Effect of interactions on molecular fluxes and fluctuations in the transport across membrane channels

Transport of molecules across membrane channels is investigated theoretically using exactly solvable one-dimensional discrete-state stochastic models. An interaction between molecules and membrane pores is modeled via a set of binding sites with different energies. It is shown that the interaction potential strongly influences the particle currents as well as fluctuations in the number of translocated molecules. For small concentration gradients, the attractive sites lead to largest currents and fluctuations, while the repulsive interactions yield the largest fluxes and dispersions for large concentration gradients. Interaction energies that lead to maximal currents and maximal fluctuations are the same only for locally symmetric potentials, where transition states are equally distant from the neighboring binding sites, while they differ for the locally asymmetric potentials. The conditions for the most optimal translocation transport with maximal current and minimal dispersion are discussed. It is argued that, in this case, the interaction strength is independent of local symmetry of the potential of mean forces. In addition, the effect of the global asymmetry of the interaction potential is investigated, and it is shown that it also strongly affects the particle translocation dynamics. These phenomena can be explained by analyzing the details of the particle entering and leaving the binding sites in the channel.     

Stochastic dynamic simulation of a protein

The internal motions of a small protein, the bovine pancreatic trypsin inhibitor (BPTI) in solution, are investigated in the framework of the Langevin equation. In this approach, the effects of the solvent molecules are incorporated by suitably defining the friction and random forces. The friction coefficients are determined from a molecular dynamics simulation. The details of the rapid fluctuations of protein atoms obtained by stochastic and molecular dynamics simulation techniques are compared by calculating the generalized density of states obtained via an incoherent neutron scattering. Presently, our stochastic dynamics simulation is one order of magnitude faster than the molecular dynamics simulation with the explicit inclusion of the water molecules. Generalizations of the present stochastic dynamics approach for studying the large-scale motion in proteins are briefly outlined and the probability of a further speedup by an additional order of magnitude is discussed.     

Conformational dynamics of ATP∕Mg:ATP in motor proteins via data mining and molecular simulation

The conformational diversity of ATP∕Mg:ATP in motor proteins was investigated using molecular dynamics and data mining. Adenosine triphosphate (ATP) conformations were found to be constrained mostly by inter cavity motifs in the motor proteins. It is demonstrated that ATP favors extended conformations in the tight pockets of motor proteins such as F(1)-ATPase and actin whereas compact structures are favored in motor proteins such as RNA polymerase and DNA helicase. The incorporation of Mg(2+) leads to increased flexibility of ATP molecules. The differences in the conformational dynamics of ATP∕Mg:ATP in various motor proteins was quantified by the radius of gyration. The relationship between the simulation results and those obtained by data mining of motor proteins available in the protein data bank is analyzed. The data mining analysis of motor proteins supports the conformational diversity of the phosphate group of ATP obtained computationally.     

Is the mobility of the pore walls and water molecules in the selectivity filter of KcsA channel functionally important?

We performed in-depth analysis of the forces which act on the K(+) ions in the selectivity filter of the KcsA channel in order to estimate the relative importance of static and dynamic influence of the filter wall and water molecules on ion permeation and selectivity. The forces were computed using the trajectories of all-atom molecular dynamics simulations. It is shown that the dynamics of the selectivity filter contributes about 3% to the net force acting on the ions and can be neglected in the studies focused on the macroscopic properties of the channel, such as the current. Among the filter atoms, only the pore-forming carbonyl groups can be considered as dynamic in the studies of microscopic events of conduction, while the dynamic effects from all other atoms are negligible. We also show that the dynamics of the water molecules in the filter can not be neglected. The fluctuating forces from the water molecules can be as strong as net forces from the pore walls and can effectively drive the ions through the local energy barriers in the filter.     

Sequence-dependent DNA dynamics by scanning force microscopy time-resolved imaging

Scanning force microscopy was used to study in fluid the conformational fluctuations of two double-stranded DNA molecules resulting from differently cut pBR322 circular DNAs. A new approach was conceived to monitor the thermodynamic equilibrium of the chain dynamics on different scale lengths. This method made it possible to demonstrate that both the observed DNA molecules were allowed to equilibrate only on their local small-scale dynamics during the time of the experiment. This capability of monitoring the length scale and the time scale of the equilibration processes in the dynamics of a DNA chain is relevant to give an insight in the thermodynamics of the DNA binding with proteins and synthetic ligands. It was also shown that the small-scale equilibration of the DNA chain during surface-restricted dynamics is enough to allow a valid measurement of the local sequence-dependent curvature.     

