Our research explores the foundations of neural information processing on various levels of organization ranging from single cells through large-scale networks to human behavior. Each level of organization defines its own mechanism of information processing. Thus, for instance, single neurons code and transfer information in the spike trains of action potentials, whereas these individual spike trains are not directly visible on more macroscopic levels of organization such as neural networks, electroencephalographic signals or human behavior. The latter systems use different quantities and processes to communicate information. But how do the level specific information and its processing depend on each other? How do the different mechanisms for communication within and between levels emerge out of each other?

Three mechanisms of neural information processing are commonly discussed in the literature:

1) Synchronization of neural oscillations; 2) informational convergence zones, which are most common in settings of multisensory integration; and 3) winner-takes-all approaches, in which different patterns compete for the most energy, information, activation or similar quantities allowing a formulation in terms of cost functions. The winner-takes-all mechanism can actually be established as a special case of either of first two mechanisms. Other types of information processing (such as chemically based mechanisms) shall not be discussed here.

The primary object of our research is the spatiotemporal activity generated by a biological network. This may appear obvious on first thought. However, most studies do not consider the entire spatiotemporal pattern but rather reduced forms thereof such as firing rates (which e.g. excludes a discussion of synchronization properties unless modulations are considered), spatial or temporal averages, stationary assumptions, etc. In addition, varying constraints will be encountered on different levels of organization. For instance, the probability density distribution of synapses of a single neuron within the grey matter will fall off exponentially as the distance to the neuron increases. This behavior is universally observed, independent of the cortical area. On a higher level of organization such as the network of cortical areas, the connectivity is very different. It does not fall off exponentially, but is rather patchy and very specific for the areas under investigation. For this reason it is very intuitive that different organizational principles will be encountered on different levels of description. These principles will obviously not be independent from each other which raises the fundamental question of what are the meaningful and relevant variables when levels of organization are traversed. In particular, the complementary pair of Connectivity and Dynamics will play an important role in our discussion, which may be considered to be equivalent to the famous pair “Structure and Function” in biology (at least since the 19^th century naturalist Charles Darwin).

How does the connectivity of a network affect its dynamics?

Obviously, individual network nodes will act independently, if they are not connected. When connections are introduced, then they impose geometries onto the network, which do not necessarily coincide with the neighborhood relations in the physical space. For instance, the network nodes can be connected as a ring or as two parallel straits or can even disconnect individual subsets of the nodes. For all these network connection topologies, the physical locations of the nodes are the same, but the network dynamics will be entirely different. This situation we encounter in the brain. Here cortical and subcortical networks of millions of neuronal elements are interconnected in highly complex structures and define the anatomical connectivity. The anatomical connectivity will determine the coordinated activations of neurons, which are thought of as the carriers of information processing in the brain and referred to as functional connectivity. Examples thereof are consecutive activations or synchronization of neural populations. To elucidate neuronal information processing we need to identify the fundamental inter-relationships of anatomical and functional connectivity.

Network dynamics controlled by individual pathways

We study the mutual effects of local homogeneous and global heterogeneous connections on spatially continuous neural fields. It has been known that cortical areas are not only connected to their nearest neighbors, but also have patchy projections to far distant areas which inevitably affect the spatiotemporal dynamics of the neural field. As a " toy model", we have used the real Ginzburg Landau equation with an embedded two-point heterogeneous connection. We study the stability of the delay differential equations obtained, and compute the stability diagrams as a function of the time delay and the local and global coupling strengths.

Contact: Murad Qubbaj

References:

1. Synchrony and Clustering in Heterogeneous Networks with Global Coupling and Parameter Dispersion CG Assisi, VK Jirsa, JAS Kelso PRL. 94, 018106 (2005)
2. Will a large complex system with time delays be stable? V.K. Jirsa, M. Ding. PRL93, 070602 ( 2004)
3. Connectivity and Dynamics of Neural Information Processing V.K. Jirsa . Neuroinformatics 2, 183-204 (2004)
   
4. Enhancement of Neural Synchrony by Time Delay M. Dhamala, V.K. Jirsa, M. Ding. . PRL 92, 074104 (2004)
5. Transitions to synchrony in coupled bursting neurons. M. Dhamala, V.K. Jirsa, M. Ding. PRL 92, 028101 (2004)
6. Spatiotemporal pattern formation in neural systems with heterogeneous connection topologies VK Jirsa, JAS Kelso PRE 62, (2000)