Lateral diffusion of proteins in the plasma membrane: spatial tessellation and percolation theory

The obstructed diffusion of proteins in the plasma membrane is studied using computer simulation and an analysis using spatial tessellation and percolation theory. The membrane is modeled as a two-dimensional space with fixed hard disc obstacles, and the proteins are modeled as hard discs. The simulations show a transition from normal to anomalous diffusion as the area fraction, phim, of obstacles is increased and to confined diffusion for area fractions above the pecolation threshold, which occurs for phim=0.22. A Voronoi tessellation procedure is used to map the continuous space system onto an effective lattice model, with the connectivity of bonds determined from a geometric criterion. The estimate of the percolation threshold obtained from this lattice model is in excellent agreement with the simulation results, although the nature of the dynamics in the continuous space model is different from lattice models. At high obstacle area fractions (but below the percolation threshold), the primary mode of transport is a hopping motion between voids, consistent with experiment. The simulations and analysis emphasize the importance of structural correlations between obstacles.     

A minimal proteinlike lattice model: an alpha-helix motif

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.     

Computational probe of cavitation events in protein systems

Previous all-atom simulations have identified several classes of proteins where hydrophobic de-wetting (cavitation) is at play. Here we develop and validate a computationally fast method that predicts in which protein systems water spontaneously cavitates. We implement a cubic lattice model, which incorporates the protein shape from crystallographic data and the protein-water interactions from thermodynamic data. Combining it with the previously developed coarse-grained model for water, we determine the extent of occupancy of water at protein-protein interfaces and in protein-ligand cavities. The model captures essential findings from all-atom molecular dynamics studies on the same systems by distinguishing protein cavities that dry from those that remain wet. We also interpret the origin of the cavitation inside the melittin tetramer on simple thermodynamic grounds, and show that part of the mellitin surface is sufficiently hydrophobic to trigger cavitation. Using Glauber/Kawasaki dynamics we obtain the time-scales for de-wetting events that are in agreement with those from all-atom simulations. The method can serve as an intermediate step between the necessary initial screening that identifies proteins with abundance of hydrophobic patches using bioinformatics tools (L. Hua, X. H. Huang, P. Liu, R. H. Zhou and B. J. Berne, J. Phys. Chem. B, 2007, 111, 9069), and computationally extensive studies that need to incorporate molecular details (e.g. single mutation studies of amino acid residues).     

Simulations of Sol-to-Gel Modeling: Effects of Mobility,Reversibility, and Quality of Solvent

Some of our recent work on computer simulation modeling of the sol-to-gel transition for the polymerization by step reaction are presented. Depending on the variants of the model, a random distribution of bifunctional and tetrafunctional monomers of concentration C₂ and C₄ respectively, and their chains (bond-fluctuating) are used as primary reacting units on a simple cubic lattice as the initial sol-phase. Effects of solvent, temperature, mobility of monomers, rate of reaction, and reversibility are considered in understanding the evolution of microgels, onset of gelation and the nature of sol-to-gel transition, inhomogeneity, etc. Gel point (p_c, gel volume fraction (P_G), weight average degree of polymerization (M_W), structure factor (S(q, t)) show various interesting variations with the conversion factor (p). For example, sol-to-gel transition seems nonuniversal with respect to quality of the solvent, degree of inhomogeneity depends on the quality of solvent and rate of reaction due to interplay between the phase-separation and cross-linking.     

Classification of polymer structures by graph theory

Compact polymers such as proteins obtain their unique conformation by appropriate nonbonded interactions among their monomer residues. Innumerable nonnative compact conformations are also possible, and it is essential to distinguish the native from the nonnative conformations. Toward this goal we have used graph‐theoretic methods to classify polymer structures formed by noncovalent interactions. All compact structures on a 4×4 two‐dimensional lattice and a few conformations on 3×3×3 cubic lattice have been investigated. The 69 compact conformations in 4×4 two‐dimensional lattice are classified into 12 groups based on the highest eigenvalue and eigenvector. The complex graphs obtained for polymers in a 3×3×3 lattice space are analyzed. Their eigenvalues and eigenvector components are correlated with the branching structure and the center of the graph. The method has application in classifying real polymers such as proteins into their substructures, cluster, and domains. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 349–356, 1999     

