101
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Matysiak S, Clementi C. Optimal combination of theory and experiment for the characterization of the protein folding landscape of S6: how far can a minimalist model go? J Mol Biol 2004; 343:235-48. [PMID: 15381433 DOI: 10.1016/j.jmb.2004.08.006] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2004] [Revised: 07/30/2004] [Accepted: 08/03/2004] [Indexed: 11/28/2022]
Abstract
The detailed characterization of the overall free energy landscape associated with the folding process of a protein is the ultimate goal in protein folding studies. Modern experimental techniques provide accurate thermodynamic and kinetic measurements on restricted regions of a protein landscape. Although simplified protein models can access larger regions of the landscape, they are oftentimes built on assumptions and approximations that affect the accuracy of the results. We present a new methodology that allows to combine the complementary strengths of theory and experiment for a more complete characterization of a protein folding landscape. We prove that this new procedure allows a simplified protein model to reproduce remarkably well (correlation coefficient > 0.9) all experimental data available on free energies differences upon single mutations for S6 ribosomal protein and two circular permutants. Our results confirm and quantify the hypothesis, recently formulated on the basis of experimental data, that the folding landscape of protein S6 is strongly affected by an atypical distribution of contact energies.
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Affiliation(s)
- Silvina Matysiak
- Department of Chemistry, Rice University, 6100 Main Street, Houston, TX 77005, USA
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102
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Liu Z, Dominy BN, Shakhnovich EI. Structural mining: self-consistent design on flexible protein-peptide docking and transferable binding affinity potential. J Am Chem Soc 2004; 126:8515-28. [PMID: 15238009 DOI: 10.1021/ja032018q] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A flexible protein-peptide docking method has been designed to consider not only ligand flexibility but also the flexibility of the protein. The method is based on a Monte Carlo annealing process. Simulations with a distance root-mean-square (dRMS) virtual energy function revealed that the flexibility of protein side chains was as important as ligand flexibility for successful protein-peptide docking. On the basis of mean field theory, a transferable potential was designed to evaluate distance-dependent protein-ligand interactions and atomic solvation energies. The potential parameters were developed using a self-consistent process based on only 10 known complex structures. The effectiveness of each intermediate potential was judged on the basis of a Z score, approximating the gap between the energy of the native complex and the average energy of a decoy set. The Z score was determined using experimentally determined native structures and decoys generated by docking with the intermediate potentials. Using 6600 generated decoys and the Z score optimization criterion proposed in this work, the developed potential yielded an acceptable correlation of R(2) = 0.77, with binding free energies determined for known MHC I complexes (Class I Major Histocompatibility protein HLA-A(*)0201) which were not present in the training set. Test docking on 25 complexes further revealed a significant correlation between energy and dRMS, important for identifying native-like conformations. The near-native structures always belonged to one of the conformational classes with lower predicted binding energy. The lowest energy docked conformations are generally associated with near-native conformations, less than 3.0 Angstrom dRMS (and in many cases less than 1.0 Angstrom) from the experimentally determined structures.
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Affiliation(s)
- Zhijie Liu
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, USA
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103
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Liwo A, Arłukowicz P, Ołdziej S, Czaplewski C, Makowski M, Scheraga HA. Optimization of the UNRES Force Field by Hierarchical Design of the Potential-Energy Landscape. 1. Tests of the Approach Using Simple Lattice Protein Models. J Phys Chem B 2004. [DOI: 10.1021/jp040327c] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Adam Liwo
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Piotr Arłukowicz
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Stanisław Ołdziej
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Cezary Czaplewski
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Mariusz Makowski
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
| | - Harold A. Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, and Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland
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104
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Abstract
Empirical force field-based studies of biological macromolecules are becoming a common tool for investigating their structure-activity relationships at an atomic level of detail. Such studies facilitate interpretation of experimental data and allow for information not readily accessible to experimental methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reproduction of experimental observables. Presented is an overview of the issues associated with the development and application of empirical force fields to biomolecular systems. This is followed by a summary of the force fields commonly applied to the different classes of biomolecules; proteins, nucleic acids, lipids, and carbohydrates. In addition, issues associated with computational studies on "heterogeneous" biomolecular systems and the transferability of force fields to a wide range of organic molecules of pharmacological interest are discussed.
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Affiliation(s)
- Alexander D Mackerell
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, Maryland 21201, USA.
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105
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Winther O, Krogh A. Teaching computers to fold proteins. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:030903. [PMID: 15524499 DOI: 10.1103/physreve.70.030903] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2003] [Revised: 04/26/2004] [Indexed: 05/24/2023]
Abstract
A new general algorithm for optimization of potential functions for protein folding is introduced. It is based upon gradient optimization of the thermodynamic stability of native folds of a training set of proteins with known structure. The iterative update rule contains two thermodynamic averages which are estimated by (generalized ensemble) Monte Carlo. We test the learning algorithm on a Lennard-Jones (LJ) force field with a torsional angle degrees-of-freedom and a single-atom side-chain. In a test with 24 peptides of known structure, none folded correctly with the initial potential functions, but two-thirds came within 3 A to their native fold after optimizing the potential functions.
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Affiliation(s)
- Ole Winther
- Center for Biological Sequence Analysis, The Technical University of Denmark, Building 208, DK-2800 Lyngby, Denmark.
