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1.  Synaptic Plasticity in Neural Networks Needs Homeostasis with a Fast Rate Detector 
PLoS Computational Biology  2013;9(11):e1003330.
Hebbian changes of excitatory synapses are driven by and further enhance correlations between pre- and postsynaptic activities. Hence, Hebbian plasticity forms a positive feedback loop that can lead to instability in simulated neural networks. To keep activity at healthy, low levels, plasticity must therefore incorporate homeostatic control mechanisms. We find in numerical simulations of recurrent networks with a realistic triplet-based spike-timing-dependent plasticity rule (triplet STDP) that homeostasis has to detect rate changes on a timescale of seconds to minutes to keep the activity stable. We confirm this result in a generic mean-field formulation of network activity and homeostatic plasticity. Our results strongly suggest the existence of a homeostatic regulatory mechanism that reacts to firing rate changes on the order of seconds to minutes.
Author Summary
Learning and memory in the brain are thought to be mediated through Hebbian plasticity. When a group of neurons is repetitively active together, their connections get strengthened. This can cause co-activation even in the absence of the stimulus that triggered the change. To avoid run-away behavior it is important to prevent neurons from forming excessively strong connections. This is achieved by regulatory homeostatic mechanisms that constrain the overall activity. Here we study the stability of background activity in a recurrent network model with a plausible Hebbian learning rule and homeostasis. We find that the activity in our model is unstable unless homeostasis reacts to rate changes on a timescale of minutes or faster. Since this timescale is incompatible with most known forms of homeostasis, this implies the existence of a previously unknown, rapid homeostatic regulatory mechanism capable of either gating the rate of plasticity, or affecting synaptic efficacies otherwise on a short timescale.
PMCID: PMC3828150  PMID: 24244138
4.  Reinforcement Learning Using a Continuous Time Actor-Critic Framework with Spiking Neurons 
PLoS Computational Biology  2013;9(4):e1003024.
Animals repeat rewarded behaviors, but the physiological basis of reward-based learning has only been partially elucidated. On one hand, experimental evidence shows that the neuromodulator dopamine carries information about rewards and affects synaptic plasticity. On the other hand, the theory of reinforcement learning provides a framework for reward-based learning. Recent models of reward-modulated spike-timing-dependent plasticity have made first steps towards bridging the gap between the two approaches, but faced two problems. First, reinforcement learning is typically formulated in a discrete framework, ill-adapted to the description of natural situations. Second, biologically plausible models of reward-modulated spike-timing-dependent plasticity require precise calculation of the reward prediction error, yet it remains to be shown how this can be computed by neurons. Here we propose a solution to these problems by extending the continuous temporal difference (TD) learning of Doya (2000) to the case of spiking neurons in an actor-critic network operating in continuous time, and with continuous state and action representations. In our model, the critic learns to predict expected future rewards in real time. Its activity, together with actual rewards, conditions the delivery of a neuromodulatory TD signal to itself and to the actor, which is responsible for action choice. In simulations, we show that such an architecture can solve a Morris water-maze-like navigation task, in a number of trials consistent with reported animal performance. We also use our model to solve the acrobot and the cartpole problems, two complex motor control tasks. Our model provides a plausible way of computing reward prediction error in the brain. Moreover, the analytically derived learning rule is consistent with experimental evidence for dopamine-modulated spike-timing-dependent plasticity.
Author Summary
As every dog owner knows, animals repeat behaviors that earn them rewards. But what is the brain machinery that underlies this reward-based learning? Experimental research points to plasticity of the synaptic connections between neurons, with an important role played by the neuromodulator dopamine, but the exact way synaptic activity and neuromodulation interact during learning is not precisely understood. Here we propose a model explaining how reward signals might interplay with synaptic plasticity, and use the model to solve a simulated maze navigation task. Our model extends an idea from the theory of reinforcement learning: one group of neurons form an “actor,” responsible for choosing the direction of motion of the animal. Another group of neurons, the “critic,” whose role is to predict the rewards the actor will gain, uses the mismatch between actual and expected reward to teach the synapses feeding both groups. Our learning agent learns to reliably navigate its maze to find the reward. Remarkably, the synaptic learning rule that we derive from theoretical considerations is similar to previous rules based on experimental evidence.
