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PubMed2002

Diffusion in a granular fluid. I. Theory.

Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic case as well. This is illustrated here for diffusion of an impurity particle in a fluid undergoing homogeneous cooling. An appropriate scaling of the Liouville equation is described such that the homogeneous cooling ensemble and associated time correlation functions map to those of a stationary state. In this form the familiar methods of linear response can be applied, leading to Green-Kubo and Einstein representations of diffusion in terms of the velocity and mean-square displacement correlation functions. These correlation functions are evaluated approximately using a cumulant expansion and from kinetic theory, providing the diffusion coefficient as a function of the density and the restitution coefficients. Comparisons with results from molecular-dynamics simulation are given in the following companion paper.

Journal Article↗
PubMed2006

A practical approach to eliminate autocorrelation artefacts for volume-rate spectral domain optical coherence tomography.

A simple method is introduced to eliminate the autocorrelation artefacts in ultrafast spectral domain optical coherence tomography (SOCT) by use of the ensemble average of spectra within an individual B scan as the background signal, and then subtracting this from all the A scans within that B scan before performing the FFTs. This is updated continuously frame by frame. The method is tested on a volume-rate (C-mode) SOCT system to image the human fingertip in vivo with a volume rate at 8 s.

Algorithms↗
PubMed1997

Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and Bayesian scoring functions.

We explore the ability of a simple simulated annealing procedure to assemble native-like structures from fragments of unrelated protein structures with similar local sequences using Bayesian scoring functions. Environment and residue pair specific contributions to the scoring functions appear as the first two terms in a series expansion for the residue probability distributions in the protein database; the decoupling of the distance and environment dependencies of the distributions resolves the major problems with current database-derived scoring functions noted by Thomas and Dill. The simulated annealing procedure rapidly and frequently generates native-like structures for small helical proteins and better than random structures for small beta sheet containing proteins. Most of the simulated structures have native-like solvent accessibility and secondary structure patterns, and thus ensembles of these structures provide a particularly challenging set of decoys for evaluating scoring functions. We investigate the effects of multiple sequence information and different types of conformational constraints on the overall performance of the method, and the ability of a variety of recently developed scoring functions to recognize the native-like conformations in the ensembles of simulated structures.

Bayes Theorem↗
PubMedDate not supplied

Arterial windkessel parameter estimation: a new time-domain method.

We developed and validated a new, more accurate, and easily applied method for calculating the parameters of the three-element Windkessel to quantitate arterial properties and to investigate ventriculoarterial coupling. This method is based on integrating the governing differential equation of the three-element Windkessel and solving for arterial compliance. It accounts for the interaction between characteristic impedance and compliance, an important phenomenon that has been ignored by previously implemented methods. The new integral method was compared with four previously published methods as well as a new independent linear least-squares analysis, using ascending aortic micromanometric and volumetric flow measurements from eight dogs. The parameters calculated by the new integral method were found to be significantly different from those obtained by the previous methods but did not differ significantly from maximum likelihood estimators obtained by a linear least-squares approach. To assess the accuracy of parameter estimation, pressure and flow waveforms were reconstructed in the time domain by numerically solving the governing differential equation of the three-element Windkessel model. Standard deviations of reconstructed waveforms from the experimental ensemble-averaged waveforms, which solely reflect the relative accuracy of the Windkessel parameters given by the various methods, were calculated. The new integral method invariably yielded the smallest error. These results demonstrate the improved accuracy of our new integral method in estimating arterial parameters of the three-element Windkessel.

Animals↗
PubMed2006

Configurational constant pressure molecular dynamics.

We propose two new algorithms for generating isothermal-isobaric molecular dynamics. The algorithms are based on an extended phase space dynamics where two extra degrees of freedom, representing the thermostat and the barostat, are included. These new methods adopt a totally different approach towards molecular dynamics simulation in the isothermal-isobaric ensemble. They are fully configurational in the sense that only the particle positions are required in the control of the system temperature and pressure. Following on from the works of Delhommelle and Evans [Mol. Phys., 99, 1825 (2001)] and of Braga and Travis [J. Chem. Phys., 123, 134101 (2005)] concerning configurational canonical dynamics, these new algorithms can be seen as a natural extension to the isothermal-isobaric ensemble. We have validated both of our new configurational isothermal-isobaric schemes by conducting molecular dynamics simulations of a Lennard-Jones fluid and comparing the static and dynamic properties for a single state point. We find that both schemes generate similar results compared with schemes which use kinetic temperature and pressure control. We have also monitored the response of the system to a series of isothermal compressions and isobaric quenches. We find that the configurational schemes performed at least as well as the kinetic based scheme in bringing the system temperature and pressure into line with the set point values of these variables. These new methods will potentially play a significant role in simulations where the calculation of the kinetic temperature and pressure can be problematic. A well known example resides in the field of nonequilibrium simulations where the kinetic temperature and pressure require a knowledge of the streaming velocity of the fluid in order to calculate the true peculiar velocities (or momenta) that enter into their definitions. These are completely avoided by using our configurational thermostats and barostats, since these are independent of momenta. By extending the analysis of Kusnezov et al. [Ann. Phys., 204, 155 (1990)] in order to derive a set of generalized Nose-Hoover equations of motion which can generate isothermal-isobaric dynamics in a number of different ways, we are able to show that both of our new configurational barostats and Hoover's kinetic isothermal-isobaric scheme are special cases of this more general set of equations. This generalization can be very powerful in generating constant pressure dynamics for a variety of systems.

