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At least 865 records · Page 48Linked to original sources
PubMed2003

Robust biased Brownian dynamics for rate constant calculation.

A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by a Brownian dynamics simulation, also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. Building on earlier work, this article completes the development of a robust importance sampling algorithm for Brownian dynamics-i.e., biased Brownian dynamics with weight control-to overcome the high energy and entropy barriers in biomolecular association reactions. The biased Brownian dynamics steers sampling by a bias force, and the weight control algorithm controls sampling by a target weight. This algorithm is optimal if the bias force and the target weight are constructed from the solution of the reaction probability problem. In reality, an approximate reaction probability has to be used to construct the bias force and the target weight. Thus, the performance of the algorithm depends on the quality of the approximation. Given here is a method to calculate a good approximation, which is based on the selection of a reaction coordinate and the variational formulation of the reaction probability problem. The numerically approximated reaction probability is shown by computer experiments to give a factor-of-two speedup over the use of a purely heuristic approximation. Also, the fully developed method is compared to unbiased Brownian dynamics. The tests for human superoxide dismutase, Escherichia coli superoxide dismutase, and antisweetener antibody NC6.8, show speedups of 17, 35, and 39, respectively. The test for reactions between two model proteins with orientations shows speedups of 2578 for one set of configurations and 3341 for another set of configurations.

Antigen-Antibody Complex↗
PubMed2003

Electrostatic tuning of permeation and selectivity in aquaporin water channels.

Water permeation and electrostatic interactions between water and channel are investigated in the Escherichia coli glycerol uptake facilitator GlpF, a member of the aquaporin water channel family, by molecular dynamics simulations. A tetrameric model of the channel embedded in a 16:0/18:1c9-palmitoyloleylphosphatidylethanolamine membrane was used for the simulations. During the simulations, water molecules pass through the channel in single file. The movement of the single file water molecules through the channel is concerted, and we show that it can be described by a continuous-time random-walk model. The integrity of the single file remains intact during the permeation, indicating that a disrupted water chain is unlikely to be the mechanism of proton exclusion in aquaporins. Specific hydrogen bonds between permeating water and protein at the channel center (at two conserved Asp-Pro-Ala "NPA" motifs), together with the protein electrostatic fields enforce a bipolar water configuration inside the channel with dipole inversion at the NPA motifs. At the NPA motifs water-protein electrostatic interactions facilitate this inversion. Furthermore, water-water electrostatic interactions are in all regions inside the channel stronger than water-protein interactions, except near a conserved, positively charged Arg residue. We find that variations of the protein electrostatic field through the channel, owing to preserved structural features, completely explain the bipolar orientation of water. This orientation persists despite water translocation in single file and blocks proton transport. Furthermore, we find that for permeation of a cation, ion-protein electrostatic interactions are more unfavorable at the conserved NPA motifs than at the conserved Arg, suggesting that the major barrier against proton transport in aquaporins is faced at the NPA motifs.

Aquaporins↗
PubMed2003

Modeling the role of myosin 1c in neuronal growth cone turning.

We addressed the mechanical basis for how embryonic chick dorsal root ganglion growth cones turn on a uniform substrate of laminin-1. Turning is significantly correlated with lamellipodial area but not with filopodial length. We assessed the lamellipodial contribution to turning by asymmetric micro-CALI of myosin isoforms that causes localized lamellipodial expansion (myosin 1c) or filopodial retraction (myosin V). Episodes of asymmetric micro-CALI of myosin 1c (or myosin 1c and V together) caused significant turning of the growth cone. In contrast, repeated micro-CALI of myosin V or irradiation without added antibody did not turn growth cones. These findings argue that lamellipodia and not filopodia are necessary for growth cone turning. To model the role of myosin 1c on growth cone turning, we fitted the measured trajectories from asymmetric micro-CALI of myosin 1c-treated and untreated growth cones to the persistent random walk model. The first parameter in this equation, root-mean-square speed, is indistinguishable between the two data sets whereas the second parameter, the persistence of motion, is significantly increased (2.5-fold) as a result of asymmetric inactivation of myosin 1c by micro-CALI. This analysis demonstrates that growth cone turning results from an increase in the persistence of directional motion rather than a change in speed. Taken together, our results suggest that myosin 1c is a molecular correlate for directional persistence underlying growth cone motility.

Animals↗
PubMed2003

Configurational temperature density of states simulations of proteins.

