Cytoplasmic motion is a key determinant of organelle transport, protein-protein interactions, RNA transport and drug delivery, to name but a few cellular phenomena. Nucleic acid trafficking is important in antisense and gene therapy based on viral and synthetic vectors. This proposal is dedicated to the theoretical study of intracellular transport of proteins, organelles and DNA particles. We propose to construct a mathematical model to quantify and predict the spatiotemporal dynamics of complex structures in the cytosol and the nucleus, based on the physical characteristics and the micro-rheology of the environment (viscosity). We model the passive motion of proteins or DNA as free or confined diffusion, while for the organelle and virus motion, we will include active cytoskeleton-dependent transport. The proposed mathematical model of cellular trafficking is based on physical principles. We propose to estimate the mean arrival time and the probability of viruses and plasmid DNA to arrive to a nuclear pore. The motion will be described by stochastic dynamics, containing both a drift (along microtubules) and a Brownian (free diffusion) component. The analysis of the equations requires the development of new asymptotic methods for the calculation of the probability and the mean arrival time of a particle to a small hole on the nucleus surface. We will extend the analysis to DNA movement in the nucleus after cellular irradiation, when the nucleus contains single and double broken DNA strands (dbDNAs). The number of remaining DNA breaks determines the activation of the repair machinery and the cell decision to enter into apoptosis. We will study the dsbDNA repair machinery engaged in the task of finding the DNA damage. We will formulate and analyze, both numerically and analytically, the equations that link the level of irradiation to apoptosis. The present project belongs to the new class of initiatives toward a quantitative analysis of intracellular trafficking.