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106
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Dominy BN, Shakhnovich EI. Native Atom Types for Knowledge-Based Potentials: Application to Binding Energy Prediction. J Med Chem 2004; 47:4538-58. [PMID: 15317465 DOI: 10.1021/jm0498046] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Knowledge-based potentials have been found useful in a variety of biophysical studies of macromolecules. Recently, it has also been shown in self-consistent studies that it is possible to extract quantities consistent with pair potentials from model structural databases. In this study, we attempt to extend the results obtained from these self-consistent studies toward the extraction of realistic pair potentials from the Protein Data Bank (PDB). The new method utilizes a clustering approach to define atom types within the PDB consistent with the optimal effective pairwise potential. The method has been integrated into the SMoG drug design package, resulting in an improved approach for the rapid and accurate estimation of binding affinities from structural information. Using this approach, it is possible to generate simple knowledge-based potentials that correlate (R = 0.61) with experimental binding affinities in a database of 118 diverse complexes. Furthermore, predictions performed on a random 1/3 of the database consistently show an average unsigned error of 1.5 log Ki units. It is also possible to generate specialized knowledge-based potentials, targeted to specific protein families. This approach is capable of generating potentials that correlate strongly with experimental binding affinities within these families (R = 0.8-0.9). Predictions on 1/3 of these family databases yield average unsigned errors ranging from 1.1 to 1.3 log Ki units. In summary, we describe a physically motivated approach to optimizing knowledge-based potentials for binding energy prediction that can be integrated into a variety of stages within a lead discovery protocol.
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Affiliation(s)
- Brian N Dominy
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, USA
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107
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Lu WC, Wang CZ, Ho KM. Effect of chain connectivity on the structure of Lennard-Jones liquid and its implicationon statistical potentials for protein folding. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061920. [PMID: 15244630 DOI: 10.1103/physreve.69.061920] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2002] [Revised: 11/21/2003] [Indexed: 05/24/2023]
Abstract
Statistical contact potentials and bead-spring models have been widely used for computational studies of protein folding. However, there has been speculation that systematic error may arise in the contact energy calculations when the statistical potentials are deduced under the assumption that the chain connectivity in proteins can be ignored. To address this issue, we have performed molecular-dynamics simulations to study the structure and dynamics of a simple liquid system in which the beads are either connected or unconnected with springs. Results from the present study provide useful information for assessing the accuracy of the statistical potentials for protein structure simulations.
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Affiliation(s)
- W C Lu
- Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
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108
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Fujitsuka Y, Takada S, Luthey-Schulten ZA, Wolynes PG. Optimizing physical energy functions for protein folding. Proteins 2004; 54:88-103. [PMID: 14705026 DOI: 10.1002/prot.10429] [Citation(s) in RCA: 66] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
We optimize a physical energy function for proteins with the use of the available structural database and perform three benchmark tests of the performance: (1) recognition of native structures in the background of predefined decoy sets of Levitt, (2) de novo structure prediction using fragment assembly sampling, and (3) molecular dynamics simulations. The energy parameter optimization is based on the energy landscape theory and uses a Monte Carlo search to find a set of parameters that seeks the largest ratio deltaE(s)/DeltaE for all proteins in a training set simultaneously. Here, deltaE(s) is the stability gap between the native and the average in the denatured states and DeltaE is the energy fluctuation among these states. Some of the energy parameters optimized are found to show significant correlation with experimentally observed quantities: (1) In the recognition test, the optimized function assigns the lowest energy to either the native or a near-native structure among many decoy structures for all the proteins studied. (2) Structure prediction with the fragment assembly sampling gives structure models with root mean square deviation less than 6 A in one of the top five cluster centers for five of six proteins studied. (3) Structure prediction using molecular dynamics simulation gives poorer performance, implying the importance of having a more precise description of local structures. The physical energy function solely inferred from a structural database neither utilizes sequence information from the family of the target nor the outcome of the secondary structure prediction but can produce the correct native fold for many small proteins.
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Affiliation(s)
- Yoshimi Fujitsuka
- Graduate School of Science and Technology, Kobe University, Nada, Kobe, Japan
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109
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Abstract
A model of the protein backbone is considered in which each residue is characterized by the location of its C(alpha) atom and one of a discrete set of conformal (phi, psi) states. We investigate the key differences between a description that offers a locally precise fit to known backbone structures and one that provides a globally accurate fit to protein structures. Using a statistical scoring scheme and threading, a protein's local best-fit conformation is highly recognizable, but its global structure cannot be directly determined from an amino acid sequence. The incorporation of information about the conformal states of neighboring residues along the chain allows one to accurately translate the local structure into a global structure. We present a two-step algorithm, which recognizes up to 95% of the tested protein native-state structures to within a 2.5 A root mean square deviation.
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Affiliation(s)
- Timothy Lezon
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania, USA.
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110
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Abstract
Selecting a protein sequence that corresponds to a specific three-dimensional protein structure is known as the protein design problem. One principal bottleneck in solving this problem is our lack of knowledge of precise atomic interactions. Using a simple model of amino acid interactions, we determine three crucial factors that are important for solving the protein design problem. Among these factors is the protein alphabet-a set of sequence elements that encodes protein structure. Our model predicts that alphabet size is independent of protein length, suggesting the possibility of designing a protein of arbitrary length with the natural protein alphabet. We also find that protein alphabet size is governed by protein structural properties and the energetic properties of the protein alphabet units. We discover that the usage of average types of amino acid in proteins is less than expected if amino acids were chosen randomly with naturally occurring frequencies. We propose three possible scenarios that account for amino acid underusage in proteins. These scenarios suggest the possibility that amino acids themselves might not constitute the alphabet of natural proteins.
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Affiliation(s)
- Nikolay V Dokholyan
- Department of Biochemistry and Biophysics, School of Medicine, University of North Carolina at Chapel Hill, 27599, USA.
