Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Traveling wave magnetophoresis for high resolution chip based separations

A new mode of magnetophoresis is described that is capable of separating micron-sized superparamagnetic beads from complex mixtures with high sensitivity to their size and magnetic moment. This separation technique employs a translating periodic potential energy landscape to transport magnetic beads horizontally across a substrate. The potential energy landscape is created by superimposing an external, rotating magnetic field on top of the local fixed magnetic field distribution near a periodic arrangement of micro-magnets. At low driving frequencies of the external field rotation, the beads become locked into the potential energy landscape and move at the same velocity as the traveling magnetic field wave. At frequencies above a critical threshold, defined by the bead's hydrodynamic drag and magnetic moment, the motion of a specific population of magnetic beads becomes uncoupled from the potential energy landscape and its magnetophoretic mobility is dramatically reduced. By exploiting this frequency dependence, highly efficient separation of magnetic beads has been achieved, based on fractional differences in bead diameter and/or their specific attachment to two microorganisms, i.e., B. globigii and S. cerevisiae.     

Acidification of three-dimensional emeraldine polymers: Search for minimum energy paths from base to salt

We present a numerical simulation of the HCl acidification process of a three-dimensional semiconducting emeraldine base (EB) polymer leading to the corresponding metallic emeraldine salt form. We have searched minimum energy paths connecting the initial configuration, composed of two EB polymer chains per cell each one attached by two HCl molecules, with the Pc2a polaronic configuration which is the final state of the acidification process. For this aim, the variational nudged elastic band method has been adopted. We provide a pictorial representation of the acidification process at T=0 K, monitoring the EB protonation and the evolution of the polymeric chains and of the positions of the Cl(-) counterions on the lowest potential energy surface. To include also temperature effects, we have explored the potential energy surface around the final equilibrium configuration, heating the system and following its dynamics by the Car-Parrinello procedure.     

Modifying the OPLS-AA force field to improve hydration free energies for several amino acid side chains using new atomic charges and an off-plane charge model for aromatic residues

The hydration free energies of amino acid side chains are an important determinant of processes that involve partitioning between different environments, including protein folding, protein complex formation, and protein-membrane interactions. Several recent papers have shown that calculated hydration free energies for polar and aromatic residues (Trp, His, Tyr, Asn, Gln, Asp, Glu) in several common molecular dynamics force fields differ significantly from experimentally measured values. We have attempted to improve the hydration energies for these residues by modifying the partial charges of the OPLS-AA force field based on natural population analysis of density functional theory calculations. The resulting differences between calculated hydration free energies and experimental results for the seven side chain analogs are less than 0.1 kcal/mol. Simulations of the synthetic Trp-rich peptide Trpzip2 show that the new charges lead to significantly improved geometries for interacting Trp-side chains. We also investigated an off-plane charge model for aromatic rings that more closely mimics their electronic configuration. This model results in an improved free energy of hydration for Trp and a somewhat altered benzene-sodium potential of mean force with a more favorable energy for direct benzene-sodium contact.     

Monte Carlo method for computing density of states and quench probability of potential energy and enthalpy landscapes

The thermodynamics and kinetics of a many-body system can be described in terms of a potential energy landscape in multidimensional configuration space. The partition function of such a landscape can be written in terms of a density of states, which can be computed using a variety of Monte Carlo techniques. In this paper, a new self-consistent Monte Carlo method for computing density of states is described that uses importance sampling and a multiplicative update factor to achieve rapid convergence. The technique is then applied to compute the equilibrium quench probability of the various inherent structures (minima) in the landscape. The quench probability depends on both the potential energy of the inherent structure and the volume of its corresponding basin in configuration space. Finally, the methodology is extended to the isothermal-isobaric ensemble in order to compute inherent structure quench probabilities in an enthalpy landscape.     

Theoretical investigation of excited states of C(3)

In this work, we present ab initio calculations for the potential energy surfaces of C(3) in different electronic configurations, including the singlet ground state [X (1)Sigma(g) (+),((1)A(1))], the triplet ground state [a (3)Pi(u),((3)B(1), (3)A(1))], and some higher excited states. The geometries studied include triangular shapes with two identical bond lengths, but different bond angles between them. For the singlet and triplet ground states in the linear geometry, the total energies resulting from the mixed density functional--Hartree-Fock and quadratic configuration interaction methods reproduce the experimental values, i.e., the triplet occurs 2.1 eV above the singlet. In the geometry of an equilateral triangle, we find a low-lying triplet state with an energy of only 0.8 eV above the energy of the singlet in the linear configuration, so that the triangular geometry yields the lowest excited state of C(3). For the higher excited states up to about 8 eV above the ground state, we apply time-dependent density functional theory. Even though the systematic error produced by this approach is of the order of 0.4 eV, the results give different prospective to insight into the potential energy landscape for higher excitation energies.     

