Monte carlo simulations of protein-like heteropolymers.

Properties of a simple model of polypeptide chains were studied by the means of the Monte Carlo method. The chains were built on the (310) hybrid lattice. The residues interacted with long-range potential. There were two kinds of residues: hydrophobic and hydrophilic forming a typical helical pattern -HHPPHPP-. Short range potential was used to prefer helical conformations of the chain. It was found that at low temperatures the model chain formes dense and partially ordered structures (non-unique). The presence of the local potential led to an increase of helicity. The effect of the interplay between the two potentials was studied. After the collapse of the chain further annealing caused rearrangement of helical structures. Dynamic properties of the chain at low temperature depended strongly on the local chain ordering.     

The effect of sequence patterns and local conformational preferences on the structure of collapsed polypeptide

We studied the structure of a polypeptide model by means of the Monte Carlo method. The model chain consisting of two kinds of residues (hydrophobic and hydrophilic) was confined on the (310) hybrid lattice. The residues interacted with the long-range contact potential. The short-range potential was also used by introducing the preferences of conformations corresponding to the helical structure. Simulations of the coil-to-globule collapse were done by an annealing process starting from high-temperature structures and then gradual cooling of the system. The parameters describing the behavior of the system were monitored. It has been found that in a case of a helical pattern -HHPPHPP- the collapsed chains consisted of helical fragments. The resulting structures were formed in such way that the polar residues were located in the outer shell of the molecule since the hydrophobic residues filled the inner part of molecule. The results showed that the proper balance between the magnitude of the potentials used in a model is important and its influence on final structures of molecules was discussed.     

Computer simulation of polypeptides in a confinement

A coarse-grained model of polypeptide chains confined in a slit formed by two parallel impenetrable surfaces was studied. The chains were flexible heteropolymers (polypeptides) built of two kinds of united atoms—hydrophobic and hydrophilic. The positions of the united atoms were restricted to the vertices of a [310] lattice. The force field consisted of a rigorous excluded volume, a long-distance potential between a pair of amino-acid residues and a local preference for forming secondary structure (helices). The properties of the chains were studied at a wide range of temperatures from good to bad solvent conditions. Monte-Carlo simulations were carried out using the algorithm based on the chain’s local changes of conformation and employing the Replica Exchange technique. The influence of the chain length, the distances between the confining surfaces, the temperature and the force field on the dimension and the structure of chains were studied. It was shown that the presence of the confinement chain complicates the process of the chain collapse to low-temperature structures. For some conditions, one can find a rapid decrease of chain size and a second transition indicated by the rapid decrease of the total energy of the system. Figure A scheme of a polypeptide chain built on a [310] lattice and confined to a slit formed by a pair of parallel impenetrable surfaces Proceedings of “Modeling Interactions in Biomolecules II,” Prague, September 5th–9th, 2005.     

Computer simulation of polypeptide translocation through a nanopore

A simplified model of polypeptide chains was designed and studied by means of computer simulations. Chains were represented by a sequence of united atoms located at the positions of the -carbons. A further assumption was the lattice approximation for the chains. We used a (310) lattice, which was found useful for studying properties of proteins. The force field used consisted of a long-range contact potential between amino-acid residues and a local preference for forming -helical states. The chain consisted of two kinds of residues: hydrophilic (P) and hydrophobic (H) ones forming model helical septets –HHPPHPP– in a sequence. The chains were placed near an impenetrable surface with a square hole in it. The size of the hole was comparable or smaller than the size of a chain. The properties of these model chains were determined using the Monte-Carlo simulation method. During the simulations, translocation of the chain through the hole in the wall was observed. The influence of the chain length, the temperature differences on both sides of the wall and the force field on the chain properties were investigated. It was shown that the translocation time scales as N^2.2 and it was found that the presence of the local helical potential significantly slows down the process of translocation.Figure: The snapshots of typical chains conformation obtained during the simulation for chain consisted of N = 60. The values of the local potential _loc = -8.     

Anion and pH-dependent conformational transition of an amphiphilic polypeptide

While several proteins, including beta-lactamase, cytochrome c and apomyoglobin, are maximally unfolded at pH 2 by HCl in the absence of salt, the addition of anions, either from salt or acid, co-operatively induces the unfolded proteins to refold to a molten globule state, because anions bind preferentially to the compact molten globule state compared to the extended unfolded state. To study the role of the anion-dependent conformational transition at neutral pH, we synthesized a model polypeptide of 51 amino acid residues, consisting of tandem repeats of a Lys-Lys-Leu-Leu sequence and containing a turn sequence, Asn-Pro-Gly, at the center of the molecule. The model polypeptide showed no significant conformation by circular dichroism under conditions of low salt at neutral pH. However, addition of anions, either from salt or acid, induced the folding transition to an alpha-helical conformational state. The order of effectiveness of various anions in inducing the folding transition was consistent with the series of anions in inducing the molten globule of the acid-denatured protein. This suggests that the helical state of the model polypeptide is equivalent to the molten globule state. At pH values above 9, the model polypeptide also took an alpha-helical conformation, which was very similar to that induced by anions. On the basis of the chloride and pH-dependent conformational transitions, a phase diagram for the conformational states was constructed. The phase diagram was explained simply by assuming that the conformational transition is linked to the proton and the anion bindings to a limited number of amino groups and that anions bind only to the protonated groups.     

Why do proteins divide into domains? Insights from lattice model simulations

It is known that larger globular proteins are built from domains, relatively independent structural units. A domain size seems to be limited, and a single domain consists of from few tens to a couple of hundred amino acids. Based on Monte Carlo simulations of a reduced protein model restricted to the face centered simple cubic lattice, with a minimal set of short-range and long-range interactions, we have shown that some model sequences upon the folding transition spontaneously divide into separate domains. The observed domain sizes closely correspond to the sizes of real protein domains. Short chains with a proper sequence pattern of the hydrophobic and polar residues undergo a two-state folding transition to the structurally ordered globular state, while similar longer sequences follow a multistate transition. Homopolymeric (uniformly hydrophobic) chains and random heteropolymers undergo a continuous collapse transition into a single globule, and the globular state is much less ordered. Thus, the factors responsible for the multidomain structure of proteins are sufficiently long polypeptide chain and characteristic, protein-like, sequence patterns. These findings provide some hints for the analysis of real sequences aimed at prediction of the domain structure of large proteins.     

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.     

Collapse transitions in protein-like lattice polymers: The effect of sequence patterns

The collapse transition of lattice protein-like heteropolymers has been studied by means of the Monte Carlo method. The protein model has been reduced to the α-carbon trace restricted to a high coordination lattice. The sequences of model heteropolymers contain two types of mers: hydrophobic/nonpolar (H) and hydrophilic/polar (P). Interactions of HH and PP pairs were assumed to be negative (weaker attractions of PP pairs) while the contact energy for HP pairs was equal to zero. All sequence-specific short-range interactions have been neglected in the present studies. It has been found that homopolymeric chains undergo a smooth collapse transition to a dense globular state. The globule lacks any signatures of local ordering that could be interpreted as a model of protein secondary structure. Hetero-polymers with the sequences of hydrophilic and hydrophobic residues characteristic for α- and β-type proteins undergo a somewhat sharper (though continuous) collapse transition to a dense globular state with elements of local ordering controlled by the sequence. The helical pattern induces more secondary structure than the β-type pattern. For all examined sequences the level of local ordering was lower than the average secondary structure content of globular proteins. The results are compared with other theoretical work and with known experimental facts. The implications for the reduced modeling of protein systems are briefly discussed. © 1997 John Wiley & Sons, Inc. Biopoly 42: 537–548, 1997     

Structural basis of folding cooperativity in model proteins: insights from a microcanonical perspective

Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states that lie energetically between folded and unfolded conformations. There are different ways to test for two-state cooperativity; however, most of these approaches probe indirect proxies of this depletion. Generalized-ensemble computer simulations allow us to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here, we present a detailed characterization of several helical peptides obtained by coarse-grained simulations. The level of resolution of the coarse-grained model allowed to study realistic structures ranging from small α-helices to a de novo three-helix bundle without biasing the force field toward the native state of the protein. By linking thermodynamic and structural features, we are able to show that whereas short α-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. A detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features that up to now have been observed only in lattice models.     

Basement membrane (type IV) collagen is a heteropolymer

Type IV collagen was isolated in high yield from bovine kidney cortex. The protein revealed Mr = 380,000 and contained, in a 2:1 ratio, two different disulfide-linked polypeptide chains, C-1 and D-1 (Mr = 125,000). Carboxymethyl-cellulose chromatography before and after reduction proved that the two polypeptide chains are arranged in a single triple helical molecule with the chain composition (C-1)2(D-1). The disulfide bridges appear to be located 180 amino acid residues from the NH2 terminus of the chains.     

The sequence TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase displays structural ambivalence and interconverts between alpha-helical and beta-hairpin conformations mediated by collapsed conformational states.

