A data-informed mean-field approach to mapping of cortical parameter landscapes

Model-agnostic neural mean field with a data-driven transfer function

As one of the most complex systems known to science, modeling brain behavior and function is both fascinating and extremely difficult. Empirical data is increasingly available from ex vivo human brain organoids and surgical samples, as well as in vivo animal models, so the problem of modeling the behavior of large-scale neuronal systems is more relevant than ever. The statistical physics concept of a mean-field model offers a tractable way to bridge the gap between single-neuron and population-level descriptions of neuronal activity, by modeling the behavior of a single representative neuron and extending this to the population. However, existing neural mean-field methods typically either take the limit of small interaction sizes, or are applicable only to the specific neuron models for which they were derived. This paper derives a mean-field model by fitting a transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. The transfer function is fitted numerically to simulated spike time data, and is entirely agnostic to the underlying neuronal dynamics. The resulting mean-field model predicts the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. Furthermore, it enables an accurate approximate bifurcation analysis as a function of the level of recurrent input. This model does not assume large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.

Desiderata for Normative Models of Synaptic Plasticity

Normative models of synaptic plasticity use computational rationales to arrive at predictions of behavioral and network-level adaptive phenomena. In recent years, there has been an explosion of theoretical work in this realm, but experimental confirmation remains limited. In this review, we organize work on normative plasticity models in terms of a set of desiderata that, when satisfied, are designed to ensure that a given model demonstrates a clear link between plasticity and adaptive behavior, is consistent with known biological evidence about neural plasticity and yields specific testable predictions. As a prototype, we include a detailed analysis of the REINFORCE algorithm. We also discuss how new models have begun to improve on the identified criteria and suggest avenues for further development. Overall, we provide a conceptual guide to help develop neural learning theories that are precise, powerful, and experimentally testable.

Learning spiking neuronal networks with artificial neural networks: neural oscillations

First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living systems. On the other hand, modern data-driven methods thrive at modeling many types of high-dimensional and noisy data. Still, the training and interpretation of these data-driven models remain challenging. Here, we combine the two types of methods to model stochastic neuronal network oscillations. Specifically, we develop a class of artificial neural networks to provide faithful surrogates to the high-dimensional, nonlinear oscillatory dynamics produced by a spiking neuronal network model. Furthermore, when the training data set is enlarged within a range of parameter choices, the artificial neural networks become generalizable to these parameters, covering cases in distinctly different dynamical regimes. In all, our work opens a new avenue for modeling complex neuronal network dynamics with artificial neural networks.

Model-Agnostic Neural Mean Field With The Refractory SoftPlus Transfer Function

Due to the complexity of neuronal networks and the nonlinear dynamics of individual neurons, it is challenging to develop a systems-level model which is accurate enough to be useful yet tractable enough to apply. Mean-field models which extrapolate from single-neuron descriptions to large-scale models can be derived from the neuron's transfer function, which gives its firing rate as a function of its synaptic input. However, analytically derived transfer functions are applicable only to the neurons and noise models from which they were originally derived. In recent work, approximate transfer functions have been empirically derived by fitting a sigmoidal curve, which imposes a maximum firing rate and applies only in the diffusion limit, restricting applications. In this paper, we propose an approximate transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. Refractory SoftPlus activation functions allow the derivation of simple empirically approximated mean-field models using simulation results, which enables prediction of the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. These models also support an accurate approximate bifurcation analysis as a function of the level of recurrent input. Finally, the model works without assuming large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.

Odor modality is transmitted to cortical brain regions from the olfactory bulb

Odor perception is the impetus for important animal behaviors with two predominate modes of processing: odors pass through the front of the nose (orthonasal) while inhaling and sniffing, or through the rear (retronasal) during exhalation and while eating. Despite the importance of olfaction for an animal's well-being and that ortho and retro naturally occur, it is unknown how the modality (ortho vs. retro) is even transmitted to cortical brain regions, which could significantly affect how odors are processed and perceived. Using multielectrode array recordings in tracheotomized anesthetized rats, which decouples ortho-retro modality from breathing, we show that mitral cells in rat olfactory bulb can reliably and directly transmit orthonasal versus retronasal modality with ethyl butyrate, a common food odor. Drug manipulations affecting synaptic inhibition via GABAA lead to worse decoding of ortho versus retro, independent of whether overall inhibition increases or decreases, suggesting that the olfactory bulb circuit may naturally favor encoding this important aspect of odors. Detailed data analysis paired with a firing rate model that captures population trends in spiking statistics shows how this circuit can encode odor modality. We have not only demonstrated that ortho/retro information is encoded to downstream brain regions but also used modeling to demonstrate a plausible mechanism for this encoding; due to synaptic adaptation, it is the slower time course of the retronasal stimulation that causes retronasal responses to be stronger and less sensitive to inhibitory drug manipulations than orthonasal responses.NEW & NOTEWORTHY Whether ortho (sniffing odors) versus retro (exhalation and eating) is encoded from the olfactory bulb to other brain areas is not completely known. Using multielectrode array recordings in anesthetized rats, we show that the olfactory bulb transmits this information downstream via spikes. Altering inhibition degrades ortho/retro information on average. We use theory and computation to explain our results, which should have implications on cortical processing considering that only food odors occur retronasally.

Desiderata for normative models of synaptic plasticity

Normative models of synaptic plasticity use a combination of mathematics and computational simulations to arrive at predictions of behavioral and network-level adaptive phenomena. In recent years, there has been an explosion of theoretical work on these models, but experimental confirmation is relatively limited. In this review, we organize work on normative plasticity models in terms of a set of desiderata which, when satisfied, are designed to guarantee that a model has a clear link between plasticity and adaptive behavior, consistency with known biological evidence about neural plasticity, and specific testable predictions. We then discuss how new models have begun to improve on these criteria and suggest avenues for further development. As prototypes, we provide detailed analyses of two specific models - REINFORCE and the Wake-Sleep algorithm. We provide a conceptual guide to help develop neural learning theories that are precise, powerful, and experimentally testable.

A neurocomputational theory of action regulation predicts motor behavior in neurotypical individuals and patients with Parkinson’s disease

Surviving in an uncertain environment requires not only the ability to select the best action, but also the flexibility to withhold inappropriate actions when the environmental conditions change. Although selecting and withholding actions have been extensively studied in both human and animals, there is still lack of consensus on the mechanism underlying these action regulation functions, and more importantly, how they inter-relate. A critical gap impeding progress is the lack of a computational theory that will integrate the mechanisms of action regulation into a unified framework. The current study aims to advance our understanding by developing a neurodynamical computational theory that models the mechanism of action regulation that involves suppressing responses, and predicts how disruption of this mechanism can lead to motor deficits in Parkinson’s disease (PD) patients. We tested the model predictions in neurotypical individuals and PD patients in three behavioral tasks that involve free action selection between two opposed directions, action selection in the presence of conflicting information and abandoning an ongoing action when a stop signal is presented. Our results and theory suggest an integrated mechanism of action regulation that affects both action initiation and inhibition. When this mechanism is disrupted, motor behavior is affected, leading to longer reaction times and higher error rates in action inhibition.