Dynamic information for cardiotoxin protein desorption from a methyl-terminated self-assembled monolayer using steered molecular dynamics simulation

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.     

Computer simulations of the translocation and unfolding of a protein pulled mechanically through a pore

Protein degradation by ATP-dependent proteases and protein import into the mitochondrial matrix involve the unfolding of proteins upon their passing through narrow constrictions. It has been hypothesized that the cellular machinery accomplishes protein unfolding by pulling mechanically at one end of the polypeptide chain. Here, we use Langevin dynamics simulations of a minimalist off-lattice model to examine this hypothesis and to study the unfolding of a protein domain pulled mechanically through a long narrow pore. We compute the potential of mean force (PMF) experienced by the domain as a function of its displacement along the pore and identify the unfolding intermediates corresponding to the local minima of the PMF. The observed unfolding mechanism is different from that found when the two termini are pulled apart, as in single-molecule mechanical unfolding experiments. It depends on the pore diameter, the magnitude of the pulling force, and on whether the force is applied at the N- or the C-terminus of the chain. Consequently, the translocation time exhibits a pulling force dependence that is more complex than a simple exponential function expected on the basis of simple phenomenological models of translocation.     

Molecular simulation of interaction between passivated gold nanoparticles in supercritical CO2

Molecular dynamics simulations have been performed to study the potential of mean force (PMF) between passivated gold nanoparticles (NPs) in supercritical CO(2) (scCO(2)). The nanoparticle model consists of a 140 atom gold nanocore and a surface self-assembled monolayer, in which two kinds of fluorinated alkanethiols were considered. The molecular origin of the thermodynamics interaction and the solvation effect has been comprehensively studied. The simulation results demonstrate that increasing the solvent density and ligand length can enhance the repulsive feature of the free energy between the passivated Au nanoparticles in scCO(2), which is in good agreement with previous experimental results. The interaction forces between the two passivated NPs have been decomposed to reveal various contributions to the free energy. It was revealed that the interaction between capping ligands and the interaction between the capping ligands and scCO(2) solvent molecules cooperatively determine the total PMF. A thermodynamic entropy-energy analysis for each PMF contribution was used to explain the density dependence of PMF in scCO(2) fluid. Our simulation study is expected to provide a novel microscopic understanding of the effect of scCO(2) solvent on the interaction between passivated Au nanoparticles, which is helpful to the dispersion and preparation of functional metal nanoparticles in supercritical fluids.     

Free energy calculation using molecular dynamics simulation combined with the three-dimensional reference interaction site model theory. II. Thermodynamic integration along a spatial reaction coordinate

We propose the thermodynamic integration along a spatial reaction coordinate using the molecular dynamics simulation combined with the three-dimensional reference interaction site model theory. This method provides a free energy calculation in solution along the reaction coordinate defined by the Cartesian coordinates of the solute atoms. The proposed method is based on the blue moon algorithm which can, in principle, handle any reaction coordinate as far as it is defined by the solute atom positions. In this article, we apply the present method to the complex formation process of the crown ether 18-Crown-6 (18C6) with the potassium ion in an aqueous solution. The separation between the geometric centers of these two molecules is taken to be the reaction coordinate for this system. The potential of mean force (PMF) becomes the maximum at the separation between the molecular centers being ～4 A?, which can be identified as the free energy barrier in the process of the molecular recognition. In a separation further than the free energy barrier, the PMF is slightly reduced to exhibit a plateau. In the region closer than the free energy barrier, approach of the potassium ion to the center of 18C6 also decreases the PMF. When the potassium ion is accommodated at the center of 18C6, the free energy is lower by -5.7 ± 0.7 kcal/mol than that at the above mentioned plateau or converged state. By comparing the results with those from the free energy calculation along the coupling parameters obtained in our previous paper [T. Miyata, Y. Ikuta, and F. Hirata, J. Chem. Phys. 133, 044114 (2010)], it is found that the effective interaction in water between 18C6 and the potassium ion vanishes beyond the molecular-center-separation of 10 A?. Furthermore, the conformation of 18C6 is found to be significantly changed depending upon the 18C6-K(+) distance. A proper conformational sampling and an accurate solvent treatment are crucial for realizing the accurate PMF, and we believe that the proposed method is useful to evaluate the PMF in a solution. A discussion upon the PMF in terms of the three-dimensional distribution function for the solvent is also presented.     

Microscopic simulations of molecular cluster decay: Does the carrier gas affect evaporation?

We develop a kinetic theory of cluster decay by considering the stochastic motion of molecules within an effective potential of mean force (PMF) due to the cluster. We perform molecular dynamics simulations on a 50-atom argon cluster to determine the mean radial force on a component atom and hence the confining potential of mean force. Comparisons between isolated clusters and clusters thermostatted through the presence of a 100-atom helium carrier gas show that the heat bath has only a slight effect upon the PMF. This confirms the validity of calculations of cluster properties using isolated cluster simulations. The PMF is used to calculate the atomic evaporation rate from these clusters, and results are compared with the predictions of the capillarity approximation together with detailed balance, both components of the classical theory of aerosol nucleation.     

Transient violations of the second law of thermodynamics in protein unfolding examined using synthetic atomic force microscopy and the fluctuation theorem

The synthetic atomic force microscopy (AFM) method is developed to simulate a periodically replicated atomistic system subject to force and length fluctuations characteristic of an AFM experiment. This new method is used to examine the forced-extension and subsequent rupture of the alpha-helical linker connecting periodic images of a spectrin protein repeat unit. A two-dimensional potential of mean force (PMF) along the length and a reaction coordinate describing the state of the linker was calculated. This PMF reveals that the basic material properties of the spectrin repeat unit are sensitive to the state of linker, an important feature that cannot be accounted for in a one-dimensional PMF. Furthermore, nonequilibrium simulations were generated to examine the rupture event in the context of the fluctuation theorem. These atomistic simulations demonstrate that trajectories which are in apparent violation of the second law can overcome unfolding barriers at significantly reduced rupture forces.     

Analysis of the unfolding process of green fluorescent protein by molecular dynamics simulation

Molecular dynamics simulation of the enforced stretching of circularly permuted green fluorescent protein (cpGFP) was performed to observe the detailed process of unfolding of beta-sheets in cpGFP and to clarify the structural change arising from the force. The simulation using the generalized Born method with original force field parameters enabled us to observe the unfolding process of the entire region of the protein and to clarify atom motion of the individual domain during the stretching. The force required for the stretching of cpGFP was estimated from the differential of the computed potential energy. A prominent rise in force appeared three times during the stretching. The amplitude and the position of these three peaks were consistent with the observation in atomic force microscopy (AFM) experiments. Further, the movements of atoms involved in each peak were shown to be closely related to the dissociation of hydrogen bonds. Additional simulations for the unfolding process of titin and spectrin also gave satisfactory interpretation of the results of previous AFM experiments. The difference in the enforced stretching process between cpGFP and wild-type GFP was further discussed through the MD simulation.     

On the mechanism of surfactant adsorption on solid surfaces: free-energy investigations

The adsorption free-energy of surfactant on solid surfaces has been calculated by molecular dynamics (MD) simulation for a model surfactant/solvent system. The umbrella-sampling with the weight histogram analysis method (WHAM) was applied. The entropic and enthalpic contributions to the full potential of mean force (PMF) were obtained to evaluate the detailed thermodynamics of surfactant adsorption in solid/liquid interfaces. Although we observed that this surfactant adsorption process is driven mainly by a favorable enthalpy change, a highly unfavorable entropic contribution still existed. By decomposing the free energy (including its entropic and enthalpic components) into the solvent-induced contribution and the surfactant-wall term, the effect of surface and solvent on the adsorption free-energy has been distinguished. The contribution to the PMF from the surface effect is thermodynamically favorable, whereas the solvent term displays an obviously unfavorable component with a monotonic increase as the surfactant approaches to the surface. The impact of various interactions from the surfaces (both solvent-philic and solvent-phobic) and the solvent on the adsorption PMF of surfactant has been compared and discussed. Compared to the solvent-philic surface, the solvent-phobic surface generates more stable site for the surfactant adsorption. However, the full PMF profile for the solvent-phobic system shows a clear positive maximum value at the bulk-interface transition region, which leads to a considerable long-range free-energy barrier to the surfactant adsorption. These results have been analyzed in terms of the local interfacial structures. In summary, this comprehensive study is expected to reveal the microscopic interaction mechanisms determining the surfactant adsorption on solid surfaces.     

The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models

Coarse-grained (CG) models provide a computationally efficient method for rapidly investigating the long time- and length-scale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarse-graining (MS-CG) method [J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force (PMF) that governs the equilibrium distribution of positions of the CG sites for the MS-CG models. A CG model that employs such a PMF as a "potential energy function" will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.     

