Folding simulations of a three-stranded antiparallel β-sheet peptide

Protein folding is a grand challenge of the postgenomic era. In this paper, 58 folding events sampled during 47 molecular dynamics trajectories for a total simulation time of more than 4 μs provide an atomic detail picture of the folding of a 20-residue synthetic peptide with a stable three-stranded antiparallel β-sheet fold. The simulations successfully reproduce the NMR solution conformation, irrespective of the starting structure. The sampling of the conformational space is sufficient to determine the free energy surface and localize the minima and transition states. The statistically predominant folding pathway involves the formation of contacts between strands 2 and 3, starting with the side chains close to the turn, followed by association of the N-terminal strand onto the preformed 2–3 β-hairpin. The folding mechanism presented here, formation of a β-hairpin followed by consolidation, is in agreement with a computational study of the free energy surface of another synthetic three-stranded antiparallel β-sheet by Bursulaya and Brooks [(1999) J. Am. Chem. Soc. 121, 9947–9951]. Hence, it might hold in general for antiparallel β-sheets with short turns.

How optimization of potential functions affects protein folding.

The relationship between the optimization of the potential function and the foldability of theoretical protein models is studied based on investigations of a 27-mer cubic-lattice protein model and a more realistic lattice model for the protein crambin. In both the simple and the more complicated systems, optimization of the energy parameters achieves significant improvements in the statistical-mechanical characteristics of the systems and leads to foldable protein models in simulation experiments. The foldability of the protein models is characterized by their statistical-mechanical properties--e.g., by the density of states and by Monte Carlo folding simulations of the models. With optimized energy parameters, a high level of consistency exists among different interactions in the native structures of the protein models, as revealed by a correlation function between the optimized energy parameters and the native structure of the model proteins. The results of this work are relevant to the design of a general potential function for folding proteins by theoretical simulations.

Thermodynamic parameters for the helix-coil transition of oligopeptides: molecular dynamics simulation with the peptide growth method.

The helix-coil transition equilibrium of polypeptides in aqueous solution was studied by molecular dynamics simulation. The peptide growth simulation method was introduced to generate dynamic models of polypeptide chains in a statistical (random) coil or an alpha-helical conformation. The key element of this method is to build up a polypeptide chain during the course of a molecular transformation simulation, successively adding whole amino acid residues to the chain in a predefined conformation state (e.g., alpha-helical or statistical coil). Thus, oligopeptides of the same length and composition, but having different conformations, can be incrementally grown from a common precursor, and their relative conformational free energies can be calculated as the difference between the free energies for growing the individual peptides. This affords a straightforward calculation of the Zimm-Bragg sigma and s parameters for helix initiation and helix growth. The calculated sigma and s parameters for the polyalanine alpha-helix are in reasonable agreement with the experimental measurements. The peptide growth simulation method is an effective way to study quantitatively the thermodynamics of local protein folding.

Submillisecond folding of monomeric lambda repressor.

The folding kinetics of a truncated form of the N-terminal domain of phage lambda repressor [lambda 6-85] has been investigated by using the technique of dynamic NMR. lambda 6-85 has been shown previously to fold in a purely two-state fashion. This allows the determination of folding and unfolding rates from simulation of the exchange-broadened aromatic resonances of Tyr-22. The folding kinetics were determined over a range of 1.35 to 3.14 M urea. The urea dependence of both folding and unfolding rate constants is exponential, suggesting that the rate-determining step is invariant at the urea concentrations studied. The folding and unfolding rates extrapolated to 0 M urea at 37 degrees C are 3600 +/- 400 s-1 and 27 +/- 6 s-1, respectively. The observed lambda 6-85 folding rate constant exceeds that of other fast-folding globular proteins by a factor of 14-54. The urea dependence of the folding and unfolding rate constants suggests that the transition state of the rate-determining step is considerably more exposed to solvent than previously studied protein-folding transition states. The surprising rapidity of lambda 6-85 folding and unfolding may be the consequence of its all-helical secondary structure. These kinetic results clearly demonstrate that all of the fundamental events of protein folding can occur on the submillisecond time scale.

