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Chen M, Chen X, Schafer NP, Clementi C, Komives EA, Ferreiro DU, Wolynes PG. Surveying biomolecular frustration at atomic resolution. Nat Commun 2020; 11:5944. [PMID: 33230150 PMCID: PMC7683549 DOI: 10.1038/s41467-020-19560-9] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Accepted: 10/13/2020] [Indexed: 01/12/2023] Open
Abstract
To function, biomolecules require sufficient specificity of interaction as well as stability to live in the cell while still being able to move. Thermodynamic stability of only a limited number of specific structures is important so as to prevent promiscuous interactions. The individual interactions in proteins, therefore, have evolved collectively to give funneled minimally frustrated landscapes but some strategic parts of biomolecular sequences located at specific sites in the structure have been selected to be frustrated in order to allow both motion and interaction with partners. We describe a framework efficiently to quantify and localize biomolecular frustration at atomic resolution by examining the statistics of the energy changes that occur when the local environment of a site is changed. The location of patches of highly frustrated interactions correlates with key biological locations needed for physiological function. At atomic resolution, it becomes possible to extend frustration analysis to protein-ligand complexes. At this resolution one sees that drug specificity is correlated with there being a minimally frustrated binding pocket leading to a funneled binding landscape. Atomistic frustration analysis provides a route for screening for more specific compounds for drug discovery. The analysis of biomolecular frustration yielded insights into several aspects of protein behavior. Here the authors describe a framework to efficiently quantify and localize biomolecular frustration within proteins at atomic resolution, and observe that drug specificity is correlated with a minimally frustrated binding pocket leading to a funneled binding landscape.
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Affiliation(s)
- Mingchen Chen
- Center for Theoretical Biological Physics, Rice University, Houston, TX, USA
| | - Xun Chen
- Center for Theoretical Biological Physics, Department of Chemistry, Rice University, Houston, TX, USA
| | - Nicholas P Schafer
- Center for Theoretical Biological Physics, Department of Chemistry, Rice University, Houston, TX, USA
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Department of Chemistry, Rice University, Houston, TX, USA
| | - Elizabeth A Komives
- Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, CA, USA
| | - Diego U Ferreiro
- Protein Physiology Laboratory, University of Buenos Aires, Buenos Aires, Argentina
| | - Peter G Wolynes
- Center for Theoretical Biological Physics, Department of Chemistry, Rice University, Houston, TX, USA. .,Department of Biosciences, Rice University, Houston, TX, USA.
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Liwo A, Czaplewski C, Sieradzan AK, Lubecka EA, Lipska AG, Golon Ł, Karczyńska A, Krupa P, Mozolewska MA, Makowski M, Ganzynkowicz R, Giełdoń A, Maciejczyk M. Scale-consistent approach to the derivation of coarse-grained force fields for simulating structure, dynamics, and thermodynamics of biopolymers. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 170:73-122. [PMID: 32145953 DOI: 10.1016/bs.pmbts.2019.12.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
In this chapter the scale-consistent approach to the derivation of coarse-grained force fields developed in our laboratory is presented, in which the effective energy function originates from the potential of mean force of the system under consideration and embeds atomistically detailed interactions in the resulting energy terms through use of Kubo's cluster-cumulant expansion, appropriate selection of the major degrees of freedom to be averaged out in the derivation of analytical approximations to the energy terms, and appropriate expression of the interaction energies at the all-atom level in these degrees of freedom. Our approach enables the developers to find correct functional forms of the effective coarse-grained energy terms, without having to import them from all-atom force fields or deriving them on a heuristic basis. In particular, the energy terms derived in such a way exhibit correct dependence on coarse-grained geometry, in particular on site orientation. Moreover, analytical formulas for the multibody (correlation) terms, which appear to be crucial for coarse-grained modeling of many of the regular structures such as, e.g., protein α-helices and β-sheets, can be derived in a systematic way. Implementation of the developed theory to the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules, which consists of the UNRES (for proteins), NARES-2P (for nucleic acids), and SUGRES-1P (for polysaccharides) components, and is being developed in our laboratory is described. Successful applications of UNICORN to the prediction of protein structure, simulating the folding and stability of proteins and nucleic acids, and solving biological problems are discussed.
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Affiliation(s)
- Adam Liwo
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland; School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea.
