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Protein Function Analysis through Machine Learning. Biomolecules 2022; 12:biom12091246. [PMID: 36139085 PMCID: PMC9496392 DOI: 10.3390/biom12091246] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Revised: 08/22/2022] [Accepted: 08/31/2022] [Indexed: 11/16/2022] Open
Abstract
Machine learning (ML) has been an important arsenal in computational biology used to elucidate protein function for decades. With the recent burgeoning of novel ML methods and applications, new ML approaches have been incorporated into many areas of computational biology dealing with protein function. We examine how ML has been integrated into a wide range of computational models to improve prediction accuracy and gain a better understanding of protein function. The applications discussed are protein structure prediction, protein engineering using sequence modifications to achieve stability and druggability characteristics, molecular docking in terms of protein–ligand binding, including allosteric effects, protein–protein interactions and protein-centric drug discovery. To quantify the mechanisms underlying protein function, a holistic approach that takes structure, flexibility, stability, and dynamics into account is required, as these aspects become inseparable through their interdependence. Another key component of protein function is conformational dynamics, which often manifest as protein kinetics. Computational methods that use ML to generate representative conformational ensembles and quantify differences in conformational ensembles important for function are included in this review. Future opportunities are highlighted for each of these topics.
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Srivastava A, Tracka MB, Uddin S, Casas-Finet J, Livesay DR, Jacobs DJ. Mutations in Antibody Fragments Modulate Allosteric Response Via Hydrogen-Bond Network Fluctuations. Biophys J 2017; 110:1933-42. [PMID: 27166802 DOI: 10.1016/j.bpj.2016.03.033] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2015] [Revised: 03/25/2016] [Accepted: 03/28/2016] [Indexed: 11/28/2022] Open
Abstract
A mechanical perturbation method that locally restricts conformational entropy along the protein backbone is used to identify putative allosteric sites in a series of antibody fragments. The method is based on a distance constraint model that integrates mechanical and thermodynamic viewpoints of protein structure wherein mechanical clamps that mimic substrate or cosolute binding are introduced. Across a set of six single chain-Fv fragments of the anti-lymphotoxin-β receptor antibody, statistically significant responses are obtained by averaging over 10 representative structures sampled from a molecular dynamics simulation. As expected, the introduced clamps locally rigidify the protein, but long-ranged increases in both rigidity and flexibility are also frequently observed. Expanding our analysis to every molecular dynamics frame demonstrates that the allosteric responses are modulated by fluctuations within the hydrogen-bond network where the native ensemble is comprised of conformations that both are, and are not, affected by the perturbation in question. Population shifts induced by the mutations alter the allosteric response by adjusting which hydrogen-bond networks are the most probable. These effects are compared using response maps that track changes across each single chain-Fv fragment, thus providing valuable insight into how sensitive allosteric mechanisms are to mutations.
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Affiliation(s)
- Amit Srivastava
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, North Carolina
| | | | - Shahid Uddin
- Formulation Sciences, MedImmune Ltd., Cambridge, UK
| | - Jose Casas-Finet
- Analytical Biochemistry Department, MedImmune LLC, Gaithersburg, Maryland
| | - Dennis R Livesay
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, North Carolina.
| | - Donald J Jacobs
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, North Carolina.
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3
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Hermans SM, Pfleger C, Nutschel C, Hanke CA, Gohlke H. Rigidity theory for biomolecules: concepts, software, and applications. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1311] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Susanne M.A. Hermans
- Institute for Pharmaceutical and Medicinal Chemistry; Heinrich Heine University Düsseldorf; Düsseldorf Germany
| | - Christopher Pfleger
- Institute for Pharmaceutical and Medicinal Chemistry; Heinrich Heine University Düsseldorf; Düsseldorf Germany
| | - Christina Nutschel
- Institute for Pharmaceutical and Medicinal Chemistry; Heinrich Heine University Düsseldorf; Düsseldorf Germany
| | - Christian A. Hanke
- Institute for Pharmaceutical and Medicinal Chemistry; Heinrich Heine University Düsseldorf; Düsseldorf Germany
| | - Holger Gohlke
- Institute for Pharmaceutical and Medicinal Chemistry; Heinrich Heine University Düsseldorf; Düsseldorf Germany
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4
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Wahome N, Sully E, Singer C, Thomas JC, Hu L, Joshi SB, Volkin DB, Fang J, Karanicolas J, Jacobs DJ, Mantis NJ, Middaugh CR. Novel Ricin Subunit Antigens With Enhanced Capacity to Elicit Toxin-Neutralizing Antibody Responses in Mice. J Pharm Sci 2016; 105:1603-1613. [PMID: 26987947 PMCID: PMC4846473 DOI: 10.1016/j.xphs.2016.02.009] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2015] [Revised: 01/26/2016] [Accepted: 02/09/2016] [Indexed: 02/07/2023]
Abstract
RiVax is a candidate ricin toxin subunit vaccine antigen that has proven to be safe in human phase I clinical trials. In this study, we introduced double and triple cavity-filling point mutations into the RiVax antigen with the expectation that stability-enhancing modifications would have a beneficial effect on overall immunogenicity of the recombinant proteins. We demonstrate that 2 RiVax triple mutant derivatives, RB (V81L/C171L/V204I) and RC (V81I/C171L/V204I), when adsorbed to aluminum salts adjuvant and tested in a mouse prime-boost-boost regimen were 5- to 10-fold more effective than RiVax at eliciting toxin-neutralizing serum IgG antibody titers. Increased toxin neutralizing antibody values and seroconversion rates were evident at different antigen dosages and within 7 days after the first booster. Quantitative stability/flexibility relationships analysis revealed that the RB and RC mutations affect rigidification of regions spanning residues 98-103, which constitutes a known immunodominant neutralizing B-cell epitope. A more detailed understanding of the immunogenic nature of RB and RC may provide insight into the fundamental relationship between local protein stability and antibody reactivity.
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Affiliation(s)
- Newton Wahome
- Department of Pharmaceutical Chemistry, Macromolecule and Vaccine Stabilization Center, University of Kansas, Lawrence, Kansas 66047
| | - Erin Sully
- Division of Infectious Disease, Wadsworth Center, New York State Department of Health, Albany, New York 12208
| | - Christopher Singer
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, North Carolina 28223
| | - Justin C Thomas
- Department of Pharmaceutical Chemistry, Macromolecule and Vaccine Stabilization Center, University of Kansas, Lawrence, Kansas 66047
| | - Lei Hu
- Department of Pharmaceutical Chemistry, Macromolecule and Vaccine Stabilization Center, University of Kansas, Lawrence, Kansas 66047
| | - Sangeeta B Joshi
- Department of Pharmaceutical Chemistry, Macromolecule and Vaccine Stabilization Center, University of Kansas, Lawrence, Kansas 66047
| | - David B Volkin
- Department of Pharmaceutical Chemistry, Macromolecule and Vaccine Stabilization Center, University of Kansas, Lawrence, Kansas 66047
| | - Jianwen Fang
- Applied Bioinformatics Laboratory, Department of Medicinal Chemistry, University of Kansas, Lawrence, Kansas 66047
| | - John Karanicolas
- Department of Molecular Biosciences, Center for Computational Biology, University of Kansas, Lawrence, Kansas 66045
| | - Donald J Jacobs
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, North Carolina 28223.
| | - Nicholas J Mantis
- Division of Infectious Disease, Wadsworth Center, New York State Department of Health, Albany, New York 12208; Department of Biomedical Sciences, School of Public Health, University at Albany, Albany, New York 12201.
| | - C Russell Middaugh
- Department of Pharmaceutical Chemistry, Macromolecule and Vaccine Stabilization Center, University of Kansas, Lawrence, Kansas 66047.
