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.     

Kinetics of loop formation in polymer chains

We investigate the kinetics of loop formation in ideal flexible polymer chains (the Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is tau(c) approximately tau(0)N(2) (where tau(0) is a microscopic time scale and N is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when a, the capture radius for contact formation, exceeds b, the average distance between two connected beads. Simulations also show that when a < b, tau(c) approximately N(alpha)(tau), where 1.5 < alpha(tau) < or = 2 in the range 7 < N < 200 used in the simulations. By using a diffusion coefficient that is dependent on the length scales a and b (with a < b), which captures the two-stage mechanism by which looping occurs when a < b, we obtain an analytic expression for tauc that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly effected when interactions between monomers are taken into account. Remarkably, for N < 100, the values of tau(c) decrease by more than 2 orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for tau(c) to a power law in N (tau(c) approximately N(alpha)(tau)) show that alpha(tau) varies from about 2.4 in a good solvent to about 1.0 in poor solvents. The effective exponent alpha(tau) decreases as the strength of the attractive monomer-monomer interactions increases. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain. The time for contact formation between beads that are interior to the chain in good solvents changes nonmonotonically as the loop length varies. In contrast, the variation in interior loop closure time is monotonic in poor solvents. The implications of our results for contact formation in polypeptide chains, RNA, and single-stranded DNA are briefly outlined.     

The intrinsic stiffness of polyglutamine peptides

We have used the method of Trp/Cys contact quenching to measure the rate of contact formation in polyglutamine and find it to be a very stiff peptide. Separation of observed rates into reaction-limited and diffusion-limited rates show that the reaction-limited rates increase (rather than decrease) slightly with length between 4 and 16 amino acids. Using Szabo, Schulten, and Schulten theory, we have modeled the results with a wormlike chain with excluded volume and find the persistence length to be about 13.0 A, much longer than has been observed for other random peptides and unfolded proteins. The preferred extended conformation of polyglutamine could account for a propensity for expanded glutamine stretches to unfold the Huntington's protein and the high propensity to aggregate from a disordered monomer.     

THE DISTRIBUTION FUNCTION OF RESIDUE-RESIDUE CONTACTS IN PROTEIN MOLECULES

In protein molecules each residue has a different ability to form contacts.In this paper,we calculated the number of contacts per residue and investigated the distribution of residue-residue contacts from 495 globular protein molecules using Contacts of Structural Units(CSU)software.It was found that the probability P(n)of amino acid residues having n pairs of contacts in all contacts fits Gaussian distribution very well.The distribution function of residue-residue contacts can be expressed as:P(n)=P_0+aexp[-b(n-n_c)~2].In our calculation,P_0=-0.06,α=11.4,b=-0.04 and n_c=9.0.According to distribution function,we found that those hydrophobic(H)residues including Leu,Val,Ile,Met,Phe,Tyr,Cys,and Trp residues have large values of the most probable number of contact n_c,and hydrophilic(P)residues including Ala,Gly,Thr, His,Glu,Gln,Asp,Asn,Lys,Ser,Arg,and Pro residues have the small ones.We also compare with Fauchere-Pliska hydrophobicity scale(FPH)and the most probable number of contact n_c for 20 amino acid residues,and find that there exists a linear relationship between Fauchere-Pliska hydrophobicity scale(FPH)and the most probable number of contact n_c, and it is expressed as:n_c=a+b×FPH,here α=8.87,and b=1.15.It is important to further explain protein folding and its stability from residue-residue contacts.     

类蛋白质分子形成紧密接触对的速率研究

采用Kolinski等建立的类蛋白质分子的格点模型,通过计算类蛋白质分子的末端距分布函数P(r)来研究类蛋白质分子形成紧密接触对的速率k .发现不同的氨基酸序列,其分布函数P(r)不同.对于序列(H) x和(P) x,分布函数P(r)有二个峰值;而对于序列(HP) x,分布函数P(r)只有一个峰值.对于类蛋白质分子形成紧密接触对的速率k ,当链长N <11,随着N的增加而增加;当N >11,形成紧密接触对的速率k随着N的增加而减少,这个趋势与实验结果一致,并存在关系k～N-α(N >11) ,系数α与氨基酸序列有关.这些研究能够帮助我们加深对蛋白质结构形成的了解.     

