Studying the Adsorption of Polymers and Biomolecules on Surfaces Using Enhanced Sampling Methods
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Studying the Adsorption of Polymers and Biomolecules on Surfaces Using Enhanced Sampling Methods Michael P. Allen and Adam D Swetnam Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom ABSTRACT We discuss how to use Wang-Landau simulations in an efficient manner to investigate the statistical mechanics of individual lattice polymers and peptides adsorbed at a planar surface. For nearest neighbor interactions, we show that a single Wang-Landau simulation, recording the density of states as a function of numbers of internal contacts and of surface beads, is sufficient to give a full description of the phase behavior of both adsorbed and desorbed states of single molecules. It is not necessary to introduce a second confining wall. Moreover, moves are never rejected due to overlap with the surface. The proposed “wall-free” method has already been applied to homo-polymers and heteropolymers (lattice peptides using the HP model) on a uniform surface, and on regularly patterned surfaces. We give here a specific example to indicate how the relative adsorption strengths of a given peptide on different surfaces may be calculated. INTRODUCTION There is considerable current interest in carrying out Monte Carlo (MC) simulations of simple models of polymers and peptides, with the aim of understanding their affinity for specific solid surfaces, and the intention of assisting in the design of new materials, which exploit this affinity. Although the model of a polymer whose monomers (beads) are confined to a regular lattice, with interactions only between nearest-neighbor beads, is a very simple one, it contains much of the essential physics and chemistry of the problem, especially the issue of locating minimum-energy folded structures, and balancing energetic and entropic effects in the thermodynamics of collapse and adsorption. The HP model of lattice peptides [1], for instance, has been described as the “Ising model of protein folding” [2]. We shall be concentrating on this model in what follows. The simulation of lattice polymers and peptides has been a fruitful area for the development of accelerated simulation methods in recent years [3–20]. The essential ideas behind the current work have been presented already in the context of the HP model and the simulation of confined ring polymers [21–24], so only a brief summary will be given here. THEORY For illustrative purposes we adopt the model of a single unbranched heteropolymer of L beads on a simple cubic lattice defined by integer values of the coordinates ( x, y, z ) . Each lattice
site may contain at most one bead. In the HP peptide model [1] each bead in the polymer is either hydrophobic (H) or polar (P). The surrounding aqueous solvent is taken to occupy all the lattice
sites that are left vacant by the peptide, and the interactions are assumed to reduce to a set of nearest-neighbor effective attractions of equal strength −ε between the hydrophobic beads. The number of these H-H nearest-neighbor contacts, nΓ , depends on the microscopic state
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