Theoretical models of neural circuit development.

Proper wiring up of the nervous system is critical to the development of organisms capable of complex and adaptable behaviors. Besides the many experimental advances in determining the cellular and molecular machinery that carries out this remarkable task precisely and robustly, theoretical approaches have also proven to be useful tools in analyzing this machinery. A quantitative understanding of these processes can allow us to make predictions, test hypotheses, and appraise established concepts in a new light. Three areas that have been fruitful in this regard are axon guidance, retinotectal mapping, and activity-dependent development. This chapter reviews some of the contributions made by mathematical modeling in these areas, illustrated by important examples of models in each section. For axon guidance, we discuss models of how growth cones respond to their environment, and how this environment can place constraints on growth cone behavior. Retinotectal mapping looks at computational models for how topography can be generated in populations of neurons based on molecular gradients and other mechanisms such as competition. In activity-dependent development, we discuss theoretical approaches largely based on Hebbian synaptic plasticity rules, and how they can generate maps in the visual cortex very similar to those seen in vivo. We show how theoretical approaches have substantially contributed to the advancement of developmental neuroscience, and discuss future directions for mathematical modeling in the field.