develop in the adult and aging brain.

Brain tissue has to be preserved within a few hours after death, and specific chemicals used to preserve the tissue, or the proteins that identify newly developing cells will be destroyed, said Maria Llorens-Martin, the paper’s senior author. Other researchers have missed the presence of these cells, because their brain tissue was not as precisely preserved, says Llorens-Martin, a neuroscientist at the Autonomous University of Madrid in Spain.

Jenny Hsieh, a professor at the University of Texas San Antonio who was not involved in the new research, said the study provides a lesson for all scientists who rely on the generosity of brain donations. “If and when we go and look at something in human postmortem, we have to be very cautious about these technical issues.”

Llorens-Martin said she began carefully collecting and preserving brain samples in 2010, when she realized that many brains stored in brain banks were not adequately preserved for this kind of research. In their study, she and her colleagues examined the brains of people who died with their memories intact, and those who died at different stages of Alzheimer’s disease. She found that the brains of people with Alzheimer’s showed few if any signs of new neurons in the hippocampus—with less signal the further along the people were in the course of the disease. This suggests that the loss of new neurons—if it could be detected in the living brain—would be an early indicator of the onset of Alzheimer’s, and that promoting new neuronal growth could delay or prevent the disease that now affects more than 5.5 million Americans.

Rusty Gage, president of the Salk Institute for Biological Studies and a neuroscientist and professor there, says he was impressed by the researchers’ attention to detail. “Methodologically, it sets the bar for future studies,” says Gage, who was not involved in the new research but was the senior author in 1998 of a paper that found the first evidence for neurogenesis. Gage says this new study addresses the concerns raised by Alvarez-Buylla’s research. “From my view, this puts to rest that one blip that occurred,” he says. “This paper in a very nice way… systematically evaluates all the issues that we all feel are very important.”

Neurogenesis in the hippocampus matters, Gage says, because evidence in animals shows that it is essential for pattern separation, “allowing an animal to distinguish between two events that are closely associated with each other.” In people, Gage says, the inability to distinguish between two similar events could explain why patients with PTSD keep reliving the same experiences, even though their circumstances have changed. Also, many deficits seen in the early stages of cognitive decline are similar to those seen in animals whose neurogenesis has been halted, he says.

In healthy animals, neurogenesis promotes resilience in stressful situations, Gage says. Mood disorders, including depression, have also been linked to neurogenesis.

Hsieh says her research on epilepsy has found that newborn neurons get miswired, disrupting brain circuits and causing seizures and potential memory loss. In rodents with epilepsy, if researchers prevent the abnormal growth of new neurons, they prevent seizures, Hsieh says, giving her hope that something similar could someday help human patients. Epilepsy increases someone’s risk of Alzheimer’s as well as depression and anxiety, she says. “So, it’s all connected somehow. We believe that the new neurons play a vital role connecting all of these pieces,” Hsieh says.

In mice and rats, researchers can stimulate the growth of new neurons by getting the rodents to exercise more or by providing them with environments that are more cognitively or socially stimulating, Llorens-Martin says. “This could not be applied to advanced stages of Alzheimer’s disease. But if we could act at earlier stages where mobility is not yet compromised,” she says, “who knows, maybe we could slow down or prevent some of the loss of plasticity [in the brain].”

research articles about neurons



Karen Weintraub is a staff writer at USA Today, where she covers COVID, vaccine development and other health issues.  Credit: Nick Higgins

Recent Articles by Karen Weintraub

Get smart. Sign up for our email newsletter.

Support science journalism.

Scientific American paper issue and on tablet

Thanks for reading Scientific American. Knowledge awaits.

Already a subscriber? Sign in.

Thanks for reading Scientific American. Create your free account or Sign in to continue.

See Subscription Options

Continue reading with a Scientific American subscription.

You may cancel at any time.

Journal of Neuroscience

Advanced Search

Current Issue Table of Contents: 8 Mar 2023 Volume 43, Issue 10

The Journal of Neuroscience: 43 (10)

About the Cover

Astrocytes (labeled for GFAP, green) surrounding a cerebrovessel (red blood cell nuclei labeled with DAPI and pseudo-colored red) in mouse barrel cortex (formalin fixed). Image acquired using a Zeiss LSM 880 with a 63x objective. Three-dimensional image rendering was performed with Imaris software. For more information, see the article by Sompol et al. (pages 1797–1813 ). Cover image: Pradoldej Sompol.

