1
|
Ooka K, Liu R, Arai M. The Wako-Saitô-Muñoz-Eaton Model for Predicting Protein Folding and Dynamics. Molecules 2022; 27:molecules27144460. [PMID: 35889332 PMCID: PMC9319528 DOI: 10.3390/molecules27144460] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 07/07/2022] [Accepted: 07/08/2022] [Indexed: 11/16/2022] Open
Abstract
Despite the recent advances in the prediction of protein structures by deep neutral networks, the elucidation of protein-folding mechanisms remains challenging. A promising theory for describing protein folding is a coarse-grained statistical mechanical model called the Wako-Saitô-Muñoz-Eaton (WSME) model. The model can calculate the free-energy landscapes of proteins based on a three-dimensional structure with low computational complexity, thereby providing a comprehensive understanding of the folding pathways and the structure and stability of the intermediates and transition states involved in the folding reaction. In this review, we summarize previous and recent studies on protein folding and dynamics performed using the WSME model and discuss future challenges and prospects. The WSME model successfully predicted the folding mechanisms of small single-domain proteins and the effects of amino-acid substitutions on protein stability and folding in a manner that was consistent with experimental results. Furthermore, extended versions of the WSME model were applied to predict the folding mechanisms of multi-domain proteins and the conformational changes associated with protein function. Thus, the WSME model may contribute significantly to solving the protein-folding problem and is expected to be useful for predicting protein folding, stability, and dynamics in basic research and in industrial and medical applications.
Collapse
Affiliation(s)
- Koji Ooka
- Department of Physics, Graduate School of Science, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan;
- Komaba Organization for Educational Excellence, College of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan
| | - Runjing Liu
- Department of Life Sciences, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan;
| | - Munehito Arai
- Department of Physics, Graduate School of Science, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan;
- Department of Life Sciences, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan;
- Correspondence:
| |
Collapse
|
2
|
Ancona M, Bentivoglio A, Caraglio M, Gonnella G, Pelizzola A. Emergence of effective temperatures in an out-of-equilibrium model of biopolymer folding. Phys Rev E 2021; 103:062415. [PMID: 34271706 DOI: 10.1103/physreve.103.062415] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Accepted: 05/26/2021] [Indexed: 11/07/2022]
Abstract
We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA or protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly interacting thermal bath. Notably, this "kinetic" temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple four-state Markov model which describes the long-time behavior of the RNA molecule.
Collapse
Affiliation(s)
- Marco Ancona
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Alessandro Bentivoglio
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
| | - Michele Caraglio
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Giuseppe Gonnella
- Dipartimento di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, 70126 Bari, Italy
| | - Alessandro Pelizzola
- Dipartimento Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.,INFN, Sezione di Torino, via Pietro Giuria 1, 10125 Torino, Italy
| |
Collapse
|
3
|
Yang C, Jang S, Pak Y. Computational Probing of Temperature-Dependent Unfolding of a Small Globular Protein: From Cold to Heat Denaturation. J Chem Theory Comput 2020; 17:515-524. [DOI: 10.1021/acs.jctc.0c01046] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Changwon Yang
- Department of Chemistry, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, South Korea
| | - Soonmin Jang
- Department of Chemistry, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, South Korea
| | - Youngshang Pak
- Department of Chemistry and Institute of Functional Materials, Pusan National University, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan 46241, South Korea
| |
Collapse
|
4
|
Iglesias-Bexiga M, Szczepaniak M, Sánchez de Medina C, Cobos ES, Godoy-Ruiz R, Martinez JC, Muñoz V, Luque I. Protein Folding Cooperativity and Thermodynamic Barriers of the Simplest β-Sheet Fold: A Survey of WW Domains. J Phys Chem B 2018; 122:11058-11071. [PMID: 29985628 DOI: 10.1021/acs.jpcb.8b05198] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Theory and experiments have shown that microsecond folding proteins exhibit characteristic thermodynamic properties that reflect the limited cooperativity of folding over marginal barriers (downhill folding). Those studies have mostly focused on proteins with large α-helical contents and small size, which tend to be the fastest folders. A key open question is whether such properties are also present in the fastest all-β proteins. We address this issue by investigating the unfolding thermodynamics of a collection of WW domains as representatives of the simplest β-sheet fold. WW domains are small microsecond folders, although they do not fold as fast as their α-helical counterparts. In previous work on the NEDD4-WW4 domain, we reported deviations from two-state thermodynamics that were less apparent and thus suggestive of an incipient downhill scenario. Here we investigate the unfolding thermodynamics of four other WW domains (NEDD4-WW3, YAP65-WW1(L30K), FBP11-WW1, and FBP11-WW2) by performing all of the thermodynamic tests for downhill folding that have been previously developed on α-helical proteins. This set of five WW domains shares low sequence identity and include examples from two specificity classes, thus providing a comprehensive survey. Thermodynamic analysis of the four new WW domains consistently reveals all of the properties of downhill folding equilibria, which are in all cases more marked than what we found before in NEDD4-WW4. Our results show that fast-folding all-β proteins do share limited cooperativity and gradual unfolding thermodynamics with fast α-helical proteins and suggest that the free energy barrier to folding of natural proteins is mostly determined by size and fold topology and much less by the specific amino acid sequence.
