Investigating the putative functional impact of heterogeneous firing responses on neocortical processing (Zerlaut & Destexhe, Plos Comp. Biol. 2017)

In this study, we wanted to investigate what could be the functional impact of the diversity in firing responses that we found in young mice visual cortex in a previous study.

On the methodological side, the points of interest are the following:

First, deriving the properties of the membrane potential fluctuations as a function of the synaptic input properties for Rall’s dendritic model was not so easy (although not conceptually elaborated, basic distribution theory and complex analysis, see Supp. Material). This was a relatively long and nasty calculus, so prone to mistakes… Hence I performed the derivation with sympy, the python library for symbolic mathematics. You can then directly export your results to numpy (for the numerical implementation) and to LateX (for the paper, the supplementary material equations have been automatically generated) without any manual manipulation (the mistakes). See the notebook for how to do this. This is, to my opinion, a great workflow for those analytically demanding problems. Note that, of course, you need to carefully set up the problem conceptually before, sympy would never have been able to give me the solution “out of the box”.

Second, the numerical simulations of theĀ  dendritic model (just to check the relative accuracy with the analytical description), I implemented it in NEURON (with its python layer, well…). I provide the code for this implementation. Note that the simulations are rather long to obtain the statistical properties of the membrane potential fluctuations (this is what motivates the analytical derivation, see paper).

The rest of the paper is quite trivial in terms of implementation once you have the analytical estimate.

The Ipython notebook associated to this paper can be found on the following link:

[[ in progress ..]]




Capturing the specific firing rate response of a single cell in the fluctuation-driven regime (Zerlaut et al., J. Physiol. 2016)

In this study, we measured the firing rate response of pyramidal cells in young mice cortex and we found quite some differences in individual responses. We thus needed a versatile procedure to capture the individual responses into an analytical description.

[[to be continued …]]

The Ipython notebook associated to this paper can be found on the following link:

[[ in progress ..]]


Accounting for state-dependency in an early sensory system (Reig et al., J. Neurosci. 2015)

In this study, in collaboration with an experimental team in Barcelona, we designed a simple theoretical framework to account for how the dependency on network state gives rise to a non-trivial relationship between the stimulus intensity and the response amplitude (here measured as evoked post-synaptic deflections) along the early auditory system (up to the primary auditory cortex).

Basically, what the modeling part brings is 1) to account for the state dependency of the recruitment of spiking neurons at a given stimulus level (an analytical estimate for the effect numerically evidenced in a previous paper from Alain), 2) give an analytical estimate for the state-dependency of postsynaptic deflections (the input conductance effect) and 3) apply this recruitment process to a network and a chain of networks.

An Ipython notebook with the code generating the figures can be found on the following link: