Pursuing Laplace’s Vision on Modern Computers

This contribution is an informal essay based on a talk delivered at the Institute for Mathematics and its Applications (IMA) in Minneapolis, under the summer program in molecular biology, July 18–22, 1994. I exclude many technical details, which can be found elsewhere, and instead focus on the basic ideas of molecular dynamics simulations, with the goal of conveying to students and non-specialists the key concepts of the theory and practice of large-scale simulations. Following a description of the basic idea in molecular dynamics, I discuss some of the practical details involved in simulations of large biological molecules, the numerical timestep problem, and approaches to this problem based on implicit-integration techniques. I end with a perspective of open challenges in the field and directions for future research.