@article {Latek2011, title = {CABS-NMR{\textendash}De novo tool for rapid global fold determination from chemical shifts, residual dipolar couplings and sparse methyl-methyl NOEs}, journal = {Journal of c\Computational Chemistry}, volume = {32}, number = {3}, year = {2011}, pages = {536{\textendash}44}, abstract = {Recent development of nuclear magnetic resonance (NMR) techniques provided new types of structural restraints that can be successfully used in fast and low-cost global protein fold determination. Here, we present CABS-NMR, an efficient protein modeling tool, which takes advantage of such structural restraints. The restraints are converted from original NMR data to fit the coarse grained protein representation of the C-Alpha-Beta-Side-group (CABS) algorithm. CABS is a Monte Carlo search algorithm that uses a knowledge-based force field. Its versatile structure enables a variety of protein-modeling protocols, including purely de novo folding, folding guided by restraints derived from template structures or, structure assembly based on experimental data. In particular, CABS-NMR uses the distance and angular restraints set derived from various NMR experiments. This new modeling technique was successfully tested in structure determination of 10 globular proteins of size up to 216 residues, for which sparse NMR data were available. Additional detailed analysis was performed for a S100A1 protein. Namely, we successfully predicted Nuclear Overhauser Effect signals on the basis of low-energy structures obtained from chemical shifts by CABS-NMR. It has been observed that utility of chemical shifts and other types of experimental data (i.e. residual dipolar couplings and methyl-methyl Nuclear Overhauser Effect signals) in the presented modeling pipeline depends mainly on size of a protein and complexity of its topology. In this work, we have provided tools for either post-experiment processing of various kinds of NMR data or fast and low-cost structural analysis in the still challenging field of new fold predictions.}, keywords = {Algorithms, Animals, Cattle, Magnetic Resonance Spectroscopy, Magnetic Resonance Spectroscopy: methods, Models, Molecular, Monte Carlo Method, Protein Conformation, Protein Folding, Proteins, Proteins: chemistry, S100 Proteins, S100 Proteins: chemistry}, issn = {1096-987X}, doi = {10.1002/jcc.21640}, url = {http://www.ncbi.nlm.nih.gov/pubmed/20806263}, author = {Dorota Latek and Andrzej Koli{\'n}ski} } @article {Gniewek2010, title = {Coarse-grained Monte Carlo simulations of mucus: structure, dynamics, and thermodynamics}, journal = {Biophysical Journal}, volume = {99}, number = {11}, year = {2010}, month = {dec}, pages = {3507{\textendash}16}, publisher = {Biophysical Society}, abstract = {A simple coarse-grained model of mucus structure and dynamics is proposed and evaluated. The model is based on simple cubic, face-centered lattice representation. Mucins are simulated as lattice chains in which each bead of the model chains represents a mucin domain, equivalent to its Kuhn segment. The remaining lattice sites are considered to be occupied by the solvent. Model mucins consist of three types of domains: polar (glycosylated central segments), hydrophobic, and cysteine-rich, located at the terminal part of the mucin chains. The sequence of these domains mimics the sequence of real mucins. Static and dynamic properties of the system were studied by means of Monte Carlo dynamics. It was shown that the model system undergoes sol-gel transition and that the interactions between hydrophobic domains are responsible for the transition and characteristic properties of the dynamic network in the gel phase. Cysteine-rich domains are essential for frictional properties of the system. Structural and dynamic properties of the model mucus observed in simulations are in qualitative agreement with known experimental facts and provide mechanistic explanation of complex properties of real mucus.}, keywords = {Cysteine, Cysteine: chemistry, Diffusion, Gels, Humans, Hydrophobic and Hydrophilic Interactions, Molecular Dynamics Simulation, Monte Carlo Method, Mucins, Mucins: chemistry, Mucus, Mucus: chemistry, Protein Structure, Tertiary, Thermodynamics}, issn = {1542-0086}, doi = {10.1016/j.bpj.2010.09.047}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2998598\&tool=pmcentrez\&rendertype=abstract}, author = {Pawel Gniewek and Andrzej Koli{\'n}ski} } @article {Kmiecik2007a, title = {Characterization of protein-folding pathways by reduced-space modeling}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {104}, number = {30}, year = {2007}, month = {jul}, pages = {12330{\textendash}5}, abstract = {Ab initio simulations of the folding pathways are currently limited to very small proteins. For larger proteins, some approximations or simplifications in protein models need to be introduced. Protein folding and unfolding are among the basic processes in the cell and are very difficult to characterize in detail by experiment or simulation. Chymotrypsin inhibitor 2 (CI2) and barnase are probably the best characterized experimentally in this respect. For these model systems, initial folding stages were simulated by using CA-CB-side chain (CABS), a reduced-space protein-modeling tool. CABS employs knowledge-based potentials that proved to be very successful in protein structure prediction. With the use of isothermal Monte Carlo (MC) dynamics, initiation sites with a residual structure and weak tertiary interactions were identified. Such structures are essential for the initiation of the folding process through a sequential reduction of the protein conformational space, overcoming the Levinthal paradox in this manner. Furthermore, nucleation sites that initiate a tertiary interactions network were located. The MC simulations correspond perfectly to the results of experimental and theoretical research and bring insights into CI2 folding mechanism: unambiguous sequence of folding events was reported as well as cooperative substructures compatible with those obtained in recent molecular dynamics unfolding studies. The correspondence between the simulation and experiment shows that knowledge-based potentials are not only useful in protein structure predictions but are also capable of reproducing the folding pathways. Thus, the results of this work significantly extend the applicability range of reduced models in the theoretical study of proteins.}, keywords = {Amino Acid Sequence, coarse-grained modeling, Computational Biology, Computer Simulation, Hydrophobic and Hydrophilic Interactions, Models, Molecular, Molecular Dynamics Simulation, Monte Carlo Method, Protein Denaturation, protein dynamics, Protein Folding, Protein Structure, Proteins, Proteins: chemistry, Proteins: metabolism, Temperature, Tertiary}, issn = {0027-8424}, doi = {10.1073/pnas.0702265104}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1941469\&tool=pmcentrez\&rendertype=abstract}, author = {Sebastian Kmiecik and Andrzej Koli{\'n}ski} } @article {Kurcinski2007a, title = {Hierarchical modeling of protein interactions}, journal = {Journal of Molecular Modeling}, volume = {13}, number = {6-7}, year = {2007}, month = {jul}, pages = {691{\textendash}698}, abstract = {A novel approach to hierarchical peptide-protein and protein-protein docking is described and evaluated. Modeling procedure starts from a reduced space representation of proteins and peptides. Polypeptide chains are represented by strings of alpha-carbon beads restricted to a fine-mesh cubic lattice. Side chains are represented by up to two centers of interactions, corresponding to beta-carbons and the centers of mass of the remaining portions of the side groups, respectively. Additional pseudoatoms are located in the centers of the virtual bonds connecting consecutive alpha carbons. These pseudoatoms support a model of main-chain hydrogen bonds. Docking starts from a collection of random configurations of modeled molecules. Interacting molecules are flexible; however, higher accuracy models are obtained when the conformational freedom of one (the larger one) of the assembling molecules is limited by a set of weak distance restraints extracted from the experimental (or theoretically predicted) structures. Sampling is done by means of Replica Exchange Monte Carlo method. Afterwards, the set of obtained structures is subject to a hierarchical clustering. Then, the centroids of the resulting clusters are used as scaffolds for the reconstruction of the atomic details. Finally, the all-atom models are energy minimized and scored using classical tools of molecular mechanics. The method is tested on a set of macromolecular assemblies consisting of proteins and peptides. It is demonstrated that the proposed approach to the flexible docking could be successfully applied to prediction of protein-peptide and protein-protein interactions. The obtained models are almost always qualitatively correct, although usually of relatively low (or moderate) resolution. In spite of this limitation, the proposed method opens new possibilities of computational studies of macromolecular recognition and mechanisms of assembly of macromolecular complexes.}, keywords = {Algorithms, Amino Acid Sequence, Amino Acids, Amino Acids: analysis, Carbon, Carbon: chemistry, Computer Simulation, Crystallography, Hydrogen Bonding, Models, Molecular, Monte Carlo Method, Peptides, Peptides: chemistry, Peptides: metabolism, Protein Binding, Protein Conformation, Protein Structure, Proteins, Proteins: chemistry, Proteins: metabolism, Secondary, Stereoisomerism, Theoretical, X-Ray}, issn = {0948-5023}, doi = {10.1007/s00894-007-0177-8}, url = {http://www.ncbi.nlm.nih.gov/pubmed/17297609}, author = {Mateusz Kurcinski and Andrzej Koli{\'n}ski} } @article {Gront2007, title = {T-Pile{\textendash}a package for thermodynamic calculations for biomolecules}, journal = {Bioinformatics (Oxford, England)}, volume = {23}, number = {14}, year = {2007}, month = {jul}, pages = {1840{\textendash}1842}, abstract = {Molecular dynamics and Monte Carlo, usually conducted in canonical ensemble, deliver a plethora of biomolecular conformations. Proper analysis of the simulation data is a crucial part of biophysical and bioinformatics studies. Sequence alignment problem can be also formulated in terms of Boltzmann distribution. Therefore tools for efficient analysis of canonical ensemble data become extremely valuable. T-Pile package, presented here provides a user-friendly implementation of most important algorithms such as multihistogram analysis and reweighting technique. The package can be used in studies of virtually any system governed by Boltzmann distribution. AVAILABILITY: T-Pile can be downloaded from: http://biocomp.chem.uw.edu.pl/services/tpile. These pages provide a comprehensive tutorial and documentation with illustrative examples of applications. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.}, keywords = {Algorithms, Biophysics, Biophysics: methods, Computational Biology, Computational Biology: methods, Computers, Hot Temperature, Models, Molecular Conformation, Monte Carlo Method, Probability, Proteins, Proteins: chemistry, Software, Temperature, Theoretical, Thermodynamics}, issn = {1367-4811}, doi = {10.1093/bioinformatics/btm259}, url = {http://www.ncbi.nlm.nih.gov/pubmed/17510173}, author = {Dominik Gront and Andrzej Koli{\'n}ski} } @article {Kmiecik2006, title = {Denatured proteins and early folding intermediates simulated in a reduced conformational space}, journal = {Acta Biochimica Polonica}, volume = {53}, number = {1}, year = {2006}, month = {jan}, pages = {131{\textendash}143}, abstract = {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{\textquoteright}s paradox.}, keywords = {Animals, Biophysics, Biophysics: methods, Chymotrypsin, Chymotrypsin: antagonists \& inhibitors, Chymotrypsin: chemistry, Computer Simulation, Cytochromes c, Cytochromes c: chemistry, Models, Molecular, Molecular Conformation, Monte Carlo Method, Protein Conformation, Protein Denaturation, Protein Folding, Ribonucleases, Ribonucleases: chemistry, src Homology Domains, Statistical}, issn = {0001-527X}, url = {http://www.ncbi.nlm.nih.gov/pubmed/16365636}, author = {Sebastian Kmiecik and Mateusz Kurcinski and Aleksandra Rutkowska and Dominik Gront and Andrzej Koli{\'n}ski} } @article {Kolinski2005, title = {Generalized protein structure prediction based on combination of fold-recognition with de novo folding and evaluation of models}, journal = {Proteins}, volume = {61 Suppl. 7}, number = {April}, year = {2005}, month = {jan}, pages = {84{\textendash}90}, abstract = {To predict the tertiary structure of full-length sequences of all targets in CASP6, regardless of their potential category (from easy comparative modeling to fold recognition to apparent new folds) we used a novel combination of two very different approaches developed independently in our laboratories, which ranked quite well in different categories in CASP5. First, the GeneSilico metaserver was used to identify domains, predict secondary structure, and generate fold recognition (FR) alignments, which were converted to full-atom models using the "FRankenstein{\textquoteright}s Monster" approach for comparative modeling (CM) by recombination of protein fragments. Additional models generated "de novo" by fully automated servers were obtained from the CASP website. All these models were evaluated by VERIFY3D, and residues with scores better than 0.2 were used as a source of spatial restraints. Second, a new implementation of the lattice-based protein modeling tool CABS was used to carry out folding guided by the above-mentioned restraints with the Replica Exchange Monte Carlo sampling technique. Decoys generated in the course of simulation were subject to the average linkage hierarchical clustering. For a representative decoy from each cluster, a full-atom model was rebuilt. Finally, five models were selected for submission based on combination of various criteria, including the size, density, and average energy of the corresponding cluster, and the visual evaluation of the full-atom structures and their relationship to the original templates. The combination of FRankenstein and CABS was one of the best-performing algorithms over all categories in CASP6 (it is important to note that our human intervention was very limited, and all steps in our method can be easily automated). We were able to generate a number of very good models, especially in the Comparative Modeling and New Folds categories. Frequently, the best models were closer to the native structure than any of the templates used. The main problem we encountered was in the ranking of the final models (the only step of significant human intervention), due to the insufficient computational power, which precluded the possibility of full-atom refinement and energy-based evaluation.}, keywords = {Algorithms, Computational Biology, Computational Biology: methods, Computer Simulation, Computers, Data Interpretation, Databases, Dimerization, Models, Molecular, Monte Carlo Method, Protein, Protein Conformation, Protein Folding, Protein Structure, Proteomics, Proteomics: methods, Reproducibility of Results, Secondary, Sequence Alignment, Software, Statistical, Tertiary}, issn = {1097-0134}, doi = {10.1002/prot.20723}, url = {http://www.ncbi.nlm.nih.gov/pubmed/16187348}, author = {Andrzej Koli{\'n}ski and Janusz M. Bujnicki} } @article {Ekonomiuk2005, title = {Protein modeling with reduced representation: statistical potentials and protein folding mechanism}, journal = {Acta Biochimica Polonica}, volume = {52}, number = {4}, year = {2005}, month = {jan}, pages = {741{\textendash}8}, abstract = {A high resolution reduced model of proteins is used in Monte Carlo dynamics studies of the folding mechanism of a small globular protein, the B1 immunoglobulin-binding domain of streptococcal protein G. It is shown that in order to reproduce the physics of the folding transition, the united atom based model requires a set of knowledge-based potentials mimicking the short-range conformational propensities and protein-like chain stiffness, a model of directional and cooperative hydrogen bonds, and properly designed knowledge-based potentials of the long-range interactions between the side groups. The folding of the model protein is cooperative and very fast. In a single trajectory, a number of folding/unfolding cycles were observed. Typically, the folding process is initiated by assembly of a native-like structure of the C-terminal hairpin. In the next stage the rest of the four-ribbon beta-sheet folds. The slowest step of this pathway is the assembly of the central helix on the scaffold of the beta-sheet.}, keywords = {Biophysical Phenomena, Biophysics, Computer Simulation, Models, Molecular, Monte Carlo Method, Protein Conformation, Protein Folding, Proteins, Proteins: chemistry, Proteins: metabolism}, issn = {0001-527X}, url = {http://www.ncbi.nlm.nih.gov/pubmed/15933762}, author = {Dariusz Ekonomiuk and Marcin Kielbasinski and Andrzej Koli{\'n}ski} } @article {Gront2005b, title = {Protein structure prediction by tempering spatial constraints}, journal = {Journal of Computer-Aided Molecular Design}, volume = {19}, number = {8}, year = {2005}, month = {aug}, pages = {603{\textendash}8}, abstract = {The probability to predict correctly a protein structure can be enhanced through introduction of spatial constraints - either from NMR experiments or from homologous structures. However, the additional constraints lead often to new local energy minima and worse sampling efficiency in simulations. In this work, we present a new parallel tempering variant that alleviates the energy barriers resulting from spatial constraints and therefore yields to an enhanced sampling in structure prediction simulations.}, keywords = {Algorithms, Computer Simulation, Monte Carlo Method, Protein Conformation, Temperature}, isbn = {1082200590160}, issn = {0920-654X}, doi = {10.1007/s10822-005-9016-0}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1473033\&tool=pmcentrez\&rendertype=abstract}, author = {Dominik Gront and Andrzej Koli{\'n}ski and Ulrich H. E. Hansmann} } @article {Maolepsza2005, title = {Theoretical model of prion propagation: a misfolded protein induces misfolding}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {102}, number = {22}, year = {2005}, month = {may}, pages = {7835{\textendash}40}, abstract = {There is a hypothesis that dangerous diseases such as bovine spongiform encephalopathy, Creutzfeldt-Jakob, Alzheimer{\textquoteright}s, fatal familial insomnia, and several others are induced by propagation of wrong or misfolded conformations of some vital proteins. If for some reason the misfolded conformations were acquired by many such protein molecules it might lead to a "conformational" disease of the organism. Here, a theoretical model of the molecular mechanism of such a conformational disease is proposed, in which a metastable (or misfolded) form of a protein induces a similar misfolding of another protein molecule (conformational autocatalysis). First, a number of amino acid sequences composed of 32 aa have been designed that fold rapidly into a well defined native-like alpha-helical conformation. From a large number of such sequences a subset of 14 had a specific feature of their energy landscape, a well defined local energy minimum (higher than the global minimum for the alpha-helical fold) corresponding to beta-type structure. Only one of these 14 sequences exhibited a strong autocatalytic tendency to form a beta-sheet dimer capable of further propagation of protofibril-like structure. Simulations were done by using a reduced, although of high resolution, protein model and the replica exchange Monte Carlo sampling procedure.}, keywords = {Amino Acid Sequence, Amino Acids, Amino Acids: metabolism, Computer Simulation, Models, Molecular, Monte Carlo Method, Prions, Prions: metabolism, Protein Conformation, Protein Folding, Theoretical}, isbn = {0409389102}, issn = {0027-8424}, doi = {10.1073/pnas.0409389102}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1142357\&tool=pmcentrez\&rendertype=abstract}, author = {Edyta Ma{\l}olepsza and Michal Boniecki and Andrzej Koli{\'n}ski and Lucjan Piela} } @article {Pokarowski2003, title = {A minimal physically realistic protein-like lattice model: designing an energy landscape that ensures all-or-none folding to a unique native state}, journal = {Biophysical Journal}, volume = {84}, number = {3}, year = {2003}, month = {mar}, pages = {1518{\textendash}26}, abstract = {A simple protein model restricted to the face-centered cubic lattice has been studied. The model interaction scheme includes attractive interactions between hydrophobic (H) residues, repulsive interactions between hydrophobic and polar (P) residues, and orientation-dependent P-P interactions. Additionally, there is a potential that favors extended beta-type conformations. A sequence has been designed that adopts a native structure, consisting of an antiparallel, six-member Greek-key beta-barrel with protein-like structural degeneracy. It has been shown that the proposed model is a minimal one, i.e., all the above listed types of interactions are necessary for cooperative (all-or-none) type folding to the native state. Simulations were performed via the Replica Exchange Monte Carlo method and the numerical data analyzed via a multihistogram method.