The folding of knotted proteins: insights from lattice simulations

We carry out systematic Monte Carlo simulations of Go lattice proteins to investigate and compare the folding processes of two model proteins whose native structures differ from each other due to the presence of a trefoil knot located near the terminus of one of the protein chains. We show that the folding time of the knotted fold is larger than that of the unknotted protein and that this difference in folding time is particularly striking in the temperature region below the optimal folding temperature. Both proteins display similar folding transition temperatures, which is indicative of similar thermal stabilities. By using the folding probability reaction coordinate as an estimator of folding progression we have found out that the formation of the knot is mainly a late folding event in our shallow knot system.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

Resonating-valence-bond theory for the square-planar lattice

The short-range resonating-valence-bond (RVB) wave function with nearest-neighbor (NN) spin pairings only is investigated as a possible description for the Heisenberg model on a square-planar lattice. A type of long-range order associated to this RVB Ansatz is identified along with some qualitative consequences involving lattice distortions, excitations, and their coupling.

Reaction-diffusion lattice gas: Theory and computer results

We report on the study of nonequilibrium ordering in the reaction-diffusion lattice gas. It is a kinetic model that relaxes towards steady states under the simultaneous competition of a thermally activated creation-annihilation $(reaction$) process at temperature T, and a diffusion process driven by a heat bath at temperature T?T. The phase diagram as one varies T and T, the system dimension d, the relative priori probabilities for the two processes, and their dynamical rates is investigated. We compare mean-field theory, new Monte Carlo data, and known exact results for some limiting cases. In particular, no evidence of Landau critical behavior is found numerically when d=2 for Metropolis rates but Onsager critical points and a variety of first-order phase transitions.

Ising critical behavior of a non-Halmiltonian lattice system

We study steady states in d-dimensional lattice systems that evolve in time by a probabilistic majority rule, which corresponds to the zero-temperature limit of a system with conflicting dynamics. The rule satisfies detailed balance for d=1 but not for d>1. We find numerically nonequilibrium critical points of the Ising class for d=2 and 3.

A comprehensive model for quantum noise characterization in digital mammography.

NlmCategory="UNASSIGNED">A version of cascaded systems analysis was developed specifically with the aim of studying quantum noise propagation in x-ray detectors. Signal and quantum noise propagation was then modelled in four types of x-ray detectors used for digital mammography: four flat panel systems, one computed radiography and one slot-scan silicon wafer based photon counting device. As required inputs to the model, the two dimensional (2D) modulation transfer function (MTF), noise power spectra (NPS) and detective quantum efficiency (DQE) were measured for six mammography systems that utilized these different detectors. A new method to reconstruct anisotropic 2D presampling MTF matrices from 1D radial MTFs measured along different angular directions across the detector is described; an image of a sharp, circular disc was used for this purpose. The effective pixel fill factor for the FP systems was determined from the axial 1D presampling MTFs measured with a square sharp edge along the two orthogonal directions of the pixel lattice. Expectation MTFs were then calculated by averaging the radial MTFs over all possible phases and the 2D EMTF formed with the same reconstruction technique used for the 2D presampling MTF. The quantum NPS was then established by noise decomposition from homogenous images acquired as a function of detector air kerma. This was further decomposed into the correlated and uncorrelated quantum components by fitting the radially averaged quantum NPS with the radially averaged EMTF(2). This whole procedure allowed a detailed analysis of the influence of aliasing, signal and noise decorrelation, x-ray capture efficiency and global secondary gain on NPS and detector DQE. The influence of noise statistics, pixel fill factor and additional electronic and fixed pattern noises on the DQE was also studied. The 2D cascaded model and decompositions performed on the acquired images also enlightened the observed quantum NPS and DQE anisotropy.

A simple model for circadian timing by mammals

Circadian timing is structured in such a way as to receive information from the external and internal environments, and its function is the timing organization of the physiological and behavioral processes in a circadian pattern. In mammals, the circadian timing system consists of a group of structures, which includes the suprachiasmatic nucleus (SCN), the intergeniculate leaflet and the pineal gland. Neuron groups working as a biological pacemaker are found in the SCN, forming a biological master clock. We present here a simple model for the circadian timing system of mammals, which is able to reproduce two fundamental characteristics of biological rhythms: the endogenous generation of pulses and synchronization with the light-dark cycle. In this model, the biological pacemaker of the SCN was modeled as a set of 1000 homogeneously distributed coupled oscillators with long-range coupling forming a spherical lattice. The characteristics of the oscillator set were defined taking into account the Kuramoto's oscillator dynamics, but we used a new method for estimating the equilibrium order parameter. Simultaneous activities of the excitatory and inhibitory synapses on the elements of the circadian timing circuit at each instant were modeled by specific equations for synaptic events. All simulation programs were written in Fortran 77, compiled and run on PC DOS computers. Our model exhibited responses in agreement with physiological patterns. The values of output frequency of the oscillator system (maximal value of 3.9 Hz) were of the order of magnitude of the firing frequencies recorded in suprachiasmatic neurons of rodents in vivo and in vitro (from 1.8 to 5.4 Hz).

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Electron-Phonon Interaction Within the Framework of the Fluctuating Valence of Copper Atoms — a Theoretical Model for High Temperature Superconductivity

Electron-phonon interaction is considered within the framework of the fluctuating valence of Cu atoms. Anderson's lattice Hamiltonian is suitably modified to take this into account. Using Green's function technique tbe possible quasiparticle excitations' are determined. The quantity 2delta k(O)/ kB Tc is calculated for Tc= 40 K. The calculated values are in good agreement with the experimental results.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

Determination of tube theory parameters using a simple grid model as an example

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slipsprings model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes.