3D-Lattice Monte Carlo simulations of model proteins. Size effects on folding thermodynamics and kinetics

Recently, we devised an energy scale to vary systematically amino-acid residue-solvent interactions for Monte Carlo simulations of lattice-model proteins in water. For 27-mer proteins, the folding behavior varies appreciably with the choice of interaction parameters. We now perform similar simulations with 64-mers to study the size dependence of the optimal energy parameter set for representing realistic behavior typical of many real proteins (i.e. fast folding and high cooperativity for single chains). We find that 64-mers are considerably more stable and more cooperative compared to 27-mers. The optimal interfacial-interaction-energy parameter set, however, is relatively size independent.     

Monte Carlo simulations of peptide solvation

To increase our understanding of peptide–water interactions, we are simulating the behavior of water molecules in the intermolecular channels of [Phe⁴Val⁶]antamanide dododecahydrate crystals. There is good overall agreement between the positions predicted using two alternative potential functions and those that have been observed by x-ray diffraction. Detailed differences between the predictions for the two potential functions are discussed.     

Biofilm model calibration and microbial diversity study using Monte Carlo simulations

Mathematical models are useful tools for studying and exploring biological conversion processes as well as microbial competition in biological treatment processes. A single‐species biofilm model was used to describe biofilm reactor operation at three different hydraulic retention times (HRT). The single‐species biofilm model was calibrated with sparse experimental data using the Monte Carlo filtering method. This calibrated single‐species biofilm model was then extended to a multi‐species model considering 10 different heterotrophic bacteria. The aim was to study microbial diversity in bulk phase biomass and biofilm, as well as the competition between suspended and attached biomass. At steady state and independently of the HRT, Monte Carlo simulations resulted only in one unique dominating bacterial species for suspended and attached biomass. The dominating bacterial species was determined by the highest specific substrate affinity (ratio of µ/K_S). At a short HRT of 20 min, the structure of the microbial community in the bulk liquid was determined by biomass detached from the biofilm. At a long HRT of 8 h, both biofilm detachment and microbial growth in the bulk liquid influenced the microbial community distribution. Biotechnol. Bioeng. 2013; 110: 1323–1332. © 2012 Wiley Periodicals, Inc.     

Monte Carlo simulations of ionic channel selectivity

Monte Carlo simulations have been developed to study the selectivityof ionic channels in biological membranes. The channel is consideredto be in either of two possible states: (i) densely packed withions, the ions moving in single file in one direction, or alternatively,(ii) sparsely packed, where holes could appear at any particulartime thereby allowing bidirectional movement of ions. The twomodels enable us to envisage a quantitative flux of permeableions in the presence of smaller sized ions, taking into considerationtheir concentrations in the bulk solutions, the ion-channelinteractions and probability with which they fill up the channel.The programs are written in FORTRAN-77 (MS-FORTRAN) for an IBM-compatiblepersonal computer. From the simulation results we observe anenzymatic function of the channel and also note that the smallersized ions tend to block the movement of permeable ions. Thesimulations represent a technique for visualization of the factorsthat decide ionic permeability and help in manipulating theireffects with ease and speed which would otherwise involve intricateexperimental setups. Received on September 7, 1990; accepted on January 14, 1991     

A novel pencil beam model for carbon-ion dose calculation derived from Monte Carlo simulations

An accurate kernel model is of vital importance for pencil-beam dose algorithm in charged particle therapy using precise spot-scanning beam delivery, in which an accurate depiction of the low dose envelope is especially crucial. Based on the Monte Carlo method, we investigated the dose contribution of secondary particles to the total dose and proposed a novel beam model to depict the lateral dose distribution of carbon-ion pencil beam in water. We demonstrated that the low dose envelope in single-spot profiles in water could be adequately modelled with the addition of a logistic distribution to a double Gaussian one, which was verified in both single carbon-ion pencil beam and superposed fields of different sizes with multiple pencil beams. Its superiority was mainly manifested at medium depths especially for high-energy beams with small fields compared with single, double and triple Gaussian models, where the secondary particles influenced the total dose considerably. The double Gaussian-logistic model could reduce the deviations from 4.1%, 1.7% to 0.3% in the plateau and peak regions, and from 19.2%, 4.9% to 1.2% in the tail region compared for the field size factor (FSF) calculations of 344 MeV/u carbon-ion pencil beam with the single and double Gaussian models. Compared with the triple Gaussian one, our newly-proposed model was on a par with it, even better than it in the plateau and peak regions. Thus our work will be helpful for improving the dose calculation accuracy for carbon-ion therapy.     

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.     

