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The interaction between two associating hydrophobic particles has traditionally been explained in terms of the release of entropically frustrated hydration shell water molecules. However, this picture cannot account for the kinetics of hydrophobic association and is therefore not capable of providing a microscopic description of the hydrophobic interaction (HI). Here, Monte Carlo simulations of a pair of molecular-scale apolar solutes in aqueous solution reveal the critical role of collective fluctuations in the hydrogen bond (HB) network for the microscopic picture of the HI. The main contribution to the HI is the relaxation of solute-water translational correlations. The existence of a heat capacity maximum at the desolvation barrier is shown to arise from softening of non-HB water fluctuations and the relaxation of many-body correlations in the labile HB network. The microscopic event governing the kinetics of hydrophobic association has turned out to be a relatively large critical collective fluctuation in hydration water displacing a substantial fraction of HB clusters from the inner to the outer region of the first hydration shell. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations of a small model solute in an aqueous solution are used to examine the effects of solute polarity on hydration structure. A judicious definition of the orientational order parameter leads to reinterpretation of the conventional picture of hydration. As the solute varies from hydrophobic to hydrophilic the ordered first shell water simultaneously fractionates into a more highly ordered and a more disordered component. The hydrogen-bond network rearranges such that the more ordered component relaxes to configurations of optimal intermolecular angles, the other fraction being released from the network. [ABSTRACT FROM AUTHOR]

The average mean-square displacement, 〈r²〉, of H atoms in a protein is frequently determined using incoherent neutron-scattering experiments. 〈r²〉 is obtained from the observed elastic incoherent dynamic structure factor, Si(Q,ω = 0), assuming the form Si(Q,ω = 0) = exp(-Q²〈r²〉/3). This is often referred to as the Gaussian approximation (GA) to Si(Q,ω = 0). 〈r²〉 obtained in this way depends on the value of the wave vector, Q considered. Equivalently, the observed Si(Q,ω = 0) deviates from the GA. We investigate the origin of the Q dependence of 〈r²〉 by evaluating the scattering functions in different approximations using molecular dynamics (MD) simulation of the protein lysozyme. We find that keeping only the Gaussian term in a cumulant expansion of S(Q,ω) is an accurate approximation and is not the origin of the Q dependence of 〈r²〉. This is demonstrated by showing that the term beyond the Gaussian is negligible and that the GA is valid for an individual atom in the protein. Rather, the Q dependence (deviation from the GA) arises from the dynamical heterogeneity of the H in the protein. Specifically it arises from representing, in the analysis of data, this diverse dynamics by a single average scattering center that has a single, average 〈r²〉. The observed Q dependence of 〈r²〉 can be used to provide information on the dynamical heterogeneity in proteins. [ABSTRACT FROM AUTHOR]

The relative motion of structural domains is essential for the biological function of many proteins. Here, by analyzing neutron scattering data and performing molecular dynamics simulations, we find that interdomain motion in several proteins obeys the principle of de Gennes narrowing, in which the wave vector dependence of the interdomain diffusion coefficient is inversely proportional to the interdomain structure factor. Thus, the rate of interdomain motion is inversely proportional to the probability distribution of the spatial configurations of domains. [ABSTRACT FROM AUTHOR]

We propose a method for obtaining the intrinsic, long-time mean square displacement (MSD) of atoms and molecules in proteins from finite-time molecular dynamics (MD) simulations. Typical data from simulations are limited to times of 1 to 10 ns, and over this time period the calculated MSD continues to increase without a clear limiting value. The proposed method consists of fitting a model to MD simulation-derived values of the incoherent intermediate neutron scattering function, Iinc(Q,t), for finite times. The infinite-time MSD, (r²), appears as a parameter in the model and is determined by fits of the model to the finite-time Iinc(Q,t). Specifically, the (r²) is defined in the usual way in terms of the Debye-Waller factor as I(Q,t=∞)=exp(-Q²(r²)/3). The method is illustrated by obtaining the intrinsic MSD (r²) of hydrated lysozyme powder (h=0.4 g water/g protein) over a wide temperature range. The intrinsic (r²) obtained from data out to 1 and to 10 ns is found to be the same. The intrinsic (r²) is approximately twice the value of the MSD that is reached in simulations after times of 1 ns which correspond to those observed using neutron instruments that have an energy resolution width of 1 µeV. [ABSTRACT FROM AUTHOR]

Flexibility, or softness, is crucial for protein function and consists of a conformational component, involving jumps between potential wells, and an elastic component, involving fluctuations within the wells. Combining molecular dynamics simulation with incoherent neutron scattering and light scattering measurements on green fluorescent protein, we reveal a relationship between the intrawell fluctuations and elastic moduli of the protein. This finding leads to a simple means of experimentally separating the conformational from the elastic atomic displacements. [ABSTRACT FROM AUTHOR]