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Rathi PC, Fulton A, Jaeger KE, Gohlke H. Application of Rigidity Theory to the Thermostabilization of Lipase A from Bacillus subtilis. PLoS Comput Biol 2016; 12:e1004754. [PMID: 27003415 PMCID: PMC4803202 DOI: 10.1371/journal.pcbi.1004754] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2015] [Accepted: 01/14/2016] [Indexed: 11/29/2022] Open
Abstract
Protein thermostability is a crucial factor for biotechnological enzyme applications. Protein engineering studies aimed at improving thermostability have successfully applied both directed evolution and rational design. However, for rational approaches, the major challenge remains the prediction of mutation sites and optimal amino acid substitutions. Recently, we showed that such mutation sites can be identified as structural weak spots by rigidity theory-based thermal unfolding simulations of proteins. Here, we describe and validate a unique, ensemble-based, yet highly efficient strategy to predict optimal amino acid substitutions at structural weak spots for improving a protein’s thermostability. For this, we exploit the fact that in the majority of cases an increased structural rigidity of the folded state has been found as the cause for thermostability. When applied prospectively to lipase A from Bacillus subtilis, we achieved both a high success rate (25% over all experimentally tested mutations, which raises to 60% if small-to-large residue mutations and mutations in the active site are excluded) in predicting significantly thermostabilized lipase variants and a remarkably large increase in those variants’ thermostability (up to 6.6°C) based on single amino acid mutations. When considering negative controls in addition and evaluating the performance of our approach as a binary classifier, the accuracy is 63% and increases to 83% if small-to-large residue mutations and mutations in the active site are excluded. The gain in precision (predictive value for increased thermostability) over random classification is 1.6-fold (2.4-fold). Furthermore, an increase in thermostability predicted by our approach significantly points to increased experimental thermostability (p < 0.05). These results suggest that our strategy is a valuable complement to existing methods for rational protein design aimed at improving thermostability. Protein thermostability is a crucial factor for biotechnological enzyme applications. However, performance studies of computational approaches for predicting effects of mutations on protein (thermo)stability have suggested that there is still room for improvement. We describe and validate a novel and unique strategy to predict optimal amino acid substitutions at structural weak spots. At variance with other rational approaches, we exploit the fact that in the majority of cases an increased structural rigidity of the folded state is the underlying cause for thermostability. When applied prospectively on lipase LipA from Bacillus subtilis, a high success rate in predicting thermostabilized lipase variants and a remarkably large increase in their thermostability is achieved. This demonstrates the value of the novel strategy, which extends the existing portfolio of methods for rational protein design.
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Affiliation(s)
- Prakash Chandra Rathi
- Institute for Pharmaceutical and Medicinal Chemistry, Department of Mathematics and Natural Sciences, Heinrich-Heine-University, Düsseldorf, Germany
| | - Alexander Fulton
- Institute of Molecular Enzyme Technology, Heinrich-Heine-University, Düsseldorf, Germany
| | - Karl-Erich Jaeger
- Institute of Molecular Enzyme Technology, Heinrich-Heine-University, Düsseldorf, Germany
- Institute of Bio- and Geosciences IBG-1: Biotechnology, Forschungszentrum Jülich GmbH, Jülich, Germany
- * E-mail: (KEJ); (HG)
| | - Holger Gohlke
- Institute for Pharmaceutical and Medicinal Chemistry, Department of Mathematics and Natural Sciences, Heinrich-Heine-University, Düsseldorf, Germany
- * E-mail: (KEJ); (HG)
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Herring CA, Singer CM, Ermakova EA, Khairutdinov BI, Zuev YF, Jacobs DJ, Nesmelova IV. Dynamics and thermodynamic properties of CXCL7 chemokine. Proteins 2015; 83:1987-2007. [PMID: 26297927 DOI: 10.1002/prot.24913] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2015] [Revised: 08/05/2015] [Accepted: 08/18/2015] [Indexed: 11/09/2022]
Abstract
Chemokines form a family of signaling proteins mainly responsible for directing the traffic of leukocytes, where their biological activity can be modulated by their oligomerization state. We characterize the dynamics and thermodynamic stability of monomer and homodimer structures of CXCL7, one of the most abundant platelet chemokines, using experimental methods that include circular dichroism (CD) and nuclear magnetic resonance (NMR) spectroscopy, and computational methods that include the anisotropic network model (ANM), molecular dynamics (MD) simulations and the distance constraint model (DCM). A consistent picture emerges for the effects of dimerization and Cys5-Cys31 and Cys7-Cys47 disulfide bonds formation. The presence of disulfide bonds is not critical for maintaining structural stability in the monomer or dimer, but the monomer is destabilized more than the dimer upon removal of disulfide bonds. Disulfide bonds play a key role in shaping the characteristics of native state dynamics. The combined analysis shows that upon dimerization flexibly correlated motions are induced between the 30s and 50s loop within each monomer and across the dimer interface. Interestingly, the greatest gain in flexibility upon dimerization occurs when both disulfide bonds are present, and the homodimer is least stable relative to its two monomers. These results suggest that the highly conserved disulfide bonds in chemokines facilitate a structural mechanism that is tuned to optimally distinguish functional characteristics between monomer and dimer.
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Affiliation(s)
- Charles A Herring
- Department of Physics and Optical Science, University of North Carolina, Charlotte, North Carolina, 28223
| | - Christopher M Singer
- Department of Physics and Optical Science, University of North Carolina, Charlotte, North Carolina, 28223
| | - Elena A Ermakova
- Kazan Institute of Biochemistry and Biophysics, Kazan, 40111, Russia
| | | | - Yuriy F Zuev
- Kazan Institute of Biochemistry and Biophysics, Kazan, 40111, Russia
| | - Donald J Jacobs
- Department of Physics and Optical Science, University of North Carolina, Charlotte, North Carolina, 28223.,Center for Biomedical Engineering, University of North Carolina, Charlotte, North Carolina, 28223
| | - Irina V Nesmelova
- Department of Physics and Optical Science, University of North Carolina, Charlotte, North Carolina, 28223.,Center for Biomedical Engineering, University of North Carolina, Charlotte, North Carolina, 28223
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Brown JR, Livesay DR. Flexibility Correlation between Active Site Regions Is Conserved across Four AmpC β-Lactamase Enzymes. PLoS One 2015; 10:e0125832. [PMID: 26018804 PMCID: PMC4446314 DOI: 10.1371/journal.pone.0125832] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2014] [Accepted: 03/26/2015] [Indexed: 11/24/2022] Open
Abstract
β-lactamases are bacterial enzymes that confer resistance to β-lactam antibiotics, such as penicillins and cephalosporins. There are four classes of β-lactamase enzymes, each with characteristic sequence and structure properties. Enzymes from class A are the most common and have been well characterized across the family; however, less is known about how physicochemical properties vary across the C and D families. In this report, we compare the dynamical properties of four AmpC (class C) β-lactamases using our distance constraint model (DCM). The DCM reliably predicts thermodynamic and mechanical properties in an integrated way. As a consequence, quantitative stability/flexibility relationships (QSFR) can be determined and compared across the whole family. The DCM calculates a large number of QSFR metrics. Perhaps the most useful is the flexibility index (FI), which quantifies flexibility along the enzyme backbone. As typically observed in other systems, FI is well conserved across the four AmpC enzymes. Cooperativity correlation (CC), which quantifies intramolecular couplings within structure, is rarely conserved across protein families; however, it is in AmpC. In particular, the bulk of each structure is composed of a large rigid cluster, punctuated by three flexibly correlated regions located at the active site. These regions include several catalytic residues and the Ω-loop. This evolutionary conservation combined with active their site location strongly suggests that these coupled dynamical modes are important for proper functioning of the enzyme.
