Spectral diffusion and the energy landscape of a protein

We present a novel type of spectral diffusion experiment in the millikelvin range to characterize the energy landscape of a protein as compared with that of a glass. We measure the time evolution of spectral holes for more than 300 hr after well-defined initial nonequilibrium conditions. We show that the model of noninteracting two-level systems can describe spectral diffusion in the glass, but fails for the protein. Our results further demonstrate that randomness in the energy landscape of a protein shows features of organization. There are “deep minimum” states separated by barriers, the heights of which we are able to estimate. The energy landscape of a glass is featureless by comparison.

Implications of macromolecular crowding for signal transduction and metabolite channeling

The effect of different total enzyme concentrations on the flux through the bacterial phosphoenolpyruvate:carbohydrate phosphotransferase system (PTS) in vitro was determined by measuring PTS-mediated carbohydrate phosphorylation at different dilutions of cell-free extract of Escherichia coli. The dependence of the flux on the protein concentration was more than linear but less than quadratic. The combined flux–response coefficient of the four enzymes constituting the glucose PTS decreased slightly from values of ≈1.8 with increasing protein concentrations in the assay. Addition of the macromolecular crowding agents polyethylene glycol (PEG) 6000 and PEG 35000 led to a sharper decrease in the combined flux–response coefficient, in one case to values of ≈1. PEG 6000 stimulated the PTS flux at lower protein concentrations and inhibited the flux at higher protein concentrations, with the transition depending on the PEG 6000 concentration. This suggests that macromolecular crowding decreases the dissociation rate constants of enzyme complexes. High concentrations of the microsolute glycerol did not affect the combined flux–response coefficient. The data could be explained with a kinetic model of macromolecular crowding in a two-enzyme group-transfer pathway. Our results suggest that, because of the crowded environment in the cell, the different PTS enzymes form complexes that live long on the time-scale of their turnover. The implications for the metabolic behavior and control properties of the PTS, and for the effect of macromolecular crowding on nonequilibrium processes, are discussed.

Directionality principles in thermodynamics and evolution

Directionality in populations of replicating organisms can be parametrized in terms of a statistical concept: evolutionary entropy. This parameter, a measure of the variability in the age of reproducing individuals in a population, is isometric with the macroscopic variable body size. Evolutionary trends in entropy due to mutation and natural selection fall into patterns modulated by ecological and demographic constraints, which are delineated as follows: (i) density-dependent conditions (a unidirectional increase in evolutionary entropy), and (ii) density-independent conditions, (a) slow exponential growth (an increase in entropy); (b) rapid exponential growth, low degree of iteroparity (a decrease in entropy); and (c) rapid exponential growth, high degree of iteroparity (random, nondirectional change in entropy). Directionality in aggregates of inanimate matter can be parametrized in terms of the statistical concept, thermodynamic entropy, a measure of disorder. Directional trends in entropy in aggregates of matter fall into patterns determined by the nature of the adiabatic constraints, which are characterized as follows: (i) irreversible processes (an increase in thermodynamic entropy) and (ii) reversible processes (a constant value for entropy). This article analyzes the relation between the concepts that underlie the directionality principles in evolutionary biology and physical systems. For models of cellular populations, an analytic relation is derived between generation time, the average length of the cell cycle, and temperature. This correspondence between generation time, an evolutionary parameter, and temperature, a thermodynamic variable, is exploited to show that the increase in evolutionary entropy that characterizes population processes under density-dependent conditions represents a nonequilibrium analogue of the second law of thermodynamics.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

Kinetics of self-assembling microtubules: an "inverse problem" in biochemistry.

Experimental time series for a nonequilibrium reaction may in some cases contain sufficient data to determine a unique kinetic model for the reaction by a systematic mathematical analysis. As an example, a kinetic model for the self-assembly of microtubules is derived here from turbidity time series for solutions in which microtubules assemble. The model may be seen as a generalization of Oosawa's classical nucleation-polymerization model. It reproduces the experimental data with a four-stage nucleation process and a critical nucleus of 15 monomers.

Spin glasses on the hypercube

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the nontrivial problem of generating these lattices. Afterward, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are the following: i the dynamics is ruled by an infinite number of time sectors, ii the aging dynamics consists of the growth of coherent domains with a nonvanishing surface-volume ratio, and iii the propagator in Fourier space follows the p4 law. We study as well the finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.

Entropy production and thermodynamic power of the squeezed thermal reservoir

We analyze the entropy production and the maximal extractable work from a squeezed thermal reservoir. The nonequilibrium quantum nature of the reservoir induces an entropy transfer with a coherent contribution while modifying its thermal part, allowing work extraction from a single reservoir, as well as great improvements in power and efficiency for quantum heat engines. Introducing a modified quantum Otto cycle, our approach fully characterizes operational regimes forbidden in the standard case, such as refrigeration and work extraction at the same time, accompanied by efficiencies equal to unity.

