The ensemble folding kinetics of the FBP28 WW domain revealed by an all-atom Monte Carlo simulation in a knowledge-based potential

In this work, we apply a detailed all‐atom model with a transferable knowledge‐based potential to study the folding kinetics of Formin‐Binding protein, FBP28, which is a canonical three‐stranded β‐sheet WW domain. Replica exchange Monte Carlo simulations starting from random coils find native‐like (Cα RMSD of 2.68 Å) lowest energy structure. We also study the folding kinetics of FBP28 WW domain by performing a large number of ab initio Monte Carlo folding simulations. Using these trajectories, we examine the order of formation of two β‐hairpins, the folding mechanism of each individual β‐hairpin, and transition state ensemble (TSE) of FBP28 WW domain and compare our results with experimental data and previous computational studies. To obtain detailed structural information on the folding dynamics viewed as an ensemble process, we perform a clustering analysis procedure based on graph theory. Further, a rigorous P_fold analysis is used to obtain representative samples of the TSEs showing good quantitative agreement between experimental and simulated Φ values. Our analysis shows that the turn structure between first and second β strands is a partially stable structural motif that gets formed before entering the TSE in FBP28 WW domain and there exist two major pathways for the folding of FBP28 WW domain, which differ in the order and mechanism of hairpin formation. Proteins 2011. © 2011 Wiley‐Liss, Inc.     

The mechanical unfolding of ubiquitin through all-atom Monte Carlo simulation with a Go-type potential

The mechanical unfolding of proteins under a stretching force has an important role in living systems and is a logical extension of the more general protein folding problem. Recent advances in experimental methodology have allowed the stretching of single molecules, thus rendering this process ripe for computational study. We use all-atom Monte Carlo simulation with a Gō-type potential to study the mechanical unfolding pathway of ubiquitin. A detailed, robust, well-defined pathway is found, confirming existing results in this vein though using a different model. Additionally, we identify the protein's fundamental stabilizing secondary structure interactions in the presence of a stretching force and show that this fundamental stabilizing role does not persist in the absence of mechanical stress. The apparent success of simulation methods in studying ubiquitin's mechanical unfolding pathway indicates their potential usefulness for future study of the stretching of other proteins and the relationship between protein structure and the response to mechanical deformation.     

The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation

We present a novel Monte Carlo simulation of protein folding, in which all heavy atoms are represented as interacting hard spheres. This model includes all degrees of freedom relevant to folding, all side-chain and backbone torsions, and uses a Go potential. In this study, we focus on the 46 residue alpha/beta protein crambin and two of its structural components, the helix and helix hairpin. For a wide range of temperatures, we recorded multiple folding events of these three structures from random coils to native conformations that differ by less than 1 A C(alpha) dRMS from their crystal structure coordinates. The thermodynamics and kinetic mechanism of the helix-coil transition obtained from our simulation shows excellent agreement with currently available experimental and molecular dynamics data. Based on insights obtained from folding its smaller structural components, a possible folding mechanism for crambin is proposed. We observed that the folding occurs via a cooperative, first order-like process, and that many folding pathways to the native state exist. One particular sequence of events constitutes a "fast-folding" pathway where kinetic traps are avoided. At very low temperatures, a kinetic trap arising from the incorrect packing of side-chains was observed. These results demonstrate that folding to the native state can be observed in a reasonable amount of time on desktop computers even when an all-atom representation is used, provided the energetics sufficiently stabilize the native state.     

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.     

Aqueous hydration of nucleic acid constituents: Monte Carlo computer simulation studies

Monte Carlo computer simulations were performed on dilute aqueous solutions of thymine, cytosine, uracil, adenine, guanine, the dimethyl phosphate anion in the gauche-gauche conformation and a ribose and deoxyribose derivative. The aqueous hydration of each molecule was analysed in terms of quasi-component distribution functions based on the Proximity Criterion, and partitioned into hydrophobic, hydrophilic and ionic contributions. Color stereo views of selected hydration complexes are also presented. A preliminary discussion of the transferability of functional group coordination numbers is given. The results enable to comment on two current problems related to the hydration of nucleic acids: a) the theory of Dickerson and coworkers on the role of water in the relative stability of the A and B form of DNA and b) the idea of water bridges and filaments emerging from the computer simulation results on the hydration of DNA fragments by Clementi.     

