Off-lattice Model Research Articles

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, ε(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of ε(AB)*, suggesting that the ratio of the energy scales--and the corresponding empty fluid regime--is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime.

On Lattice Protein Structure Prediction Revisited

Protein structure prediction is regarded as a highly challenging problem both for the biology and for the computational communities. In recent years, many approaches have been developed, moving to increasingly complex lattice models and off-lattice models. This paper presents a Large Neighborhood Search (LNS) to find the native state for the Hydrophobic-Polar (HP) model on the Face-Centered Cubic (FCC) lattice or, in other words, a self-avoiding walk on the FCC lattice having a maximum number of H-H contacts. The algorithm starts with a tabu-search algorithm, whose solution is then improved by a combination of constraint programming and LNS. The flexible framework of this hybrid algorithm allows an adaptation to the Miyazawa-Jernigan contact potential, in place of the HP model, thus suggesting its potential for tertiary structure prediction. Benchmarking statistics are given for our method against the hydrophobic core threading program HPstruct, an exact method which can be viewed as complementary to our method.

Comparison of the Adsorption Transition for Grafted and Nongrafted Polymers

We compare the thermodynamic behavior of a finite single nongrafted polymer near an attractive substrate with that of a polymer grafted to that substrate. After we recently found first-order-like signatures in the microcanonical entropy at the adsorption transition in the nongrafted case, and given the fact that many studies on polymer adsorption in the past have been performed for grafted polymers, the question arises, to what extent and in what way does grafting change the nature of the adsorption transition? This question is tackled here using a coarse-grained off-lattice polymer model and covers not only the adsorption transition but also all other transitions a single polymer near an attractive substrate of varying strengths undergoes. Because of the impact of grafting especially on the translational but also on the conformational entropy of desorbed chains, the adsorption transition is affected the strongest. Our results are obtained by a combined canonical and microcanonical analysis of parallel tempering Monte Carlo data.

Unified regression model of binding equilibria in crowded environments

Molecular crowding is a critical feature distinguishing intracellular environments from idealized solution-based environments and is essential to understanding numerous biochemical reactions, from protein folding to signal transduction. Many biochemical reactions are dramatically altered by crowding, yet it is extremely difficult to predict how crowding will quantitatively affect any particular reaction systems. We previously developed a novel stochastic off-lattice model to efficiently simulate binding reactions across wide parameter ranges in various crowded conditions. We now show that a polynomial regression model can incorporate several interrelated parameters influencing chemistry under crowded conditions. The unified model of binding equilibria accurately reproduces the results of particle simulations over a broad range of variation of six physical parameters that collectively yield a complicated, non-linear crowding effect. The work represents an important step toward the long-term goal of computationally tractable predictive models of reaction chemistry in the cellular environment.

Discrete breathers in a realistic coarse-grained model of proteins

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin, discrete breathers (DBs), emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. DBs are time-periodic, space-localized vibrational modes that exist generically in nonlinear discrete systems and are known for their resilience and ability to concentrate energy for long times. In the case of the small β-barrel structure that we consider, DB-mediated localization occurs on the turns connecting the strands. At high energies, DBs stabilize the structure by concentrating energy on a few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of these two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.

CafeMol: A Coarse-Grained Biomolecular Simulator for Simulating Proteins at Work.

For simulating proteins at work in millisecond time scale or longer, we develop a coarse-grained (CG) molecular dynamics (MD) method and software, CafeMol. At the resolution of one-particle-per-residue, CafeMol equips four structure-based protein models: (1) the off-lattice Go model, (2) the atomic interaction based CG model for native state and folding dynamics, (3) the multiple-basin model for conformational change dynamics, and (4) the elastic network model for quasiharmonic fluctuations around the native structure. Ligands can be treated either explicitly or implicitly. For mimicking functional motions of proteins driven by some external force, CafeMol has various and flexible means to "switch" the energy functions that induce active motions of the proteins. CafeMol can do parallel computation with modest sized PC clusters. We describe CafeMol methods and illustrate it with several examples, such as rotary motions of F1-ATPase and drug exports from a transporter. The CafeMol source code is available at www.cafemol.org .

A case study of 3D protein structure prediction with genetic algorithm and Tabu search

This paper describes a case study of 3D protein structure prediction of six sequences from protein data bank (PDB) by genetic algorithm and tabu search (GATS), where off-lattice AB model is considered as a simplified model of protein structure. The lowest-energy values required for forming the native conformation of proteins are searched by GATS, and then the coarse structures (i.e., simplified structure) of the proteins are obtained according to the multiple angle parameters corresponding to the lowest energies. All the coarse structures form single hydrophobic cores surrounded by hydrophilic residues, which stay on the right side of the actual characteristic of protein structure. It demonstrates that this approach can predict the 3D protein structure effectively.