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111
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112
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113
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Deeds EJ, Dokholyan NV, Shakhnovich EI. Protein evolution within a structural space. Biophys J 2003; 85:2962-72. [PMID: 14581198 PMCID: PMC1303574 DOI: 10.1016/s0006-3495(03)74716-x] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2003] [Accepted: 07/28/2003] [Indexed: 10/21/2022] Open
Abstract
Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might impact protein structural evolution. We approach this question using lattice polymers as a completely characterized model of this space. We develop a measure of structural comparison of lattice structures that is analogous to the one used to understand structural similarities between real proteins. We use this measure of structural relatedness to create a graph of lattice structures and compare this graph (in which nodes are lattice structures and edges are defined using structural similarity) to the graph obtained for real protein structures. We find that the graph obtained from all compact lattice structures exhibits a distribution of structural neighbors per node consistent with a random graph. We also find that subgraphs of 3500 nodes chosen either at random or according to physical constraints also represent random graphs. We develop a divergent evolution model based on the lattice space which produces graphs that, within certain parameter regimes, recapitulate the scale-free behavior observed in similar graphs of real protein structures.
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Affiliation(s)
- Eric J Deeds
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts 02138, USA
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114
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Fain B, Levitt M. Funnel sculpting for in silico assembly of secondary structure elements of proteins. Proc Natl Acad Sci U S A 2003; 100:10700-5. [PMID: 12925740 PMCID: PMC293046 DOI: 10.1073/pnas.1732312100] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2003] [Indexed: 11/18/2022] Open
Abstract
We present a method for designing a funnel-shaped free-energy surface that reproducibly assembles secondary structure elements of proteins into their native conformations from a random extended configuration. Assuming a priori knowledge of secondary structure, our method can design a funnel-shaped surface for folding of alpha, beta, and alphabeta structures individually. We design energy surfaces that fold up to five unrelated sequences with the same energy parameters. We develop a measure of the foldability of an energy landscape in silico and present an alternative way to view energy landscapes.
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Affiliation(s)
- Boris Fain
- Department of Structural Biology, Stanford University, Stanford, CA 94305, USA.
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115
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Pattabiraman N. Role of residue packing in protein folding. Trends Analyt Chem 2003. [DOI: 10.1016/s0165-9936(03)00906-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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116
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Abstract
Here we present a simplified form of threading that uses only a 20 x 20 two-body residue-based potential and restricted number of gaps. Despite its simplicity and transparency the Monte Carlo-based threading algorithm performs very well in a rigorous test of fold recognition. The results suggest that by simplifying and constraining the decoy space, one can achieve better fold recognition. Fold recognition results are compared with and supplemented by a PSI-BLAST search. The statistical significance of threading results is rigorously evaluated from statistics of extremes by comparison with optimal alignments of a large set of randomly shuffled sequences. The statistical theory, based on the Random Energy Model, yields a cumulative statistical parameter, epsilon, that attests to the likelihood of correct fold recognition. A large epsilon indicates a significant energy gap between the optimal alignment and decoy alignments and, consequently, a high probability that the fold is correctly recognized. For a particular number of gaps, the epsilon parameter reaches its maximal value, and the fold is recognized. As the number of gaps further increases, the likelihood of correct fold recognition drops off. This is because the decoy space is small when gaps are restricted to a small number, but the native alignment is still well approximated, whereas unrestricted increase of the number of gaps leads to rapid growth of the number of decoys and their statistical dominance over the correct alignment. It is shown that best results are obtained when a combination of one-, two-, and three-gap threading is used. To this end, use of the epsilon parameter is crucial for rigorous comparison of results across the different decoy spaces belonging to a different number of gaps.
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Affiliation(s)
- William Chen
- Department of Biophysics, Harvard University, Boston, Massachusetts, USA
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117
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Eastwood MP, Hardin C, Luthey-Schulten Z, Wolynes PG. Statistical mechanical refinement of protein structure prediction schemes. II. Mayer cluster expansion approach. J Chem Phys 2003. [DOI: 10.1063/1.1565106] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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118
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Saven JG. Connecting statistical and optimized potentials in protein folding via a generalized foldability criterion. J Chem Phys 2003. [DOI: 10.1063/1.1565995] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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119
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Seok C, Rosen JB, Chodera JD, Dill KA. MOPED: method for optimizing physical energy parameters using decoys. J Comput Chem 2003; 24:89-97. [PMID: 12483678 DOI: 10.1002/jcc.10124] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
We present a method called MOPED for optimizing energetic and structural parameters in computational models, including all-atom energy functions, when native structures and decoys are given. The present method goes beyond previous approaches in treating energy functions that are nonlinear in the parameters and continuous in the degrees of freedom. We illustrate the method by improving solvation parameters in the energy function EEF1, which consists of the CHARMM19 polar hydrogen force field augmented by a Gaussian solvation term. Although the published parameters for EEF1 correctly discriminate the native from decoys in the decoy sets of Levitt et al., they fail on several of the more difficult decoy sets of Baker et al. MOPED successfully finds improved parameters that allow EEF1 to discriminate native from decoy structures on all protein structures that do not have metals or prosthetic groups.
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Affiliation(s)
- Chaok Seok
- Department of Pharmaceutical Chemistry, University of California in San Francisco, San Francisco, California 94118, USA
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120
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Kuznetsov IB, Rackovsky S. Discriminative ability with respect to amino acid types: assessing the performance of knowledge-based potentials without threading. Proteins 2002; 49:266-84. [PMID: 12211006 DOI: 10.1002/prot.10211] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
We present a novel method designed to analyze the discriminative ability of knowledge-based potentials with respect to the 20 residue types. The method is based on the preference of amino acids for specific types of protein environment, and uses a virtual mutagenesis experiment to estimate how much information a given potential can provide about environments of each amino acid type. This allows one to test and optimize the performance of real potentials at the level of individual amino acids, using actual data on residue environments from a dataset of known protein structures. We have applied our method to long-range and medium-range pairwise distance-dependent potentials. The results of our study indicate that these potentials are only able to discriminate between a very limited number of residue types, and that discriminative ability is extremely sensitive to the choice of parameters used to construct the potentials, and even to the size of the training dataset. We also show that different types of pairwise distance potentials are dominated by different types of interactions. These dominant interactions strongly depend on the type of approximation used to define residue position. For each potential, our methodology is able to identify a potential-specific amino acid distance matrix and a reduced amino acid alphabet of any specified size, which may have implications for sequence alignment and multibody models.
