Multidimensional Dynamical Systems with Noise : Population Density Techniques for Neuroscience.

The problem of how to create efficient multi-scale models of large networks of neurons is a pressing one. It requires a balance between computational efficiency and a reduction of the number of parameters involved against biological realism. Simulations of point-model neurons show very realistic features of neural dynamics but are very hard to configure and to analyse. Instead of using hundreds or thousands of point-model neurons, a population can often be modeled by a single density function in a way that accurately reproduces quantities aggregated over the population, such as population firing rate or average membrane potential. These techniques have been widely applied in neuroscience, mainly on populations comprised of one-dimensional point-model neurons, such as leaky-integrate-and-fire neurons. Here, we present very general density methods that can be applied to point-model neurons of higher dimensionality that can represent biological features not present in simpler ones, such as adaptation and bursting. The methods are geometrical in nature and lend themselves to immediate visualisation of the population state. By decoupling the neural dynamics and the stochastic processes that model inter-neuron communication, an efficient GPGPU implementation is possible that makes the study of such high-dimensional models feasible. This decoupling also allows the study of different noise models, such as Poisson, white noise, and gamma-distributed interspike intervals, which broadens the application domain considerably compared to the Fokker-Planck equations that have traditionally dominated this approach. We will present several examples based on high-dimensional neural models. We will use dynamical systems that represent point-model neurons, but inherently there is nothing to restrict the approach presented here to neuroscience. MIIND is an open-source simulator that contains an implementation of these techniques.

Global organization of neuronal activity only requires unstructured local connectivity.

Modern electrophysiological recordings simultaneously capture single-unit spiking activities of hundreds of neurons spread across large cortical distances. Yet, this parallel activity is often confined to relatively low-dimensional manifolds. This implies strong coordination also among neurons that are most likely not even connected. Here, we combine in vivo recordings with network models and theory to characterize the nature of mesoscopic coordination patterns in macaque motor cortex and to expose their origin: We find that heterogeneity in local connectivity supports network states with complex long-range cooperation between neurons that arises from multi-synaptic, short-range connections. Our theory explains the experimentally observed spatial organization of covariances in resting state recordings as well as the behaviorally related modulation of covariance patterns during a reach-to-grasp task. The ubiquity of heterogeneity in local cortical circuits suggests that the brain uses the described mechanism to flexibly adapt neuronal coordination to momentary demands.

MIIND : A Model-Agnostic Simulator of Neural Populations.

MIIND is a software platform for easily and efficiently simulating the behaviour of interacting populations of point neurons governed by any 1D or 2D dynamical system. The simulator is entirely agnostic to the underlying neuron model of each population and provides an intuitive method for controlling the amount of noise which can significantly affect the overall behaviour. A network of populations can be set up quickly and easily using MIIND's XML-style simulation file format describing simulation parameters such as how populations interact, transmission delays, post-synaptic potentials, and what output to record. During simulation, a visual display of each population's state is provided for immediate feedback of the behaviour and population activity can be output to a file or passed to a Python script for further processing. The Python support also means that MIIND can be integrated into other software such as The Virtual Brain. MIIND's population density technique is a geometric and visual method for describing the activity of each neuron population which encourages a deep consideration of the dynamics of the neuron model and provides insight into how the behaviour of each population is affected by the behaviour of its neighbours in the network. For 1D neuron models, MIIND performs far better than direct simulation solutions for large populations. For 2D models, performance comparison is more nuanced but the population density approach still confers certain advantages over direct simulation. MIIND can be used to build neural systems that bridge the scales between an individual neuron model and a population network. This allows researchers to maintain a plausible path back from mesoscopic to microscopic scales while minimising the complexity of managing large numbers of interconnected neurons. In this paper, we introduce the MIIND system, its usage, and provide implementation details where appropriate.