A novel method has been implemented to compute the density of states of proteins. A united atom representation and the CHARMM (Brooks et al., 1983) force-field parameters have been adopted for all the simulations. In this approach, an intrinsic temperature is computed based on configurational information about the protein. A random walk is performed in potential energy space and the configurational temperature is collected as a function of potential energy of the system. The density of states is then calculated by integrating the reciprocal of temperature. Unlike previously available methods, this approach does not involve calculations based on histograms of stochastic visits to distinct energy states. It is found that the proposed method is more efficient than earlier, related schemes for simulation of protein folding. Furthermore, it directly provides thermodynamic information, including free energies. The usefulness of the method is discussed by presenting results of simulations of the 16-residue beta-hairpin taken from the C-terminal fragment (41-56) of protein G.

Algorithms↗
PubMed2003

The circularization of amyloid fibrils formed by apolipoprotein C-II.

Amyloid fibrils have historically been characterized by diagnostic dye-binding assays, their fibrillar morphology, and a "cross-beta" x-ray diffraction pattern. Whereas the latter demonstrates that amyloid fibrils have a common beta-sheet core structure, they display a substantial degree of morphological variation. One striking example is the remarkable ability of human apolipoprotein C-II amyloid fibrils to circularize and form closed rings. Here we explore in detail the structure of apoC-II amyloid fibrils using electron microscopy, atomic force microscopy, and x-ray diffraction studies. Our results suggest a model for apoC-II fibrils as ribbons approximately 2.1-nm thick and 13-nm wide with a helical repeat distance of 53 nm +/- 12 nm. We propose that the ribbons are highly flexible with a persistence length of 36 nm. We use these observed biophysical properties to model the apoC-II amyloid fibrils either as wormlike chains or using a random-walk approach, and confirm that the probability of ring formation is critically dependent on the fibril flexibility. More generally, the ability of apoC-II fibrils to form rings also highlights the degree to which the common cross-beta superstructure can, as a function of the protein constituent, give rise to great variation in the physical properties of amyloid fibrils.

Amyloid↗
PubMed2003

Temporal variations in cell migration and traction during fibroblast-mediated gel compaction.

Current models used in our laboratory to assess the migration and traction of a population of cells within biopolymer gels are extended to investigate temporal changes in these parameters during compaction of mechanically constrained gels. The random cell migration coefficient, micro (t) is calculated using a windowing technique by regressing the mean-squared displacement of cells tracked at high magnification in three dimensions with a generalized least squares algorithm for a subset of experimental time intervals, and then shifting the window interval-by-interval until all time points are analyzed. The cell traction parameter, tau(0)(t), is determined by optimizing the solution of our anisotropic biphasic theory to tissue equivalent compaction. The windowing technique captured simulated sinusoidal and step changes in cell migration superposed on a persistent random walk in simulated cell movement. The optimization software captured simulated time dependence of compaction on cell spreading. Employment of these techniques on experimental data using rat dermal fibroblasts (RDFs) and human foreskin fibroblasts (HFFs) demonstrated that these cells exhibit different migration-traction relationships. Rat dermal fibroblast migration was negatively correlated to traction, suggesting migration was not the driving force for compaction with these cells, whereas human foreskin fibroblast migration was positively correlated to traction.

Algorithms↗
PubMed1976

Theoretical model of the ionic mechanism of 1/f noise in nerve membrane.

A model is presented for the ionic mechanism of low frequency 1/f electrical noise which has been observed in axonal membranes. The model consists of narrow channels which open randomly throughout the membrane and remain open for only a short time compared with f-1max where fmax approximately 2 kHz is the maximum frequency for which 1/f noise is observed. The fluctuation in channel formation is coupled to low frequency normal mode vibrations in liquid crystals which have properties similar to nerve membranes. Ionic current flow through the channels is assumed to occur via single file diffusion. The diffusion process is regarded as a non-Markovian random walk on a one-dimensional lattice which is mathematically decomposed into its spatial and temporal components. This technique allows calculation of the mean and variance of the number of ions which flow through any single short-lived channel. The final result for the current noise power spectrum, S, is S(f) = (A + k/I/2)/f, where I is the mean membrane current and A and k are parameters which are independent of membrane voltage. The theoretical result is consistent with observations of 1/f noise in lobster axon by Poussart (1971, Biophys. J. 11:212.) on the dependence of S(f) on the mean steady-state current and the external potassium concentration. We also calculate the mean channel density and the Frank elastic constant of the membrane. This work is an extension of a macroscopic model of Lundström and McQueen (1974, J. Theor. Biol. 45:405.) who obtain a spectral density of the form S approximately /I/2/f.