}, keywords = {Amino Acid Motifs, Computer Simulation, Crystallography, Crystallography: methods, Energy Transfer, Entropy, Mechanical, Models, Molecular, Monte Carlo Method, Peptides, Peptides: chemistry, Protein Conformation, Protein Folding, Protein Structure, Proteins, Proteins: chemistry, Static Electricity, Stress, Tertiary}, issn = {0006-3495}, doi = {10.1016/S0006-3495(03)74964-9}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1302725\&tool=pmcentrez\&rendertype=abstract}, author = {Piotr Pokarowski and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Kolinski2003, title = {A simple lattice model that exhibits a protein-like cooperative all-or-none folding transition}, journal = {Biopolymers}, volume = {69}, number = {3}, year = {2003}, month = {jul}, pages = {399{\textendash}405}, abstract = {In a recent paper (D. Gront et al., Journal of Chemical Physics, Vol. 115, pp. 1569, 2001) we applied a simple combination of the Replica Exchange Monte Carlo and the Histogram methods in the computational studies of a simplified protein lattice model containing hydrophobic and polar units and sequence-dependent local stiffness. A well-defined, relatively complex Greek-key topology, ground (native) conformations was found; however, the cooperativity of the folding transition was very low. Here we describe a modified minimal model of the same Greek-key motif for which the folding transition is very cooperative and has all the features of the "all-or-none" transition typical of real globular proteins. It is demonstrated that the all-or-none transition arises from the interplay between local stiffness and properly defined tertiary interactions. The tertiary interactions are directional, mimicking the packing preferences seen in proteins. The model properties are compared with other minimal protein-like models, and we argue that the model presented here captures essential physics of protein folding (structurally well-defined protein-like native conformation and cooperative all-or-none folding transition).}, keywords = {Biopolymers, Biopolymers: chemistry, Biopolymers: metabolism, Chemical, Models, Molecular, Monte Carlo Method, Protein Folding, Protein Structure, Proteins, Proteins: chemistry, Proteins: metabolism, Secondary, Thermodynamics}, issn = {0006-3525}, doi = {10.1002/bip.10385}, url = {http://www.ncbi.nlm.nih.gov/pubmed/12833266}, author = {Andrzej Koli{\'n}ski and Dominik Gront and Piotr Pokarowski and Jeffrey Skolnick} } @article {Kolinski2003a, title = {Unfolding of globular proteins: monte carlo dynamics of a realistic reduced model}, journal = {Biophysical Journal}, volume = {85}, number = {5}, year = {2003}, month = {nov}, pages = {3271{\textendash}3278}, abstract = {Reduced lattice models of proteins and Monte Carlo dynamics were used to simulate the initial stages of the unfolding of several proteins of various structural types, and the results were compared to experiment. The models semiquantitatively reproduce the approximate order of events of unfolding as well as subtle mutation effects and effects resulting from differences in sequences of similar folds. The short-time mobility of particular residues, observed in simulations, correlates with the crystallographic temperature factor. The main factor controlling unfolding is the native state topology, with sequence playing a less important role. The correlation with various experiments, especially for sequence-specific effects, strongly suggests that properly designed reduced models of proteins can be used for qualitative studies (or prediction) of protein unfolding pathways.}, keywords = {Apoproteins, Apoproteins: chemistry, Bacterial Proteins, Chemical, DNA-Binding Proteins, DNA-Binding Proteins: chemistry, Leghemoglobin, Leghemoglobin: chemistry, Models, Molecular, Monte Carlo Method, Myoglobin, Myoglobin: chemistry, Nerve Tissue Proteins, Nerve Tissue Proteins: chemistry, Plastocyanin, Plastocyanin: chemistry, Protein Denaturation, Protein Folding, Proteins, Proteins: chemistry, Statistical}, issn = {0006-3495}, doi = {10.1016/S0006-3495(03)74745-6}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1303603\&tool=pmcentrez\&rendertype=abstract}, author = {Andrzej Koli{\'n}ski and Piotr Klein and Piotr Romiszowski and Jeffrey Skolnick} } @article {Kihara2002, title = {Ab initio protein structure prediction on a genomic scale: application to the Mycoplasma genitalium genome}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {99}, year = {2002}, month = {apr}, pages = {5993{\textendash}5998}, abstract = {An ab initio protein structure prediction procedure, TOUCHSTONE, was applied to all 85 small proteins of the Mycoplasma genitalium genome. TOUCHSTONE is based on a Monte Carlo refinement of a lattice model of proteins, which uses threading-based tertiary restraints. Such restraints are derived by extracting consensus contacts and local secondary structure from at least weakly scoring structures that, in some cases, can lack any global similarity to the sequence of interest. Selection of the native fold was done by using the convergence of the simulation from two different conformational search schemes and the lowest energy structure by a knowledge-based atomic-detailed potential. Among the 85 proteins, for 34 proteins with significant threading hits, the template structures were reasonably well reproduced. Of the remaining 51 proteins, 29 proteins converged to five or fewer clusters. In the test set, 84.8\% of the proteins that converged to five or fewer clusters had a correct fold among the clusters. If this statistic is simply applied, 24 proteins (84.8\% of the 29 proteins) may have correct folds. Thus, the topology of a total of 58 proteins probably has been correctly predicted. Based on these results, ab initio protein structure prediction is becoming a practical approach.}, keywords = {Algorithms, Bacterial, Databases as Topic, Genome, Models, Molecular, Monte Carlo Method, Mycoplasma, Mycoplasma: genetics, Protein Folding, Proteins, Proteins: chemistry, Software}, issn = {0027-8424}, doi = {10.1073/pnas.092135699}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=122890\&tool=pmcentrez\&rendertype=abstract}, author = {Daisuke Kihara and Yang Zhang and Hui Lu and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Sikorski2002, title = {Computer simulations of protein folding with a small number of distance restraints}, journal = {Acta Biochimica Polonica}, volume = {49}, number = {3}, year = {2002}, month = {jan}, pages = {683{\textendash}692}, abstract = {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.}, keywords = {Algorithms, Amino Acids, Amino Acids: chemistry, Chemical, Computer Simulation, Hydrogen Bonding, Models, Molecular, Monte Carlo Method, Nerve Tissue Proteins, Nerve Tissue Proteins: chemistry, Plastocyanin, Plastocyanin: chemistry, Protein Conformation, Protein Folding, Protein Kinases, Thermodynamics}, issn = {0001-527X}, doi = {024903683}, url = {http://www.ncbi.nlm.nih.gov/pubmed/12422238}, author = {Andrzej Sikorski and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Vinals2002, title = {Numerical study of the entropy loss of dimerization and the folding thermodynamics of the GCN4 leucine zipper}, journal = {Biophysical Journal}, volume = {83}, number = {5}, year = {2002}, month = {nov}, pages = {2801{\textendash}2811}, abstract = {A lattice-based model of a protein and the Monte Carlo simulation method are used to calculate the entropy loss of dimerization of the GCN4 leucine zipper. In the representation used, a protein is a sequence of interaction centers arranged on a cubic lattice, with effective interaction potentials that are both of physical and statistical nature. The Monte Carlo simulation method is then used to sample the partition functions of both the monomer and dimer forms as a function of temperature. A method is described to estimate the entropy loss upon dimerization, a quantity that enters the free energy difference between monomer and dimer, and the corresponding dimerization reaction constant. As expected, but contrary to previous numerical studies, we find that the entropy loss of dimerization is a strong function of energy (or temperature), except in the limit of large energies in which the motion of the two dimer chains becomes largely uncorrelated. At the monomer-dimer transition temperature we find that the entropy loss of dimerization is approximately five times smaller than the value that would result from ideal gas statistics, a result that is qualitatively consistent with a recent experimental determination of the entropy loss of dimerization of a synthetic peptide that also forms a two-stranded alpha-helical coiled coil.