蛋白质分子的HNP格点模型

从 6 0种球形蛋白质的结构出发 ,采用Miyazawa Jernigan相互作用矩阵 ,计算了蛋白质分子中氨基酸之间的相互作用能 .发现构成蛋白质分子的 2 0种氨基酸可分成疏水 (Hydrophobic ,H)、中性 (Neutral,N)、亲水(Hydrophilic ,P)基团 .在计算它们之间相互作用能的基础上 ,建立了蛋白质分子的HNP格点模型 .用这个模型计算了二维蛋白质分子在自然态 (Nativestate)时的构象性质 .同时研究了氨基酸序列为HHNHNPNHPP HPNPPHPHPPHHPHNH的折叠过程 ,得到其基态能量为 - 6 4 89RT .这能为研究球形蛋白质的构象性质及折叠过程提供一种更合理的格点模型     

Percolation of polyatomic species with the presence of impurities

In this paper, the percolation of (a) linear segments of size k and (b) k-mers of different structures and forms deposited on a square lattice contaminated with previously adsorbed impurities have been studied. The contaminated or diluted lattice is built by randomly selecting a fraction of the elements of the lattice (either bonds or sites) which are considered forbidden for deposition. Results are obtained by extensive use of finite size scaling theory. Thus, in order to test the universality of the phase transition occurring in the system, the numerical values of the critical exponents were determined. The characteristic parameters of the percolation problem are dependent not only on the form and structure of the k-mers but also on the properties of the lattice where they are deposited. A phase diagram separating a percolating from a nonpercolating region is determined as a function of the parameters of the problem. A comparison between random site and random bond percolation in the presence of impurities on the lattice is presented.     

New hydrocarbon side chain liquid crystalline polysiloxane polymers: Synthesis,characterization, and thermotropic behavior

A series of new and high-purity hydrocarbon liquid crystal monomers were synthesized through the acylation reaction, deoxygenation reaction, and Grignard reaction. ¹H-NMR spectra and elemental analyses were used to examine their purity. The liquid crystalline polysiloxane polymers were obtained by grafting the monomers onto poly(methylhydrosiloxane). The thermal transition temperature, mesomorphic properties, and mesophase textures of the monomers and the polymers were determined by differential scanning calorimetry (dsc), polarized optical microscopy, and X-ray diffraction analysis. Moreover, we observed the even–odd effect of the smectic/isotropic transition temperature with the length variation of the substituents. In this study, we found by X-ray diffraction that the liquid crystalline polysiloxane polymers undergo a transition from smectic B to smectic E mesophase. However, dsc has difficulty detecting the phase transition process. By considering the spin–lattice relaxation time (T₁), we can systematically explain the relation between the flexibility of the substituent with the smectic/isotropic transition temperature. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2849–2863, 1998     

The effect of sequence on the conformational stability of a model heteropolymer in explicit water

We investigate the properties of a two-dimensional lattice heteropolymer model for a protein in which water is explicitly represented. The model protein distinguishes between hydrophobic and polar monomers through the effect of the hydrophobic monomers on the entropy and enthalpy of the hydrogen bonding of solvation shell water molecules. As experimentally observed, model heteropolymer sequences fold into stable native states characterized by a hydrophobic core to avoid unfavorable interactions with the solvent. These native states undergo cold, pressure, and thermal denaturation into distinct configurations for each type of unfolding transition. However, the heteropolymer sequence is an important element, since not all sequences will fold into stable native states at positive pressures. Simulation of a large collection of sequences indicates that these fall into two general groups, those exhibiting highly stable native structures and those that do not. Statistical analysis of important patterns in sequences shows a strong tendency for observing long blocks of hydrophobic or polar monomers in the most stable sequences. Statistical analysis also shows that alternation of hydrophobic and polar monomers appears infrequently among the most stable sequences. These observations are not absolute design rules and, in practice, these are not sufficient to rationally design very stable heteropolymers. We also study the effect of mutations on improving the stability of the model proteins, and demonstrate that it is possible to obtain a very stable heteropolymer from directed evolution of an initially unstable heteropolymer.     

Novel methacrylate copolymers with fluorine containing: Synthesis, characterization, reactivity ratios, thermal properties and biological activity

New methacrylate based monomers 2-(4-benzoylphenoxy)-2-oxoethyl-2-methylacrylate (BOEMA), 2-(4-acetylphenoxy)-2-oxoethyl-2-methylacrylate (AOEMA), and 2-[(4-fluorophenyl)amino]-2-oxoethyl-2-methylacrylate (FPAMA), were synthesized first time. The free-radical-initiated copolymerization of AOEMA and BOEMA with FPAMA were carried out in 1,4-dioxane solution at 65 °C using 2,2′-azobisisobutyronitrile (AIBN) as an initiator with different monomer-to-monomer ratios in the feed. The monomers and copolymers were characterized by FTIR, ¹H NMR and ¹³C NMR spectral studies. The copolymer compositions were evaluated by nitrogen content in polymers. The reactivity ratios of the monomers were determined by the application of Fineman-Ross and Kelen-Tudos methods. The analysis of reactivity ratios revealed that BOEMA and AOEMA are less reactive than FPAMA, and copolymers formed are statistically in nature. The molecular weights ( and ) and polydispersity index of the polymers were determined using gel permeation chromatography. Thermogravimetric analysis of the polymers reveals that the thermal stability of the copolymers increases with an increase in the mole fraction of FPAMA in the copolymers. Glass transition temperatures of the copolymers were found to decrease with an increase in the mole fraction of FPAMA in the copolymers. The prepared homo and copolymers were tested for their antimicrobial activity against bacteria, fungi and yeast.     

