Localization properties of electronic states in a polaron model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers

We numerically investigate localization properties of electronic states in a static model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with realistic parameters obtained by quantum-chemical calculation. The randomness in the on-site energies caused by the electron-phonon coupling is completely correlated to the off-diagonal parts. In the single electron model, the effect of the hydrogen-bond stretchings, the twist angles between the base pairs and the finite system size effects on the energy dependence of the localization length and on the Lyapunov exponent are given. The localization length is reduced by the influence of the fluctuations in the hydrogen bond stretchings. It is also shown that the helical twist angle affects the localization length in the poly(dG)-poly(dC) DNA polymer more strongly than in the poly(dA)-poly(dT) one. Furthermore, we show resonance structures in the energy dependence of the localization length when the system size is relatively small.     

Studies of bosons in optical lattices in a harmonic potential

We present a theoretical study of Bose condensation and specific heat of non-interacting bosons in finite lattices in harmonic potentials in one, two, and three dimensions. We numerically diagonalize the Hamiltonian to obtain the energy levels of the systems. Using the energy levels thus obtained, we investigate the temperature dependence, dimensionality effects, lattice size dependence, and evolution to the bulk limit of the condensate fraction and the specific heat. Some preliminary results on the specific heat of fermions in optical lattices are also presented. The results obtained are contextualized within the current experimental and theoretical scenario.     

Further Discussion on Polaron Existence in Dry DNA

We study the interaction between holes and molecular vibrations on dry DNA by using the extended Firsov＇s model. The ground state energy, calculated by using two Hilbert spaces, Fock state space and coherent state space, is confirmed. The polaron binding energy, defined with the ground state energy, is 0.014eV, much less than the thermal energy 0.026eV at room temperature 300K, which means that polarons are difficult to form self-trapping at room temperature and Anderson localization will prevent a metallic state on dry DNA. The results are consistent with the available experiments.     

Optically-induced defect states in photonic lattices: formation of?defect channels, directional couplers, and disordered lattices leading to Anderson-like light localization

Formation of defect states by optical induction in one-dimensional photonic lattices fabricated in photorefractive lithium niobate is investigated experimentally. First, by using a moving narrow laser beam for defect recording, we investigate light propagation in samples containing single line defects and adjacent channel defects forming directional couplers. Then, these results are used to create lattices with randomly distributed defects, resembling a disordered optical potential. In such lattices, wave propagation is found to change from ballistic transport to transverse Anderson-like light localization as a function of induced disorder.     

Lattice bosons in quartic confinement

We present a theoretical study of bose condensation of non-interacting bosons in finite lattices in quartic potentials in one, two, and three dimensions. We investigate dimensionality effects and quartic potential effects on single boson density of energy states, condensation temperature, condensate fraction, and specific heat. The results obtained are compared with corresponding results for lattice bosons in harmonic traps.     

Growth kinetics of polymer crystals in bulk

Temperature-dependent measurements of spherulite growth rates carried out for i-polystyrene, poly(ε -caprolactone) and linear polyethylene show that the controlling activation barrier diverges at a temperature which is 14K, 22K and 12K, respectively, below the equilibrium melting points. We discuss the existence of such a “zero growth temperature” T _zg in the framework of a recently introduced thermodynamic multiphase scheme and identify T _zg with the temperature of a (hidden) transition between the melt and a mesomorphic phase which mediates the crystal growth. The rate-determining step in our model of crystal growth is the attachment of chain sequences from the melt onto the lateral face of a mesomorphic layer at the growth front. The necessary straightening of the sequence prior to an attachment is the cause of the activation barrier. A theory based on this view describes correctly the observations. With a knowledge of T _zg it is possible to fully establish the nanophase diagram describing the stability ranges of crystalline and mesomorphic layers in a melt. An evaluation of data from small-angle X-ray scattering, calorimetry and optical growth rate measurements yields heats of transition and surface free energies of crystals and mesophase layers, as well as the activation barrier per monomer associated with the chain stretching. According to the theory, the temperature dependence of the crystallization rate is determined by both the activation energy per monomer and the surface free energy of the preceding mesomorphic layer. Data indicate that the easiness of crystallization in polyethylene is first of all due to a particularly low surface free energy of the mesomorphic layer.     

