Multiscale Simulations: From Enzyme Kinetics to Fluctuating Hydrodynamics

The development of multiscale methods for computational simulation of biophysical systems represents a significant challenge. Effective computational models that bridge physical insights obtained from atomistic simulations and experimental findings are lacking. An accurate passing of information between these scales would enable: (1) an improved physical understanding of structure-function relationships, and (2) enhanced rational strategies for molecular engineering and materials design. Two approaches are described in this dissertation to facilitate these multiscale goals./nIn Part I, we develop a lattice kinetic Monte Carlo model to simulate cellulose decomposition by cellulase enzymes and to understand the effects of spatial confinement on enzyme kinetics. An enhanced mechanistic understanding of this reaction system could enhance the design of cellulose bioconversion technologies for renewable and sustainable energy. Using our model, we simulate the reaction up to experimental conversion times of days, while simultaneously capturing the microscopic kinetic behaviors. Therefore, the influence of molecular-scale kinetics on the macroscopic conversion rate is made transparent. The inclusion of spatial constraints in the kinetic model represents a significant advance over classical mass-action models commonly used to describe this reaction system. We find that restrictions due to enzyme jamming and substrate heterogeneity at the molecular level play a dominate role in limiting cellulose conversion./nWe identify that the key rate limitations are the slow rates of enzyme complexation with glucan chains and the competition between enzyme processivity and jamming. We show that the kinetics of complexation, which involves extraction of a glucan chain end from the cellulose surface and threading through the enzyme active site, occurs slowly on the order of hours, while intrinsic hydrolytic bond cleavage occurs on the order of seconds. We also elucidate the subtle trade-off between processivity and jamming. Highly processive enzymes cleave a large fraction of a glucan chain during each processive run but are prone to jamming at obstacles. Less processive enzymes avoid jamming but cleave only a small fraction of a chain. Optimizing this trade-off maximizes the cellulose conversion rate./nWe also elucidate the molecular-scale kinetic origins for synergy among cellulases in enzyme mixtures. In contrast to the currently accepted theory, we show that the ability of an endoglucanase to increase the concentration of chain ends for exoglucanases is insufficient for synergy to occur. Rather, endoglucanases must enhance the rate of complexation between exoglucanases and the newly created chain ends. This enhancement occurs when the endoglucanase is able to partially decrystallize the cellulose surface. We show generally that the driving forces for complexation and jamming, which govern the kinetics of pure exoglucanases, also control the degree of synergy in endo-exo mixtures./nIn Part II, we focus our attention on a different multiscale problem. This challenge is the development of coarse-grained models from atomistic models to access larger length- and time-scales in a simulation. This problem is difficult because it requires a delicate balance between maintaining (1) physical simplicity in the coarse-grained model and (2) physical consistency with the atomistic model. To achieve these goals, we develop a scheme to coarse-grain an atomistic fluid model into a fluctuating hydrodynamics (FHD) model. The FHD model describes the solvent as a field of fluctuating mass, momentum, and energy densities. The dynamics of the fluid are governed by continuum balance equations and fluctuation-dissipation relations based on the constitutive transport laws. The incorporation of both macroscopic transport and microscopic fluctuation phenomena could provide richer physical insight into the behaviors of biophysical systems driven by hydrodynamic fluctuations, such as hydrophobic assembly and crystal nucleation./nTo develop the FHD model, we map all-atom molecular dynamics trajectories onto mass, momentum, and energy density grids to generate a corresponding field trajectory. From the field statistics, the response functions and transport coefficients of the atomistic model are computed. These thermophysical properties are then used to parameterize an FHD model for the fluid that reproduces the hydrodynamic correlations underlying the atomistic model. We show that an FHD description of the fluid is preserved down to length scales of 5 Å, enabling application of this coarse-graining approach to molecular systems./nWe further extend our coarse-graining method by developing an interfacial FHD model using information obtained from simulations of an atomistic liquid-vapor interface. We illustrate that a phenomenological Ginzburg-Landau free energy employed in the FHD model can effectively represent the attractive molecular interactions of the atomistic model, which give rise to phase separation. For argon and water, we show that the interfacial FHD model can reproduce the compressibility, surface tension, and capillary wave spectrum of the atomistic model. Via this approach, simulations that explore the coupling between hydrodynamic fluctuations and phase equilibria with molecular-scale consistency are now possible./nIn both Parts I and II, the emerging theme is that the combination of bottom-up coarse graining and top-down phenomenology is essential for enabling a multiscale approach to remain physically consistent with molecular-scale interactions while simultaneously capturing the collective macroscopic behaviors. This hybrid strategy enables the resulting computational models to be both physically insightful and practically meaningful.

Advisor: Chu, Jhih-Wei