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Affiliation(s)
- Jenna R. Brown
- Department of Biological Sciences, University of North Carolina at Charlotte, Charlotte, NC, 28262, United States of America
| | - Dennis R. Livesay
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, NC, 28262, United States of America
- * E-mail:
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A virtual pebble game to ensemble average graph rigidity. Algorithms Mol Biol 2015; 10:11. [PMID: 25904973 PMCID: PMC4406122 DOI: 10.1186/s13015-015-0039-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2012] [Accepted: 02/18/2015] [Indexed: 11/28/2022] Open
Abstract
Background The body-bar Pebble Game (PG) algorithm is commonly used to calculate network rigidity properties in proteins and polymeric materials. To account for fluctuating interactions such as hydrogen bonds, an ensemble of constraint topologies are sampled, and average network properties are obtained by averaging PG characterizations. At a simpler level of sophistication, Maxwell constraint counting (MCC) provides a rigorous lower bound for the number of internal degrees of freedom (DOF) within a body-bar network, and it is commonly employed to test if a molecular structure is globally under-constrained or over-constrained. MCC is a mean field approximation (MFA) that ignores spatial fluctuations of distance constraints by replacing the actual molecular structure by an effective medium that has distance constraints globally distributed with perfect uniform density. Results The Virtual Pebble Game (VPG) algorithm is a MFA that retains spatial inhomogeneity in the density of constraints on all length scales. Network fluctuations due to distance constraints that may be present or absent based on binary random dynamic variables are suppressed by replacing all possible constraint topology realizations with the probabilities that distance constraints are present. The VPG algorithm is isomorphic to the PG algorithm, where integers for counting “pebbles” placed on vertices or edges in the PG map to real numbers representing the probability to find a pebble. In the VPG, edges are assigned pebble capacities, and pebble movements become a continuous flow of probability within the network. Comparisons between the VPG and average PG results over a test set of proteins and disordered lattices demonstrate the VPG quantitatively estimates the ensemble average PG results well. Conclusions The VPG performs about 20% faster than one PG, and it provides a pragmatic alternative to averaging PG rigidity characteristics over an ensemble of constraint topologies. The utility of the VPG falls in between the most accurate but slowest method of ensemble averaging over hundreds to thousands of independent PG runs, and the fastest but least accurate MCC.
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Sim J, Sim J, Park E, Lee J. Method for identification of rigid domains and hinge residues in proteins based on exhaustive enumeration. Proteins 2015; 83:1054-67. [DOI: 10.1002/prot.24799] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2014] [Revised: 02/28/2015] [Accepted: 03/10/2015] [Indexed: 11/07/2022]
Affiliation(s)
- Jaehyun Sim
- Department of Oral Microbiology and Immunology; School of Dentistry, Seoul National University; Seoul 110-749 Korea
| | - Jun Sim
- Department of Bioinformatics and Life Science; Soongsil University; Seoul 156-743 Korea
| | - Eunsung Park
- Administrative Service Division, Apsun Dental Hospital; Seoul 135-590 Korea
| | - Julian Lee
- Department of Oral Microbiology and Immunology; School of Dentistry, Seoul National University; Seoul 110-749 Korea
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Brown MC, Verma D, Russell C, Jacobs DJ, Livesay DR. A case study comparing quantitative stability-flexibility relationships across five metallo-β-lactamases highlighting differences within NDM-1. Methods Mol Biol 2014; 1084:227-38. [PMID: 24061924 PMCID: PMC4676803 DOI: 10.1007/978-1-62703-658-0_12] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
The Distance Constraint Model (DCM) is an ensemble-based biophysical model that integrates thermodynamic and mechanical viewpoints of protein structure. The DCM outputs a large number of structural characterizations that collectively allow for Quantified Stability-Flexibility Relationships (QSFR) to be identified and compared across protein families. Using five metallo-β-lactamases (MBLs) as a representative set, we demonstrate how QSFR properties are both conserved and varied across protein families. Similar to our characterizations on other protein families, the backbone flexibility of the five MBLs are overall visually conserved, yet there are interesting specific quantitative differences. For example, the plasmid-encoded NDM-1 enzyme, which leads to a fast spreading drug-resistant version of Klebsiella pneumoniae, has several regions of significantly increased rigidity relative to the other four. In addition, the set of intramolecular couplings within NDM-1 are also atypical. While long-range couplings frequently vary significantly across protein families, NDM-1 is distinct because it has limited correlated flexibility, which is isolated within the active site S3/S4 and S11/H6 loops. These loops are flexibly correlated in the other members, suggesting it is important to function, but the others also have significant amounts of correlated flexibility throughout the rest of their structures.
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Affiliation(s)
- Matthew C. Brown
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, NC 28262
| | - Deeptak Verma
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, NC 28262
| | - Christian Russell
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, NC 28262
| | - Donald J. Jacobs
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28262
| | - Dennis R. Livesay
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, NC 28262, To whom correspondence should be addressed:
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11
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Pfleger C, Gohlke H. Efficient and robust analysis of biomacromolecular flexibility using ensembles of network topologies based on fuzzy noncovalent constraints. Structure 2013; 21:1725-34. [PMID: 23994009 DOI: 10.1016/j.str.2013.07.012] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2013] [Revised: 07/04/2013] [Accepted: 07/17/2013] [Indexed: 11/19/2022]
Abstract
We describe an approach (ENT(FNC)) for performing rigidity analyses of biomacromolecules on ensembles of network topologies (ENT) generated from a single input structure. The ENT is based on fuzzy noncovalent constraints, which considers thermal fluctuations of biomacromolecules without actually sampling conformations. Definitions for fuzzy noncovalent constraints were derived from persistency data from molecular dynamics (MD) simulations. A very good agreement between local flexibility and rigidity characteristics from ENT(FNC) and MD simulations-generated ensembles is found. Regarding global characteristics, convincing results were obtained when relative thermostabilities of citrate synthase and lipase A structures were computed. The ENT(FNC) approach significantly improves the robustness of rigidity analyses, is highly efficient, and does not require a protein-specific parameterization. Its low computational demand makes it especially valuable for the analysis of large data sets, e.g., for data-driven protein engineering.
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Affiliation(s)
- Christopher Pfleger
- Mathematisch-Naturwissenschaftliche Fakultät, Institut für Pharmazeutische und Medizinische Chemie, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
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Verma D, Jacobs DJ, Livesay DR. Variations within class-A β-lactamase physiochemical properties reflect evolutionary and environmental patterns, but not antibiotic specificity. PLoS Comput Biol 2013; 9:e1003155. [PMID: 23874193 PMCID: PMC3715408 DOI: 10.1371/journal.pcbi.1003155] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2012] [Accepted: 06/10/2013] [Indexed: 11/19/2022] Open
Abstract
The bacterial enzyme β-lactamase hydrolyzes the β-lactam ring of penicillin and chemically related antibiotics, rendering them ineffective. Due to rampant antibiotic overuse, the enzyme is evolving new resistance activities at an alarming rate. Related, the enzyme's global physiochemical properties exhibit various amounts of conservation and variability across the family. To that end, we characterize the extent of property conservation within twelve different class-A β-lactamases, and conclusively establish that the systematic variations therein parallel their evolutionary history. Large and systematic differences within electrostatic potential maps and pairwise residue-to-residue couplings are observed across the protein, which robustly reflect phylogenetic outgroups. Other properties are more conserved (such as residue pKa values, electrostatic networks, and backbone flexibility), yet they also have systematic variations that parallel the phylogeny in a statistically significant way. Similarly, the above properties also parallel the environmental condition of the bacteria they are from in a statistically significant way. However, it is interesting and surprising that the only one of the global properties (protein charge) parallels the functional specificity patterns; meaning antibiotic resistance activities are not significantly constraining the global physiochemical properties. Rather, extended spectrum activities can emerge from the background of nearly any set of electrostatic and dynamic properties.