Stochastic amperometric fluctuations as a probe for dynamic adsorption in nanofluidic electrochemical systems

Adsorption of analyte molecules is ubiquitous in nanofluidic channels due to their large surface-to-volume ratios. It is also difficult to quantify due to the nanometric scale of these channels. We propose a simple method to probe dynamic adsorption at electrodes that are embedded in nanofluidic channels or which enclose nanoscopic volumes. The amperometric method relies on measuring the amplitude of the fluctuations of the redox cycling current that arise when the channel is diffusively coupled to a bulk reservoir. We demonstrate the versatility of this new method by quantifying adsorption for several redox couples, investigating the dependence of adsorption on the electrode potential and studying the effect of functionalizing the electrodes with self-assembled monolayers of organothiol molecules bearing polar end groups. These self-assembled monolayer coatings are shown to significantly reduce the adsorption of the molecules on to the electrodes. The detection method is not limited to electrodes in nanochannels and can be easily extended to redox cycling systems that enclose very small volumes, in particular scanning electrochemical microscopy with nanoelectrodes. It thus opens the way for imaging spatial heterogeneity with respect to adsorption, as well as rational design of interfaces for redox cycling based sensors.     

A generalized Langevin dynamics approach to model solvent dynamics effects on proteins via a solvent-accessible surface. The carboxypeptidase A inhibitor protein as a model

A generalized Langevin dynamics (GLD) scheme is derived for (bio)macromolecules having internal structure, arbitrary shapes and a size larger than solvent molecules (i.e. proteins). The concept of solvent-accessible surface area (SASA) is used to incorporate solvent effects via external forces thereby avoiding its explicit molecular representation. A simulation algorithm is implemented in the GROMOS molecular dynamics (MD) program including random forces and memory effects, while solvation effects enter via derivatives of the surface area. The potato carboxypeptidase inhibitor (PCI), a small protein, is used to numerically test the approach. This molecule has N- and C-terminal tails whose structure and fluctuations are solvent dependent. A 1-ns MD trajectory was analyzed in depth. X-ray and NMR structures are used in conjunction with MD simulations with and without explicit solvent to gauge the quality of the results. All the analyses showed that the GLD simulation approached the results obtained for the MD simulation with explicit simple-point-charge-model water molecules. The SASAs of the polar atoms show a natural exposure towards the solvent direction. A FLS solvent simulation was completed in order to sense memory effects. The approach and results presented here could be of great value for developing alternatives to the use of explicit solvent molecules in the MD simulation of proteins, expanding its use and the time-scale explored. Received: 2 February 2000 / Revised: 12 March 2000 / Accepted: 26 May 2000 / Published online: 2 November 2000     

Ultrafast dynamics of nonequilibrium resonance energy transfer and probing globular protein flexibility of myoglobin

Protein structural plasticity is critical to many biological activities and accurate determination of its temporal and spatial fluctuations is challenging and difficult. Here, we report our extensive characterization of global flexibility of a globular heme protein of myoglobin using resonance energy transfer as a molecular ruler. With site-directed mutagenesis, we use a tryptophan scan to examine local structural fluctuations from B to H helices utilizing 10 tryptophan-heme energy transfer pairs with femtosecond resolution. We observed ultrafast resonance energy transfer dynamics by following a nearly single exponential behavior in 10-100 ps, strongly indicating that the globular structure of myoglobin is relatively rigid, with no observable static or slow dynamic conformational heterogeneity. The observation is against our molecular dynamics simulations, which show large local fluctuations and give multiple exponential energy transfer behaviors, suggesting too flexible of the global structure and thus raising a serious issue of the force fields used in simulations. Finally, these ultrafast energy transfer dynamics all occur on the similar time scales of local environmental relaxations (solvation), leading to nonexponential processes caused by energy relaxations, not structural fluctuations. Our analyses of such processes reveal an intrinsic compressed- and/or stretched-exponential behaviors and elucidate the nature of inherent nonequilibrium of ultrafast resonance energy transfer in proteins. This new concept of compressed nonequilibrium transfer dynamics should be applied to all protein studies by time-resolved F?rster resonance energy transfer (FRET).     