Controlling protein molecular dynamics:how to accelerate folding while preserving the native state

The dynamics of peptides and proteins generated by classical molecular dynamics (MD) is described by using a Markov model. The model is built by clustering the trajectory into conformational states and estimating transition probabilities between the states. Assuming that it is possible to influence the dynamics of the system by varying simulation parameters, we show how to use the Markov model to determine the parameter values that preserve the folded state of the protein and at the same time, reduce the folding time in the simulation. We investigate this by applying the method to two systems. The first system is an imaginary peptide described by given transition probabilities with a total folding time of 1 micros. We find that only small changes in the transition probabilities are needed to accelerate (or decelerate) the folding. This implies that folding times for slowly folding peptides and proteins calculated using MD cannot be meaningfully compared to experimental results. The second system is a four residue peptide valine-proline-alanine-leucine in water. We control the dynamics of the transitions by varying the temperature and the atom masses. The simulation results show that it is possible to find the combinations of parameter values that accelerate the dynamics and at the same time preserve the native state of the peptide. A method for accelerating larger systems without performing simulations for the whole folding process is outlined.

Why are MD simulated protein folding times wrong?

The question of significant deviations of protein folding times simulated using molecular dynamics from experimental values is investigated. It is shown that in the framework of Markov State Model (MSM) describing the conformational dynamics of peptides and proteins, the folding time is very sensitive to the simulation model parameters, such as forcefield and temperature. Using two peptides as examples, we show that the deviations in the folding times can reach an order of magnitude for modest variations of the molecular model. We, therefore, conclude that the folding rate values obtained in molecular dynamics simulations have to be treated with care.

The thermodynamics and statistical mechanics of protein folding

The physics of self-organization and complexity is manifested on a variety of biological scales, from large ecosystems to the molecular level. Protein molecules exhibit characteristics of complex systems in terms of their structure, dynamics, and function. Proteins have the extraordinary ability to fold to a specific functional three-dimensional shape, starting from a random coil, in a biologically relevant time. How they accomplish this is one of the secrets of life. In this work, theoretical research into understanding this remarkable behavior is discussed. Thermodynamic and statistical mechanical tools are used in order to investigate the protein folding dynamics and stability. Theoretical analyses of the results from computer simulation of the dynamics of a four-helix bundle show that the excluded volume entropic effects are very important in protein dynamics and crucial for protein stability. The dramatic effects of changing the size of sidechains imply that a strategic placement of amino acid residues with a particular size may be an important consideration in protein engineering. Another investigation deals with modeling protein structural transitions as a phase transition. Using finite size scaling theory, the nature of unfolding transition of a four-helix bundle protein was investigated and critical exponents for the transition were calculated for various hydrophobic strengths in the core. It is found that the order of the transition changes from first to higher order as the strength of the hydrophobic interaction in the core region is significantly increased. Finally, a detailed kinetic and thermodynamic analysis was carried out in a model two-helix bundle. The connection between the structural free-energy landscape and folding kinetics was quantified. I show how simple protein engineering, by changing the hydropathy of a small number of amino acids, can enhance protein folding by significantly changing the free energy landscape so that kinetic traps are removed. The results have general applicability in protein engineering as well as understanding the underlying physical mechanisms of protein folding. ^

Studies of Protein-Protein and Protein-Water Interactions by Small Angle X-Ray Scattering, Terahertz Spectroscopy, ASMOS, And Computer Simulation

The protein folding problem has been one of the most challenging subjects in biological physics due to its complexity. Energy landscape theory based on statistical mechanics provides a thermodynamic interpretation of the protein folding process. We have been working to answer fundamental questions about protein-protein and protein-water interactions, which are very important for describing the energy landscape surface of proteins correctly. At first, we present a new method for computing protein-protein interaction potentials of solvated proteins directly from SAXS data. An ensemble of proteins was modeled by Metropolis Monte Carlo and Molecular Dynamics simulations, and the global X-ray scattering of the whole model ensemble was computed at each snapshot of the simulation. The interaction potential model was optimized and iterated by a Levenberg-Marquardt algorithm. Secondly, we report that terahertz spectroscopy directly probes hydration dynamics around proteins and determines the size of the dynamical hydration shell. We also present the sequence and pH-dependence of the hydration shell and the effect of the hydrophobicity. On the other hand, kinetic terahertz absorption (KITA) spectroscopy is introduced to study the refolding kinetics of ubiquitin and its mutants. KITA results are compared to small angle X-ray scattering, tryptophan fluorescence, and circular dichroism results. We propose that KITA monitors the rearrangement of hydrogen bonding during secondary structure formation. Finally, we present development of the automated single molecule operating system (ASMOS) for a high throughput single molecule detector, which levitates a single protein molecule in a 10 µm diameter droplet by the laser guidance. I also have performed supporting calculations and simulations with my own program codes.

