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At least 235 records · Page 13Linked to original sources

PubMed1996

On the mechanical characterization of compact bone structure using the homogenization theory.

In a previous paper (Crolet et al., 1993, J. Biomechanics 26, 677-687), a modelling of the mechanical behavior of compact bone was presented, in which the homogenization theory was the basic tool of computation. In this simulation, approximations were used for the modelling of the lamellae and the osteons: the lamella and the osteon were divided into cylindrical sectors, each sector being approximated as a parallelepiped having a periodic structure (fibrous composite for the lamella, superimposition of plates for the osteon). The present study deals with a new model without these approximations. First, it can be proved that the homogenized elasticity tensor for a lamella, which has non-periodic structure, is obtained at each geometrical point as a homogenized tensor of a periodic problem. Similarly, for the osteonal structure, the components of the homogenized tensor are determined at each point as the result of a periodic homogenization. The software OSTEON, which is the computational method associated with this model, allows one to obtain a better understanding of the effects of many bony parameters. The obtained results are in accordance with experimental data.

Algorithms↗

PubMed1993

Protein unfolding pathways explored through molecular dynamics simulations.

Herein we describe the results of molecular dynamics simulations of the bovine pancreatic trypsin inhibitor (BPTI) in solution at a variety of temperatures both with and without disulfide bonds. The reduced form of the protein unfolded at high temperature to an ensemble of conformations with all the properties of the molten globule state. In this account we outline the structural details of the actual unfolding process between the native and molten globule states. The first steps of unfolding involved expansion of the protein, which disrupted packing interactions. The solvent-accessible surface area also quickly increased. The unfolding was localized mostly to the turn and loop regions of the molecule, while leaving the secondary structure intact. Then, there was more gradual unfolding of the secondary structure and non-native turns became prevalent. This same trajectory was continued and more drastic unfolding occurred that resulted in a relatively compact state devoid of stable secondary structure.

Aprotinin↗

PubMed1999

Mapping the interactions present in the transition state for unfolding/folding of FKBP12.

The structure of the transition state for folding/unfolding of the immunophilin FKBP12 has been characterised using a combination of protein engineering techniques, unfolding kinetics, and molecular dynamics simulations. A total of 34 mutations were made at sites throughout the protein to probe the extent of secondary and tertiary structure in the transition state. The transition state for folding is compact compared with the unfolded state, with an approximately 30 % increase in the native solvent-accessible surface area. All of the interactions are substantially weaker in the transition state, as probed by both experiment and molecular dynamics simulations. In contrast to some other proteins of this size, no element of structure is fully formed in the transition state; instead, the transition state is similar to that found for smaller, single-domain proteins, such as chymotrypsin inhibitor 2 and the SH3 domain from alpha-spectrin. For FKBP12, the central three strands of the beta-sheet, beta-strand 2, beta-strand 4 and beta-strand 5, comprise the most structured region of the transition state. In particular Val101, which is one of the most highly buried residues and located in the middle of the central beta-strand, makes approximately 60 % of its native interactions. The outer beta-strands and the ends of the central beta-strands are formed to a lesser degree. The short alpha-helix is largely unstructured in the transition state, as are the loops. The data are consistent with a nucleation-condensation model of folding, the nucleus of which is formed by side-chains within beta-strands 2, 4 and 5, and the C terminus of the alpha-helix. The precise residues involved in the nucleus differ in the two simulated transition state ensembles, but the interacting regions of the protein are conserved. These residues are distant in the primary sequence, demonstrating the importance of tertiary interactions in the transition state. The two independently derived transition state ensembles are structurally similar, which is consistent with a Bronsted analysis confirming that the transition state is an ensemble of states close in structure.

Computer Simulation↗

PubMed2003

Stochastic roadmap simulation: an efficient representation and algorithm for analyzing molecular motion.

