Study of the Villin headpiece folding dynamics by combining coarse-grained Monte Carlo evolution and all-atom molecular dynamics

The folding mechanism of the Villin headpiece (HP36) is studied by means of a novel approach which entails an initial coarse-grained Monte Carlo (MC) scheme followed by all-atom molecular dynamics (MD) simulations in explicit solvent. The MC evolution occurs in a simplified free-energy landscape and allows an efficient selection of marginally-compact structures which are taken as viable initial conformations for the MD. The coarse-grained MC structural representation is connected to the one with atomic resolution through a "fine-graining" reconstruction algorithm. This two-stage strategy is used to select and follow the dynamics of seven different unrelated conformations of HP36. In a notable case the MD trajectory rapidly evolves towards the folded state, yielding a typical root-mean-square deviation (RMSD) of the core region of only 2.4 A from the closest NMR model (the typical RMSD over the whole structure being 4.0 A). The analysis of the various MC-MD trajectories provides valuable insight into the details of the folding and mis-folding mechanisms and particularly about the delicate influence of local and nonlocal interactions in steering the folding process.     

All-atom Monte Carlo simulation of GCAA RNA folding

We report a detailed all-atom simulation of the folding of the GCAA RNA tetraloop. The GCAA tetraloop motif is a very common and thermodynamically stable secondary structure in natural RNAs. We use our simulation methods to study the folding behavior of a 12-base GCAA tetraloop structure with a four-base helix adjacent to the tetraloop proper. We implement an all-atom Monte Carlo (MC) simulation of RNA structural dynamics using a Go potential. Molecular dynamics (MD) simulation of RNA and protein has realistic energetics and sterics, but is extremely expensive in terms of computational time. By coarsely treating non-covalent energetics, but retaining all-atom sterics and entropic effects, all-atom MC techniques are a useful method for the study of protein and now RNA. We observe a sharp folding transition for this structure, and in simulations at room temperature the state histogram shows three distinct minima: an unfolded state (U), a more narrow intermediated state (I), and a narrow folded state (F). The intermediate consists primarily of structures with the GCAA loop and some helix hydrogen bonds formed. Repeated kinetic folding simulations reveal that the number of helix base-pairs forms a simple 1D reaction coordinate for the I-->N transition.     

Folding small proteins via annealing stochastic approximation Monte Carlo

Recently, the stochastic approximation Monte Carlo algorithm has been proposed by Liang et al. (2007) as a general-purpose stochastic optimization and simulation algorithm. An annealing version of this algorithm was developed for real small protein folding problems. The numerical results indicate that it outperforms simulated annealing and conventional Monte Carlo algorithms as a stochastic optimization algorithm. We also propose one method for the use of secondary structures in protein folding. The predicted protein structures are rather close to the true structures.     

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

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

Insertion of peptide chains into lipid membranes: An off-lattice Monte Carlo dynamics model

A combination of dynamic Monte Carlo simulation techniques with a hydropathy scale method for the prediction of the location of transmembrane fragments in membrane proteins is described. The new hydropathy scale proposed here is based on experimental data for the interactions of tripeptides with phospholipid membranes (Jacobs, R.E., White, S.H. Biochemistry 26:6127–6134, 1987) and the self-solvation effect in protein systems (Roseman, M.A., J. Mol. Biol. 200:513–522, 1988). The simulations give good predictions both for the state of association and the orientation of the peptide relative to the membrane surface of a number of peptides including Magainin2, M2δ, and melittin. Furthermore, for Pf1 bacterio-phage coat protein, in accord with experiment, the simulations predict that the C-terminus forms a transmembrane helix and the N-terminus forms a helix which is adsorbed on the surface of the bilayer. Finally, the present series of simulations provide a number of insights into the mechanism of insertion of peptides into cell membranes. © 1993 Wiley-Liss, Inc.     

Monte Carlo folding of trans-membrane helical peptides in an implicit generalized Born membrane

An efficient Monte Carlo (MC) algorithm using concerted backbone rotations is combined with a recently developed implicit membrane model to simulate the folding of the hydrophobic transmembrane domain M2TM of the M2 protein from influenza A virus and Sarcolipin at atomic resolution. The implicit membrane environment is based on generalized Born theory and has been calibrated against experimental data. The MC sampling has previously been used to fold several small polypeptides and been shown to be equivalent to molecular dynamics (MD). In combination with a replica exchange algorithm, M2TM is found to form continuous membrane spanning helical conformations for low temperature replicas. Sarcolipin is only partially helical, in agreement with the experimental NMR structures in lipid bilayers and detergent micelles. Higher temperature replicas exhibit a rapidly decreasing helicity, in agreement with expected thermodynamic behavior. To exclude the possibility of an erroneous helical bias in the simulations, the model is tested by sampling a synthetic Alanine-rich polypeptide of known helicity. The results demonstrate there is no overstabilization of helical conformations, indicating that the implicit model captures the essential components of the native membrane environment for M2TM and Sarcolipin.     