A ruler for determining the position of proteins in membranes

Both the oxygen diffusion rate and the oxygen solubility vary with depth into the interior of biological membranes. The product of these two gradients generates a single gradient, a permeability gradient, which is a smooth continuous function of the distance from the center of the membrane. Using electron paramagnetic resonance and the spin-probe method, the relaxation gradient of oxygen, which is directly proportional to the permeability gradient, is the quantity that can be directly measured in membranes under physiological conditions. The gradient obtained provides a calibrated ruler for determining the membrane depth of residues either from loop regions of membrane-binding proteins or from the membrane-exposed residues of transmembrane proteins. We have determined the relaxation gradient of oxygen in zwitterionic and anionic phospholipid membranes by attaching a single nitroxide probe to a transmembrane alpha-helical polypeptide at specific residues. The peptide ruler was used to determine the depth of penetration of the calcium-binding loops of the C2 domain of cytosolic phospholipase A(2). The positions of selected residues of this membrane-binding protein that penetrate into the membrane, determined using this ruler, compared favorably with previous determinations using more complex methods. The relaxation gradient constrains the possible values of the membrane-dependent oxygen concentration and the oxygen diffusion gradients. The average oxygen diffusion coefficient is estimated to be at least 2-fold smaller in the membrane than that in water.     

Experimental evidence of distance-dependent diffusion coefficients of a globular protein observed in polymer aqueous solution forming a network structure on nanometer scale

The distance dependence of the diffusion coefficient (DDDC) of a globular protein (cytochrome c) in aqueous hyaluronan (HA) solution, which is a model system for extracellular matrices (ECMs), was measured by a combination of three kinds of spectroscopic measurements of diffusion coefficients, the time and space samplings of which are different. The results of the three methods are plotted against the diffusion distance derived from the consideration of each experimental condition. Due to the characteristic morphology of HA with an effective mesh structure, the proteins showed two extreme diffusion modes: (1) short (<10 nm) diffusion with rare contact with polymer chains; (2) long (>100 nm) diffusion significantly disrupted by polymer chains showing an approximately 30% reduction in diffusion coefficient. The transition from the short diffusion to the long one occurs in a very narrow range (10-100 nm) of diffusion distance and this unique character of HA realizing anomalous diffusion should provide suitable environments for various bioactivities when involved in ECM.     

Termination rate constant in free-radical polymerization

The specific rate constant for the termination reaction between two flexible polymer molecules with active chain ends has been considered in relation to the segmental diffusion of chain ends in solution. The probability of reaction between two chain ends per unit time when the centers of gravity of two polymer molecules are at a distance of separation has been calculated by using the Smoluchowski equation and a Gaussian distribution of chain ends. The time during which two polymer molecules are in contact has also been calculated by using the diffusion equation and the potential energy function for intermolecular interaction. The rate constant may then be completely expressed as a complex function of the intramolecular linear expansion factor, molecular weight, and the frictional properties of the reacting polymers' segment. This expression predicts that the rate constant is inversely proportional to solvent viscosity, decreasing with increasing molecular weight to some extent, and is affected by the excluded volume effect and chain flexibility. The complete expression for the rate constant has been simplified and the result compared with experimental data. Close agreement is found between the calculated rate constants and those experimentally obtained.     

二DMF-μ-四酞酰替对甲苯胺合二铜的晶体结构和电子结构的研究

本文报导了的晶体结构。晶体属三斜晶系, 空间群P_1, 晶胞参数: a=1.0761(2), b=1.3930(4), c=1.5117(4) nm; α=114.74(2)°,β=101.82(2)°,γ=95.85(2)°; Z=1。标题化合物为四羧基桥的双核铜(II)簇合物, DMF占据端基位置。Cu-Cu距离0.2635(2) nm, 有微弱成键作用。SCC-EHMO计算表明前线轨道38A_g, 37B_u, 21A_u和20B_g能级相当接近, 化合物为顺磁性, μ(eff)=1.82B.M., 根据顺磁谱出现的由三组峰组成的一套谱, 其中在低场的一组峰分裂7条超精细结构峰, 判断化合物顺磁性应是占据38A_g, 和37B_u分子轨道上未配对电子的贡献。Cu-Cu的成键和反键的σ, π和δ型轨道都填满电子, 因此对成键不起作用。Cu-Cu之间的微弱成键作用, 主要是通过铜与羧基桥原子形成的非定域键的34B_u和18A_u分子轨道的贡献。     