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Affiliation(s)
- Igor B Kuznetsov
- Department of Biomathematical Sciences, Mount Sinai School of Medicine, New York, New York 10029, USA
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121
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Eastwood MP, Hardin C, Luthey-Schulten Z, Wolynes PG. Statistical mechanical refinement of protein structure prediction schemes: Cumulant expansion approach. J Chem Phys 2002. [DOI: 10.1063/1.1494417] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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122
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Chhajer M, Crippen GM. A protein folding potential that places the native states of a large number of proteins near a local minimum. BMC STRUCTURAL BIOLOGY 2002; 2:4. [PMID: 12165098 PMCID: PMC126205 DOI: 10.1186/1472-6807-2-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/05/2002] [Accepted: 08/06/2002] [Indexed: 11/22/2022]
Abstract
BACKGROUND We present a simple method to train a potential function for the protein folding problem which, even though trained using a small number of proteins, is able to place a significantly large number of native conformations near a local minimum. The training relies on generating decoys by energy minimization of the native conformations using the current potential and using a physically meaningful objective function (derivative of energy with respect to torsion angles at the native conformation) during the quadratic programming to place the native conformation near a local minimum. RESULTS We also compare the performance of three different types of energy functions and find that while the pairwise energy function is trainable, a solvation energy function by itself is untrainable if decoys are generated by minimizing the current potential starting at the native conformation. The best results are obtained when a pairwise interaction energy function is used with solvation energy function. CONCLUSIONS We are able to train a potential function using six proteins which places a total of 42 native conformations within approximately 4 A rmsd and 71 native conformations within approximately 6 A rmsd of a local minimum out of a total of 91 proteins. Furthermore, the threading test using the same 91 proteins ranks 89 native conformations to be first and the other two as second.
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Affiliation(s)
- Mukesh Chhajer
- Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599, U.S.A
| | - Gordon M Crippen
- College of Pharmacy, University of Michigan, Ann Arbor, MI 48109-1065, U.S.A
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123
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Fain B, Xia Y, Levitt M. Design of an optimal Chebyshev-expanded discrimination function for globular proteins. Protein Sci 2002; 11:2010-21. [PMID: 12142455 PMCID: PMC2373672 DOI: 10.1110/ps.0200702] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
We describe the construction of a scoring function designed to model the free energy of protein folding. An optimization technique is used to determine the best functional forms of the hydrophobic, residue-residue and hydrogen-bonding components of the potential. The scoring function is expanded by use of Chebyshev polynomials, the coefficients of which are determined by minimizing the score, in units of standard deviation, of native structures in the ensembles of alternate decoy conformations. The derived effective potential is then tested on decoy sets used conventionally in such studies. Using our scoring function, we achieve a high level of discrimination between correct and incorrect folds. In addition, our method is able to represent functions of arbitrary shape with fewer parameters than the usual histogram potentials of similar resolution. Finally, our representation can be combined easily with many optimization methods, because the total energy is a linear function of the parameters. Our results show that the techniques of Z-score optimization and Chebyshev expansion work well.
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Affiliation(s)
- Boris Fain
- Department of Structural Biology, Stanford University, Stanford University School of Medicine, California 94305, USA.
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124
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Abstract
Stabilization centers (SCs) were shown to play an important role in preventing decay of three-dimensional protein structures. These residue clusters, stabilized by cooperative long-range interactions, were proposed to serve as anchoring points for arranging secondary structure elements. In all-alpha proteins, SC elements appear less frequently than in all-beta, alpha/beta, and alpha+beta proteins suggesting that tertiary structure formation of all-alpha proteins is governed by different principles than in other protein classes. Here we analyzed the relation between the formation of stabilization centers and the inter-axial angles (Omega) of alpha-helices in 4 helix bundle proteins. In the distance range, where dipoles have dominant effect on the helix pair arrangement, those helix pairs, where residues from both helices participate in SC elements, appear as parallel more frequently than those helices where no SC elements are present. For SC containing helix pairs, the energetic difference between the parallel and anti-parallel states decreases considerably from 1.1 kcal/mol to 0.4 kcal/mol. Although the observed effect is weak for more distant helices, a competition between the SC element formation and the optimal dipole-dipole interaction of alpha-helices is proposed as a mechanism for tertiary structure formation in 4 helix bundle proteins. The SC-forming potential of different arrangements as well as the pitfalls of the SC definition are also discussed.
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Affiliation(s)
- M Fuxreiter
- Institute of Enzymology, Hungarian Academy of Sciences, Budapest, Hungary
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125
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Abstract
Multiple sequence alignments are a routine tool in protein fold recognition, but multiple structure alignments are computationally less cooperative. This work describes a method for protein sequence threading and sequence-to-structure alignments that uses multiple aligned structures, the aim being to improve models from protein threading calculations. Sequences are aligned into a field due to corresponding sites in homologous proteins. On the basis of a test set of more than 570 protein pairs, the procedure does improve alignment quality, although no more than averaging over sequences. For the force field tested, the benefit of structure averaging is smaller than that of adding sequence similarity terms or a contribution from secondary structure predictions. Although there is a significant improvement in the quality of sequence-to-structure alignments, this does not directly translate to an immediate improvement in fold recognition capability.
