Theoretical Perspectives for Biomolecular Crystallization Prediction.

Biocrystallization has played a fundamental role in revealing the complexity of crystallization such as the role of metastable crystallization precursors and nonclassical nucleation pathways. This chapter describes some modern theoretical developments developed to address the challenges posed by these discoveries to our understanding of both the thermodynamics and dynamics of clusters of molecules. After briefly recalling the thermodynamic model of Gibbs that underlies classical nucleation theory and subsequent heuristic improvements such as the van der Waals diffuse interface model, the recent development of fundamental statistical-mechanical methods known collectively as classical density functional theory (cDFT) is described. These methods allow for ab inito prediction of crystal structures and thermodynamics with molecular-level resolution using only the molecular interaction potential as input. The dynamics of nucleation, traditionally modeled using rate equations to describe the evolution of cluster sizes based on monomer attachment/detatchment, is then addressed by incorporating the molecular-level thermodynamics into a dynamical description of thermal fluctuations that allows one to predict the kind of nonclassical nucleation pathways seen in experiment and simulation as well as the associated nucleation rates without the need for macroscopic concepts such as order parameters and collective variables.