Classic molecular motion simulation techniques, such as Monte Carlo (MC) simulation, generate motion pathways one at a time and spend most of their time in the local minima of the energy landscape defined over a molecular conformation space. Their high computational cost prevents them from being used to compute ensemble properties (properties requiring the analysis of many pathways). This paper introduces stochastic roadmap simulation (SRS) as a new computational approach for exploring the kinetics of molecular motion by simultaneously examining multiple pathways. These pathways are compactly encoded in a graph, which is constructed by sampling a molecular conformation space at random. This computation, which does not trace any particular pathway explicitly, circumvents the local-minima problem. Each edge in the graph represents a potential transition of the molecule and is associated with a probability indicating the likelihood of this transition. By viewing the graph as a Markov chain, ensemble properties can be efficiently computed over the entire molecular energy landscape. Furthermore, SRS converges to the same distribution as MC simulation. SRS is applied to two biological problems: computing the probability of folding, an important order parameter that measures the "kinetic distance" of a protein's conformation from its native state; and estimating the expected time to escape from a ligand-protein binding site. Comparison with MC simulations on protein folding shows that SRS produces arguably more accurate results, while reducing computation time by several orders of magnitude. Computational studies on ligand-protein binding also demonstrate SRS as a promising approach to study ligand-protein interactions.

Algorithms↗

PubMed1995

Partially folded states of proteins: characterization by X-ray scattering.

Partially folded states of proteins are found to occur with a wide variety of degrees of unfolding, ranging from the compact molten globule to the fully unfolded forms, depending on solvent conditions and the specific protein involved. Small to intermediate angle X-ray scattering from partially folded states of proteins yields low resolution scattering profiles that may be used to explore the degree of folding of a protein under given solution conditions. By Monte Carlo simulation of a highly simplified homopolymer model, we show that such partially folded states will yield a characteristic scattering profile that may be written as a linear superposition of scattering from a compact core and of scattering from random coil loops that emerge from this core. We also find a term resulting from interference of X-rays scattering from the core with those scattering from the loops. This interference term oscillates in sign and tends to enhance the core portion of the scattering profile. We compare the model calculations of the scattering profile with measurements of the scattering profile as a function of salt concentration for cytochrome c at pH 2. Because of our characterization of the scattering profiles, we suggest that these results may be re-interpreted in terms of the presence of a range of partially folded states as a function of pH and salt concentration, and that the observed scattering profiles are consistent with the characterization of the partially folded states in terms of random coil loops emerging from a compact core with the loop fraction increasing as the salt concentration is decreased. This characterization is consistent with data on amide protection against H-2H exchange of compact regions within partially folded states observed for a number of proteins, including cytochrome c.

Computer Simulation↗

PubMed1979

The efficient numerical solution of biological simulation problems.

A subroutine called DESOL for the numerical solution of ordinary differential equations of the type arising in biological simulation problems is described. DESOL is about as efficient as current high quality integrators, but because of its compactness it can be easily used on small computers. The subroutine has excellent stability properties and functions with very little required input from the user. In addition, it has features which aid in debugging associated programs. Several test and example problems are given, as is the derivation of the major formulae used in the package.

Computers↗

PubMed1993

Structure and Energetics of model amphiphilic molecules at the water liquid-vapor interface. A molecular dynamics study.

A molecular dynamics study of adsorption of p-n-pentylphenol at infinite dilution at the water liquid-vapor interface is reported. The calculated free energy of adsorption is -8.8 +/- 0.7 kcal/mol, in good agreement with the experimental value of -7.3 kcal/mol. The transition between the interfacial region and the bulk solution is sharp and well-defined by energetic, conformational, and orientational criteria. At the water surface, the phenol head group is mostly immersed in aqueous solvent. The most frequent orientation of the hydrocarbon tail is parallel to the interface, due to dispersion interactions with the water surface. This arrangement of the phenol ring and the alkyl chain requires that the chain exhibits a kink. As the polar head group is being moved into the solvent, the chain length increases and the tail becomes increasingly aligned toward the surface normal, such that the nonpolar part of the molecule exposed to water is minimized. The same effect was achieved when phenol was replaced by a more polar head group, phenolate. This result underscores the difference between hydrophobic hydration at the surface and in the bulk solvent, when nonpolar molecular fragments adopt compact conformations.

Adsorption↗

PubMed2002

Using robotics to fold proteins and dock ligands.

