Stochastic Intra-Cellular Modeling

Air Force personnel may sometimes come into contact with potentially harmful chemicals while performing their duties. Of course the Air Force desires to keep any potential health risks to its members to a minimum. To this end the Air Force would like to identify which chemicals are toxic, their level of toxicity, and the processes by which these chemicals disrupt normal biological activities at the cellular level. The development of mathematical models can be of great benefit to toxicity studies. Because real world systems involve randomness, that is noise, and the desire is to create mathematical models to represent those systems, it is necessary to study approaches used to add noise to mathematical models. This document examines different methods for incorporating noise into biochemical systems. The various quantities involved in the reactions are treated as random variables. The methods can be separated into two categories: those which treat the random variable as having a continuous state space and those which treat the random variable as having a discrete state space. These different approaches are compared in order to better understand what type of method would be best used for adding noise to a model and how the model is affected.