Department of Mathematics

Speaker: Amir H. Assadi
Title: New Topological Methods to Investigate Old Biological Problems: Mathematical Insights in Darwin's Power of Movement in Plants
Affiliation: University of Wisconsin-Madison
Date: Friday, November 19, 2010
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Over 150 years ago, Charles and Francis Darwin published their treatise in plant biology: The Power of Movement in Plants. They discuss experiments, data and beautiful mathematical models in order to explain the biological phenomena underlying plant development and growth, and subsequently make predictions, such as the primary role of a hypothetical chemical, many years later to be discovered as the Auxin, a member of a family of plant hormones that govern development, growth and response behavior.

In this lecture, I start with Darwin's measurements of the effect of gravity on plants, and use it to motivate the central problem of biology, namely, mapping the genotypic and phenotypic trait variation, that is observed every day abundantly in all biological species around us. I will argue the advantages of a physics-based approach to quantify natural variation in genotypic and phenotypic traits. In particular, I outline how the synergy of experiments, computation and theoretical considerations are necessary to discover the physical principles that govern variation in gene expression and the resulting morphological pattern formation and behavioral responses in biological organisms. A concrete case study for this preliminary progress report is based on the model plant Arabidopsis that has been studied in great detail.

Part I of the talk explains the implications of the physics-based approach to capture new quantitative invariants that measure the topological variations in massive data sets that are collected from the dynamics of spatial organization in biological development and growth of the Arabidopsis primary root. The basic external force that is known to have a profound impact in this case is gravity. Thus, our theory will be discussed in the context of the role of gravity on variation of morphology of plant roots.

Part II, I combine mathematical and heuristic evidence from dynamical systems theory and differential topology to argue in favor of a hypothesis that is likely to provide a solution to the problem of relating genotypic and morphological variations in a large number of cases and in a general setting.