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Affiliation(s)
- Deeptak Verma
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, North Carolina, United States of America
| | - Donald J. Jacobs
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, North Carolina, United States of America
| | - Dennis R. Livesay
- Department of Bioinformatics and Genomics, University of North Carolina at Charlotte, Charlotte, North Carolina, United States of America
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13
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Protein mechanics: how force regulates molecular function. Biochim Biophys Acta Gen Subj 2013; 1830:4762-8. [PMID: 23791949 DOI: 10.1016/j.bbagen.2013.06.005] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2012] [Revised: 05/26/2013] [Accepted: 06/04/2013] [Indexed: 12/13/2022]
Abstract
BACKGROUND Regulation of proteins is ubiquitous and vital for any organism. Protein activity can be altered chemically, by covalent modifications or non-covalent binding of co-factors. Mechanical forces are emerging as an additional way of regulating proteins, by inducing a conformational change or by partial unfolding. SCOPE We review some advances in experimental and theoretical techniques to study protein allostery driven by mechanical forces, as opposed to the more conventional ligand driven allostery. In this respect, we discuss recent single molecule pulling experiments as they have substantially augmented our view on the protein allostery by mechanical signals in recent years. Finally, we present a computational analysis technique, Force Distribution Analysis, that we developed to reveal allosteric pathways in proteins. MAJOR CONCLUSIONS Any kind of external perturbation, being it ligand binding or mechanical stretching, can be viewed as an external force acting on the macromolecule, rendering force-based experimental or computational techniques, a very general approach to the mechanics involved in protein allostery. GENERAL SIGNIFICANCE This unifying view might aid to decipher how complex allosteric protein machineries are regulated on the single molecular level.
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14
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Csermely P, Korcsmáros T, Kiss HJM, London G, Nussinov R. Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review. Pharmacol Ther 2013; 138:333-408. [PMID: 23384594 PMCID: PMC3647006 DOI: 10.1016/j.pharmthera.2013.01.016] [Citation(s) in RCA: 506] [Impact Index Per Article: 46.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2013] [Accepted: 01/22/2013] [Indexed: 02/02/2023]
Abstract
Despite considerable progress in genome- and proteome-based high-throughput screening methods and in rational drug design, the increase in approved drugs in the past decade did not match the increase of drug development costs. Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design. We give a comprehensive assessment of the analytical tools of network topology and dynamics. The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets is summarized. We propose that network targeting follows two basic strategies. The "central hit strategy" selectively targets central nodes/edges of the flexible networks of infectious agents or cancer cells to kill them. The "network influence strategy" works against other diseases, where an efficient reconfiguration of rigid networks needs to be achieved by targeting the neighbors of central nodes/edges. It is shown how network techniques can help in the identification of single-target, edgetic, multi-target and allo-network drug target candidates. We review the recent boom in network methods helping hit identification, lead selection optimizing drug efficacy, as well as minimizing side-effects and drug toxicity. Successful network-based drug development strategies are shown through the examples of infections, cancer, metabolic diseases, neurodegenerative diseases and aging. Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality. Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.
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Affiliation(s)
- Peter Csermely
- Department of Medical Chemistry, Semmelweis University, P.O. Box 260, H-1444 Budapest 8, Hungary.
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15
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Pfleger C, Radestock S, Schmidt E, Gohlke H. Global and local indices for characterizing biomolecular flexibility and rigidity. J Comput Chem 2012; 34:220-33. [PMID: 23007873 DOI: 10.1002/jcc.23122] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2012] [Revised: 08/26/2012] [Accepted: 08/28/2012] [Indexed: 12/24/2022]
Abstract
Understanding flexibility and rigidity characteristics of biomolecules is a prerequisite for understanding biomolecular structural stability and function. Computational methods have been implemented that directly characterize biomolecular flexibility and rigidity by constraint network analysis. For deriving maximal advantage from these analyses, their results need to be linked to biologically relevant characteristics of a structure. Such links are provided by global and local measures ("indices") of biomolecular flexibility and rigidity. To date, more than 14 indices are available with sometimes overlapping or only vague definitions. We present concise definitions of these indices, analyze the relation between, and the scope and limitations of them, and compare their informative value. For this, we probe the structural stability of the calcium binding protein α-lactalbumin as a showcase, both in the "ground state" and after perturbing the system by changing the network topology. In addition, we introduce three indices for the first time that extend the application domain of flexibility and rigidity analyses. The results allow us to provide guidelines for future studies suggesting which of these indices could best be used for analyzing, understanding, and quantifying structural features that are important for biomolecular stability and function. Finally, we make suggestions for proper index notations in future studies to prevent the misinterpretation and to facilitate the comparison of results obtained from flexibility and rigidity analyses.
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Affiliation(s)
- Christopher Pfleger
- Department of Mathematics and Natural Sciences, Institute for Pharmaceutical and Medicinal Chemistry, Heinrich-Heine-University, Düsseldorf, Germany
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16
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Rader AJ, Yennamalli RM, Harter AK, Sen TZ. A rigid network of long-range contacts increases thermostability in a mutant endoglucanase. J Biomol Struct Dyn 2012; 30:628-37. [PMID: 22731517 DOI: 10.1080/07391102.2012.689696] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
Thermodynamic stability of a protein at elevated temperatures is a key factor for thermostable enzymes to catalyze their specific reactions. Yet our understanding of biological determinants of thermostability is far from complete. Many different atomistic factors have been suggested as possible means for such proteins to preserve their activity at high temperatures. Among these factors are specific local interatomic interactions or enrichment of specific amino acid types. The case of glycosyl hydrolase family endoglucanase of Trichoderma reesei defies current hypotheses for thermostability because a single mutation far from the active site (A35 V) converts this mesostable protein into a thermostable protein without significant change in the protein structure. This substantial change in enzymatic activity cannot be explained on the basis of local intramolecular interactions alone. Here we present a more global view of the induced thermostability and show that the A35 V mutation affects the underlying structural rigidity of the whole protein via a number of long-range, non-local interactions. Our analysis of this structure reveals a precisely tuned, rigid network of atomic interactions. This cooperative, allosteric effect promotes the transformation of this mesostable protein into a thermostable one.
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Affiliation(s)
- A J Rader
- Department of Physics, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USA.
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17
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Rathi PC, Radestock S, Gohlke H. Thermostabilizing mutations preferentially occur at structural weak spots with a high mutation ratio. J Biotechnol 2012; 159:135-44. [PMID: 22326626 DOI: 10.1016/j.jbiotec.2012.01.027] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2011] [Revised: 01/16/2012] [Accepted: 01/24/2012] [Indexed: 10/14/2022]
Abstract
We apply Constraint Network Analysis (CNA) to investigate the relationship between structural rigidity and thermostability of five citrate synthase (CS) structures over a temperature range from 37 °C to 100 °C. For the first time, we introduce an ensemble-based variant of CNA and model the temperature-dependence of hydrophobic interactions in the constraint network. A very good correlation between the predicted thermostabilities of CS and optimal growth temperatures of their source organisms (R²=0.88, p=0.017) is obtained, which validates that CNA is able to quantitatively discriminate between less and more thermostable proteins even within a series of orthologs. Structural weak spots on a less thermostable CS, predicted by CNA to be in the top 5% with respect to the frequency of occurrence over an ensemble, have a higher mutation ratio in a more thermostable CS than other sequence positions. Furthermore, highly ranked weak spots that are also highly conserved with respect to the amino acid type found at that sequence position are nevertheless found to be mutated in the more stable CS. As for mechanisms at an atomic level that lead to a reinforcement of weak spots in more stable CS, we observe that the thermophilic CS achieve a higher thermostability by better hydrogen bonding networks whereas hyperthermophilic CS incorporate more hydrophobic contacts to reach the same goal. Overall, these findings suggest that CNA can be applied as a pre-filter in data-driven protein engineering to focus on residues that are highly likely to improve thermostability upon mutation.
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Affiliation(s)
- Prakash C Rathi
- Department of Mathematics and Natural Sciences, Heinrich Heine-University, Düsseldorf, Germany
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18
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Abstract
The distance constraint model (DCM) is a unique computational modeling paradigm that integrates mechanical and thermodynamic descriptions of macromolecular structure. That is, network rigidity calculations are used to account for nonadditivity within entropy components, thus restoring the utility of free-energy decomposition. The DCM outputs a large number of structural characterizations that collectively allow for quantified stability-flexibility relationships (QSFR) to be identified. In this review, we describe the theoretical underpinnings of the DCM and introduce several common QSFR metrics. Application of the DCM across protein families highlights the sensitivity within the set of protein structure residue-to-residue couplings. Further, we have developed a perturbation method to identify putative allosteric sites, where large changes in QSFR upon rigidification (mimicking ligand-binding) detect sites likely to invoke allosteric changes.
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19
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Vitalis A, Caflisch A. 50 Years of Lifson-Roig Models: Application to Molecular Simulation Data. J Chem Theory Comput 2011; 8:363-73. [PMID: 26592894 DOI: 10.1021/ct200744s] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Simple helix-coil transition theories have been indispensable tools in the analysis of data reporting on the reversible folding of α-helical polypeptides. They provide a transferable means to not only characterize different systems but to also compare different techniques, viz., experimental probes monitoring helix-coil transitions in vitro or biomolecular force fields in silico. This article addresses several issues with the application of Lifson-Roig theory to helix-coil transition data. We use computer simulation to generate two sets of ensembles for the temperature-controlled, reversible folding of the 21-residue, alanine-rich FS peptide. Ensembles differ in the rigidity of backbone bond angles and are analyzed using two distinct descriptors of helicity. The analysis unmasks an underlying phase diagram that is surprisingly complex. The complexities give rise to fitted nucleation and propagation parameters that are difficult to interpret and that are inconsistent with the distribution of isolated residues in the α-helical basin. We show that enthalpies of helix formation are more robustly determined using van't Hoff analysis of simple measures of helicity rather than fitted propagation parameters. To overcome some of these issues, we design a simple variant of the Lifson-Roig model that recovers physical interpretability of the obtained parameters by allowing bundle formation to be described in simple fashion. The relevance of our results is discussed in relation to the applicability of Lifson-Roig models to both in silico and in vitro data.
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Affiliation(s)
- Andreas Vitalis
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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20
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Vorov OK, Livesay DR, Jacobs DJ. Nonadditivity in conformational entropy upon molecular rigidification reveals a universal mechanism affecting folding cooperativity. Biophys J 2011; 100:1129-38. [PMID: 21320459 DOI: 10.1016/j.bpj.2011.01.027] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2010] [Accepted: 01/07/2011] [Indexed: 11/15/2022] Open
Abstract
Previously, we employed a Maxwell counting distance constraint model (McDCM) to describe α-helix formation in polypeptides. Unlike classical helix-coil transition theories, the folding mechanism derives from nonadditivity in conformational entropy caused by rigidification of molecular structure as intramolecular cross-linking interactions form along the backbone. For example, when a hydrogen bond forms within a flexible region, both energy and conformational entropy decrease. However, no conformational entropy is lost when the region is already rigid because atomic motions are not constrained further. Unlike classical zipper models, the same mechanism also describes a coil-to-β-hairpin transition. Special topological features of the helix and hairpin structures allow the McDCM to be solved exactly. Taking full advantage of the fact that Maxwell constraint counting is a mean field approximation applied to the distribution of cross-linking interactions, we present an exact transfer matrix method that does not require any special topological feature. Upon application of the model to proteins, cooperativity within the folding transition is yet again appropriately described. Notwithstanding other contributing factors such as the hydrophobic effect, this simple model identifies a universal mechanism for cooperativity within polypeptide and protein-folding transitions, and it elucidates scaling laws describing hydrogen-bond patterns observed in secondary structure. In particular, the native state should have roughly twice as many constraints as there are degrees of freedom in the coil state to ensure high fidelity in two-state folding cooperativity, which is empirically observed.
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Affiliation(s)
- Oleg K Vorov
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, North Carolina, USA
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21
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Wood GG, Clinkenbeard DA, Jacobs DJ. Nonadditivity in the alpha-helix to coil transition. Biopolymers 2011; 95:240-53. [PMID: 21280020 DOI: 10.1002/bip.21572] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2010] [Revised: 10/04/2010] [Accepted: 11/26/2010] [Indexed: 11/08/2022]
Abstract
The Lifson-Roig Model (LRM) and all its variants describe the α-helix to coil transition in terms of additive component-free energies within a free energy decomposition scheme, and these contributions are interpreted through sequence-context dependent nucleation and propagation parameters. Although this phenomenological approach is able to adequately fit experimental data on helix content and heat capacity, the number of required parameters increases dramatically with additional sequence variation. Moreover, due to nonadditive competing microscopic effects that are difficult to disentangle within a LRM, large uncertainties within the parameters emerge. We offer an alternative view that removes the need for sequence-context parameterization by focusing on individual microsopic interactions within a free energy decomposition and explicitly account for nonadditivity in conformational entropy through network rigidity using a Distance Constraint Model (DCM). We apply a LRM and a DCM to previously published experimental heat capacity and helix content data for a series of heterogeneous polypeptides. Both models describe the experimental data well, and the parameters from both models are consistent with prior work. However, the number of DCM parameters is independent of sequence-variability, the parameter values exhibit better transferability, and the helix nucleation is predicted by the DCM explicitly through the nonadditive nature of conformational entropy. The importance of these results is that the DCM offers a system-independent approach for modeling stability within polypeptides and proteins, where the demonstrated accuracy for the α-helix to coil transition over a series of heterogeneous polypeptides described here is one case in point.
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Affiliation(s)
- Gregory G Wood
- Department of Mathematics and Applied Physics, CSU Channel Islands, Camarillo, CA 93012, USA
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22
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Jacobs DJ. Ensemble-based methods for describing protein dynamics. Curr Opin Pharmacol 2010; 10:760-9. [PMID: 20965786 PMCID: PMC2998175 DOI: 10.1016/j.coph.2010.09.014] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2010] [Accepted: 09/23/2010] [Indexed: 01/02/2023]
Abstract
Molecular dynamics (MD) simulation is a natural approach for studying protein dynamics, and coupled with the ideas of multiscale modeling, MD proves to be the gold standard in computational biology to investigate mechanistic details related to protein function. In principle, if MD trajectories are long enough, the ensemble of protein conformations generated allows thermodynamic and kinetic properties to be predicted. We know from experiments that proteins exhibit a high degree of fidelity in function, and that empirical kinetic models are successful in describing kinetics, suggesting that the ensemble of conformations cluster into well-defined thermodynamic states, which are frequently metastable. The experimental evidence suggest that more efficient computational models that retain only essential properties of the protein can be constructed to faithfully reproduce the relatively few observed thermodynamic states, and perhaps describe transition states if the model is sufficiently detailed. Indeed, there are many so-called ensemble-based methods that attempt to generate more complete ensembles than MD can provide by focusing on the most important driving forces through simplified representations of how elements within the protein interact. Although coarse-graining is employed in MD and other approaches, such as in elastic network models, the key distinguishing factor of ensemble-based methods is that they are meant to efficiently generate a large ensemble of conformations without solving explicit equations of motion. This review highlights three types of ensemble-based methods, illustrated by 'COREX' and the Wako-Saito-Munoz-Eaton (WSME) model, the Framework Rigidity Optimized Dynamic Algorithm (FRODA) and the distance constraint model (DCM).
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Affiliation(s)
- Donald J Jacobs
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA.
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23
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Vorov OK, Livesay DR, Jacobs DJ. Helix/coil nucleation: a local response to global demands. Biophys J 2010; 97:3000-9. [PMID: 19948130 DOI: 10.1016/j.bpj.2009.09.013] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2009] [Revised: 09/04/2009] [Accepted: 09/09/2009] [Indexed: 11/18/2022] Open
Abstract
A complete description of protein structure and function must include a proper treatment of mechanisms that lead to cooperativity. The helix/coil transition serves as a simple example of a cooperative folding process, commonly described by a nucleation-propagation mechanism. The prevalent view is that coil structure must first form a short segment of helix in a localized region despite paying a free energy cost (nucleation). Afterward, helical structure propagates outward from the nucleation site. Both processes entail enthalpy-entropy compensation that derives from the loss in conformational entropy on helix formation with concomitant gain in favorable interactions. Nucleation-propagation models inherently assume that cooperativity arises from a sequential series of local events. An alternative distance constraint model asserts there is a direct link between available degrees of freedom and cooperativity through the nonadditivity in conformational entropy. That is, helix nucleation is a concerted manifestation of rigidity propagating through atomic structure. The link between network rigidity and nonadditivity of conformational entropy is shown in this study by solving the distance constraint model using a simple global constraint counting approximation. Cooperativity arises from competition between excess and deficiency in available degrees of freedom in the coil and helix states respectively.
