II Generalized Integrate-and-Fire Neurons

Chapter 11 Encoding and Decoding with Stochastic Neuron models

In the ten preceding chapters, we went a long way: starting from the biophysical basis of neuronal dynamics we have arrived at a description of neurons that we called generalized integrate-and-fire models. We have seen that neurons contain multiple types of ion channels embedded in a capacitive membrane (Chapter 2). We have seen how basic principles regulate the dynamics of electrical current and membrane potential in synapses, dendrites and axons (Chapter 3). We have seen that sodium and potassium ion channel form an excitable system characterized by a threshold mechanism (Chapter 4) and that other ion channels shape the spike after-effects (Chapter 6). Finally, we have seen in Chapters 4, 5 and 6 how biophysical models can be reduced by successive approximations to other, simpler, models such as the LIF, EIF, AdEx, and SRM. Moreover, we have added noise to our neuron models (Chapters 7 and 9). At this point, it is natural to step back and check whether our assumptions were too stringent, whether the biophysical assumptions were well-founded, and whether the generalized models can explain neuronal data. We laid out the mathematical groundwork in Chapter 10 we can now set out to apply these statistical methods to real data.

We can test the performance of these, and other, models by using them as predictive models of encoding. Given a stimulus, will the model be able to predict the neuronal response? Will it be able to predict spike times observed in real neurons when driven by the same stimulus – or only the mean firing rate or PSTH? Will the model be able to account for the variability observed in neuronal data across repetitions?

Testing the performance of models addresses yet a bigger question. What information is discarded in the neural code? What features of the stimulus are most important? If we understand the neural code, will we be able to reconstruct the image that the eye is actually seeing at any given moment from spike trains observed in the brain? The problem of decoding neuronal activity is central both for our basic understanding of neural information processing (437) and for engineering ‘neural prosthetic’ devices that can interact with the brain directly (130). Given a spike train observed in the brain, can we read out intentions, thoughts, or movement plans? Can we use the data to control a prosthetic device?

In Section 11.1 we use the generalized integrate-and-fire models of Chapters 6 and 9 to predict membrane voltage and spike timings of real neurons during stimulation with an arbitrary time-dependent input current in vitro. In Section 11.2, we use the same model class to predict spike timings in vivo. Finally, in Section 11.3 we examine the question of decoding: given a measured spike train can we reconstruct the stimulus, or control a prosthetic arm?