PMCID: PMC3623741  PMID: 23592970
5.  Changing the responses of cortical neurons from sub- to suprathreshold using single spikes in vivo 
eLife  2013;2:e00012.
Action Potential (APs) patterns of sensory cortex neurons encode a variety of stimulus features, but how can a neuron change the feature to which it responds? Here, we show that in vivo a spike-timing-dependent plasticity (STDP) protocol—consisting of pairing a postsynaptic AP with visually driven presynaptic inputs—modifies a neurons' AP-response in a bidirectional way that depends on the relative AP-timing during pairing. Whereas postsynaptic APs repeatedly following presynaptic activation can convert subthreshold into suprathreshold responses, APs repeatedly preceding presynaptic activation reduce AP responses to visual stimulation. These changes were paralleled by restructuring of the neurons response to surround stimulus locations and membrane-potential time-course. Computational simulations could reproduce the observed subthreshold voltage changes only when presynaptic temporal jitter was included. Together this shows that STDP rules can modify output patterns of sensory neurons and the timing of single-APs plays a crucial role in sensory coding and plasticity.
eLife digest
Nerve cells, called neurons, are one of the core components of the brain and form complex networks by connecting to other neurons via long, thin ‘wire-like’ processes called axons. Axons can extend across the brain, enabling neurons to form connections—or synapses—with thousands of others. It is through these complex networks that incoming information from sensory organs, such as the eye, is propagated through the brain and encoded.
The basic unit of communication between neurons is the action potential, often called a ‘spike’, which propagates along the network of axons and, through a chemical process at synapses, communicates with the postsynaptic neurons that the axon is connected to. These action potentials excite the neuron that they arrive at, and this excitatory process can generate a new action potential that then propagates along the axon to excite additional target neurons. In the visual areas of the cortex, neurons respond with action potentials when they ‘recognize’ a particular feature in a scene—a process called tuning. How a neuron becomes tuned to certain features in the world and not to others is unclear, as are the rules that enable a neuron to change what it is tuned to. What is clear, however, is that to understand this process is to understand the basis of sensory perception.
Memory storage and formation is thought to occur at synapses. The efficiency of signal transmission between neurons can increase or decrease over time, and this process is often referred to as synaptic plasticity. But for these synaptic changes to be transmitted to target neurons, the changes must alter the number of action potentials. Although it has been shown in vitro that the efficiency of synaptic transmission—that is the strength of the synapse—can be altered by changing the order in which the pre- and postsynaptic cells are activated (referred to as ‘Spike-timing-dependent plasticity’), this has never been shown to have an effect on the number of action potentials generated in a single neuron in vivo. It is therefore unknown whether this process is functionally relevant.
Now Pawlak et al. report that spike-timing-dependent plasticity in the visual cortex of anaesthetized rats can change the spiking of neurons in the visual cortex. They used a visual stimulus (a bar flashed up for half a second) to activate a presynaptic cell, and triggered a single action potential in the postsynaptic cell a very short time later. By repeatedly activating the cells in this way, they increased the strength of the synaptic connection between the two neurons. After a small number of these pairing activations, presenting the visual stimulus alone to the presynaptic cell was enough to trigger an action potential (a suprathreshold response) in the postsynaptic neuron—even though this was not the case prior to the pairing.
This study shows that timing rules known to change the strength of synaptic connections—and proposed to underlie learning and memory—have functional relevance in vivo, and that the timing of single action potentials can change the functional status of a cortical neuron.
PMCID: PMC3552422  PMID: 23359858
synaptic plasticity; STDP; visual cortex; circuits; in vivo; spiking patterns; rat
6.  The Silent Period of Evidence Integration in Fast Decision Making 
PLoS ONE  2013;8(1):e46525.
In a typical experiment on decision making, one out of two possible stimuli is displayed and observers decide which one was presented. Recently, Stanford and colleagues (2010) introduced a new variant of this classical one-stimulus presentation paradigm to investigate the speed of decision making. They found evidence for “perceptual decision making in less than 30 ms”. Here, we extended this one-stimulus compelled-response paradigm to a two-stimulus compelled-response paradigm in which a vernier was followed immediately by a second vernier with opposite offset direction. The two verniers and their offsets fuse. Only one vernier is perceived. When observers are asked to indicate the offset direction of the fused vernier, the offset of the second vernier dominates perception. Even for long vernier durations, the second vernier dominates decisions indicating that decision making can take substantial time. In accordance with previous studies, we suggest that our results are best explained with a two-stage model of decision making where a leaky evidence integration stage precedes a race-to-threshold process.
