Binary level set method for variational implicit solvation model

In this article, we apply the binary level set method and techniques from image segmentation to the variational implicit solvent model (VISM), a theoretical and computational setting for studying biomolecular systems with complex topology. Central in VISM is an effective free energy on interfaces that separate solutes, such as proteins, from solvent, such as water. In previous work, the level set method is used to represent the separating interfaces, and an evolution partial differential equation derived from gradient descent on the energy is solved to capture a locally minimizing solute-solvent interface. In this work, we replace the continuous level set function with a binary level set function, which only takes on one of two values, one negative and one positive, and work in this setting. We introduce, under this discrete framework, an approximation of the original free energy, using results in threshold dynamics, and apply to it a fast flipping algorithm based on fast algorithms in image segmentation for local minimization. Numerical experiments in model problems and on real-world proteins show the algorithm's extremely fast speed, even exceeding that of threshold dynamics using fast Fourier transforms in certain cases, while retaining first order accuracy, the maximum allowed by the binary setting.