The effect of surface hydration water on internal protein motion is of fundamental interest in molecular biophysics. Here, by decomposing the picosecond to nanosecond atomic motion in molecular dynamics simulations of lysozyme at different hydration levels into three components--localized single-well diffusion, methyl group rotation, and nonmethyl jumps--we show that the effect of surface hydration is mainly to increase the volume of the localized single-well diffusion. These diffusive motions are coupled in such a way that the hydration effect propagates from the protein surface into the dry core [ABSTRACT FROM AUTHOR]

A simplified description of the 295 K dynamics of a globular protein over a wide frequency range (1-1000 GHz) is obtained by combining neutron scattering of lysozyme with molecular dynamics simulation. The molecular dynamics simulation agrees quantitatively with experiment for both the protein and the hydration water and shows that, whereas the hydration water molecules subdiffuse, the protein atoms undergo confined motion decomposable into three distinct classes: localized diffusion, methyl group rotations, and jumps. Each of the three classes gives rise to a characteristic neutron susceptibility signal. [ABSTRACT FROM AUTHOR]

Lignin, a major polymeric component of plant cell walls, forms aggregates in vivo and poses a barrier to cellulosic ethanol production. Here, neutron scattering experiments and molecular dynamics simulations reveal that lignin aggregates are characterized by a surface fractal dimension that is invariant under change of scale from ∼1-1000 Å. The simulations also reveal extensive water penetration of the aggregates and heterogeneous chain dynamics corresponding to a rigid core with a fluid surface. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) simulation of linear peptides reveals configurational subdiffusion at equilibrium extending from 10-12 to 10-8 s. Rouse chain and continuous-time random walk models of the subdiffusion are critically discussed. Network approaches to analyzing MD simulations are shown to reproduce the time dependence of the subdiffusive mean squared displacement, which is found to arise from the fractal-like geometry of the accessible volume in the configuration space. Convergence properties of the simulation pertaining to the subdiffusive dynamics are characterized and the effect on the subdiffusive properties of representing the solvent explicitly or implicitly is compared. Non-Markovianity and other factors limiting the range of applicability of the network models are examined. [ABSTRACT FROM AUTHOR]

Water is widely assumed to be essential for protein dynamics and function. In particular, the well-documented "dynamical" transition at ~200 K, at which the protein changes from a rigid, nonfunctional form to a flexible, functional state, as detected in hydrogenated protein by incoherent neutron scattering, requires hydration. Here, we report on coherent neutron scattering experiments on perdeuterated proteins and reveal that a transition occurs in dry proteins at the same temperature resulting primarily from the collective heavy-atom motions. The dynamical transition discovered is intrinsic to the energy landscape of dry proteins. [ABSTRACT FROM AUTHOR]

A correction to the article "Elastic and Conformational Softness of a Globular Protein" that was published in the 2013 issue is presented.

Water is widely assumed to be essential for protein dynamics and function. In particular, the well-documented "dynamical" transition at ∼200  K, at which the protein changes from a rigid, nonfunctional form to a flexible, functional state, as detected in hydrogenated protein by incoherent neutron scattering, requires hydration. Here, we report on coherent neutron scattering experiments on perdeuterated proteins and reveal that a transition occurs in dry proteins at the same temperature resulting primarily from the collective heavy-atom motions. The dynamical transition discovered is intrinsic to the energy landscape of dry proteins.

The relative motion of structural domains is essential for the biological function of many proteins. Here, by analyzing neutron scattering data and performing molecular dynamics simulations, we find that interdomain motion in several proteins obeys the principle of de Gennes narrowing, in which the wave vector dependence of the interdomain diffusion coefficient is inversely proportional to the interdomain structure factor. Thus, the rate of interdomain motion is inversely proportional to the probability distribution of the spatial configurations of domains.

Flexibility, or softness, is crucial for protein function and consists of a conformational component, involving jumps between potential wells, and an elastic component, involving fluctuations within the wells. Combining molecular dynamics simulation with incoherent neutron scattering and light scattering measurements on green fluorescent protein, we reveal a relationship between the intrawell fluctuations and elastic moduli of the protein. This finding leads to a simple means of experimentally separating the conformational from the elastic atomic displacements.

The effect of surface hydration water on internal protein motion is of fundamental interest in molecular biophysics. Here, by decomposing the picosecond to nanosecond atomic motion in molecular dynamics simulations of lysozyme at different hydration levels into three components--localized single-well diffusion, methyl group rotation, and nonmethyl jumps--we show that the effect of surface hydration is mainly to increase the volume of the localized single-well diffusion. These diffusive motions are coupled in such a way that the hydration effect propagates from the protein surface into the dry core.

A simplified description of the 295 K dynamics of a globular protein over a wide frequency range (1-1000 GHz) is obtained by combining neutron scattering of lysozyme with molecular dynamics simulation. The molecular dynamics simulation agrees quantitatively with experiment for both the protein and the hydration water and shows that, whereas the hydration water molecules subdiffuse, the protein atoms undergo confined motion decomposable into three distinct classes: localized diffusion, methyl group rotations, and jumps. Each of the three classes gives rise to a characteristic neutron susceptibility signal.