Animals↗
PubMed1983

Motility of mouse fibroblasts in tissue culture.

The growth and motion of mouse L-cells in vitro have been studied by means of time-lapse photography. In particular, the mitotic period and the motility, defined in terms of [R2], the mean square displacement of an ensemble of cells, have been measured as a function of temperature. The motility is a function of the phase of the cell cycle. For approximately the first one-eighth of the mitotic period the motility is well described as a random walk with persistence, the duration of the persistence being determined by the time of extension of the filopodic spindle. The temperature dependence of the diffusion constant follows the Arrhenius factor. The mitotic period, which varies exponentially as (1/T), exhibits a large variance, and the time difference in replication of daughter pairs follows approximately a Poisson distribution with a mean difference of 138 min at T = 37 degrees C. There is no evidence of mirror symmetry in the motion of daughter pairs for fibroblast cells plated in vitro in Corning tissue culture flasks.

Animals↗
PubMed1988

Internal motions in proteins and gating kinetics of ionic channels.

Single-channel current recordings have revealed a complex kinetic behavior of ionic channels. Many channels exhibit closed-time distributions in which long waiting times occur with a much higher frequency than predicted by a simple exponential decay function. In this paper a model for opening-closing transitions that accounts for internal motions in the protein matrix is discussed. The model is based on the notion that the transition between a conductive and a nonconductive state of the channel represents a local process in the protein, such as the movement of a small segment of a peptide chain or the rotation of a single amino-acid residue. When the blocking group moves into the ion pathway, a structural defect is created consisting in a region of loose packing and/or poor hydrogen bonding. By rearrangements of neighboring groups, the defect may migrate within the protein matrix, carrying out a kind of random walk. Once the defect has moved away from the site where it was formed, a transition back to the open state of the channel is possible only when the defect has returned by chance to the original position. The kinetic properties of this model are analyzed by stochastic simulation of defect diffusion in a small domain of the protein. With a suitable choice of domain size and diffusion rate, the model is found to predict closed-time distributions that agree with experimental observations.

Animals↗
PubMed1989

Lateral diffusion in an archipelago. Distance dependence of the diffusion coefficient.

An understanding of the distance dependence of the lateral diffusion coefficient is useful in comparing the results of diffusion measurements made over different length scales, and in analyzing the kinetics of mobile redox carriers in organelles. A distance-dependent, concentration-dependent diffusion coefficient is defined, and it is evaluated by Monte Carlo calculations of a random walk by mobile point tracers in the presence of immobile obstacles on a triangular lattice, representing the diffusion of a lipid or a small protein in the presence of immobile membrane proteins. This work confirms and extends the milling crowd model of Eisinger, J., J. Flores, and W. P. Petersen (1986. Biophys J. 49:987-1001). Similar calculations for diffusion of mobile particles interacting by a hard-core repulsion yield the distance dependence of the self-diffusion coefficient. An expression for the range of short-range diffusion is obtained, and the distance scales for various diffusion measurements are summarized.

Diffusion↗
PubMed1989

Complement proteins C5b-9 induce transbilayer migration of membrane phospholipids.

Transbilayer migration of membrane phospholipid arising from membrane insertion of the terminal human complement proteins has been investigated. Asymmetric vesicles containing pyrene-labeled phosphatidylcholine (pyrenePC) concentrated in the inner monolayer were prepared by outer monolayer exchange between pyrenePC-containing large unilamellar vesicles and excess (unlabeled) small unilamellar vesicles, using bovine liver phosphatidylcholine-specific exchange protein. After depletion of pyrenePC from the outer monolayer, the asymmetric large unilamellar vesicles were isolated by gel filtration and exposed to the purified C5b-9 proteins at 37 degrees C. Transbilayer exchange of phospholipid between inner and outer monolayers during C5b-9 assembly was monitored by changes in pyrene excimer and monomer fluorescence. Membrane deposition of the C5b67 complex (by incubation with C5b6 + C7) caused no change in pyrenePC fluorescence. Addition of C8 to the C5b67 vesicles resulted in a dose-dependent decrease in the excimer/monomer ratio. This change was observed both in the presence and absence of complement C9. No change in fluorescence was observed for control vesicles exposed to C8 (in the absence of membrane C5b67), or upon C5b-9 addition to vesicles containing pyrenePC symmetrically distributed between inner and outer monolayers. These data suggest that a transbilayer exchange of phospholipid between inner and outer monolayers is initiated upon C8 binding to C5b67. The fluorescence data were analyzed according to a "random walk" model for excimer formation developed for the case where pyrenePC is asymmetrically distributed between lipid bilayers. Based on this analysis, we estimate that a net transbilayer migration of approximately 1% of total membrane phospholipid is initiated upon C8 binding to C5b67. The potential significance of this transbilayer exchange of membrane phospholipid to the biological activity of the terminal complement proteins is considered.

