[Show abstract][Hide abstract] ABSTRACT: Modern theories of the hydrophobic effect highlight its dependence on length
scale, emphasizing in particular the importance of interfaces that emerge in
the vicinity of sizable hydrophobes. We recently showed that a faithful
treatment of such nanoscale interfaces requires careful attention to the
statistics of capillary waves, with significant quantitative implications for
the calculation of solvation thermodynamics. Here we show that a coarse-grained
lattice model in the spirit of those pioneered by Chandler and coworkers, when
informed by this understanding, can capture a broad range of hydrophobic
behaviors with striking accuracy. Specifically, we calculate probability
distributions for microscopic density fluctuations that agree very well with
results of atomistic simulations, even many standard deviations from the mean,
and even for probe volumes in highly heterogeneous environments. This accuracy
is achieved without adjustment of free parameters, as the model is fully
specified by well-known properties of liquid water. As illustrative examples of
its utility, we characterize the free energy profile for a solute crossing the
air-water interface, and compute the thermodynamic cost of evacuating the space
between extended nanoscale surfaces. Together, these calculations suggest that
a highly reduced model for aqueous solvation can serve as the basis for
efficient multiscale modeling of spatial organization driven by hydrophobic and
[Show abstract][Hide abstract] ABSTRACT: Importance sampling of trajectories has proved a uniquely successful strategy
for exploring rare dynamical behaviors of complex systems in an unbiased way.
Carrying out this sampling, however, requires an ability to propose changes to
dynamical pathways that are substantial, yet sufficiently modest to obtain
reasonable acceptance rates. Satisfying this requirement becomes very
challenging in the case of long trajectories, due to the characteristic
divergences of chaotic dynamics. Here we examine schemes for addressing this
problem, which engineer correlation between a trial trajectory and its
reference path, for instance using artificial forces. Our analysis is
facilitated by a modern perspective on Markov Chain Monte Carlo sampling,
inspired by non-equilibrium statistical mechanics, which clarifies the types of
sampling strategies that can scale to long trajectories. Viewed in this light,
the most promising such strategy guides a trial trajectory by manipulating the
sequence of random numbers that advance its stochastic time evolution, as done
in a handful of existing methods. In cases where this "noise guidance"
synchronizes trajectories effectively, such as the Glauber dynamics of a
two-dimensional Ising model, we show that efficient path sampling can be
performed even for very long trajectories.
The Journal of Chemical Physics 04/2015; 142(23). DOI:10.1063/1.4922343 · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Folded protein structures are both stable and dynamic. Historically, our clearest window into these structures came from X-ray crystallography, which generally provided a static image of each protein’s singular “folded state”, highlighting its stability. Deviations away from that crystallographic structure were difficult to quantify, and as a result, their potential functional consequences were often neglected. However, several dynamical and statistical studies now highlight the structural variability that is present within the protein’s folded state. Here we review mounting evidence of the importance of these structural rearrangements; both experiment and computation indicate that folded proteins undergo substantial fluctuations that can greatly influence their function.
Accounts of Chemical Research 02/2015; 48(4). DOI:10.1021/ar500351b · 24.35 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In a stochastic heat engine driven by a cyclic non-equilibrium protocol,
fluctuations in work and heat give rise to a fluctuating efficiency. Using
computer simulations and tools from large deviation theory, we have examined
these fluctuations in detail for a model two-state engine. We find in general
that the form of efficiency probability distributions is similar to those
described by Verley et al. [arXiv:1404.3095 (2014)], in particular featuring a
local minimum in the long-time limit. In contrast to the time-symmetric engine
protocols studied previously, however, this minimum need not occur at the value
characteristic of a reversible Carnot engine. Furthermore, while the local
minimum may reside at the global minimum of a large deviation rate function, it
does not generally correspond to the least likely efficiency measured over any
New Journal of Physics 09/2014; 16(10). DOI:10.1088/1367-2630/16/10/102003 · 3.67 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Photoautotrophic organisms efficiently regulate absorption of light energy to sustain photochemistry while promoting photoprotection. Photoprotection is achieved in part by triggering a series of dissipative processes termed non-photochemical quenching (NPQ), which depend on the re-organization of photosystem (PS) II supercomplexes in thylakoid membranes. Using atomic force microscopy, we characterized the structural attributes of grana thylakoids from Arabidopsis thaliana to correlate differences in PSII organization with the role of SOQ1, a recently discovered thylakoid protein that prevents formation of a slowly reversible NPQ state. We developed a statistical image analysis suite to discriminate disordered from crystalline particles and classify crystalline arrays according to their unit cell properties. Through detailed analysis of the local organization of PSII supercomplexes in ordered and disordered phases, we found evidence that interactions among light-harvesting antenna complexes are weakened in the absence of SOQ1, inducing protein rearrangements that favor larger separations between PSII complexes in the majority (disordered) phase and reshaping the PSII crystallization landscape. The features we observe are distinct from known protein rearrangements associated with NPQ, providing further support for a role of SOQ1 in a novel NPQ pathway. The particle clustering and unit cell methodology developed here is generalizable to multiple types of microscopy and will enable unbiased analysis and comparison of large data sets.
