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In the preceding paper by Stork and Tavan, [J. Chem. Phys. 126, 165105 (2007)], the authors have reformulated an electrostatic theory which treats proteins surrounded by dielectric solvent continua and approximately solves the associated Poisson equation [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)]. The resulting solution comprises analytical expressions for the electrostatic reaction field (RF) and potential, which are generated within the protein by the polarization of the surrounding continuum. Here the field and potential are represented in terms of Gaussian RF dipole densities localized at the protein atoms. Quite like in a polarizable force field, also the RF dipole at a given protein atom is induced by the partial charges and RF dipoles at the other atoms. Based on the reformulated theory, the authors have suggested expressions for the RF forces, which obey Newton’s third law. Previous continuum approaches, which were also built on solutions of the Poisson equation, used to violate the reactio principle required by this law, and thus were inapplicable to molecular dynamics (MD) simulations. In this paper, the authors suggest a set of techniques by which one can surmount the few remaining hurdles still hampering the application of the theory to MD simulations of soluble proteins and peptides. These techniques comprise the treatment of the RF dipoles within an extended Lagrangian approach and the optimization of the atomic RF polarizabilities. Using the well-studied conformational dynamics of alanine dipeptide as the simplest example, the authors demonstrate the remarkable accuracy and efficiency of the resulting RF-MD approach. [ABSTRACT FROM AUTHOR]

The Histone-like Nucleoid Structuring protein (H-NS) is a nucleoid-associated protein, which is involved in both gene regulation and DNA compaction. Although it is a key player in genome organization by forming bridges between DNA duplexes, the precise structure of complexes of DNA and H-NS proteins is still not well understood. In particular, it is not clear whether the structure of DNA/H-NS complexes in the living cell is similar to that of complexes deposited on mica surfaces, which may be observed by AFM microscopy. A coarse-grained model, which helps getting more insight into this question, is described and analyzed in the present paper. This model is able of describing both the bridging of bacterial DNA by H-NS in the bulk and the deposition and equilibration of the complex on a charged surface. Simulations performed with the model reveal that a slight attraction between DNA and the charged surface is sufficient to let DNA/H-NS complexes reorganize from 3D coils to planar plasmids bridged by H-NS proteins similar to those observed by AFM microscopy. They furthermore highlight the antagonistic effects of the interactions between DNA and the surface. Indeed, increasing these interactions slows down the equilibration of naked plasmids on the surface but, on the other hand, enables a faster equilibration of DNA/H-NS complexes. Based on the distribution of the lifetimes of H-NS bridges and the time evolution of the number of trans-binding protein dimers during equilibration of the complexes on the surface, it is argued that the decrease of the equilibration time of the complex upon increase of the interaction strength between DNA and the surface is ascribable to the associated decrease of the probability to form new bridges between DNA and the proteins. [ABSTRACT FROM AUTHOR]

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies. [ABSTRACT FROM AUTHOR]

In this paper, we present a detailed dynamics study of the catalytic core domain (CCD) of HIV-1 integrase using both polarized and nonpolarized force fields. The numerical results reveal the critical role of protein polarization in stabilizing Mg2+ coordination complex in CCD. Specifically, when nonpolarized force field is used, a remarkable drift of the Mg2+ complex away from its equilibrium position is observed, which causes the binding site blocked by the Mg2+ complex. In contrast, when polarized force field is employed in MD simulation, HIV-1 integrase CCD structure is stabilized and both the position of the Mg2+ complex and the binding site are well preserved. The detailed analysis shows the transition of α-helix to 310-helix adjacent to the catalytic loop (residues 139–147), which correlates with the dislocation of the Mg2+ complex. The current study demonstrates the importance of electronic polarization of protein in stabilizing the metal complex in the catalytic core domain of HIV-1 integrase. [ABSTRACT FROM AUTHOR]