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Affiliation(s)
- Anthony J Russell
- Research School of Chemistry, Australian National University, Canberra, Australia
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126
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Kussell E, Shimada J, Shakhnovich EI. A structure-based method for derivation of all-atom potentials for protein folding. Proc Natl Acad Sci U S A 2002; 99:5343-8. [PMID: 11943859 PMCID: PMC122771 DOI: 10.1073/pnas.072665799] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A method for deriving all-atom protein folding potentials is presented and tested on a three-helix bundle protein, as well as on hairpin and helical sequences. The potentials obtained are composed of a contact term between pairs of atoms, and a local density term for each atom, mimicking solvent exposure preferences. Using this potential in an all-atom protein folding simulation, we repeatedly folded the three-helix bundle, with the lowest energy conformations having a C(alpha) distance rms from the native structure of less than 2 A. Similar results were obtained for the hairpin and helices by using different potentials. We derived potentials for several different proteins and found a high correlation between the derived parameters, suggesting that a potential of this form eventually could be found that folds multiple, unrelated proteins at the atomic level of detail.
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Affiliation(s)
- Edo Kussell
- Department of Biophysics, Harvard University, 240 Longwood Avenue, Boston, MA 02115, USA
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127
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128
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Chang I, Cieplak M, Dima RI, Maritan A, Banavar JR. Protein threading by learning. Proc Natl Acad Sci U S A 2001; 98:14350-5. [PMID: 11717394 PMCID: PMC64685 DOI: 10.1073/pnas.241133698] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2001] [Indexed: 11/18/2022] Open
Abstract
By using techniques borrowed from statistical physics and neural networks, we determine the parameters, associated with a scoring function, that are chosen optimally to ensure complete success in threading tests in a training set of proteins. These parameters provide a quantitative measure of the propensities of amino acids to be buried or exposed and to be in a given secondary structure and are a good starting point for solving both the threading and design problems.
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Affiliation(s)
- I Chang
- Department of Physics, 104 Davey Laboratory, Pennsylvania State University, University Park, PA 16802, USA
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129
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Fariselli P, Olmea O, Valencia A, Casadio R. Prediction of contact maps with neural networks and correlated mutations. PROTEIN ENGINEERING 2001; 14:835-43. [PMID: 11742102 DOI: 10.1093/protein/14.11.835] [Citation(s) in RCA: 149] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Contact maps of proteins are predicted with neural network-based methods, using as input codings of increasing complexity including evolutionary information, sequence conservation, correlated mutations and predicted secondary structures. Neural networks are trained on a data set comprising the contact maps of 173 non-homologous proteins as computed from their well resolved three-dimensional structures. Proteins are selected from the Protein Data Bank database provided that they align with at least 15 similar sequences in the corresponding families. The predictors are trained to learn the association rules between the covalent structure of each protein and its contact map with a standard back propagation algorithm and tested on the same protein set with a cross-validation procedure. Our results indicate that the method can assign protein contacts with an average accuracy of 0.21 and with an improvement over a random predictor of a factor >6, which is higher than that previously obtained with methods only based either on neural networks or on correlated mutations. Furthermore, filtering the network outputs with a procedure based on the residue coordination numbers, the accuracy of predictions increases up to 0.25 for all the proteins, with an 8-fold deviation from a random predictor. These scores are the highest reported so far for predicting protein contact maps.
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Affiliation(s)
- P Fariselli
- CIRB and Department of Biology, University of Bologna, via Irnerio 42, Bologna, Italy
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130
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Affiliation(s)
- J G Saven
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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131
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Lu H, Skolnick J. A distance-dependent atomic knowledge-based potential for improved protein structure selection. Proteins 2001; 44:223-32. [PMID: 11455595 DOI: 10.1002/prot.1087] [Citation(s) in RCA: 218] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
A heavy atom distance-dependent knowledge-based pairwise potential has been developed. This statistical potential is first evaluated and optimized with the native structure z-scores from gapless threading. The potential is then used to recognize the native and near-native structures from both published decoy test sets, as well as decoys obtained from our group's protein structure prediction program. In the gapless threading test, there is an average z-score improvement of 4 units in the optimized atomic potential over the residue-based quasichemical potential. Examination of the z-scores for individual pairwise distance shells indicates that the specificity for the native protein structure is greatest at pairwise distances of 3.5-6.5 A, i.e., in the first solvation shell. On applying the current atomic potential to test sets obtained from the web, composed of native protein and decoy structures, the current generation of the potential performs better than residue-based potentials as well as the other published atomic potentials in the task of selecting native and near-native structures. This newly developed potential is also applied to structures of varying quality generated by our group's protein structure prediction program. The current atomic potential tends to pick lower RMSD structures than do residue-based contact potentials. In particular, this atomic pairwise interaction potential has better selectivity especially for near-native structures. As such, it can be used to select near-native folds generated by structure prediction algorithms as well as for protein structure refinement.
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Affiliation(s)
- H Lu
- Laboratory of Computational Genomics, Donald Danforth Plant Science Center, St. Louis, Missouri 63141, USA
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132
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Ota M, Isogai Y, Nishikawa K. Knowledge-based potential defined for a rotamer library to design protein sequences. PROTEIN ENGINEERING 2001; 14:557-64. [PMID: 11579224 DOI: 10.1093/protein/14.8.557] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
A knowledge-based potential for a rotamer library was developed to design protein sequences. Protein side-chain conformations are represented by 56 templates. Each of their fitness to a given structural site-environment is evaluated by a combined function of the three knowledge-based terms, i.e. two-body side-chain packing, one-body hydration and local conformation. The number of matches between the native sequence and the structural site-environment in the database and that of the virtually settled mismatches, counted in advance, were transformed into the energy scores. In the best-14 test (assessment for the reproduction ability of the native rotamer on its structural site within a quarter of 56 fitness rank positions), the structural stability analysis on mutants of human and T4 lysozymes and the inverse-folding search by a structure profile against the sequence database, this function performs better than the function deduced with the conventional normalization and our previously developed function. Targeting various structural motifs, de novo sequence design was conducted with the function. The sequences thus obtained exhibit reasonable molecular masses and hydrophobic/hydrophilic patterns similar to the native sequences of the target and act as if they were the homologs to the target proteins in BLASTP search. This significant improvement is discussed in terms of the reference state for normalization and the crucial role of short-range repulsion to prohibit residue bumps.