}, keywords = {Biophysical Phenomena, Biophysics, Databases as Topic, Dimerization, DNA-Binding Proteins, DNA-Binding Proteins: chemistry, Entropy, Hot Temperature, Leucine Zippers, Models, Monte Carlo Method, Protein Folding, Protein Kinases, Protein Kinases: chemistry, Saccharomyces cerevisiae Proteins, Saccharomyces cerevisiae Proteins: chemistry, Temperature, Theoretical, Thermodynamics}, issn = {0006-3495}, doi = {10.1016/S0006-3495(02)75289-2}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1302364\&tool=pmcentrez\&rendertype=abstract}, author = {Jorge Vi{\~n}als and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Kolinski2001, title = {Generalized comparative modeling (GENECOMP): a combination of sequence comparison, threading, and lattice modeling for protein structure prediction and refinement}, journal = {Proteins}, volume = {44}, number = {2}, year = {2001}, month = {aug}, pages = {133{\textendash}149}, abstract = {An improved generalized comparative modeling method, GENECOMP, for the refinement of threading models is developed and validated on the Fischer database of 68 probe-template pairs, a standard benchmark used to evaluate threading approaches. The basic idea is to perform ab initio folding using a lattice protein model, SICHO, near the template provided by the new threading algorithm PROSPECTOR. PROSPECTOR also provides predicted contacts and secondary structure for the template-aligned regions, and possibly for the unaligned regions by garnering additional information from other top-scoring threaded structures. Since the lowest-energy structure generated by the simulations is not necessarily the best structure, we employed two structure-selection protocols: distance geometry and clustering. In general, clustering is found to generate somewhat better quality structures in 38 of 68 cases. When applied to the Fischer database, the protocol does no harm and in a significant number of cases improves upon the initial threading model, sometimes dramatically. The procedure is readily automated and can be implemented on a genomic scale.}, keywords = {Algorithms, Chemical, Combinatorial Chemistry Techniques, Combinatorial Chemistry Techniques: methods, Computational Biology, Computational Biology: methods, Computer Simulation, Databases, Factual, Models, Molecular, Monte Carlo Method, Protein Folding, Proteins, Proteins: chemistry, Sequence Alignment, Sequence Alignment: methods}, issn = {0887-3585}, url = {http://www.ncbi.nlm.nih.gov/pubmed/11391776}, author = {Andrzej Koli{\'n}ski and Marcos Betancourt and Daisuke Kihara and Piotr Rotkiewicz and Jeffrey Skolnick} } @article {Bujnicki2001, title = {Three-dimensional modeling of the I-TevI homing endonuclease catalytic domain, a GIY-YIG superfamily member, using NMR restraints and Monte Carlo dynamics}, journal = {Protein Engineering}, volume = {14}, number = {10}, year = {2001}, month = {oct}, pages = {717{\textendash}721}, abstract = {Using a recent version of the SICHO algorithm for in silico protein folding, we made a blind prediction of the tertiary structure of the N-terminal, independently folded, catalytic domain (CD) of the I-TevI homing endonuclease, a representative of the GIY-YIG superfamily of homing endonucleases. The secondary structure of the I-TevI CD has been determined using NMR spectroscopy, but computational sequence analysis failed to detect any protein of known tertiary structure related to the GIY-YIG nucleases (Kowalski et al., Nucleic Acids Res., 1999, 27, 2115-2125). To provide further insight into the structure-function relationships of all GIY-YIG superfamily members, including the recently described subfamily of type II restriction enzymes (Bujnicki et al., Trends Biochem. Sci., 2000, 26, 9-11), we incorporated the experimentally determined and predicted secondary and tertiary restraints in a reduced (side chain only) protein model, which was minimized by Monte Carlo dynamics and simulated annealing. The subsequently elaborated full atomic model of the I-TevI CD allows the available experimental data to be put into a structural context and suggests that the GIY-YIG domain may dimerize in order to bring together the conserved residues of the active site.}, keywords = {Algorithms, Binding Sites, Biomolecular, Endodeoxyribonucleases, Endodeoxyribonucleases: chemistry, Models, Molecular, Monte Carlo Method, Nuclear Magnetic Resonance, Protein Structure, Sequence Alignment, Tertiary}, issn = {0269-2139}, url = {http://www.ncbi.nlm.nih.gov/pubmed/11739889}, author = {Janusz M. Bujnicki and Piotr Rotkiewicz and Andrzej Koli{\'n}ski and Leszek Rychlewski} } @article {Kihara2001, title = {TOUCHSTONE: an ab initio protein structure prediction method that uses threading-based tertiary restraints}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {98}, number = {18}, year = {2001}, month = {aug}, pages = {10125{\textendash}30}, abstract = {The successful prediction of protein structure from amino acid sequence requires two features: an efficient conformational search algorithm and an energy function with a global minimum in the native state. As a step toward addressing both issues, a threading-based method of secondary and tertiary restraint prediction has been developed and applied to ab initio folding. Such restraints are derived by extracting consensus contacts and local secondary structure from at least weakly scoring structures that, in some cases, can lack any global similarity to the sequence of interest. Furthermore, to generate representative protein structures, a reduced lattice-based protein model is used with replica exchange Monte Carlo to explore conformational space. We report results on the application of this methodology, termed TOUCHSTONE, to 65 proteins whose lengths range from 39 to 146 residues. For 47 (40) proteins, a cluster centroid whose rms deviation from native is below 6.5 (5) A is found in one of the five lowest energy centroids. The number of correctly predicted proteins increases to 50 when atomic detail is added and a knowledge-based atomic potential is combined with clustered and nonclustered structures for candidate selection. The combination of the ratio of the relative number of contacts to the protein length and the number of clusters generated by the folding algorithm is a reliable indicator of the likelihood of successful fold prediction, thereby opening the way for genome-scale ab initio folding.}, keywords = {Algorithms, Computer Simulation, Models, Molecular, Monte Carlo Method, Protein Folding, Protein Structure, Proteins, Proteins: chemistry, Tertiary}, issn = {0027-8424}, doi = {10.1073/pnas.181328398}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=56926\&tool=pmcentrez\&rendertype=abstract}, author = {Daisuke Kihara and Hui Lu and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {289, title = {Monte Carlo simulation of designed helical proteins}, journal = {Acta Poloniae Pharmaceutica {\textendash} Drug Research}, volume = {57 Suppl}, year = {2000}, month = {2000 Nov}, pages = {119-21}, keywords = {Monte Carlo Method, Protein Conformation, Protein Folding, Protein Structure, Secondary}, issn = {0001-6837}, author = {Andrzej Sikorski and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Ortiz1999, title = {Ab initio folding of proteins using restraints derived from evolutionary information}, journal = {Proteins}, volume = {Suppl. 3}, number = {May}, year = {1999}, month = {jan}, pages = {177{\textendash}185}, abstract = {We present our predictions in the ab initio structure prediction category of CASP3. Eleven targets were folded, using a method based on a Monte Carlo search driven by secondary and tertiary restraints derived from multiple sequence alignments. Our results can be qualitatively summarized as follows: The global fold can be considered "correct" for targets 65 and 74, "almost correct" for targets 64, 75, and 77, "half-correct" for target 79, and "wrong" for targets 52, 56, 59, and 63. Target 72 has not yet been solved experimentally. On average, for small helical and alpha/beta proteins (on the order of 110 residues or smaller), the method predicted low resolution structures with a reasonably good prediction of the global topology. Most encouraging is that in some situations, such as with target 75 and, particularly, target 77, the method can predict a substantial portion of a rare or even a novel fold. However, the current method still fails on some beta proteins, proteins over the 110-residue threshold, and sequences in which only a poor multiple sequence alignment can be built. On the other hand, for small proteins, the method gives results of quality at least similar to that of threading, with the advantage of not being restricted to known folds in the protein database. Overall, these results indicate that some progress has been made on the ab initio protein folding problem. Detailed information about our results can be obtained by connecting to http:/(/)www.bioinformatics.danforthcenter.org/+ ++CASP3.}, keywords = {Algorithms, Amino Acid Sequence, Evolution, Models, Molecular, Molecular Sequence Data, Monte Carlo Method, Protein Folding, Proteins, Proteins: chemistry}, issn = {0887-3585}, url = {http://www.ncbi.nlm.nih.gov/pubmed/10526366}, author = {Angel. R. Ortiz and Andrzej Koli{\'n}ski and Piotr Rotkiewicz and Bartosz Ilkowski and Jeffrey Skolnick} } @article {Mohanty1999, title = {De novo simulations of the folding thermodynamics of the GCN4 leucine zipper}, journal = {Biophysical Journal}, volume = {77}, number = {1}, year = {1999}, month = {jul}, pages = {54{\textendash}69}, abstract = {Entropy Sampling Monte Carlo (ESMC) simulations were carried out to study the thermodynamics of the folding transition in the GCN4 leucine zipper (GCN4-lz) in the context of a reduced model. Using the calculated partition functions for the monomer and dimer, and taking into account the equilibrium between the monomer and dimer, the average helix content of the GCN4-lz was computed over a range of temperatures and chain concentrations. The predicted helix contents for the native and denatured states of GCN4-lz agree with the experimental values. Similar to experimental results, our helix content versus temperature curves show a small linear decline in helix content with an increase in temperature in the native region. This is followed by a sharp transition to the denatured state. van{\textquoteright}t Hoff analysis of the helix content versus temperature curves indicates that the folding transition can be described using a two-state model. This indicates that knowledge-based potentials can be used to describe the properties of the folded and unfolded states of proteins.