Collapse
Affiliation(s)
- Manuel Iglesias-Bexiga
- Department of Physical Chemistry and Institute of Biotechnology , University of Granada , Granada 18010 , Spain
| | - Malwina Szczepaniak
- Centro Nacional de Biotecnología , Consejo Superior de Investigaciones Científicas (CSIC) , Darwin 3 , 28049 Madrid , Spain
| | - Celia Sánchez de Medina
- Centro Nacional de Biotecnología , Consejo Superior de Investigaciones Científicas (CSIC) , Darwin 3 , 28049 Madrid , Spain
| | - Eva S Cobos
- Department of Physical Chemistry and Institute of Biotechnology , University of Granada , Granada 18010 , Spain
| | - Raquel Godoy-Ruiz
- Department of Chemistry & Biochemistry , University of Maryland , College Park , Maryland 20742 , United States
| | - Jose C Martinez
- Department of Physical Chemistry and Institute of Biotechnology , University of Granada , Granada 18010 , Spain
| | - Victor Muñoz
- Centro Nacional de Biotecnología , Consejo Superior de Investigaciones Científicas (CSIC) , Darwin 3 , 28049 Madrid , Spain.,Department of Bioengineering , University of California Merced , Merced , California 95343 , United States
| | - Irene Luque
- Department of Physical Chemistry and Institute of Biotechnology , University of Granada , Granada 18010 , Spain
| |
Collapse
|
5
|
Hutton RD, Wilkinson J, Faccin M, Sivertsson EM, Pelizzola A, Lowe AR, Bruscolini P, Itzhaki LS. Mapping the Topography of a Protein Energy Landscape. J Am Chem Soc 2015; 137:14610-25. [PMID: 26561984 DOI: 10.1021/jacs.5b07370] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Protein energy landscapes are highly complex, yet the vast majority of states within them tend to be invisible to experimentalists. Here, using site-directed mutagenesis and exploiting the simplicity of tandem-repeat protein structures, we delineate a network of these states and the routes between them. We show that our target, gankyrin, a 226-residue 7-ankyrin-repeat protein, can access two alternative (un)folding pathways. We resolve intermediates as well as transition states, constituting a comprehensive series of snapshots that map early and late stages of the two pathways and show both to be polarized such that the repeat array progressively unravels from one end of the molecule or the other. Strikingly, we find that the protein folds via one pathway but unfolds via a different one. The origins of this behavior can be rationalized using the numerical results of a simple statistical mechanics model that allows us to visualize the equilibrium behavior as well as single-molecule folding/unfolding trajectories, thereby filling in the gaps that are not accessible to direct experimental observation. Our study highlights the complexity of repeat-protein folding arising from their symmetrical structures; at the same time, however, this structural simplicity enables us to dissect the complexity and thereby map the precise topography of the energy landscape in full breadth and remarkable detail. That we can recapitulate the key features of the folding mechanism by computational analysis of the native structure alone will help toward the ultimate goal of designed amino-acid sequences with made-to-measure folding mechanisms-the Holy Grail of protein folding.