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Affiliation(s)
- Oleg K Vorov
- Department of Physics, University of North Carolina at Charlotte, Charlotte, North Carolina, USA
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24
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Abstract
The source of increased stability in proteins from organisms that thrive in extreme thermal environments is not well understood. Previous experimental and theoretical studies have suggested many different features possibly responsible for such thermostability. Many of these thermostabilizing mechanisms can be accounted for in terms of structural rigidity. Thus a plausible hypothesis accounting for this remarkable stability in thermophilic enzymes states that these enzymes have enhanced conformational rigidity at temperatures below their native, functioning temperature. Experimental evidence exists to both support and contradict this supposition. We computationally investigate the relationship between thermostability and rigidity using rubredoxin as a case study. The mechanical rigidity is calculated using atomic models of homologous rubredoxin structures from the hyperthermophile Pyrococcus furiosus and mesophile Clostridium pasteurianum using the FIRST software. A global increase in structural rigidity (equivalently a decrease in flexibility) corresponds to an increase in thermostability. Locally, rigidity differences (between mesophilic and thermophilic structures) agree with differences in protection factors.
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Affiliation(s)
- A J Rader
- Department of Physics and Center for Mathematical Biosciences, Indiana University-Purdue University at Indianapolis, Indianapolis, IN, USA.
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25
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Mottonen JM, Xu M, Jacobs DJ, Livesay DR. Unifying mechanical and thermodynamic descriptions across the thioredoxin protein family. Proteins 2009; 75:610-27. [PMID: 19004018 DOI: 10.1002/prot.22273] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
We compare various predicted mechanical and thermodynamic properties of nine oxidized thioredoxins (TRX) using a Distance Constraint Model (DCM). The DCM is based on a nonadditive free energy decomposition scheme, where entropic contributions are determined from rigidity and flexibility of structure based on distance constraints. We perform averages over an ensemble of constraint topologies to calculate several thermodynamic and mechanical response functions that together yield quantitative stability/flexibility relationships (QSFR). Applied to the TRX protein family, QSFR metrics display a rich variety of similarities and differences. In particular, backbone flexibility is well conserved across the family, whereas cooperativity correlation describing mechanical and thermodynamic couplings between the residue pairs exhibit distinctive features that readily standout. The diversity in predicted QSFR metrics that describe cooperativity correlation between pairs of residues is largely explained by a global flexibility order parameter describing the amount of intrinsic flexibility within the protein. A free energy landscape is calculated as a function of the flexibility order parameter, and key values are determined where the native-state, transition-state, and unfolded-state are located. Another key value identifies a mechanical transition where the global nature of the protein changes from flexible to rigid. The key values of the flexibility order parameter help characterize how mechanical and thermodynamic response is linked. Variation in QSFR metrics and key characteristics of global flexibility are related to the native state X-ray crystal structure primarily through the hydrogen bond network. Furthermore, comparison of three TRX redox pairs reveals differences in thermodynamic response (i.e., relative melting point) and mechanical properties (i.e., backbone flexibility and cooperativity correlation) that are consistent with experimental data on thermal stabilities and NMR dynamical profiles. The results taken together demonstrate that small-scale structural variations are amplified into discernible global differences by propagating mechanical couplings through the H-bond network.
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Affiliation(s)
- James M Mottonen
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
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26
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Robinson JM. Physical limits on computation by assemblies of allosteric proteins. PHYSICAL REVIEW LETTERS 2008; 101:178104. [PMID: 18999791 DOI: 10.1103/physrevlett.101.178104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2008] [Indexed: 05/27/2023]
Abstract
Assemblies of allosteric proteins are the principle information processing devices in biology. Using the Ca2+-sensitive cardiac regulatory assembly as a paradigm for Brownian computation, I examine how system complexity and system resetting impose physical limits on computation. Nearest-neighbor-limited interactions among assembly components constrain the topology of the system's macrostate free energy landscape and produce degenerate transition probabilities. As a result, signaling fidelity and deactivation kinetics cannot be simultaneously optimized. This imposes an upper limit on the rate of information processing by assemblies of allosteric proteins that couple to a single ligand type.
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Affiliation(s)
- John M Robinson
- Department of Biochemistry and Molecular Genetics, University of Alabama at Birmingham, Birmingham, AL 35294, USA.
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27
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Abstract
We present a novel analytical method to calculate conformational entropy of ideal cross-linking polymers from the configuration integral by employing a Mayer series expansion. Mayer-functions describing chemical bonds within the chain and for cross-links are sharply peaked over the temperature range of interest, and, are well approximated as statistically weighted Dirac delta-functions that enforce distance constraints. All geometrical deformations consistent with a set of distance constraints are integrated over. Exact results for a contiguous series of connected loops are employed to substantiate the validity of a previous phenomenological distance constraint model that describes protein thermodynamics successfully based on network rigidity.
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28
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Livesay DR, Huynh DH, Dallakyan S, Jacobs DJ. Hydrogen bond networks determine emergent mechanical and thermodynamic properties across a protein family. Chem Cent J 2008; 2:17. [PMID: 18700034 PMCID: PMC2533333 DOI: 10.1186/1752-153x-2-17] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2008] [Accepted: 08/12/2008] [Indexed: 11/23/2022] Open
Abstract
Background Gram-negative bacteria use periplasmic-binding proteins (bPBP) to transport nutrients through the periplasm. Despite immense diversity within the recognized substrates, all members of the family share a common fold that includes two domains that are separated by a conserved hinge. The hinge allows the protein to cycle between open (apo) and closed (ligated) conformations. Conformational changes within the proteins depend on a complex interplay of mechanical and thermodynamic response, which is manifested as an increase in thermal stability and decrease of flexibility upon ligand binding. Results We use a distance constraint model (DCM) to quantify the give and take between thermodynamic stability and mechanical flexibility across the bPBP family. Quantitative stability/flexibility relationships (QSFR) are readily evaluated because the DCM links mechanical and thermodynamic properties. We have previously demonstrated that QSFR is moderately conserved across a mesophilic/thermophilic RNase H pair, whereas the observed variance indicated that different enthalpy-entropy mechanisms allow similar mechanical response at their respective melting temperatures. Our predictions of heat capacity and free energy show marked diversity across the bPBP family. While backbone flexibility metrics are mostly conserved, cooperativity correlation (long-range couplings) also demonstrate considerable amount of variation. Upon ligand removal, heat capacity, melting point, and mechanical rigidity are, as expected, lowered. Nevertheless, significant differences are found in molecular cooperativity correlations that can be explained by the detailed nature of the hydrogen bond network. Conclusion Non-trivial mechanical and thermodynamic variation across the family is explained by differences within the underlying H-bond networks. The mechanism is simple; variation within the H-bond networks result in altered mechanical linkage properties that directly affect intrinsic flexibility. Moreover, varying numbers of H-bonds and their strengths control the likelihood for energetic fluctuations as H-bonds break and reform, thus directly affecting thermodynamic properties. Consequently, these results demonstrate how unexpected large differences, especially within cooperativity correlation, emerge from subtle differences within the underlying H-bond network. This inference is consistent with well-known results that show allosteric response within a family generally varies significantly. Identifying the hydrogen bond network as a critical determining factor for these large variances may lead to new methods that can predict such effects.
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Affiliation(s)
- Dennis R Livesay
- Department of Computer Science and Bioinformatics Research Center, University of North Carolina at Charlotte, Charlotte, NC, USA.