PLoS ONE 07/2014; 9(7):e101470. DOI:10.1371/journal.pone.0101470 · 3.23 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We solve a simple model that supports a dynamic phase transition and show
conditions for the existence of the transition. Using methods of large
deviation theory we analytically compute the joint rate function for activity
and entropy production rates of the trajectories on a large ring with a single
heterogeneous link. The joint rate function demonstrates two dynamical phases -
one localized and the other delocalized, but the marginal rate functions do not
always exhibit the underlying transition. We discuss how symmetries in dynamic
order parameters influence the transition, such that distributions for certain
dynamic order parameters need not reveal an underlying bistability. We discuss
the implications of the transition on the response of bacterial cells to
antibiotic treatment, arguing that even the simple models of a cell cycle
lacking an explicit bistability will exhibit a bistability of dynamical phases.
Physical Review E 06/2014; 90(4-1). DOI:10.1103/PhysRevE.90.042123 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Nanoparticles with "sticky patches" have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they could form. Using computer simulations, we show that structures of the same genre can be obtained from a solution of simple isotropic spheres, provided control only over their sizes and a small number of binding affinities. In a first step, finite clusters of well-defined structure and composition emerge from natural dynamics with high yield. In effect a kind of patchy particle, these clusters can further assemble into a variety of complex superstructures, including filamentous networks, ordered sheets, and highly porous crystals.
[Show abstract][Hide abstract] ABSTRACT: We explore the dynamical large deviations of a lattice heteropolymer model of a protein by means of path sampling of trajectories. We uncover the existence of nonequilibrium dynamical phase transitions in ensembles of trajectories between active and inactive dynamical phases, whose nature depends on the properties of the interaction potential. We consider three potentials: two heterogeneous interaction potentials and a homogeneous Gō potential. When preserving the full heterogeneity of interactions due to a given amino acid sequence, either in a fully interacting model or in a native contacts interacting model (heterogeneous Gō model), the observed dynamic transitions occur between equilibrium highly native states and highly native but kinetically trapped states. A native activity is defined that allows us to distinguish these dynamic phases. In contrast, for the homogeneous Gō model, where all native interaction energies are uniform and the amino acid sequence plays no role, the dynamical transition is a direct consequence of the static bistability between the unfolded and the native state. In the two heterogeneous interaction models the native-active and native-inactive states, despite their thermodynamic similarity, have widely varying dynamical properties, and the transition between them occurs even in lattice proteins whose sequences are designed to make them optimal folders.
Physical Review E 03/2014; 89(3-1):032109. DOI:10.1103/PhysRevE.89.032109 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Basic principles of statistical mechanics require that proteins sample an ensemble of conformations at any nonzero temperature. However, it is still common to treat the crystallo-graphic structure of a protein as the structure of its native state, largely because high-resolution structural characterization of protein flexibility remains a profound challenge. To as-sess the typical degree of conformational heterogeneity within folded proteins, we construct Markov state models describing the thermodynamics and kinetics of proteins ranging from 72 to 263 residues in length. Each of these models is built from hundreds of microseconds of atomically detailed molecular dynamics simulations. Examination of the side-chain degrees of freedom reveals that almost every residue visits at least two rotameric states over this time frame, with rotamer transition rates spanning a wide range of timescales (from nanoseconds to tens of microseconds). We also report substantial backbone dynamics on timescales longer than are typically addressed by experimental measures of protein flexibility, such as NMR or-der parameters. Finally, we demonstrate that these extensive rearrangements are consistent with NMR and crystallographic data, which supports the validity of our models. Altogether, the-se results depict the interior of proteins not as well-ordered solids, as is often imagined, but instead as dense fluids, which undergo substantial structural fluctuations despite their high packing fraction.
The Journal of Physical Chemistry B 02/2014; 118(24). DOI:10.1021/jp4105823 · 3.30 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The physics of air-water interfaces plays a central role in modern theories
of the hydrophobic effect. Implementing these theories, however, has been
hampered by the difficulty of addressing fluctuations in the shape of such soft
interfaces. We show that this challenge is a fundamental consequence of mapping
long wavelength density variations onto discrete degrees of freedom. Drawing
from studies of surface roughness in lattice models, we account for the
resulting nonlinearities simply but accurately. Simulations show that this
approach captures complex solvation behaviors quantitatively.
