Percolation transition of hydration water: from planar hydrophilic surfaces to proteins

The formation of a spanning hydrogen-bonded network of hydration water is found to occur via a 2D percolation transition in various systems: smooth hydrophilic surfaces, the surface of a single protein molecule, protein powder, and diluted peptide solution. The average number of water-water hydrogen bonds at the percolation threshold varies from 2.0 to 2.3, depending on temperature, system size, and surface properties. Calculation of nH allows an easy estimation of the percolation threshold of hydration water in various systems, including biomolecules.     

Definition of percolation thresholds on self-affine surfaces

We study the percolation transition on a two-dimensional substrate with long-range self-affine correlations. We find that the position of the percolation threshold on a correlated lattice is no longer unique and depends on the spanning rule employed. Numerical results are provided for spanning across the lattice in specified (horizontal or vertical), either or both directions.     

Efficient Monte Carlo algorithm and high-precision results for percolation

We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at p(c) = 0.592 746 21(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.     

Water dynamics as affected by interaction with biomolecules and change of thermodynamic state: a neutron scattering study

The dynamics of water as subtly perturbed by both the interaction with biomolecules and the variation of temperature and pressure has been investigated via neutron scattering spectroscopy. A measurement of inelastic neutron scattering devoted to the study of the coherent THz dynamics of water in a water-rich mixture with DNA (hydration level of 1 g DNA/15 g D(2)O) at room temperature is reported. The DNA hydration water coherent dynamics is characterised by the presence of collective modes, whose dispersion relations are similar to those observed in bulk water. These dispersion relations are well described by the interaction model developed in the case of bulk water, and the existence of a fast sound is experimentally demonstrated. The behaviour of the collective water dynamics was complemented by studying the single-particle dynamics of bulk water along the isotherm T = 298 K in the pressure range 0.1-350 MPa by means of incoherent scattering. This experiment is an attempt to simulate the change of the water molecular arrangement due to the interaction with DNA, by increasing the pressure as the presence of the biomolecule produces an increase in the density. An anomaly is found in the behaviour of the relaxation time derived from the quasi-elastic scattering signal, which can be related to the hypothetical second critical point in water. This anomaly and the transition from slow to fast sound take place in the same Q range, thus suggesting that the two phenomena could be related at some microscopic level.     

Glass transition in biomolecules and the liquid-liquid critical point of water

Using molecular dynamics simulations, we investigate the relation between the dynamic transitions of biomolecules (lysozyme and DNA) and the dynamic and thermodynamic properties of hydration water. We find that the dynamic transition of the macromolecules, sometimes called a "protein glass transition," occurs at the temperature of dynamic crossover in the diffusivity of hydration water and also coincides with the maxima of the isobaric specific heat C_{P} and the temperature derivative of the orientational order parameter. We relate these findings to the hypothesis of a liquid-liquid critical point in water. Our simulations are consistent with the possibility that the protein glass transition results from crossing the Widom line, which is defined as the locus of correlation length maxima emanating from the hypothesized second critical point of water.     

Explosive percolation in the human protein homology network

We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process and is markedly different from regular random percolation. The underlying mechanism of this transition can be described by slow-growing clusters that remain isolated until the later stages of the process, when the addition of a small number of links leads to the rapid interconnection of these modules into a giant cluster. Our results indicate that the evolutionary-based process that shapes the topology of the H-PHN through duplication-divergence events may occur in sudden steps, similarly to what is seen in first-order phase transitions.     