Journal Article↗
PubMed1995

Modeling protein loops using a phi i + 1, psi i dimer database.

We present an automated method for modeling backbones of protein loops. The method samples a database of phi i + 1 and psi i angles constructed from a nonredundant version of the Protein Data Bank (PDB). The dihedral angles phi i + 1 and psi i completely define the backbone conformation of a dimer when standard bond lengths, bond angles, and a trans planar peptide configuration are used. For the 400 possible dimers resulting from 20 natural amino acids, a list of allowed phi i + 1, psi i pairs for each dimer is created by pooling all such pairs from the loop segments of each protein in the nonredundant version of the PDB. Starting from the N-terminus of the loop sequence, conformations are generated by assigning randomly selected pairs of phi i + 1, psi i for each dimer from the respective pool using standard bond lengths, bond angles, and a trans peptide configuration. We use this database to simulate protein loops of lengths varying from 5 to 11 amino acids in five proteins of known three-dimensional structures. Typically, 10,000-50,000 models are simulated for each protein loop and are evaluated for stereochemical consistency. Depending on the length and sequence of a given loop, 50-80% of the models generated have no stereochemical strain in the backbone atoms. We demonstrate that, when simulated loops are extended to include flanking residues from homologous segments, only very few loops from an ensemble of sterically allowed conformations orient the flanking segments consistent with the protein topology. The presence of near-native backbone conformations for loops from five different proteins suggests the completeness of the dimeric database for use in modeling loops of homologous proteins. Here, we take advantage of this observation to design a method that filters near-native loop conformations from an ensemble of sterically allowed conformations. We demonstrate that our method eliminates the need for a loop-closure algorithm and hence allows for the use of topological constraints of the homologous proteins or disulfide constraints to filter near-native loop conformations.

Amino Acid Sequence↗
PubMed2005

Automated use of mutagenesis data in structure prediction.

In the absence of experimental structural determination, numerous methods are available to indirectly predict or probe the structure of a target molecule. Genetic modification of a protein sequence is a powerful tool for identifying key residues involved in binding reactions or protein stability. Mutagenesis data is usually incorporated into the modeling process either through manual inspection of model compatibility with empirical data, or through the generation of geometric constraints linking sensitive residues to a binding interface. We present an approach derived from statistical studies of lattice models for introducing mutation information directly into the fitness score. The approach takes into account the phenotype of mutation (neutral or disruptive) and calculates the energy for a given structure over an ensemble of sequences. The structure prediction procedure searches for the optimal conformation where neutral sequences either have no impact or improve stability and disruptive sequences reduce stability relative to wild type. We examine three types of sequence ensembles: information from saturation mutagenesis, scanning mutagenesis, and homologous proteins. Incorporating multiple sequences into a statistical ensemble serves to energetically separate the native state and misfolded structures. As a result, the prediction of structure with a poor force field is sufficiently enhanced by mutational information to improve accuracy. Furthermore, by separating misfolded conformations from the target score, the ensemble energy serves to speed up conformational search algorithms such as Monte Carlo-based methods.

Algorithms↗
PubMed1986

Poststenotic flow disturbance in the dog aorta as measured with pulsed Doppler ultrasound.

Blood flow velocity was measured in the dog aorta distal to mechanically induced constrictions of various degrees of severity employing an 8-MHz pulsed Doppler ultrasound velocimeter and a phase-lock loop frequency tracking method for extracting velocity from the Doppler quadrature signals. The data were analyzed to construct ensemble average velocity waveforms and random velocity disturbances. In any individual animal the effect of increasing the degree of stenosis beyond approximately 25 percent area reduction was to produce increasing levels of random velocity disturbance. However, variability among animals was such that the sensitivity of random behavior to the degree of stenosis was degraded to the point that it appears difficult to employ Doppler ultrasound measurements of random disturbances to discriminate among stenoses with area reductions less than approximately 75 percent. On the other hand, coherent vortex structures in velocity waveforms consistently occurred distal to mild constrictions (25-50 percent area reduction). Comparison of the phase-lock loop Doppler ultrasound data with simultaneous measurements using invasive hot-film anemometry, which possesses excellent frequency response, demonstrates that the ultrasound method can reliably detect those flow phenomena in such cases. Thus, the identification of coherent, rather than random, flow disturbances may offer improved diagnostic capability for noninvasively detecting arteriosclerotic plaques at relatively early stages of development.