[Show abstract][Hide abstract] ABSTRACT: We present the first nearly atomistic molecular dynamics study of nanorod-nanorod association in explicit solvent, showing that inter-rod forces can be dominated by microscopic factors absent in common continuum descriptions. Specifically, we find that alkane ligands on faceted CdS nanorods in n-hexane undergo a temperature-dependent order-disorder transition akin to that of self-assembled monolayers on macroscopic substrates. This collective ligand alignment organizes nearby solvent molecules, strongly influencing the statistics of rod-rod separation. The strong temperature-dependence of this mechanism could be exploited in the laboratory to manipulate and optimize the assembly of ordered structures.
[Show abstract][Hide abstract] ABSTRACT: Photosystem II (PSII) and its associated light-harvesting complex II (LHCII) are highly concentrated in the stacked grana regions of photosynthetic thylakoid membranes. PSII-LHCII supercomplexes can be arranged in disordered packings, ordered arrays, or mixtures thereof. The physical driving forces underlying array formation are unknown, complicating attempts to determine a possible functional role for arrays in regulating light harvesting or energy conversion efficiency. Here, we introduce a coarse-grained model of protein interactions in coupled photosynthetic membranes, focusing on just two particle types that feature simple shapes and potential energies motivated by structural studies. Reporting on computer simulations of the model's equilibrium fluctuations, we demonstrate its success in reproducing diverse structural features observed in experiments, including extended PSII-LHCII arrays. Free energy calculations reveal that the appearance of arrays marks a phase transition from the disordered fluid state to a system-spanning crystal. The predicted region of fluid-crystal coexistence is broad, encompassing much of the physiologically relevant parameter regime; we propose experiments that could test this prediction. Our results suggest that grana membranes lie at or near phase coexistence, conferring significant structural and functional flexibility to this densely packed membrane protein system.
[Show abstract][Hide abstract] ABSTRACT: We analyze the probability distribution for entropy production rates of
trajectories evolving on a class of out-of-equilibrium kinetic networks. These
networks can serve as simple models for driven dynamical systems, which are of
particular importance in biological processes, where energy fluxes typically
result in non-equilibrium dynamics. By analyzing the fluctuations in the
entropy production, we demonstrate the emergence, in a large system size limit,
of a dynamic phase transition between two distinct dynamical regimes.
Physical Review E 07/2013; 89(6). DOI:10.1103/PhysRevE.89.062108 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Liquid water consistently expands our appreciation of the rich statistical mechanics that can emerge from simple molecular constituents. Here I review several interrelated areas of recent work on aqueous systems that aim to explore and explain this richness by revealing molecular arrangements, their thermodynamic origins, and the timescales on which they change. Vibrational spectroscopy of OH stretching features prominently in these discussions, with an emphasis on efforts to establish connections between spectroscopic signals and statistics of intermolecular structure. For bulk solutions, the results of these efforts largely verify and enrich existing physical pictures of hydrogen-bond network connectivity, dynamics, and response. For water at interfaces, such pictures are still emerging. As an important example I discuss the solvation of small ions at the air-water interface, whose surface propensities challenge a basic understanding of how aqueous fluctuations accommodate solutes in heterogeneous environments. Expected final online publication date for the Annual Review of Physical Chemistry Volume 64 is March 31, 2013. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
[Show abstract][Hide abstract] ABSTRACT: The adsorption behavior of ions at liquid-vapor interfaces exhibits several unexpected yet generic features. In particular, energy and entropy are both minimum when the solute resides near the surface, for a variety of ions in a range of polar solvents, contrary to predictions of classical theories. Motivated by this generality, and by the simple physical ingredients implicated by computational studies, we have examined interfacial solvation in highly schematic models, which resolve only coarse fluctuations in solvent density and cohesive energy. Here we show that even such lattice gas models recapitulate surprising thermodynamic trends observed in detailed simulations and experiments. Attention is focused on the case of two dimensions, for which approximate energy and entropy profiles can be calculated analytically. Simulations and theoretical analysis of the lattice gas highlight the role of capillary wave-like fluctuations in mediating adsorption. They further point to ranges of temperature and solute-solvent interaction strength where surface propensity is expected to be strongest.
[Show abstract][Hide abstract] ABSTRACT: Coarse-grained simulation is a powerful and well-established suite of computational methods for studying structure and dynamics in nanoscale biophysical systems. As our understanding of the plant photosynthetic apparatus has become increasingly nuanced, opportunities have arisen for coarse-grained simulation to complement experiment by testing hypotheses and making predictions. Here, we give an overview of best practices in coarse-grained simulation, with a focus on techniques and results that are applicable to the plant thylakoid membrane-protein system. We also discuss current research topics for which coarse-grained simulation has the potential to play a key role in advancing the field.