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Affiliation(s)
- M Ota
- National Institute of Genetics, Mishima, Shizuoka 411-8540. The Institute of Physical and Chemical Research (RIKEN), Wako,Saitama 351-0198, Japan.
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133
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Bastolla U, Farwer J, Knapp EW, Vendruscolo M. How to guarantee optimal stability for most representative structures in the Protein Data Bank. Proteins 2001; 44:79-96. [PMID: 11391771 DOI: 10.1002/prot.1075] [Citation(s) in RCA: 101] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
We proposed recently an optimization method to derive energy parameters for simplified models of protein folding. The method is based on the maximization of the thermodynamic average of the overlap between protein native structures and a Boltzmann ensemble of alternative structures. Such a condition enforces protein models whose ground states are most similar to the corresponding native states. We present here an extensive testing of the method for a simple residue-residue contact energy function and for alternative structures generated by threading. The optimized energy function guarantees high stability and a well-correlated energy landscape to most representative structures in the PDB database. Failures in the recognition of the native structure can be attributed to the neglect of interactions between different chains in oligomeric proteins or with cofactors. When these are taken into account, only very few X-ray structures are not recognized. Most of them are short inhibitors or fragments and one is a structure that presents serious inconsistencies. Finally, we discuss the reasons that make NMR structures more difficult to recognizeCopyright 2001 Wiley-Liss, Inc.
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Affiliation(s)
- U Bastolla
- Free University of Berlin, Department of Biology, Chemistry and Pharmacy, Institute of Chemistry, Berlin, Germany.
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134
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Pillardy J, Czaplewski C, Liwo A, Wedemeyer WJ, Lee J, Ripoll DR, Arłukowicz P, Ołdziej S, Arnautova YA, Scheraga HA. Development of Physics-Based Energy Functions that Predict Medium-Resolution Structures for Proteins of the α, β, and α/β Structural Classes. J Phys Chem B 2001. [DOI: 10.1021/jp0111012] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jarosław Pillardy
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - Cezary Czaplewski
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - Adam Liwo
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - William J. Wedemeyer
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - Jooyoung Lee
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - Daniel R. Ripoll
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - Piotr Arłukowicz
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - Stanisław Ołdziej
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - Yelena A. Arnautova
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
| | - Harold A. Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, Faculty of Chemistry, University of Gdańsk, Sobieskiego 18, 80-952 Gdańsk, Poland, and Cornell Theory Center, Ithaca, New York 14853-3801
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135
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Kim W, Wilbur WJ. Amino acid residue environments and predictions of residue type. COMPUTERS & CHEMISTRY 2001; 25:411-22. [PMID: 11459355 DOI: 10.1016/s0097-8485(01)00075-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
The determination of a protein's structure from the knowledge of its linear chain is one of the important problems that remains as a bottleneck in interpreting the rapidly increasing repository of genetic sequence data. One approach to this problem that has shown promise and given a measure of success is threading. In this approach contact energies between different amino acids are first determined by statistical methods applied to known structures. These contact energies are then applied to a sequence whose structure is to be determined by threading it through various known structures and determining the total threading energy for each candidate structure. That structure that yields the lowest total energy is then considered the leading candidate among all the structures tested. Additional information is often needed in order to support the results of threading studies, as it is well known in the field that the contact potentials used are not sufficiently sensitive to allow definitive conclusions. Here, we investigate the hypothesis that the environment of an amino acid residue realized as all those residues not local to it on the chain but sufficiently close spatially can supply information predictive of the type of that residue that is not adequately reflected in the individual contact energies. We present evidence that confirms this hypothesis and suggests a high order cooperativity between the residues that surround a given residue and how they interact with it. We suggest a possible application to threading.
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Affiliation(s)
- W Kim
- National Center for Biotechnology Information, National Library of Medicine, National Institutes of Health, Bethesda, MD 20894, USA.
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136
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Vendruscolo M. Assessment of the quality of energy functions for protein folding by using a criterion derived with the help of the noisy go model. J Biol Phys 2001; 27:205-15. [PMID: 23345744 PMCID: PMC3456590 DOI: 10.1023/a:1013152026788] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We propose a simple criterion based on the Z-scoreto assess the quality of energy functions for protein folding: one should obtain Z>-10 for the equilibrium ensembleat about native conditions. We derive this criterionby studying a Go model with random errors added to the native interactions. The dependence of the Z-score on the thermodynamic parameters,including the noise, can be precisely obtained in this case,as the ground state of the model is known exactly.We apply this criterion to rapidly rule out two otherwise promisingpairwise energy approximations.The advantage of adopting the present criterionis that it is not necessary to know the ground state of an energy function to assess its quality. It is sufficient to compute the Z-scorefrom a single equilibrium simulation at around the folding temperature.