The problems of protein folding and ligand docking have been explored largely using molecular dynamics or Monte Carlo methods. These methods are very compute intensive because they often explore a much wider range of energies, conformations and time than necessary. In addition, Monte Carlo methods often get trapped in local minima. We initially showed that robotic motion planning permitted one to determine the energy of binding and dissociation of ligands from protein binding sites (Singh et al., 1999). The robotic motion planning method maps complicated three-dimensional conformational states into a much simpler, but higher dimensional space in which conformational rearrangements can be represented as linear paths. The dimensionality of the conformation space is of the same order as the number of degrees of conformational freedom in three-dimensional space. We were able to determine the relative energy of association and dissociation of a ligand to a protein by calculating the energetics of interaction for a few thousand conformational states in the vicinity of the protein and choosing the best path from the roadmap. More recently, we have applied roadmap planning to the problem of protein folding (Apaydin et al., 2002a). We represented multiple conformations of a protein as nodes in a compact graph with the edges representing the probability of moving between neighboring states. Instead of using Monte Carlo simulation to simulate thousands of possible paths through various conformational states, we were able to use Markov methods to calculate the steady state occupancy of each conformation, needing to calculate the energy of each conformation only once. We referred to this Markov method of representing multiple conformations and transitions as stochastic roadmap simulation or SRS. We demonstrated that the distribution of conformational states calculated with exhaustive Monte Carlo simulations asymptotically approached the Markov steady state if the same Boltzman energy distribution was used in both methods. SRS permits one to calculate contributions from all possible paths simultaneously with far fewer energy calculations than Monte Carlo or molecular dynamics methods. The SRS method also permits one to represent multiple unfolded starting states and multiple, near-native, folded states and all possible paths between them simultaneously. The SRS method is also independent of the function used to calculate the energy of the various conformational states. In a paper to be presented at this conference (Apaydin et al., 2002b) we have also applied SRS to ligand docking in which we calculate the dynamics of ligand-protein association and dissociation in the region of various binding sites on a number of proteins. SRS permits us to determine the relative times of association to and dissociation from various catalytic and non-catalytic binding sites on protein surfaces. Instead of just following the best path in a roadmap, we can calculate the contribution of all the possible binding or dissociation paths and their relative probabilities and energies simultaneously.

Algorithms↗

PubMed1999

Simple model with facilitated dynamics for granular compaction.

A simple lattice model is used to study compaction in granular media. As in real experiments, we consider a series of taps separated by large enough waiting times. The relaxation of the density exhibits the characteristic inverse logarithmic law. Moreover, we have been able to identify analytically the relevant time scale, leading to a relaxation law independent of the specific values of the parameters. Also, an expression for the asymptotic density reached in the compaction process has been derived. The theoretical predictions agree fairly well with the results from the Monte Carlo simulation.

Journal Article↗

PubMed2003

Crystal nucleation in the hard sphere system.

The structure and growth of crystal nuclei that spontaneously form during computer simulations of the simplest nontrivial model of a liquid, the hard sphere system, is described in this work. Compact crystal nuclei are observed to form at densities within the coexistence region of the phase diagram. The nuclei possess a range of morphologies with a predominance of multiply twinned particles possessing in some cases a significant decahedral character. However the multiply twinned particles do not form from an initial decahedral core but appear to nucleate as blocks of a face-centered cubic crystal partially bounded by stacking faults.

Journal Article↗

PubMed2003

Determination of field capacity of municipal solid waste with surcharge simulation.

The following study was carried out as part of the environmental monitoring of a landfill in Nuevo Laredo, Tamaulipas (Mexico). The parameter of field capacity is important in predicting the amount of leachate generated by solid waste disposal sites, because of the polluting potential of leachate. This paper describes how the field capacity for municipal solid waste was determined, and the purpose of this document is to present a methodology, and to describe the devices designed for determining the field capacity of municipal solid waste. The method consists of applying a surcharge to a representative sample of rubbish, to simulate the effects of the overlying layers in a landfill. The experimental results showed that the higher the compaction of the sample, the smaller the amount of water required to satisfy the field capacity and thus to start the leaching process. Standardisation of the methodology for determining this parameter is required in order to be able to compare the results with those obtained in other parts of the world.

Forecasting↗

PubMed1997

Modeling mechanical cardiopulmonary interactions for virtual environments.

We have developed a computer system for modeling mechanical cardiopulmonary behavior in an interactive, 3D virtual environment. The system consists of a compact, scalar description of cardiopulmonary mechanics, with an emphasis on respiratory mechanics, that drives deformable 3D anatomy to simulate mechanical behaviors of and interactions between physiological systems. Such an environment can be used to facilitate exploration of cardiopulmonary physiology, particularly in situations that are difficult to reproduce clinically. We integrate 3D deformable body dynamics with new, formal models of (scalar) cardiorespiratory physiology, associating the scalar physiological variables and parameters with corresponding 3D anatomy. Our approach is amenable to modeling patient-specific circumstances in two ways. First, using CT scan data, we apply semi-automatic methods for extracting and reconstructing the anatomy to use in our simulations. Second, our scalar models are defined in terms of clinically-measurable, patient-specific parameters. This paper describes our approach and presents a sample of results showing normal breathing and acute effects of pneumothoraces.

