Executive Summary : | This proposal aims to develop mathematical modelling and analysis of stochastic search phenomena in natural sciences. The project focuses on three seemingly unrelated phenomena: first passage of intermittent random walk searchers, localization by a protein of a specific DNA sequence along a long DNA, and enzyme kinetics. The first passage of intermittent random walk searchers involves foraging animals, robots, and drones returning to their homes or bases to rest, recharge, and refuel while engaged in search activities. The project aims to derive a theoretical framework for home-range search based on renewal theory, predicting how living systems can locate food and resources quickly and efficiently. The second passage of the project focuses on protein localization by a protein of a specific DNA sequence along a long DNA, which requires self-designed organization and intelligence from the living organism to optimize cost and time. The proposal aims to build a unified theoretical framework that captures non-diffusive search/reactive motion of proteins along the DNA and arbitrary non-reactive motion, tailored to identify one specific target sequence or a few. The project will also explore how non-classical anomalies in enzymes can be used to facilitate kinetic proofreading, specifically the intelligent design of "Michaelian filters" with sophisticated discriminatory capabilities between desired and undesired substrates. |