Protein refolding to its native state in vitro is a challenging problem in biotechnology, i.e., in the biomedical, pharmaceutical, and food industry. Protein aggregation and misfolding usually inhibit the recovery of proteins with their native states. These problems can be partially solved by adding a surfactant into a suitable solution environment. However, the process of this surfactant-assisted protein refolding is not well understood. In this paper, we wish to report on the first-ever simulations of surfactant-assisted protein refolding. For these studies, we defined a simple model for the protein and the surfactant and investigated how a surfactant affected the folding behavior of a two-dimensional lattice protein molecule. The model protein and model surfactant were chosen such that we could capture the important features of the folding process and the interaction between the protein and the surfactant, namely, the hydrophobic interaction. It was shown that, in the absence of surfactants, a protein in an “energy trap” conformation, i.e., a local energy minima, could not fold into the native form, which was characterized by a global energy minimum. The addition of surfactants created folding pathways via the formation of protein-surfactant complexes and thus enabled the conformations that fell into energy trap states to escape from these traps and to form the native proteins. The simulation results also showed that it was necessary to match the hydrophobicity of surfactant to the concentration of denaturant, which was added to control the folding or unfolding of a protein. The surfactants with different hydrophobicity had their own concentration range on assisting protein refolding. All of these simulations agreed well with experimental results reported elsewhere, indicating both the validity of the simulations presented here and the potential application of the simulations for the design of a surfactant on assisting protein refolding. [ABSTRACT FROM AUTHOR]

An efficient molecular dynamics (MD) algorithm is presented in this paper for biomolecular systems, which incorporates a novel variation on the fast multipole method (FMM) coupled to the reversible reference system propagator algorithm (r-RESPA). A top-down FMM is proposed which calculates multipoles recursively from the top of the box tree instead of from the bottom in Greengard’s original FMM, in an effort to be more efficient for noncubic or nonuniform systems. In addition, the use of noncubic box subdivisions of biomolecular systems is used and discussed. Reversible RESPA based on a Trotter factorization of the Liouville propagator in generating numerical integration schemes is coupled to the top-down FMM and applied to a MD study of proteins in vacuo, and is shown to be able to use a much larger time-step than the standard velocity Verlet method for a comparable level of accuracy. Furthermore, by using the FMM it becomes possible to perform MD simulations for very large biomolecules, since memory and CPU time requirements are now nearly of order of O(N) instead of O(N2). For a protein with 9513 atoms (the photosynthetic reaction center), the efficient MD algorithm leads to 20-fold reduction in CPU time for the Coulomb interaction and approximately 15-fold reduction in total CPU time over the standard velocity Verlet algorithm with a direct evaluation of Coulomb forces. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report molecular dynamics (MD) simulations of three protein-water systems (ubiquitin, apo-calbindin D9K, and the C-terminal SH2 domain of phospholipase C-γ1), from which we compute the dielectric properties of the solutions. Since two of the proteins studied have a net charge, we develop the necessary theory to account for the presence of charged species in a form suitable for computer simulations. In order to ensure convergence of the time correlation functions needed for the analysis, the minimum length of the MD simulations was 20 ns. The system sizes (box length, number of waters) were chosen so that the resulting protein concentrations are comparable to experimental conditions. A dielectric component analysis was carried out to analyze the contributions from protein and water to the frequency-dependent dielectric susceptibility χ(ω) of the solutions. Additionally, an even finer decomposition into protein, two solvation shells, and the remaining water (bulk water) was carried out. The results of these dielectric decompositions were used to study protein solvation at mesoscopic resolution, i.e., in terms of protein, first and second solvation layers, and bulk water. This study, therefore, complements the structural and dynamical analyses at molecular resolution that are presented in the companion paper. The dielectric component contributions from the second shell and bulk water are very similar in all three systems. We find that the proteins influence the dielectric properties of water even beyond the second solvation shell, in agreement with what was observed for the mean residence times of water molecules in protein solutions. By contrast, the protein contributions, as well as the contributions of the first solvation shell, are system specific. Most importantly, the protein and the first water shell around ubiquitin and apo-calbindin are anticorrelated, whereas the first water shell around the SH2 domain is positively correlated. [ABSTRACT FROM AUTHOR]

