Mesoscale modeling of molecular machines: Cyclic dynamics and hydrodynamical fluctuations

Abstract

Proteins acting as molecular machines can undergo cyclic internal conformational motions that are coupled to ligand binding and dissociation events. In contrast to their macroscopic counterparts, nanomachines operate in a highly fluctuating environment, which influences their operation. To bridge the gap between detailed microscopic and simple phenomenological descriptions, a mesoscale approach, which combines an elastic network model of a machine with a particle-based mesoscale description of the solvent, is employed. The time scale of the cyclic hinge motions of the machine prototype is strongly affected by hydrodynamical coupling to the solvent. Molecular machines, acting as motors, enzymes, or ion pumps, are involved in the function of biological cells ͓1,2͔ and are fundamental elements in applications in soft matter nanotechnology ͓3͔. Their operation relies on conformational motions in proteins, with time scales typically ranging between milliseconds and seconds. Although structures of machine proteins are known, full molecular dynamics simulations of such slow internal motions are currently not feasible. Therefore, theoretical analysis of stochastic dynamics of molecular machines is often based on simple models that describe these complex biomolecules as single-coordinate ratchets or oscillators ͓4,5͔. This approach has been successful in clarifying some principal aspects of machine operation ͓6͔, but the connection between simple phenomenological models and actual protein machines is often not evident. The gap between realistic microscopic models and simplified phenomenological approaches is an obstacle to the theoretical understanding of machine operation.Mesoscale models, which can fill this gap, are already broadly used to describe polymer dynamics and protein folding ͓7͔. In elastic network models, a protein is represented by a set of identical beads ͑coarse grained atomic groups͒ connected by identical elastic bonds; the pattern of connections is determined by the known equilibrium conformation of a given protein ͓8͔. Remarkably, elastic network models can reproduce large-amplitude slow conformational motions in many proteins ͓9͔, including some aspects of nonlinear conformational relaxation ͓10,11͔.Protein machines operate in molecular environments and solvent hydrodynamical effects play an important role in their dynamics. Solvent particles can be included in microscopic molecular dynamics simulations, but this is computationally challenging. In contrast, continuum hydrodynamical models cannot account for either molecular fluctuations or specific interactions. Coarse grained molecular dynamics schemes for the solvent can be used to incorporate both interactions and fluctuations ͓12͔.In this paper, we show that mesoscale models, combining coarse grained descriptions for molecular machines and their solvent environment, can provide an efficient intermediatelevel approach, bridging the gap between microscopic and macroscopic schemes. As an example, we consider an elastic network prototype of a molecu...

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