Testing a new Monte Carlo algorithm for protein folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences. Proteins 32:52–66, 1998. © 1998 Wiley-Liss, Inc.     

Configuration and validation of an analytical model predicting secondary neutron radiation in proton therapy using Monte Carlo simulations and experimental measurements

PurposeThis study focuses on the configuration and validation of an analytical model predicting leakage neutron doses in proton therapy.MethodsUsing Monte Carlo (MC) calculations, a facility-specific analytical model was built to reproduce out-of-field neutron doses while separately accounting for the contribution of intra-nuclear cascade, evaporation, epithermal and thermal neutrons. This model was first trained to reproduce in-water neutron absorbed doses and in-air neutron ambient dose equivalents, H*(10), calculated using MCNPX. Its capacity in predicting out-of-field doses at any position not involved in the training phase was also checked. The model was next expanded to enable a full 3D mapping of H*(10) inside the treatment room, tested in a clinically relevant configuration and finally consolidated with experimental measurements.ResultsFollowing the literature approach, the work first proved that it is possible to build a facility-specific analytical model that efficiently reproduces in-water neutron doses and in-air H*(10) values with a maximum difference less than 25%. In addition, the analytical model succeeded in predicting out-of-field neutron doses in the lateral and vertical direction. Testing the analytical model in clinical configurations proved the need to separate the contribution of internal and external neutrons. The impact of modulation width on stray neutrons was found to be easily adjustable while beam collimation remains a challenging issue. Finally, the model performance agreed with experimental measurements with satisfactory results considering measurement and simulation uncertainties.ConclusionAnalytical models represent a promising solution that substitutes for time-consuming MC calculations when assessing doses to healthy organs.     

Domains in folding of model proteins.

By means of Monte Carlo simulation, we investigated the equilibrium between folded and unfolded states of lattice model proteins. The amino acid sequences were designed to have pronounced energy minimum target conformations of different length and shape. For short fully compact (36-mer) proteins, the all-or-none transition from the unfolded state to the native state was observed. This was not always the case for longer proteins. Among 12 designed sequences with the native structure of a fully compact 48-mer, a simple all-or-none transition was observed in only three cases. For the other nine sequences, three states of behavior-the native, denatured, and intermediate states-were found. The contiguous part of the native structure (domain) was conserved in the intermediate state, whereas the remaining part was completely unfolded and structureless. These parts melted separately from each other.     

Tertiary structure prediction of the KIX domain of CBP using Monte Carlo simulations driven by restraints derived from multiple sequence alignments

Using a recently developed protein folding algorithm, a prediction of the tertiary structure of the KIX domain of the CREB binding protein is described. The method incorporates predicted secondary and tertiary restraints derived from multiple sequence alignments in a reduced protein model whose conformational space is explored by Monte Carlo dynamics. Secondary structure restraints are provided by the PHD secondary structure prediction algorithm that was modified for the presence of predicted U-turns, i.e., regions where the chain reverses global direction. Tertiary restraints are obtained via a two-step process: First, seed side-chain contacts are identified from a correlated mutation analysis, and then, a threading-based algorithm expands the number of these seed contacts. Blind predictions indicate that the KIX domain is a putative three-helix bundle, although the chirality of the bundle could not be uniquely determined. The expected root-mean-square deviation for the correct chirality of the KIX domain is between 5.0 and 6.2 Å. This is to be compared with the estimate of 12.9 Å that would be expected by a random prediction, using the model of F. Cohen and M. Sternberg (J. Mol. Biol. 138:321–333, 1980). Proteins 30:287–294, 1998. © 1998 Wiley-Liss, Inc.     

On the origin of the cooperativity of protein folding: Implications from model simulations

There is considerable experimental evidence that the cooperativity of protein folding resides in the transition from the molten globule to the native state. The objective of this study is to examine whether simplified models can reproduce this cooperativity and if so, to identify its origin. In particular, the thermodynamics of the conformational transition of a previously designed sequence (A. Kolinski, W. Galazka, and J. Skolnick, J. Chem. Phys. 103: 10286–10297, 1995), which adopts a very stable Greek-key β-barrel fold has been investigated using the entropy Monte Carlo sampling (ESMC) technique of Hao and Scheraga (M.-H. Hao and H.A. Scheraga, J. Phys. Chem. 98: 9882–9883, 1994). Here, in addition to the original potential, which includes one body and pair interactions between side chains, the force field has been supplemented by two types of multi-body potentials describing side chain interactions. These potentials facilitate the proteinlike pattern of side chain packing and consequently increase the cooperativity of the folding process. Those models that include an explicit cooperative side chain packing term exhibit a well-defined all-or-none transition from a denatured, random coil state to a high-density, well-defined, nativelike low-energy state. By contrast, models lacking such a term exhibit a conformational transition that is essentially continuous. Finally, an examination of the conformations at the free-energy barrier between the native and denatured states reveals that they contain a substantial amount of native-state secondary structure, about 50% of the native contacts, and have an average root mean square radius of gyration that is about 15% larger than native. © 1996 Wiley-Liss, Inc.     