PMCID: PMC3549915  PMID: 23349660
7.  Reward-based learning under hardware constraints—using a RISC processor embedded in a neuromorphic substrate 
In this study, we propose and analyze in simulations a new, highly flexible method of implementing synaptic plasticity in a wafer-scale, accelerated neuromorphic hardware system. The study focuses on globally modulated STDP, as a special use-case of this method. Flexibility is achieved by embedding a general-purpose processor dedicated to plasticity into the wafer. To evaluate the suitability of the proposed system, we use a reward modulated STDP rule in a spike train learning task. A single layer of neurons is trained to fire at specific points in time with only the reward as feedback. This model is simulated to measure its performance, i.e., the increase in received reward after learning. Using this performance as baseline, we then simulate the model with various constraints imposed by the proposed implementation and compare the performance. The simulated constraints include discretized synaptic weights, a restricted interface between analog synapses and embedded processor, and mismatch of analog circuits. We find that probabilistic updates can increase the performance of low-resolution weights, a simple interface between analog synapses and processor is sufficient for learning, and performance is insensitive to mismatch. Further, we consider communication latency between wafer and the conventional control computer system that is simulating the environment. This latency increases the delay, with which the reward is sent to the embedded processor. Because of the time continuous operation of the analog synapses, delay can cause a deviation of the updates as compared to the not delayed situation. We find that for highly accelerated systems latency has to be kept to a minimum. This study demonstrates the suitability of the proposed implementation to emulate the selected reward modulated STDP learning rule. It is therefore an ideal candidate for implementation in an upgraded version of the wafer-scale system developed within the BrainScaleS project.
PMCID: PMC3778319  PMID: 24065877
neuromorphic hardware; wafer-scale integration; large-scale spiking neural networks; spike-timing dependent plasticity; reinforcement learning; hardware constraints analysis
8.  Inference of neuronal network spike dynamics and topology from calcium imaging data 
Two-photon calcium imaging enables functional analysis of neuronal circuits by inferring action potential (AP) occurrence (“spike trains”) from cellular fluorescence signals. It remains unclear how experimental parameters such as signal-to-noise ratio (SNR) and acquisition rate affect spike inference and whether additional information about network structure can be extracted. Here we present a simulation framework for quantitatively assessing how well spike dynamics and network topology can be inferred from noisy calcium imaging data. For simulated AP-evoked calcium transients in neocortical pyramidal cells, we analyzed the quality of spike inference as a function of SNR and data acquisition rate using a recently introduced peeling algorithm. Given experimentally attainable values of SNR and acquisition rate, neural spike trains could be reconstructed accurately and with up to millisecond precision. We then applied statistical neuronal network models to explore how remaining uncertainties in spike inference affect estimates of network connectivity and topological features of network organization. We define the experimental conditions suitable for inferring whether the network has a scale-free structure and determine how well hub neurons can be identified. Our findings provide a benchmark for future calcium imaging studies that aim to reliably infer neuronal network properties.
PMCID: PMC3871709  PMID: 24399936
calcium; action potential; reconstruction; connectivity; scale-free; hub neurons
9.  Coding and Decoding with Adapting Neurons: A Population Approach to the Peri-Stimulus Time Histogram 
PLoS Computational Biology  2012;8(10):e1002711.
The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a ‘quasi-renewal equation’ which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.
Author Summary
How can information be encoded and decoded in populations of adapting neurons? A quantitative answer to this question requires a mathematical expression relating neuronal activity to the external stimulus, and, conversely, stimulus to neuronal activity. Although widely used equations and models exist for the special problem of relating external stimulus to the action potentials of a single neuron, the analogous problem of relating the external stimulus to the activity of a population has proven more difficult. There is a bothersome gap between the dynamics of single adapting neurons and the dynamics of populations. Moreover, if we ignore the single neurons and describe directly the population dynamics, we are faced with the ambiguity of the adapting neural code. The neural code of adapting populations is ambiguous because it is possible to observe a range of population activities in response to a given instantaneous input. Somehow the ambiguity is resolved by the knowledge of the population history, but how precisely? In this article we use approximation methods to provide mathematical expressions that describe the encoding and decoding of external stimuli in adapting populations. The theory presented here helps to bridge the gap between the dynamics of single neurons and that of populations.