The peptide TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase adopts a helical conformation in the crystal structure and is a site for two hydrated helical segments, which are thought to be helical folding intermediates. Overlapping sequences of four to five residues from the peptide, sample both helical and strand conformations in known protein structures, which are dissimilar to glyceraldehyde-3-phosphate dehydrogenase suggesting that the peptide may have a structural ambivalence. Molecular dynamics simulations of the peptide sequence performed for a total simulation time of 1.2 micros, starting from the various initial conformations using GROMOS96 force field under NVT conditions, show that the peptide samples a large number of conformational forms with transitions from alpha-helix to beta-hairpin and vice versa. The peptide, therefore, displays a structural ambivalence. The mechanism from alpha-helix to beta-hairpin transition and vice versa reveals that the compact bends and turns conformational forms mediate such conformational transitions. These compact structures including helices and hairpins have similar hydrophobic radius of gyration (Rgh) values suggesting that similar hydrophobic interactions govern these conformational forms. The distribution of conformational energies is Gaussian with helix sampling lowest energy followed by the hairpins and coil. The lowest potential energy of the full helix may enable the peptide to take up helical conformation in the crystal structure of the glyceraldehyde-3-phosphate dehydrogenase, even though the peptide has a preference for hairpin too. The relevance of folding and unfolding events observed in our simulations to hydrophobic collapse model of protein folding are discussed.     

Simulation of α-helix–coil transitions in simplified polyvaline: Equilibrium properties and brownian dynamics

A quantitative understanding of helix–coil dynamics will help explain their role in protein folding and in folded proteins. As a contribution to the understanding, the equilibrium and dynamical aspects of the helix–coil transition in polyvaline have been studied by computer simulation using a simplified model of the polypeptide chain. Each amino acid residue is treated as a single quasiparticle in an effective potential that approximates the potential of mean force in solution. The equilibrium properties examined include the helix–coil transition and its dependence on chain position and well depth at the coil–helix interface. A stochastic simulation of the Brownian motion of the chain in its solvent surroundings has been used to investigate dynamical properties. Time histories of the dihedral angles have been used to study the behavior of the helical structure. Auto and cross-correlation functions have been calculated from the time histories and from the state (helix or coil) functions of the residues with relaxation times of tens to hundreds of picoseconds. Helix–coil rate constants of tens of ns^?1 were found for both directions of the transition. © 1993 John Wiley & Sons, Inc.     

Computer simulations of protein folding with a small number of distance restraints

A high coordination lattice model was used to represent the protein chain. Lattice points correspond to amino-acid side groups. A complicated force field was designed in order to reproduce a protein-like behavior of the chain. Long-distance tertiary restraints were also introduced into the model. The Replica Exchange Monte Carlo method was applied to find the lowest energy states of the folded chain and to solve the problem of multiple minima. In this method, a set of replicas of the model chain was simulated independently in different temperatures with the exchanges of replicas allowed. The model chains, which consisted of up to 100 residues, were folded to structures whose root-mean-square deviation (RMSD) from their native state was between 2.5 and 5 A. Introduction of restrain based on the positions of the backbone hydrogen atoms led to an improvement in the number of successful simulation runs. A small improvement (about 0.5 A) was also achieved in the RMSD of the folds. The proposed method can be used for the refinement of structures determined experimentally from NMR data.     

Mosaic structure of globular domains in the human type VI collagen alpha 3 chain: similarity to von Willebrand factor, fibronectin, actin, salivary proteins and aprotinin type protease inhibitors.

Human collagen alpha 3(VI) chain mRNA (approximately 10 kb) was cloned and shown by sequence analysis to encode a 25 residue signal peptide, a large N-terminal globule (1804 residues), a central triple helical segment (336 residues) and a C-terminal globule (803 residues). Some of the sequence was confirmed by Edman degradation of peptides. The N-terminal globular segment consists of nine consecutive 200 residue repeats (N1 to N9) showing internal homology and also significant identity (17-25%) to the A domains of von Willebrand Factor and similar domains present in some other proteins. Deletions were found in the N3 and N9 domains of several cDNA clones suggesting variation of these structures by alternative splicing. The C-terminal globule starts immediately after the triple helical segment with two domains C1 (184 residues) and C2 (248 residues) being similar to the N domains. They are followed by a proline rich, repetitive segment C3 of 122 residues, with similarity to some salivary proteins, and domain C4 (89 residues), which is similar to the type III repeats present in fibronectin and tenascin. The most C-terminal domain C5 (70 residues) shows 40-50% identity to a variety of serine protease inhibitors of the Kunitz type. The whole sequence contains 29 cysteines which are mainly clustered in short segments connecting domains N1, C1, C2 and the triple helix, and in the inhibitor domain. Five putative Arg-Gly-Asp cell-binding sequences are exclusively localized in the triple helical segment.(ABSTRACT TRUNCATED AT 250 WORDS)     

Improved side‐chain torsion potentials for the Amber ff99SB protein force field

Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side‐chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha‐helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side‐chain torsion potentials of these residues to match new, high‐level quantum‐mechanical calculations. Finally, we used microsecond‐timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side‐chain conformations. The new force field, which we have termed Amber ff99SB‐ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Molecular dynamics model structures for the molten globule state of alpha-lactalbumin: aromatic residue clusters I and II