Monte Carlo Simulation Of The Response Functions Of Cdte Detectors To Be Applied In X-ray Spectroscopy.

In this work, the energy response functions of a CdTe detector were obtained by Monte Carlo (MC) simulation in the energy range from 5 to 160keV, using the PENELOPE code. In the response calculations the carrier transport features and the detector resolution were included. The computed energy response function was validated through comparison with experimental results obtained with (241)Am and (152)Eu sources. In order to investigate the influence of the correction by the detector response at diagnostic energy range, x-ray spectra were measured using a CdTe detector (model XR-100T, Amptek), and then corrected by the energy response of the detector using the stripping procedure. Results showed that the CdTe exhibits good energy response at low energies (below 40keV), showing only small distortions on the measured spectra. For energies below about 80keV, the contribution of the escape of Cd- and Te-K x-rays produce significant distortions on the measured x-ray spectra. For higher energies, the most important correction is the detector efficiency and the carrier trapping effects. The results showed that, after correction by the energy response, the measured spectra are in good agreement with those provided by a theoretical model of the literature. Finally, our results showed that the detailed knowledge of the response function and a proper correction procedure are fundamental for achieving more accurate spectra from which quality parameters (i.e., half-value layer and homogeneity coefficient) can be determined.

Influence of intrapulpal pressure simulation on the bond strength of adhesive systems to dentin

The purpose of this study was to evaluate the influence of intrapulpal pressure simulation on the bonding effectiveness of etch & rinse and self-etch adhesives to dentin. Eighty sound human molars were distributed into eight groups, according to the permeability level of each sample, measured by an apparatus to assess hydraulic conductance (Lp). Thus, a similar mean permeability was achieved in each group. Three etch & rinse adhesives (Prime & Bond NT - PB, Single Bond -SB, and Excite - EX) and one self-etch system (Clearfil SE Bond - SE) were employed, varying the presence or absence of an intrapulpal pressure (IPP) simulation of 15 cmH2O. After adhesive and restorative procedures were carried out, the samples were stored in distilled water for 24 hours at 37°C, and taken for tensile bond strength (TBS) testing. Fracture analysis was performed using a light microscope at 40 X magnification. The data, obtained in MPa, were then submitted to the Kruskal-Wallis test ( a = 0.05). The results revealed that the TBS of SB and EX was significantly reduced under IPP simulation, differing from the TBS of PB and SE. Moreover, SE obtained the highest bond strength values in the presence of IPP. It could be concluded that IPP simulation can influence the bond strength of certain adhesive systems to dentin and should be considered when in vitro studies are conducted.

Evaluation of thermal simulation of households in the metropolitan region of São Paulo, Brazil

Abstract This paper aims at assessing the performance of a program of thermal simulation (Arquitrop) in different households in the city of Sao Paulo, Brazil. The households were selected for the Wheezing Project which followed up children under 2 years old to monitor the occurrence of respiratory diseases. The results show that in all three study households there is a good approximation between the observed and the simulated indoor temperatures. It was also observed a fairly consistent and realistic behavior between the simulated indoor and the outdoor temperatures, describing the Arquitrop model as an efficient estimator and good representative of the thermal behavior of households in the city of Sao Paulo. The worst simulation is linked to the poorest type of construction. This may be explained by the bad quality of the construction, which the Architrop could not simulate adequately

The Process of Simulation Authoring/Creation by Chemistry Teachers: A Service Learning Experience

Two case studies are presented to describe the process of public school teachers authoring and creating chemistry simulations. They are part of the Virtual Didactic Laboratory for Chemistry, a project developed by the School of the Future of the University of Sao Paulo. the documental analysis of the material produced by two groups of teachers reflects different selection process for both themes and problem-situations when creating simulations. The study demonstrates the potential for chemistry learning with an approach that takes students' everyday lives into account and is based on collaborative work among teachers and researches. Also, from the teachers' perspectives, the possibilities of interaction that a simulation offers for classroom activities are considered.