Collapse
Affiliation(s)
- Richard D Hutton
- Hutchison/MRC Research Centre , Hills Road, Cambridge CB2 0XZ, U.K
| | - James Wilkinson
- Hutchison/MRC Research Centre , Hills Road, Cambridge CB2 0XZ, U.K
| | - Mauro Faccin
- ICTEAM, Université Catholique de Lovain , Euler Building 4, Avenue Lemaître, B-1348 Louvain-la-Neuve, Belgium
| | - Elin M Sivertsson
- Department of Pharmacology, University of Cambridge , Tennis Court Road, Cambridge CB2 1PD, U.K
| | - Alessandro Pelizzola
- Dipartimento di Scienza Applicata e Tecnologia, CNISM, and Center for Computational Studies, Politecnico di Torino , Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.,INFN, Sezione di Torino , via Pietro Giuria 1, I-10125 Torino, Italy.,Human Genetics Foundation (HuGeF) , Via Nizza 52, I-10126 Torino, Italy
| | - Alan R Lowe
- Institute of Structural and Molecular Biology and London Centre for Nanotechnology, University College London and Birkbeck College , London WC1E 7HX, U.K
| | - Pierpaolo Bruscolini
- Departamento de Física Teórica and Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza , c/Mariano Esquillor s/n, 50018 Zaragoza, Spain
| | - Laura S Itzhaki
- Department of Pharmacology, University of Cambridge , Tennis Court Road, Cambridge CB2 1PD, U.K
| |
Collapse
|
6
|
Lee J. Exact partition function zeros of the Wako-Saitô-Muñoz-Eaton protein model. PHYSICAL REVIEW LETTERS 2013; 110:248101. [PMID: 25165962 DOI: 10.1103/physrevlett.110.248101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2012] [Indexed: 06/03/2023]
Abstract
I compute exact partition function zeros of the Wako-Saitô-Muñoz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, by using both analytic and numerical methods. Two-state and barrierless downhill folding transitions can be distinguished by a gap in the distribution of zeros at the positive real axis.
Collapse
Affiliation(s)
- Julian Lee
- Department of Bioinformatics and Life Science, Soongsil University, Seoul 156-743, Korea
| |
Collapse
|
7
|
Lin C, Culik RM, Gai F. Using VIPT-jump to distinguish between different folding mechanisms: application to BBL and a Trpzip. J Am Chem Soc 2013; 135:7668-73. [PMID: 23642153 PMCID: PMC3706100 DOI: 10.1021/ja401473m] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Protein folding involves a large number of sequential molecular steps or conformational substates. Thus, experimental characterization of the underlying folding energy landscape for any given protein is difficult. Herein, we present a new method that can be used to determine the major characteristics of the folding energy landscape in question, e.g., to distinguish between activated and barrierless downhill folding scenarios. This method is based on the idea that the conformational relaxation kinetics of different folding mechanisms at a given final condition will show different dependences on the initial condition. We show, using both simulation and experiment, that it is possible to differentiate between disparate kinetic folding models by comparing temperature jump (T-jump) relaxation traces obtained with a fixed final temperature and varied initial temperatures, which effectively varies the initial potential (VIP) of the system of interest. We apply this method (hereafter refer to as VIPT-jump) to two model systems, tryptophan zipper (Trpzip)-2c and BBL, and our results show that BBL exhibits characteristics of barrierless downhill folding, whereas Trpzip-2c folding encounters a free energy barrier. In addition, using the T-jump data of BBL we are able to provide, via Langevin dynamics simulations, a realistic estimate of its conformational diffusion coefficient.
