“Neurons and Neuronal Populations: from Recordings in vivo to Simulations of Cortical Tissue” Lyle Graham

Summary: Neural processing relies on two basic elements: First, the intrinsic properties of neurons that allow processing of synaptic input from other neurons, and generation of action potentials as the computational result; second, the network of excitatory and inhibitory pathways. How these elements interact to generate computational function in the brain is the question that we are addressing with a symbiosis of experiments -electrophysiology and histology in the early visual system, and theoretical models – both biophysically-detailed and formal mathematical models of neurons and networks.

Each neuron in the brain instantiates a complex mapping from typically thousands of synaptic and many contextual inputs, to the eventual action potential output. The biophysical structure underlying this transformation includes the non-linear interactions between synaptic inputs across neuron’s dendritic tree, the neuron’s voltage and second-messenger dependent membrane channels and, finally, the intracellular systems that regulate synaptic and membrane properties. Our work aims to characterize this mapping in neurons of the hippocampus and cortex, with particular attention to the integrated analysis of the responses of neurons to both artificial (electrophysiological) and functional (visual) stimuli [1].

To describe neuronal populations, equations for population dynamics with an age-structured modeling approach are applied, which originate from the papers devoted to epidemiology by Sharpe and Lotka (1911), McKendrick (1926) [2] and von Foerster (1959). Applied to neural systems, the McKendrick-Foerster continuity equation is known as the refractory density equation since the work by Wulfram Gerstner and Leo van Hemmen (1992). In our works we have developed single neuron models that reflects experimentally observed biophysical detail and derived from them biophysically detailed neuronal population models [3]. Finally, we will discuss how these models are employed to explain mechanisms of such phenomena observed in the cortex as orientation and direction tuning, propagating waves etc. [4]

The mini-course is structured as follows:

• Overview (LG): Biophysics of Computation - Information Processing by Single Neurons
• Overview (AC): Refractory Density Descriptions of Network Dynamics
• Case Studies (LG): In Vivo Measurements of Neuronal Biophysics
• Case Studies (AC): Modelling Neurons and Networks with Refractory Density Approach

[1] Borg-Graham L. // Cereb Cortex (1999)
[2] McKendrick AG. // Proc. Edinburgh Math. Soc. (1926)
[3] Chizhov AV, Graham LJ. // Physical Review E. (2007)
[4] Chizhov AV, Graham LJ. // PLOS CB (2021)