Topological Properties and Variations of Cells in Proliferating Epithelia: Impact of Mechanical Force and Division Orientation

Proliferating epithelia are sheets of dividing cells that tightly adhere to each other in many metazoans. Regulation of cell division is important for both normal and diseased epithelia. Quantitative analysis of epithelia shows significant conservation in the dominance of hexagonal cells in both animal and plant. However, there exist species with significant varied amount of hexagonal cells. The mechanism controlling these distributions is poorly understood. In this study, we use a computational method called cellGPS (cell global pattern simulator) to study the dynamic process of proliferating epithelia based on a mechanical off-lattice cellular model. This method keeps track of full geometric and biomechanical properties of epithelia. It models cell shape, area, perimeters and surface tension. Two biologically relevant division rules, namely, the orthogonal orientation found in plants and the largest-side orientation found in the mitotic spindle in human cells, are also incorporated in the division process. With this method, we found that regardless of division rules, our mechanical model can produce the common epithelia pattern of the dominance of hexagonal cells. In addition, we found that division rule of largest-side orientation lead to the formation of cell pattern with around 45% hexagons, which is observed in many animal epithelia and some plant tissues. This suggests that reducing stress on the cell wall by dividing the largest side is widely used in animal epithelia. The percentage of hexagons from division following orthogonal orientation is found to be about 60%, consistent with observations found in certain plant tissues. We conclude that both mechanical force and division orientation play important roles during epithelial proliferation. Mechanical model itself leads to topological dominance of hexagonal cells, and different rules of division orientation lead to varying amount of hexagonal cells.

Multiresolution Molecular Dynamics Simulations of Crystalline Nanofibrils

We introduce a multiresolution computational approach for the study of crystalline nanofibrils.Our multiresolution approach integrates fully-atomistic and coarse-grained levels of detail and it's particularly suited for the study of structural transitions between crystalline allomorphs. First, fully-atomistic simulations are used to gain a detailed understanding of the main structural differences between the crystalline phases under consideration. Second, we introduce a new coarse-grained, off-lattice model for the crystalline fibrils whose relevant degrees of freedom have been identified from the analysis of our fully-atomistic simulations. Both the structural transition and the relative thermal stability of the two allomorphs are studied at the coarse-grained level by means of Replica exchange molecular dynamics. The structural transition is analyzed within the framework of the Ginzburg-Landau formalism. As an example application of our method we consider two different allomorphs of crystalline cellulose nanofibrils, namely cellulose I-beta (the naturally--occurring form of cellulose) and cellulose III(I) (obtained from cellulose I-beta via ammonia pretreatment). Recent experiments show that the enzymatic degradation rate increases 2-5 times in cellulose III(I) respect to cellulose I-beta. Understanding the factors that regulate enzyme degradation of crystalline cellulose is a major challenge in the context of biofuels production from cellulosic biomass. Our multiresolution computational approach sheds new light on how the main structural and thermodynamic differences between these two cellulose crystalline forms affect their different enzyme activity rates.

GPU Based Molecular Dynamics Simulations of Polymer Rings in Concentrated Solution: Structure and Scaling

We report on equilibrium properties of a concentrated solution of non-concatenated ring polymers by Molecular dynamics simulations using HooMD-blue, a fast implementation on graphics processor units (GPUs). We are able to identify the intermediate scaling regime for the radius of gyration Rg ∝ N as well as indication for a crossover to Rg ∝ N for rings with chain length N in our fully flexible off-lattice polymer model. This crossover takes place between a ring size of 2500 and 7500 monomers for monomer density ρ = 0.5. Our results are in agreement with recent studies for lattice and stiff off-lattice models and show once again that this scaling is not model dependent at all. Furthermore this study demonstrates that GPUs are suited to tackle large scale problems in computational polymer science. To this end we present performance measurements relating the computing performance of a single NVidias GTX580 consumer graphic card to conventional state of the art supercomputers.