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29
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Balankin AS, Huerta OS. Entropic rigidity of a crumpling network in a randomly folded thin sheet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:051124. [PMID: 18643043 DOI: 10.1103/physreve.77.051124] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2007] [Revised: 03/07/2008] [Indexed: 05/26/2023]
Abstract
We have studied experimentally and theoretically the response of randomly folded hyperelastic and elastoplastic sheets on the uniaxial compression loading and the statistical properties of crumpling networks. The results of these studies reveal that the mechanical behavior of randomly folded sheets in the one-dimensional stress state is governed by the shape dependence of the crumpling network entropy. Following up on the original ideas by Edwards for granular materials, we derive an explicit force-compression relationship which precisely fits the experimental data for randomly folded matter. Experimental data also indicate that the entropic rigidity modulus scales as the power of the mass density of the folded ball with universal scaling exponent.
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Affiliation(s)
- Alexander S Balankin
- Fractal Mechanics Group, National Polytechnic Institute, Avanzados del Instituto Politécnico Nacional, México D.F., Mexico 07738
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30
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Istomin AY, Gromiha MM, Vorov OK, Jacobs DJ, Livesay DR. New insight into long-range nonadditivity within protein double-mutant cycles. Proteins 2008; 70:915-24. [PMID: 17803237 PMCID: PMC4667956 DOI: 10.1002/prot.21620] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Additivity principles in chemistry, biochemistry, and biophysics have been used extensively for decades. Nevertheless, it is well known that additivity frequently breaks down in complex biomacromolecules. Nonadditivity within protein double mutant free energy cycles of spatially close residue pairs is a generally well-understood phenomenon, whereas a robust description of nonadditivity extending over large distances remains to be developed. Here, we test the hypothesis that the mutational effects tend to be nonadditive if two structurally well-separated mutated residues belong to the same rigid cluster within the wild type protein, and additive if they are located within different clusters. We find the hypothesis to be statistically significant with P-values that range from 10(-5) to 10(-6). To the best of our knowledge, this result represents the first demonstration of a statistically significant preponderance for nonadditivity over long distances. These findings provide new insight into the origins of long-range nonadditivity in double mutant cycles, which complements the conventional wisdom that nonadditivity arises in double mutations involving contacting residues. Consequently, these results should have far-reaching implications for a proper understanding of protein stability, structure/function analyses, and protein design.
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Affiliation(s)
- Andrei Y. Istomin
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC, USA
| | - M. Michael Gromiha
- Computational Biology Research Center (CBRC), National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan
| | - Oleg K. Vorov
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC, USA
| | - Donald J. Jacobs
- Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC, USA
- Correspondence to: Donald J. Jacobs, Department of Physics and Optical Science, University of North Carolina, 9201 University City Blvd, Charlotte, NC 28223, USA, and Dennis R. Livesay, Department of Computer Science and Bioinformatics Research Center, University of North Carolina, 9201 University City Blvd, Charlotte, NC 28223, USA,
| | - Dennis R. Livesay
- Department of Computer Science and Bioinformatics Research Center, University of North Carolina, Charlotte, NC 28223, USA
- Correspondence to: Donald J. Jacobs, Department of Physics and Optical Science, University of North Carolina, 9201 University City Blvd, Charlotte, NC 28223, USA, and Dennis R. Livesay, Department of Computer Science and Bioinformatics Research Center, University of North Carolina, 9201 University City Blvd, Charlotte, NC 28223, USA,
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31
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Computational Methods - II. Biophys J 2008. [DOI: 10.1016/s0006-3495(08)79143-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
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32
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Protein Structure Prediction. Biophys J 2008. [DOI: 10.1016/s0006-3495(08)79195-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022] Open
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33
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Costa JR, Yaliraki SN. Role of Rigidity on the Activity of Proteinase Inhibitors and Their Peptide Mimics. J Phys Chem B 2006; 110:18981-8. [PMID: 16986893 DOI: 10.1021/jp0575299] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The Bowman-Birk inhibitors (BBIs) are a family of proteins that share a canonical loop structure whose presence in a conserved conformation is linked to their inhibitory activity. We study the conformational properties of the canonical loop using a graph theoretical approach as implemented in the floppy inclusions and rigid substructure topography (FIRST). We find that the canonical loop is an independent rigid cluster in the natural inhibitors. We have further used this technique to identify residues that play an important role in the structural rigidity of the protein by quantifying their contribution to the overall rigidity of the inhibitor. We find that the conserved elements among the natural and synthetic peptides are the ones that contribute the most to rigidity, even if they are located far from the active site, as rigidity effects are nonlinear and hence nonlocal. The results help to elucidate why certain mutations in the loop of the BBI produce peptides that fail to have the designed inhibitory activity.
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Affiliation(s)
- Joao R Costa
- Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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34
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Chubynsky MV, Brière MA, Mousseau N. Self-organization with equilibration: a model for the intermediate phase in rigidity percolation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:016116. [PMID: 16907160 DOI: 10.1103/physreve.74.016116] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2006] [Indexed: 05/11/2023]
Abstract
Recent experimental results for covalent glasses suggest the existence of an intermediate phase attributed to the self-organization of the glass network resulting from the tendency to minimize its internal stress. However, the exact nature of this experimentally measured phase remains unclear. We modified a previously proposed model of self-organization by generating a uniform sampling of stress-free networks. In our model, studied on a diluted triangular lattice, an unusual intermediate phase appears, in which both rigid and floppy networks have a chance to occur, a result also observed in a related model on a Bethe lattice by Barré et al[Phys. Rev. Lett. 94, 208701 (2005)]. Our results for the bond-configurational entropy of self-organized networks, which turns out to be only about 2% lower than that of random networks, suggest that a self-organized intermediate phase could be common in systems near the rigidity percolation threshold.
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Affiliation(s)
- M V Chubynsky
- Département de Physique, Université de Montréal, C.P. 6128, Succursale Centre-ville, Montréal, Québec, Canada H3C 3J7.
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Livesay DR, Jacobs DJ. Conserved quantitative stability/flexibility relationships (QSFR) in an orthologous RNase H pair. Proteins 2006; 62:130-43. [PMID: 16287093 PMCID: PMC4678005 DOI: 10.1002/prot.20745] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Many reports qualitatively describe conserved stability and flexibility profiles across protein families, but biophysical modeling schemes have not been available to robustly quantify both. Here we investigate an orthologous RNase H pair by using a minimal distance constraint model (DCM). The DCM is an all atom microscopic model [Jacobs and Dallakyan, Biophys J 2005;88(2):903-915] that accurately reproduces heat capacity measurements [Livesay et al., FEBS Lett 2004;576(3):468-476], and is unique in its ability to harmoniously calculate thermodynamic stability and flexibility in practical computing times. Consequently, quantified stability/flexibility relationships (QSFR) can be determined using the DCM. For the first time, a comparative QSFR analysis is performed, serving as a paradigm study to illustrate the utility of a QSFR analysis for elucidating evolutionarily conserved stability and flexibility profiles. Despite global conservation of QSFR profiles, distinct enthalpy-entropy compensation mechanisms are identified between the RNase H pair. In both cases, local flexibility metrics parallel H/D exchange experiments by correctly identifying the folding core and several flexible regions. Remarkably, at appropriately shifted temperatures (e.g., melting temperature), these differences lead to a global conservation in Landau free energy landscapes, which directly relate thermodynamic stability to global flexibility. Using ensemble-based sampling within free energy basins, rigidly, and flexibly correlated regions are quantified through cooperativity correlation plots. Five conserved flexible regions are identified within the structures of the orthologous pair. Evolutionary conservation of these flexibly correlated regions is strongly suggestive of their catalytic importance. Conclusions made herein are demonstrated to be robust with respect to the DCM parameterization.
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Affiliation(s)
- Dennis R. Livesay
- Department of Chemistry and Center for Macromolecular Modeling and Materials Design, California State Polytechnic University, Northridge, California
| | - Donald J. Jacobs
- Department of Physics and Astronomy, California State University, Northridge, California
- Correspondence to: Donald Jacobs, Department of Physics and Optical Science, University of North Carolina, Charlotte, 9201 University City Blvd, Charlotte, NC 28223.
