Effective minimal threshold models of neuronal activity

This work investigates the capacity of Integrate-and-Fire-type (I&F-type) models to quantitatively predict spike trains of real neurons in various laboratory and in vivo-like settings. A step-by-step methodology is developed to build an equivalent effective model of the threshold type, namely the Spike Response Model, from intracellular recordings. The methodology provides a simple and flexible framework and allows straightforward estimation of model parameters, all of which except the threshold are directly extracted from sample recordings without approximations. Additional features like spike-frequency adaptation, simulated synaptic conductances (as opposed to direct current injection) or stochastic spike initiation can be easily included in a second step. The methodology is tested with a simulated detailed Hodgkin-Huxley-type model of an interneuron as well as with layer 5 neocortical pyramidal neurons. The effective model performs well in predicting the spike train of cortical neurons. We show that the timing of spikes can be predicted with great accuracy as well as other typical measures of neuronal activity like the average discharge rate and the interspike interval distribution. To some extent, even the subthreshold voltage between spikes is correctly predicted. The ability of the effective model to predict spikes of layer 5 pyramidal neurons with a correct timing is closely related to the input characteristics. In this sense, the model follows the same lines as real neurons when evaluating their input-dependent ability to repetitively and reliably produce the same output spike train given the same input. I&F-type models of neuronal activity are commonly thought to be too simple to account for the rich firing behavior of real neurons. This work suggests that, at least in the considered settings, the picture of a neuron that combines linear summation with a threshold criterion is not too wrong and provides a justification to the use of I&F-type models in large scale network simulations.

A new Mathematical Framework to Understand Single Neuron Computations

Skander Mensi

An important feature of the nervous system is its ability to adapt to new stimuli. This adaptation allows for optimal encoding of the incoming information by dynamically changing the coding strategy based upon the incoming inputs to the neuron. At the level of single cells, this widespread phenomena is often referred to as spike-frequency adaptation, since it manifests as a history-dependent modulation of the neurons firing frequency. In this thesis I focus on how a neuron is able to adapt its activity to a specific input as well as on the function of such adaptive mechanisms. To study these adaptive processes different approaches have been used, from empirical observations of neural activities to detailed modeling of single cells. Here, I approach these problems by using simplified threshold models. In particular, I introduced a new generalization of the integrate-and-fire model (GIF) along with a convex fitting method allowing for efficient estimation of model parameters. Despite its relative simplicity I show that this neuron model is able to reproduce neuron behaviors with a high degree of accuracy. Moreover, using this method I was able to show that cortical neurons are equipped with two distinct adaptation mechanisms. First, a spike-triggered current that captures the complex influx of ions generated after the emission of a spike. While the second is a movement of the firing threshold, which possibly reflects the slow inactivation of sodium channels induced by the spiking activity. The precise dynamics of these adaptation processes is cell-type specific, explaining the difference of firing activity reported in different neuron types. Consequently, neuronal types can be classified based on model parameters. In Pyramidal neurons spike-dependent adaptation lasts for seconds and follows a scale-free dynamics, which is optimally tuned to encodes the natural inputs that pyramidal neurons receive in vivo. Finally using an extended version of the GIF model, I show that adaptation is not only a spike-dependent phenomenon, but also acts at the subthreshold level. In Pyramidal neurons the dynamics of the firing threshold is influenced by the subthreshold membrane potential. Spike-dependent and voltage-dependent adaptation interact in an activity-dependent way to ultimately shape the filtering properties of the membrane on the input statistics. Equipped with such a mechanism, Pyramidal neurons behave as integrators at low inputs and as a coincidence detectors at high inputs, maintaining sensitivity to input fluctuations across all regimes.

EPFL2014

Simple Neuron Models and Adaptation

Skander Mensi

Predicting activity of single neuron is an important part of the computational neuroscience and a great challenge. Several mathematical models exist, from the simple (one compartment and few parameters, like the SRM or the IF-type models), to the more complex (biophysical model like the Hodgkin-Huxley model). All these models have their own advantages and limitations, but no one is able to reproduce the exact behavior of real neurons. Multiple projects try to simulate complex neural networks, or even the whole brain (i.e. the blue brain project or other big network simulation). To achieve this goal it is very important that simple neuron models simulate, for a low computational cost, the precise activities of all neuron classes. It is well-known that neurons exhibit a lot of different activity patterns (from an electro-physiological point of view). Here we have focused on pyramidal neurons from the layer 5 of the neocortex. They are classified as regular spiking-cells. This cell type shows adaptation and like other neurons, refractoriness. Adaptation and refractoriness are very common neuronal activity in the brain, and so it is important to have a simple model which can reproduce this kind of activity. This project deals with two classical simple neuron models: the adaptive exponential integrate-and-fire model (AdEx) and the spike response model (SRM). We deter- mined the parameters of these two models using data generated with a detailed model, the Destexhe's model which is a HH-like model for cortical pyramidal cells, stimulated with different current injection scenarios. In a second time the model parameters have been set using data from in-vitro recordings of 4 layer 5 pyramidal rat neurons, stimulated with a sinusoid in vivo-like protocol, injected somatically in current-clamp configuration. Then we show that this type of model can capture adaptation and can reproduce the activity of neuron with a high reliability

2008

Simple Neuron Models and Adaptation

Skander Mensi

2008

A new Mathematical Framework to Understand Single Neuron Computations

Skander Mensi

EPFL2014