The effect of matrix structure on the diffusion of fluids in porous media

The effect of matrix structure on the transport properties of adsorbed fluids is studied using computer simulations and percolation theory. The model system consists of a fluid of hard spheres diffusing in a matrix of hard spheres fixed in space. Three different arrangements of the fixed spheres, random, templated, and polymeric, are investigated. For a given matrix volume fraction the diffusion coefficient of the fluid, D, is sensitive to the manner in which the matrix is constructed, with large differences between the three types of matrices. The matrix is mapped onto an effective lattice composed of vertices and bonds using a Voronoi tessellation method where the connectivity of bonds is determined using a geometric criterion, i.e., a bond is connected if a fluid particle can pass directly between the two pores the bond connects, and disconnected otherwise. The percolation threshold is then determined from the connectivity of the bonds. D displays universal scaling behavior in the reduced volume fraction, i.e., D approximately (1-phi(m)phi(c))(gamma), where phi(m) is the matrix volume fraction and phi(c) is the matrix volume fraction at the percolation threshold. We find that gamma approximately 2.2, independent of matrix type, which is different from the result gamma approximately 1.53 for diffusion in lattice models, but similar to that for conduction in Swiss cheese models. Lattice simulations with biased hopping probabilities are consistent with the continuous-space simulations, and this shows that the universal behavior of diffusion is sensitive to details of local dynamics.     

Exact sequence analysis for three-dimensional hydrophobic-polar lattice proteins

We have exactly enumerated all sequences and conformations of hydrophobic-polar (HP) proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the HP model, where only two types of monomers are distinguished, we determined and statistically analyzed designing sequences, i.e., sequences that have a nondegenerate ground state. Furthermore we were interested in characteristic thermodynamic properties of HP proteins with designing sequences. In order to be able to perform these exact studies, we applied an efficient enumeration method based on contact sets.     

Simulating the collapse transition of a two-dimensional semiflexible lattice polymer

It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness epsilon(b). In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first order as long as epsilon(b) is positive [H. Zhou et al., Phys. Rev. Lett. 97, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a two-dimensional lattice polymer. The system's phase diagram at zero force is obtained. Depending on epsilon(b) and the temperature T, the polymer can be in one of the three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous and the globule-coil transition is continuous. At moderate or high values of epsilon(b) the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition.     

Synthesis and Characterization of Novel Methacrylate Monomers Having Pendant Oxime Esters and Their Copolymerization with Styrene

New methacrylate monomers, 2‐{[(diphenylmethylene)amino]oxy}‐2‐oxoethyl methacrylate (DPOMA) and 2‐{[(1‐phenylethylidene)ami no]oxy}‐2‐oxoethyl methacrylate (MMOMA) were prepared by reaction of sodium methacrylate with diphenylmethanone O‐(2‐chloroacetyl) oxime and 1‐phenylethanone O‐(2‐chloroacetyl) oxime, respectively. They were obtained from a reaction of chloroacetyl chloride with benzophenone oxime or acetophenone oxime. The free‐radical‐initiated copolymerization of (DPOMA) and (MMOMA) with styrene (St) were carried out in 1,4‐dioxane solution at 65°C using 2,2‐azobisisobutyronitrile (AIBN) as an initiator with different monomer‐to‐monomer ratios in the feed. The monomers and copolymers were characterized by FTIR, ¹H‐ and ¹³C‐NMR spectral studies. The copolymer compositions were evaluated by nitrogen content in polymers. The reactivity ratios of the monomers were determined by the application of Fineman–Ross and Kelen–Tüdös methods. The molecular weights (M¯_w and M¯_n) and polydispersity index of the polymers were determined by using gel permeation chromatography. Thermogravimetric analysis of the polymers reveals that the thermal stability of the copolymers increases with an increase in the mole fraction of St in the copolymers. The activation energies of the thermal degradation of the polymers were calculated with the MHRK method. Glass transition temperatures of the copolymers were found to decrease with an increase in the mole fraction of DPOMA or MMOMA in the copolymers. The antibacterial and antifungal effects of the monomers and polymers were also investigated on various bacteria and fungi. The photochemical properties of the polymers were investigated by UV and FTIR spectra.     