Simulations of the gyroid phase in diblock copolymers with the Gaussian disphere model

Pure melts of asymmetric diblock copolymers are studied by means of the off-lattice Gaussian disphere model with Monte-Carlo kinetics. In this model, a diblock copolymer chain is mapped onto two soft repulsive spheres with fluctuating radii of gyration and distance between centers of mass of the spheres. Microscopic input quantities of the model such as the combined probability distribution for the radii of gyration and the distance between the spheres as well as conditional monomer number densities assigned to each block were derived in the previous work of F. Eurich and P. Maass [J. Chem. Phys. 114, 7655 (2001)] within an underlying Gaussian chain model. The polymerization degree of the whole chain as well as those of the individual blocks are freely tunable parameters thus enabling a precise determination of the regions of stability of various phases. The model neglects entanglement effects which are irrelevant for the formation of ordered structures in diblock copolymers and which would otherwise unnecessarily increase the equilibration time of the system. The gyroid phase was reproduced in between the cylindrical and lamellar phases in systems with box sizes being commensurate with the size of the unit cell of the gyroid morphology. The region of stability of the gyroid phase was studied in detail and found to be consistent with the prediction of the mean-field theory. Packing frustration was observed in the form of increased radii of gyration of both blocks of the chains located close to the gyroid nodes.

An off-lattice frustrated model protein with a six-stranded β-barrel structure

We apply a global optimization method, which is conformational space annealing (CSA) to a challenging problem of the 69-residue protein with the sequence B(9)N(3)(LB)(4)N(3)B(9)N(3)(LB)(4)N(3)B(9)N(3)(LB)(5)L, where B, L, and N designate hydrophobic, hydrophilic, and neutral residues, respectively. The 69-residue BLN protein folds into a six-stranded β-barrel structure. The CSA method always maintains the diversity of sampling and is able to cross the high energy barriers between local minima. The CSA successfully located the global minimum of the 69-residue BLN protein for all 100 independent runs. For a single run, it takes about 3 h and 30 min on average to obtain the global minimum on a Linux PC. Also, we investigate the properties of the 69-residue BLN protein, and the general behavior of the M-residue BLN protein for CSA runs.

Higher-order Galilean-invariant lattice Boltzmann model for microflows: Single-component gas

We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.

Effective 3D protein structure prediction with local adjustment genetic-annealing algorithm

The protein folding problem consists of predicting protein tertiary structure from a given amino acid sequence by minimizing the energy function. The protein folding structure prediction is computationally challenging and has been shown to be NP-hard problem when the 3D off-lattice AB model is employed. In this paper, the local adjustment genetic-annealing (LAGA) algorithm was used to search the ground state of 3D offlattice AB model for protein folding structure. The algorithm included an improved crossover strategy and an improved mutation strategy, where a local adjustment strategy was also used to enhance the searching ability. The experiments were carried out with the Fibonacci sequences. The experimental results demonstrate that the LAGA algorithm appears to have better performance and accuracy compared to the previous methods.

3D Protein structure prediction with genetic tabu search algorithm

BackgroundProtein structure prediction (PSP) has important applications in different fields, such as drug design, disease prediction, and so on. In protein structure prediction, there are two important issues. The first one is the design of the structure model and the second one is the design of the optimization technology. Because of the complexity of the realistic protein structure, the structure model adopted in this paper is a simplified model, which is called off-lattice AB model. After the structure model is assumed, optimization technology is needed for searching the best conformation of a protein sequence based on the assumed structure model. However, PSP is an NP-hard problem even if the simplest model is assumed. Thus, many algorithms have been developed to solve the global optimization problem. In this paper, a hybrid algorithm, which combines genetic algorithm (GA) and tabu search (TS) algorithm, is developed to complete this task.ResultsIn order to develop an efficient optimization algorithm, several improved strategies are developed for the proposed genetic tabu search algorithm. The combined use of these strategies can improve the efficiency of the algorithm. In these strategies, tabu search introduced into the crossover and mutation operators can improve the local search capability, the adoption of variable population size strategy can maintain the diversity of the population, and the ranking selection strategy can improve the possibility of an individual with low energy value entering into next generation. Experiments are performed with Fibonacci sequences and real protein sequences. Experimental results show that the lowest energy obtained by the proposed GATS algorithm is lower than that obtained by previous methods.ConclusionsThe hybrid algorithm has the advantages from both genetic algorithm and tabu search algorithm. It makes use of the advantage of multiple search points in genetic algorithm, and can overcome poor hill-climbing capability in the conventional genetic algorithm by using the flexible memory functions of TS. Compared with some previous algorithms, GATS algorithm has better performance in global optimization and can predict 3D protein structure more effectively.