Increasingly, theoretical studies of proteins focus on large systems. This trend demands the development of computational models that are fast, to overcome the growing complexity, and accurate, to capture the physically relevant features. To address this demand, we introduce a protein model that uses all-atom architecture to ensure the highest level of chemical detail while employing effective pair potentials to represent the effect of solvent to achieve the maximum speed. The effective potentials are derived for amino acid residues based on the condition that the solvent-free model matches the relevant pair-distribution functions observed in explicit solvent simulations. As a test, the model is applied to alanine polypeptides. For the chain with 10 amino acid residues, the model is found to reproduce properly the native state and its population. Small discrepancies are observed for other folding properties and can be attributed to the approximations inherent in the model. The transferability of the generated effective potentials is investigated in simulations of a longer peptide with 25 residues. A minimal set of potentials is identified that leads to qualitatively correct results in comparison with the explicit solvent simulations. Further tests, conducted for multiple peptide chains, show that the transferable model correctly reproduces the experimentally observed tendency of polyalanines to aggregate into β-sheets more strongly with the growing length of the peptide chain. Taken together, the reported results suggest that the proposed model could be used to succesfully simulate folding and aggregation of small peptides in atomic detail. Further tests are needed to assess the strengths and limitations of the model more thoroughly. [ABSTRACT FROM AUTHOR]

Biological membranes are complex environments whose physico-chemical properties are of utmost importance for the understanding of many crucial biological processes. Much attention has been given in the literature to the description of membranes along the z-axis perpendicular to the membrane. Here, we instead consider the lateral dynamics of lipids and peripheral proteins due to their electrostatic interaction. Previously, we constructed a Monte Carlo automaton capable of simulating mutual diffusive dynamics of charged lipids and associated positively charged peptides. Here, we derive and numerically analyze a system of Poisson-Boltzmann-Nernst-Planck (PBNP) equations that provide a mean-field approximation compatible with our Monte Carlo model. The thorough comparison between the mean-field PBNP equations and Monte Carlo simulations demonstrates that both the approaches are in a good qualitative agreement in all tested scenarios. We find that the two methods quantitatively deviate when the local charge density is high, presumably because the Poisson-Boltzmann formalism is applicable in the so-called weak coupling limit, whose validity is restricted to low charge densities. Nevertheless, we conclude that the mean-field PBNP approach provides a good approximation for the considerably more detailed Monte Carlo model at only a fraction of the associated computational cost and allows simulation of the membrane lateral dynamics on the space and time scales relevant for the realistic biological problems. [ABSTRACT FROM AUTHOR]

We use mixed classical/quantum simulations to study the time dependence of an excitation of a C=O vibration on a 3-10 helix of α-aminoisobutyric acid, a system which represents a test case for the formation of self-trapped vibrational excitation states on protein helices. Due to the inherent disorder in the system caused by the finite temperature and fluctuations in hydrogen bonding, the excitation tunnels randomly among C=O sites along the helix. Quantum forces are insufficient to establish a coherent relationship between the location of the excitation and the contraction of hydrogen bonds around this site. Our simulations indicate that the excitation frequently becomes localized on the end of the helix due to the defect in helical structure caused by unwinding. Our results generally do not support the existence of Davydov type solitons in biological helix systems under physiological conditions. [ABSTRACT FROM AUTHOR]

Dynamic information, such as force, structural change, interaction energy, and potential of mean force (PMF), about the desorption of a single cardiotoxin (CTX) protein from a methyl-terminated self-assembled monolayer (SAM) surface was investigated by means of steered molecular dynamics (SMD) simulations. The simulation results indicated that Loop I is the first loop to depart from the SAM surface, which is in good agreement with the results of the nuclear magnetic resonance spectroscopy experiment. The free energy landscape and the thermodynamic force of the CTX desorption process was represented by the PMF and by the derivative of PMF with respect to distance, respectively. By applying Jarzynski's equality, the PMF can be reconstructed from the SMD simulation. The PMFs, calculated by different estimators based upon Jarzynski's equality, were compared with the conventional umbrella sampling method. The best estimation was obtained by using the fluctuation-dissipation estimator with a pulling velocity of v = 0.25 nm/ns for the present study. [ABSTRACT FROM AUTHOR]