}, keywords = {Computer Simulation, Dimerization, DNA-Binding Proteins, Fungal Proteins, Fungal Proteins: chemistry, Leucine Zippers, Monte Carlo Method, Protein Conformation, Protein Denaturation, Protein Folding, Protein Kinases, Protein Kinases: chemistry, Protein Structure, Saccharomyces cerevisiae Proteins, Secondary, Temperature, Thermodynamics}, isbn = {6197848821}, issn = {0006-3495}, doi = {10.1016/S0006-3495(99)76872-4}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1300312\&tool=pmcentrez\&rendertype=abstract}, author = {Debasisa Mohanty and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Kolinski1999, title = {Dynamics and thermodynamics of beta-hairpin assembly: insights from various simulation techniques}, journal = {Biophysical Journal}, volume = {77}, number = {6}, year = {1999}, month = {dec}, pages = {2942{\textendash}52}, abstract = {Small peptides that might have some features of globular proteins can provide important insights into the protein folding problem. Two simulation methods, Monte Carlo Dynamics (MCD), based on the Metropolis sampling scheme, and Entropy Sampling Monte Carlo (ESMC), were applied in a study of a high-resolution lattice model of the C-terminal fragment of the B1 domain of protein G. The results provide a detailed description of folding dynamics and thermodynamics and agree with recent experimental findings (. Nature. 390:196-197). In particular, it was found that the folding is cooperative and has features of an all-or-none transition. Hairpin assembly is usually initiated by turn formation; however, hydrophobic collapse, followed by the system rearrangement, was also observed. The denatured state exhibits a substantial amount of fluctuating helical conformations, despite the strong beta-type secondary structure propensities encoded in the sequence.}, keywords = {Amino Acid Sequence, Animals, Biophysical Phenomena, Biophysics, Models, Molecular, Molecular Sequence Data, Monte Carlo Method, Nerve Tissue Proteins, Nerve Tissue Proteins: chemistry, Protein Conformation, Protein Folding, Protein Structure, Proteins, Proteins: chemistry, Secondary, Thermodynamics}, issn = {0006-3495}, doi = {10.1016/S0006-3495(99)77127-4}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1300567\&tool=pmcentrez\&rendertype=abstract}, author = {Andrzej Koli{\'n}ski and Bartosz Ilkowski and Jeffrey Skolnick} } @article {Kolinski1998, title = {Assembly of protein structure from sparse experimental data: an efficient Monte Carlo model}, journal = {Proteins}, volume = {32}, number = {4}, year = {1998}, month = {sep}, pages = {475{\textendash}494}, abstract = {A new, efficient method for the assembly of protein tertiary structure from known, loosely encoded secondary structure restraints and sparse information about exact side chain contacts is proposed and evaluated. The method is based on a new, very simple method for the reduced modeling of protein structure and dynamics, where the protein is described as a lattice chain connecting side chain centers of mass rather than Calphas. The model has implicit built-in multibody correlations that simulate short- and long-range packing preferences, hydrogen bonding cooperativity and a mean force potential describing hydrophobic interactions. Due to the simplicity of the protein representation and definition of the model force field, the Monte Carlo algorithm is at least an order of magnitude faster than previously published Monte Carlo algorithms for structure assembly. In contrast to existing algorithms, the new method requires a smaller number of tertiary restraints for successful fold assembly; on average, one for every seven residues as compared to one for every four residues. For example, for smaller proteins such as the B domain of protein G, the resulting structures have a coordinate root mean square deviation (cRMSD), which is about 3 A from the experimental structure; for myoglobin, structures whose backbone cRMSD is 4.3 A are produced, and for a 247-residue TIM barrel, the cRMSD of the resulting folds is about 6 A. As would be expected, increasing the number of tertiary restraints improves the accuracy of the assembled structures. The reliability and robustness of the new method should enable its routine application in model building protocols based on various (very sparse) experimentally derived structural restraints.}, keywords = {Algorithms, Computer Simulation, Models, Molecular, Monte Carlo Method, Protein Conformation, Protein Folding, Protein Structure, Secondary, Tertiary}, issn = {0887-3585}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9726417}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Sikorski1998, title = {Computer simulations of de novo designed helical proteins}, journal = {Biophysical Journal}, volume = {75}, number = {1}, year = {1998}, month = {jul}, pages = {92{\textendash}105}, abstract = {In the context of reduced protein models, Monte Carlo simulations of three de novo designed helical proteins (four-member helical bundle) were performed. At low temperatures, for all proteins under consideration, protein-like folds having different topologies were obtained from random starting conformations. These simulations are consistent with experimental evidence indicating that these de novo designed proteins have the features of a molten globule state. The results of Monte Carlo simulations suggest that these molecules adopt four-helix bundle topologies. They also give insight into the possible mechanism of folding and association, which occurs in these simulations by on-site assembly of the helices. The low-temperature conformations of all three sequences have the features of a molten globule state.}, keywords = {Amino Acid Sequence, Biophysical Phenomena, Biophysics, Computer Simulation, Dimerization, Drug Design, Hydrogen Bonding, Models, Molecular, Molecular Sequence Data, Monte Carlo Method, Protein Conformation, Protein Folding, Protein Structure, Proteins, Proteins: chemistry, Secondary, Thermodynamics}, issn = {0006-3495}, doi = {10.1016/S0006-3495(98)77497-1}, url = {http://www.ncbi.nlm.nih.gov/pubmed/10651035}, author = {Andrzej Sikorski and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Ortiz1998, title = {Fold assembly of small proteins using monte carlo simulations driven by restraints derived from multiple sequence alignments}, journal = {Journal of Molecular Biology}, volume = {277}, number = {2}, year = {1998}, month = {mar}, pages = {419{\textendash}448}, abstract = {The feasibility of predicting the global fold of small proteins by incorporating predicted secondary and tertiary restraints into ab initio folding simulations has been demonstrated on a test set comprised of 20 non-homologous proteins, of which one was a blind prediction of target 42 in the recent CASP2 contest. These proteins contain from 37 to 100 residues and represent all secondary structural classes and a representative variety of global topologies. Secondary structure restraints are provided by the PHD secondary structure prediction algorithm that incorporates multiple sequence information. Predicted tertiary restraints are derived from multiple sequence alignments via a two-step process. First, seed side-chain contacts are identified from correlated mutation analysis, and then a threading-based algorithm is used to expand the number of these seed contacts. A lattice-based reduced protein model and a folding algorithm designed to incorporate these predicted restraints is described. Depending upon fold complexity, it is possible to assemble native-like topologies whose coordinate root-mean-square deviation from native is between 3.0 A and 6.5 A. The requisite level of accuracy in side-chain contact map prediction can be roughly 25\% on average, provided that about 60\% of the contact predictions are correct within +/-1 residue and 95\% of the predictions are correct within +/-4 residues. Precision in tertiary contact prediction is more critical than absolute accuracy. Furthermore, only a subset of the tertiary contacts, on the order of 25\% of the total, is sufficient for successful topology assembly. Overall, this study suggests that the use of restraints derived from multiple sequence alignments combined with a fold assembly algorithm holds considerable promise for the prediction of the global topology of small proteins.}, keywords = {Amino Acid Sequence, Chemical, Models, Molecular Sequence Data, Monte Carlo Method, Protein Folding, Protein Structure, Secondary, Tertiary}, issn = {0022-2836}, doi = {10.1006/jmbi.1997.1595}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9514747}, author = {Angel. R. Ortiz and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Ortiz1998a, title = {Nativelike topology assembly of small proteins using predicted restraints in Monte Carlo folding simulations}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {95}, number = {3}, year = {1998}, month = {feb}, pages = {1020{\textendash}1025}, abstract = {By incorporating predicted secondary and tertiary restraints derived from multiple sequence alignments into ab initio folding simulations, it has been possible to assemble native-like tertiary structures for a test set of 19 nonhomologous proteins ranging from 29 to 100 residues in length and representing all secondary structural classes. Secondary structural restraints are provided by the PHD secondary structure prediction algorithm that incorporates multiple sequence information. Multiple sequence alignments also provide predicted tertiary restraints via a two-step process: First, seed side chain contacts are selected from a correlated mutation analysis, and then an inverse folding algorithm expands these seed contacts. The predicted secondary and tertiary restraints are incorporated into a lattice-based, reduced protein model for structure assembly and refinement. The resulting native-like topologies exhibit a coordinate root-mean-square deviation from native for the whole chain between 3.1 and 6.7 A, with values ranging from 2.6 to 4.1 A over approximately 80\% of the structure. Overall, this study suggests that the use of restraints derived from multiple sequence alignments combined with a fold assembly algorithm is a promising approach to the prediction of the global topology of small proteins.