Observation of diffusion and tunneling recombination of dye-photoinjected electrons in ultrathin TiO2 layers by surface photovoltage transients

Surface photovoltage transients were used to monitor both the short time dynamics (>10 ns) and the spatial distribution of electrons photoinjected in thin (2-20 nm) TiO2 layers from dye molecules adsorbed at the surface. At low temperatures (100-250 K), the dynamics are governed exclusively by spatially dependent tunneling recombination, with a rate that varies with the distance from the surface x as exp(-2x/a), and an initial exponential distribution of photoinjected electrons, n0 exp(-x/b). This model is confirmed by the observation of power law decay in time t(-a/2b) with a ratio a/b = 0.28 +/- 0.04. The stability of cis-di(isothiocyanato)-N-bis(2,2'-bipyridine-4,4'-dicarboxy) ruthenium(II) (N3) dye molecules on TiO2 during treatment in a vacuum at high temperatures was proven. For high temperatures (250-540 K), the thickness dependence of the decays indicates that the dynamics of surface recombination are retarded by the diffusion of electrons toward the interior of the film. The implications for thin layer coating in dye-sensitized solar cells are discussed.     

Contact pair dynamics during folding of two small proteins: chicken villin head piece and the Alzheimer protein beta-amyloid

The folding of an extended protein to its unique native state requires establishment of specific, predetermined, often distant, contacts between amino acid residue pairs. The dynamics of contact pair formation between various hydrophobic residues during folding of two different small proteins, the chicken villin head piece (HP-36) and the Alzheimer protein beta-amyloid (betaA-40), are investigated by Brownian dynamics (BD) simulations. These two proteins represent two very different classes-HP-36 being globular while betaA-40 is nonglobular, stringlike. Hydropathy scale and nonlocal helix propensity of amino acids are used to model the complex interaction potential among the various amino acid residues. The minimalistic model we use here employs a connected backbone chain of atoms of equal size while an amino acid is attached to each backbone atom as an additional atom of differing sizes and interaction parameters, determined by the characteristics of each amino acid. Even for such simple models, we find that the low-energy structures obtained by BD simulations of both the model proteins mimic the native state of the real protein rather well, with a best root-mean-square deviation of 4.5 A for HP-36. For betaA-40 (where a single well-defined structure is not available), the simulated structures resemble the reported ensemble rather well, with the well-known beta-bend correctly reproduced. We introduce and calculate a contact pair distance time correlation function, C(P) (ij)(t), to quantify the dynamical evolution of the pair contact formation between the amino acid residue pairs i and j. The contact pair time correlation function exhibits multistage dynamics, including a two stage fast collapse, followed by a slow (microsecond long) late stage dynamics for several specific pairs. The slow late stage dynamics is in accordance with the findings of Sali et al. Analysis of the individual trajectories shows that the slow decay is due to the attempt of the protein to form energetically more favorable pair contacts to replace the less favorable ones. This late stage contact formation is a highly cooperative process, involving participation of several pairs and thus entropically unfavorable and expected to face a large free energy barrier. This is because any new pair contact formation among hydrophobic pairs will require breaking of several contacts, before the favorable ones can be formed. This aspect of protein folding dynamics is similar to relaxation in glassy liquids, where also alpha relaxation requires highly cooperative process of hopping. The present analysis suggests that waiting time for the necessary pair contact formation may obey the Poissonian distribution. We also study the dynamics of Forster energy transfer during folding between two tagged amino acid pairs. This dynamics can be studied by fluorescence resonance energy transfer (FRET). It is found that suitably placed donor-acceptor pairs can capture the slow dynamics during folding. The dynamics probed by FRET is predicted to be nonexponential.     