| | | | - Adam K Sieradzan
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland; School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Republic of Korea
| | - Emilia A Lubecka
- Institute of Informatics, Faculty of Mathematics, Physics, and Informatics, University of Gdańsk, Gdańsk, Poland
| | | | - Łukasz Golon
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland
| | | | - Paweł Krupa
- Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
| | | | | | | | - Artur Giełdoń
- Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland
| | - Maciej Maciejczyk
- Department of Physics and Biophysics, Faculty of Food Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland
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Krupa P, Hałabis A, Żmudzińska W, Ołdziej S, Scheraga HA, Liwo A. Maximum Likelihood Calibration of the UNRES Force Field for Simulation of Protein Structure and Dynamics. J Chem Inf Model 2017; 57:2364-2377. [DOI: 10.1021/acs.jcim.7b00254] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Paweł Krupa
- Faculty of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, United States
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland
| | - Anna Hałabis
- Laboratory of Biopolymer
Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Abrahama 58, 80-307 Gdańsk, Poland
| | - Wioletta Żmudzińska
- Laboratory of Biopolymer
Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Abrahama 58, 80-307 Gdańsk, Poland
| | - Stanisław Ołdziej
- Laboratory of Biopolymer
Structure, Intercollegiate Faculty of Biotechnology, University of Gdańsk and Medical University of Gdańsk, Abrahama 58, 80-307 Gdańsk, Poland
| | - Harold A. Scheraga
- Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853-1301, United States
| | - Adam Liwo
- Faculty of Chemistry, University of Gdańsk, ul. Wita Stwosza 63, 80-308 Gdańsk, Poland
- School of Computational Sciences, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea
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Prentiss MC, Hardin C, Eastwood MP, Zong C, Wolynes PG. Protein Structure Prediction: The Next Generation. J Chem Theory Comput 2015; 2:705-16. [PMID: 26626675 DOI: 10.1021/ct0600058] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Over the last 10-15 years a general understanding of the chemical reaction of protein folding has emerged from statistical mechanics. The lessons learned from protein folding kinetics based on energy landscape ideas have benefited protein structure prediction, in particular the development of coarse grained models. We survey results from blind structure prediction. We explore how second generation prediction energy functions can be developed by introducing information from an ensemble of previously simulated structures. This procedure relies on the assumption of a funneled energy landscape keeping with the principle of minimal frustration. First generation simulated structures provide an improved input for associative memory energy functions in comparison to the experimental protein structures chosen on the basis of sequence alignment.
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Affiliation(s)
- Michael C Prentiss
- Center for Theoretical Biological Physics, La Jolla, California 92093, Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093, Department of Physics, University of California, La Jolla, California 92093, and Department of Chemistry, University of Illinois, Urbana [Formula: see text] Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801
| | - Corey Hardin
- Center for Theoretical Biological Physics, La Jolla, California 92093, Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093, Department of Physics, University of California, La Jolla, California 92093, and Department of Chemistry, University of Illinois, Urbana [Formula: see text] Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801
| | - Michael P Eastwood
- Center for Theoretical Biological Physics, La Jolla, California 92093, Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093, Department of Physics, University of California, La Jolla, California 92093, and Department of Chemistry, University of Illinois, Urbana [Formula: see text] Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801
| | - Chenghang Zong
- Center for Theoretical Biological Physics, La Jolla, California 92093, Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093, Department of Physics, University of California, La Jolla, California 92093, and Department of Chemistry, University of Illinois, Urbana [Formula: see text] Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801
| | - Peter G Wolynes
- Center for Theoretical Biological Physics, La Jolla, California 92093, Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093, Department of Physics, University of California, La Jolla, California 92093, and Department of Chemistry, University of Illinois, Urbana [Formula: see text] Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801
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Schafer NP, Kim BL, Zheng W, Wolynes PG. Learning To Fold Proteins Using Energy Landscape Theory. Isr J Chem 2014; 54:1311-1337. [PMID: 25308991 PMCID: PMC4189132 DOI: 10.1002/ijch.201300145] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
This review is a tutorial for scientists interested in the problem of protein structure prediction, particularly those interested in using coarse-grained molecular dynamics models that are optimized using lessons learned from the energy landscape theory of protein folding. We also present a review of the results of the AMH/AMC/AMW/AWSEM family of coarse-grained molecular dynamics protein folding models to illustrate the points covered in the first part of the article. Accurate coarse-grained structure prediction models can be used to investigate a wide range of conceptual and mechanistic issues outside of protein structure prediction; specifically, the paper concludes by reviewing how AWSEM has in recent years been able to elucidate questions related to the unusual kinetic behavior of artificially designed proteins, multidomain protein misfolding, and the initial stages of protein aggregation.
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Affiliation(s)
- N P Schafer
- Department of Physics, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - B L Kim
- Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - W Zheng
- Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - P G Wolynes
- Department of Physics, Rice University, Houston, TX 77005, USA ; Department of Chemistry, Rice University, Houston, TX 77005, USA ; Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
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Abstract
We introduce a theoretical framework that exploits the ever-increasing genomic sequence information for protein structure prediction. Structure-based models are modified to incorporate constraints by a large number of non-local contacts estimated from direct coupling analysis (DCA) of co-evolving genomic sequences. A simple hybrid method, called DCA-fold, integrating DCA contacts with an accurate knowledge of local information (e.g., the local secondary structure) is sufficient to fold proteins in the range of 1-3 Å resolution.