Androgen-Binding Protein↗
PubMed1989

Orientational exchange approach to fluorescence anisotropy decay.

Fluorescence depolarization is a powerful technique in resolving dynamics of molecular systems. Data obtained in fluorescence depolarization experiments are highly complex. Mathematical models for analyzing data from depolarization due to rotational motion have been largely based on the rotational diffusion equation. These results have been verified by Monte Carlo simulations. It has been implicitly stated that a 90 degrees jump model between predefined orientations such as presented by G. Weber (1971. J. Chem. Phys. 55:2399-2411) should, for the specific case of fluorescence depolarization, give the same answer as the diffusion equation. Since the highly symmetric cases considered by G. Weber gave the same result as the diffusion equation, it has been desirable to use this method in cases where depolarization arises from both discrete processes and rotational diffusion. We have derived, in a compartmental formalism, the general result for excitation and emission dipoles not necessarily coincident with any of the principal rotational axes of the fluorophore from this exchange model, and have found it to be different from that of the diffusion equation approach. We have also verified this difference with a Monte Carlo simulation of our exchange model. This derivation allows us to define the limits of validity of the 90 degrees exchanges to model rotational diffusion. Also, for systems where movements may be jumps between a few preferred orientations, the actual physical mechanism of depolarization may not be accurately represented by continuous diffusion. The compartmental formalism developed here can be used to easily combine rotational motions with discrete position jumps or other level kinetics. While the difference between the diffusion equation and random walk of finite step size derivations has been presented for observations of different order properties for the compartmental formalism, we discuss the possibility of finding this difference by using the ratio of relaxation rates from a single experiment. Also,the temperature dependence of the exchange rates is calculated in relation to the Kramer's theory.

Biopolymers↗
PubMed1990

Lateral diffusion in a mixture of mobile and immobile particles. A Monte Carlo study.

The lateral diffusion coefficient for mixtures of mobile and immobile particles is obtained from Monte Carlo calculations of random walks by mobile tracers in the presence of immobile obstacles on a triangular lattice. The diffusion coefficient of the mobile species is obtained as a function of the area fractions of mobile and immobile species. The results are applied to diffusion of band 3 in the erythrocyte membrane, and indicate that obstruction of diffusion of mobile band 3 by band 3 and glycophorin attached to the membrane skeleton is not sufficient to explain the observed diffusion coefficient.

Animals↗
PubMed1990

Fractal mechanisms for the allosteric effects of proteins and enzymes.

Investigations have been made on the reaction kinetics of proteins and enzymes by the statistical methods of random walks on fractal structures. From the point of view of networks of Trap (R) and Free (T) sites, the relationships between the Hill coefficients (h) and the fractal (df) as well as spectral (ds) dimensions of protein molecules are obtained. For example, h = (1 + 2/df) for the one-step conformational changes and hb = (2 + 2/ds) for the multistep conformational changes, respectively. In comparison with that of the literature, the theoretical value is reasonable, thus suggesting a new mechanism for the allosteric effects of proteins and enzymes.

Allosteric Site↗
PubMed1992

Dynamics of energy transfer and trapping in the light-harvesting antenna of Rhodopseudomonas viridis.

By low intensity picosecond absorption spectroscopy it is shown that the exciton lifetime in the light-harvesting antenna of Rhodopseudomonas (Rps.) viridis membranes with photochemically active reaction centers at room temperature is 60 +/- 10 ps. This lifetime reflects the overall trapping rate of the excitation energy by the reaction center. With photochemically inactive reaction centers, in the presence of P+, the exciton lifetime increases to 150 +/- 15 ps. Prereducing the secondary electron acceptor QA does not prevent primary charge separation, but slows it down from 60 to 90 +/- 10 ps. Picosecond kinetics measured at 77 K with inactive reaction centers indicates that the light-harvesting antenna is spectrally homogeneous. Picosecond absorption anisotropy measurements show that energy transfer between identical Bchlb molecules occurs on the subpicosecond time scale. Using these experimental results as input to a random-walk model, results in strict requirements for the antenna-RC coupling. The model analysis prescribes fast trapping (approximately 1 ps) and an approximately 0.5 escape probability from the reaction center, which requires a more tightly coupled RC and antenna, as compared with the Bchla-containing bacteria Rhodospirillum (R.) rubrum and Rhodobacter (Rb.) sphaeroides.

