The project describes a series of theoretical and experimental studies of morphogen gradients, defined as the concentration fields of chemical substances that control spatial patterns of cell differentiation in developing tissues. Molecular studies of embryogenesis have identified morphogen gradients in systems as diverse as body axes specification in insects and patterning of mammalian neocortex. Current studies of morphogen gradients move in an increasingly quantitative direction and demand the development of a rigorous theoretical framework that can be used to interpret experimental results and guide systems-level analyses of pattern formation mechanisms. This project develops such a framework, emphasizing the dynamics of morphogen gradient formation. This research combines rigorous mathematical and computational analysis of a general class of reaction-diffusion models of morphogen gradient formation and application of these models to a specific pattern formation event in Drosophila embryo.

Broader impacts of proposed work include the development of a general mathematical framework for a highly conserved biological process. One of the main outcomes of proposed activity is a set of analytical results that can be used for the back-of-the-envelope analysis of pattern formation dynamics in a wide range of developmental systems. The proposed theoretical and experimental studies go hand-in-hand with the development of educational program that provides interdisciplinary training in the emerging field of developmental systems biology.

Project Report

Our work led to the new analytical techniques for studies of chemical signals that pattern developing tissues. We focused on the formation of spatially nonuniform distribution of chemical signals that act as dose-dependent regyulators of cell differentiation and gene expression. These concentration profiles are called morphogen gradients and play a key role in conceptual and mathematical models of embryogenesis. Mos of the work on morphogen gradients have focused on their steady state behavior and emphasized numerical analysis. In contrast, our work focused on their dynamics and established new and broadly applicable analytical techniques. Our work relied on the introduction of the concept of local accumulation time, defined as the characteristic time scale for establishing steady state concentration at a given position within the tissue. We have derived analytical expression for local accumulation times for a number of well-established biophysical models and used our results to interpret data from our own and published experiments. The derived expressions have a very transparent probabilistic interpretation and can be viewed as conditional mean first passage time. We have also considered nonlinear models of morphogen gradient formation and derived a self-similar solution in a classical problem where the diffusible chemical signals accelerates its own degradation. The work resulted in several publications and one Ph.D. thesis.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Mary Ann Horn
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Princeton University
United States
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