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Lätzer J, Eastwood MP, Wolynes PG. Simulation studies of the fidelity of biomolecular structure ensemble recreation. J Chem Phys 2007; 125:214905. [PMID: 17166047 DOI: 10.1063/1.2375121] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We examine the ability of Bayesian methods to recreate structural ensembles for partially folded molecules from averaged data. Specifically we test the ability of various algorithms to recreate different transition state ensembles for folding proteins using a multiple replica simulation algorithm using input from "gold standard" reference ensembles that were first generated with a Go-like Hamiltonian having nonpairwise additive terms. A set of low resolution data, which function as the "experimental" phi values, were first constructed from this reference ensemble. The resulting phi values were then treated as one would treat laboratory experimental data and were used as input in the replica reconstruction algorithm. The resulting ensembles of structures obtained by the replica algorithm were compared to the gold standard reference ensemble, from which those "data" were, in fact, obtained. It is found that for a unimodal transition state ensemble with a low barrier, the multiple replica algorithm does recreate the reference ensemble fairly successfully when no experimental error is assumed. The Kolmogorov-Smirnov test as well as principal component analysis show that the overlap of the recovered and reference ensembles is significantly enhanced when multiple replicas are used. Reduction of the multiple replica ensembles by clustering successfully yields subensembles with close similarity to the reference ensembles. On the other hand, for a high barrier transition state with two distinct transition state ensembles, the single replica algorithm only samples a few structures of one of the reference ensemble basins. This is due to the fact that the phi values are intrinsically ensemble averaged quantities. The replica algorithm with multiple copies does sample both reference ensemble basins. In contrast to the single replica case, the multiple replicas are constrained to reproduce the average phi values, but allow fluctuations in phi for each individual copy. These fluctuations facilitate a more faithful sampling of the reference ensemble basins. Finally, we test how robustly the reconstruction algorithm can function by introducing errors in phi comparable in magnitude to those suggested by some authors. In this circumstance we observe that the chances of ensemble recovery with the replica algorithm are poor using a single replica, but are improved when multiple copies are used. A multimodal transition state ensemble, however, turns out to be more sensitive to large errors in phi (if appropriately gauged) and attempts at successful recreation of the reference ensemble with simple replica algorithms can fall short.
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Affiliation(s)
- Joachim Lätzer
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093-0365, USA.
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Cho SS, Levy Y, Wolynes PG. P versus Q: structural reaction coordinates capture protein folding on smooth landscapes. Proc Natl Acad Sci U S A 2006; 103:586-91. [PMID: 16407126 PMCID: PMC1334664 DOI: 10.1073/pnas.0509768103] [Citation(s) in RCA: 174] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Minding your p's and q's has become as important to protein-folding theorists as it is for those being instructed in the rules of etiquette. To assess the quality of structural reaction coordinates in predicting the transition-state ensemble (TSE) of protein folding, we benchmarked the accuracy of four structural reaction coordinates against the kinetic measure P(fold), whose value of 0.50 defines the stochastic separatrix for a two-state folding mechanism. For two proteins that fold by a simple two-state mechanism, c-src SH3 and CI-2, the Phi-values of the TSEs predicted by native topology-based reaction coordinates (including Q, the fraction of native contacts) are almost identical to those of the TSE based on P(fold), with correlation coefficients of >0.90. For proteins with complex folding mechanisms that have especially broad, asymmetrical free energy barriers such as the designed 3-ankyrin repeating protein (3ANK) or proteins with distinct intermediates such as cyanovirin-N (CV-N), we show that the ensemble of structures with P(fold) = 0.50 generally does not include the chemically relevant transition states. This weakness of P(fold) limits its usefulness in protein folding studies. For such systems, elucidating the essential features of folding mechanisms requires using multiple reaction coordinates, although the number is still rather small. At the same time, for simple folding mechanisms, there is no indication of superiority for P(fold) over structurally chosen and thermodynamically relevant reaction coordinates that correctly measure the degree of nativeness.
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Affiliation(s)
- Samuel S Cho
- Center for Theoretical Biological Physics and Department of Chemistry, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
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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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Papoian GA, Ulander J, Eastwood MP, Luthey-Schulten Z, Wolynes PG. Water in protein structure prediction. Proc Natl Acad Sci U S A 2004; 101:3352-7. [PMID: 14988499 PMCID: PMC373465 DOI: 10.1073/pnas.0307851100] [Citation(s) in RCA: 233] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Proteins have evolved to use water to help guide folding. A physically motivated, nonpairwise-additive model of water-mediated interactions added to a protein structure prediction Hamiltonian yields marked improvement in the quality of structure prediction for larger proteins. Free energy profile analysis suggests that long-range water-mediated potentials guide folding and smooth the underlying folding funnel. Analyzing simulation trajectories gives direct evidence that water-mediated interactions facilitate native-like packing of supersecondary structural elements. Long-range pairing of hydrophilic groups is an integral part of protein architecture. Specific water-mediated interactions are a universal feature of biomolecular recognition landscapes in both folding and binding.
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Affiliation(s)
- Garegin A Papoian
- Department of Chemistry and Biochemistry and Center for Theoretical Biological Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0371, USA
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