Fellow Shashaank Vattikuti and I have been exploring how genetic and anatomical perturbations can give rise to autism spectrum disorder traits. In particular, we used a local cortical circuit at the sub-millimetre level as a bridge between genotype and phenotype. We have found that synaptic imbalance and changes in the minicolumn structure of cortex can effect performance in visual saccade tasks that match experiments. The model also makes predictions for possible pharmacological therapeutics. We are now collaborating with Steve Gotts and Alex Martin to develop psychophysical tests to probe cortical circuit dynamics. One cognitive phenomenon that may be usefully exploited to probe cortical circuit function is binocular rivalry, where each eye is presented with a different image and the brain's perception alternates between the two images. For the past decade, I have been developing a cortical circuit model involving mutual inhibition that can explain much of the physiology of rivalry. However, recent worked showed that the simple mutual inhibition model demonstrated a regime where dominance times decrease as the contrast of the images decreased contrary to experimental evidence. With former fellow Jeffrey Seely, I showed that this anamolous behavior could be eliminated in a mutual inhibition model with some simple biophysically plausible adjustments. Fellow Phyllis Thangaraj and I are extending the rivalry model to incorporate spatial dependence. Most of the past work on the dynamics of interacting neurons or oscillators have focused on the infinite system size limit where fluctuations due to the connections do not appear. However, many biological and neural networks are large but finite sized. The dynamics of such networks are not well understood. Former fellow Michael Buice and I examined the dynamics of a large but finite size network of globally connected oscillators. The model is the weak coupling limit of a mutually connected network of neurons that have a tendency to synchronize due to the connections. We showed that ideas from the kinetic theory of gases and plasmas could be applied to analyze the fluctuations and correlations due to system size effects. In particular, we showed that finite population size could stabilize the marginal asynchronous mode. This had been an open problem for twenty years. We showed how to derive an effective stochastic equation for a neuron embedded in network of unmeasured neurons. We have also developed a scheme to generalize population rate equations to account for correlations. The approach shows how a moment hierarchy can be generated from an underlying Master equation. We are now generalizing the result to deterministic systems.
| Vattikuti, Shashaank; Thangaraj, Phyllis; Xie, Hua W et al. (2016) Canonical Cortical Circuit Model Explains Rivalry, Intermittent Rivalry, and Rivalry Memory. PLoS Comput Biol 12:e1004903 |
| Chow, Carson C; Buice, Michael A (2015) Path integral methods for stochastic differential equations. J Math Neurosci 5:8 |
| Buice, Michael A; Chow, Carson C (2013) Dynamic finite size effects in spiking neural networks. PLoS Comput Biol 9:e1002872 |
| Buice, Michael A; Chow, Carson C (2013) Generalized activity equations for spiking neural network dynamics. Front Comput Neurosci 7:162 |
| Buice, Michael A; Chow, Carson C (2011) Effective stochastic behavior in dynamical systems with incomplete information. Phys Rev E Stat Nonlin Soft Matter Phys 84:051120 |
| Seely, Jeffrey; Chow, Carson C (2011) Role of mutual inhibition in binocular rivalry. J Neurophysiol 106:2136-50 |
| Buice, Michael A; Cowan, Jack D; Chow, Carson C (2010) Systematic fluctuation expansion for neural network activity equations. Neural Comput 22:377-426 |
| Vattikuti, Shashaank; Chow, Carson C (2010) A computational model for cerebral cortical dysfunction in autism spectrum disorders. Biol Psychiatry 67:672-8 |