Growth of attached actin filaments

In several studies of actin-based cellular motility, the barbed ends of actin filaments have been observed to be attached to moving obstacles. Filament growth in the presence of such filament-obstacle interactions is studied via Brownian dynamics simulations of a three-dimensional energy-based model. We find that with a binding energy greater than 24k _B T and a highly directional force field, a single actin filament is able to push a small obstacle for over a second at a speed of half of the free filament elongation rate. These results are consistent with experimental observations of plastic beads in cell extracts. Calculations of an external force acting on a single-filament-pushed obstacle show that for typical in vitro free-actin concentrations, a 3pN pulling force maximizes the obstacle speed, while a 4pN pushing force almost stops the obstacle. Extension of the model to treat beads propelled by many filaments suggests that most of the propulsive force could be generated by attached filaments.     

Effect of spermine and DNase on DNA release from bacteriophage T5

Bacterial viruses (bacteriophages) consist of nucleic acid protected by a protein envelope called capsid. At the start of infection, the phage genome is translocated into the bacterial cytoplasm. In vitro (and also in vivo), this DNA release can be triggered by binding a specific receptor protein to the phage tail. The force responsible for the release arises from energy stored in the capsid due to strong confinement of the DNA. We show that this force can be modified by adding molecules like spermine that affect DNA conformation. The tetravalent cation spermine can reduce the pressure inside the capsid and induce condensation of the released DNA. We examine the effect of spermine on DNA ejection from phage T5 by using light scattering and gel electrophoresis to measure the amount of DNA remaining in the capsid at the end of ejection. We discuss the results in terms of free energy minimization and we demonstrate that the presence of a DNA condensate outside the phage generates an additional force pulling passively on the DNA remaining inside the capsid.     

Topology invariance in percolation thresholds

An universal invariant for site and bond percolation thresholds ( and respectively) is proposed. The invariant writes where and are positive constants, and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d. The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6. Received: 7 July 1997 / Accepted: 5 November 1997     

DNA分子链电子结构特性研究

在单电子紧束缚近似下，建立了一维无序二元DNA分子链模型，计算了链长为2×10⁴个碱基对的DNA分子链的电子态密度、局域化特性，并探讨了碱基对的不同组分、格点能量无序度对电子局域态的影响.结果表明：由于DNA分子链中格点能量无序及碱基对的不同组分的存在，其电子波函数呈现出局域化的特性，而局域长度作为衡量电子局域化程度的一个尺度，受碱基对的组分及格点能量无序度的影响. 关键词： DNA分子链 电子结构 电子局域态 局域长度     

Dynamics of alpha helix formation in the CSAW model

We study the folding dynamics of polyalanine (Ala20), a protein fragment with 20 residues whose native state is a single alpha helix. We use the CSAW model (conditioned self-avoiding walk), which treats the protein molecule as a chain in Brownian motion, with interactions that include hydrophobic force and internal hydrogen bonding. We find that large-scale structures form before small-scale structures, and obtain the relevant relaxation times. We find that helix nucleation occurs at two separate points on the protein chain, one near each end. The evolution of small- and large-scale structures involves different mechanisms. While the former can be described by rate equations that govern the growth of helical content, the latter is akin to the relaxation of an elastic solid.     

Exact diagonalization of the S = 1/2 XY ferromagnet on finite bcc lattices to estimate T = 0 properties on the infinite lattice

In this paper finite bcc lattices are defined by a triple of vectors in two different ways - upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for S _z = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates. Received 1st August 2000 and Received in final form 22 December 2000     

A study of Barstar folding events using boundary value simulations

From extensive biophysical studies of protein folding, two competing mechanisms emerged: hydrophobic collapse and the framework model. Our protein of choice is Barstar—a barnase inhibitor. The approximation algorithm we used to study Barstar folding trajectories is called SDEL—stochastic difference equation in length. Using the native structure as the final boundary value and a collection of unfolded structures as the varying initial boundary value, SDEL calculates an ensemble of least action pathways between these boundaries. The results are atomically detailed folding pathways, with as many intermediate structures as you request in the input. We generated 12 pathways, starting from a structurally wide selection of unfolded conformations. Using the protein's radius of gyration as our primary reaction coordinate, we tracked H-bonds, dihedral angles, native and non-native contacts, and energy along the folding pathways. This paper will follow our findings, with special emphasis on pinpointing hydrophobic collapse as a more appropriate mechanism for Barstar. Comparison with pathway predictions for Barstar using experimental techniques will also be discussed.     

