Inferring synaptic conductances from spike trains under a biophysically inspired point process model
A popular approach to neural characterization describes neural responses in terms of a cascade of linear and nonlinear stages: a linear filter to describe stimulus integration, followed by a nonlinear function to convert the filter output to spike rate. However, real neurons respond to stimuli in a manner that depends on the nonlinear integration of excitatory and inhibitory synaptic inputs. Here we introduce a biophysically inspired point process model that explicitly incorporates stimulus-induced changes in synaptic conductance in a dynamical model of neuronal membrane potential. Our work makes two important contributions. First, on a theoretical level, it offers a novel interpretation of the popular generalized linear model (GLM) for neural spike trains. We show that the classic GLM is a special case of our conductance-based model in which the stimulus linearly modulates excitatory and inhibitory conductances in an equal and opposite "push-pull" fashion. Our model can therefore be viewed as a direct extension of the GLM in which we relax these constraints; the resulting model can exhibit shunting as well as hyperpolarizing inhibition, and time-varying changes in both gain and membrane time constant. Second, on a practical level, we show that our model provides a tractable model of spike responses in early sensory neurons that is both more accurate and more interpretable than the GLM. Most importantly, we show that we can accurately infer intracellular synaptic conductances from extracellularly recorded spike trains. We validate these estimates using direct intracellular measurements of excitatory and inhibitory conductances in parasol retinal ganglion cells. The stimulus-dependence of both excitatory and inhibitory conductances can be well described by a linear-nonlinear cascade, with the filter driving inhibition exhibiting opposite sign and a slight delay relative to the filter driving excitation. We show that the model fit to extracellular spike trains can predict excitatory and inhibitory conductances elicited by novel stimuli with nearly the same accuracy as a model trained directly with intracellular conductances.
The authors propose a conductance based spiking model (CBSM) that is more biophysically realistic than the currently popular generalized linear model (GLM). Furthermore, the authors present CBSM as a generalization of the GLM and propose a set of constraints that can reduce it to a GLM and a GLM variant that would be as adaptive as the CBSM.The proposed model is an interesting extension to current spiking models in that it is parametrizedin a more descriptive way of the spiking process without sacrificing much of the mathematicalconvenience of the GLM. One thing that could raise some concerns stems from the last paragraph of page 6. The behaviour of the inhibitory filter described in line 322 is reminiscent of overfitting. The authors deal with thatby adding the regularizing penalty of Eq. 22. However, it seems that they don't use cross-validation in the experimental results to show the applicability of their model in a more natural environment.Some small things that might need correction:	line 121: fourth subscript should be i?	line 214: chose our an?