Phase behavior of semiflexible polymer chains

Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01sigma and 1.05sigma (where sigma is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02sigma and 2.1sigma. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10相似文献   

Adsorption-driven translocation of polymer chain into nanopores

The polymer translocation into nanopores is generally facilitated by external driving forces, such as electric or hydrodynamic fields, to compensate for entropic restrictions imposed by the confinement. We investigate the dynamics of translocation driven by polymer adsorption to the confining walls that is relevant to chromatographic separation of macromolecules. By using the self-consistent field theory, we study the passage of a chain trough a small opening from cis to trans compartments of spherical shape with adsorption potential applied in the trans compartment. The chain transfer is modeled as the Fokker-Plank diffusion along the free energy landscape of the translocation pass represented as a sum of the free energies of cis and trans parts of the chain tethered to the pore opening. We investigate how the chain length, the size of trans compartment, the magnitude of adsorption potential, and the extent of excluded volume interactions affect the translocation time and its distribution. Interplay of these factors brings about a variety of different translocation regimes. We show that excluded volume interactions within a certain range of adsorption potentials can cause a local minimum on the free energy landscape, which is absent for ideal chains. The adsorption potential always leads to the decrease of the free energy barrier, increasing the probability of successful translocation. However, the translocation time depends non-monotonically of the magnitude of adsorption potential. Our calculations predict the existence of the critical magnitude of adsorption potential, which separates favorable and unfavorable regimes of translocation.     

A recipe for the computation of the free energy barrier and the lowest free energy path of concerted reactions

The recently introduced hills method (Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) is a powerful tool to compute the multidimensional free energy surface of intrinsically concerted reactions. We have extended this method by focusing our attention on localizing the lowest free energy path that connects the stable reactant and product states. This path represents the most probable reaction mechanism, similar to the zero temperature intrinsic reaction coordinate, but also includes finite temperature effects. The transformation of the multidimensional problem to a one-dimensional reaction coordinate allows for accurate convergence of the free energy profile along the lowest free energy path using standard free energy methods. Here we apply the hills method, our lowest free energy path search algorithm, and umbrella sampling to the prototype S(N)2 reaction. The hills method replaces the in many cases difficult problem of finding a good reaction coordinate with choosing relatively simple collective variables, such as the bond lengths of the broken and formed chemical bonds. The second part of the paper presents a guide to using the hills method, in which we test and fine-tune the method for optimal accuracy and efficiency using the umbrella sampling results as a reference.     

Conformational and packing stability of crystalline polymers. VI. Stable chain packing of polyethylene

The stable packings of polyethylene chains were investigated by intermolecular potential energy calculations based on various chain-assembly models. The structures of the two crystal modifications of polyethylene (i.e., orthorhombic and the monoclinic), together with their cell constants and the setting angles, were well reproduced. The packing modes of polymethylene chains found in various alkane derivatives were also explained by the energy minima of the chain-assembly models. In these calculations, several sets of potential functions were tried and three sets of functions were found to reproduce conformations of single polymer chains, the cell constants of polyethylene at low temperature, and those at room temperature.     

ADSORPTION OF SHORT TWO-DIMENSIONAL COMPACT CHAINS

Short two-dimensional compact chains adsorbed on the attractive surface at different temperatures were investigated by using the enumeration calculation method. First we investigate the chain size and shape of adsorbed chains, such as characteristic ratios of mean-square radii of gyration 〈S^2〉x/N and 〈S^2〉y/N, shape factor 〈δ〉, and the orientation of chain bonds 〈cos^2 θ〉 to illuminate how the size and shape of adsorbed compact chains change with increasing temperatures. There are some special behaviors for the chain size and shape at low temperature, especially for strong attraction interaction. In the meantime, adsorbed compact chains have different behaviors from general adsorbed polymer chains. Some thermodynamics properties are also discussed here. Heat capacity changes non-monotonously, first increases and then reduces. The transition temperature Tc is nearly 1.0, 1.4, 2.0 and 4.2 （in the unit of To） for the case of ε = 0, -1, -2 and -4 （in the unit of kTo）, respectively. Average energy per bond increases while average Helmholtz free energy per bond decreases with increasing temperatures. From these two thermodynamics parameters we can also get another transition temperature Tc＇, and it is close to 0.7, 1.1, 1.5 and 3.4 for ε= 0, -1, -2, and -4, respectively. Therefore, Tc is greater than Tc＇ under the same condition. These investigations may provide some insights into the thermodynamics behaviors of adsorbed protein-like chains.     

Coupled ion and network dynamics in polymer electrolytes: Monte Carlo study of a lattice model

Monte Carlo simulations are used to study ion and polymer chain dynamic properties in a simplified lattice model with only one species of mobile ions. The ions interact attractively with specific beads in the host chains, while polymer beads repel each other. Cross linking of chains by the ions reduces chain mobilities which in turn suppresses ionic diffusion. Diffusion constants for ions and chains as a function of temperature follow the Vogel-Tammann-Fulcher (VTF) law with a common VTF temperature at low ion concentration, but both decouple at higher concentrations, in agreement with experimental observations. Our model allows us to introduce pressure as an independent variable through calculations of the equation of state using the quasichemical approximation, and to detect an exponential pressure dependence of the ionic diffusion.     

Intramolecularly ordered globules and the collapse of short chains

We investigate the poor-solvent collapse of short chains having different stiffness through self-consistent minimization of the intramolecular free energy under the constraint of fixed segment lengths between adjacent beads. At first the chains form the Random Gaussian Globule, where the beads are distributed at random at the same average distance from the centre of mass, while the segments show very little correlation. At a larger attractive potential, this collapsed globule undergoes a transition to one or more ordered compact states, depending on the chain stiffness. Under very strong contraction, all chains are described as a Compact Ordered Globule: the beads are again at a constant average distance from the centre of mass, while the segments jump back and forth at the globule's wall with a very large correlation. At intermediate contraction, the thinner and stiffer chains form the Oscillating Ordered Globule wherein the beads are alternatively distributed on two concentric on two concentric shells. In this case, we also find metastable states with nonsymmetrical conformations of the chain with respect to its ends. We also briefly discuss the thermodynamics of the coil-globule and globule-globule transitions, showing that in long polymer chains these ordered conformations cannot involve the whole chain. However, we suggest that they might still be found as local globules that form for kinetic reasons.     

EFFECTS OF SECONDARY STRUCTURE ON ELASTIC BEHAVIOR OF PROTEIN-LIKE CHAINS

The elastic behavior of protein-like chains was investigated by using the Pruned-Enriched-Rosenbluth Method (PERM).Three typical protein-like chains such as all-α,all-β,and α+β(α/β) proteins were studied in our modified orientation dependent monomer-monomer interaction (ODI) model.We calculated the ratio of /N and shape factor <δ*> of protein-like chains in the process of elongation.In the meantime,we discussed the average energy per bond ＜U＞/N,average contact energy per bond ＜U＞c/N,average helical energy per bond ＜U＞h/N and average sheet energy per bond ＜U＞b/N.Three maps of contact formation,α-helix formation,β-sheet formation were depicted.All the results educe a view that the helix structure is the most stable structure,while the other two structures are easy to be destroyed.Besides,the average Helmholtz free energy per bond ＜A＞/Nis was presented.The force f obtained from the free energy was also discussed.It was shown that the chain extended itself spontaneously first.The force was studied in the process of elongation.Lastly,the energy contribution to elastic force fu was calculated too.It was noted that fu for all-β chains increased first,and then decreased with x0 increasing.     

Elucidating Peptide and Protein Structure and Dynamics: UV Resonance Raman Spectroscopy

UV resonance Raman spectroscopy (UVRR) is a powerful method that has the requisite selectivity and sensitivity to incisively monitor biomolecular structure and dynamics in solution. In this perspective, we highlight applications of UVRR for studying peptide and protein structure and the dynamics of protein and peptide folding. UVRR spectral monitors of protein secondary structure, such as the Amide III(3) band and the C(α)-H band frequencies and intensities can be used to determine Ramachandran Ψ angle distributions for peptide bonds. These incisive, quantitative glimpses into conformation can be combined with kinetic T-jump methodologies to monitor the dynamics of biomolecular conformational transitions. The resulting UVRR structural insight is impressive in that it allows differentiation of, for example, different α-helix-like states that enable differentiating π- and 3(10)- states from pure α-helices. These approaches can be used to determine the Gibbs free energy landscape of individual peptide bonds along the most important protein (un)folding coordinate. Future work will find spectral monitors that probe peptide bond activation barriers that control protein (un)folding mechanisms. In addition, UVRR studies of sidechain vibrations will probe the role of side chains in determining protein secondary, tertiary and quaternary structures.     

