Synaptic integration is a prominent aspect of neuronal information processing. The detailed mechanisms that modulate synaptic inputs determine the computational properties of any given neuron. We study a simple model for the summation of excitatory inputs from synapses and illustrate its use by characterizing some functional properties of postsynaptic neurons. In this regard, we study the response of postsynaptic neurons as defined by the model to two well known noise driven processes: stochastic and coherence resonance. The model requires a small number of parameters and is especially useful to isolate the role of integration mechanisms that rely on summation of inputs with little dendritic processing.
We derive analytical formulae for the firing rate of integrate-and-fire neurons endowed with realistic synaptic dynamics. In particular we include the possibility of multiple synaptic inputs as well as the effect of an absolute refractory period into the description.
Intensity-tuned auditory cortex neurons may be formed by intensity-tuned synaptic excitation. Synaptic inhibition has also been shown to enhance, and possibly even create intensity-tuned neurons. Here we show, using in vivo whole cell recordings in pentobarbital-anesthetized rats, that some intensity-tuned neurons are indeed created solely through disproportionally large inhibition at high intensities, without any intensity-tuned excitation. Since inhibition is essentially cortical in origin, these neurons provide examples of auditory feature-selectivity arising de novo at the cortex.
The effect of environmental temperature on neuronal spiking behaviors is investigated by numerically simulating the temperature dependence of spiking threshold of the Hodgkin-Huxley neuron subject to synaptic stimulus. We find that the spiking threshold exhibits a global minimum in a "comfortable temperature" range where spike initiation needs weakest synaptic strength, indicating the occurrence of optimal use of synaptic transmission in neural system. We further explore the biophysical origin of this phenomenon in ion channel gating kinetics and also discuss its possible biological relevance …
We compute the firing rate of a leaky integrate-and-fire (LIF) neuron with stochastic conductance-based inputs in the limit when synaptic decay times are much shorter than the membrane time constant. A comparison of our analytical results to numeric simulations is presented for a range of biophysically-realistic parameters.
Our mysterious brain is believed to operate near a non-equilibrium point and generate critical self-organized avalanches in neuronal activity. Recent experimental evidence has revealed significant heterogeneity in both synaptic input and output connectivity, but whether the structural heterogeneity participates in the regulation of neuronal avalanches remains poorly understood. By computational modelling, we predict that different types of structural heterogeneity contribute distinct effects on avalanche neurodynamics. In particular, neuronal avalanches can be triggered at an intermediate leve…
Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Heuristic models of this process of synaptic plasticity can provide excellent fits to results from in-vitro experiments in which pre- and post-synaptic spiking is varied in a controlled fashion. However, the plasticity rules inferred from fitting such data are inevitably unstable, in that given constant pre- and post-synaptic activity the synapse will either fully potentiate or depress. This instability can be held in check by adding additional mechanisms, such as homeostasis. Here we consider a…
Cortical neurons are subject to sustained and irregular synaptic activity which causes important fluctuations of the membrane potential (Vm). We review here different methods to characterize this activity and its impact on spike generation. The simplified, fluctuating point-conductance model of synaptic activity provides the starting point of a variety of methods for the analysis of intracellular Vm recordings. In this model, the synaptic excitatory and inhibitory conductances are described by Gaussian-distributed stochastic variables, or colored conductance noise. The matching of experimental…
When a neuron fires and the resulting action potential travels down its axon toward other neurons' dendrites, the effect on each of those neurons is mediated by the weight of the synapse that separates it from the firing neuron. This weight, in turn, is affected by the postsynaptic neuron's response through a mechanism that is thought to underlie important processes such as learning and memory. Although of difficult quantification, cortical synaptic weights have been found to obey a long-tailed unimodal distribution peaking near the lowest values, thus confirming some of the predictive models …
Synaptic plasticity depends on the interaction between electrical activity in neurons and the synaptic proteome, the collection of over 1000 proteins in the post-synaptic density (PSD) of synapses. To construct models of synaptic plasticity with realistic numbers of proteins, we aim to combine rule-based models of molecular interactions in the synaptic proteome with compartmental models of the electrical activity of neurons. Rule-based models allow interactions between the combinatorially large number of protein complexes in the postsynaptic proteome to be expressed straightforwardly. Simulati…
We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling can cause sustained firing or oscillatory behavior which is necessarily antiphase. Additive Gaussian white noise can transiently terminate the oscillations, hence destroying the stable limit cycle. Further application of the noise may return the system to spiking activity. In a particular noise range, the transition times between the oscillating and the rest…
Understanding how movement is controlled by the central nervous system remains a major challenge, with ongoing debate about basic features underlying this control. In this review, we introduce a new conceptual framework for the distribution of common input to spinal motor neurons. Specifically, this framework is based on the following assumptions: 1) motor neurons are grouped into functional groups (clusters) based on the common inputs they receive; 2) clusters may significantly differ from the classical definition of motor neuron pools, such that they may span across muscles and/or involve on…
We investigated the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We found spike death phenomena, namely, the state of neurons transits from limit cycle to fixed point or transient state. The phenomena occur under the perturbation of excitatory synaptic interaction that has a high efficacy. We showed that the decrease of synaptic current results in spike death through depressing the feedback of sodium ionic current. In the networks with spike death property the degree of synchronization is lower and unsensitive to the heterogeneity of …
Correlated electrical activity in neurons is a prominent characteristic of cortical microcircuits. Despite a growing amount of evidence concerning both spike-count and subthreshold membrane potential pairwise correlations, little is known about how different types of cortical neurons convert correlated inputs into correlated outputs. We studied pyramidal neurons and two classes of GABAergic interneurons of layer 5 in neocortical brain slices obtained from rats of both sexes, and we stimulated them with biophysically realistic correlated inputs, generated using dynamic clamp. We found that the …
One of the central problems in neuroscience is reconstructing synaptic connectivity in neural circuits. Synapses onto a neuron can be probed by sequentially stimulating potentially pre-synaptic neurons while monitoring the membrane voltage of the post-synaptic neuron. Reconstructing a large neural circuit using such a "brute force" approach is rather time-consuming and inefficient because the connectivity in neural circuits is sparse. Instead, we propose to measure a post-synaptic neuron's voltage while stimulating sequentially random subsets of multiple potentially pre-synaptic neurons. To re…
Using a realistic model of activity dependent dynamical synapses and a standard integrate and fire neuron model we study, both analytically and numerically, the conditions in which a postsynaptic neuron efficiently detects temporal coincidences of spikes arriving at certain frequency from N different afferents. We extend a previous work that only considers synaptic depression as the most important mechanism in the transmission of information through synapses, to a more general situation including also synaptic facilitation. Our study shows that: 1) facilitation enhances the detection of correl…
In an all-to-all network of integrate-fire oscillators in which there is a disorder in the intrinsic firing rates of the neurons, we show that through spike timing-dependent plasticity the links which have the faster oscillators as presynaptic, tend to be strengthened while the links originated from the slow spiking neurons are weakened. The emergent effective flow of directed connections, introduces the faster neurons as the more influent elements in the network and facilitates synchronization by decreasing the synaptic cost for onset of synchronization.
Working memory (WM) has been intensively used to enable the temporary storing of information for processing purposes, playing an important role in the execution of various cognitive tasks. Recent studies have shown that information in WM is not only maintained through persistent recurrent activity but also can be stored in activity-silent states such as in short-term synaptic plasticity (STSP). Motivated by important applications of the STSP mechanisms in WM, the main focus of the present work is on the analysis of the effects of random inputs on a leaky integrate-and-fire (LIF) synaptic condu…
The studies described in this dissertation have attempted to address the cellular mechanisms of information storage by the brain. My work has focused primarily on the postsynaptic events that occur during and after induction of long-term potentiation (LTP) and long-term depression (LTD) at the Schaffer collateral-CA1 synapse of the hippocampus. I have explored various aspects of the role of postsynaptic Ca$^{2+}$ in the induction of LTP and LTD using both extracellular and whole-cell recording techniques, as well as fluorescence imaging of Ca$^{2+}$. I have also examined the possible role of m…
Based on numerical simulation of Hodgkin and Huxley type neuron stimulated from many synaptic inputs, an abstract concept of signal processing in individual neuron is proposed. In the concept proposed, neuron performs binding of synaptic inputs into a single output event, based on the degree of temporal coherence between the inputs. Inhibition serves as controlling factor of this type of binding.
Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics like an effective inertia. In biological neuron networks this inertia is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of inertia affect the network dynamics is an open issue not yet addressed due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field di…
Synaptic plasticity is the capacity of a preexisting connection between two neurons to change in strength as a function of neural activity. Because synaptic plasticity is the major candidate mechanism for learning and memory, the elucidation of its constituting mechanisms is of crucial importance in many aspects of normal and pathological brain function. In particular, a prominent aspect that remains debated is how the plasticity mechanisms, that encompass a broad spectrum of temporal and spatial scales, come to play together in a concerted fashion. Here we review and discuss evidence that pin…
We have added a simplified neuromorphic model of Spike Time Dependent Plasticity (STDP) to the Synapto-dendritic Kernel Adapting Neuron (SKAN). The resulting neuron model is the first to show synaptic encoding of afferent signal to noise ratio in addition to the unsupervised learning of spatio temporal spike patterns. The neuron model is particularly suitable for implementation in digital neuromorphic hardware as it does not use any complex mathematical operations and uses a novel approach to achieve synaptic homeostasis. The neurons noise compensation properties are characterized and tested o…
Two elements of neural information processing have primarily been proposed: firing rate and spike timing of neurons. In the case of synaptic plasticity, although spike-timing-dependent plasticity (STDP) depending on presynaptic and postsynaptic spike times had been considered the most common rule, recent studies have shown the inhibitory nature of the brain in vivo for precise spike timing, which is key to the STDP. Thus, the importance of the firing frequency in synaptic plasticity in vivo has been recognized again. However, little is understood about how the frequency-dependent synaptic plas…
Universidad de La Rioja（拉里奥哈大学）；Instituto de Neurociencias（神经科学研究所）；Universidad Autónoma de Barcelona（巴塞罗那自治大学）
The quantification of synapses is instrumental to measure the evolution of synaptic densities of neurons under the effect of some physiological conditions, neuronal diseases or even drug treatments. However, the manual quantification of synapses is a tedious, error-prone, time-consuming and subjective task; therefore, tools that might automate this process are desirable. In this paper, we present SynapCountJ, an ImageJ plugin, that can measure synaptic density of individual neurons obtained by immunofluorescence techniques, and also can be applied for batch processing of neurons that have been…
We study the characteristics of weak signal detection by a recurrent neuronal network with plastic synaptic coupling. It is shown that in the presence of an asynchronous component in synaptic transmission, the network acquires selectivity with respect to the frequency of weak periodic stimuli. For non-periodic frequency-modulated stimuli, the response is quantified by the mutual information between input (signal) and output (network's activity), and is optimized by synaptic depression. Introducing correlations in signal structure resulted in the decrease of input-output mutual information. Our…
Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter d…
The connectome is a wiring diagram mapping all the neural connections in the brain. At the cellular level, it provides a map of the neurons and synapses within a part or all of the brain of an organism. In recent years, significant advances have been made in the study of the connectome via network science and graph theory. This analysis is fundamental to understand neurotransmission (fast synaptic transmission) networks. However, neurons use other forms of communication as neuromodulation that, instead of conveying excitation or inhibition, change neuronal and synaptic properties. This additio…
In this work we study the detection of weak stimuli by spiking neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level…
The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent t…
We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called `phasic', is the network period proportional to the synaptic decay time. These results are discussed in co…
We study a learning rule based upon the temporal correlation (weighted by a learning kernel) between incoming spikes and the internal state of the postsynaptic neuron, building upon previous studies of spike timing dependent synaptic plasticity (\cite{KGvHW,KGvH1,vH}). Our learning rule for the synaptic weight $w_{ij}$ is $$ \dot w_{ij}(t)= ε\int_{-\infty}^\infty \frac{1}{T_l} \int_{t-T_l}^t \sum_μδ(τ+s-t_{j,μ}) u(τ) dτ Γ(s)ds $$ where the $t_{j,μ}$ are the arrival times of spikes from the presynaptic neuron $j$ and the function $u(t)$ describes the state of the postsynaptic neuron $i$. Thus, …
The task of the brain is to look for structure in the external input. We study a network of integrate-and-fire neurons with several types of recurrent connections that learns the structure of its time-varying feedforward input by attempting to efficiently represent this input with spikes. The efficiency of the representation arises from incorporating the structure of the input into the decoder, which is implicit in the learned synaptic connectivity of the network. While in the original work of [Boerlin, Machens, Denève 2013] and [Brendel et al., 2017] the structure learned by the network to ma…
The interplay between excitatory and inhibitory neurons imparts rich functions of the brain. To understand the underlying synaptic mechanisms, a fundamental approach is to study the dynamics of excitatory and inhibitory conductances of each neuron. The traditional method of determining conductance employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Using theoretical analysis, electrophysiological experiments, and realistic simulations, here we demonstrate that the traditional method conceptually fails to measure the conductance due to the neglect of a nonlinear inte…