Computer Simulation↗

PubMed1994

Theoretical conformational analysis of the opioid delta antagonist H-Tyr-Tic-Phe-OH and the mu agonist H-Tyr-D-Tic-Phe-NH2.

A molecular mechanics study (grid search and energy minimization) of the highly delta receptor-selective delta opioid antagonist H-Tyr-Tic-Phe-OH (TIP; Tic: tetrahydroisoquinoline-3-carboxylic acid) resulted in four low energy conformers with energies within 2 kcal/mol of that of the lowest energy structure. These four conformers contain trans peptide bonds only and represent compact structures showing various patterns of aromatic ring stacking. The centrally located Tic residue imposes several conformational constraints on the N-terminal dipeptide segment; however, the results of molecular dynamics simulations indicated that this tripeptide still shows some structural flexibility, particularly at the Phe3 residue. Analogous studies performed with the structurally related mu receptor-selective mu agonist H-Tyr-D-Tic-Phe-NH2 resulted in low energy structures that were also compact but showed patterns of ring stacking different from those obtained with TIP. Superimposition of low energy conformers of TIP and H-Tyr-D-Tic-Phe-NH2 revealed that the Phe3 residues of the L-Tic- and the D-Tic peptide were always located on opposite sides of the plane defined by the Tic residue, thus providing an explanation for the distinct activity profiles of the two compounds in structural terms. Attempts to demonstrate spatial overlap between the pharmacophoric moieties of low energy conformers of TIP and the nonpeptide delta antagonist naltrindole were made by superimposing either the Tyr1 and Tic2 aromatic rings and the N-terminal amino group or the Tyr1 and Phe3 aromatic rings and the N-terminal amino group of the peptide with the corresponding aromatic rings and nitrogen atom in the alkaloid structure.(ABSTRACT TRUNCATED AT 250 WORDS)

Amino Acid Sequence↗

PubMed2000

Staphylococcal protein A: unfolding pathways, unfolded states, and differences between the B and E domains.

We present multiple native and denaturation simulations of the B and E domains of the three-helix bundle protein A, totaling 60 ns. The C-terminal helix (H3) consistently denatures later than either of the other two helices and contains residual helical structure in the denatured state. These results are consistent with experiments suggesting that the isolated H3 fragment is more stable than H1 and H2 and that H3 forms early in folding. Interestingly, the denatured state of the B domain is much more compact than that of the E domain. This sequence-dependent effect on the dimensions of the denatured state and the lack of correlation with structure suggest that the radius of gyration can be a misleading reaction coordinate for unfolding/folding. Various unfolding and refolding events are observed in the denaturation simulations. In some cases, the transitions are facilitated through interactions with other portions of the protein-contact-assisted helix formation. In the native simulations, the E domain is very stable: after 6 ns, the C(alpha) root-mean-square deviation from the starting structure is less than 1.4 A. In contrast, the native state of the B domain deviates more and its inter-helical angles fluctuate. In apparent contrast, we note that the B domain is thermodynamically more stable than the E domain. The simulations suggest that the increased stability of the B domain may be due to heightened mobility, and therefore entropy, in the native state and decreased mobility/entropy in the more compact denatured state.

Amino Acid Sequence↗

PubMed1992

Folding protein alpha-carbon chains into compact forms by Monte Carlo methods.

A method is presented for generating folded chains of specific amino acid sequences on a simple cubic lattice. Monte Carlo simulations are used to transform extended geometries of simplified alpha-carbon chains for eight small monomeric globular proteins into folded states. Permitted chain transitions are limited to a few types of moves, all restricted to occur on the lattice. Crude residue-residue potentials derived from statistical structure data are used to describe the energies for each conformer. The low resolution structures obtained by this procedure contain many of the correct gross features of the native folded architectures with respect to average residue energy per nonbonded contact, segment density, and location of surface loops and disulfide pairs. Rms deviations between these and the native X-ray structures and percentage of native long-range contacts found in these final folded structures are 7.6 +/- 0.7 A and 48 +/- 3%, respectively. This procedure can be useful for predicting approximate tertiary interactions from amino acid sequence.