}, keywords = {Algorithms, Models, Molecular, Monte Carlo Method, Protein Folding, Protein Structure, Secondary, Sequence Alignment, Software, Tertiary}, issn = {0027-8424}, url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=18658\&tool=pmcentrez\&rendertype=abstract}, author = {Angel. R. Ortiz and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Ortiz1998b, title = {Tertiary structure prediction of the KIX domain of CBP using Monte Carlo simulations driven by restraints derived from multiple sequence alignments}, journal = {Proteins}, volume = {30}, number = {3}, year = {1998}, pages = {287{\textendash}294}, abstract = {Using a recently developed protein folding algorithm, a prediction of the tertiary structure of the KIX domain of the CREB binding protein is described. The method incorporates predicted secondary and tertiary restraints derived from multiple sequence alignments in a reduced protein model whose conformational space is explored by Monte Carlo dynamics. Secondary structure restraints are provided by the PHD secondary structure prediction algorithm that was modified for the presence of predicted U-turns, i.e., regions where the chain reverses global direction. Tertiary restraints are obtained via a two-step process: First, seed side-chain contacts are identified from a correlated mutation analysis, and then, a threading-based algorithm expands the number of these seed contacts. Blind predictions indicate that the KIX domain is a putative three-helix bundle, although the chirality of the bundle could not be uniquely determined. The expected root-mean-square deviation for the correct chirality of the KIX domain is between 5.0 and 6.2 A. This is to be compared with the estimate of 12.9 A that would be expected by a random prediction, using the model of F. Cohen and M. Sternberg (J. Mol. Biol. 138:321-333, 1980).}, keywords = {Algorithms, Amino Acid Sequence, CREB-Binding Protein, Databases as Topic, Models, Molecular, Molecular Sequence Data, Monte Carlo Method, Mutation, Mutation: genetics, Nuclear Proteins, Nuclear Proteins: chemistry, Protein Folding, Protein Structure, Secondary, Sequence Alignment, Tertiary, Trans-Activators, Transcription Factors, Transcription Factors: chemistry}, issn = {0887-3585}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9517544}, author = {Angel. R. Ortiz and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {266, title = {Collapse transitions in protein-like lattice polymers: The effect of sequence patterns}, journal = {Biopolymers}, volume = {42}, year = {1997}, pages = {537{\textendash}548}, abstract = {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. {\textcopyright} 1997 John Wiley \& Sons, Inc. Biopoly 42: 537{\textendash}548, 1997}, keywords = {collapse transition, Lattice proteins, Monte Carlo Method, protein models, sequence patterns}, doi = {10.1002/(SICI)1097-0282(19971015)42:5<537::AID-BIP4>3.0.CO;2-R}, author = {Andrzej Koli{\'n}ski and Pawel Madziar} } @article {Olszewski1996, title = {Does a backwardly read protein sequence have a unique native state?}, journal = {Protein Engineering}, volume = {9}, number = {1}, year = {1996}, month = {jan}, pages = {5{\textendash}14}, abstract = {Amino acid sequences of native proteins are generally not palindromic. Nevertheless, the protein molecule obtained as a result of reading the sequence backwards, i.e. a retro-protein, obviously has the same amino acid composition and the same hydrophobicity profile as the native sequence. The important questions which arise in the context of retro-proteins are: does a retro-protein fold to a well defined native-like structure as natural proteins do and, if the answer is positive, does a retro-protein fold to a structure similar to the native conformation of the original protein? In this work, the fold of retro-protein A, originated from the retro-sequence of the B domain of Staphylococcal protein A, was studied. As a result of lattice model simulations, it is conjectured that the retro-protein A also forms a three-helix bundle structure in solution. It is also predicted that the topology of the retro-protein A three-helix bundle is that of the native protein A, rather than that corresponding to the mirror image of native protein A. Secondary structure elements in the retro-protein do not exactly match their counterparts in the original protein structure; however, the amino acid side chain contract pattern of the hydrophobic core is partly conserved.}, keywords = {Amino Acid Sequence, Computer Simulation, Models, Molecular, Molecular Sequence Data, Monte Carlo Method, Protein Conformation, Protein Engineering, Protein Folding, Protein Structure, Secondary, Staphylococcal Protein A, Staphylococcal Protein A: chemistry, Tertiary}, issn = {0269-2139}, url = {http://www.ncbi.nlm.nih.gov/pubmed/9053902}, author = {Krzysztof A. Olszewski and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Olszewski1996a, title = {Folding simulations and computer redesign of protein A three-helix bundle motifs}, journal = {Proteins}, volume = {25}, number = {3}, year = {1996}, month = {jul}, pages = {286{\textendash}299}, abstract = {In solution, the B domain of protein A from Staphylococcus aureus (B domain) possesses a three-helix bundle structure. This simple motif has been previously reproduced by Kolinski and Skolnick (Proteins 18: 353-366, 1994) using a reduced representation lattice model of proteins with a statistical interaction scheme. In this paper, an improved version of the potential has been used, and the robustness of this result has been tested by folding from the random state a set of three-helix bundle proteins that are highly homologous to the B domain of protein A. Furthermore, an attempt to redesign the B domain native structure to its topological mirror image fold has been made by multiple mutations of the hydrophobic core and the turn region between helices I and II. A sieve method for scanning a large set of mutations to search for this desired property has been proposed. It has been shown that mutations of native B domain hydrophobic core do not introduce significant changes in the protein motif. Mutations in the turn region were also very conservative; nevertheless, a few mutants acquired the desired topological mirror image motif. A set of all atom models of the most probable mutant was reconstructed from the reduced models and refined using a molecular dynamics algorithm in the presence of water. The packing of all atom structures obtained corroborates the lattice model results. We conclude that the change in the handedness of the turn induced by the mutations, augmented by the repacking of hydrophobic core and the additional burial of the second helix N-cap side chain, are responsible for the predicted preferential adoption of the mirror image structure.}, keywords = {Computer Simulation, Monte Carlo Method, Mutation, Protein Conformation, Protein Folding, Staphylococcal Protein A, Staphylococcal Protein A: chemistry}, issn = {0887-3585}, doi = {10.1002/(SICI)1097-0134(199607)25:3\<286::AID-PROT2\>3.0.CO;2-E}, url = {http://www.ncbi.nlm.nih.gov/pubmed/8844865}, author = {Krzysztof A. Olszewski and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Vieth1995, title = {Prediction of quaternary structure of coiled coils. Application to mutants of the GCN4 leucine zipper}, journal = {Journal of Molecular Biology}, volume = {251}, number = {3}, year = {1995}, month = {aug}, pages = {448{\textendash}67}, abstract = {Using a simplified protein model, the equilibrium between different oligomeric species of the wild-type GCN4 leucine zipper and seven of its mutants have been predicted. Over the entire experimental concentration range, agreement with experiment is found in five cases, while in two cases agreement is found over a portion of the concentration range. These studies demonstrate a methodology for predicting coiled coil quaternary structure and allow for the dissection of the interactions responsible for the global fold. In agreement with the conclusion of Harbury et al., the results of the simulations indicate that the pattern of hydrophobic and hydrophilic residues alone is insufficient to define a protein{\textquoteright}s three-dimensional structure. In addition, these simulations indicate that the degree of chain association is determined by the balance between specific side-chain packing preferences and the entropy reduction associated with side-chain burial in higher-order multimers.}, keywords = {Computer Simulation, DNA-Binding Proteins, Fungal Proteins, Fungal Proteins: chemistry, Hydrogen Bonding, Leucine Zippers, Monte Carlo Method, Mutation, Protein Conformation, Protein Folding, Protein Kinases, Protein Kinases: chemistry, Saccharomyces cerevisiae Proteins, Thermodynamics}, issn = {0022-2836}, doi = {10.1006/jmbi.1995.0447}, url = {http://www.ncbi.nlm.nih.gov/pubmed/7650742}, author = {Michal Vieth and Andrzej Koli{\'n}ski and Charles L. Brooks III and Jeffrey Skolnick} } @article {Vieth1995a, title = {A simple technique to estimate partition functions and equilibrium constants from Monte Carlo simulations}, journal = {Journal of Chemical Physics}, volume = {102}, number = {April}, year = {1995}, pages = {6189{\textendash}6193}, abstract = {A combined Monte Carlo (MC) simulation-statistical mechanical treatment is proposed to calculate the internal partition function and equilibrium constant. The method has been applied to a number of one and multidimensional analytical functions. When sampling is incomplete, various factorization approximations for estimating the partition function are discussed. The resulting errors are smaller when the ratios of the partition functions are calculated (as in the determination of equilibrium constants) as opposed to the partition function itself. {\textcopyright} 1995 American Institute of Physics.}, keywords = {equilibrium, factorization, molecules, Monte Carlo Method, partition functions, simulation, statistical mechanics}, doi = {http://link.aip.org/link/doi/10.1063/1.469063}, url = {http://smartech.gatech.edu/handle/1853/27021}, author = {Michal Vieth and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {287, title = {Monte Carlo simulations of protein folding. I. Lattice model and interaction scheme}, journal = {Proteins}, volume = {18}, year = {1994}, month = {1994 Apr}, pages = {338-52}, abstract = {A new hierarchical method for the simulation of the protein folding process and the de novo prediction of protein three-dimensional structure is proposed. The reduced representation of the protein alpha-carbon backbone employs lattice discretizations of increasing geometrical resolution and a single ball representation of side chain rotamers. In particular, coarser and finer lattice backbone descriptions are used. The coarser (finer) lattice represents C alpha traces of native proteins with an accuracy of 1.0 (0.7) A rms. Folding is simulated by means of very fast Monte Carlo lattice dynamics. The potential of mean force, predominantly of statistical origin, contains several novel terms that facilitate the cooperative assembly of secondary structure elements and the cooperative packing of the side chains. Particular contributions to the interaction scheme are discussed in detail. In the accompanying paper (Kolinski, A., Skolnick, J. Monte Carlo simulation of protein folding. II. Application to protein A, ROP, and crambin. Proteins 18:353-366, 1994), the method is applied to three small globular proteins.