(360a) Path Sampling Based Coupling of Fast and Slow Dynamical Modes in Biomolecular Reactions: Implications for Enzyme Catalysis and Implications for Mixed Quantum Mechanics Molecular Mechanics Simulations

The structure-function relationship in biomolecular systems involves regulatory elements such as conformational changes in structure, which often serve toward the enzymes' function as catalysts. Consequently, the development of long-time dynamics and sampling algorithms is a well appreciated central objective of single molecule biophysics. We have recently developed the BOLAS algorithm, which is inspired from the transition path sampling method, to perform free energy simulations as well as the dynamic characterization of molecular pathways of conformational changes and catalytic events. The highlight of BOLAS is the identification of the elusive transient intermediates in biomolecular systems (1Å-100nm) at atomic resolution. This has paved the path for us to delineate complex reaction pathways involved in conformational changes and catalysis in biomolecules.

Path based methodologies such as transition path sampling, nudged elastic band, finite-temperature string exploit the separation in timescales in activated processes, namely, the existence of a shorter time scale of relaxation at the kinetic bottle neck or the transition state (T_relax), in comparison a much longer timescale of activation to the transition state itself (T_TS). In biomolecular systems, the ubiquitous coupling of slower (often diffusive) modes of relaxation (such as changes in secondary structure) to the fast modes of reactive processes poses a significant problem by increasing (T_relax). Moreover, multiple-pathways for the transition present an additional challenge in conformational sampling. These pose severe limitations on the (routine) use of mixed quantum mechanics molecular mechanics (QMMM) approach to characterize complex reaction pathways in biomolecular catalysis. For instance, this problem in the case of the self-cleaving reaction of the enigmatic Hammerhead ribozyme manifests by selecting a reaction pathway leading to a phosphoryl transfer with retention configuration about the scissile phosphorous rather than the experimentally observed inversion configuration.

To address the issue, we have identified the dynamic coupling between fast and slow modes through the Principal Component Analysis of long molecular dynamics (MD) trajectories followed by importance (i.e. umbrella, density of states, or configurational bias) sampling along the slow modes and BOLAS sampling along the fast modes. A similar treatment extended to the process of nucleotide incorporation in polymerase systems explains the non-trivial effect on the incorporation rate due to a tensile force on the bound DNA in force spectroscopy experiments due to the possible coupling of the slow DNA degrees of freedom to the reaction coordinate of phosphoryl transfer.