Study of the antimicrobial peptide indolicidin and a mutant in micelle medium by molecular dynamics simulation

The antimicrobial peptide indolicidin (IND) and the mutant CP10A in hydrated micelles were studied using molecular dynamics simulations in order to observe whether the molecular dynamics and experimental data could be sufficiently correlated and a detailed description of the interaction of the antimicrobial peptides with a model of the membrane provided by a hydrated micelle system could be obtained. In agreement with the experiments, the simulations showed that the peptides are located near the surface of the micelles. Peptide insertions agree with available experimental data, showing deeper insertion of the mutant compared with the peptide IND. Major insertion into the hydrophobic core of the micelle by all tryptophan and mutated residues of CP10A in relation to IND was observed. The charged residues of the terminus regions of both peptides present similar behavior, indicating that the major differences in the interactions with the micelles of the peptides IND and CP10A occur in the case of the hydrophobic residues.

Fossil groups in the Millennium Simulation Evolution of the brightest galaxies

Aims. We create a catalogue of simulated fossil groups and study their properties, in particular the merging histories of their first-ranked galaxies. We compare the simulated fossil group properties with those of both simulated non-fossil and observed fossil groups. Methods. Using simulations and a mock galaxy catalogue, we searched for massive (>5 x 10(13) h(-1) M-circle dot) fossil groups in the Millennium Simulation Galaxy Catalogue. In addition, we attempted to identify observed fossil groups in the Sloan Digital Sky Survey Data Release 6 using identical selection criteria. Results. Our predictions on the basis of the simulation data are: (a) fossil groups comprise about 5.5% of the total population of groups/clusters with masses larger than 5 x 10(13) h(-1) M-circle dot. This fraction is consistent with the fraction of fossil groups identified in the SDSS, after all observational biases have been taken into account; (b) about 88% of the dominant central objects in fossil groups are elliptical galaxies that have a median R-band absolute magnitude of similar to-23.5-5 log h, which is typical of the observed fossil groups known in the literature; (c) first-ranked galaxies of systems with M > 5 x 10(13) h(-1) M-circle dot, regardless of whether they are either fossil or non-fossil, are mainly formed by gas-poor mergers; (d) although fossil groups, in general, assembled most of their virial masses at higher redshifts in comparison with non-fossil groups, first-ranked galaxies in fossil groups merged later, i.e. at lower redshifts, compared with their non-fossil-group counterparts. Conclusions. We therefore expect to observe a number of luminous galaxies in the centres of fossil groups that show signs of a recent major merger.

Fossil groups in the Millennium simulation Their environment and its evolution

Context. Fossil systems are defined to be X- ray bright galaxy groups ( or clusters) with a two- magnitude difference between their two brightest galaxies within half the projected virial radius, and represent an interesting extreme of the population of galaxy agglomerations. However, the physical conditions and processes leading to their formation are still poorly constrained. Aims. We compare the outskirts of fossil systems with that of normal groups to understand whether environmental conditions play a significant role in their formation. We study the groups of galaxies in both, numerical simulations and observations. Methods. We use a variety of statistical tools including the spatial cross- correlation function and the local density parameter Delta(5) to probe differences in the density and structure of the environments of "" normal"" and "" fossil"" systems in the Millennium simulation. Results. We find that the number density of galaxies surrounding fossil systems evolves from greater than that observed around normal systems at z = 0.69, to lower than the normal systems by z = 0. Both fossil and normal systems exhibit an increment in their otherwise radially declining local density measure (Delta(5)) at distances of order 2.5 r(vir) from the system centre. We show that this increment is more noticeable for fossil systems than normal systems and demonstrate that this difference is linked to the earlier formation epoch of fossil groups. Despite the importance of the assembly time, we show that the environment is different for fossil and non- fossil systems with similar masses and formation times along their evolution. We also confirm that the physical characteristics identified in the Millennium simulation can also be detected in SDSS observations. Conclusions. Our results confirm the commonly held belief that fossil systems assembled earlier than normal systems but also show that the surroundings of fossil groups could be responsible for the formation of their large magnitude gap.