PMCID: PMC3464223  PMID: 23055914
10.  Paradoxical Evidence Integration in Rapid Decision Processes 
PLoS Computational Biology  2012;8(2):e1002382.
Decisions about noisy stimuli require evidence integration over time. Traditionally, evidence integration and decision making are described as a one-stage process: a decision is made when evidence for the presence of a stimulus crosses a threshold. Here, we show that one-stage models cannot explain psychophysical experiments on feature fusion, where two visual stimuli are presented in rapid succession. Paradoxically, the second stimulus biases decisions more strongly than the first one, contrary to predictions of one-stage models and intuition. We present a two-stage model where sensory information is integrated and buffered before it is fed into a drift diffusion process. The model is tested in a series of psychophysical experiments and explains both accuracy and reaction time distributions.
Author Summary
In models of decision making, evidence is accumulated until it crosses a threshold. The amount of evidence is directly related to the strength of the sensory input for the decision alternatives. Such one-stage models predict that if two stimulus alternatives are presented in succession, the stimulus alternative presented first dominates the decision, as the accumulated evidence will reach the threshold for this alternative first. Here, we show that for short stimulus durations decision making is not dominated by the first, but by the second stimulus. This result cannot be explained by classical one-stage decision models. We present a two-stage model where sensory input is first integrated before its outcome is fed into a classical decision process.
PMCID: PMC3280955  PMID: 22359494
14.  Synaptic tagging and capture: a bridge from molecular to behaviour 
BMC Neuroscience  2011;12(Suppl 1):P122.
PMCID: PMC3240215
15.  Efficient modeling of neural activity using coupled renewal processes 
BMC Neuroscience  2011;12(Suppl 1):P123.
PMCID: PMC3240216
18.  Extraction of Network Topology From Multi-Electrode Recordings: Is there a Small-World Effect? 
The simultaneous recording of the activity of many neurons poses challenges for multivariate data analysis. Here, we propose a general scheme of reconstruction of the functional network from spike train recordings. Effective, causal interactions are estimated by fitting generalized linear models on the neural responses, incorporating effects of the neurons’ self-history, of input from other neurons in the recorded network and of modulation by an external stimulus. The coupling terms arising from synaptic input can be transformed by thresholding into a binary connectivity matrix which is directed. Each link between two neurons represents a causal influence from one neuron to the other, given the observation of all other neurons from the population. The resulting graph is analyzed with respect to small-world and scale-free properties using quantitative measures for directed networks. Such graph-theoretic analyses have been performed on many complex dynamic networks, including the connectivity structure between different brain areas. Only few studies have attempted to look at the structure of cortical neural networks on the level of individual neurons. Here, using multi-electrode recordings from the visual system of the awake monkey, we find that cortical networks lack scale-free behavior, but show a small, but significant small-world structure. Assuming a simple distance-dependent probabilistic wiring between neurons, we find that this connectivity structure can account for all of the networks’ observed small-world ness. Moreover, for multi-electrode recordings the sampling of neurons is not uniform across the population. We show that the small-world-ness obtained by such a localized sub-sampling overestimates the strength of the true small-world structure of the network. This bias is likely to be present in all previous experiments based on multi-electrode recordings.