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Jacobs DJ, Livesay DR, Hules J, Tasayco ML. Elucidating quantitative stability/flexibility relationships within thioredoxin and its fragments using a distance constraint model. J Mol Biol 2006; 358:882-904. [PMID: 16542678 PMCID: PMC4667950 DOI: 10.1016/j.jmb.2006.02.015] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2005] [Revised: 01/17/2006] [Accepted: 02/07/2006] [Indexed: 11/21/2022]
Abstract
Numerous quantitative stability/flexibility relationships, within Escherichia coli thioredoxin (Trx) and its fragments are determined using a minimal distance constraint model (DCM). A one-dimensional free energy landscape as a function of global flexibility reveals Trx to fold in a low-barrier two-state process, with a voluminous transition state. Near the folding transition temperature, the native free energy basin is markedly skewed to allow partial unfolded forms. Under native conditions the skewed shape is lost, and the protein forms a compact structure with some flexibility. Predictions on ten Trx fragments are generally consistent with experimental observations that they are disordered, and that complementary fragments reconstitute. A hierarchical unfolding pathway is uncovered using an exhaustive computational procedure of breaking interfacial cross-linking hydrogen bonds that span over a series of fragment dissociations. The unfolding pathway leads to a stable core structure (residues 22-90), predicted to act as a kinetic trap. Direct connection between degree of rigidity within molecular structure and non-additivity of free energy is demonstrated using a thermodynamic cycle involving fragments and their hierarchical unfolding pathway. Additionally, the model provides insight about molecular cooperativity within Trx in its native state, and about intermediate states populating the folding/unfolding pathways. Native state cooperativity correlation plots highlight several flexibly correlated regions, giving insight into the catalytic mechanism that facilitates access to the active site disulfide bond. Residual native cooperativity correlations are present in the core substructure, suggesting that Trx can function when it is partly unfolded. This natively disordered kinetic trap, interpreted as a molten globule, has a wide temperature range of metastability, and it is identified as the "slow intermediate state" observed in kinetic experiments. These computational results are found to be in overall agreement with a large array of experimental data.
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Affiliation(s)
- Donald J Jacobs
- Department of Physics and Optical Science, University of North Carolina, Charlotte, 9201 University City Blvd, Charlotte, NC 28227, USA.
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Mousseau N, Derreumaux P, Gilbert G. Navigation and analysis of the energy landscape of small proteins using the activation–relaxation technique. Phys Biol 2005; 2:S101-7. [PMID: 16280615 DOI: 10.1088/1478-3975/2/4/s04] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
The resolution of the protein folding problem has been tied to the development of a detailed understanding of the configurational energy or of the free energy landscape associated with these molecules. Using the activation-relaxation technique and a simplified energy model, we present here a detailed analysis of the energy landscape of 16-residue peptide that folds into a beta-hairpin. Our results support the concept of an energy landscape with an effective topology consistent with a scale-free network.
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Affiliation(s)
- Normand Mousseau
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, Case Postale 6128, Succursale Centre-Ville, Montréal, Québec, H3C 3J7, Canada
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Jacobs DJ, Dallakyan S. Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity. Biophys J 2004; 88:903-15. [PMID: 15542549 PMCID: PMC1305163 DOI: 10.1529/biophysj.104.048496] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Given the three-dimensional structure of a protein, its thermodynamic properties are calculated using a recently introduced distance constraint model (DCM) within a mean-field treatment. The DCM is constructed from a free energy decomposition that partitions microscopic interactions into a variety of constraint types, i.e., covalent bonds, salt-bridges, hydrogen-bonds, and torsional-forces, each associated with an enthalpy and entropy contribution. A Gibbs ensemble of accessible microstates is defined by a set of topologically distinct mechanical frameworks generated by perturbing away from the native constraint topology. The total enthalpy of a given framework is calculated as a linear sum of enthalpy components over all constraints present. Total entropy is generally a nonadditive property of free energy decompositions. Here, we calculate total entropy as a linear sum of entropy components over a set of independent constraints determined by a graph algorithm that builds up a mechanical framework one constraint at a time, placing constraints with lower entropy before those with greater entropy. This procedure provides a natural mechanism for enthalpy-entropy compensation. A minimal DCM with five phenomenological parameters is found to capture the essential physics relating thermodynamic response to network rigidity. Moreover, two parameters are fixed by simultaneously fitting to heat capacity curves for histidine binding protein and ubiquitin at five different pH conditions. The three free parameter DCM provides a quantitative characterization of conformational flexibility consistent with thermodynamic stability. It is found that native hydrogen bond topology provides a key signature in governing molecular cooperativity and the folding-unfolding transition.
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Affiliation(s)
- Donald J Jacobs
- Physics and Astronomy Department, California State University, Northridge, California, USA.
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Livesay DR, Dallakyan S, Wood GG, Jacobs DJ. A flexible approach for understanding protein stability. FEBS Lett 2004; 576:468-76. [PMID: 15498582 DOI: 10.1016/j.febslet.2004.09.057] [Citation(s) in RCA: 64] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2004] [Accepted: 09/20/2004] [Indexed: 11/25/2022]
Abstract
A distance constraint model (DCM) is presented that identifies flexible regions within protein structure consistent with specified thermodynamic condition. The DCM is based on a rigorous free energy decomposition scheme representing structure as fluctuating constraint topologies. Entropy non-additivity is problematic for naive decompositions, limiting the success of heat capacity predictions. The DCM resolves non-additivity by summing over independent entropic components determined by an efficient network-rigidity algorithm. A minimal 3-parameter DCM is demonstrated to accurately reproduce experimental heat capacity curves. Free energy landscapes and quantitative stability-flexibility relationships are obtained in terms of global flexibility. Several connections to experiment are made.
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Affiliation(s)
- D R Livesay
- Department of Chemistry, California State Polytechnic University, Pomona, 3801 W Temple Ave, Pomona, CA 91768, USA
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Jacobs DJ, Wood GG. Understanding the alpha-helix to coil transition in polypeptides using network rigidity: predicting heat and cold denaturation in mixed solvent conditions. Biopolymers 2004; 75:1-31. [PMID: 15307195 PMCID: PMC4667961 DOI: 10.1002/bip.20102] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Thermodynamic stability in polypeptides is described using a novel Distance Constraint Model (DCM). Here, microscopic interactions are represented as constraints. A topological arrangement of constraints define a mechanical framework. Each constraint in the framework is associated with an enthalpic and entropic contribution. All accessible topological arrangements of distance constraints form an ensemble of mechanical frameworks, each representing a microstate of the polypeptide. A partition function is calculated exactly using a transfer matrix approach, where in many respects the DCM is similar to the Lifson-Roig model. The crucial difference is that the effect of network rigidity is explicitly calculated for each mechanical framework in the ensemble. Network rigidity is a mechanical interaction that provides a mechanism for long-range molecular cooperativity and enables a proper treatment of the nonadditivity of a microscopic free energy decomposition. Accounting for (1) helix <--> coil conformation changes along the backbone similar to the Lifson-Roig model, (2) i to i + 4 hydrogen-bond formation <--> breaking similar to the Zimm-Bragg model, and (3) structured <--> unstructured solvent interaction (hydration effects), a six-parameter DCM describes normal and inverted helix-coil transitions in polypeptides. Under suitable mixed solvent conditions heat and cold denaturation is predicted. Model parameters are fitted to experimental data showing different degrees of cold denaturation in monomeric polypeptides in aqueous hexafluoroisopropanol (HFIP) solution at various HFIP concentrations. By assuming a linear HFIP concentration dependence (up to 6% by mole fraction) on model parameters, all essential experimentally observed features are captured.
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Affiliation(s)
- Donald J Jacobs
- Physics and Astronomy Department, California State University, Northridge, 18111 Nordhoff Street, Northridge, CA 91330-82684, USA.
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