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Affiliation(s)
- M. Vendruscolo
- Oxford Centre for Molecular Sciences, New Chemistry Laboratory, University of Oxford, Oxford, OX1 3QT UK
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137
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Dwyer DS. Electronic properties of the amino acid side chains contribute to the structural preferences in protein folding. J Biomol Struct Dyn 2001; 18:881-92. [PMID: 11444376 DOI: 10.1080/07391102.2001.10506715] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
A database of 118 non-redundant proteins was examined to determine the preferences of amino acids for secondary structures: alpha-helix, beta-strand and coil conformations. To better understand how the physicochemical properties of amino acid side chains might influence protein folding, several new scales have been suggested for quantifying the electronic effects of amino acids. These include the pKa at the amino group, localized effect substituent constants (esigma), and a composite of these two scales (epsilon). Amino acids were also classified into 5 categories on the basis of their electronic properties: O (strong electron donor), U (weak donor), Z (ambivalent), B (weak electron acceptor), and X (strong acceptor). Certain categories of amino acid appeared to be critical for particular conformations, e.g., O and U-type residues for alpha-helix formation. Pairwise analysis of the database according to these categories revealed significant context effects in the structural preferences. In general, the propensity of an amino acid for a particular conformation was related to the electronic features of the side chain. Linear regression analyses revealed that the electronic properties of amino acids contributed about as much to the folding preferences as hydrophobicity, which is a well-established determinant of protein folding. A theoretical model has been proposed to explain how the electronic properties of the side chain groups might influence folding along the peptide backbone.
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Affiliation(s)
- D S Dwyer
- Department of Psychiatry, LSU Health Sciences Center-Shreveport, 71130-3932, USA.
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138
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Ohkubo YZ, Crippen GM. Potential energy function for continuous state models of globular proteins. J Comput Biol 2001; 7:363-79. [PMID: 11108468 DOI: 10.1089/106652700750050835] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
One of the approaches to protein structure prediction is to obtain energy functions which can recognize the native conformation of a given sequence among a zoo of conformations. The discriminations can be done by assigning the lowest energy to the native conformation, with the guarantee that the native is in the zoo. Well-adjusted functions, then, can be used in the search for other (near-) natives. Here the aim is the discrimination at relatively high resolution (RMSD difference between the native and the closest nonnative is around 1 A) by pairwise energy potentials. The potential is trained using the experimentally determined native conformation of only one protein, instead of the usual large survey over many proteins. The novel feature is that the native structure is compared to a vastly wider and more challenging array of nonnative structures found not only by the usual threading procedure, but by wide-ranging local minimization of the potential. Because of this extremely demanding search, the native is very close to the apparent global minimum of the potential function. The global minimum property holds up for one other protein having 60% sequence identity, but its performance on completely dissimilar proteins is of course much weaker.
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Affiliation(s)
- Y Z Ohkubo
- College of Pharmacy, University of Michigan, Ann Arbor 48109-1065, USA
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139
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Bieńkowska JR, Rogers RG, Smith TF. Performance of threading scoring functions designed using new optimization method. J Comput Biol 2001; 6:299-311. [PMID: 10582568 DOI: 10.1089/106652799318283] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We present a new procedure for optimization of a threading scoring function. A scoring function is usually formulated in terms of the structural environment states that describe the protein fold model. We propose a method for the optimal selection of those structural environment states that naturally follows from the probabilistic description of the threading problem and is done prior to threading experiments. We demonstrate the selection of the optimal structural environment states for the solvent exposure of the amino acid position, and present the results of threading experiments performed using scoring functions designed with and without the optimization of the structural environment states. These results confirm that the optimal scoring function predicts the sequence-to-structure alignments most accurately. Threading experiments performed with 15 optimally designed scoring functions show that the correlation coefficient between the information content of the amino acid distribution that determines the scoring function and the accuracy of the optimal sequence-to-structure alignment is 0.94.
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Affiliation(s)
- J R Bieńkowska
- BioMolecular Engineering Research Center, College of Engineering, Boston University, Massachusetts 02215, USA.
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140
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Kono H, Saven JG. Statistical theory for protein combinatorial libraries. Packing interactions, backbone flexibility, and the sequence variability of a main-chain structure. J Mol Biol 2001; 306:607-28. [PMID: 11178917 DOI: 10.1006/jmbi.2000.4422] [Citation(s) in RCA: 107] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Combinatorial experiments provide new ways to probe the determinants of protein folding and to identify novel folding amino acid sequences. These types of experiments, however, are complicated both by enormous conformational complexity and by large numbers of possible sequences. Therefore, a quantitative computational theory would be helpful in designing and interpreting these types of experiment. Here, we present and apply a statistically based, computational approach for identifying the properties of sequences compatible with a given main-chain structure. Protein side-chain conformations are included in an atom-based fashion. Calculations are performed for a variety of similar backbone structures to identify sequence properties that are robust with respect to minor changes in main-chain structure. Rather than specific sequences, the method yields the likelihood of each of the amino acids at preselected positions in a given protein structure. The theory may be used to quantify the characteristics of sequence space for a chosen structure without explicitly tabulating sequences. To account for hydrophobic effects, we introduce an environmental energy that it is consistent with other simple hydrophobicity scales and show that it is effective for side-chain modeling. We apply the method to calculate the identity probabilities of selected positions of the immunoglobulin light chain-binding domain of protein L, for which many variant folding sequences are available. The calculations compare favorably with the experimentally observed identity probabilities.
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Affiliation(s)
- H Kono
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, USA
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141
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Abstract
The prediction of the three-dimensional structures of the native states of proteins from the sequences of their amino acids is one of the most important challenges in molecular biology. An essential task for solving this problem within coarse-grained models is the deduction of effective interaction potentials between the amino acids. Over the years, several techniques have been developed to extract potentials that are able to discriminate satisfactorily between the native and nonnative folds of a preassigned protein sequence. In general, when these potentials are used in actual dynamical folding simulations, they lead to a drift of the native structure outside the quasinative basin. In this article, we present and validate an approach to overcome this difficulty. By exploiting several numerical and analytical tools, we set up a rigorous iterative scheme to extract potentials satisfying a prerequisite of any viable potential: the stabilization of proteins within their native basin (less than 3-4 A RMSD). The scheme is flexible and is demonstrated to be applicable to a variety of parameterizations of the energy function, and it provides in each case the optimal potentials.
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Affiliation(s)
- C Micheletti
- International School for Advanced Studies and INFM, Trieste, Italy.