Animals↗
PubMed2006

A general framework for non-Boltzmann Monte Carlo sampling.

Non-Boltzmann sampling (NBS) methods have been extensively employed in recent years, mainly due to their ability to enhance ergodicity in simulations of complex systems. In addition, they make possible reliable computation of equilibrium properties (ensemble averages, free-energy differences, and potentials of mean force) over continuous ranges of thermodynamic conditions. In this work, we put forward a general and systematic framework for NBS methods that allows a single set of equations and procedures to be applied to diverse systems. Moreover, we show how to exploit simulation data most effectively by obtaining continuous profiles of any mechanical properties, including structural quantities not directly related to the ensemble parameters. Finally, we demonstrate the usefulness of the developed formulation by applying it to spin systems, Lennard-Jones fluids, and a model protein molecule (both in isolation and in the proximity of a flat wall).

Algorithms↗
PubMed2006

Simulation of vibrational dephasing of I(2) in solid Kr using the semiclassical Liouville method.

In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.

Algorithms↗
PubMed1991

Development of an equation for potentiometric titration of polyelectrolytes using a periodic lattice model. A numerical analysis of interactions among ionizable groups.

A numerical method is presented for analysing the potentiometric titration behavior of linear polyelectrolytes. A polyelectrolyte molecule is treated as a one-dimensional lattice containing a large number of lattice points, each of which has an identical ionizable group. In this method, the polyelectrolyte model lattice is divided into identical repeating unit cell systems with a finite number of ionizable groups to calculate the thermodynamic partition function of the system of polyelectrolyte solution. The electrostatic interaction between ionized groups adopted in the present study is given by the Debye-Hückel type screened Coulombic potential. The titration behavior as well as several thermodynamic quantities is derived by making a canonical ensemble summation of all states in a unit cell system under an appropriate periodic boundary condition. This method serves as a model of the two-step ionization often appearing in polyions with strong neighboring interactions such as homo- and copolymers of maleic acid. Several characteristics of the titration behavior of these polyelectrolytes are well reproduced by using a lattice model with pairwise intervals, including the effects of hydrogen bond formation and change in dielectric constant of the medium around an ionizable group. In addition, this method is valid for a more detailed analysis of the titration behavior of polyelectrolytes with various kinds of arrangements of charged groups.

Journal Article↗
PubMed1983

Identification of presynaptic neurons by laser photostimulation.

An optical method involving the use of a laser and a novel fluorescent dye as a photostimulation probe has been developed to identify presynaptic neurons in a large ensemble of cells. Illumination of an extracellularly stained neuron by the laser microbeam evokes action potentials. With this technique an interneuron connecting identified leech neurons was quickly located. The method speeds up the elucidation of neuronal networks, especially when small cells are involved.

Action Potentials↗
PubMedDate not supplied

Prediction of P-glycoprotein substrates by a support vector machine approach.

P-glycoproteins (P-gp) actively transport a wide variety of chemicals out of cells and function as drug efflux pumps that mediate multidrug resistance and limit the efficacy of many drugs. Methods for facilitating early elimination of potential P-gp substrates are useful for facilitating new drug discovery. A computational ensemble pharmacophore model has recently been used for the prediction of P-gp substrates with a promising accuracy of 63%. It is desirable to extend the prediction range beyond compounds covered by the known pharmacophore models. For such a purpose, a machine learning method, support vector machine (SVM), was explored for the prediction of P-gp substrates. A set of 201 chemical compounds, including 116 substrates and 85 nonsubstrates of P-gp, was used to train and test a SVM classification system. This SVM system gave a prediction accuracy of at least 81.2% for P-gp substrates based on two different evaluation methods, which is substantially improved against that obtained from the multiple-pharmacophore model. The prediction accuracy for nonsubstrates of P-gp is 79.2% using 5-fold cross-validation. These accuracies are slightly better than those obtained from other statistical classification methods, including k-nearest neighbor (k-NN), probabilistic neural networks (PNN), and C4.5 decision tree, that use the same sets of data and molecular descriptors. Our study indicates the potential of SVM in facilitating the prediction of P-gp substrates.

ATP Binding Cassette Transporter, Subfamily B, Mem↗
PubMed2001

Weighted density functional theory for simple fluids: supercritical adsorption of a Lennard-Jones fluid in an ideal slit pore.