Monte Carlo simulations on marker grouping and ordering

Four global algorithms, maximum likelihood (ML), sum of adjacent LOD score (SALOD), sum of adjacent recombinant fractions (SARF) and product of adjacent recombinant fraction (PARF), and one approximation algorithm, seriation (SER), were used to compare the marker ordering efficiencies for correctly given linkage groups based on doubled haploid (DH) populations. The Monte Carlo simulation results indicated the marker ordering powers for the five methods were almost identical. High correlation coefficients were greater than 0.99 between grouping power and ordering power, indicating that all these methods for marker ordering were reliable. Therefore, the main problem for linkage analysis was how to improve the grouping power. Since the SER approach provided the advantage of speed without losing ordering power, this approach was used for detailed simulations. For more generality, multiple linkage groups were employed, and population size, linkage cutoff criterion, marker spacing pattern (even or uneven), and marker spacing distance (close or loose) were considered for obtaining acceptable grouping powers. Simulation results indicated that the grouping power was related to population size, marker spacing distance, and cutoff criterion. Generally, a large population size provided higher grouping power than small population size, and closely linked markers provided higher grouping power than loosely linked markers. The cutoff criterion range for achieving acceptable grouping power and ordering power differed for varying cases; however, combining all situations in this study, a cutoff criterion ranging from 50 cM to 60 cM was recommended for achieving acceptable grouping power and ordering power for different cases.     

Monte Carlo simulations of plasma membrane corral-induced EGFR clustering

Experimental evidence suggests that the cell membrane is a highly organized structure that is compartmentalized by the underlying membrane cytoskeleton (MSK). The interaction between the cell membrane and the cytoskeleton led to the “picket-fence” model, which was proposed to explain certain aspects of membrane compartmentalization. This model assumes that the MSK hinders and confines the motion of receptors and lipids to compartments in the membrane. However, the impact of the MSK on receptor clustering, aggregation, and downstream signaling remains unclear. For example, some evidence suggests that the MSK enhances dimerization, while other evidence suggests decreased dimerization and signaling. Herein, we use computational Monte Carlo simulations to examine the effects of MSK density and receptor concentration on receptor dimerization and clustering. Preliminary results suggest that the MSK may have the potential to induce receptor clustering, which is a function of both picket-fence density and receptor concentration.     

Monte Carlo simulations shed light on Bathsheba's suspect breast

In 1654, Rembrandt van Rijn painted his famous painting Bathsheba at her Bath. Over the years, the depiction of Bathsheba's left breast and especially the presence of local discoloration, has generated debate on whether Rembrandt's Bathsheba suffered from breast cancer. Historical, medical and artistic arguments appeared to be not sufficient to prove if Bathsheba's model truly suffered from breast cancer. However, the bluish discoloration of the breast is an intriguing aspect from a biomedical optics point of view that might help us ending the old debate. By using Monte Carlo simulations in combination with the retinex theory of color vision, we showed that is highly unlikely that breast cancer results in a local bluish discoloration of the skin as is present on Bathsheba's breast. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lipid-cholesterol interactions. Monte Carlo simulations and theory.

Results of Monte Carlo calculations of order parameter profiles of lipid chains interacting with cholesterol are presented. Cholesterol concentrations in the simulations are sufficiently large that it is possible to analyze profiles for chains which are near neighbors of two or more cholesterol molecules, chains which are neighbors to a single cholesterol, and chains which are not near any cholesterol molecules. The profiles, show that cholesterol acts to significantly decrease the ability of neighboring chains to undergo trans-gauche isomeric rotations, although these chains are not all forced into all-trans conformations. The effect is significantly greater for chains which are neighbors to more than one cholesterol. The Monte Carlo results are next used as a guide to develop a theoretical model for lipid-cholesterol mixtures. The properties of this model and the phase diagram which it predicts are described. The phase diagram is then compared with experimentally determined phase diagrams. The model calculations and the computer simulations upon which they are based yield a molecular mechanism for several of the observed phases exhibited by lipid-cholesterol mixtures. The theoretical model predicts that at low temperatures the system should exhibit solid phase immiscibility.     

Monte Carlo simulations of voltage-driven translocation of a signal sequence

CD1d-deficient (CD1d-/-) mouse lymphocytes were analyzed to classify the natural killer T (NKT) cells without reactivity to CD1d. The cells bearing a V(alpha)19.1-J(alpha)26 (AV19-AJ33) invariant TCR alpha chain, originally found in the peripheral blood lymphocytes, were demonstrated to be abundant in the NK1.1+ but not NK1.1- T cell population isolated from CD1d-/- mice. Moreover, more than half (11/21) of the hybrid cell lines established from CD1d-/- NKT cells expressed the V(alpha)19.1-J(alpha)26 invariant TCR alpha chain. The expression of the invariant V(alpha)19.1-J(alpha)26 mRNA was absent in beta2-microglobulin-deficient mice. Collectively, the present findings suggest the presence of a second NKT cell repertoire characterized by an invariant TCR alpha chain (V(alpha)19.1-J(alpha)26) that is selected by an MHC class I-like molecule other than CD1d.     