To model the molten globule structure of alpha-lactalbumin, molecular dynamics (MD) simulations were carried out for the protein in explicit water at high temperature. In these simulations, long-range Coulomb interactions were evaluated explicitly with an original method (particle-particle and particle-cell: PPPC) to avoid artifacts caused by the cut-off. The MD simulations were started from two initial conditions to verify that similar results would be obtained. From the last 150 ps trajectories of the two MD simulations, two partially unfolded average structures were obtained. These structures had the following common structural features which are characteristic of the molten globule state. The radii of gyration for these conformations were 7.4 and 9.6% larger than that of the native state. These values were almost the same as the experimental value (9.6%) observed recently by small-angle X-ray scattering (Kataoka,M., Kuwajima,K., Tokunaga,F. and Goto,Y., 1997, Protein Sci., 6, 422-430). Furthermore, aromatic residues of clusters I and II in these structures were far apart from each other except for Try103-Trp104. This result is in good agreement with NMR experimental results for the acid-denatured molten globule state (Alexandrescu et al., 1992, 1993); that is, NOE signals between the aromatic residues were not observed, except for that of Try103-Trp104 in the molten globule state. Other structural features of these models for the molten globule state are discussed with reference to native state structures.     

Roles of non‐native hydrogen‐bonding interaction in helix‐coil transition of a single polypeptide as revealed by comparison between Gō‐like and non‐Gō models

To explore the role of non‐native interactions in the helix‐coil transition, a detailed comparison between a Gō‐like model and a non‐Gō model has been performed via lattice Monte Carlo simulations. Only native hydrogen bonding interactions occur in the Gō‐like model, and the non‐native ones with sequence interval more than 4 is also included into the non‐Gō model. Some significant differences between the results from those two models have been found. The non‐native hydrogen bonds were found most populated at temperature around the helix‐coil transition. The rearrangement of non‐native hydrogen bonds into native ones in the formation of α‐helix leads to the increase of susceptibility of chain conformation, and even two peaks of susceptibility of radius of gyration versus temperature exist in the case of non‐Gō model for a non‐short peptide, while just a single peak exists in the case of Gō model for a single polypeptide chain with various chain lengths. The non‐native hydrogen bonds have complicated the temperature‐dependence of Zimm‐Bragg nucleation constant. The increase of relative probability of non‐native hydrogen bonding for long polypeptide chains leads to non‐monotonous chain length effect on the transition temperature. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Denatured proteins and early folding intermediates simulated in a reduced conformational space

Conformations of globular proteins in the denatured state were studied using a high-resolution lattice model of proteins and Monte Carlo dynamics. The model assumes a united-atom and high-coordination lattice representation of the polypeptide conformational space. The force field of the model mimics the short-range protein-like conformational stiffness, hydrophobic interactions of the side chains and the main-chain hydrogen bonds. Two types of approximations for the short-range interactions were compared: simple statistical potentials and knowledge-based protein-specific potentials derived from the sequence-structure compatibility of short fragments of protein chains. Model proteins in the denatured state are relatively compact, although the majority of the sampled conformations are globally different from the native fold. At the same time short protein fragments are mostly native-like. Thus, the denatured state of the model proteins has several features of the molten globule state observed experimentally. Statistical potentials induce native-like conformational propensities in the denatured state, especially for the fragments located in the core of folded proteins. Knowledge-based protein-specific potentials increase only slightly the level of similarity to the native conformations, in spite of their qualitatively higher specificity in the native structures. For a few cases, where fairly accurate experimental data exist, the simulation results are in semiquantitative agreement with the physical picture revealed by the experiments. This shows that the model studied in this work could be used efficiently in computational studies of protein dynamics in the denatured state, and consequently for studies of protein folding pathways, i.e. not only for the modeling of folded structures, as it was shown in previous studies. The results of the present studies also provide a new insight into the explanation of the Levinthal's paradox.     

Computer simulations of the properties of the alpha2, alpha2C, and alpha2D de novo designed helical proteins

Reduced lattice models of the three de novo designed helical proteins alpha2, alpha2C, and alpha2D were studied. Low temperature stable folds were obtained for all three proteins. In all cases, the lowest energy folds were four-helix bundles. The folding pathway is qualitatively the same for all proteins studied. The energies of various topologies are similar, especially for the alpha2 polypeptide. The simulated crossover from molten globule to native-like behavior is very similar to that seen in experimental studies. Simulations on a reduced protein model reproduce most of the experimental properties of the alpha2, alpha2C, and alpha2D proteins. Stable four-helix bundle structures were obtained, with increasing native-like behavior on-going from alpha2 to alpha2D that mimics experiment.