Simulations of the residual configurational entropy of a protein in the native state suggest that it is nearly an order of magnitude larger than the entropy of denaturation. The implications of this result are discussed.

Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled. Experimental Tests of Molecular DynamicsClassical molecular dynamics is a computational technique to simulate the behaviors, both thermodynamic and dynamic, of an atomic model. In the long time limit, the sampled trajectory yields detailed information about the approximate model Hamiltonian. Shorter trajectories yield incomplete information and confound comparison of the model with experiment. Relatively short trajectories of biological macromolecules, on the order of 1 ns, have been used with reasonable success for a number of experimental comparisons-for example, crystallographic B values (1) from x-ray scattering, incoherent structure factors from neutron scattering (2, 3), and order parameters from NMR spectroscopy (4). Because these experimental techniques probe the movement of single atoms we can conclude that the amplitude and frequency of displacement for particular individual atoms in the protein are being simulated accurately.However, on the basis of such local results we cannot also conclude that these same molecular dynamics calculations accurately simulate, or converge on, the correlation between two or more atoms in a protein (e.g., whether one part of a protein tends to act concertedly with another). The state of our present models, then, is not completely tested by our experimental methods. In this article we consider a particular test set to measure the convergence of two-body properties in protein simulations.An experimental technique that is sensitive to statistics between pairs of atoms, and thus to collective behavior in macromolecules, is diffuse x-ray scattering (5, 6). All x-ray intensity on a detector besides the sharp Bragg peaks is typically ignored in structural studies. However, this remaining intensity, Diffuse scattering experiments on several proteins and nucleic acids (7-10) demonstrate that correlations in displacements of neighboring atoms fall off roughly exponentially with the distance between the atoms, with a characteristic length of 4-8 A. That is, (8iA8) = e(Wx(J)exp(-Jr| rjl/y), where the correlation length y is less than the dimension of the protein molecule. Thus, in analogy with liquid structures, where the correlations in atomicpositions decay approximately exponentially with pair separation, the motion in proteins is often called liquid-like, in the sense that correlations in atomic displacements fall off rapidly with distance.As a test of whether the pair corr...

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The hydrophobic association of two parallel graphene sheets is studied using the 3D-RISM HNC integral equations with several theoretical methods for the solvent distribution functions. The potential of mean force is calculated to study the effects of the aqueous solvent models and methods on the plates as a function of distance. The results of several integral equations (IE) are compared to MD simulations for the same model. The 3D-IEs are able to qualitatively reproduce the nature of the solvent effects on the potential of mean force but not quantitatively. The local minima in the potential of mean force occur at distances allowing well defined layers of solvent between the plates but are not coincident with those found in simulation of the same potential regardless of the theoretical methods tested here. The dewetting or drying transition between the plates is generally incorrectly dependent on steric effects with these methods even for very hydrophobic systems without solutesolvent attractions, in contradiction with simulation.