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A molecular dynamics study of the structural stability of HIV-1 protease under physiological conditions: the role of Na+ ions in stabilizing the active site.

HIV-1 protease is most active under weakly acidic conditions (pH 3.5-6.5), when the catalytic Asp25 and Asp25' residues share 1 proton. At neutral pH, this proton is lost and the stability of the structure is reduced. Here we present an investigation of the effect of pH on the dynamics of HIV-1 protease using MD simulation techniques. MD simulations of the solvated HIV-1 protease with the Asp25/25' residues monoprotonated and deprotonated have been performed. In addition we investigated the effect of the inclusion of Na(+) and Cl(-) ions to mimic physiological salt conditions. The simulations of the monoprotonated form and deprotonated form including Na(+) show very similar behavior. In both cases the protein remained stable in the compact, "self-blocked" conformation in which the active site is blocked by the tips of the flaps. In the deprotonated system a Na(+) ion binds tightly to the catalytic dyad shielding the repulsion between the COO(-) groups. Ab initio calculations also suggest the geometry of the active site with the Na(+) bound closely resembles that of the monoprotonated case. In the simulations of the deprotonated form (without Na(+) ions), a water molecule bound between the Asp25 Asp25' side-chains. This disrupted the dimerization interface and eventually led to a fully open conformation.

Aspartic Acid↗

Local current spread in electrically compact neurons of the fly.

Analyses of active and passive membrane properties predict an asymmetry in the spread of electrical current through a neuron. Simulated current injection into a large-diameter compartment of a biophysically realistic model neuron causes a local potential shift that can spread throughout the cell. In contrast, causing the same local potential shift in the dendritic tip of the same neuron results in only minimal changes in electrical potential in the rest of the cell. Using calcium as a reporter of electrical activity in neurons in the fly's lobula plate we find that current injected into the thick axon caused depolarization throughout the cell, whereas activation of a dendritic region remained local. These results have important implications for the ability of integrating neurons to perform local computations of synaptic input without additional hardware.

Animals↗

Monte Carlo Simulation of Particle Aggregation and Simultaneous Restructuring.

Ultrafine ("nano"-) particles produced from highly supersaturated vapors or liquids often undergo rapid coagulation and slow interspherule coalescence. Resulting "aggregates" typically contain hundreds of small spherules bound together in tenuous structures characterized by mass fractal dimensions much less than 3. Such aggregates have large and relatively accessible initial surface area but are metastable with respect to more compact configurations, especially in high temperature environments (e.g., flames). Subject to deliberately idealized "uncoupled" rate laws for coagulation and coalescence, we illustrate the power of Monte Carlo simulation methods to obtain the self-preserving joint distribution function (with respect to both particle size and surface area) of populations of coagulating fractal aggregates in the continuum regime, simultaneously undergoing finite-rate restructuring (e.g., via surface-energy-driven viscous flow). Unconditional distributions with respect to either particle volume or area are also obtained from the Monte Carlo simulations. These are conveniently quantified by fitting them to log-normal distributions and we report the sensitivity of the associated spreads to characteristic fusion/coagulation time ratio, chi, and particle fractal dimension, Df, here prespecified. We also calculate and report selected "mixed" moments of the joint pdf with respect to particle volume and surface area needed for engineering calculations of deposition or diffusion-controlled vapor scavenging, as well as the important ratio of actual mean area to that area corresponding to the mean particle volume in the aerosol population. This work sets the stage for tractable simulations of particle dynamics in more complex coagulating systems requiring multi-internal (state-) variables for their more realistic and self-consistent description. Copyright 1999 Academic Press.

Journal Article↗

Kinetics of protein folding. A lattice model study of the requirements for folding to the native state.