Collapse
Affiliation(s)
- Chun–Wei Lin
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104
| | - Robert M. Culik
- Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA 19104
| | - Feng Gai
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104
| |
Collapse
|
8
|
Aioanei D, Brucale M, Tessari I, Bubacco L, Samorì B. Worm-like Ising model for protein mechanical unfolding under the effect of osmolytes. Biophys J 2012; 102:342-50. [PMID: 22339871 PMCID: PMC3260691 DOI: 10.1016/j.bpj.2011.12.007] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2011] [Revised: 10/12/2011] [Accepted: 12/06/2011] [Indexed: 10/14/2022] Open
Abstract
We show via single-molecule mechanical unfolding experiments that the osmolyte glycerol stabilizes the native state of the human cardiac I27 titin module against unfolding without shifting its unfolding transition state on the mechanical reaction coordinate. Taken together with similar findings on the immunoglobulin-binding domain of streptococcal protein G (GB1), these experimental results suggest that osmolytes act on proteins through a common mechanism that does not entail a shift of their unfolding transition state. We investigate the above common mechanism via an Ising-like model for protein mechanical unfolding that adds worm-like-chain behavior to a recent generalization of the Wako-Saitô-Muñoz-Eaton model with support for group-transfer free energies. The thermodynamics of the model are exactly solvable, while protein kinetics under mechanical tension can be simulated via Monte Carlo algorithms. Notably, our force-clamp and velocity-clamp simulations exhibit no shift in the position of the unfolding transition state of GB1 and I27 under the effect of various osmolytes. The excellent agreement between experiment and simulation strongly suggests that osmolytes do not assume a structural role at the mechanical unfolding transition state of proteins, acting instead by adjusting the solvent quality for the protein chain analyte.
Collapse
Affiliation(s)
- Daniel Aioanei
- Department of Biochemistry G. Moruzzi, University of Bologna, Bologna, Italy.
| | | | | | | | | |
Collapse
|
9
|
Caraglio M, Pelizzola A. Effects of confinement on thermal stability and folding kinetics in a simple Ising-like model. Phys Biol 2012; 9:016006. [PMID: 22313579 DOI: 10.1088/1478-3975/9/1/016006] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
In a cellular environment, confinement and macromolecular crowding play an important role in thermal stability and folding kinetics of a protein. We have resorted to a generalized version of the Wako-Saitô-Muñoz-Eaton model for protein folding to study the behavior of six different protein structures confined between two walls. Changing the distance 2R between the walls, we found, in accordance with previous studies, two confinement regimes: starting from large R and decreasing R, confinement first enhances the stability of the folded state as long as this is compact and until a given value of R; then a further decrease of R leads to a decrease of folding temperature and folding rate. We found that in the low confinement regime, both unfolding temperatures and logarithm of folding rates scale as R(-γ) where γ values lie in between 1.42 and 2.35.
Collapse
Affiliation(s)
- M Caraglio
- Dipartimento di Fisica, CNISM and Center for Computational Studies, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.
| | | |
Collapse
|
10
|
Faccin M, Bruscolini P, Pelizzola A. Analysis of the equilibrium and kinetics of the ankyrin repeat protein myotrophin. J Chem Phys 2011; 134:075102. [PMID: 21341874 DOI: 10.1063/1.3535562] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We apply the Wako-Saito-Muñoz-Eaton model to the study of myotrophin, a small ankyrin repeat protein, whose folding equilibrium and kinetics have been recently characterized experimentally. The model, which is a native-centric with binary variables, provides a finer microscopic detail than the Ising model that has been recently applied to some different repeat proteins, while being still amenable for an exact solution. In partial agreement with the experiments, our results reveal a weakly three-state equilibrium and a two-state-like kinetics of the wild-type protein despite the presence of a nontrivial free-energy profile. These features appear to be related to a careful "design" of the free-energy landscape, so that mutations can alter this picture, stabilizing some intermediates and changing the position of the rate-limiting step. Also, the experimental findings of two alternative pathways, an N-terminal and a C-terminal one, are qualitatively confirmed, even if the variations in the rates upon the experimental mutations cannot be quantitatively reproduced. Interestingly, the folding and unfolding pathways appear to be different, even if closely related: a property that is not generally considered in the phenomenological interpretation of the experimental data.