Comparison of the Parallel Tempering Algorithm and Multicanonical Method as Applied to Coarse-Grained Off-lattice Models for Folding Heteropolymers

We have performed Parallel Tempering simulations of hydrophobic-hydrophilic heteropolymers with a simple effective, coarse-grained off-lattice model with the selected monomers and compare the global energy minimums found with Parallel Tempering algorithm with the lowest energy states identified within the multicanonical algorithm.

Polymer desorption under pulling a 1st — order phase transition without phase coexistence

We show that when a self-avoiding polymer chain is pulled off a sticky surface by force applied to the end segment, it undergoes a first-order thermodynamic phase transition albeit without phase coexistence. This unusual feature is demonstrated analytically by means of a Grand Canonical Ensemble (GCE) description of adsorbed macromolecules as well as by Monte Carlo simulations of an off-lattice bead-spring model of a polymer chain.Theoretical treatment and computer experiment can be carried out both in the constant force statistical ensembl whereby at fixed pulling force f one measures the mean height 〈h〉 of the chain end above the adsorbing plane, and in the constant-height ensemble where for a given height h one monitors the resulting force 〈f〉 applied at the last segment. We find that the force-assisted desorption undergoes a first-order dichotomic phase transition whereby phase coexistence between adsorbed and desorbed states does not exist. In the f-ensemble the order parameter (the fraction of chain contacts with the surface) is characterized by huge fluctuations when the pulling force attains a critical value fD. In the h-ensemble, in contrast, fluctuations are always finite at the critical height hD.The derived analytical expressions for the probability distributions of the basic structural units of an adsorbed polymer, such as loops, trains and tails, in terms of the adhesive potential and f, or h, provide a full description of the polymer structure and behavior upon force-assisted detachment. In addition, one finds that the hitherto controversial value of the universal critical adsorption exponent ϕ depends essentially on the extent of interaction between the loops adsorbed chain so that ϕ may vary within the limits 0.34≤ϕ≤0.59.

Universal distribution of protein evolution rates as a consequence of protein folding physics

The hypothesis that folding robustness is the primary determinant of the evolution rate of proteins is explored using a coarse-grained off-lattice model. The simplicity of the model allows rapid computation of the folding probability of a sequence to any folded conformation. For each robust folder, the network of sequences that share its native structure is identified. The fitness of a sequence is postulated to be a simple function of the number of misfolded molecules that have to be produced to reach a characteristic protein abundance. After fixation probabilities of mutants are computed under a simple population dynamics model, a Markov chain on the fold network is constructed, and the fold-averaged evolution rate is computed. The distribution of the logarithm of the evolution rates across distinct networks exhibits a peak with a long tail on the low rate side and resembles the universal empirical distribution of the evolutionary rates more closely than either distribution resembles the log-normal distribution. The results suggest that the universal distribution of the evolutionary rates of protein-coding genes is a direct consequence of the basic physics of protein folding.

A differential evolution approach for protein structure optimisation using a 2D off-lattice model

Protein structure optimisation is a well-known problem in bioinformatics. This work applies an evolutionary algorithm to solve the protein structure optimisation problem based on the AB off-lattice model. Three different implementations of the differential evolution (DE) algorithm were developed, a sequential and two parallel. The parallel implementations (master-slave and ring-island) showed superior performance than the sequential one. Experiments were done using a benchmark of toy sequences with 13 to 55 monomers long. Results of the DE implementations were compared with other works in the literature. Good results were achieved for most sequences, not achieving the optimal values, but competitive with other specialised methods. Overall results encourage further research towards the use of knowledge-based operators to improve performance of DE.

Biomolecular Coarse-Grained Simulation Program CafeMol

Our group are developing biomolecular coarse-grained (CG) simulation program, which we call CafeMol. CG molecular dynamics (MD) simulation is able to reach much larger time- and spatial- resolution than conventional all-atom MD simulation. Thus, CG model have been used for long time simulation of biomolecular system, such as protein folding, DNA duplex melting, and self-assembly of lipid bilayer. CafeMol includes CG- protein, nucleotide, lipid models. We are developing to applicable protein-nucleotide and protein-lipid system.For protein model, we use off-lattice Go model and multi-basin model. Go model is minimal model for representing funnel-like energy landscape of protein folding, and multi-basin model, is extension of Go model, can treat large conformational change. CG DNA chain is repeat of three bead, which are represent base, sugar, and phosphate, respectively. This model distinguishes major- and minor- groove of DNA duplex. CG lipid molecules are composed of several beads. These lipid molecules self-assemble into bilayer vesicle. Now, CafeMol beta-version is released at http://www.cafemol.org/, which includes only CG protein model and attaches source code, manual, and some examples.