New in the Journal

Listen to "encore interview: marina picciotto on the history of jneurosci " the new episode of the neuro current podcast, jneurosci is encouraging submissions of new primary research and review articles. click here to find out more..

Annual Spotlight Articles

Featured Articles

Early Release

The Scientist Magazine®

The organoids could one day be used to treat brain injuries in humans. 

a white mouse sits on a blue exercise wheel, looking out onto the shavings below

Hatchlings from eggs incubated in a natural nest were larger, exhibited faster neuronal development, and performed better on a motor activity test than those from eggs that were incubated in a hatchery, a study finds.

Fluorescent cells in culture connected by tunneling nanotubules

Neuroscience News logo for mobile.

New Release of Blue Brain Project Atlas Sheds Light on Neuron Types

This shows neurons

How Huntington’s Disease Affects Different Neurons

This shows models of neurons

A New Field of Neuroscience Aims to Map Connections in the Brain

This shows a neuron

How Neurons Autonomously Regulate Their Excitability

This shows neurons in the motor cortex

New Findings on Neuronal Activities in the Sensorimotor Cortex

This shows a neuron

Genes That Maintain Healthy Neurons Identified

This shows a neuron

Autism-Linked Gene Found to Shape Nerve Connections

This shows motor neurons

Nerve Cell Discovery May Lead to Better Treatment for Diseases of the Nervous System

This shows a drawing of a neuron

Recording Neurons to Pinpoint Synaptic Links

This shows a brain

An Animal-Free Method of Creating Human Brain Cells for Research

This shows different brain cells in the origanoid

Human Brain Cells in a Dish Learn to Play Pong

This shows an older man

Superager Brains Contain ‘Super Neurons’

Neuroscience News Small Logo

Complex Learned Social Behavior Discovered in Bee’s Waggle Dance

This shows a brain

First Complete Wiring Map of Neurons in Insect Brain: 3016 Neurons and 548,000 Synapses Mapped

This shows a woman listening to music on headphones

Unlocking the Power of Goosebumps: The Surprising Emotional Effects of Aesthetic Chills

This shows "words have power" typed out

How Swearing Gets Its Power to Elicit Emotional Responses


  1. Artificial neurons compute faster than the human brain

    research articles about neurons

  2. IBM creates world’s first artificial phase-change neurons

    research articles about neurons

  3. 300 neurons traced in extensive brain wiring map

    research articles about neurons

  4. Can Adults Grow More Neurons?

    research articles about neurons

  5. Epilepsy: New findings 'could change textbooks'

    research articles about neurons

  6. Neuronal changes

    research articles about neurons


  1. Unit 2

  2. Neuron Terminology

  3. Lecture On Neuron

  4. "Emergent Computation and Learning from Assemblies of Neurons"

  5. Neurons



  1. Neuron

    Neuron publishes outstanding research spanning all neuroscience sub-disciplines- from molecular, to systems-level, including cognitive and theoretical

  2. New articles: Neuron

    Seguin et al. use a large dataset of direct electrical stimulation to empirically study the propagation of electrical pulses across the entire human brain

  3. Invisible Brain: Knowledge in Research Works and Neuron Activity

    Here we show that the neuron activity mechanism seems to represent much of the knowledge learned in the past decades based on published articles

  4. Neuron

    Read the latest articles of Neuron at ScienceDirect.com, Elsevier's leading platform of peer-reviewed scholarly literature.

  5. New Types of Experiments Reveal that a Neuron Functions ...

    Neurons are the computational elements that compose the brain and their ... Scientific Reports volume 7, Article number: 18036 (2017) Cite

  6. Neurons

    Adaptable neurons are tied to learning and memory but also to neurological disorders. By studying fruit flies, researchers found a mechanism that controls

  7. The Adult Brain Does Grow New Neurons After All, Study Says

    A growing body of research suggested they could, but then a Nature paper last year raised doubts. Now, a new study published in March in

  8. Journal of Neuroscience

    Research Articles, Neurobiology of Disease. Activation of PPARα Exhibits Therapeutic Efficacy in a Mouse Model of Juvenile Neuronal Ceroid... March 08, 2023.

  9. Neuron News, Articles

    Researchers Transplant Human Neurons into Rat Brains. Katherine Irving | Oct 12, 2022 | 2 min read. The human cells, engineered to respond to blue light

  10. neurons News Research Tags Articles

    neurons · New Release of Blue Brain Project Atlas Sheds Light on Neuron Types · How Huntington's Disease Affects Different Neurons · A New Field of Neuroscience