| The development of many powerful experimental techniques in cell biology has created the opportunity to observe many biological phenomena at an unprecedented level of detail. In this thesis, we use such experimental data to develop stochastic models of three cell biological phenomena: (I) gene expression, (II) diffusion of messenger ribonucleic acids (mRNAs) in the nucleus, and (III) the segregation of chromosomes during the anaphase A stage of mitosis. In the first two cases, we create and describe novel laboratory methods to obtain new forms of data upon which our models are based.;I. We model gene expression as a stochastic process consisting of the random creation and destruction of individual molecules. We develop a new experimental technique to accurately count the numbers of mRNA molecules in individual cells and find that mRNA are synthesized in short but intense bursts of transcription. We present a model explaining the molecular mechanisms that control these bursts. We also explore the mathematical consequences of burst-like gene expression upon cellular function.;II. We model the motion of mRNA in the nucleus as a stochastic diffusive process. We develop a new experimental technique that allows us to visualize individual mRNAs in live cells, finding that the mRNA move by random diffusion in the regions of the nucleus not occupied by chromatin. Moreover, they randomly transition between mobile and immobile states. We examine the mathematical implications of these experimental findings upon long-range diffusion coefficients and exit time problems.;III. We model the motion of chromosomes during anaphase A as a stochastic, diffusive process. We postulate that the forward motion of the chromosome is caused by a Brownian ratchet, a mechanism that relies upon diffusive motion to generate force. Through computer simulations, we examine the role that chromosome flexibility plays in the dynamics of this mechanism. We find that the flexibility is a critical determinant of the motion and is able to explain the long-standing puzzle about how chromosomes of different sizes seem to move at the same speed. |