A three-dimensional lattice model of a protein is used to investigate the properties required for its folding to the native state. The polypeptide chain is represented as a 27 bead heteropolymer whose lowest energy (native) state can be determined by an exhaustive enumeration of all fully compact conformations. A total of 200 sequences with random interactions are generated and subjected to Monte Carlo simulations to determine which chains find the ground state in a short time; i.e. which sequences overcome the folding problem referred to as the Levinthal paradox. Comparison of the folding and non-folding sequences is used to identify the features that are required for fast folding to the global energy minimum. It is shown that successful folding does not require certain attributes that have been previously proposed as necessary for folding; these include a high number of short versus long-range contacts in the native state, a high content of the secondary structure in the native state, a strong correlation between the native contact map and the interaction parameters, and the existence of a high number of low energy states with near-native conformation. Instead, the essential difference between the folding and the non-folding sequences is the nature of the energy spectrum. The necessary and sufficient condition for a sequence to fold rapidly in the present model is that the native state is a pronounced energy minimum. As a consequence, the thermodynamic stability of the native state of a folding sequence has a sigmoidal dependence on temperature. This permits such a sequence to satisfy both the thermodynamic and the kinetic requirements for folding; i.e. the native state predominates thermodynamically at temperatures that are high enough for folding to be kinetically possible. The applicability of the present results to real proteins is discussed.

Algorithms↗

Structural and functional implications of tau hyperphosphorylation: information from phosphorylation-mimicking mutated tau proteins.

Abnormal tau-immunoreactive filaments are a hallmark of tauopathies, including Alzheimer's disease (AD). A higher phosphorylation ("hyperphosphorylation") state of tau protein may represent a critical event. To determine the potential role of tau hyperphosphorylation in these disorders, mutated tau proteins were produced where serine/threonine residues known to be highly phosphorylated in tau filaments isolated from AD patients were substituted for glutamate to simulate a paired helical filament (PHF)-like tau hyperphosphorylation. We demonstrate that, like hyperphosphorylation, glutamate substitutions induce compact structure elements and SDS-resistant conformational domains in tau protein. Hyperphosphorylation-mimicking glutamate-mutated tau proteins display a complete functional loss in its ability to promote microtubule nucleation which can partially be overcome by addition of the osmolyte trimethylamine N-oxide (TMAO), which is similar to phosphorylated tau. In addition, glutamate-mutated tau proteins fail to interact with the dominant brain protein phosphatase 2A isoform ABalphaC, and exhibit a reduced ability to assemble into filaments. Interestingly, wild-type tau and phosphorylation-mimicking tau similarly bind to microtubules when added alone, but the mutated tau is almost completely displaced from the microtubule surface by equimolar concentrations of wild-type tau. The data indicate that glutamate-mutated tau proteins provide a useful model for analyzing the functional consequences of tau hyperphosphorylation. They suggest that several mechanisms contribute to the abnormal tau accumulation observed during tauopathies, in particular a selective displacement of hyperphosphorylated tau from microtubules, a functional loss in promoting microtubule nucleation, and a failure to interact with phosphatases.

Actin Cytoskeleton↗

Solution structure of microcin J25, the single macrocyclic antimicrobial peptide from Escherichia coli.

The three-dimensional solution structure of microcin J25, the single cyclic representative of the microcin antimicrobial peptide class produced by enteric bacteria, was determined using two-dimensional 1H NMR spectroscopy and molecular modeling. This hydrophobic 21-residue peptide exhibits potent activity directed to Gram-negative bacteria. Its primary structure, cyclo(-V1GIGTPISFY10GGGAGHVPEY20F-), has been determined previously [Blond, A., Péduzzi, J., Goulard, C., Chiuchiolo, M. J., Barthélémy, M., Prigent, Y., Salomón, R.A., Farías, R.N., Moreno, F. & Rebuffat, S. (1999) Eur. J. Biochem., 259, 747-755]. Conformational parameters (3JNHCalphaH coupling constants, quantitative nuclear Overhauser enhancement data, chemical shift deviations, temperature coefficients of amide protons, NH-ND exchange rates) were obtained in methanol solution. Structural restraints consisting of 190 interproton distances inferred from NOE data, 11 phi backbone dihedral angle and 9 chi1 angle restraints derived from the coupling constants and three hydrogen bonds in agreement with the amide exchange rates were used as input for simulated annealing calculations and energy minimization in the program XPLOR. Microcin J25 adopts a well-defined compact structure consisting of a distorted antiparallel beta sheet, which is twisted and folded back on itself, thus resulting in three loops. Residues 7-10 and 17-20 form the more regular part of the beta sheet. The region encompassing residues Gly11-His16 consists of a distorted beta hairpin, which divides into two small loops and is stabilized by an inverse gamma turn and a type I' beta turn. The reversal of the chain leading to the Phe21-Pro6 loop results from a mixed beta/gamma turn. A cavity, in which the hydrophilic Ser8 side-chain is confined, is delimited by two crab pincer-like regions that comprise residues 6-8 and 18-1.