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142
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Akkermans RLC, Briels WJ. A structure-based coarse-grained model for polymer melts. J Chem Phys 2001. [DOI: 10.1063/1.1330744] [Citation(s) in RCA: 108] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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143
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Abstract
Models in computational biology, such as those used in binding, docking, and folding, are often empirical and have adjustable parameters. Because few of these models are yet fully predictive, the problem may be nonoptimal choices of parameters. We describe an algorithm called ENPOP (energy function parameter optimization) that improves-and sometimes optimizes-the parameters for any given model and for any given search strategy that identifies the stable state of that model. ENPOP iteratively adjusts the parameters simultaneously to move the model global minimum energy conformation for each of m different molecules as close as possible to the true native conformations, based on some appropriate measure of structural error. A proof of principle is given for two very different test problems. The first involves three different two-dimensional model protein molecules having 12 to 37 monomers and four parameters in common. The parameters converge to the values used to design the model native structures. The second problem involves nine bumpy landscapes, each having between 4 and 12 degrees of freedom. For the three adjustable parameters, the globally optimal values are known in advance. ENPOP converges quickly to the correct parameter set.
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Affiliation(s)
- J B Rosen
- Computer Science and Engineering Department, University of California at San Diego, San Diego, California 92093 USA
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144
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Xia Y, Levitt M. Extracting knowledge-based energy functions from protein structures by error rate minimization: Comparison of methods using lattice model. J Chem Phys 2000. [DOI: 10.1063/1.1320823] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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145
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Abstract
Success in the protein structure prediction problem relies heavily on the choice of an appropriate potential function. One approach toward extracting these potentials from a database of known protein structures is to maximize the Z-score of the database proteins, which represents the ability of the potential to discriminate correct from random conformations. These optimization methods model the entire distribution of alternative structures, reducing their ability to concentrate on the lowest energy structures most competitive with the native state and resulting in an unfortunate tendency to underestimate the repulsive interactions. This leads to reduced accuracy and predictive ability. Using a lattice model, we demonstrate how we can weight the distribution to suppress the contributions of the high-energy conformations to the Z-score calculation. The result is a potential that is more accurate and more likely to yield correct predictions than other Z-score optimization methods as well as potentials of mean force.
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Affiliation(s)
- T L Chiu
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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146
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Vijayakumar M, Zhou HX. Prediction of Residue−Residue Pair Frequencies in Proteins. J Phys Chem B 2000. [DOI: 10.1021/jp001757f] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- M. Vijayakumar
- Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104
| | - Huan-Xiang Zhou
- Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104
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147
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Shan Y, Zhou HX. Correspondence of potentials of mean force in proteins and in liquids. J Chem Phys 2000. [DOI: 10.1063/1.1288920] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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148
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Abstract
A well-established experimental criterion for two-state thermodynamic cooperativity in protein folding is that the van't Hoff enthalpy DeltaH(vH) around the transition midpoint is equal, or very nearly so, to the calorimetric enthalpy DeltaH(cal) of the entire transition. This condition is satisfied by many small proteins. We use simple lattice models to provide a statistical mechanical framework to elucidate how this calorimetric two-state picture may be reconciled with the hierarchical multistate scenario emerging from recent hydrogen exchange experiments. We investigate the feasibility of using inverse Laplace transforms to recover the underlying density of states (i.e., enthalpy distribution) from calorimetric data. We find that the constraint imposed by DeltaH(vH)/DeltaH(cal) approximately 1 on densities of states of proteins is often more stringent than other "two-state" criteria proposed in recent theoretical studies. In conjunction with reasonable assumptions, the calorimetric two-state condition implies a narrow distribution of denatured-state enthalpies relative to the overall enthalpy difference between the native and the denatured conformations. This requirement does not always correlate with simple definitions of "sharpness" of a transition and has important ramifications for theoretical modeling. We find that protein models that assume capillarity cooperativity can exhibit overall calorimetric two-state-like behaviors. However, common heteropolymer models based on additive hydrophobic-like interactions, including highly specific two-dimensional Gō models, fail to produce proteinlike DeltaH(vH)/DeltaH(cal) approximately 1. A simple model is constructed to illustrate a proposed scenario in which physically plausible local and nonlocal cooperative terms, which mimic helical cooperativity and environment-dependent hydrogen bonding strength, can lead to thermodynamic behaviors closer to experiment. Our results suggest that proteinlike thermodynamic cooperativity may require a cooperative interplay between local and nonlocal interactions. The prospect of using calorimetric data to constrain Z-scores of knowledge-based potentials is discussed.
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Affiliation(s)
- H S Chan
- Department of Biochemistry and Department of Medical Genetics and Microbiology, Faculty of Medicine, University of Toronto, Ontario, Canada.
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149
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Mirny LA, Finkelstein AV, Shakhnovich EI. Statistical significance of protein structure prediction by threading. Proc Natl Acad Sci U S A 2000; 97:9978-83. [PMID: 10954732 PMCID: PMC27644 DOI: 10.1073/pnas.160271197] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
In this study, we estimate the statistical significance of structure prediction by threading. We introduce a single parameter epsilon that serves as a universal measure determining the probability that the best alignment is indeed a native-like analog. Parameter epsilon takes into account both length and composition of the query sequence and the number of decoys in threading simulation. It can be computed directly from the query sequence and potential of interactions, eliminating the need for sequence reshuffling and realignment. Although our theoretical analysis is general, here we compare its predictions with the results of gapless threading. Finally we estimate the number of decoys from which the native structure can be found by existing potentials of interactions. We discuss how this analysis can be extended to determine the optimal gap penalties for any sequence-structure alignment (threading) method, thus optimizing it to maximum possible performance.
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Affiliation(s)
- L A Mirny
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
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