Neural assemblies as core elements for modeling neural networks in the brain

How does the brain process and memorize information? We all know that the neuron (also known as nerve cell) is the processing unit in the brain. But how do neurons work together in networks? The connectivity structure of neural networks plays an important role in information processing. Therefore, it is worthwhile to investigate modeling of neural networks. Experiments extract different kinds of datasets (ranging from pair-wise connectivity to membrane potential of individual neurons) and provide an understanding of neuronal activity. However, due to technical limitations of experiments, and complexity and variety of neural architectures, the experimental datasets do not yield a model of neural networks on their own. Roughly speaking, the experimental datasets are not enough for modeling neural networks. Therefore, in addition to these datasets, we have to utilize assumptions, hand-tuned features, parameter tuning and heuristic methods for modeling networks. In this thesis, we present different models of neural networks that are able to produce several behaviors observed in mammalian brain and cell cultures, e.g., up-state/down-state oscillations, different stimulus-evoked responses of cortical layers, activity propagation with tunable speed and several activity patterns of mice barrel cortex. An element which is embedded in all of these models is a network feature called neural assembly. A neural assembly is a group (also called population) of neurons with dense recurrent connectivity and strong internal synaptic weights. We study the dynamics of neural assemblies using analytical approaches and computer simulations. We show that network models containing assemblies exhibit dynamics similar to activity observed in the brain.

Estimation of small-world topology of cortical networks using Generalized Linear Models

Joao Emanuel Felipe Gerhard, Wulfram Gerstner

Since the seminal work of Watts & Strogatz and others in the late 90s [1], graph-theoretic analyses have been performed on many complex dynamic networks, including brain structures. Most studies have focused on functional connectivity defined between whole brain regions, using imaging techniques such as fMRI, EEG or MEG [2]. Only very few studies have attempted to look at the structure of neural networks on the level of individual neurons [3,4]. To the best of our knowledge, these studies have only considered undirected connectivity networks and have derived connectivity based on estimates on small subsets or even pairs of neurons from the recorded networks. Here, we investigate scale-free and small-world properties of neuronal networks, based on multi-electrode recordings from the awake monkey on a larger data set than in previous approaches. We estimate effective, i.e. causal, interactions by fitting Generalized Linear Models on the neural responses to natural stimulation, incorporating effects from the neurons’ self-history, coupling terms and modulation by the external stimulus. The resulting connectivity matrix is directed and a link between two neurons represents a causal influence from one neuron to the other, given the observation of all other neurons from the population. We use this connectivity matrix to estimate scale-free and small-world properties of the network samples. For this, the quantity proposed by [5] for quantifying small-world-ness is generalized to directed networks. We find that the networks under consideration lack scale-free behavior, but show a small, but significant small-world structure. Finally, we show that the experimental design of multi-electrode recordings typically enforces a particular network structure that can have a considerate impact on how the small-world structure of the network should be evaluated. Since for multi-electrode recordings the sampling of neurons is not uniform across the population (one electrode usually captures signals from a small local population), we expect the wiring probability between neurons of the same local spot to be much higher than the wiring probability between neurons from different electrodes. Thus, random graphs that take the different wiring probabilities into account can serve as a more refined null model than the homogeneous Erdös-Renyi random graphs that are usually proposed as reference models to evaluate small-world properties. Moreover, as the set of recorded neurons in a given experiment always represents only a subpopulation of the overall network, we investigate how the evaluation of small-world structure is affected by this undersampling bias.

2011

Cortical Dynamics in Presence of Assemblies of Densely Connected Weight-Hub Neurons

Moritz Deger, Wulfram Gerstner, Hesam Setareh

Experimental measurements of pairwise connection probability of pyramidal neurons together with the distribution of synaptic weights have been used to construct randomly connected model networks. However, several experimental studies suggest that both wiring and synaptic weight structure between neurons show statistics that differ from random networks. Here we study a network containing a subset of neurons which we call weight-hub neurons, that are characterized by strong inward synapses. We propose a connectivity structure for excitatory neurons that contain assemblies of densely connected weight-hub neurons, while the pairwise connection probability and synaptic weight distribution remain consistent with experimental data. Simulations of such a network with generalized integrate-and-fire neurons display regular and irregular slow oscillations akin to experimentally observed up/down state transitions in the activity of cortical neurons with a broad distribution of pairwise spike correlations. Moreover, stimulation of a model network in the presence or absence of assembly structure exhibits responses similar to light-evoked responses of cortical layers in optogenetically modified animals. We conclude that a high connection probability into and within assemblies of excitatory weight-hub neurons, as it likely is present in some but not all cortical layers, changes the dynamics of a layer of cortical microcircuitry significantly.

Frontiers Research Foundation2017

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

Moritz Deger, Wulfram Gerstner, Tilo Schwalger

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50 -- 2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics like finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly simulate a model of a local cortical microcircuit consisting of eight neuron types. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Public Library of Science2017

Estimation of small-world topology of cortical networks using Generalized Linear Models

Joao Emanuel Felipe Gerhard, Wulfram Gerstner

2011