Testing a new Monte Carlo algorithm for protein folding

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

Conformational space exploration of Met- and Leu-enkephalin using the MOLS method, molecular dynamics, and Monte Carlo simulation--a comparative study

We report here a comparative study of the molecular conformational energy landscape generated using the mutually orthogonal Latin squares (MOLS) method, molecular dynamics (MD), and Monte Carlo (MC) simulation. The MOLS method, as described earlier from our laboratory, uses an experimental design technique to rapidly and exhaustively sample the low energy conformations of a molecule. MD and MC simulations have been used to perform similar tasks. In the comparison reported here, the three methods were applied to a pair of neuropeptides, namely Met- and Leu-enkephalin. A set of 1500 conformations of these enkephalins were generated using these methods with CHARMM22 force field, and the resulting samples were analyzed to determine the extent and nature of coverage of the conformational space. The results indicate that the MOLS method samples a larger number of possible conformations and identifies conformations closer to the experimental structures than the MD and MC simulations.     

A computer model to dynamically simulate protein folding: studies with crambin

The current work describes a simplified representation of protein structure with uses in the simulation of protein folding. The model assumes that a protein can be represented by a freely rotating rigid chain with a single atom approximating the effect of each side chain. Potentials describing the attraction or repulsion between different types of amino acids are determined directly from the distribution of amino acids in the database of known protein structures. The optimization technique of simulated annealing has been used to dynamically sample the conformations available to this simple model, allowing the protein to evolve from an extended, random coil into a compact globular structure. Many characteristics expected of true proteins, such as the sequence-dependent formation of secondary structure, the partitioning of hydrophobic residues, and specific disulfide pairing, are reproduced by the simulation, suggesting the model may accurately simulate the folding process.     

Folding of Top7 in unbiased all‐atom Monte Carlo simulations

For computational studies of protein folding, proteins with both helical and β‐sheet secondary structure elements are very challenging, as they expose subtle biases of the physical models. Here, we present reproducible folding of a 92 residue α/β protein (residues 3–94 of Top7, PDB ID: 1QYS) in computer simulations starting from random initial conformations using a transferable physical model which has been previously shown to describe the folding and thermodynamic properties of about 20 other smaller proteins of different folds. Top7 is a de novo designed protein with two α‐helices and a five stranded β‐sheet. Experimentally, it is known to be unusually stable for its size, and its folding transition distinctly deviates from the two‐state behavior commonly seen in natural single domain proteins. In our all‐atom implicit solvent parallel tempering Monte Carlo simulations, Top7 shows a rapid transition to a group of states with high native‐like secondary structure, and a much slower subsequent transition to the native state with a root mean square deviation of about 3.5 Å from the experimentally determined structure. Consistent with experiments, we find Top7 to be thermally extremely stable, although the simulations also find a large number of very stable non‐native states with high native‐like secondary structure. Proteins 2013; 81:1446–1456. © 2013 Wiley Periodicals, Inc.     

Monte Carlo simulation of protein folding with orientation-dependent monomer–monomer interactions

We present the results of lattice Monte Carlo simulations of protein folding in the framework of a model taking into account (i) the dependence of the energy of interaction of amino-acid residues on their orientation and (ii) the rigidity of the polypeptide chain with respect to the formation of kinks. If the chain is flexible, the final protein structures are predicted to be compact. Increasing the energy cost of creation of kinks is found to favor the formation of flat structures mimicking an ideal antiparallel β sheet. For compact structures, the kinetics of folding exhibit the standard two-phase regime (a rapid collapse to one of the metastable state, followed by slow reconfiguration of the chain to the native structure). For flat structures, the transition to the native state is often gradual. Proteins 29:508–516, 1997. © 1997 Wiley-Liss, Inc.     

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.     

Phylogenetic tree construction using sequential stochastic approximation Monte Carlo

Monte Carlo methods have received much attention recently in the literature of phylogenetic tree construction. However, they often suffer from two difficulties, the curse of dimensionality and the local-trap problem. The former one is due to that the number of possible phylogenetic trees increases at a super-exponential rate as the number of taxa increases. The latter one is due to that the phylogenetic tree has often a rugged energy landscape. In this paper, we propose a new phylogenetic tree construction method, which attempts to alleviate these two difficulties simultaneously by making use of the sequential structure of phylogenetic trees in conjunction with stochastic approximation Monte Carlo (SAMC) simulations. The use of the sequential structure of the problem provides substantial help to reduce the curse of dimensionality in simulations, and SAMC effectively prevents the system from getting trapped in local energy minima. The new method is compared with a variety of existing Bayesian and non-Bayesian methods on simulated and real datasets. Numerical results are in favor of the new method in terms of quality of the resulting phylogenetic trees.     

Simulating proteins at constant pH: An approach combining molecular dynamics and Monte Carlo simulation

For the structure and function of proteins, the pH of the solution is one of the determining parameters. Current molecular dynamics (MD) simulations account for the solution pH only in a limited way by keeping each titratable site in a chosen protonation state. We present an algorithm that generates trajectories at a Boltzmann distributed ensemble of protonation states by a combination of MD and Monte Carlo (MC) simulation. The algorithm is useful for pH-dependent structural studies and to investigate in detail the titration behavior of proteins. The method is tested on the acidic residues of the protein hen egg white lysozyme. It is shown that small structural changes may have a big effect on the pK(A) values of titratable residues.     