Design of a protective shield for a radiological emergency intervention using Monte Carlo simulation and an anthropomorphic phantom

Due to the increasing use of radioactive sources, new challenges appear for the protection of humans and the environment against ionizing radiation. Thus, organizations handling these sources must be endowed with plans how to react in case of any radiological emergency situations. Monte Carlo simulations are among the most widely employed methods used for the management and reconstruction of radiological incidents and accidents. In this work, results of a Monte Carlo simulation study with the Geant4 simulation toolkit using a digital anthropomorphic phantom are reported. The investigated scenario included an emergency intervention carried out inside the ionization cell of the National Institute of Agronomic Research (NIAR) of Tangier/Morocco, which houses a ⁶⁰Co gamma irradiator. In this scenario, a radiological incident was assumed where the source cage of the gamma irradiator is stuck in the guide tube and not completely inserted into its storage container. The objective of this work was to design a radiation shield to protect an operator during the emergency intervention and make sure that any radiation exposure is below the recommended dose limits, taking into account the date of occurrence (which determines the activity of the source at the time of the emergency situation) of the accident and economic aspects of shielding design. In this work, the maximum time available for the operator to accomplish the operation intervention while remaining protected is calculated. The results obtained show that the shielding prototype developed gives the operator a time between 3 and 300 s, depending on shielding design. It is concluded that shielding of the type investigated in the present study will allow any facility to manage the assumed emergency scenario, should it occur.

     

Nature of the stacking of nucleic acid bases in water: a Monte Carlo simulation

The results of a Monte Carlo simulation of the hydration of uracil and thymine molecules, their stacked dimers and hydrogen-bonded base pairs are presented. Simulations have been performed in a cluster approximation. The semiempirical atom-atom potential functions have been used (cluster consisting of 200 water molecules). It has been shown that the stacking interactions of uracil and thymine molecules in water arise mainly due to the increase in the water-water interaction during the transition from monomers to dimer. It has been found out that stacked base associates are more preferable than base pairs in water. This preference is mainly due to the energetically more favourable structure of water around the stack.     

Hydration of uracil and thymine methylderivatives: a Monte Carlo simulation

The simulation performed shows that under methylation of uracil and thymine NH-groups the interaction energy between a base and water (Uwb) is increased. It is also detected that the increase in this energy was observed in the 1st and the 3rd sectors. These conclusions do not confirm the assumption made in the literature on the character of an interaction between methylated bases and water. According to this assumption, when the NH-groups are methylated, the energy of Uwb in these sectors decreases as a result of the van der Waals interactions between a methyl group and water, whose energy compensates the increase in the Uwb energy due to the breaking of an H-bond. Regularity of water molecules near a hydrophobic group under the hydration of polar molecules is detected for the first time.     

Geometrical properties of gel and fluid clusters in DMPC/DSPC bilayers: Monte Carlo simulation approach using a two-state model

In this paper the geometrical properties of gel and fluid clusters of equimolar dimyristoylphosphatidylcholine/distearoylphosphatidylcholine (DMPC/DSPC) lipid bilayers are calculated by using an Ising-type model (Sugar, I. P., T. E. Thompson, and R. L. Biltonen. 1999. Biophys. J. 76:2099-2110). The model is able to predict the following properties in agreement with the respective experimental data: the excess heat capacity curves, fluorescence recovery after photobleaching (FRAP) threshold temperatures at different mixing ratios, the most frequent center-to-center distance between DSPC clusters, and the fractal dimension of gel clusters. In agreement with the neutron diffraction and fluorescence microscopy data, the simulations show that below the percolation threshold temperature of gel clusters many nanometer-size gel clusters co-exist with one large gel cluster of size comparable with the membrane surface area. With increasing temperature the calculated effective fractal dimension and capacity dimension of gel and fluid clusters decrease and increase, respectively, within the (0, 2) interval. In the region of the gel-to-fluid transition the following geometrical properties are independent from the temperature and the state of the cluster: 1) the cluster perimeter linearly increases with the number of cluster arms at a rate of 8.2 nm/arm; 2) the average number of inner islands in a cluster increases with increasing cluster size, S, according to a power function of 0.00427 x S(1.3); 3) the following exponential function describes the average size of an inner island versus the size of the host cluster, S: 1 + 1.09(1 - e(-0.0072xS)). By means of the equations describing the average geometry of the clusters the process of the association of clusters is investigated.     