Amino Acid Sequence↗

Activation of cell division protein FtsZ. Control of switch loop T3 conformation by the nucleotide gamma-phosphate.

The effect of bound nucleotide on the conformation of cell division protein FtsZ from Methanococcus jannaschii has been investigated using molecular dynamics and site-directed mutagenesis. The molecular dynamics indicate that the gamma-phosphate of GTP induces a conformational perturbation in loop T3 (Gly88-Gly99 segment), in a position structurally equivalent to switch II of Ha-ras-p21. In the simulated GTP-bound state, loop T3 is pulled by the gamma-phosphate into a more compact conformation than with GDP, related to that observed in the homologous proteins alpha- and beta-tubulin. The existence of a nucleotide-induced structural change in loop T3 has been confirmed by mutating Thr92 into Trp (T92W-W319Y FtsZ). This tryptophan (12 A away from gamma-phosphate) shows large differences in fluorescence emission, depending on which nucleotide is bound to FtsZ monomers. Loop T3 is located at a side of the contact interface between two FtsZ monomers in the current model of FtsZ filament. Such a structural change may bend the GDP filament upon hydrolysis by pushing against helix H8 of next monomer, thus, generating force on the membrane during cell division. A related curvature mechanism may operate in tubulin activation.

Amino Acid Sequence↗

On multiscale approaches to three-dimensional modelling of morphogenesis.

In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction-diffusion model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.

Animals↗

High Q-factor Bragg-reflection sapphire-loaded cavity TE01delta mode resonators.

An innovative method of enhancing the quality factor of TE01delta cavity resonators with a dielectric tube made of monolithic sapphire is presented. Very high Q-factor is achieved by employing a Bragg reflection technique. A TE01delta mode in a copper cavity was measured to have a Q-factor of 1 x 10(5) at 8.78 GHz and 290 K. This is only 30% less than the limit due to the loss tangent of the dielectric material. The technique confines electromagnetic energy in the sapphire dielectric and in the vacuum well away from the cavity walls, thus reducing the surface losses in the copper shield. The technique offers some significant advantages over other methods. One advantage is the very low spurious mode density, which can improve filter and resonator design capabilities. Another is the small compact design, with a single sapphire piece, as compared to previously published Bragg reflection techniques. Finite element simulations and experimental data for this method were compared and found to be in very good agreement. The cavity dimensions were optimized to achieve maximum quality factor.

Aluminum Oxide↗

Maximum-likelihood methods for detecting recent positive selection and localizing the selected site in the genome.

Two maximum-likelihood methods are proposed for detecting recent, strongly positive selection and for localizing the target of selection along a recombining chromosome. The methods utilize the compact mutation frequency spectrum at multiple neutral loci that are partially linked to the selected site. Using simulated data, we show that the power of the tests lies between 80 and 98% in most cases, and the false positive rate could be as low as approximately 10% when the number of sampled marker loci is sufficiently large (> or = 20). The confidence interval around the estimated position of selection is reasonably narrow. The methods are applied to X chromosome data of Drosophila melanogaster from a European and an African population. Evidence of selection was found for both populations (including a selective sweep that was shared between both populations).

Africa↗

Use of MM-PB/SA in estimating the free energies of proteins: application to native, intermediates, and unfolded villin headpiece.

