My main scientific interests are in the area of theoretical neuroscience. My research is aimed at understanding connectivity principles in the human brain. This is one of the oldest and most important challenges in neuroscience. Unraveling connectivity is complicated in part by the fact that the human brain presents a highly interconnected network of about a hundred billion neurons. The geometry of neuronal arbors can provide valuable clues to the solution of the connectivity problem. By analyzing shapes of cortical neurons I attempt to answer a number of important questions: 1. Is there potential for the reorganization of neuronal circuits in the adult brain? 2. What are the substrates of specificity and randomness in neuronal connectivity? 3. Is the cortex optimally designed to store information in synaptic connectivity patterns? The answers to these basic questions will improve our understanding of essential brain functions, such as learning and memory.

Learning and memory depend on structural plasticity of neuronal connectivity. An important contribution to structural plasticity is associated with changes in synaptic connectivity patterns through the formation and elimination of dendritic spines. To characterize this contribution quantitatively, we calculated the number of different synaptic connectivity patterns attainable without major arbor remodeling. This number is determined by the ratio of actual synapses and the number of axons that pass within a spine length of a given dendrite. We called this ratio the filling fraction and estimated it to be much smaller than one. This implies that spine remodeling can make a large contribution to the reorganization of neuronal circuits.

Brain function relies on the specificity of synaptic connectivity patterns among different classes of neurons. Understanding this specificity is crucial in formulating a canonical cortical circuit. Different classes of neurons may use different strategies to achieve specificity. Our analysis of three-dimensional reconstructions of neuronal pairs revealed specificity in the layout of axons of inhibitory interneurons. These axons are correlated with their dendritic targets. Axons of excitatory neurons show no such correlation. However, wiring patterns among excitatory cells hold a large potential for specificity through growth and retraction of dendritic spines. These results identify both specific and random features in cortical micro-circuits

It is believed that the structural design of neurons has been optimized in the course of evolution to match the functional demand on neural micro-circuitry. There is some scattered evidence of such optimization. For example, we have shown that cortical circuits are optimally designed to store information in synaptic connectivity patterns. Optimization methods have been also successfully applied to explain different aspects of neuron morphology.

• "Class-specific Features of Neuronal Wiring" Stepanyants, A., Tams, G., and Chklovskii, D.B., Neuron 43, 251-259 (2004)
• "Power-law for axon diameters at branch point" Chklovskii, D.B. and Stepanyants, A., BMC Neuroscience, 4:18 (2003)
• "Geometry and Structural Plasticity of Synaptic Connectivity" Stepanyants, A., Hof, and P.R., Chklovskii, D.B., Neuron, 34, 275-88 (2002)
• "Diffusion and Localization of Surface Gravity Waves over Irregular Bathymetry" Stepanyants, A., Phys.Rev. E, 63, 3, 031202 (2001)