Energy Transfer↗
PubMed1993

Macromolecular diffusion in crowded solutions.

The effects of crowding on the self or tracer diffusion of macromolecules in concentrated solutions is an important but difficult problem, for which, so far, there has been no rigorous treatment. Muramatsu and Minton suggested a simple model to calculate the diffusion coefficient of a hard sphere among other hard spheres. In this treatment, scaled particle theory is used to evaluate the probability that the target volume for a step in a random walk is free of any macromolecules. We have improved this approach by using a more appropriate target volume which also allows the calculation to be extended to the diffusion of a hard sphere among hard spherocylinders. We conclude that, to the extent that proteins can be approximated as hard particles, the hindrance of globular proteins by other proteins is reduced when the background proteins aggregate (the more so the greater the decrease in particle surface area), the hindrance due to rod-shaped background particles is reduced slightly if the rod-like particles are aligned, and the anisotropy of the diffusion of soluble proteins among cytoskeletal proteins will normally be small.

Biophysical Phenomena↗
PubMed1994

Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position.

We present a novel optical technique for three-dimensional tracking of single fluorescent particles using a modified epifluorescence microscope containing a weak cylindrical lens in the detection optics and a microstepper-controlled fine focus. Images of small, fluorescent particles were circular in focus but ellipsoidal above and below focus; the major axis of the ellipsoid shifted by 90 degrees in going through focus. Particle z position was determined from the image shape and orientation by applying a peak detection algorithm to image projections along the x and y axes; x, y position was determined from the centroid of the particle image. Typical spatial resolution was 12 nm along the optical axis and 5 nm in the image plane with a maximum sampling rate of 3-4 Hz. The method was applied to track fluorescent particles in artificial solutions and living cells. In a solution of viscosity 30 cP, the mean squared distance (MSD) traveled by a 264 nm diameter rhodamine-labeled bead was linear with time to 20 s. The measured diffusion coefficient, 0.0558 +/- 0.001 micron2/s (SE, n = 4), agreed with the theoretical value of 0.0556 micron2/s. Statistical variability of MSD curves for a freely diffusing bead was in quantitative agreement with Monte Carlo simulations of three-dimensional random walks. In a porous glass matrix, the MSD data was curvilinear and showed reduced bead diffusion. In cytoplasm of Swiss 3T3 fibroblasts, bead diffusion was restricted. The water permeability in individual Chinese Hamster Ovary cells was measured from the z movement of a fluorescent bead fixed at the cell surface in response osmotic gradients; water permeability was increased by > threefold in cells expressing CHIP28 water channels. The simplicity and precision of this tracking method may be useful to quantify the complex trajectories of fluorescent particles in living cells.

3T3 Cells↗
PubMed1994

"Simulated molecular evolution" or computer-generated artifacts?

1. The authors define a function with value 1 for the positive examples and 0 for the negative ones. They fit a continuous function but do not deal at all with the error margin of the fit, which is almost as large as the function values they compute. 2. The term "quality" for the value of the fitted function gives the impression that some biological significance is associated with values of the fitted function strictly between 0 and 1, but there is no justification for this kind of interpretation and finding the point where the fit achieves its maximum does not make sense. 3. By neglecting the error margin the authors try to optimize the fitted function using differences in the second, third, fourth, and even fifth decimal place which have no statistical significance. 4. Even if such a fit could profit from more data points, the authors should first prove that the region of interest has some kind of smoothness, that is, that a continuous fit makes any sense at all. 5. "Simulated molecular evolution" is a misnomer. We are dealing here with random search. Since the margin of error is so large, the fitted function does not provide statistically significant information about the points in search space where strings with cleavage sites could be found. This implies that the method is a highly unreliable stochastic search in the space of strings, even if the neural network is capable of learning some simple correlations. 6. Classical statistical methods are for these kind of problems with so few data points clearly superior to the neural networks used as a "black box" by the authors, which in the way they are structured provide a model with an error margin as large as the numbers being computed.7. And finally, even if someone would provide us with a function which separates strings with cleavage sites from strings without them perfectly, so-called simulated molecular evolution would not be better than random selection.Since a perfect fit would only produce exactly ones or zeros,starting a search in a region of space where all strings in the neighborhood get the value zero would not provide any kind of directional information for new iterations. We would just skip from one point to the other in a typical random walk manner.

Amino Acid Sequence↗