This dissertation consists of several parts. The first two chapters are devoted to of study of dynamic processes in cellular organelles called filopodia. A stochastic kinetics approach is used to describe non-equilibrium evolution of the filopodial system from nano- to micro scales. Dynamic coupling between chemistry and mechanics is also taken into account in order to investigate the influence of focal adhesions on cell motility. The second chapter explores the possibilities and effects of motor enhanced delivery of actin monomers to the polymerizing tips of filopodia, and how the steady-state filopodial length can exceed the limit set by pure diffusion. Finally, we also challenge the currently existing view of active transport and propose a new theoretical model that accurately describes the motor dynamics and concentration profiles seen in experiments in a physically meaningful way. The third chapter is a result of collaboration between three laboratories, as a part of Energy Frontier Research Center at the University of North Carolina at Chapel Hill. The work presented here unified the fields of synthetic chemistry, photochemistry, and computational physical chemistry in order to investigate a novel bio-synthetic compound and its energy transfer capabilities. This particular peptide-based design has never been studied via Molecular Dynamics with high precision, and it is the first attempt known to us to simulate the whole chromophore-peptide complex in solution in order to gain detailed information about its structural and dynamic features. The fourth chapter deals with the non-equilibrium relaxation induced transport of water molecules in a microemulsion. This problem required a different set of methodologies and a more detailed, all-atomistic treatment of the system. We found interesting water clustering effects and elucidated the most probable mechanism of water transfer through oil under the condition of saturated Langmuir monolayers. Together these computational and theoretical studies compose a powerful and diverse set of physical approaches and both analytical and numerical methodologies, that can be successfully applied in the fields of biology, chemistry and biophysics.