Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics

Dynamic Characteristics of Neuron Models and Active Areas in Potential Functions

AbstractWe present a simple neuron model that shows a rich property in spite of the simple structure derived from a simplification of the Hindmarsh-Rose, the Morris-Lecar, and the Hodgkin-Huxley models. The model is a typical example whose characteristics can be discussed through the concept of potential with active areas. A potential function is able to provide a global landscape for dynamics of a model, and the dynamics is explained in connection with the disposition of the active areas on the potential, and hence we are able to discuss the global dynamic behaviors and the common properties among these realistic models

Acceleration of Spiking Neural Networks on Multicore Architectures

The human cortex is the seat of learning and cognition. Biological scale implementations of cortical models have the potential to provide significantly more power problem solving capabilities than traditional computing algorithms. The large scale implementation and design of these models has attracted significant attention recently. High performance implementations of the models are needed to enable such large scale designs. This thesis examines the acceleration of the spiking neural network class of cortical models on several modern multicore processors. These include the Izhikevich, Wilson, Morris-Lecar, and Hodgkin-Huxley models. The architectures examined are the STI Cell, Sun UltraSPARC T2+, and Intel Xeon E5345. Results indicate that these modern multicore processors can provide significant speed-ups and thus are useful in developing large scale cortical models. The models are then implemented on a 50 TeraFLOPS 336 node PlayStation 3 cluster. Results indicate that the models scale well on this cluster and can emulate 108 neurons and 1010 synapses. These numbers are comparable to the large scale cortical model implementation studies performed by IBM using the Blue Gene/L supercomputer. This study indicates that a cluster of PlayStation 3s can provide an economical, yet powerful, platform for simulating large scale biological models

Comparison of Langevin and Markov channel noise models for neuronal signal generation

The stochastic opening and closing of voltage-gated ion channels produces noise in neurons. The effect of this noise on the neuronal performance has been modelled using either approximate or Langevin model, based on stochastic differential equations or an exact model, based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either $Na^{+}$ and $K^{+}$, or only $K^{+}$ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and non-spiking membranes. Even with increasing numbers of channels the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels