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.     

A simple lattice model that exhibits a protein-like cooperative all-or-none folding transition

In a recent paper (D. Gront et al., Journal of Chemical Physics, Vol. 115, pp. 1569, 2001) we applied a simple combination of the Replica Exchange Monte Carlo and the Histogram methods in the computational studies of a simplified protein lattice model containing hydrophobic and polar units and sequence-dependent local stiffness. A well-defined, relatively complex Greek-key topology, ground (native) conformations was found; however, the cooperativity of the folding transition was very low. Here we describe a modified minimal model of the same Greek-key motif for which the folding transition is very cooperative and has all the features of the "all-or-none" transition typical of real globular proteins. It is demonstrated that the all-or-none transition arises from the interplay between local stiffness and properly defined tertiary interactions. The tertiary interactions are directional, mimicking the packing preferences seen in proteins. The model properties are compared with other minimal protein-like models, and we argue that the model presented here captures essential physics of protein folding (structurally well-defined protein-like native conformation and cooperative all-or-none folding transition).     

Preliminary results in using Deep Learning to emulate BLOB,a nuclear interaction model

PurposeA reliable model to simulate nuclear interactions is fundamental for Ion-therapy. We already showed how BLOB (“Boltzmann-Langevin One Body”), a model developed to simulate heavy ion interactions up to few hundreds of MeV/u, could simulate also ¹²C reactions in the same energy domain. However, its computation time is too long for any medical application. For this reason we present the possibility of emulating it with a Deep Learning algorithm.MethodsThe BLOB final state is a Probability Density Function (PDF) of finding a nucleon in a position of the phase space. We discretised this PDF and trained a Variational Auto-Encoder (VAE) to reproduce such a discrete PDF. As a proof of concept, we developed and trained a VAE to emulate BLOB in simulating the interactions of ¹²C with ¹²C at 62 MeV/u. To have more control on the generation, we forced the VAE latent space to be organised with respect to the impact parameter (b) training a classifier of b jointly with the VAE.ResultsThe distributions obtained from the VAE are similar to the input ones and the computation time needed to use the VAE as a generator is negligible.ConclusionsWe show that it is possible to use a Deep Learning approach to emulate a model developed to simulate nuclear reactions in the energy range of interest for Ion-therapy. We foresee the implementation of the generation part in C++ and to interface it with the most used Monte Carlo toolkit: Geant4.     

Exploring protein aggregation and self-propagation using lattice models: phase diagram and kinetics

Many seemingly unrelated neurodegenerative disorders, such as amyloid and prion diseases, are associated with propagating fibrils whose structures are dramatically different from the native states of the corresponding monomers. This observation, along with the experimental demonstration that any protein can aggregate to form either fibrils or amorphous structures (inclusion bodies) under appropriate external conditions, suggest that there must be general principles that govern aggregation mechanisms. To probe generic aspects of prion-like behavior we use the model of Harrison, Chan, Prusiner, and Cohen. In this model, aggregation of a structure, that is conformationally distinct from the native state of the monomer, occurs by three parallel routes. Kinetic partitioning, which leads to parallel assembly pathways, occurs early in the aggregation process. In all pathways transient unfolding precedes polymerization and self-propagation. Chain polymerization is consistent with templated assembly, with the dimer being the minimal nucleus. The kinetic effciency of R(n-1) + G --> R(n) (R is the aggregation prone state and G is either U, the unfolded state, or N, the native state of the monomer) is increased when polymerization occurs in the presence of a "seed" (a dimer). These results support the seeded nucleated-polymerization model of fibril formation in amyloid peptides. To probe generic aspects of aggregation in two-state proteins, we use lattice models with side chains. The phase diagram in the (T,C) plane (T is the temperature and C is the polypeptide concentration) reveals a bewildering array of "phases" or structures. Explicit computations for dimers show that there are at least six phases including ordered structures and amorphous aggregates. In the ordered region of the phase diagram there are three distinct structures. We find ordered dimers (OD) in which each monomer is in the folded state and the interaction between the monomers occurs via a well-defined interface. In the domain-swapped structures a certain fraction of intrachain contacts are replaced by interchain contacts. In the parallel dimers the interface is stabilized by favorable intermolecular hydrophobic interactions. The kinetics of folding to OD shows that aggregation proceeds directly from U in a dynamically cooperative manner without populating partially structured intermediates. These results support the experimental observation that ordered aggregation in the two-state folders U1A and CI2 takes place from U. The contrasting aggregation processes in the two models suggest that there are several distinct mechanisms for polymerization that depend not only on the polypeptide sequence but also on external conditions (such as C, T, pH, and salt concentration).     

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).     

Topological information embodied in local juxtaposition geometry provides a statistical mechanical basis for unknotting by type-2 DNA topoisomerases

Topoisomerases may unknot by recognizing specific DNA juxtapositions. The physical basis of this hypothesis is investigated by considering single-loop conformations in a coarse-grained polymer model. We determine the statistical relationship between the local geometry of a juxtaposition of two chain segments and whether the loop is knotted globally, and ascertain how the knot/unknot topology is altered by a topoisomerase-like segment passage at the juxtaposition. Segment passages at a "free" juxtaposition tend to increase knot probability. In contrast, segment passages at a "hooked" juxtaposition cause more transitions from knot to unknot than vice versa, resulting in a steady-state knot probability far lower than that at topological equilibrium. The reduction in knot population by passing chain segments through a hooked juxtaposition is more prominent for loops of smaller sizes, n, but remains significant even for larger loops: steady-state knot probability is only approximately 2%, and approximately 5% of equilibrium, respectively, for n=100 and 500 in the model. An exhaustive analysis of approximately 6000 different juxtaposition geometries indicates that the ability of a segment passage to unknot correlates strongly with the juxtaposition's "hookedness". Remarkably, and consistent with experiments on type-2 topoisomerases from different organisms, the unknotting potential of a juxtaposition geometry in our polymer model correlates almost perfectly with its corresponding decatenation potential. These quantitative findings suggest that it is possible for topoisomerases to disentangle by acting selectively on juxtapositions with "hooked" geometries.     

Protein folding mechanisms and the multidimensional folding funnel

An important idea that emerges from the energy landscape theory of protein folding is that subtle global features of the protein landscape can profoundly affect the apparent mechanism of folding. The relationship between various characteristic temperatures in the phase diagrams and landmarks in the folding funnel at fixed temperatures can be used to classify different folding behaviors. The one-dimensional picture of a folding funnel classifies folding kinetics into four basic scenarios, depending on the relative location of the thermodynamic barrier and the glass transition as a function of a single-order parameter. However, the folding mechanism may not always be quantitatively described by a single-order parameter. Several other order parameters, such as degree of secondary structure formation, collapse and topological order, are needed to establish the connection between minimalist models and proteins in the laboratory. In this article we describe a simple multidimensional funnel based on two-order parameters that measure the degree of collapse and topological order. The appearance of several different “mechanisms” is illustrated by analyzing lattice models with different potentials and sequences with different degrees of design. In most cases, the two-dimensional analysis leads to a classification of mechanisms totally in keeping with the one-dimensional scheme, but a topologically distinct scenario of fast folding with traps also emerges. The nature of traps depends on the relative location of the glass transition surface and the thermodynamic barrier in the multidimensional funnel. Proteins 32:136–158, 1998. © 1998 Wiley-Liss, Inc.     

Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation

In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56?Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.     

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.     

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.     

Assembly of protein structure from sparse experimental data: An efficient Monte Carlo model

A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Cαs. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 Å from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 Å are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 Å. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints. Proteins 32:475–494, 1998. © 1998 Wiley-Liss, Inc.     

Advancing simulations of biological materials: applications of coarse-grained models on graphics processing unit hardware

The timescales of biological processes, primarily those inherent to the molecular mechanisms of disease, are long (>μs) and involve complex interactions of systems consisting of many atoms (>10⁶). Simulating these systems requires an advanced computational approach, and as such, coarse-grained (CG) models have been developed and highly optimised for accelerator hardware, primarily graphics processing units (GPUs). In this review, I discuss the implementation of CG models for biologically relevant systems, and show how such models can be optimised and perform well on GPU-accelerated hardware. Several examples of GPU implementations of CG models for both molecular dynamics and Monte Carlo simulations on purely GPU and hybrid CPU/GPU architectures are presented. Both the hardware and algorithmic limitations of various models, which depend greatly on the application of interest, are discussed.     

Simulation of two-dimensional streptavidin crystallization

We present lattice Monte Carlo simulations of the growth of streptavidin islands at a biotinylated lipid layer. The model employed takes into account attractive anisotropic lateral interactions between streptavidin tetramers. With a minimal set of interactions, we reproduce the formation of rectangular islands experimentally observed at pH > or = 9.0. Specifically, we analyze two scenarios of the island growth. First, if streptavidin is rapidly adsorbed at t = 0 (stepwise coverage change without ongoing adsorption), the average linear island size is found to grow according to the Lifshitz-Slyozov law, R proportional to t(1/3). Second, if the island growth occurs in parallel with streptavidin adsorption limited by diffusion in the solution, the Lifshitz-Slyozov law is also applicable, but only at the late stage, when the streptavidin coverage is appreciable.     

Effect of temperature on adsorption of mixtures in porous materials

The effect of temperature on the adsorption of a simple mixture (Ar/Kr) in disordered porous materials is investigated by means of molecular simulation. In the larger mesopores of porous silica glasses, capillary condensation occurs upon decreasing the temperature. At temperatures above the capillary condensation temperature, Kr is preferentially adsorbed at the pore surface and Ar adsorption occurs in regions of low Kr density. For temperatures below the capillary condensation temperature, Ar density surprisingly increases as temperature increases, the behaviour that is consistent with an over-solubility effect. In contrast, in the disordered sub-nanoporous carbon, filling of the pores occurs in a reversible and continuous way upon decreasing the temperature, owing to the small size and amorphous shape of the pores. These results show that the crossover between capillary condensation and continuous reversible filling observed for pure fluids in pores also exists for mixtures. We also show that the Kr selectivity exhibits a minimum in the disordered porous silica that is located at the capillary condensation temperature. In contrast, in the disordered porous carbon where no capillary condensation occurs, the selectivity decreases monotonically with increasing the temperature. These results shed light on low-temperature adsorption of mixtures confined in porous materials and provide a guide to design efficient phase separation processes.     

Bias in Markov models of disease

We examine bias in Markov models of diseases, including both chronic and infectious diseases. We consider two common types of Markov disease models: ones where disease progression changes by severity of disease, and ones where progression of disease changes in time or by age. We find sufficient conditions for bias to exist in models with aggregated transition probabilities when compared to models with state/time dependent transition probabilities. We also find that when aggregating data to compute transition probabilities, bias increases with the degree of data aggregation. We illustrate by examining bias in Markov models of Hepatitis C, Alzheimer’s disease, and lung cancer using medical data and find that the bias is significant depending on the method used to aggregate the data. A key implication is that by not incorporating state/time dependent transition probabilities, studies that use Markov models of diseases may be significantly overestimating or underestimating disease progression. This could potentially result in incorrect recommendations from cost-effectiveness studies and incorrect disease burden forecasts.     

Vacancy clustering and diffusion in germanium using kinetic lattice Monte Carlo simulations

We investigated vacancy-assisted self-diffusion in germanium by means of kinetic lattice Monte Carlo (KLMC) simulations below the melting temperature, for a vacancy concentration of 1 × 10¹⁸/cm³. At higher temperatures, fewer clusters formed, but there was less variation in the number of clusters than at lower temperatures as the time increased. Equilibrium diffusivities in the clustering region were 10² lower than those of free vacancies in the initial stage of KLMC simulations. They were expressed according to three temperature regimes: 6.5 × 10^? 4 exp(–0.35/k _B T) cm²/s at temperatures above 1100 K, 5.2 × 10⁵ exp(–2.32/k _B T) cm²/s at temperatures of 900–1100 K and 6.0 × 0^–7 exp(–0.19/k _B T) cm²/s at temperatures below 900 K. The effective mean migration energy, 1.1 eV, closely coincided with that of the 1.0–1.2 eV in experiments and was very different from the migration energy of the free vacancy.     

Making good choices with variable information: a stochastic model for nest-site selection by honeybees

A density-dependent Markov process model is constructed for information transfer among scouts during nest-site selection by honeybees (Apis mellifera). The effects of site quality, competition between sites and delays in site discovery are investigated. The model predicts that bees choose the better of two sites more reliably when both sites are of low quality than when both sites are of high quality and that delay in finding a second site has most effect on the final choice when both sites are of high quality. The model suggests that stochastic effects in honeybee nest-site selection confer no advantage on the swarm.