The Roles of Randomness in Biophysics: From Cell Growth to Behavioral Control

Abstract

This dissertation concerns problems involving stochastic processes and uncertainty, focusing on questions in the field of biophysics. It begins in Part I with a review of continuous time Gaussian processes (Gaussian signals) and multidimensional processes (Gaussian fields) from a constructionist framework that does not require the central limit theorem. It continues in Part II with two problems at the molecular and cellular level. The first is an analysis of the ability of single-celled organisms to maintain stable population-level cell volume distributions despite asymmetric cell division and stochastic growth. The second is essentially a tutorial on the wormlike chain model of a polymer with bending resistance in which we expand upon the usual treatment in physics texts by applying the aforementioned Gaussian signal approach. Part III then takes up two problems in the field of behavioral control. The first of these behavioral control problems concerns how a fish is able to catch falling fruits right as they hit the water's surface. The second problem details a currently ongoing project in which we are attempting to study man's ability to trade off speed and accuracy in a simplified game of roulette. At this time, the game and the theory have been completed and we are slated to send out the program and collect performance data. Finally, Part III takes up a particularly interesting question in neuroscience and psychology: are there low level visual cues that can be used to perform high level image classification tasks? The chapters within argue that the geometric information contained in the level sets of an image (which we summarize in the normalized contour curvature distribution) serves as a very useful cue for such tasks, though the complexity of our brains guarantees that it is not the only cue we use. Part III ends with a speculative chapter outlining a methodology for producing artificial images whose normalized contour curvature distributions mimic those observed for the class of animate objects.