The experimentally well-known convergence of solvation entropies and enthalpies of different small hydrophobic solutes at universal temperatures seems to indicate that hydrophobic solvation is dominated by universal water features and not so much by solute specifics. The reported convergence of the denaturing entropy of a group of different proteins at roughly the same temperature as hydrophobic solutes was consequently argued to indicate that the denaturing entropy of proteins is dominated by the hydrophobic effect and used to estimate the hydrophobic contribution to protein stability. However, this appealing picture was subsequently questioned since the initially claimed universal convergence of denaturing entropies holds only for a small subset of proteins; for a larger data collection no convergence is seen. We report extensive simulation results for the solvation of small spherical solutes in explicit water with varying solute-water potentials. We show that convergence of solvation properties for solutes of different radii exists but that the convergence temperatures depend sensitively on solute-water potential features such as stiffness of the repulsive part and attraction strength, not so much on the attraction range. Accordingly, convergence of solvation properties is only expected for solutes of a homologous series that differ in the number of one species of subunits (which attests to the additivity of solvation properties) or solutes that are characterized by similar solute-water interaction potentials. In contrast, for peptides that arguably consist of multiple groups with widely disperse interactions with water, it means that thermodynamic convergence at a universal temperature cannot be expected, in general, in agreement with experimental results. [ABSTRACT FROM AUTHOR]

We discuss the use of velocity rescaling for generating rejection-free exchange moves in replica exchange molecular dynamics. We test the efficiency of this approach for a common test case, the trp-cage protein. Advantages and limitations of the approach are discussed and possible extensions outlined. [ABSTRACT FROM AUTHOR]

Protein dynamics evolves in a high-dimensional space, comprising aharmonic, strongly correlated motional modes. Such correlation often plays an important role in analyzing protein function. In order to identify significantly correlated collective motions, here we employ independent subspace analysis based on the subspace joint approximate diagonalization of eigenmatrices algorithm for the analysis of molecular dynamics (MD) simulation trajectories. From the 100 ns MD simulation of T4 lysozyme, we extract several independent subspaces in each of which collective modes are significantly correlated, and identify the other modes as independent. This method successfully detects the modes along which long-tailed non-Gaussian probability distributions are obtained. Based on the time cross-correlation analysis, we identified a series of events among domain motions and more localized motions in the protein, indicating the connection between the functionally relevant phenomena which have been independently revealed by experiments. [ABSTRACT FROM AUTHOR]

The depletion interaction between proteins caused by addition of either uncharged or partially charged oligomers was studied using the canonical Monte Carlo simulation technique and the integral equation theory. A protein molecule was modeled in two different ways: either as (i) a hard sphere of diameter 30.0 Å with net charge 0, or +5, or (ii) as a hard sphere with discrete charges (depending on the pH of solution) of diameter 45.4 Å. The oligomers were pictured as tangentially jointed, uncharged, or partially charged, hard spheres. The ions of a simple electrolyte present in solution were represented by charged hard spheres distributed in the dielectric continuum. In this study we were particularly interested in changes of the protein-protein pair-distribution function, caused by addition of the oligomer component. In agreement with previous studies we found that addition of a nonadsorbing oligomer reduces the phase stability of solution, which is reflected in the shape of the protein-protein pair-distribution function. The value of this function in protein-protein contact increases with increasing oligomer concentration, and is larger for charged oligomers. The range of the depletion interaction and its strength also depend on the length (number of monomer units) of the oligomer chain. The integral equation theory, based on the Wertheim Ornstein-Zernike approach applied in this study, was found to be in fair agreement with Monte Carlo results only for very short oligomers. The computer simulations for a model mimicking the lysozyme molecule (ii) are in qualitative agreement with small-angle neutron experiments for lysozyme-dextran mixtures. [ABSTRACT FROM AUTHOR]