DNA Structural Changes Under Different Stretching Methods Studied By Molecular Dynamics Simulations

We present a molecular dynamics simulation study of 22‐mer DNA conformational variations obtained by stretching both 3′‐termini and both 5′‐termini. Stretching 3′‐termini by 3.5 nm required 142 kJ mol^?1 and the force plateau was ～80 pN, whereas stretching 5′‐termini by the same length required 190 kJ mol^?1 and the force plateau was ～100 pN. Stretching 3′‐termini led to a larger untwisting of the double helix and the successive base pairs rolled to the side of the DNA minor groove, while stretching 5′‐termini resulted in the base pairs rolling to the major groove side and reducing of the diameter of DNA molecule. The most distinctive difference between stretching 3′‐termini and 5′‐termini was that at the force plateau region stretching the 5′‐termini resulted in breakage of the base pairs, which considerably disturbed the structure of the DNA double helix. All of the variations of base rotation and translation for both stretching methods took place when the relative length of DNA l was longer than 1.2, which was the point the force plateau appeared.     

Calculating potentials of mean force from steered molecular dynamics simulations

Steered molecular dynamics (SMD) permits efficient investigations of molecular processes by focusing on selected degrees of freedom. We explain how one can, in the framework of SMD, employ Jarzynski's equality (also known as the nonequilibrium work relation) to calculate potentials of mean force (PMF). We outline the theory that serves this purpose and connects nonequilibrium processes (such as SMD simulations) with equilibrium properties (such as the PMF). We review the derivation of Jarzynski's equality, generalize it to isobaric--isothermal processes, and discuss its implications in relation to the second law of thermodynamics and computer simulations. In the relevant regime of steering by means of stiff springs, we demonstrate that the work on the system is Gaussian-distributed regardless of the speed of the process simulated. In this case, the cumulant expansion of Jarzynski's equality can be safely terminated at second order. We illustrate the PMF calculation method for an exemplary simulation and demonstrate the Gaussian nature of the resulting work distribution.     

The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models

The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM(+)NO(3) (-) ionic liquid are provided to illustrate the method.     

碳纳米管膜分离Li+/Mg2+的分子动力学模拟

采用"扶手椅"型碳纳米管建立了连续的碳纳米管膜模型,利用分子动力学模拟方法研究了Li+和Mg2+在膜中的传导行为.模拟研究了不同管径的碳纳米管CNTs(7,7),(8,8),(9,9),(10,10),(11,11)对Li+和Mg2+的通透性,检测了两种离子进入管内时的平均力势,探索了两种离子在碳纳米管内的径向、轴向密度分布,观测了个别离子在管内的运动轨迹.结果表明,模拟中CNTs(9,9)用于有效分离Li+和Mg2+的效果较好.管径不同,导致Li+和Mg2+通量不同,平均力势(PMF)差值不同,同时离子的轨迹和径向、轴向密度分布也有所差异.总之,碳纳米管是一种可将Li+和Mg2+分离的潜在材料.     

Molecular dynamics simulation of the association of nonpolar spheres in water

We apply molecular dynamics (MD) simulations to the study of the association of nonpolar spheres of effective radii between 1.6 and 6.1 A dissolved in water. The constrained MD method is used to calculate the potential of mean force (PMF) of the interaction between spheres. The depth of the potential of mean force increases with increasing radius of the nonpolar sphere. Our results suggest that the PMF is largely governed by size or entropic effects, and that energetic effects associated with the breaking or distortion of hydrogen bonds are of minor importance.     

Absolute free energy calculations by thermodynamic integration in four spatial dimensions

An optimized technique for calculating the excess chemical potential of small molecules in dense liquids and the binding affinity of molecular ligands to biomolecules is reported. In this method, a molecular species is coupled to the system of interest via a nonphysical fourth spatial dimension w through which insertion or extraction can be carried out [R. Pomes, E. Eisenmesser, C. B. Post et al., J. Chem. Phys. 111, 3387 (1999)]. Molecular simulations are used to compute the potential of mean force (PMF) acting on the solute molecule in the fourth dimension. The excess chemical potential of that molecule is obtained as the difference in the PMF between fully coupled and fully decoupled systems. The simplicity, efficiency, and generality of the method are demonstrated for the calculation of the hydration free energies of water and methanol as well as sodium, cesium, and chloride ions. A significant advantage over other methods is that the 4D-PMF approach provides a single effective and general route for decoupling all nonbonded interactions (i.e., both Lennard-Jones and Coulombic) at once for both neutral and charged solutes. Direct calculation of the mean force from thermodynamic integration is shown to be more computationally efficient than calculating the PMF from umbrella sampling. Statistical error analysis suggests a simple strategy for optimizing sampling. The detailed analysis of systematic errors arising from the truncation of Coulombic interactions in a solvent droplet of finite size leads to straightforward corrections to ionic hydration free energies.     