Lattice models of branched polymers with specified topologies

As a step towards understanding the thermodynamics of multi-branched polymer systems, we look at a lattice model of a uniform branched polymer with fixed topology interacting with a surface and ask for the free energy of the polymer as the number of monomers which compose the polymer goes to infinity. The conformations of a uniform branched polymer with fixed topology are modelled by embeddings of a graph in the simple cubic lattice. Rigorous results about this model are reviewed. The results suggest that large branched polymers in three dimensions interacting with a plane have the same free energy as large linear polymers interacting with a plane; the same is not true, however, for the corresponding two-dimensional problem where the polymer interacts with a line.     

Properties of grafted amphiphilic chains. A computer simulation study

The model of a heteropolymer film formed by polypeptide chains was used for theoretical considerations. The linear chains consisting of amino acid residues were approximated by alpha carbon chains. Each chain was constructed on a very flexible [310] lattice. The inter- and intramolecular interactions consisted of the long-range contact potential between residues. The chains were built of hydrophilic and hydrophobic residues. Chains were terminally attached to an impenetrable surface with lateral motions possible. The Monte Carlo simulations of this model were carried out by using the Metropolis algorithm. The influence of the grafting density, the sequence of the amino acid residues, and the temperature on the static properties of the formed layer were studied and discussed. It was shown that homopolymer chains collapsed at higher temperature than the heteropolymers. The size of the polymers forming brush was smaller for homopolymers than for heteropolymers. The structure of the resulting polymer film and of its external surface was determined. The block copolymers formed well defined hydrophobic and hydrophilic layers, while for the amphiphilic case the composition of the brush layers changed continuously at high temperature. It was observed that the latter effect vanished at the collapsed amphiphilic copolymer.     

氨基酸功能化环辛烯单体的区域及立体选择性开环易位聚合

合成具有可控初级结构的侧链型氨基酸聚合物,使其与具有完全精确初级结构的生物大分子相媲美,在高分子合成化学中仍然是一个长期的挑战。 在本文中,设计与合成了(环辛基-2-烯-1-羰基)-L-亮氨酸酰胺甲酯(1)和(环辛基-2-烯-1-羰基)-L-亮氨酸酰胺(2),通过Grubbs二代催化的开环易位聚合,合成了具有高反式双键选择性、高头尾区域选择性的亮氨酸衍生均聚物以及共聚物,这些聚合物具有相对较窄的相对分子质量分布(1.3~1.6)。 当组成为n(1)：n(2)=50：50嵌段共聚物在丙酮中形成以亲水嵌段poly(2)为核,疏水嵌段poly(1)为壳的半径为30 nm的反相胶束。 然而,相同组成的无规共聚物则难溶于丙酮中。这些具有明确的区域及立体结构的氨基酸衍生聚合物为仿生材料的相关应用奠定了基础。     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

Affinity Polymers Tailored for the Protein A Binding Site of Immunoglobulin G Proteins

Rational design in combination with a screening process was used to develop affinity polymers for a specific binding site on the surface of immunoglobulin G (IgG) proteins. The concept starts with the identification of critical amino acid residues on the protein interface and their topological arrangement. Appropriate binding monomers were subsequently synthesized. Together with a sugar monomer (2–5 equiv) for water solubility and a dansyl monomer (0.5 equiv) as a fluorescent label, they were subjected in aqueous solution to linear radical copolymerization in various compositions (e.g., azobisisobutyronitrile (AIBN), homogeneous water/DMF mixtures). After ultrafiltration and lyophilization, colorless dry water‐soluble powders were obtained. NMR spectroscopic and gel permeation chromatography (GPC) characterization indicated molecular weights between 30 and 500 kD and confirmed retention of monomer composition as well as the absence of monomers. In a competitive enzyme‐linked immunosorbent assay (ELISA) screen of the polymer libraries (20–50 members), few copolymers qualified as strong and selective binders for the protein A binding site on the Fc fragment of the antibody. Their monomer composition precisely reflected the critical amino acids found at the interface. The simple combination of a charged and a nonpolar binding monomer sufficed for selective submicromolar IgG recognition by the synthetic polymer. Affinities were confirmed by fluorescence titrations; they increased with decreasing salt load but remained largely unaltered at lowered pH. Other proteins, including those of similar size and isoelectric point (pI), were bound 10–1000 times less tightly. This example indicates that interaction domains in other proteins may also be targeted by synthetic polymers if their comonomer composition reflects the nature and arrangement of amino acid residues on the protein surface.