Using the constrained molecular dynamics simulation method in combination with quantum chemistry calculation, Hessian matrix reconstruction, and fragmentation approximation methods, the authors have established computational schemes for numerical simulations of amide I IR absorption, vibrational circular dichroism (VCD), and two-dimensional (2D) IR photon echo spectra of the protein ubiquitin in water. Vibrational characteristic features of these spectra in the amide I vibration region are discussed. From the semiempirical quantum chemistry calculation results on an isolated ubiquitin, amide I local mode frequencies and vibrational coupling constants were fully determined. It turns out that the amide I local mode frequencies of ubiquitin in both gas phase and aqueous solution are highly heterogeneous and site dependent. To directly test the quantitative validity of thus obtained spectroscopic properties, they compared the experimentally measured amide I IR, 2D IR, and electronic circular dichroism spectra with experiments, and found good agreements between theory and experiments. However, the simulated VCD spectrum is just qualitatively similar to the experimentally measured one. This indicates that, due to delicate cancellations between the positive and negative VCD contributions, the prediction of protein VCD spectrum is critically relied on quantitative accuracy of the theoretical model for predicting amide I local mode frequencies. On the basis of the present comparative investigations, they found that the site dependency of amide I local mode frequency, i.e., diagonal heterogeneity of the vibrational Hamiltonian matrix in the amide I local mode basis, is important. It is believed that the present computational methods for simulating various vibrational and electronic spectra of proteins will be of use in further refining classical force fields and in addressing the structure-spectra relationships of proteins in solution. [ABSTRACT FROM AUTHOR]

Mechanical stretching of ubiquitin and of its several repeats are studied through molecular-dynamics simulations. A Go-type model [H. Abe and N. Go, Biopolymers 20, 1013 (1981)] with a realistic contact map and with Lennard-Jones contact interactions is used. The model qualitatively reproduces the experimentally observed differences between force-extension patterns obtained on polyubiquitins stretched by various linkages. The terminal-to-terminal stretching of polyubiquitin results in peak forces similar to those measured for titin-based polyproteins and of a magnitude that matches measurements. Consistent with the experimental measurements, the simulated peak forces depend on the pulling speed logarithmically when thermal fluctuations are explicitly introduced. These results validate the application of topology-based models in the study of the mechanical stretching of proteins. [ABSTRACT FROM AUTHOR]

A simple protein model of a four-helix bundle motif on a face-centered cubic lattice has been studied. Total energy of a conformation includes attractive interactions between hydrophobic residues, repulsive interactions between hydrophobic and polar residues, and a potential that favors helical turns. Using replica exchange Monte Carlo simulations we have estimated a set of parameters for which the native structure is a global minimum of conformational energy. Then we have shown that all the above types of interactions are necessary to guarantee the cooperativity of folding transition and to satisfy the thermodynamic hypothesis. [ABSTRACT FROM AUTHOR]

By using molecular dynamics simulation, the dynamic behaviors of particle permeation through a four-helix-bundle model channel are studied. The interior cavity of the four-helix-bundle provides the “routes” for particle permeation. The main structural properties of the model channel are similar to those that appear in natural four-helix-bundle proteins. It is found that the interior structure of the model channel may greatly influence the permeation process. At the narrow necks of the model channel, the particle would be trapped during the permeation. There is a threshold value for the driving force. When the driving force is larger than this threshold value, the mean first permeation time decreases sharply and tends to be saturated. Increasing the temperature of either the model channel or the particle reservoir can also facilitate the permeation. Enhancing the interaction strength between the particle and monomer on the four-helix-bundle model chain will hinder the permeation. Hence, the electrical current which is induced by the particle permeation is a function of the driving force and temperature. It is found that this current increases monotonically as the strength of the driving force or the temperature increases, but decreases as the interaction strength between the particle and monomer increases. It is also found that the larger the friction coefficient, the slower the permeation is. In addition, the multiparticle (or multi-ion) permeation process is also studied. The permeation of multiparticle is usually quicker than that of the single particle. The permeation of particle through a five-helix-bundle shows similar properties as that through a four-helix-bundle. [ABSTRACT FROM AUTHOR]

