Theoretical Problems in Soft Matter and Quantitative Biology

Harvard University, Cambridge MA

Investigators

Abstract

TECHNICAL SUMMARY The Division of Mathematical Sciences and the Division of Materials Research contribute funds to this award. It supports theoretical research and education on soft condensed matter and non-equilibrium statistical mechanics at the interface of materials research and mathematics with biology. The research includes the study of population dynamics and properties of pollen grains and polymersomes. In various ways, the research contributes to the advance of non-equilibrium statistical mechanics, and biologically inspired materials and nanostructures. The PI aims to use methods from theoretical physics to understand the population waves which have played a crucial role in the evolutionary history of many species, including humans. Neutral genetic markers can be used to infer information about growth, ancestral population size and colonization pathways. Such phenomena can be studied experimentally by tracking the genetic de-mixing of pioneer micro-organisms arising from razor blade inoculations in a Petri dish. Enhanced fluctuations due to small population sizes at a growing front can lead to remarkable effects, such as "gene surfing". The PI plans to study such phenomena through a combination of techniques from non-equilibrium statistical mechanics, probability theory, and population genetics, with particular emphasis understanding how "inflation" impedes de-mixing of radial expansions in two and three dimensions. The PI also plans to construct a detailed theory of sector numbers, fixation probabilities and genetic instabilities at moving population frontiers. Using analytical and numerical methods for solving the Foppl-von Karman equations for thin shells, the PI will explore folding strategies and shapes of pollen grains during dehydration as they migrate from flower to flower. The grain can be modeled as a pressurized high-Young-modulus sphere with a weak sector and a nonzero spontaneous curvature. In the absence of such a weak sector, these shells crumple irreversibly under pressure via a strong instability. The weak sectors of both one and three-sector pollen grains eliminate the hysteresis and allow easy rehydration at the pollination site, somewhat like the collapse and subsequent reassembly of a folding chair. The PI aims to determine the optimal shape and position of the weak sectors, and see if nature has indeed adopted such strategies in specific cases. In addition, the PI will study how thermal fluctuations affect thin-shelled polymersomes, a new kind of vesicle that resists shear and is made from diblock copolymers. This award also supports interdisciplinary training for graduate students through the opportunities provided by the research. NONTECHNICAL SUMMARY: The Division of Mathematical Sciences and the Division of Materials Research contribute funds to this award. It supports theoretical research and education on soft condensed matter and non-equilibrium statistical mechanics at the interface of materials research and mathematics with biology. The research includes the study of population dynamics and properties of pollen grains and polymersomes. In various ways, the research contributes to the advance of non-equilibrium statistical mechanics, and biologically inspired materials and nanostructures. The PI will use techniques from non-equilibrium statistical mechanics and mathematics to understand migrations of biological organisms. Potential applications include impeding harmful bacteria, such as Pseudomonas aeruginosa, which can grow along the surfaces of medical tubing or prosthetic devices. In such bacterial infections and more generally some diseases, the rate at which the attacking genome at the frontier evolves to evade the immune system, can determine whether patients live or die. A second thrust of the research is to understand how a pollen grain folds onto itself when it is exposed to a dry environment and polymersomes crumple using the fundamental principles of materials and geometry. Polymersomes are vesicles that are made of long chain-like molecules and surround liquid. The investigation of polymersomes could lead to a better understanding of the strength of these drug encapsulation devices. A better understanding of how natural materials function contributes to efforts to discover new materials that mimic biology and exploit nature's design ideas. This research contributes to the intellectual foundations of the discovery of new materials, new technologies, and disease control through a better understanding of the design principles and forces of nature. This award also supports interdisciplinary training for graduate students through the opportunities provided by the research.