Grazers and grass: Monte Carlo simulations

To illustrate the interplay between grazers and grass, we present a novel Monte Carlo model including grass-island growth, consumption of grass by grazers, and birth, migration and death of grazers. The rates of the former and three latter processes are assumed to depend on the environment so that the conventional mean-field approximation does not hold (in particular, the model takes into account that grass grows on the grass-island boundaries, and grazers are mobile and prefer to stay on the areas covered by grass). Due to the feedback between various processes, as expected, the model predicts stable regimes and irregular oscillations of the area of the grass islands and grazer population. The patterns observed are however different compared to those predicted by conventional Monte Carlo prey-predator models. Specifically, there is no tendency for grazers and grass to segregate. The mean-field version of the model is briefly discussed as well.     

TOUCHSTONEX: protein structure prediction with sparse NMR data

TOUCHSTONEX, a new method for folding proteins that uses a small number of long-range contact restraints derived from NMR experimental NOE (nuclear Overhauser enhancement) data, is described. The method employs a new lattice-based, reduced model of proteins that explicitly represents C(alpha), C(beta), and the sidechain centers of mass. The force field consists of knowledge-based terms to produce protein-like behavior, including various short-range interactions, hydrogen bonding, and one-body, pairwise, and multibody long-range interactions. Contact restraints were incorporated into the force field as an NOE-specific pairwise potential. We evaluated the algorithm using a set of 125 proteins of various secondary structure types and lengths up to 174 residues. Using N/8 simulated, long-range sidechain contact restraints, where N is the number of residues, 108 proteins were folded to a C(alpha)-root-mean-square deviation (RMSD) from native below 6.5 A. The average RMSD of the lowest RMSD structures for all 125 proteins (folded and unfolded) was 4.4 A. The algorithm was also applied to limited experimental NOE data generated for three proteins. Using very few experimental sidechain contact restraints, and a small number of sidechain-main chain and main chain-main chain contact restraints, we folded all three proteins to low-to-medium resolution structures. The algorithm can be applied to the NMR structure determination process or other experimental methods that can provide tertiary restraint information, especially in the early stage of structure determination, when only limited data are available.     

Monte Carlo simulation of protein folding in the presence of residue-specific binding sites

Ensemble growth Monte Carlo (EGMC) and dynamic Monte Carlo (DMC) simulations are used to study sequential folding and thermodynamic stability of hydrophobic-polar (HP) chains that fold to a compact structure. Molecularly imprinted cavities are modeled as hard walls having sites that are attractive to specific polar residues on the chain. Using EGMC simulation, we find that the folded conformation can be stabilized using a small number of carefully selected residue-specific sites while a random selection of surface-bound residues may only slightly contribute toward stabilizing the folded conformation, and in some cases may hinder the folding of the chain. DMC simulations of the surface-bound chain confirm increased stability of the folded conformation over a free chain. However, a different trend of the equilibrium population of folded chains as a function of residue-external site interactions is predicted with the two simulation methods.     

Monte Carlo sampling of near-native structures of proteins with applications

Since a protein's dynamic fluctuation inside cells affects the protein's biological properties, we present a novel method to study the ensemble of near-native structures (NNS) of proteins, namely, the conformations that are very similar to the experimentally determined native structure. We show that this method enables us to (i) quantify the difficulty of predicting a protein's structure, (ii) choose appropriate simplified representations of protein structures, and (iii) assess the effectiveness of knowledge-based potential functions. We found that well-designed simple representations of protein structures are likely as accurate as those more complex ones for certain potential functions. We also found that the widely used contact potential functions stabilize NNS poorly, whereas potential functions incorporating local structure information significantly increase the stability of NNS.     

Generalized comparative modeling (GENECOMP): a combination of sequence comparison, threading, and lattice modeling for protein structure prediction and refinement

An improved generalized comparative modeling method, GENECOMP, for the refinement of threading models is developed and validated on the Fischer database of 68 probe-template pairs, a standard benchmark used to evaluate threading approaches. The basic idea is to perform ab initio folding using a lattice protein model, SICHO, near the template provided by the new threading algorithm PROSPECTOR. PROSPECTOR also provides predicted contacts and secondary structure for the template-aligned regions, and possibly for the unaligned regions by garnering additional information from other top-scoring threaded structures. Since the lowest-energy structure generated by the simulations is not necessarily the best structure, we employed two structure-selection protocols: distance geometry and clustering. In general, clustering is found to generate somewhat better quality structures in 38 of 68 cases. When applied to the Fischer database, the protocol does no harm and in a significant number of cases improves upon the initial threading model, sometimes dramatically. The procedure is readily automated and can be implemented on a genomic scale.     

MONTE: An automated Monte Carlo based approach to nuclear magnetic resonance assignment of proteins

A general-purpose Monte Carlo assignment program has been developed to aid in the assignment of NMR resonances from proteins. By virtue of its flexible data requirements the program is capable of obtaining assignments of both heavily deuterated and fully protonated proteins. A wide variety of source data, such as inter-residue scalar connectivity, inter-residue dipolar (NOE) connectivity, and residue specific information, can be utilized in the assignment process. The program can also use known assignments from one form of a protein to facilitate the assignment of another form of the protein. This attribute is useful for assigning protein-ligand complexes when the assignments of the unliganded protein are known. The program can be also be used as an interactive research tool to assist in the choice of additional experimental data to facilitate completion of assignments. The assignment of a deuterated 45 kDa homodimeric Glutathione-S-transferase illustrates the principal features of the program.     

Homogeneous vs. patient specific breast models for Monte Carlo evaluation of mean glandular dose in mammography

PurposeTo compare, via Monte Carlo simulations, homogeneous and non-homogenous breast models adopted for mean glandular dose (MGD) estimates in mammography vs. patient specific digital breast phantoms.MethodsWe developed a GEANT4 Monte Carlo code simulating four homogenous cylindrical breast models featured as follows: (1) semi-cylindrical section enveloped in a 5-mm adipose layer; (2) semi-elliptical section with a 4-mm thick skin; (3) semi-cylindrical section with a 1.45-mm skin layer; (4) semi-cylindrical section in a 1.45-mm skin layer and 2-mm subcutaneous adipose layer. Twenty patient specific digital breast phantoms produced from a dedicated CT scanner were assumed as reference in the comparison. We simulated two spectra produced from two anode/filter combinations. An additional digital breast phantom was produced via BreastSimulator software.ResultsWith reference to the results for patient-specific breast phantoms and for W/Al spectra, models #1 and #3 showed higher MGD values by about 1% (ranges [–33%; +28%] and [−31%; +30%], respectively), while for model #4 it was 2% lower (range [−34%; +26%]) and for model #2 –11% (range [−39%; +14%]), on average. On the other hand, for W/Rh spectra, models #1 and #4 showed lower MGD values by 2% and 1%, while for model #2 and #3 it was 14% and 8% lower, respectively (ranges [−43%; +13%] and [−41%; +21%]). The simulation with the digital breast phantom produced with BreastSimulator showed a MGD overestimation of +33%.ConclusionsThe homogeneous breast models led to maximum MGD underestimation and overestimation of 43% and 28%, respectively, when compared to patient specific breast phantoms derived from clinical CT scans.     

Monte Carlo estimation of the number of possible protein folds: effects of sampling bias and folds distributions

The estimation of the number of protein folds in nature is a matter of considerable interest. In this study, a Monte Carlo method employing the broken stick model is used to assign a given number of proteins into a given number of folds. Subsequently, random, integer, non-repeating numbers are generated in order to simulate the process of fold discovery. With this conceptual framework at hand, the effects of two factors upon the fold identification process were investigated: (1) the nature of folds distributions and (2) preferential sampling bias of previously identified folds. Depending on the type of distribution, dividing 100,000 proteins into 1,000 folds resulted in 10-30% of the folds having 10 proteins or less per fold, approximately 10% of the folds having 10-20 proteins per fold, 31-45% having 20-100 proteins per fold, and >30% of the folds having more than 100 proteins per fold. After randomly sampling one tenth of the proteins, 68-96% of the folds were identified. These percentages depend both on folds distribution and biased/non-biased sampling. Only upon increasing the sampling bias for previously identified folds to 1,000, did the model result in a reduction of the number of proteins identified by an order of magnitude (approximately 9%). Thus, assuming the structures of one tenth of the population of proteins in nature have been solved, the results of the Monte Carlo simulation are more consistent with recent lower estimates of the number of folds, 相似文献   

Measurement-based model of a wide-bore CT scanner for Monte Carlo dosimetric calculations with GMCTdospp software

The aim of this work was to create a model of a wide-bore Siemens Somatom Sensation Open CT scanner for use with GMCTdospp, which is an EGSnrc-based software tool dedicated for Monte Carlo calculations of dose in CT examinations.The method was based on matching spectrum and filtration to half value layer and dose profile, and thus was similar to the method of Turner et al. (Med. Phys. 36, pp. 2154–2164). Input data on unfiltered beam spectra were taken from two sources: the TASMIP model and IPEM Report 78. Two sources of HVL data were also used, namely measurements and documentation. Dose profile along the fan-beam was measured with Gafchromic RTQA-1010 (QA+) film. Two-component model of filtration was assumed: bow-tie filter made of aluminum with 0.5 mm thickness on central axis, and flat filter made of one of four materials: aluminum, graphite, lead, or titanium.Good agreement between calculations and measurements was obtained for models based on the measured values of HVL. Doses calculated with GMCTdospp differed from the doses measured with pencil ion chamber placed in PMMA phantom by less than 5%, and root mean square difference for four tube potentials and three positions in the phantom did not exceed 2.5%. The differences for models based on HVL values from documentation exceeded 10%. Models based on TASMIP spectra and IPEM78 spectra performed equally well.     

Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Bayes factors. Current implementations of any of these criteria suffer from the limitation that only a small set of models are examined, or that the test does not allow easy comparison of non-nested models. In this article, we expand the pool of candidate substitution models to include all possible time-reversible models. This set includes seven models that have already been described. We show how Bayes factors can be calculated for these models using reversible jump Markov chain Monte Carlo, and apply the method to 16 DNA sequence alignments. For each data set, we compare the model with the best Bayes factor to the best models chosen using AIC and BIC. We find that the best model under any of these criteria is not necessarily the most complicated one; models with an intermediate number of substitution types typically do best. Moreover, almost all of the models that are chosen as best do not constrain a transition rate to be the same as a transversion rate, suggesting that it is the transition/transversion rate bias that plays the largest role in determining which models are selected. Importantly, the reversible jump Markov chain Monte Carlo algorithm described here allows estimation of phylogeny (and other phylogenetic model parameters) to be performed while accounting for uncertainty in the model of DNA substitution.     

Monte Carlo Simulation of Binary Gas Adsorption in Zeolite Cavities

Abstract

Grand canonical Monte Carlo simulations have been performed for binary adsorption of Lennard-Jones molecules with point multipole moments in zeolite cavities of type X. Fluid-solid electrostatic interactions were taken into account. Phase diagrams and total coverage were calculated for three binaries and compared with experimental measurements. MC simulations gave good agreement with experiment for two mixtures (C₂H₄-CO₂ and CO₂-CH₄) but there were discrepancies between simulation and experiment for the system i-C₄H₁₀-C₂H₄. The dependence of excess Gibbs free energy on the composition and pressure was studied. Negative deviations from ideality are due to energetic heterogeneity and size effects. Unlike liquid-vapor equilibrium, deviations from the Lorentz-Berthelot mixing rules for the adsorbates have little effect upon the phase behavior. Density distributions show that the components compete for the high energy sites inside the cavity; depending on its relative strength of adsorption, one component may be excluded from such positions (CH₄ in CO₂-CH₄), or the two species may share sites inside the cavity (C₂H₄-CO₂).     

Vapour-Liquid Phase Equilibria of n-alkanes by Direct Monte Carlo Simulations

Abstract

We report results of direct Monte Carlo simulations of n-pentane and n-decane at the liquidvapour interface for a number of temperatures. The intermolecular interactions are modeled using the last version of the anisotropic united atom model (AUA4). We have used the local long range correction energy and an algorithm allowing to select randomly with equal probability two different displacements. The liquid and vapour densities are in excellent agreement with experimental data and with those previously calculated using the GEMC method.     

Exhaustive enumeration of protein conformations using experimental restraints.

We present an efficient new algorithm that enumerates all possible conformations of a protein that satisfy a given set of distance restraints. Rapid growth of all possible self-avoiding conformations on the diamond lattice provides construction of alpha-carbon representations of a protein fold. We investigated the dependence of the number of conformations on pairwise distance restraints for the proteins crambin, pancreatic trypsin inhibitor, and ubiquitin. Knowledge of between one and two contacts per monomer is shown to be sufficient to restrict the number of candidate structures to approximately 1,000 conformations. Pairwise RMS deviations of atomic position comparisons between pairs of these 1,000 structures revealed that these conformations can be grouped into about 25 families of structures. These results suggest a new approach to assessing alternative protein folds given a very limited number of distance restraints. Such restraints are available from several experimental techniques such as NMR, NOESY, energy transfer fluorescence spectroscopy, and crosslinking experiments. This work focuses on exhaustive enumeration of protein structures with emphasis on the possible use of NOESY-determined distance restraints.     

A Monte Carlo Study of the Argon Fluid Around a Benzene Molecule

Abstract

Monte Carlo simulations have been carried out for argon fluid containing one benzene molecule at the supercritical region. The purpose in this study is to examine the effect of plate-like molecule on the structure of neighboring fluid composed of simple spherical molecules of the system. In the first neighbor shell of argon from the center of benzene molecule, the average potential energy of argon atoms is confirmed to have a large density dependence. This potential energy is relatively large in the high density region. It is found that the spatial distribution of argon fluid is significantly affected by the molecular shape of benzene and it has little direct connection with the attractive interaction between benzene and argon.