Interaction of hydrophobized filaments in aqueous electrolyte solutions

The apparatus developed earlier to measure dispersion forces has been applied in the measurement of the forces of attraction between hydrophobic (θ ≈ 100°) silica filaments immersed in water and the disjoining pressure before the samples are brought into contact, as a function of the distance separating the filaments, H (for gaps H=20 to 60 nm). The attraction forces and disjoining pressure exceeded by one to two orders of magnitude the dispersion forces, and decayed exponentially as the distance increased. The decay length was 12 to 13 nm — considerably larger than for the structural repulsive forces in thin interlayers of polar liquids adjoining lyophilic surfaces.

The result for gaps H<20 nm (the decay length equal to about 3 nm) is in qualitative agreement with the works of Israelachvili, Pashley and Claesson.

The attractive forces decayed still more slowly as the distance increased after the samples' contact position was reached. The presence of hysteresis of forces allows a conclusion to be drawn on the formation of a vapour-gas bubble when the samples are brought into contact. This confirms the Schchukin-Yushchenko statement.     

α-Fe和γ-Fe长程F-S势的分子动力学模拟

根据Sutton等推导面心立方金属长程F-S势函数的方法推导得到α-Fe 和γ-Fe 的最优参数分别为, ε=0.2453, a=0.28664 nm, n=7, m=4, c=7.7525 和ε=0.0006, a=0.36467 nm, n=15, m=4, c=1104.7351. 用所推导的势参数对常压下不同温度时α-Fe和γ-Fe的性质进行了分子动力学(MD)模拟, 结果表明, 计算得到的Fe的微观结构(径向分布函数, 配位数, 原子的配位状态)和宏观物性(线性膨胀, 密度)都能与实验结果相吻合, 说明所推导的长程F-S势函数参数适用于α-Fe和γ-Fe的MD模拟.     

Quantifying the protein core flexibility through analysis of cavity formation

We present an extensive analysis of cavity statistics in the interior of three different proteins, in liquid n-hexane, and in water performed using molecular-dynamics simulations. The heterogeneity of packing density over atomic length scales in different parts of proteins is evident in the wide range of values observed for the average cavity size, the probability of cavity formation, and the corresponding free energy of hard-sphere insertion. More interestingly, however, the distribution of cavity sizes observed at various points in the protein interior is surprisingly homogeneous in width. That width is significantly smaller than that measured for similar distributions in liquid n-hexane or water, indicating that protein interior is much less flexible than liquid hexane. The width of the cavity size distribution correlates well with the experimental isothermal compressibility data for liquids and proteins. An analysis of cavity statistics thus provides an efficient method to quantify local properties, such as packing, stiffness, or compressibility in heterogeneous condensed media.     

Long distance energy transfer in a polymer matrix doped with a perylene dye

Exciton migration over long distances is a key issue for various applications in organic electronics. We investigate a disordered material system which has the potential for long exciton diffusion lengths in combination with a high versatility. The perylene bisimide dye Perylene Red is incorporated in a polymer matrix with a high concentration. The dye molecules represent active sites with a narrow energy distribution for the electronically excited states. Excitons can be efficiently exchanged between them by F?rster resonance energy transfer (FRET). The narrow energy distribution reduces drastically the trapping probability of the excitons compared to polymers and allows for long transfer distances. To characterize the mobility of the excitons and their diffusion length the dye Oxazine 1 is added as an acceptor in low concentration and the transfer probability to the acceptor is determined by measuring the reduction of Perylene Red fluorescence. The quenched quantum yield is measured for dye concentrations varying from 0.05?M to 0.15 M for Perylene Red and from 0.3 mM to 3 mM for Oxazine 1. The experimental results are compared to a model which assumes that excitons can diffuse through the material by FRET between Perylene Red sites and are trapped at an acceptor with a final hetero FRET step. We find a quite good match between theory and experiment though the observed diffusion constant is about two times smaller than the calculated one. The exciton diffusion length extracted from the data is 30 nm for a Perylene Red concentration of 0.1 M and demonstrates that long distance energy transfer is possible in this disordered material system.     