The fifth order contributions to the signals of ultrafast infrared spectrally resolved stimulated vibrational echoes at high intensities have been investigated in carbonmonoxy heme proteins. High intensities are often required to obtain good data. Intensity dependent measurements are presented on hemoglobin-CO (Hb–CO) and a mutant of myoglobin, H64V–CO. The spectrally resolved vibrational echoes demonstrate that fifth order effects arise at both the 1-0 and the 2-1 emission frequencies of the stretching mode of the CO chromophore bound at the active site of heme proteins. Unlike one-dimensional experiments, in which the signal is integrated over all emission frequencies, spectrally resolving the signal shows that the fifth order contributions have a much more pronounced influence on the 2-1 transition than on the 1-0 transition. By spectrally isolating the 1-0 transition, the influence of fifth order contributions to vibrational echo data can be substantially reduced. Analysis of fifth order Feynman diagrams that contribute in the vibrational echo phase-matched direction demonstrates the reason for the greater influence of fifth order processes on the 1-2 transition, and that the fifth order contributions are heterodyne amplified by the third order signal. Finally, it is shown that the anharmonic oscillations in vibrational echo data of Hb–CO that previous work had attributed strictly to fifth order effects arise even without fifth order contributions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Simulations were performed for up to 150 simplified spherical horse heart cytochrome c molecules in the presence of a charged surface, which serves as an approximate model for a lipid membrane. Screened electrostatic and short-ranged attractive as well as repulsive van der Waals forces for interparticle and particle–membrane interactions are utilized in the simulations. At a distance from the membrane, where particle–membrane interactions are negligible, the simulation is coupled to a noninteraction continuum analogous to a heat bath [Geyer et al., J. Chem. Phys. 120, 4573 (2004)]. From the particles’ density profiles perpendicular to the planar surface binding isotherms are derived and compared to experimental results [Heimburg et al. (1999)]. Using a negatively charged structureless membrane surface a saturation effect was found for relatively large particle concentrations. Since biological membranes often contain membrane proteins, we also studied the influence of additional charges on our model membrane mimicking bacterial reaction centers. We find that the onset of the saturation occurs for much lower concentrations and is sensitive to the detailed implementation. Therefore we suggest that local distortion of membrane planarity (undulation), or lipid demixing, or the presence of charged integral membrane proteins create preferential binding sites on the membrane. Only then do we observe saturation at physiological concentrations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The native structure of fast-folding proteins, albeit a deep local free-energy minimum, may involve a relatively small energetic penalty due to nonoptimal, though favorable, contacts between amino acid residues. The weak energetic frustration that such contacts represent varies among different proteins and may account for folding behavior not seen in unfrustrated models. Minimalist model proteins with heterogeneous contacts—as represented by lattice heteropolymers consisting of three types of monomers—also give rise to weak energetic frustration in their corresponding native structures, and the present study of their equilibrium and nonequilibrium properties reveals some of the breadth in their behavior. In order to capture this range within a detailed study of only a few proteins, four candidate protein structures (with their cognate sequences) have been selected according to a figure of merit called the winding index—a characteristic of the number of turns the protein winds about an axis. The temperature-dependent heat capacities reveal a high-temperature collapse transition, and an infrequently observed low-temperature rearrangement transition that arises because of the presence of weak energetic frustration. Simulation results motivate the definition of a new measure of folding affinity as a sequence-dependent free energy—a function of both a reduced stability gap and high accessibility to non-native structures—that correlates strongly with folding rates. [ABSTRACT FROM AUTHOR]