}, keywords = {Amino Acid Sequence, Amino Acids, Computer Simulation, Hydrogen Bonding, Models, Chemical, Models, Molecular, Models, Theoretical, Molecular Sequence Data, Monte Carlo Method, Protein Folding, Protein Structure, Tertiary}, issn = {0887-3585}, doi = {10.1002/prot.340180405}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Kolinski1992, title = {Discretized model of proteins. I. Monte Carlo study of cooperativity in homopolypeptides}, journal = {Journal of Chemical Physics}, volume = {97}, number = {December}, year = {1992}, pages = {9412{\textendash}9426}, abstract = {A discretized model of globular proteins is employed in a Monte Carlo study of the helix{\textendash}coil transition of polyalanine and the collapse transition of polyvaline. The present lattice realization permits real protein crystal structures to be represented at the level of 1 {\r A} resolution. Furthermore, the Monte Carlo dynamic scheme is capable of moving elements of assembled secondary and supersecondary structure. The potentials of mean force for the interactions are constructed from the statistics of a set of high resolution x-ray structures of nonhomologous proteins. The cooperativity of formation of ordered structures is found to be larger when the major contributions to the conformational energy of the low temperature states come from hydrogen bonds and short range conformational propensities. The secondary structure seen in the folded state is the result of an interplay between the short and long range interactions. Compactness itself, driven by long range, nonspecific interactions, seems to be insufficient to generate any appreciable secondary structure. A detailed examination of the dynamics of highly helical model proteins demonstrates that all elements of secondary structure are mobile in the present algorithm, and thus the folding pathways do not depend on the use of a lattice approximation. Possible applications of the present model to the prediction of protein 3D structures are briefly discussed.}, keywords = {Conformational Changes, Coupling, Globular Clusters, Lattice Gas, Molecular Models, Monte Carlo Method, Polypeptides, Proteins, Randomness, Resolution}, doi = {10.1063/1.463317}, url = {http://link.aip.org/link/doi/10.1063/1.463317}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Rey1992, title = {Effect of double bonds on the dynamics of hydrocarbon chains}, journal = {Journal of Chemical Physics}, volume = {97}, year = {1992}, pages = {1240{\textendash}1249}, abstract = {Brownian dynamics simulations of isolated 18-carbon chains have been performed, both for saturated and unsaturated hydrocarbons. The effect of one or several (nonconjugated) double bonds on the properties of the chains is discussed in terms of both equilibrium and dynamic properties. The introduction of a cis double bond increases the relaxation rates of the unsaturated chain with respect to the saturated alkane. On the other hand, coupling effects in the torsional transitions around a trans double bond make the dynamics of this unsaturated chain very similar to the saturated one. Based on these results, the parameters and moves of a dynamic Monte Carlo algorithm are tuned to reproduce the observed behavior, providing an efficient method for the study of more complicated systems.}, keywords = {Algorithms, Brownian Movement, Chains, Coupling, Double Bonds, dynamics, equilibrium, Hydrocarbons, Monte Carlo Method, Relaxation, Saturation, simulation, Torsion}, doi = {10.1063/1.463250}, url = {http://smartech.gatech.edu/handle/1853/26936}, author = {Antonio Rey and Andrzej Koli{\'n}ski and Jeffrey Skolnick and Yehudi K. Levine} } @article {Levine1991, title = {Monte Carlo dynamics study of motions in cis-unsaturated hydrocarbon chains}, journal = {The Journal of Chemical Physics}, volume = {95}, year = {1991}, pages = {3826{\textendash}3834}, abstract = {A Monte Carlo dynamics study of the motions of hydrocarbon chains containing cis double bonds is presented. The simulations utilize the high-coordination {2 1 0} lattice for the simultaneous representation of the tetrahedrally bonded carbon atoms and the planar unsaturated segment. Results on single chains undergoing free motion in space and tethered to an impenetrable planar interface are reported. The introduction of a cis double bond into a hydrocarbon chain induces a slowdown in the dynamics. The simulations show this to be a universal result independent of the representation of the chain on the lattice. In contrast, polyunsaturated chains are found to be more mobile than saturated ones.}, keywords = {Bilayers, Chains, Chemical Bonds, Hydrocarbons, Hydrogen Bonds, Lipids, Molecular Motion, Monte Carlo Method, Temperature Effects}, doi = {10.1063/1.460782}, url = {http://smartech.gatech.edu/handle/1853/26899}, author = {Yehudi K. Levine and Jeffrey Skolnick and Andrzej Koli{\'n}ski} } @article {Milik1990, title = {Monte Carlo dynamics of a dense system of chain molecules constrained to lie near an interface. A simplified membrane model}, journal = {The Journal of Chemical Physics}, volume = {93}, number = {6}, year = {1990}, pages = {4440{\textendash}4446}, abstract = {The static and dynamic properties of a dense system of flexible lattice chain molecules, one of whose ends is constrained to lie near an impenetrable interface, have been studied by means of the dynamic Monte Carlo method. It is found that increasing the surface density of the chains in the layer increases the orientational order. The value of the order parameter of the chain segments decreases with increasing distance from the interace. The short time dynamics of the model chains are similar to those observed in polymer melts. Then, there is a time regime of strongly hindered collective motion at intermediate distance scales. Finally, for distances greater than the chain dimensions, free lateral diffusion of the chains is recovered. It is shown that the model exhibits many features of the real systems such as detergents on a surface and lipid bilayers.}, keywords = {Bilayers, Chains, Constraints, Density, Interface Phenomena, Lipids, Liquid Structure, Membranes, Monte Carlo Method, Order Parameters, Orientation}, url = {http://link.aip.org/link/JCPSA6/v93/i6/p4440/s1}, author = {Mariusz Milik and Andrzej Koli{\'n}ski and Jeffrey Skolnick} } @article {Skolnick1989, title = {Monte Carlo studies on equilibrium globular protein folding. II. Beta-barrel globular protein models}, journal = {Biopolymers}, volume = {28}, number = {6}, year = {1989}, month = {jun}, pages = {1059{\textendash}95}, abstract = {In the context of dynamic Monte Carlo simulations on a model protein confined to a tetrahedral lattice, the interplay of protein size and tertiary structure, and the requirements for an all-or-none transition to a unique native state, are investigated. Small model proteins having a primary sequence consisting of a central bend neutral region flanked by two tails having an alternating hydrophobic/hydrophilic pattern of residues are seen to undergo a continuous transition to a beta-hairpin collapsed state. On increasing the length of the tails, the beta-hairpin structural motif is found to be in equilibrium with a four-member beta-barrel. Further increase of the tail length results in the shift of the structural equilibrium to the four-member beta-barrel. The random coil to beta-barrel transition is of an all-or-none character, but while the central turn is always the desired native bend, the location of the turns involving the two external strands is variable. That is, beta-barrels having the external stands that are two residues out of register are also observed in the transition region. Introduction into the primary sequence of two additional regions that are at the very least neutral toward turn formation produces an all-or-none transition to the unique, native, four-member beta-barrel. Various factors that can augment the stability of the native conformation are explored. Overall, these folding simulations strongly indicate that the general rules of globular protein folding are rather robust{\textendash}namely, one requires a general pattern of hydrophobic/hydrophilic residues that allow the protein to have a well-defined interior and exterior and the presence of regions in the amino acid sequence that at the very least are locally indifferent to turn formation. Since no site-specific interactions between hydrophobic and hydrophilic residues are required to produce a unique four-member beta-barrel, these simulations strongly suggest that site specificity is involved in structural fine-tuning.