Interactions of cationic-hydrophobic peptides with lipid bilayers: a Monte Carlo simulation method

We present a computational model of the interaction between hydrophobic cations, such as the antimicrobial peptide, Magainin2, and membranes that include anionic lipids. The peptide's amino acids were represented as two interaction sites: one corresponds to the backbone alpha-carbon and the other to the side chain. The membrane was represented as a hydrophobic profile, and its anionic nature was represented by a surface of smeared charges. Thus, the Coulombic interactions between the peptide and the membrane were calculated using the Gouy-Chapman theory that describes the electrostatic potential in the aqueous phase near the membrane. Peptide conformations and locations near the membrane, and changes in the membrane width, were sampled at random, using the Metropolis criterion, taking into account the underlying energetics. Simulations of the interactions of heptalysine and the hydrophobic-cationic peptide, Magainin2, with acidic membranes were used to calibrate the model. The calibrated model reproduced structural data and the membrane-association free energies that were measured also for other basic and hydrophobic-cationic peptides. Interestingly, amphipathic peptides, such as Magainin2, were found to adopt two main membrane-associated states. In the first, the peptide resided mostly outside the polar headgroups region. In the second, which was energetically more favorable, the peptide assumed an amphipathic-helix conformation, where its hydrophobic face was immersed in the hydrocarbon region of the membrane and the charged residues were in contact with the surface of smeared charges. This dual behavior provides a molecular interpretation of the available experimental data.     

Monte Carlo simulation of simultaneous gas flow and diffusion in an asymmetric distal pulmonary airway model

In order to evaluate the effect of anatomic asymmetries on the gas concentration distribution in the pulmonary airways, a Monte Carlo simulation of combined bulk flow and molecular diffusion was carried out in a realistic distal airway model (Parkeret al., 1971). This airway model, composed of branches distal to the 0.5-ram diameter airways, contained an upper symmetric segment consisting of four generations of conducting airways and a lower asymmetric segment of alveolar ducts and sacs arranged in five transport paths of varying lengths. In accounting for the volume increases of these ducts and sacs occurring during normal respiration, uniform alveolar filling rates and a fixed length-to-diameter ratio of all airways were assumed. For a pulse injection of inert tracer gas, the simulation was employed to determine the longitudinal concentration profiles in the conducting airways. In the alveolated airways, not only were the longitudinal profiles determined along each path, but radial transport from the core to the periphery of the airways was considered. The results of the simulations indicate that geometric asymmetries alone contribute substantially to regional concentration variations in the distal airways. For example, when a gas bolus is injected at mid*inspiration, there are concentration differences as great as 40% between two points along different transport paths located equi-distant from the proximal end of the model. As viewed from the terminal end of the model (acinus), average concentration differences as large as 6-to-1 exist between the longest and shortest transport paths respectively for gas boli introduced near the end of inspiration. The results further indicate because of large radial diffusion rates, no significant concentration differences exist between the periphery a-ld the central core of alveolated airways. Simulation of the expired concentration profiles indicate that boll injected very late during inspiration exhibit a sloping tail, unlike the earlier injected boll whose tails are virtually horizontal. Through the use of superposition teehniqnes, it was found that these sloping tails correspond to an alveolar slope of 1.5 vol% between 750 and 1250 ml expired for a continuous washing of tracer. This result is in disagreement with other transport analyses which did not directly account for the effect of geometric asymmetries.     

A molecular model and Monte Carlo simulation of flavivirus envelope building block

Ryanodine receptors (RyRs) are mainly located on the endoplasmic reticulum (ER) and play an important role in regulating glucose-induced cytosolic Ca(2+) oscillation in pancreatic β-cells. However, subcellular locations and functions of RyRs on other cell organelles such as nuclear envelope are not well understood. In order to investigate the role of RyRs in nuclear Ca(2+) oscillation we designed and conducted experiments in intact primary pancreatic β-cells. Immunocytochemistry was used to examine the expression of RYRs on the nuclear envelope. Confocal microscopy was used to evaluate the function of RYRs on the nuclear envelope. We found that RyRs are expressed on the nuclear envelope in single primary pancreatic β-cells and isolated nuclei. Laser scanning confocal microscopy studies indicated that application of glucose to the cells co-incubated with Ca(2+) indicator Fluo-4 AM and cell-permeable nuclear indicator Hoechst 33342 resulted in nuclear Ca(2+) oscillation. The pattern of glucose-induced Ca(2+) oscillation in the nucleus and cytosol was similar. The reduction of Ca(2+) oscillation amplitude by ryanodine was much greater in the nucleus though both the cytosol and the nucleus Ca(2+) amplitude decreased by ryanodine. Our results suggest that functional ryanodine receptors not only exist in endoplasmic reticulum but are also expressed in nuclear envelope of pancreatic β-cells.     

