A novel density-based neural mass model for simulating neuronal network dynamics with conductance-based synapses and membrane current adaptation

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.

A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.

New biophysical rate-based modeling of long-term plasticity in mean-field neuronal population models

The formation of customized neural networks as the basis of brain functions such as receptive field selectivity, learning or memory depends heavily on the long-term plasticity of synaptic connections. However, the current mean-field population models commonly used to simulate large-scale neural network dynamics lack explicit links to the underlying cellular mechanisms of long-term plasticity. In this study, we developed a new mean-field population model, the plastic density-based neural mass model (pdNMM), by incorporating a newly developed rate-based plasticity model based on the calcium control hypothesis into an existing density-based neural mass model. Derivation of the plasticity model was carried out using population density methods. Our results showed that the synaptic plasticity represented by the resulting rate-based plasticity model exhibited Bienenstock-Cooper-Munro-like learning rules. Furthermore, we demonstrated that the pdNMM accurately reproduced previous experimental observations of long-term plasticity, including characteristics of Hebbian plasticity such as longevity, associativity and input specificity, on hippocampal slices, and the formation of receptive field selectivity in the visual cortex. In conclusion, the pdNMM is a novel approach that can confer long-term plasticity to conventional mean-field neuronal population models.

In silico Effects of Synaptic Connections in the Visual Thalamocortical Pathway

We have studied brain connectivity using a biologically inspired in silico model of the visual pathway consisting of the lateral geniculate nucleus (LGN) of the thalamus, and layers 4 and 6 of the primary visual cortex. The connectivity parameters in the model are informed by the existing anatomical parameters from mammals and rodents. In the base state, the LGN and layer 6 populations in the model oscillate with dominant alpha frequency, while the layer 4 oscillates in the theta band. By changing intra-cortical hyperparameters, specifically inhibition from layer 6 to layer 4, we demonstrate a transition to alpha mode for all the populations. Furthermore, by increasing the feedforward connectivities in the thalamo-cortico-thalamic loop, we could transition into the beta band for all the populations. On looking closely, we observed that the origin of this beta band is in the layer 6 (infragranular layers); lesioning the thalamic feedback from layer 6 removed the beta from the LGN and the layer 4. This agrees with existing physiological studies where it is shown that beta rhythm is generated in the infragranular layers. Lastly, we present a case study to demonstrate a neurological condition in the model. By changing connectivities in the network, we could simulate the condition of significant (P < 0.001) decrease in beta band power and a simultaneous increase in the theta band power, similar to that observed in Schizophrenia patients. Overall, we have shown that the connectivity changes in a simple visual thalamocortical in silico model can simulate state changes in the brain corresponding to both health and disease conditions.