Cadenes de Markov i experiment d'unzipping

Abstract

Markov models are stochastic processes without memory: processes in which the next state of the system depends only on its immediately previous state and not on the whole chain of states. Although it may appear to be a very simple model, it is widely seen in real life and used in a variety of fields like biology, physics, engineering, medicine or even social sciences. If we have physically unobservable states and the only thing we can know are probabilistic functions depending on them, we can treat the system with an extension of Markov models, hidden Markov models (HMM). Hidden Markov models have been widely used for speech recognition and in computational molecular biology, among others. Driven by my curiosity for that type of models and my interest in biophysics I decided to dedicate this undergraduate thesis to the study of different variations of Markov models and to see how one can apply them to a specific experiment of molecular biophysics, the DNA unzipping. As we will see later, the unzipping experiment consists in pulling a double stranded DNA molecule from each end so the bonds between them are broken. Plotting force versus distance curve we obtain a very characteristic sawtooth pattern that can be used, for example, to find the specific places where proteins and enzymes are fixed to the DNA. In these experiments we find cooperative unzipping-zipping regions, in other words, zones where several base-pairs of different length are involved in the transition, behaving like an all or nothing. Our goal is to determine the distribution of DNA unzipping to find how many base-pairs are opened in each step. To do that we treat the system as a variable-stepsize hidden Markov model, a kind of HMM adapted in order to describe at the same time the molecular state and the position of a processive molecular motor. This dissertation has two parts, one theoretical and the other applied. The first one, which includes chapters 1, 2 and 3, is an introduction to homogeneous Markov models and hidden Markov models. In the last chapter we present the unzipping experiment and apply the algorithms seen in previous chapters in order to determine the DNA’s unzipping pattern.