The role of cell death in the growth of preneoplastic lesions: a Monte Carlo simulation model

Abstract. A variety of experimental and clinical examples of preneoplasia demonstrate that regression of early lesions is common. This paper examines the hypothesis that early lesions operate under the identical growth kinetics of 'late' lesions (neoplasms), but that kinetic features favouring continuous growth in established lesions tend to favour extinction of lesions composed of small numbers of cells. Growth simulations of early lesions were produced using the Monte Carlo method, a technique demanding intensive computations. With the advent of powerful personal computers, this technique is now widely available to biologists. Simulating growth under conditions of cell loss similar to those observed in established tumours, the model predicts that the great majority of initiated cell clusters are expected to reach extinction within a few cell doubling times, and most early (promoted) lesions would not likely progress to the size of a clinically detectable lesion within the life span of the host organism. These Monte Carlo simulations provide a model of initiated cell growth consistent with the recently demonstrated role of early lesion cell death in the development of human lymphomas and in transgenic mice expressing the bcl-2 oncogene. The model demonstrates that small increments in the intrinsic cell loss probability in even the earliest progenitors of malignancy can strongly influence the subsequent development of neoplasia from initiated foci.     

Monte Carlo simulation of the water in a channel with charges.

A Monte Carlo simulation of water in a channel with charges suggests the existence of water in immobile, high density, essentially glasslike form near the charges. The channel model has a conical section with an opening through which water molecules can pass, at the narrow end of the cone, and a cylindrical section at the other end. When the charges are placed near the narrow section of the model, the "glass" effectively blocks the channel; with the charges removed, the channel opens. The effect can be determined from the rate of passage of the water molecules through the pore, from the average orientation of the water molecule, and from distortion of the distribution of molecules. In the simulations carried out to date, no external ions have been considered. In addition to the energy, the Helmholtz free energy has been calculated.     

Monte Carlo simulation of branched alkanes and long chain n -alkanes with anisotropic united atoms intermolecular potential

The anisotropic united atoms potential for linear alkanes proposed by Ungerer (J. Chem. Phys. , 112 , 5499, 2000), called AUA4, has been used to predict several equilibrium properties (vapour pressure, vaporisation enthalpies, and liquid densities) of alkanes by Gibbs ensemble Monte Carlo simulation. In order to extend the potential to branched alkanes, potential parameters for the CH group have been determined by optimisation on the basis of equilibrium properties of isobutane, keeping the same parameters as AUA4 for the CH 3 groups. The resulting CH parameters form a regular sequence with those previously determined for CH 3 and CH 2 groups, so that a physically consistent parameter set is obtained. Simulations have been performed at temperatures ranging from 450 to 800 u K for long n -alkanes (C20, C25 and C30) and from 350 to 450 u K for four heptane isomers (n -heptane, 2-methylhexane, 2,4-dimethylpentane and 2-ethylpentane). In order to achieve internal relaxation of long chains with a good efficiency, a specific Monte Carlo move was used in which a united atom is rotated around its nearest neighbours. Equilibrium properties of long chain alkanes are well predicted, and small differences between heptane isomers are represented with a good accuracy. It is concluded that the AUA4 potential shows an interesting degree of transferability.     

The effect of weekend curfews on epidemics: a Monte Carlo simulation

The ongoing COVID-19 pandemic is being responded with various methods, applying vaccines, experimental treatment options, total lockdowns or partial curfews. Weekend curfews are among the methods for reducing the number of infected persons, and this method is practically applied in some countries such as Turkey. In this study, the effect of weekend curfews on reducing the spread of a contagious disease, such as COVID-19, is modeled using a Monte Carlo algorithm with a hybrid lattice model. In the simulation setup, a fictional country with three towns and 26,610 citizens were used as a model. Results indicate that applying a weekend curfew reduces the ratio of ill cases from 0.23 to 0.15. The results also show that applying personal precautions such as social distancing is important for reducing the number of cases and deaths. If the probability of disease spread can be reduced to 0.1, in that case, the death ratio can be minimized down to 0.