Small-angle light scattering studies of dense AOT-water-decane microemulsions

Summary We have performed extensive studies of a three-component microemulsion system composed of AOT-water-decane (AOT=sodium-bis-ethylhexyl-sulfosuccinate is an ionic surfactant) using small-angle light scattering (SALS). The small-angle scattering intensities are measured in the angular interval 0.001–0.1 radians, corresponding to a Bragg wave number range of 0.14 μm⁻¹<Q<<1.4 μm⁻¹. The measurements were made by changing temperature and volume fraction ϕ of the dispersed phase (water + AOT) in the range 0.05<ϕ<0.75. All samples have a fixed water-to-AOT molar ratio,w=[water]/[AOT]=40.8, in order to keep the same average droplet size in the stable one-phase region. With the SALS technique, we have been able to observe all the phase boundaries of a very complex phase diagram with a percolation line and many structural organizations within it. We observe at the percolation transition threshold, a scaling behavior of the intensity data. This behavior is a consequence of a clustering among microemulsion droplets near the percolation threshold. In addition, we describe in detail a structural transition from a droplet microemulsion to a bicontinuous one as suggested by a recent small-angle neutron scattering experiment. The loci of this transition are located several degrees above the percolation temperatures and are coincident with the maxima previously observed in shear viscosity. From the data analysis, we show that both the percolation phenomenon and this novel structural transition are derived from a large-scale aggregation between microemulsion droplets.     

Percolation in Media with Columnar Disorder

We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power-law tails with continuously varying non-universal powers. This region is very similar to the Griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction, and the proof follows essentially the same arguments as in that case. But in contrast to directed percolation in disordered media, the number of active (“growth”) sites in a growing cluster at criticality shows a power law, while the probability of a cluster to continue to grow shows logarithmic behavior.     

On a sharp transition from area law to perimeter law in a system of random surfaces

We introduce and study a phase transition which is associated with the spontaneous formation of infinite surface sheets in a Bernoulli system of random plaquettes. The transition is manifested by a change in the asymptotic behavior of the probability of the formation of a surface, spanning a prescribed loop. As such, this transition offers a generalization of the bond percolation phenomenon. At low plaquette densities, the probability for large loops is shown to decay exponentially with the loops' area, whereas for high densities the decay is by a perimeter law. Furthermore, we show that the two phases of the three dimensional plaquette system are in a precise correspondence with the two phases of the dual system of random bonds. Thus, if a natural conjecture about the phase structure of the bond percolation model is true, then there is a sharp transition in the asymptotic behavior of the surface events. Our analysis incorporates block variables, in terms of which a non-critical system is transformed into one which is close to a trivial, high or low density, fixed point. Stochastic geometric effects like those discussed here play an important role in lattice gauge theories.     

Optical percolation in ceramics assisted by porous clusters

We investigated optical transparency in ceramics assisted by disordered porous clusters. The structure and statistical properties of three-dimensional (3D) well porous ceramics is studied. Theoretical model based on the percolation theory and numerical simulations are applied to interpret the observed phase transition from an optically opaque state to a transparent state. The porous ceramic samples were fabricated by the technique of slurry casting. The transmission of optical radiation (optical percolation) over the entire porous samples is observed since the critical concentration of porosity was exceeded. We explain this effect by the rising of the spanning cluster inside of the porous structure that produces a network of porous voids. Our experimental results are in good agreement with the numerical simulations.     

Limited universality at the percolation threshold in 2 to 6 dimensions

The universality of the spanning fraction R(p) of percolation is confirmed by comparing bond percolation with site-bond percolation in four to six dimensions. However, different boundary conditions change the universality class, as shown also for site percolation in two dimensions.     

Dynamic facilitation picture of a higher-order glass singularity

We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a discontinuous glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions.     

水合作用与pH调控聚电解质刷的构象转变

我们基于Flory-Huggins理论,建立理论模型研究水合作用与pH调控聚电解质刷的构象转变.理论模型考虑聚电解质链与水分子间的作用(聚电解质链的水合作用)、体系中的静电作用.研究发现,随着水合作用的改变,聚电解质刷出现由溶胀到塌缩的构象转变.由此表明了水合作用可在很大程度调节聚电解质刷的相变.通过分析pH的调控效应我们还发现,在碱性环境中(pH=8),聚电解质链单体的解离度增大,静电排斥会使得聚电解质刷溶胀.由此表明,聚电解质刷内水合作用与静电效应的耦合,将会共同决定聚电解质刷的构象转变特性.理论结果深刻揭示了水合作用的改变,会使得聚电解质刷体系发生相变,pH可在很大程度上改变其相变特性.     