Monte Carlo simulations of a protein molecule with and without hydration energy calculated by the hydration-shell model

Monte Carlo simulations of a small protein, carmbin, were carried out with and without hydration energy. The methodology presented here is characterized, as compared with the other similar simulations of proteins in solution, by two points: (1) protein conformations are treated in fixed geometry so that dihedral angles are independent variables rather than cartesian coordinates of atoms; and (2) instead of treating water molecules explicitly in the calculation, hydration energy is incorporated in the conformational energy function in the form of g _i A _i, whereA _i is the accessible surface area of an atomic groupi in a given conformation, andg _i is the free energy of hydration per unit surface area of the atomic group (i.e., hydration-shell model). Reality of this model was tested by carrying out Monte Carlo simulations for the two kinds of starting conformations, native and unfolded ones, and in the two kinds of systems,in vacuo and solution. In the simulations starting from the native conformation, the differences between the mean propertiesin vacuo and solution simulations are not very large, but their fluctuations around the mean conformation during the simulation are relatively smaller in solution thanin vacuo. On the other hand, in the simulations starting from the unfolded conformation, the molecule fluctuates much more largely in solution thanin vacuo, and the effects of taking into account the hydration energy are pronounced very much. The results suggest that the method presented in this paper is useful for the simulations of proteins in solution.     

基于HP模型的大麻素受体CB2折叠研究

Cannabinoid receptor Type 2(简称CB2)是大麻素受体的一种亚型,因为其无中枢神经副作用,不会产生成瘾性及耐受性,显示出了非常好的开发前景和潜在的应用价值。其作为免疫调节剂、神经保护剂和抗癌药等将具有巨大市场价值。目前,CB2蛋白的空间结构还未被测定出来,对于CB2的折叠问题研究也开展的较少,为了研究大麻素受体亚型蛋白CB2的折叠问题以及方便更多的研究人员对CB2空间结构和相关药理特性的研究,本文提出了一种基于HP模型的折叠求解方法。通过使用回溯机制和蒙特卡罗方法对此优化问题进行求解,算法可有效的在全局范围内进行寻找最优解,避免了掉入局部最优问题。实验结果表明,本文方法获取的CB2蛋白空间构象具有较低的能量值,折叠情况较好。     

Protein conformational transitions coupled to binding in molecular recognition of unstructured proteins: hierarchy of structural loss from all-atom Monte Carlo simulations of p27Kip1 unfolding-unbinding and structural determinants of the binding mechanism

Conformational transitions coupled to binding are studied for the p27(Kip1) protein which undergoes a functional disorder-to-order folding transition during tertiary complex formation with the phosphorylated cyclin A-cyclin-dependent kinase 2 (Cdk2) binary complex. Temperature-induced Monte Carlo simulations of p27(Kip1) unfolding-unbinding carried out from the crystal structure of the tertiary complex have revealed a systematic trend in the hierarchy of structural loss for p27(Kip1) and a considerable difference in mobility of p27(Kip1) secondary structure elements. The most persistent interactions of p27(Kip1) at the intermolecular interface during unfolding-unbinding simulations are formed by beta-hairpin and beta-strand that on average maintain their structural integrity considerably longer than other p27(Kip1) elements. We have found that the ensemble of unfolded p27(Kip1) conformations is characterized by transitions between mostly unbound, collapsed conformations and entropically favorable p27(Kip1) conformations, which are weakly bound to the cyclin A side of the binary complex. The results of this study are consistent with the experimental evidence pointing to this region of the intermolecular interface as a potential initiation docking site during binding reaction and may reconcile conflicting experimental hypotheses on the recognition of substrate recruitment motifs.     

A Monte Carlo method for the simulation of kinetie models

The purpose of this note is to illustrate the feasibility of simulating kinetic systems, such as commonly encountered in photosynthesis research, using the Monte Carlo (MC) method. In this approach, chemical events are considered at the molecular level where they occur randomly and the macroscopic kinetic evolution results from averaging a large number of such events. Their repeated simulation is easily accomplished using digital computing. It is shown that the MC approach is well suited to the capabilities and resources of modern microcomputers. A software package is briefly described and discussed, allowing a simple programming of any kinetic model system and its resolution. The execution is reasonably fast and accurate; it is not subject to such instabilities as found with the conventional analytical approach.Abbreviations MC Monte Carlo - RN random number - PSU photosynthetic unit Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement.     

Water dynamics clue to key residues in protein folding

A computational method independent of experimental protein structure information is proposed to recognize key residues in protein folding, from the study of hydration water dynamics. Based on all-atom molecular dynamics simulation, two key residues are recognized with distinct water dynamical behavior in a folding process of the Trp-cage protein. The identified key residues are shown to play an essential role in both 3D structure and hydrophobic-induced collapse. With observations on hydration water dynamics around key residues, a dynamical pathway of folding can be interpreted.