The adsorption of a Lennard-Jones fluid in an ideal slit pore is studied using weighted density functional theory. The intrinsic Helmholtz free-energy functional is separated into repulsive and attractive contributions. Rosenfeld's accurate fundamental measure functional is employed for the repulsive functional while another weighted density functional method is employed for the attractive functional. This other method requires an accurate equation of state for the bulk fluid and an accurate pair-direct correlation function for a uniform fluid, determined analytically or numerically. The results for this theory are compared against mean-field density functional theory and grand canonical ensemble simulation results, modeling the adsorption of ethane in a graphite slit. The results indicate that the weighted density functional method applied to the attractive functional can offer a significant increase in accuracy over the mean-field theory.

Journal Article↗
PubMed2004

Multivariate receptive field mapping in marmoset auditory cortex.

We describe a novel method for estimation of multivariate neuronal receptive fields that is based on least-squares (LS) regression. The method is shown to account for the relationship between the spike train of a given neuron, the activity of other neurons that are recorded simultaneously, and a variety of time-varying features of acoustic stimuli, e.g. spectral content, amplitude, and sound source direction. Vocalization-evoked neuronal responses from the marmoset auditory cortex are used to illustrate the method. Optimal predictions of single-unit activity were obtained by using the recent-time history of the target neuron and the concurrent activity of other simultaneously recorded neurons (R: 0.82 +/- 0.01, approximately 67% of variance). Predictions based on ensemble activity alone (R: 0.63 +/- 0.18) were equivalent to those based on the combination of ensemble activity and spectral features of the vocal calls (R: 0.61 +/- 0.24). This result suggests that all information derived from the spectrogram is embodied in ensemble activity and that there is a high level of redundancy in the marmoset auditory cortex. We also illustrate that the method allows for quantification of relative and shared contributions of each variable (spike train, spectral feature) to predictions of neuronal activity and describe a novel "neurolet" transform that arises from the method and that may serve as a tool for computationally efficient processing of natural sounds.

Acoustic Stimulation↗
PubMed1997

Conformational studies of the N-terminal lipid-associating domain of human apolipoprotein C-I by CD and 1H NMR spectroscopy.

A peptide comprising the N-terminal 38 residues of human apolipoprotein C-I (apoC-I(1-38)) was synthesized using solid-phase methods and its solution conformation studied by CD and 1H NMR spectroscopy. The CD data indicate that apoC-I(1-38) has a similar helical content (55%) in the presence of saturating amounts of SDS or egg yolk lysophosphatidylcholine. A structural ensemble of SDS-bound apoC-I(1-38) was calculated from 464 NOE-based distance restraints using distance geometry methods. ApoC-I(1-38) adopts a helical structure between residues V4 and K30 and an extended C-terminus from Q31 when associated with SDS. The region K12-G15 undergoes slow conformational exchange as indicated by above-average amide resonance linewidths, large temperature coefficients, and fast exchange (< 2 h) of backbone amide protons with deuterium. The mobility of K12-G15 is reflected in the poorly defined dihedral angles of K12 and E13 in the calculated ensemble of structures. The average structure of apoC-I(1-38) is curved toward its hydrophobic face with bends of 125 degrees, centered at K12/E13, and 150 degrees, centered at K21. This curvature appears to be driven by the interaction of two hydrophobic clusters, one formed by residues L8, L11, F14, and L18, and the other by L25, I26, and I29, with the amphiphile SDS. Based on our present structural definition of apoC-I(1-38) and the previously obtained structure of the fragment apoC-I(35-53), we propose the secondary structure of intact apolipoprotein C-I.

Apolipoprotein C-I↗
PubMed1993

A method to recognize distant repeats in protein sequences.

An automated algorithm is presented that delineates protein sequence fragments which display similarity. The method incorporates a selection of a number of local nonoverlapping sequence alignments with the highest similarity scores and a graph-theoretical approach to elucidate the consistent start and end points of the fragments comprising one or more ensembles of related subsequences. The procedure allows the simultaneous identification of different types of repeats within one sequence. A multiple alignment of the resulting fragments is performed and a consensus sequence derived from the ensemble(s). Finally, a profile is constructed from the multiple alignment to detect possible and more distant members within the sequence. The method tolerates mutations in the repeats as well as insertions and deletions. The sequence spans between the various repeats or repeat clusters may be of different lengths. The technique has been applied to a number of proteins where the repeating fragments have been derived from information additional to the protein sequences.

Algorithms↗
PubMed2003

Pharmacophore-based molecular docking to account for ligand flexibility.

Rapid computational mining of large 3D molecular databases is central to generating new drug leads. Accurate virtual screening of large 3D molecular databases requires consideration of the conformational flexibility of the ligand molecules. Ligand flexibility can be included without prohibitively increasing the search time by docking ensembles of precomputed conformers from a conformationally expanded database. A pharmacophore-based docking method whereby conformers of the same or different molecules are overlaid by their largest 3D pharmacophore and simultaneously docked by partial matches to that pharmacophore is presented. The method is implemented in DOCK 4.0.

Algorithms↗