PMCID: PMC3036953  PMID: 21344015
generalized linear models; effective connectivity; small-world networks; random sampling; scale-free networks; network topology; awake monkey recordings; visual system
19.  A History of Spike-Timing-Dependent Plasticity 
How learning and memory is achieved in the brain is a central question in neuroscience. Key to today’s research into information storage in the brain is the concept of synaptic plasticity, a notion that has been heavily influenced by Hebb's (1949) postulate. Hebb conjectured that repeatedly and persistently co-active cells should increase connective strength among populations of interconnected neurons as a means of storing a memory trace, also known as an engram. Hebb certainly was not the first to make such a conjecture, as we show in this history. Nevertheless, literally thousands of studies into the classical frequency-dependent paradigm of cellular learning rules were directly inspired by the Hebbian postulate. But in more recent years, a novel concept in cellular learning has emerged, where temporal order instead of frequency is emphasized. This new learning paradigm – known as spike-timing-dependent plasticity (STDP) – has rapidly gained tremendous interest, perhaps because of its combination of elegant simplicity, biological plausibility, and computational power. But what are the roots of today’s STDP concept? Here, we discuss several centuries of diverse thinking, beginning with philosophers such as Aristotle, Locke, and Ribot, traversing, e.g., Lugaro’s plasticità and Rosenblatt’s perceptron, and culminating with the discovery of STDP. We highlight interactions between theoretical and experimental fields, showing how discoveries sometimes occurred in parallel, seemingly without much knowledge of the other field, and sometimes via concrete back-and-forth communication. We point out where the future directions may lie, which includes interneuron STDP, the functional impact of STDP, its mechanisms and its neuromodulatory regulation, and the linking of STDP to the developmental formation and continuous plasticity of neuronal networks.
PMCID: PMC3187646  PMID: 22007168
synaptic plasticity; spike-timing-dependent plasticity; bidirectional plasticity; long term depression; long term plasticity; history; learning; memory
20.  STDP in Adaptive Neurons Gives Close-To-Optimal Information Transmission 
Spike-frequency adaptation is known to enhance the transmission of information in sensory spiking neurons by rescaling the dynamic range for input processing, matching it to the temporal statistics of the sensory stimulus. Achieving maximal information transmission has also been recently postulated as a role for spike-timing-dependent plasticity (STDP). However, the link between optimal plasticity and STDP in cortex remains loose, as does the relationship between STDP and adaptation processes. We investigate how STDP, as described by recent minimal models derived from experimental data, influences the quality of information transmission in an adapting neuron. We show that a phenomenological model based on triplets of spikes yields almost the same information rate as an optimal model specially designed to this end. In contrast, the standard pair-based model of STDP does not improve information transmission as much. This result holds not only for additive STDP with hard weight bounds, known to produce bimodal distributions of synaptic weights, but also for weight-dependent STDP in the context of unimodal but skewed weight distributions. We analyze the similarities between the triplet model and the optimal learning rule, and find that the triplet effect is an important feature of the optimal model when the neuron is adaptive. If STDP is optimized for information transmission, it must take into account the dynamical properties of the postsynaptic cell, which might explain the target-cell specificity of STDP. In particular, it accounts for the differences found in vitro between STDP at excitatory synapses onto principal cells and those onto fast-spiking interneurons.
PMCID: PMC3001990  PMID: 21160559
STDP; plasticity; spike-frequency adaptation; information theory; optimality
21.  Voltage and Spike Timing Interact in STDP – A Unified Model 
A phenomenological model of synaptic plasticity is able to account for a large body of experimental data on spike-timing-dependent plasticity (STDP). The basic ingredient of the model is the correlation of presynaptic spike arrival with postsynaptic voltage. The local membrane voltage is used twice: a first term accounts for the instantaneous voltage and the second one for a low-pass filtered voltage trace. Spike-timing effects emerge as a special case. We hypothesize that the voltage dependence can explain differential effects of STDP in dendrites, since the amplitude and time course of backpropagating action potentials or dendritic spikes influences the plasticity results in the model. The dendritic effects are simulated by variable choices of voltage time course at the site of the synapse, i.e., without an explicit model of the spatial structure of the neuron.
PMCID: PMC3059665  PMID: 21423511
synaptic plasticity; computational neuroscience; STDP; LTP; LTD; voltage; model; frequency
23.  Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves 
Biological Cybernetics  2008;99(4-5):361-370.
The dynamic I–V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons.
PMCID: PMC2798053  PMID: 19011924
I-V curve; Exponential integrate-and-fire; Refractoriness
24.  Firing patterns in the adaptive exponential integrate-and-fire model 
Biological Cybernetics  2008;99(4-5):335-347.
For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.
PMCID: PMC2798047  PMID: 19011922
Simplified single-neuron models; Firing patterns; Chaos; Electrophysiological taxonomy
25.  Correction: Spike-Based Reinforcement Learning in Continuous State and Action Space: When Policy Gradient Methods Fail 
PLoS Computational Biology  2009;5(12):10.1371/annotation/307ea250-3792-4ceb-b905-162d86c96baf.
PMCID: PMC2804701

Results 1-25 (28)