}, keywords = {Algorithms, Models, Monte Carlo Method, Protein Conformation, Proteins, Theoretical}, issn = {0006-3525}, doi = {10.1002/bip.360280604}, url = {http://www.ncbi.nlm.nih.gov/pubmed/2730942}, author = {Jeffrey Skolnick and Andrzej Koli{\'n}ski and Robert Yaris} } @article {Kolinski1987b, title = {Does reptation describe the dynamics of entangled, finite length polymer systems? A model simulation}, journal = {The Journal of Chemical Physics}, volume = {86}, year = {1987}, pages = {1567{\textendash}1585}, abstract = {In order to examine the validity of the reptation model of motion in a dense collection of polymers, dynamic Monte Carlo (MC) simulations of polymer chains composed of n beads confined to a diamond lattice were undertaken as a function of polymer concentration ϕ and degree of polymerization n. We demonstrate that over a wide density range these systems exhibit the experimentally required molecular weight dependence of the center-of-mass self-diffusion coefficient D\~{}n-2.1 and the terminal relaxation time of the end-to-end vector τR\~{}n3.4. Thus, these systems should represent a highly entangled collection of polymers appropriate to look for the existence of reptation. The time dependence of the average single bead mean-square displacement, as well as the dependence of the single bead displacement on position in the chain were examined, along with the time dependence of the center-of-mass displacement. Furthermore, to determine where in fact a well-defined tube exists, the mean-square displacements of a polymer chain down and perpendicular to its primitive path defined at zero time were calculated, and snapshots of the primitive path as a function of time are presented. For an environment where all the chains move, no evidence of a tube, whose existence is central to the validity of the reptation model, was found. However, if a single chain is allowed to move in a partially frozen matrix of chains (where all chains but one are pinned every ne beads, and where between pin points the other chains are free to move), reptation with tube leakage is recovered for the single mobile chain. The dynamics of these chains possesses aspects of Rouse-like motion; however, unlike a Rouse chain, these chains undergo highly cooperative motion that appears to involve a backflow between chains to conserve constant average density. While these simulations cannot preclude the onset of reptation at higher molecular weight, they strongly argue at a minimum for the existence with increasing n of a crossover regime from simple Rouse dynamics in which reptation plays a minor role at best.}, keywords = {Chains, Computerized Simulation, dynamics, Monte Carlo Method, Polymers}, doi = {10.1063/1.452196}, url = {http://link.aip.org/link/JCPSA6/v86/i3/p1567/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1987, title = {Monte Carlo studies on equilibrium globular protein folding. I. Homopolymeric lattice models of beta-barrel proteins}, journal = {Biopolymers}, volume = {26}, number = {6}, year = {1987}, month = {jun}, pages = {937{\textendash}62}, abstract = {Dynamic Monte Carlo studies have been performed on various diamond lattice models of β-proteins. Unlike previous work, no bias toward the native state is introduced; instead, the protein is allowed to freely hunt through all of phase space to find the equilibrium conformation. Thus, these systems may aid in the elucidation of the rules governing protein folding from a given primary sequence; in particular, the interplay of short- vs long-range interaction can be explored. Three distinct models (A[BOND]C) were examined. In model A, in addition to the preference for trans (t) over gauche states (g+ and g-) (thereby perhaps favoring β-sheet formation), attractive interactions are allowed between all nonbonded, nearest neighbor pairs of segments. If the molecules possess a relatively large fraction of t states in the denatured form, on cooling spontaneous collapse to a well-defined β-barrel is observed. Unfortunately, in model A the denatured state exhibits too much secondary structure to correctly model the globular protein collapse transition. Thus in models B and C, the local stiffness is reduced. In model B, in the absence of long-range interactions, t and g states are equally weighted, and cooperativity is introduced by favoring formation of adjacent pairs of nonbonded (but not necessarily parallel) t states. While the denatured state of these systems behaves like a random coil, their native globular structure is poorly defined. Model C retains the cooperativity of model B but allows for a slight preference of t over g states in the short-range interactions. Here, the denatured state is indistinguishable from a random coil, and the globular state is a well-defined β-barrel. Over a range of chain lengths, the collapse is well represented by an all-or-none model. Hence, model C possesses the essential qualitative features observed in real globular proteins. These studies strongly suggest that the uniqueness of the globular conformation requires some residual secondary structure to be present in the denatured state.}, keywords = {Biological, Models, Monte Carlo Method, Protein Conformation, Proteins}, issn = {0006-3525}, doi = {10.1002/bip.360260613}, url = {http://www.ncbi.nlm.nih.gov/pubmed/3607251}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1987a, title = {Monte Carlo studies on the long time dynamic properties of dense cubic lattice multichain systems. I. The homopolymeric melt}, journal = {The Journal of Chemical Physics}, volume = {86}, year = {1987}, pages = {7164{\textendash}7174}, abstract = {Dynamic Monte Carlo simulations of long chains confined to a cubic lattice system at a polymer volume fraction of ϕ=0.5 were employed to investigate the dynamics of polymer melts. It is shown that in the range of chain lengths n, from n=64 to n=800 there is a crossover from a weaker dependence of the diffusion coefficient on chain length to a much stronger one, consistent with D\~{}n-2. Since the n-2 scaling relation signals the onset of highly constrained dynamics, an analysis of the character of the chain contour motion was performed. We found no evidence for the well-defined tube required by the reptation model of polymer melt dynamics. The lateral motions of the chain contour are still large even in the case when n=800, and the motion of the chain is essentially isotropic in the local coordinates. Hence, the crossover to the D\~{}n-2 regime with increasing chain length of this monodisperse model melt is not accompanied by the onset of reptation dynamics.}, keywords = {Chains, Computerized Simulation, dynamics, Liquid Structure, Melts, Monte Carlo Method, Polymers}, url = {http://link.aip.org/link/JCPSA6/v86/i12/p7164/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1987c, title = {Monte Carlo studies on the long time dynamic properties of dense cubic lattice multichain systems. II. Probe polymer in a matrix of different degrees of polymerization}, journal = {The Journal of Chemical Physics}, volume = {86}, year = {1987}, pages = {7174{\textendash}7180}, abstract = {The dynamics of a probe chain consisting of nP =100 segments in a matrix of chains of length of nM=50 up to nM=800 at a total volume fraction of polymer ϕ=0.5 have been simulated by means of cubic lattice Monte Carlo dynamics. The diffusion coefficient of the probe chain over the range of nM under consideration decreases by about 30\%, a behavior rather similar to that seen in real melts of very long chains. Furthermore, the analysis of the probe chain motion shows that the mechanism of motion is not reptation-like and that the cage effect of the matrix is negligible. That is, the local fluctuations of the topological constraints imposed by the long matrix chains (even for nM=800) are sufficiently large to provide for essentially isotropic, but somewhat slowed down, motion of the probe, nP =100, chains relative to the homopolymer melt. The results of these MC experiments are discussed in the context of theoretical predictions and experimental findings for related systems.}, keywords = {Chains, Computerized Simulation, dynamics, Liquid Structure, Matrix Isolation, Melts, Monte Carlo Method, Polymerization, Polymers}, doi = {10.1063/1.452367}, url = {http://link.aip.org/link/JCPSA6/v86/i12/p7174/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {Kolinski1986b, title = {The collapse transition of semiflexible polymers. A Monte Carlo simulation of a model system}, journal = {The Journal of Chemical Physics}, volume = {85}, year = {1986}, pages = {3585{\textendash}3597}, abstract = {Monte Carlo simulations have been performed on a diamond lattice model of semiflexible polymers for a range of flexibilities and a range of chain lengths from 50 to 800 segments. The model includes both repulsive (excluded volume) and attractive segment{\textendash}segment interactions. It is shown that the polymers group into two classes, {\textquoteleft}{\textquoteleft}flexible{\textquoteright}{\textquoteright} and {\textquoteleft}{\textquoteleft}stiff.{\textquoteright}{\textquoteright} The flexible polymers exhibit decreasing chain dimensions as the temperature decreases with a gradual collapse from a loose random coil, high temperature state to a dense random coil, low temperature state. The stiffer polymers, on the other hand, exhibit increasing chain dimensions with decreasing temperature until at a critical temperature there is a sudden collapse to an ordered high density, low temperature state. This difference is due to the relative strength of the segment{\textendash}segment attractive interactions compared to the energetic preference for a trans conformational state over a gauche state. When the attractive interaction is relatively strong (flexible case) the polymer starts to collapse before rotational degrees of freedom freeze out, leading to a disordered dense state. When the attractive interaction is relatively weak (stiff case) the polymer starts to freeze out rotational degrees of freedom before it finally collapses to a highly ordered dense state.}, keywords = {Chains, Computerized Simulation, Conformational Changes, Diamond Lattices, Flexibility, Mathematical Models, Molecular Structure, Monte Carlo Method, Polymers}, doi = {10.1063/1.450930}, url = {http://link.aip.org/link/JCPSA6/v85/i6/p3585/s1}, author = {Andrzej Koli{\'n}ski and Jeffrey Skolnick and Robert Yaris} } @article {277, title = {Monte Carlo study of dynamics of the multichain polymer system on the tetrahedral lattice}, journal = {The Journal of Chemical Physics}, volume = {79}, year = {1983}, pages = {1523-1526}, publisher = {AIP}, abstract = {Diffusion of the chain molecules in the concentrated solutions was studied by means of the computer simulation method. The computations were made for various chain lengths and polymer concentrations. It was observed that the rate of diffusion of the polymer chains strongly depends on the chain length according to the relation D∝n-b. It was found that the value of exponent b increases with the polymer concentration.}, keywords = {Chains, Computerized Simulation, Diffusion, dynamics, Monte Carlo Method, Polymers, solutions}, doi = {10.1063/1.445944}, url = {http://link.aip.org/link/?JCP/79/1523/1}, author = {Andrzej Koli{\'n}ski and Piotr Romiszowski} }