Amino acid side chain interactions in the presence of salts

The effects of salt on the intermolecular interactions between polar/charged amino acids are investigated through molecular dynamics simulations. The mean forces and associated potentials are calculated for NaCl salt in the 0-2 M concentration range at 298 K. It is found that the addition of salt may stabilize or destabilize the interactions, depending on the nature of the interacting molecules. The degree of (de)stabilization is quantified, and the origin of the salt-dependent modulation is discussed based upon an analysis of solvent density profiles. To gain insight into the molecular origin of the salt modulation, spatial distribution functions (sdf's) are calculated, revealing a high degree of solvent structuredness in all cases. The peaks in the sdf's are consistent with long-range hydrogen-bonding networks connecting the solute hydrophilic groups, and that contribute to their intermolecular solvent-induced forces. The restructuring of water around the solutes as they dissociate from close contact is analyzed. This analysis offers clues on how the solvent structure modulates the effective intermolecular interactions in complex solutes. This modulation results from a critical balance between bulk electrostatic forces and those exerted by (i) the water molecules in the structured region between the monomers, which is disrupted by ions that transiently enter the hydration shells, and (ii) the ions in the hydration shells in direct interactions with the solutes. The implications of these findings in protein/ligand (noncovalent) association/dissociation mechanisms are briefly discussed.     

Boundary element solution of the linear Poisson-Boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution

The Poisson-Boltzmann equation is widely used to describe the electrostatic potential of molecules in an ionic solution that is treated as a continuous dielectric medium. The linearized form of this equation, applicable to many biologic macromolecules, may be solved using the boundary element method. A single-layer formulation of the boundary element method, which yields simpler integral equations than the direct formulations previously discussed in the literature, is given. It is shown that the electrostatic force and torque on a molecule may be calculated using its boundary element representation and also the polarization charge for two rigid molecules may be rapidly calculated using a noniterative scheme. An algorithm based on a fast adaptive multipole method is introduced to further increase the speed of the calculation. This method is particularly suited for Brownian dynamics or molecular dynamics simulations of large molecules, in which the electrostatic forces must be calculated for many different relative positions and orientations of the molecules. It has been implemented as a set of programs in C++, which are used to study the accuracy and speed of this method for two actin monomers.     

DLVO AND NON-DLVO SURFACE FORCES AND INTERACTIONS IN COLLOIDAL DISPERSIONS

Some aspects of DLVO and non-DLVO forces in colloidal systems are over-viewed. The influence of long range interactions on some kinetic properties of dispersions, as Brownian diffusion, is discussed. It is shown, both theoretically and experimentally, that the electrostatic repulsion increases the collective diffusivity. The film stratification and oscillatory structure forces in colloidal suspensions are considered within the framework of an uniform approach The presence of small colloidal species (e. g. micelles or polymer molecules) may lead to several maxima and minima in the disjoining pressure isotherm. The particular case of interacting emulsion droplets is examined accounting for the interfacial deformability. The droplet deformation acts as a soft repulsion but affects also the remaining contributions to the interaction energy due to changes of the droplet shape. A general procedure for calculating the inter-droplet interaction energy, as well as the equilibrium film radius and thickness in a doublet of droplets, is suggested. The energy of interaction between charged colloidal particles, due to correlations of the density fluctuations in the electric double layer is also studied. It is found that this effect may lead to attraction greater than the van der Waals contribution, especially when multivale counter ions are present.     

Stress tensor in model polymer systems with periodic boundaries

The calculation of the stress tensor from molecular simulations of atomistic model polymer systems employing periodic boundary conditions is discussed. Starting from the dynamical equations governing the motion of sites, correct double summation forms of the atomic and the molecular virial equations are derived, which are valid for flexible, infinitely stiff and rigid chain models even in the presence of interactions between different images of the same parent macromolecule. A new expression for the true instantaneous stress (flux of momentum through the faces of the simulation box) is derived and shown to exhibit large fluctuations when applied in molecular dynamics simulations. A new equation for the thermodynamic stress, cast exclusively in terms of intermolecular forces on interaction sites, is also derived. Application to Monte Carlo simulations shows that the molecular virial expression exhibits the smallest fluctuations among all stress expressions discussed, and thus allows computation of the thermodynamic stress with least uncertainty. A scheme is developed for the calculation of surface tension from intermolecular forces only.     

Local dynamics and glass transition

The dynamics of polymer chains in the bulk state are discussed at three different temperature scales: (i) Well above the glass transition temperature where the basic step of motion is the rotameric transition of bonds. In this regime, the dynamics may conveniently be analyzed by the rotational isomeric state model, (ii) In the vicinity of glass transition where friction forces from the environment dominate. In this regime, the dynamics may be modeled according to the cooperative kinematics model, (iii) Well below glass transition. Here, an analogy with a native protein is made, and the mean-squared fluctuations are analyzed by adopting the Gaussian Network Model, which recently proved successful in describing fluctuations in native proteins.     