Models, Molecular↗

PubMed2002

Temperature-dependent H/D exchange of compact and elongated cytochrome c ions in the gas phase.

Isotopic exchange reactions of compact and elongated conformations of gaseous cytochrome c ions (+5 and +9 states) with D2O have been measured as a function of temperature (from 300 to approximately 440 K) using ion mobility techniques. Rate constants for those sites that exchange at high temperatures (>400 K) are about an order of magnitude smaller than rate constants for sites that exchange at 300 K. Although the exchange rates decrease, the maximum exchange levels for rapidly exchanging sites increase with temperature. At 300 K, exchange levels of 53 +/- 3 and 63 +/- 3 are measured for the compact and elongated states, respectively. From 300 to 335 K, the exchange levels increase slightly to approximately 60 to 70 hydrogens. Above 335 K, the levels increase to a value of approximately 200 for the +5 state and approximately 190 for the +9 state, near the maximum possible levels, 200 and 204 for these respective charge states. Molecular dynamics simulations have been carried out on structures having calculated cross sections that are near the experimental values in order to explore the exchange process. Overall, it appears that charge site and exchange site proximities are important factors in the exchange profiles for the elongated +9 ion and the compact +5 ion.

Algorithms↗

PubMed2001

Native topology or specific interactions: what is more important for protein folding?

Fifty-five molecular dynamics runs of two three-stranded antiparallel beta-sheet peptides were performed to investigate the relative importance of amino acid sequence and native topology. The two peptides consist of 20 residues each and have a sequence identity of 15 %. One peptide has Gly-Ser (GS) at both turns, while the other has d-Pro-Gly ((D)PG). The simulations successfully reproduce the NMR solution conformations, irrespective of the starting structure. The large number of folding events sampled along the trajectories at 360 K (total simulation time of about 5 micros) yield a projection of the free-energy landscape onto two significant progress variables. The two peptides have compact denatured states, similar free-energy surfaces, and folding pathways that involve the formation of a beta-hairpin followed by consolidation of the unstructured strand. For the GS peptide, there are 33 folding events that start by the formation of the 2-3 beta-hairpin and 17 with first the 1-2 beta-hairpin. For the (D)PG peptide, the statistical predominance is opposite, 16 and 47 folding events start from the 2-3 beta-hairpin and the 1-2 beta-hairpin, respectively. These simulation results indicate that the overall shape of the free-energy surface is defined primarily by the native-state topology, in agreement with an ever-increasing amount of experimental and theoretical evidence, while the amino acid sequence determines the statistically predominant order of the events.

Computer Simulation↗

PubMed1990

Cyclic fatigue-crack propagation, stress-corrosion, and fracture-toughness behavior in pyrolytic carbon-coated graphite for prosthetic heart valve applications.

Fracture-mechanics tests were performed to characterize the cyclic fatigue, stress-corrosion cracking, and fracture-toughness behavior of a pyrolytic carbon-coated graphite composite material used in the manufacture of cardiac valve prostheses. Testing was carried out using compact tension C(T) samples containing "atomically" sharp precracks, both in room-temperature air and principally in a simulated physiological environment of 37 degrees C Ringer's lactate solution. Under sustained (monotonic) loads, the composite exhibited resistance-curve behavior, with a fracture toughness (KIc) between 1.1 and 1.9 MPa square root of m, and subcritical stress-corrosion crack velocities (da/dt) which were a function of the stress intensity K raised to the 74th power (over the range approximately 10(-9) to over 10(-5) m/s). More importantly, contrary to common perception, under cyclic loading conditions the composite was found to display true (cyclic) fatigue failure in both environments; fatigue-crack growth rates (da/dN) were seen to be a function of the 19th power of the stress-intensity range delta K (over the range approximately 10(-11) to over 10(-8) m/cycle). As subcritical crack velocities under cyclic loading were found to be many orders of magnitude faster than those measured under equivalent monotonic loads and to occur at typically 45% lower stress-intensity levels, cyclic fatigue in pyrolytic carbon-coated graphite is reasoned to be a vital consideration in the design and life-prediction procedures of prosthetic devices manufactured from this material.

Biocompatible Materials↗