Refractory density model of cortical direction selectivity: Lagged-nonlagged, transient-sustained, and On-Off thalamic neuron-based mechanisms and intracortical amplification

Response retention and apparent motion effect in visual cortex models

Apparent motion is a visual illusion in which stationary stimuli, flashing in distinct spatial locations at certain time intervals, are perceived as one stimulus moving between these locations. In the primary visual cortex, apparent-motion stimuli produce smooth spatio-temporal patterns of activity similar to those produced by continuously moving stimuli. An important prerequisite for producing such activity patterns is prolongation of responses to brief stimuli. Indeed, a brief stimulus can evoke in the visual cortex a long response, outlasting the stimulus by hundreds of milliseconds. Here we use firing-rate based models with simple ring structure, and biologically-detailed conductance-based refractory density (CBRD) model with retinotopic space representation to analyze the response retention and the origin of smooth profiles of activity in response to apparent-motion stimuli. We show that the strength of recurrent connectivity is the major factor that endorses neuronal networks with the ability for response retention. The same strengths of recurrent connections mediate the appearance of bump attractor in the ring models. Factors such as synaptic depression, NMDA receptor mediated currents, and conductances regulating spike adaptation influence response retention, but cannot substitute for the weakness of recurrent connections to reproduce response retention in models with weak connectivity. However, the weakness of lateral recurrent connections can be compensated by layering: in multi-layer models even with weaker connections the activity retains due to its feedforward propagation from layer to layer. Using CBRD model with retinotopic space representation we further show that smooth spatio-temporal profiles of activity in response to apparent-motion stimuli are produced in the models expressing response retention, but not in the models that fail to produce response retention. Together, these results demonstrate a link between response retention and the ability of neuronal networks to generate spatio-temporal patterns of activity, which are compatible with perception of apparent motion.

A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex

A fundamental challenge for the theoretical study of neuronal networks is to make the link between complex biophysical models based directly on experimental data, to progressively simpler mathematical models that allow the derivation of general operating principles. We present a strategy that successively maps a relatively detailed biophysical population model, comprising conductance-based Hodgkin-Huxley type neuron models with connectivity rules derived from anatomical data, to various representations with fewer parameters, finishing with a firing rate network model that permits analysis. We apply this methodology to primary visual cortex of higher mammals, focusing on the functional property of stimulus orientation selectivity of receptive fields of individual neurons. The mapping produces compact expressions for the parameters of the abstract model that clearly identify the impact of specific electrophysiological and anatomical parameters on the analytical results, in particular as manifested by specific functional signatures of visual cortex, including input-output sharpening, conductance invariance, virtual rotation and the tilt after effect. Importantly, qualitative differences between model behaviours point out consequences of various simplifications. The strategy may be applied to other neuronal systems with appropriate modifications.

A hierarchy of theoretical approaches to study a neuronal network depends on a tradeoff between biological fidelity and mathematical tractibility. Biophysically-detailed models consider cellular mechanisms and anatomically defined synaptic circuits, but are often too complex to reveal insights into fundamental principles. In contrast, increasingly abstract reduced models facilitate analytical insights. To better ground the latter to the underlying biology, we describe a systematic procedure to move across the model hierarchy that allows understanding how changes in biological parameters—physiological, pathophysiological, or because of new data—impact the behaviour of the network. We apply this approach to mammalian primary visual cortex, and examine how the different models in the hierarchy reproduce functional signatures of this area, in particular the tuning of neurons to the orientation of a visual stimulus. Our work provides a navigation of the complex parameter space of neural network models faithful to biology, as well as highlighting how simplifications made for mathematical convenience can fundamentally change their behaviour.