We investigated the stability of three different ensembles of the 36-mer villin headpiece subdomain, the native, a compact folding intermediate, and the random coil. Structures were taken from a 1-micros molecular dynamics folding simulation and a 100-ns control simulation on the native structure. Our approach for each conformation is to first determine the solute internal energy from the molecular mechanics potential and then to add the change resulting from solvation (DeltaG(solv)). Explicit water was used to run the simulation, and a continuum model was used to estimate DeltaG(solv) with the finite difference Poisson-Boltzmann model accounting for the polarization part and a linearly surface area-dependent term for the non-polar part. We leave out the solute vibrational entropy from these values but demonstrate that there is no statistical difference among the native, folding intermediate, and random coil ensembles. We find the native ensemble to be approximately 26 kcal/mol more stable than the folding intermediate and approximately 39 kcal/mol more stable than the random coil ensemble. With an experimental estimate for the free energy of denaturation equal to 3 kcal/mol, we approximate the non-native degeneracy to lie between 10(16) and 10.(25) We also present a possible scheme for the mechanism of folding, first-order exponential decay of a putative transition state, with an estimate for the t(1/2) of folding of approximately 1 micros.

Carrier Proteins↗

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↗

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↗

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↗

The array and interfacial activity of sodium dodecyl benzene sulfonate and sodium oleate at the oil/water interface.

There is a close correlation between the interfacial activity and the adsorption of the surfactant at the interface, but the detailed molecular standard information was scarce. The interfacial activity of two traditional anionic surfactants sodium dodecyl benzene sulfonate (SDBS) and sodium oleate (OAS) were studied by experimental and computer simulation methods. With the spinning drop method and the suspension drop method, the interfacial tension of oil/aqueous surfactant systems was measured, and the influence of surfactant concentration and salinity on the interfacial tension was investigated. The dissipative particle dynamics (DPD) method was used to simulate the adsorption of SDBS and OAS at the oil/water interface. It was shown that it is beneficial to decrease interfacial tension if the hydrophobic chains of the surfactant and the oil have similar structure. The accession of inorganic salts causes surfactant molecules to form more compact and ordered arrangements and helps to decrease the interfacial tension. There is an osculation relation between interfacial density and interfacial activity. The interfacial density calculated by molecular simulation is an effective parameter to exhibit the interfacial activity.

Journal Article↗

Structure factor scaling in colloidal phase separation.

The dynamical scaling hypothesis for the structure factor, S (q) , in depletion-driven colloidal phase separation is studied by carrying out Brownian dynamics simulations. A true dynamical scaling is observed for shallow quenches into the two-phase coexistence region. In such a quench, compact clusters nucleate and grow with time and there is only one characteristic length scale in the system after an initial transient period. Scaling is satisfied beyond this initial period. In contrast, deep quenches lead to fractal cluster growth, and the system is controlled by two characteristic lengths that evolve differently in time [Huang, Oh, and Sorensen (HOS), Phys. Rev. E 57, 875 (1998)]. True dynamical scaling thus cannot be expected to hold. However, an apparent scaling for the structure factor is observed over some period of time when these two characteristic length scales become comparable to each other. We compare our simulation results for the total structure factor to theoretical predictions by HOS by writing it as a product of cluster-cluster and the averaged single-cluster structure factors, each with its own characteristic length.

Journal Article↗

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↗

Modeling H3 histone N-terminal tail and linker DNA interactions.

Molecular dynamics computer simulations were performed for the 25-residue N-terminal tail of the H3 histone protein in the proximity of a DNA segment of 10 base pairs (bp), representing a model for the linker DNA in chromatin. Several least biased configurations were used as initial configurations. The secondary structure content of the protein was increased by the presence of DNA close to it, but the locations of the secondary motifs were different for different initial orientations of the DNA grooves with respect to the protein. As a common feature to all simulations, the electrostatic attraction between negatively charged DNA and positively charged protein was screened by the water solvent and counterbalanced by the intrinsic compaction of the protein due to hydrophobic effects. The protein secondary structure limited the covering of DNA by the protein to 4-5 bp. The degree of compaction and charge density of the bound protein suggests a possible role of H3 tail in a nonspecific bending and plasticity of the linker DNA when the protein is located in the crowded dense chromatin.

Amino Acid Sequence↗