In this dissertation, we develop a method for molecular simulation based on principal component analysis (PCA) of a molecular dynamics trajectory and least squares approximation of a potential energy function. Molecular dynamics (MD) simulation is a computational tool used to study molecular systems as they evolve through time. With respect to protein dynamics, local motions, such as bond stretching, occur within femtoseconds, while rigid body and large-scale motions, occur within a range of nanoseconds to seconds. To capture motion at all levels, time steps on the order of a femtosecond are employed when solving the equations of motion and simulations must continue long enough to capture the desired large-scale motion. To date, simulations of solvated proteins on the order of nanoseconds have been reported. It is typically the case that simulations of a few nanoseconds do not provide adequate information for the study of large-scale motions. Thus, the development of techniques that allow longer simulation times can advance the study of protein function and dynamics. In this dissertation we use principal component analysis (PCA) to identify the dominant characteristics of an MD trajectory and to represent the coordinates with respect to these characteristics. We augment PCA with an updating scheme based on a reduced representation of a molecule and consider equations of motion with respect to the reduced representation. We apply our method to butane and BPTI and compare the results to standard MD simulations of these molecules. Our results indicate that the molecular activity with respect to our simulation method is analogous to that observed in the standard MD simulation with simulations on the order of picoseconds.