Brains and computers are complex networks of simpler components whose main function is performing difficult computations. Despite being built by different processes, these networks must be implemented in the physical world and, therefore, are subject to similar constraints arising from limitations on physical resources, such as space, time, and energy. Impact of these limitations on the computer architecture is an active area of research driven by the multi-billion dollar market for chip design. My main research work focuses on applying disciplines from computer engineering to understanding brain architecture.

Implementing connectivity in brain networks requires extensive wiring, which comes at a cost. Therefore, wiring optimization is an important consideration in brain design. Among all the possible costs, conduction delay is one of the major factors, but has received little attention in neurobiology.

I explore features of brain architecture that could be the result of minimizing conduction delays. We find that one such feature is the segregation of the brain into the white and gray matter. The gray matter contains neuron somata, synapses, and local wiring, such as dendrites and mostly non-myelinated axons. The white matter contains long-range and, in large brains, mostly myelinated axons that implement global communication. What is the advantage of such segregation? Alternatively, the network with the same local and global connectivity can be wired so that the long-range and local connections are finely inter-mixed. We search for the design with minimum conduction delays by quantitatively comparing different candidate designs. We find that the optimal design depends on the network size, connectivity, and axon diameter. In particular, the requirement to connect neurons with many fast axons drives the segregation of the brain into the white and gray matter. These results provide a possible explanation for observed structure of vertebrate brains, such as the mammalian neocortex and neostriatum, the avian telencephalon, and the spinal cord.

Figure 1: Segregation of the brain into gray and white matter in the cerebral cortex (adapted from http://www.brainmuseum.org).

Figure 2: Phase Diagram of Candidate Designs. In this phase diagram, we show that different candidate designs display their optimality in different parameter regions, which depend on the global axon diameter D, local wire diameter d, total neuron number N and the number of local connections per neuron n. Here, HS is the homogeneous structure, in which gray and white matter are finely intermixed. PS is the pipe structure, in which white matter tracts form a scaffold within gray matter and resemble one- dimensional pipes. CS is the cluster structure, in which white matter tracts can form two-dimensional sheets, dividing the gray matter into clusters. The neocortex can be viewed as CS with a particular spatial distribution of clusters, i.e. where clusters abut each other and merge into a continuous configuration (Wen Q. Chklovskii DB. Submitted).

Our results have the following important implications. First, understanding major factors driving evolution of the vertebrate brain satisfies scientific curiosity and may illuminate the reason for the uniqueness of the human mind. Second, understanding functional reasons for the observed brain design helps paint a self-consistent picture of the brain, which is crucial for choosing the level of abstraction in building theoretical models and guiding further experiments.

I also apply minimization of conduction delays to explaining the shape and topology of axonal and dendritic arbors, such as the branching feature of axons and dendrites and the variability in the shape of different neurons: from Purkinje neuron of the cerebellum to the pyramidal neuron of the neocortex (manuscript in preparation). These are the questions that have puzzled neurobiologists since the time of Cajal. Hopefully, our theoretical approach will provide a better understanding of the structure via function relationships. In particular, we determine that how much of the neuronal shape can be explained by the limitations on physical resources rather than demand on computation.

Figure 3: Variability in the dendritic shapes in different types of neurons (adapted from Masland RH Current Biology 2004).