Folding/unfolding kinetics of lattice proteins studied using a simple statistical mechanical model for protein folding, I: Dependence on native structures and amino acid sequences

The folding/unfolding kinetics of a three-dimensional lattice protein was studied using a simple statistical mechanical model for protein folding that we developed earlier. We calculated a characteristic relaxation rate for the free energy profile starting from a completely unfolded structure (or native structure) that is assumed to be associated with a folding rate (or an unfolding rate). The chevron plot of these rates as a function of the inverse temperature was obtained for four lattice proteins, namely, proteins a1, a2, b1, and b2, in order to investigate the dependency of the folding and unfolding rates on their native structures and amino acid sequences. Proteins a1 and a2 fold to the same native conformation, but their amino acid sequences differ. The same is the case for proteins b1 and b2, but their native conformation is different from that of proteins a1 and a2. However, the chevron plots of proteins a1 and a2 are very similar to each other, and those of proteins b1 and b2 differ considerably. Since the contact orders of proteins b1 and b2 are identical, the differences in their kinetics should be attributed to the amino acid sequences and consequently to the interactions between the amino acid residues. A detailed analysis revealed that long-range interactions play an important role in causing the difference in the folding rates. The chevron plots for the four proteins exhibit a chevron rollover under both strongly folding and strongly unfolding conditions. The slower relaxation time on the broad and flat free energy surfaces of the unfolding conformations is considered to be the main origin of the chevron rollover, although the free energy surfaces have features that are rather complicated to be described in detail here. Finally, in order to concretely examine the relationship between changes in the free energy profiles and the chevron plots, we illustrate some examples of single amino acid substitutions that increase the folding rate.     

The Static Modes: An alternative approach for the treatment of macro- and bio-molecular induced-fit flexibility

We present a new competitive method for the atomic scale treatment of macromolecular flexibility called Static Mode method. This method is based on the “induced-fit” concept, i.e. it maps the intrinsic deformations of a macromolecule subject to diverse external excitations. The algorithm makes it possible to obtain a set of deformations, each one corresponding to a specific interaction on a specific molecular site, in terms of force constants contained in the energy model. In this frame, the docking problem can be expressed in terms of interaction sites between the two molecules, the molecular deformations being extracted from the pre-calculated Static Modes of each molecule. Some preliminary basic examples aimed at illustrating potential applications where macro- or bio-molecular flexibility is of key importance are given: flexibility inducing conformational changes in the case of furanose ring and flexibility for the characterization, including allostery, of poly(N-isopropylacrylamide)(P-NIPAM) active sites. We also discuss how this procedure allows “induced-fit” flexible molecular docking, beyond state-of-the-art semi-rigid methods.     

Spin glasses on Bethe lattices for large coordination number

We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within the replica symmetry breaking scheme at two steps, we compute the free energy at the first order in the expansion in inverse powers of the average connectivity (z), both for the fixed connectivity and for the fluctuating connectivity random lattices. It is well known that the coefficient of the 1/z correction for the free energy is divergent at low temperatures if computed in the one step approximation. We find that this annoying divergence becomes much smaller if computed in the framework of the more accurate two steps breaking. Comparing the temperature dependance of the coefficients of this divergence in the replica symmetric, one step and two steps replica symmetry breaking, we conclude that this divergence is an artefact due to the use of a finite number of steps of replica symmetry breaking. The 1/z expansion is well defined also in the zero temperature limit. Received 15 July 2002 Published online 31 December 2002     

Stable and metastable states and the formation and destruction of breathers in the discrete nonlinear Schrödinger equation

Statistical mechanics explains many localization phenomena of lattices such as the discrete nonlinear Schrödinger equation. However, numerical simulations show that the complete thermalization is rarely achieved. Instead, one observes metastable statistical states that are robust when excited locally. This paper investigates thermodynamically metastable states where the trajectory is confined to some part of the energy shell. The partition function and the entropy are computed with a perturbation method. This method is applicable to stable and metastable states, and it allows us to give approximative analytic expressions for the entropy in the complete thermodynamic state space.     

Bilayers of neutral lipids bear a small but significant charge

Many experiments done on neutral lipid bilayers in pure water show weak repulsions. These weak forces prevent vesicles from adhering and are generally overcome by adding some salt in the aqueous medium. They also appear as stray repulsions in surface forces measurements made on lipid bilayers. Using a surface forces apparatus in pure water and in salt solution, we have measured the forces between two stearoyl-oleoyl-phosphatidyl-choline (SOPC) bilayers and between two dimiristoyl-phosphatidyl-ethanolamine (DMPE) bilayers. The results show that the repulsions are due to a small amount of negative charges coming from impurities in SOPC. This was quantitatively confirmed by electrophoretic measurements. There are 3 times less charges in the case of DMPE layers. The effect of these charges which is negligible at high salt concentration may significantly affect the adhesion energy and behaviour of neutral lipid bilayers between 0 and salt. Received 18 December 1998