Potential of mean force calculations of ligand binding to ion channels from Jarzynski's equality and umbrella sampling

Potential of mean force (PMF) calculations provide a reliable method for determination of the absolute binding free energies for protein-ligand systems. The common method used for this purpose -- umbrella sampling with weighted histogram analysis -- is computationally very laborious, which limits its applications. Recently, a much simpler alternative for PMF calculations has become available, namely, using Jarzynski's equality in steered molecular dynamics simulations. So far, there have been a few comparisons of the two methods and mostly in simple systems that do not reflect the complexities of protein-ligand systems. Here, we use both methods to calculate the PMF for ion permeation and ligand binding to ion channels. Comparison of results indicate that Jarzynski's method suffers from relaxation problems in complex systems and would require much longer simulation times to yield reliable PMFs for protein-ligand systems.     

A comparison of methods to compute the potential of mean force.

Most processes occurring in a system are determined by the relative free energy between two or more states because the free energy is a measure of the probability of finding the system in a given state. When the two states of interest are connected by a pathway, usually called reaction coordinate, along which the free-energy profile is determined, this profile or potential of mean force (PMF) will also yield the relative free energy of the two states. Twelve different methods to compute a PMF are reviewed and compared, with regard to their precision, for a system consisting of a pair of methane molecules in aqueous solution. We analyze all combinations of the type of sampling (unbiased, umbrella-biased or constraint-biased), how to compute free energies (from density of states or force averaging) and the type of coordinate system (internal or Cartesian) used for the PMF degree of freedom. The method of choice is constraint-bias simulation combined with force averaging for either an internal or a Cartesian PMF degree of freedom.     

单分子操作技术在核酸研究中的应用

单分子操作技术,如原子力显微镜技术、光镊技术和单分子荧光光谱技术,能够对单分子局部力进行测量,因而能在单分子水平上研究核酸的弹性性质和机械诱导的结构转变。单分子操作技术已越来越多地应用于相关的核酸研究中,如DNA的打开与修饰、DNA．蛋白质相互作用、DNA凝聚、复制和转录。与经典的分子生物学技术相比,单分子操作技术避免了从大量实验结果中取平均的需要,因而可以提供更为详细的生物信息。本文概述了单分子操作技术的原理及其在核酸研究中的应用。     

Interaction of cationic liposomes with cell membrane models

The colloidal dispersion stability of nano-sized graphene sheets in supercritical fluid (SCF) media is very important for developing SCF-based exfoliation and dispersion technologies for stabilization and solubilization of graphenes. We carried out molecular dynamics simulations to elucidate the stability mechanism of graphene in supercritical CO(2) (scCO(2)). The potential of mean force (PMF) between two graphene nanosheets in scCO(2) was simulated, and the effect of scCO(2) density and temperature on the PMF behavior has been investigated. The simulation results demonstrate that there exists a free energy barrier between graphenes in the scCO(2) fluid, possibly obstructing the aggregation of graphenes. The single-layer confined CO(2) molecules between the graphene sheets can induce a dominating repulsion interaction between graphene sheets. At higher scCO(2) fluid density, there are more confined CO(2) molecules within the interplate regions, resulting in a stronger repulsive free energy barrier. The effect of temperature on the PMF is relatively minor. The scCO(2) solvent structure shows layered confined arrangement in the interfacial region near the graphene nanosheets, which is correlated well with the PMF profile curve.     

钙离子对表面活性剂单层膜聚集结构的影响

采用分子动力学模拟研究了气液界面上钙离子对阴离子表面活性剂十二烷基苯磺酸钠单层膜聚集结构的影响.结果表明,单层膜结构与表面覆盖度及Ca2＋离子存在与否均有关系.Ca2＋离子能够压缩表面活性剂极性头使聚集结构排列更加紧密,均力势体现了Ca2＋离子与极性头之间的结合能力强弱,二者之间的相互作用与稳定的溶剂分离极小值有关,而Ca2＋离子需要克服一个溶剂能障才能与之发生相互作用,并引起极性头周围水分子结构的重排.模拟表明,分子动力学方法可以在分子水平上研究无机盐离子对表面活性剂单层膜水化结构的影响,解释无机盐离子在界面膜中的动力学行为.