Monte Carlo simulations of structure and entanglements in polymer melts

Atomistic models of short chain branched (SCB) polyethylene melts have been equilibrated at 450 K using a connectivity altering Monte Carlo method. Quantities related to the chain dimensions and entanglements have been determined. The simulated tube diameters, 〈a_pp〉, of SCB melts are found to scale with the backbone weight fraction, ?, as 〈a_pp〉～?^? 0.46, close to the scaling predicted by the binary contact model, 〈a_pp〉～?^? 0.5. Similar relationships are observed experimentally for polymer solutions, and reproduced by the present methods.     

Monte Carlo simulation of denaturation of adsorbed proteins

Denaturation of model proteinlike molecules at the liquid–solid interface is simulated over a wide temperature range by employing the lattice Monte Carlo technique. Initially, the molecule containing 27 monomers of two types (A and B) is assumed to be adsorbed in the native folded state (a 3 × 3 × 3 cube) so that one of its sides is in contact with the surface. The details of the denaturation kinetics are found to be slightly dependent on the choice of the side, but the main qualitative conclusions hold for all the sides. In particular, the kinetics obey approximately the conventional first-order law at T > T_c (T_c is the collapse temperature for solution). With decreasing temperature, below T_c but above T_f (T_f is the folding temperature for solution), deviations appear from the first-order kinetics. For the most interesting temperatures, that is, below T_f, the denaturation kinetics are shown to be qualitatively different from the conventional ones. In particular, the denaturation process occurs via several intermediate steps due to trapping in metastable states. Mathematically, this means that (i) the transition to the denatured state of a given molecule is nonexponential, and (ii) the denaturation process cannot be described by a single rate constant k_r. One should rather introduce a distribution of values of this rate constant (different values of k_r correspond to the transitions to the altered state via different metastable states). Proteins 30:168–176, 1998. © 1998 Wiley-Liss, Inc.     

Prediction of protein conformation in water and on surfaces by Monte Carlo simulations using united-atom method

The united-atom method has been used to model an avian pancreatic polypeptide (APP) in water and the adsorption process of an albumin subdomain (AS) onto graphite surface to observe the capability of this lumped modelling approach to generate structures observed in protein data bank (PDB) and from atomistic modelling. The subdomain structure of a protein is simplified by the united-atom approximation where the side chains and peptide groups are represented by lumped spheres. The total potential energy of the adsorption process involves the interaction between these lumped spheres by means of virtual bond chain interaction and the interaction of the spheres with the graphite surface by means of Lennard-Jones potential. The protein/polypeptide structure has been perturbed by Monte Carlo with energy minimisation to obtain the global minimum. Results on the APP in water showed a near-to-experimental PDB conformation revealing the two α-helix structures of this small protein molecule with the root mean square deviation among carbon backbone atoms of 5.9 Å. Protein adsorption on biosurfaces has been made by modelling AS, which has 60 amino acids. The surface is graphite, which is characterised by its hydrophobicity. Graphite was chosen because of its widely used applications in certain implants that interact with blood. Our simulation results showed final conformation close to that obtained by atomistic modelling. It also proved that the whole pattern of intramolecular hydrogen bonds was distorted. The model also demonstrated the random conformation of the original α-helix secondary structures of AS consistent with experimental and atomistic results. While atomistic simulation works well for simulating individual small proteins, the united-atom model is more efficient when simulating macromolecular and multiple protein adsorption where time and limiting computer capacity are key factors.     

Monte Carlo simulations of nucleotide crystal hydrates and their counter-ions

A knowledge of structural and energetic aspects of water- and ion-nucleic acid interactions is essential for the understanding of the role of solvent and counterions in stabilising the various helical forms of nucleic acids. In this study, Monte Carlo computer simulation techniques have been used to predict structural properties of solvent networks in small nucleic acid crystal hydrates containing the ions sodium, ammonium and calcium. Appropriate parameters to describe the interaction potentials of the ions are added to those previously developed for water and nucleic acid atoms. A comparison is made between the predicted and experimental results and it is concluded that the potential functions used lead to simulated solvent structure in reasonable agreement with experimental data, at least in the cases of sodium and calcium. It is now feasible to use these functions in studies of hydration of larger helical fragments of nucleic acids of more direct biological interest.     

Ammonium ion representation in Monte Carlo simulations of biomolecular solutions

Monte Carlo computer simulation techniques may be used to predict structural properties of solvent networks in helical fragments of nucleic acids, provided that suitable potential functions are available to describe the interactions between nucleic acid atoms, water and counterions. Previous studies have shown that simple non-bonded and point charge parameters are adequate for mononuclear ions such as sodium and calcium. In this study a model interaction potential for the polynuclear ammonium ion is evaluated. The parameters used take account of the distribution of charge over the constituent atoms in the ion. Simulations are carried out on the ammonium salt of a small nucleic acid crystal hydrate and a comparison is made between the predicted and experimental results. It is shown that the simulated structure is in reasonable agreement with experiment. It is therefore feasible to use this potential in studies of ammonium-containing bimolecular systems.