Certain techniques characterizing diffusive processes, such as single-particle tracking or molecular dynamics simulation, provide time averages rather than ensemble averages. Whereas the ensemble-averaged mean-squared displacement (MSD) of an unbounded continuous time random walk (CTRW) with a broad distribution of waiting times exhibits subdiffusion, the time-averaged MSD, delta2, does not. We demonstrate that, in contrast to the unbounded CTRW, in which delta2 is linear in the lag time Delta, the time-averaged MSD of the CTRW of a walker confined to a finite volume is sublinear in Delta, i.e., for long lag times delta2 approximately Delta1-alpha. The present results permit the application of CTRW to interpret time-averaged experimental quantities.

Molecular dynamics simulation of oligopeptide chains reveals configurational subdiffusion at equilibrium extending from 10(-12) to 10(-8) s. Trap models, involving a random walk with a distribution of waiting times, cannot account for the subdiffusion, which is found rather to arise from the fractal-like structure of the accessible configuration space.

Interprotein motions in low and fully hydrated carboxymyoglobin crystals are investigated using molecular dynamics simulation. Below approximately 240 K, the calculated dynamic structure factor exhibits a peak arising from interprotein vibration. Above approximately 240 K, the intermolecular fluctuations of the fully hydrated crystal increase drastically, whereas the low-hydration model exhibits no transition. Autocorrelation function analysis shows the transition to be dominated by the activation of diffusive intermolecular motion. The potential of mean force for the interaction remains quasiharmonic. The results indicate useful experimental avenues on protein:protein interactions to be explored using next-generation neutron sources.

All-atom lattice-dynamical calculations are reported for a crystalline protein, ribonuclease A. The sound velocities, density of states, heat capacity (C(V)) and thermal diffuse scattering are all consistent with available experimental data. C(V) proportional, variant T(1.68) for T < 35 K, significantly deviating from a Debye solid. In Bragg peak vicinity, inelastic scattering of x rays by phonons is found to originate from acoustic mode scattering. The results suggest an approach to protein crystal physics combining all-atom lattice-dynamical calculations with experiments on next-generation neutron sources.

Molecular dynamics simulations of a crystalline protein, Staphylococcal nuclease, over the pressure range 1 bar to 15 kbar reveal a qualitative change in the internal protein motions at approximately 4 kbar. This change involves the existence of two linear regimes in the mean-square displacement for internal protein motion, (P) with a twofold decrease in the slope for P>4 kbar. The major effect of pressure on the dynamics is a loss, with increasing pressure of large amplitude, collective protein modes below 2 THz effective frequency, accompanied by restriction of large-scale solvent translational motion.

The dynamical origin of the x-ray diffuse scattering by crystals of a protein, Staphylococcal nuclease, is determined using molecular dynamics simulation. A smooth, nearly isotropic scattering shell at originates from equal contributions from correlations in nearest-neighbor water molecule dynamics and from internal protein motions, the latter consisting of -helix pitch and inter--strand fluctuations. Superposed on the shell are intense, three-dimensional scattering features that originate from a very small number of slowly varying (>10 ns) collective motions. The individual three-dimensional features are assigned to specific collective motions in the protein, and some of these explicitly involve potentially functional active-site deformations.

The change in the vibrational density of states of a protein (dihydrofolate reductase) on binding a ligand (methotrexate) is determined using inelastic neutron scattering. The vibrations of the complex soften significantly relative to the unbound protein. The resulting free-energy change, which is directly determined by the density of states change, is found to contribute significantly to the binding equilibrium.

Proteins exhibit a solvent-driven dynamical transition at 180-220 K, manifested by nonlinearity in the temperature dependence of the average mean-square displacement. Here, molecular dynamics simulations of hydrated myoglobin show that the onset of the transition at approximately 180 K is characterized by the appearance of a single double-well principal component mode involving a global motion of two groups of helices. As the temperature is raised a few more quasiharmonic and multiminimum components successively appear. The results indicate an underlying simplicity in the protein dynamical transition.

Incoherent neutron scattering is widely used to probe picosecond-nanosecond time scale dynamics of molecular systems. In systems of spatially confined atoms the relatively high intensity of elastic incoherent neutron scattering is often used to obtain a first estimate of the dynamics present. For many complex systems, however, experimental elastic scattering is difficult to interpret unambiguously using analytical dynamical models that go beyond the determination of an average mean-square displacement. To circumvent this problem a description of the scattering is derived here that encompasses a variety of analytical models in a common framework. The framework describes the time-converged part of the dynamic structure factor [the elastic incoherent scattering function (EISF)] and lends itself to practical use by explicitly incorporating effects due to the finite energy resolution of the instrument used. The dependence of the elastic scattering on wave vector is examined, and it is shown how heterogeneity in the distribution of mean-square displacements can be related to deviations of the scattering from Gaussian behavior. In this case, a correction to fourth order in the scattering vector can be used to extract the variance of the distribution of mean-square displacements. The formalism is used in a discussion of measurements on dynamics accompanying the glass transition in molecular systems. By fitting to experimental data obtained on a protein solution the present methodology is used to show how the existence of a temperature-dependent relaxation frequency can lead to a transition in the measured mean-square displacement in the absence of an EISF change.