Spin dynamics of current-driven single magnetic adatoms and molecules

A scanning tunneling microscope can probe the inelastic spin excitations of a single magnetic atom in a surface via spin-flip assisted tunneling in which transport electrons exchange spin and energy with the atomic spin. If the inelastic transport time, defined as the average time elapsed between two inelastic spin flip events, is shorter than the atom spin-relaxation time, the scanning tunnel microscope (STM) current can drive the spin out of equilibrium. Here we model this process using rate equations and a model Hamiltonian that describes successfully spin-flip-assisted tunneling experiments, including a single Mn atom, a Mn dimer, and Fe Phthalocyanine molecules. When the STM current is not spin polarized, the nonequilibrium spin dynamics of the magnetic atom results in nonmonotonic dI/dV curves. In the case of spin-polarized STM current, the spin orientation of the magnetic atom can be controlled parallel or antiparallel to the magnetic moment of the tip. Thus, spin-polarized STM tips can be used both to probe and to control the magnetic moment of a single atom.

Exact and analytic-numerical solutions of lagging models of heat transfer in a semi-infinite medium

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

Bayesian inferences on the recent island colonization history by the bird Zosterops lateralis lateralis

The founding of new populations by small numbers of colonists has been considered a potentially important mechanism promoting evolutionary change in island populations. Colonizing species, such as members of the avian species complex Zosterops lateralis, have been used to support this idea. A large amount of background information on recent colonization history is available for one Zosterops subspecies, Z. lateralis lateralis, providing the opportunity to reconstruct the population dynamics of its colonization sequence. We used a Bayesian approach to combine historical and demographic information available on Z. l. lateralis with genotypic data from six microsatellite loci, and a rejection algorithm to make simultaneous inferences on the demographic parameters describing the recent colonization history of this subspecies in four southwest Pacific islands. Demographic models assuming mutation–drift equilibrium or a large number of founders were better supported than models assuming founder events for three of four recently colonized island populations. Posterior distributions of demographic parameters supported (i) a large stable effective population size of several thousands individuals with point estimates around 4000–5000; (ii) a founder event of very low intensity with a large effective number of founders around 150–200 individuals for each island in three of four islands, suggesting the colonization of those islands by one flock of large size or several flocks of average size; and (iii) a founder event of higher intensity on Norfolk Island with an effective number of founders around 20 individuals, suggesting colonization by a single flock of moderate size. Our inferences on demographic parameters, especially those on the number of founders, were relatively insensitive to the precise choice of prior distributions for microsatellite mutation processes and demographic parameters, suggesting that our analysis provides a robust description of the recent colonization history of the subspecies.

Effector dynamics of rhythmic wrist activity and its implications for (modeling) bimanual coordination

To examine the role of the effector dynamics of the wrist in the production of rhythmic motor activity, we estimated the phase shifts between the EMG and the task-related output for a rhythmic isometric torque production task and an oscillatory movement, and found a substantial difference (45-52degrees) between the two. For both tasks, the relation between EMG and task-related output (torque or displacement) was adequately reproduced with a physiologically motivated musculoskeletal model. The model simulations demonstrated the importance of the contribution of passive structures to the overall dynamics and provided an account for the observed phase shifts in the dynamic task. Additional simulations of the musculoskeletal model with added load suggested that particular changes in the phase relation between EMG and movement may follow largely from the intrinsic muscle dynamics, rather than being the result of adaptations in the neural control of joint stiffness. The implications of these results are discussed in relation to (models of) interlimb coordination in rhythmic tasks. (C) 2004 Elsevier B.V. All rights reserved.

Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed. (C) 2004 American Institute of Physics.

Modeling molecular transport in slit pores

We examine the transport of methane in microporous carbon by performing equilibrium and nonequilibrium molecular dynamics simulations over a range of pore sizes, densities, and temperatures. We interpret these simulation results using two models of the transport process. At low densities, we consider a molecular flow model, in which intermolecular interactions are neglected, and find excellent agreement between transport diffusion coefficients determined from simulation, and those predicted by the model. Simulation results indicate that the model can be applied up to fluid densities of the order to 0.1-1 nm(-3). Above these densities, we consider a slip flow model, combining hydrodynamic theory with a slip condition at the solid-fluid interface. As the diffusion coefficient at low densities can be accurately determined by the molecular flow model, we also consider a model where the slip condition is supplied by the molecular flow model. We find that both density-dependent models provide a useful means of estimating the transport coefficient that compares well with simulation. (C) 2004 American Institute of Physics.

Critical fluctuations and entanglement in the nondegenerate parametric oscillator

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

Comparisons of diffusive and viscous contributions to transport coefficients of light gases in single-walled carbon nanotubes

We examine here the relative importance of different contributions to transport of light gases in single walled carbon nanotubes, using methane and hydrogen as examples. Transport coefficients at 298 K are determined using molecular dynamics simulation with atomistic models of the nanotube wall, from which the diffusive and viscous contributions are resolved using a recent approach that provides an explicit expression for the latter. We also exploit an exact theory for the transport of Lennard-Jones fluids at low density considering diffuse reflection at the tube wall, thereby permitting the estimation of Maxwell coefficients for the wall reflection. It is found that reflection from the carbon nanotube wall is nearly specular, as a result of which slip flow dominates, and the viscous contribution is small in comparison, even for a tube as large as 8.1 nm in diameter. The reflection coefficient for hydrogen is 3-6 times as large as that for methane in tubes of 1.36 nm diameter, indicating less specular reflection for hydrogen and greater sensitivity to atomic detail of the surface. This reconciles results showing that transport coefficients for hydrogen and methane, obtained in simulation, are comparable in tubes of this size. With increase in adsorbate density, the reflection coefficient increases, suggesting that adsorbate interactions near the wall serve to roughen the local potential energy landscape perceived by fluid molecules.