The transport of many solutes across biological membranes happens with the help of specialized proteins that form water-filled channels traversing the membranes. Recent experimental and theoretical work demonstrates that solute translocation can be facilitated by attractive interactions between the channel and penetrating particle. Here we consider an important aspect of channel-facilitated passive transport, the average lifetimes in the channel for those particles that traverse the channel and those that return, as well as the total average lifetime of the particle in the channel. Exact expressions for the average lifetimes are derived in the framework of a one-dimensional diffusion model. The validity of our one-dimensional analysis is verified by good agreement of the theoretical predictions with the average lifetimes found in three-dimensional Brownian dynamics simulations. [ABSTRACT FROM AUTHOR]

We report the results of a molecular dynamics (MD) study of the effects of confinement and molecular crowding on the thermodynamics and kinetics of folding of a 46 residue off-lattice minimalist β-barrel protein. Crowding was mimicked by restricting the protein to a sphere with a soft well repulsive potential. MD simulations were performed on the protein in an unconfined environment, as well as confined to spheres of two different radii, 5.88σ and 11.76σ. Here, s is the bond length between two adjacent residues and the radius of gyration of the protein in its native state is 2.87σ. We find that for the larger sphere (1.76σ) the folding and collapse temperatures are virtually unchanged from their bulk values, but the average folding time is decreased by 35%. By contrast, the smaller sphere has a much more significant thermodynamic effect (the folding temperature is raised by 28%) but the average folding time is only decreased by 58%. Confinement is also seen to restrict the conformational space accessible to the protein in its denatured state. In addition, confinement appears to change the folding mechanism for this protein, as long-lived intermediates present in the bulk are both modified and have shorter lifetimes when the protein is confined. [ABSTRACT FROM AUTHOR]

Equilibrium configurations of rigid building blocks with multiple embedded interaction sites are investigated, as a coarse-grained approach for conformational sampling of protein structures with known secondary structure. First, hypothetical structures of asymmetric shapes, and pairs of rods composed of multiple interaction sites are considered. The rods are either disconnected or joined by a flexible loop. The sites are assumed to interact with a classical 6-12 Lennard-Jones potential. Subsequently, the investigation is extended to the study of two disconnected α helices composed of homogeneous interaction sites and to the ROP monomer, a small protein consisting of two heterogeneous α helices connected by a loop. Residue-specific long-range and short-range potentials extracted from a protein database are used. A Monte Carlo procedure combined with an energy minimization algorithm, originally developed by Li and Scheraga [Proc. Natl. Acad. Sci. USA 84, 6611 (1987)] is used to generate a set of low energy conformations over the full conformational space. Results show that: (i) The potential of mean force between two rods as a whole exhibits an inverse linear dependence on the separation between rods despite the individual sites interacting via a 6-12 Lennard-Jones potential. (ii) As the length of the rods (or helices) increases, they tend to align parallel to one other. (iii) This tendency to become parallel is enhanced when the density of interaction sites is higher. (iv) The angle between the principal axes of the rods is found to scale as n-5/3 with the number n of sites. (v) The native conformation of the ROP monomer, including the detailed rotational states of the virtual bonds located in the loop connecting the α helices is correctly predicted. This lends support to the adoption of such a coarse-grained model and its parameters for future simulations. © 1997 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Temperature quench echoes are analyzed in terms of the temperature–temperature correlation function in the harmonic approximation, and the resulting expressions are compared with molecular dynamics simulations. The relationship between the time dependence of the echo depth and the density of states is demonstrated for harmonic systems. For a protein, which has significant anharmonicity, the time dependence is dominated by relaxation effects that originate from dephasing of the periodic motions. A simple relaxation model is shown to provide a good description of the results observed in the simulations. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In order to characterise the dynamics of proteins, a well-established method is to incorporate experimental parameters as replica-averaged structural restraints into molecular dynamics simulations. Here, we justify this approach in the case of interproton distance information provided by nuclear Overhauser effects by showing that it generates ensembles of conformations according to the maximum entropy principle. These results indicate that the use of replica-averaged structural restraints in molecular dynamics simulations, given a force field and a set of experimental data, can provide an accurate approximation of the unknown Boltzmann distribution of a system. [ABSTRACT FROM AUTHOR]