Cortical populations of neurons develop sparse representations adapted to the statistics of the environment. While existing synaptic plasticity models reproduce some of the observed receptive-field properties, a major obstacle is the sensitivity of Hebbian learning to omnipresent spurious correlations in cortical networks which can overshadow relevant latent input features. Here we develop a theory for synaptic plasticity that is invariant to second-order correlations in the input. Going beyond classical Hebbian learning, we show how Hebbian long-term depression (LTD) cancels the sensitivity t…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of firing rate neurons in which the synaptic weights are Gaussian correlated random variables, we describe the asymptotic law of the network when the number of neurons goes to infinity. We introduce the process-level empirical measure of the trajectories of the solutions to the equations of the finite network of neurons and the averaged law (with respect to the synaptic weights) of the trajectories of the solutions to the equations of the network of …
Two recent experimental observations pose a challenge to many cortical models. First, the activity in the auditory cortex is sparse, and firing rates can be described by a lognormal distribution. Second, the distribution of non-zero synaptic strengths between nearby cortical neurons can also be described by a lognormal distribution. Here we use a simple model of cortical activity to reconcile these observations. The model makes the experimentally testable prediction that synaptic efficacies onto a given cortical neuron are statistically correlated, i.e. it predicts that some neurons receive ma…
Brain plasticity refers to brain's ability to change neuronal connections, as a result of environmental stimuli, new experiences, or damage. In this work, we study the effects of the synaptic delay on both the coupling strengths and synchronisation in a neuronal network with synaptic plasticity. We build a network of Hodgkin-Huxley neurons, where the plasticity is given by the Hebbian rules. We verify that without time delay the excitatory synapses became stronger from the high frequency to low frequency neurons and the inhibitory synapses increases in the opposite way, when the delay is incre…
Alzheimer's disease (AD) is a common form of dementia observed in the elderly due to neurodegenerative disorder and dysfunction. This arises from alterations in synaptic functioning of neurons leading to cognitive impairment and memory loss. Recent experimental studies indicate that the amyloid beta (A beta) protein, in its dimer and oligomer forms, affects the synaptic activity of neurons in the early stages of AD. However, the precise mechanism underlying A beta induced synaptic depression is still not clearly understood. In this paper, we introduce an electrical model that provides a possib…
We consider a noise driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system to obtain the mean activity level for the system as a function of the mean synaptic weight, which predicts a first-order transition and hysteresis between a noise-dominated regime and a regime of persistent neural activity. Assuming Poisson firing statistics for the neurons, the plasticity dynamics of a synapse under the influence of the mean-field environmen…
Theoretical models of neuronal function consider different mechanisms through which networks learn, classify and discern inputs. A central focus of these models is to understand how associations are established amongst neurons, in order to predict spiking patterns that are compatible with empirical observations. Although these models have led to major insights and advances, they still do not account for the astonishing velocity with which the brain solves certain problems and what lies behind its creativity, amongst others features. We examine two important components that may crucially aid co…
Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimul…
Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For ini…
Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled oscillators have sparked the development of a new generation of neural mass models. Of notable interest are mean-field descriptions of all-to-all coupled quadratic integrate-and-fire (QIF) neurons, which have already seen numerous extensions and applications. These extensions include different forms of short-term adaptation (STA) considered to play an important rol…
How extracellular electric fields, as generated endogenously or through transcranial brain stimulation, affect the dynamics of large neuronal populations is of great interest but not well understood. To study the collective dynamics of large populations single-compartment (point) model neurons have been proven very successful. These models, however, lack the dendritic morphology to biophysically account for the effects of electric fields, and for changes in synaptic integration due to morphology alone. Here we (i) characterize the response of a canonical spatial (ball-and-stick) model neuron t…
An associative memory has been discussed of neural networks consisting of spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which memorize P patterns in their synaptic weights. In addition to excitatory synapses whose strengths are modified after the Willshaw-type learning rule with the 0/1 code for quiescent/active states, the network includes uniform inhibitory synapses which are introduced to reduce cross-talk noises. Our simulations of the HH neuron network for the noise-free state have shown to yield a fairly good performance with the storage capacity of $α_c = P_{…
Spike timing dependent plasticity (STDP) is believed to play an important role in shaping the structure of neural circuits. Here we show that STDP generates effective interactions between synapses of different neurons, which were neglected in previous theoretical treatments, and can be described as a sum over contributions from structural motifs. These interactions can have a pivotal influence on the connectivity patterns that emerge under the influence of STDP. In particular, we consider two highly ordered forms of structure: wide synfire chains, in which groups of neurons project to each oth…
The optimal patterns of synaptic conductances for spike generation in central neurons is a subject of considerable interest. Ideally, such conductance time courses should be extracted from membrane potential (Vm) activity, but this is difficult because the nonlinear contribution of conductances to the Vm renders their estimation from the membrane equation extremely sensitive. We outline here a solution to this problem based on a discretization of the time axis. This procedure can extract the time course of excitatory and inhibitory conductances solely from the analysis of Vm activity. We test …
Due to rapid advances in multielectrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both basic research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining the efficiency of commonly used simplified point-neuron network models with the biophysical principles underlying LFP gen…