Common features in the microscopic dynamics of hydration water on organic and inorganic surfaces

The microscopic dynamics of hydration water exhibits some universal features that do not depend on the nature of the hydrated surface. We show that the hydration level dependence of the dynamic transition in the mean squared atomic displacements measured by means of elastic neutron scattering is qualitatively similar for hydration water in inorganic and organic hosts. The difference is that the former are 'rigid', whereas the dynamics of the latter can be enhanced by the motions of the hydration water. The overall hydration level appears to be the main parameter governing the magnitude of the mean squared atomic displacements in the hydration water, irrespective of the details of the hydrated host.     

Dynamical scaling of the structure factor of some non-Euclidean systems

Predictions of nonlinear theories on dynamics of new phase formation have been examined for the hydration of calcium silicates with light water and heavy water. In the case of hydration with light water, reasonable agreement has been observed with dynamical scaling hypothesis with a new measure of the characteristic length. The characteristic length does not follow a power law relation with time. Hydrating mass is found to be mass fractal throughout hydration, with mass fractal dimension increasing with time. But, in the case of hydration with heavy water, no agreement has been observed with the scaling hypothesis. Hydrating mass undergoes transition from mass fractal to surface fractal and finally again to mass fractal. The qualitative features of the kinetics of hydration, as measured in small-angle scattering experiments, are strikingly different for hydration with light water and heavy water.     

Explosive percolation transition is actually continuous

Recently a discontinuous percolation transition was reported in a new "explosive percolation" problem for irreversible systems [D. Achlioptas, R. M. D'Souza, and J. Spencer, Science 323, 1453 (2009)] in striking contrast to ordinary percolation. We consider a representative model which shows that the explosive percolation transition is actually a continuous, second order phase transition though with a uniquely small critical exponent of the percolation cluster size. We describe the unusual scaling properties of this transition and find its critical exponents and dimensions.     

水溶液中结合水的定义与量化

水溶液中溶质的结合水具有不同于远离溶质的自由水的结构和性质.结合水的存在对水和溶质结构和动力学性质均具有显著甚至决定性的影响.然而,对结合水动力学和热力学性质的定量理解在诸多方面一直存在争议甚至严重分歧,其中重点包括如何定义和量化结合水,如何表征结合水和自由水的动力学差别,结合水如何参与生物大分子各种生物功能过程,以及溶质或界面影响结合水结构与性质的途径等.给出结合水定义的物理学依据和量化方法,是深入理解上述问题的第一步.本文简述了各种不同谱学方法定义结合水的基本原理及量化的困难,强调具有不同时间和空间响应尺度的测试方法所得结合水数不必完全可比.此外,系列水溶液物性随浓度升高会明显改变其浓度依赖关系,相应拐点浓度常被用于量化稀溶液中的溶质结合水数.我们近期研究的水溶液玻璃化转变温度-浓度关系,为结合水的定义、量化和水溶液的三区划分提供了物理依据,同时揭示了上述利用性质-浓度关系拐点浓度量化结合水方法的不足.     

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%_b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study.     

Transition rates and sequential decay of excited nuclei

We present two possible sequential decay mechanisms which correspond either to an inverse fusion process (detailed balance) or to a generalised fission process (transition state theory). We compare the corresponding transition rates and try to understand the implications of these two different choices on the behaviour of mass and charge multiplicities. Deviations from percolation calculation predictions and the experiment are also analysed.     

Hofmeister series and ionic effects of alkali metal ions on DNA conformation transition in normal and less polarised water solvent

Normal and less polarised water models are used as the solvent to investigate Hofmeister effects and alkali metal ionic effects on dodecamer d(CGCGAATTCGCG) B-DNA with atomic dynamics simulations. As normal water solvent is replaced by less polarised water, the Hofmeister series of alkali metal ions is changed from Li⁺ > Na⁺ ? K⁺ ? Cs⁺ ? Rb⁺ to Li⁺ > Na⁺ > K⁺ > Rb⁺ > Cs⁺. In less polarised water, DNA experiences the B→A conformational transition for the lighter alkali metal counterions (Li⁺, Na⁺ and K⁺). However, it keeps B form for the heavier ions (Rb⁺ and Cs⁺). We find that the underlying cause of the conformation transition for these alkali metal ions except K⁺ is the competition between water molecules and counterions coupling to the free oxygen atoms of the phosphate groups. For K⁺ ions, the ‘economics’ of phosphate hydration and ‘spine of hydration’ are both concerned with the DNA helixes changing.