| Due to thermal fluctuations, systems at small length scales are different than their large length scale counterparts. For example, bacterial viruses, (phages) have thousands of nanometers of DNA packed inside a hollow capsid of tens of nanometers. This tight compaction leads to large forces on the phage DNA (tens of pico-newtons) which can be subsequently utilized for DNA ejection during the infection phase. Developments in optics, biochemistry, microfluidics, etc., have enabled the experimental quantification of these forces, and the rate of DNA packing and ejection. Similarly, eukaryotic genome is compacted into nanometer-size structures called nucleosomes. The conformational changes in the nucleosome due to the thermal fluctuations of the DNA are instrumental in making the DNA accessible for key genomic processes. Developments in FRET, gel electrophoresis, spectroscopy, etc., have made it possible to quantify the equilibrium constant and the rates of these fluctuations. The first part of the thesis involves formulation of simple models for the phage and nucleosome to respond to the existing experimental data and predicts results to stimulate further experimentation.; Many problems in biology of current interest involve small systems that are out of equilibrium. Unfortunately, there is no general theoretical frame-work to model these dissipative systems. E. T. Jaynes suggested the use of dynamical microtrajectories to write down the trajectory entropy, or caliber, for such systems. Maximization of this trajectory entropy, subject to the external constraints, provides one with the probabilities of the underlying microtrajectories. Jaynes calls this the "principle of maximum caliber." Advances in optics, video-microscopy, etc., have made it possible to experimentally measure these microtrajectories for various systems. In the second part of the thesis we develop simple microtrajectory models for small systems like molecular motors, ion channels, etc., and apply the maximum caliber principle to obtain the probabilities of the underlying microtrajectories. Our goal is to respond to these experiments and make new predictions. |
