An Efficient Population Density Method for Modeling Neural Networks with Synaptic Dynamics Manifesting Finite Relaxation Time and Short-Term Plasticity

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.

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

Despite its success in understanding brain rhythms, the neural mass model, as a low-dimensional mean-field network model, is phenomenological in nature, so that it cannot replicate some of rich repertoire of responses seen in real neuronal tissues. Here, using a colored-synapse population density method, we derived a novel neural mass model, termed density-based neural mass model (dNMM), as the mean-field description of network dynamics of adaptive exponential integrate-and-fire (aEIF) neurons, in which two critical neuronal features, i.e., voltage-dependent conductance-based synaptic interactions and adaptation of firing rate responses, were included. Our results showed that the dNMM was capable of correctly estimating firing rate responses of a neuronal population of aEIF neurons receiving stationary or time-varying excitatory and inhibitory inputs. Finally, it was also able to quantitatively describe the effect of spike-frequency adaptation in the generation of asynchronous irregular activity of excitatory-inhibitory cortical networks. We conclude that in terms of its biological reality and calculation efficiency, the dNMM is a suitable candidate to build significantly large-scale network models involving multiple brain areas, where the neuronal population is the smallest dynamic unit.