The Spike Response Model: A Framework to Predict Neuronal Spike Trains

Wulfram Gerstner, Renaud Jolivet
Springer-Verlag, 2003
Conference paper

Abstract

We propose a simple method to map a generic threshold model, namely the Spike Response Model, to artificial data of neuronal activity using a minimal amount of a priori information. Here, data are generated by a detailed mathematical model of neuronal activity. The model neuron is driven with in-vivo-like current injected, and we test to which extent it is possible to predict the spike train of the detailed neuron model from that of the Spike Response Model. In particular, we look at the number of spikes correctly predicted within a biologically relevant time window. We find that the Spike Response Model achieves prediction of up to $80\%$ of the spikes with correct timing ( $\pm2$ ms). Other characteristics of activity, such as mean rate and coefficient of variation of spike trains, are predicted in the correct range as well.

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https://infoscience.epfl.ch/record/97812?ln=en

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Wulfram Gerstner, Renaud Jolivet
Springer-Verlag, 2003
Conference paper

Abstract

Official source

https://infoscience.epfl.ch/record/97812?ln=en

About this result

Related concepts (11)

Related concepts

Related publications (14)

Related publications

Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy

Wulfram Gerstner, Renaud Jolivet

We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically-detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrate-and-fire models. In the first variant (non-linear integrate-and-fire model), parameters depend on the instantaneous membrane potential whereas in the second variant, they depend on the time elapsed since the last spike (Spike Response Model). The direct reduction links features of the simple models to biophysical features of the full conductance based model. To quantitatively test the predictive power of the Spike Response Model and of the non-linear integrate-and-fire model, we compare spike trains in the simple models to those in the full conductance-based model when the models are subjected to identical randomly fluctuating input. For random current input, the simple models reproduce 70-80 percent of the spikes in the full model (with temporal precision of +/- 2ms over a wide range of firing frequencies. For random conductance injection, up to 73 percent of spikes are coincident. We also present a technique for numerically optimizing parameters in the Spike Response Model and the non-linear integrate-and-fire model based on spike trains in the full conductance-based model. This technique can be used to tune simple models to reproduce spike trains of real neurons.

American Physiological Society2004

Complexity and performance in simple neuron models

Wulfram Gerstner, Skander Mensi, Richard Naud

The ability of simple mathematical models to predict the activity of single neurons is important for computational neuroscience. In neurons, stimulated by a time-dependent current or conductance, we want to predict precisely the timing of spikes and the sub-threshold voltage. During the last years several models have been tested on this type of data but never compared with the same protocol. One of the major outcome is that, from a certain degree of complexity, all are very efficient and gave statistically indistinguishable results. We studied a class of integrate-and-fire models (IF), with each member of the class implementing a selection of possible improvements: exponential voltage non-linearity1, spike-triggered adaptation current2, spike-triggered change in conductance, moving threshold3, sub-threshold voltage-dependent currents4. Each refinement adds a new term to the equations of the IF model. This IF family is extendable and adaptable to different neuron types and is able to deal with complex neural activities (i.e. adaptation, facilitation, bursting, relative refractoriness, ...). To systematically explore the effects of a given term of the model a new fitting procedure based on linear regression of voltage change5 is used. This method is fast, robust and allows the extraction of all the models parameters from a few seconds recordings of fluctuating injected current and membrane potential with hundreds spikes without any prior knowledge. To investigate the effect of our modifications, we used as training data three different Hodgkin-Huxley-like models, and two experimental recordings of fast spiking and regular spiking cells and then evaluate each IF model on a given test set. We observe that it is possible to fit a model that can reproduce the activity of neurons with high reliability (i.e. almost 100 % of the spike time and less than 1 mV of sub-threshold voltage difference). Using this framework one can classify IF models in terms of complexity and performance and evaluate the importance of each term for different stimulation paradigms.

2010

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Changes of synaptic connections between neurons are thought to be the physiological basis of learning. These changes can be gated by neuromodulators that encode the presence of reward. We study a family of reward-modulated synaptic learning rules for spiking neurons on a learning task in continuous space inspired by the Morris Water maze. The synaptic update rule modifies the release probability of synaptic transmission and depends on the timing of presynaptic spike arrival, postsynaptic action potentials, as well as the membrane potential of the postsynaptic neuron. The family of learning rules includes an optimal rule derived from policy gradient methods as well as reward modulated Hebbian learning. The synaptic update rule is implemented in a population of spiking neurons using a network architecture that combines feedforward input with lateral connections. Actions are represented by a population of hypothetical action cells with strong mexican-hat connectivity and are read out at theta frequency. We show that in this architecture, a standard policy gradient rule fails to solve the Morris watermaze task, whereas a variant with a Hebbian bias can learn the task within 20 trials, consistent with experiments. This result does not depend on implementation details such as the size of the neuronal populations. Our theoretical approach shows how learning new behaviors can be linked to reward-modulated plasticity at the level of single synapses and makes predictions about the voltage and spike-timing dependence of synaptic plasticity and the influence of neuromodulators such as dopamine. It is an important step towards connecting formal theories of reinforcement learning with neuronal and synaptic properties

Public Library of Science2009

Complexity and performance in simple neuron models

Wulfram Gerstner, Skander Mensi, Richard Naud

2010