Key intermolecular interactions in the E. coli 70S ribosome revealed by coarse-grained analysis

The ribosome is a very large complex that consists of many RNA and protein molecules and plays a central role in protein biosynthesis in all organisms. Extensive interactions between different molecules are critical to ribosomal functional dynamics. In this work, intermolecular interactions in the Escherichia coli 70S ribosome are investigated by coarse-grained (CG) analysis. CG models are defined to preserve dynamic domains in RNAs and proteins and to capture functional motions in the ribosome, and then the CG sites are connected by harmonic springs, and spring constants are obtained by matching the computed fluctuations to those of an all-atom molecular dynamics (MD) simulation. Those spring constants indicate how strong the interactions are between the ribosomal components, and they are in good agreement with various experimental data. Nearly all the bridges between the small and large ribosomal subunits are indicated by CG interactions with large spring constants. The head of the small subunit is very mobile because it has minimal CG interactions with the rest of the subunit; however, a large number of small subunit proteins bind to maintain the internal structure of the head. The results show a clear connection between the intermolecular interactions and the structural and functional properties of the ribosome because of the reduced complexity in domain-based CG models. The present approach also provides a useful strategy to map interactions between molecules within large biomolecular complexes since it is not straightforward to investigate these by either atomistic MD simulations or residue-based elastic network models.     

Effect of equilibrium fluctuations on microcrystalline particles on adsorption isotherms and reaction rates

The effect of the finiteness of face areas and equilibrium fluctuations on the adsorption isotherms of binary molecular mixtures and the rate of surface processes occurring on nanosized particles is studied. The adsorption process is considered in the grand canonical ensemble; the rates of elementary stages are calculated in the kinetic mode. The surface region on the face is found to contain a number of adsorption centers ranging from 10 to 10⁵. The effect of density fluctuations of adsorbed molecules on the partial adsorption isotherms and rate fluctuations is discussed. A calculation procedure for density fluctuations in heterogeneous microparticles with different faces and different binding energies of molecules with the surface is considered. It is shown that the greatest effect of density fluctuations is manifested at a low occupancy of each face of the particle.     

Influence of thermal fluctuations on interfacial electron transfer in functionalized TiO2 semiconductors

The influence of thermal fluctuations on the dynamics of interfacial electron transfer in sensitized TiO2-anatase semiconductors is investigated by combining ab initio DFT molecular dynamics simulations and quantum dynamics propagation of transient electronic excitations. It is shown that thermal nuclear fluctuations speed up the underlying interfacial electron transfer dynamics by introducing nonadiabatic transitions between electron acceptor states, localized in the vicinity of the photoexcited adsorbate, and delocalized states extended throughout the semiconductor material, creating additional relaxation pathways for carrier diffusion. Furthermore, it is shown that room-temperature thermal fluctuations reduce the anisotropic character of charge diffusion along different directions in the anatase crystal and make similar the rates for electron injection from adsorbate states of different character. The reported results are particularly relevant to the understanding of temperature effects on surface charge separation mechanisms in molecular-based photo-optic devices.     

Stochastic bi-resonance in non-isothermal carbon monoxide catalytic oxidation system

The Pt(110)/CO O2 system subject to reaction heat, heat conduction and radiative heat transfer is non-isothermal and its temperature varies in time and space. In this paper, taking support temperature (ST) as the control parameter, the effect of the ST fluctuations in the oscillatory dynamics of the non-isothermal Pt(110)/CO O2 system is numerically studied. It is found that the ST fluctuations may induce stochastic oscillations and the oscillations exhibit stochastic bi-resonance (SBR) with the change of the strength or correlation time of the fluctuations. This result shows that the temperature fluctuations may enhance the chemical reaction oscillations. Moreover, the system can selectively and repeatedly employ the temperature fluctuations to enhance its reaction oscillations. It is also shown when the distance of the ST temperature to the oscillatory region increases a little, the effect of the temperature fluctuations would obviously weaken.     

Incorporating solvent and ion screening into molecular dynamics using the finite-difference Poisson–Boltzmann method

The finite difference method for solving the Poisson–Boltzmann equation is used to calculate the reaction field acting on a macromolecular solute due to the surrounding water and ions. Comparisons with analytical test cases indicate that the solvation forces can be calculated rapidly and accurately with this method. These forces act to move charged solute atoms towards the solvent where they are better solvated, and to screen interactions between charges. A way of combining such calculations with conventional molecular dynamics force fields is proposed which requires little modification of existing molecular dynamics programs. Simulations on the alanine dipeptide show that solvent forces affect the conformational dynamics by reducing the preference for internal H-bonding forms, increasing the R-alpha helix preference and reducing transition barriers. These solvent effects are similar to previous explicit solvent simulations, but require little more computation than vacuum simulations. The method should scale up with little increase in computational cost to larger molecules such as proteins and nucleic acids.