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     

Kinetics of interior loop formation in semiflexible chains

Loop formation between monomers in the interior of semiflexible chains describes elementary events in biomolecular folding and DNA bending. We calculate analytically the interior distance distribution function for semiflexible chains using a mean field approach. Using the potential of mean force derived from the distance distribution function we present a simple expression for the kinetics of interior looping by adopting Kramers theory. For the parameters, that are appropriate for DNA, the theoretical predictions in comparison with the case are in excellent agreement with explicit Brownian dynamics simulations of wormlike chain (WLC) model. The interior looping times (tauIC) can be greatly altered in the cases when the stiffness of the loop differs from that of the dangling ends. If the dangling end is stiffer than the loop then tauIC increases for the case of the WLC with uniform persistence length. In contrast, attachment of flexible dangling ends enhances rate of interior loop formation. The theory also shows that if the monomers are charged and interact via screened Coulomb potential then both the cyclization (tauc) and interior looping (tauIC) times greatly increase at low ionic concentration. Because both tauc and tauIC are determined essentially by the effective persistence length [lp(R)] we computed lp(R) by varying the range of the repulsive interaction between the monomers. For short range interactions lp(R) nearly coincides with the bare persistence length which is determined largely by the backbone chain connectivity. This finding rationalizes the efficacy of describing a number of experimental observations (response of biopolymers to force and cyclization kinetics) in biomolecules using WLC model with an effective persistence length.     

(α/β)_8桶状蛋白质中紧密接触对的统计性质研究

在计算蛋白质分子中的氨基酸紧密接触对时采用以氨基酸的重心代替Cα 原子的新方法 ,通过计算(α/β) 8桶状蛋白质中的中程和远程紧密接触对的数目 ,研究了不同氨基酸在形成紧密接触对时所具有的不同能力以及在蛋白质结构稳定性中所起的不同作用 .发现在 (α β) 8桶状蛋白质中氨基酸形成的远程紧密接触对数目与它的Fauchere Pliska疏水性实验数值 (FPH)存在着非常好的线性关系 ,而对于氨基酸所形成的中程紧密接触对数目不存在这种关系 .同时还研究了 (α β) 8桶状蛋白质分子大小 ,发现其回转半径大小与表示远程接触对数目的远程次序值LRO存在着关系 .表明这一类 (α β) 8桶状蛋白质具有相似的结构 ,分子的远程接触对数目越多 ,分子越紧密 ,分子尺寸就越小 .同时还研究了不同氨基酸之间形成紧密接触对的能力 .     

Understanding diffusion in confined systems: methane in a ZK4 molecular sieve. A molecular dynamics simulation study

The equilibrium probability distribution of N methane molecules adsorbed in the interior of n alpha cages of the ZK4 zeolite, the all-silica analogue of zeolite A, is modeled by a modified hypergeometric distribution where the effects of mutual exclusion between particles are extracted from long molecular dynamics simulations. The trajectories are then analyzed in terms of time-correlation functions for the fluctuations in the occupation number of the alpha cages. The analysis digs out the correlations induced by the spatial distribution of the adsorbed molecules coupled with a migration mechanism where a molecule can pass from one alpha cage to another, one-by-one. These correlations lead to cooperative motion, which manifests itself as a nonexponential decay of the correlators. Our results suggest ways of developing improved lattice approaches that may be useful for studying diffusion in much larger systems and for a much longer observation time.     

Interfacial Activity of the Diprotonated 222 Cryptand at the Water/"Oil" Interface Revealed by Molecular Dynamics Simulations

Abstract

Orange II (I) is easily soluble in H₂O. It requires several months for the formation of needle-like crystals from a 0.16 M (saturated) aqueous solution. But when 0.03 M γ-cyclodextrin (γ-CD) is added to an equivalent of (I) at RT, the solution exhibits enhancement of the viscosity in an hour, and the microscopic viewing indicates the formation of a pine needle-like aggregate. Enough old millet jelly-like one shows well arranged stripe pattern upon rubbing. In the induced c.d. spectrum, the π→π* band of this complex appears at ～500 nm in the solution state, but in the aggregate state, it changes to the J-band due to the head-to-tail stacking of (I) and the H-band due to parallel stacking. When MeOH is poured onto the aggregate, the latter changes colour from orange to silver-gray, but keeps the same shape. The driving force for the aggregate formation may be 1. van der Walls contact between γ-CD and two molecules of (I),

2. π-π interaction between the two molecules of (I) in γ-CD,

3. H-bonding and stacking effects between γ-CD.

In this chiral aggregate, γ-CD works as an adhesive for the azo dye.