Elastic Behaviors of Adsorbed Protein-like Chains

Elastic behaviors of protein-like chains are investigated by Pruned-Enriched-Rosenbluth method and modified orientation-dependent monomer-monomer interactions model. The protein-like chain is pulled away from the attractive surface slowly with elastic force acting on it. Strong adsorption interaction and no adsorption interaction are both considered. We calculate the characteristic ratio and shape factor of protein-like chains in the process of elongation. The conformation change of the protein-like chain is well depicted. The shape of chain changes from “rod” to “sphere” at the beginning of elongation. Then, the shape changes from “sphere” to “rod”. In the end, the shape becomes a “sphere” as the chain leaves away from the surface. In the meantime, we discuss average Helmoholtz free energy per bond, average energy per bond, average adsorbed energy per bond, average α-helical energy per bond, average β-sheet energy per bond and average contact energy per bond.On the other hand, elastic force is also studied. It is found that elastic force has a long plateau during the tensile elongation when there exists adsorption interaction. This result is consistent with SMFS experiment of general polymers. Energy contribution to elastic force and contact energy contribution to elastic force are both discussed. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

Direct UV Raman monitoring of 3(10)-helix and pi-bulge premelting during alpha-helix unfolding

We used UV resonance Raman (UVRR) spectroscopy exciting at approximately 200 nm within the peptide bond pi --> pi* transitions to selectively study the amide vibrations of peptide bonds during alpha-helix melting. The dependence of the amide frequencies on their Psi Ramachandran angles and hydrogen bonding enables us, for the first time, to experimentally determine the temperature dependence of the peptide bond Psi Ramachandran angle population distribution of a 21-residue mainly alanine peptide. These Psi distributions allow us to easily discriminate between alpha-helix, 3(10)-helix and pi-helix/bulge conformations, obtain their individual melting curves, and estimate the corresponding Zimm and Bragg parameters. A striking finding is that alpha-helix melting is more cooperative and shows a higher melting temperature than previously erroneously observed. These Psi distributions also enable the experimental determination of the Gibbs free energy landscape along the Psi reaction coordinate, which further allows us to estimate the free energy barriers along the AP melting pathway. These results will serve as a benchmark for the numerous untested theoretical studies of protein and peptide folding.     

Conformational transition free energy profiles of an adsorbed, lattice model protein by multicanonical Monte Carlo simulation

Proteins often undergo changes in internal conformation upon interacting with a surface. We investigate the thermodynamics of surface induced conformational change in a lattice model protein using a multicanonical Monte Carlo method. The protein is a linear heteropolymer of 27 segments (of types A and B) confined to a cubic lattice. The segmental order and nearest neighbor contact energies are chosen to yield, in the absence of an adsorbing surface, a unique 3x3x3 folded structure. The surface is a plane of sites interacting either equally with A and B segments (equal affinity surface) or more strongly with the A segments (A affinity surface). We use a multicanonical Monte Carlo algorithm, with configuration bias and jump walking moves, featuring an iteratively updated sampling function that converges to the reciprocal of the density of states 1/Omega(E), E being the potential energy. We find inflection points in the configurational entropy, S(E)=k ln Omega(E), for all but a strongly adsorbing equal affinity surface, indicating the presence of free energy barriers to transition. When protein-surface interactions are weak, the free energy profiles F(E)=E-TS(E) qualitatively resemble those of a protein in the absence of a surface: a free energy barrier separates a folded, lowest energy state from globular, higher energy states. The surface acts in this case to stabilize the globular states relative to the folded state. When the protein surface interactions are stronger, the situation differs markedly: the folded state no longer occurs at the lowest energy and free energy barriers may be absent altogether.     

Folding of the 25 residue Abeta(12-36) peptide in TFE/water: temperature-dependent transition from a funneled free-energy landscape to a rugged one

The free-energy landscape of the Alzheimer beta-amyloid peptide Abeta(12-36) in a 40% (v/v) 2,2,2-trifluoroethanol (TFE)/water solution was determined by using multicanonical molecular dynamics simulations. Simulations using this enhanced conformational sampling technique were initiated from a random unfolded polypeptide conformation. Our simulations reliably folded the peptide to the experimental NMR structure, which consists of two linked helices. The shape of the free energy landscape for folding was found to be strongly dependent on temperature: Above 325 K, the overall shape was funnel-like, with the bottom of the funnel coinciding exactly with the NMR structure. Below 325 K, on the other hand, the landscape became increasingly rugged, with the emergence of new conformational clusters connected by low free-energy pathways. Finally, our simulations reveal that water and TFE solvate the polypeptide in different ways: The hydrogen bond formation between TFE and Abeta was enhanced with decreasing temperature, while that between water and Abeta was depressed.     

Adsorption‐Induced Structural Phase Transformation in Nanopores

We report a new type of structural transformation occurring in methane adsorbed in micropores. The observed methane structures are defined by probability distributions of molecular positions. The mechanism of the transformation has been modeled using Monte Carlo method. The transformation is totally determined by a reconstruction of the probability distribution functions of adsorbed molecules. The methane molecules have some freedom to move in the pore but most of the time they are confined to the positions around the high probability adsorption sites. The observed high‐probability structures evolve as a function of temperature and pressure. The transformation is strongly discontinuous at low temperature and becomes continuous at high temperature. The mechanism of the transformation is influenced by a competition between different components of the interaction and the thermal energy. The methane structure represents a new state of matter, intermediate between solid and liquid.