Collapse
Affiliation(s)
- Mauro Faccin
- Departamento de Física Teórica & Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza, Spain
| | | | | |
Collapse
|
11
|
Aioanei D, Tessari I, Bubacco L, Samorì B, Brucale M. Observing the osmophobic effect in action at the single molecule level. Proteins 2011; 79:2214-23. [DOI: 10.1002/prot.23045] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2010] [Revised: 03/04/2011] [Accepted: 03/13/2011] [Indexed: 11/08/2022]
|
12
|
Mi D, Meng WQ, Sun YQ. Unifying model for two-state and downhill protein folding. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:041901. [PMID: 21599197 DOI: 10.1103/physreve.83.041901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2010] [Revised: 09/06/2010] [Indexed: 05/30/2023]
Abstract
A protein-folding model is proposed at the amino acid level, in which the folding process is divided into two successive stages: the rate-determining step, dominated by the "stochastic interactions"of solvent molecules, and the rapid phase, dominated by the "order interactions"among atoms in polypeptide. The master equation approach is used to investigate the folding kinetics, and an analytical treatment of the master equation yields a simple three-parameter expression for folding time. It is found that both two-state and downhill protein-folding kinetics can be described by a unifying model.
Collapse
Affiliation(s)
- D Mi
- Department of Physics, Dalian Maritime University, Dalian 116026, People's Republic of China.
| | | | | |
Collapse
|
13
|
Bruscolini P, Naganathan AN. Quantitative prediction of protein folding behaviors from a simple statistical model. J Am Chem Soc 2011; 133:5372-9. [PMID: 21417380 DOI: 10.1021/ja110884m] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The statistical nature of the protein folding process requires the use of equally detailed yet simple models that lend themselves to characterize experiments. One such model is the Wako-Saitô-Muñoz-Eaton model, that we extend here to include solvation effects (WSME-S), introduced via empirical terms. We employ the novel version to analyze the folding of two proteins, gpW and SH3, that have similar size and thermodynamic stability but with the former folding 3 orders of magnitude faster than SH3. A quantitative analysis reveals that gpW presents at most marginal barriers, in contrast to SH3 that folds following a simple two-state approximation. We reproduce the observed experimental differences in melting temperature in gpW as seen by different experimental spectroscopic probes and the shape of the rate-temperature plot. In parallel, we predict the folding complexity expected in gpW from the analysis of both the residue-level thermodynamics and kinetics. SH3 serves as a stringent control with neither folding complexity nor dispersion in melting temperatures being observed. The extended model presented here serves as an ideal tool not only to characterize folding data but also to make experimentally testable predictions.
Collapse
Affiliation(s)
- Pierpaolo Bruscolini
- Departamento de Física Teórica & Instituto de Biocomputacíon y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza, Spain.
| | | |
Collapse
|
14
|
Caraglio M, Imparato A, Pelizzola A. Pathways of mechanical unfolding of FnIII10: Low force intermediates. J Chem Phys 2010; 133:065101. [DOI: 10.1063/1.3464476] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
15
|
Liu F, Maynard C, Scott G, Melnykov A, Hall KB, Gruebele M. A natural missing link between activated and downhill protein folding scenarios. Phys Chem Chem Phys 2010; 12:3542-9. [PMID: 20336253 PMCID: PMC7382783 DOI: 10.1039/b925033f] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
We propose protein PTB1 : 4W as a good candidate for engineering into a downhill folder. PTB1 : 4W has a probe-dependent thermal unfolding curve and sub-millisecond T-jump relaxation kinetics on more than one time scale. Its refolding rate in denaturant is a non-linear function of denaturant concentration (curved chevron plot). Yet at high denaturant concentration its unfolding is probe-independent, and the folding kinetics can be fitted to a single exponential decay. The domain appears to fold via a mechanism between downhill folding and activated folding over several small barriers, and when denaturant is added, one of these barriers greatly increases and simplifies the observed folding to apparent two-state kinetics. We predict the simplest free energy function consistent with the thermal denaturation and kinetics experiments by using the singular value Smoluchowski dynamics (SVSD) model. PTB1 : 4W is a natural 'missing link' between downhill and activated folding. We suggest mutations that could move the protein into the downhill folding limit.
Collapse
Affiliation(s)
- Feng Liu
- Center for Biophysics and Computational Biology, University of Illinois at Urbana-Champaign, IL 61801, USA
| | - Caroline Maynard
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, MO 63110, USA
| | - Gregory Scott
- Department of Chemistry, University of Illinois at Urbana-Champaign, IL 61801, USA
| | - Artem Melnykov
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, MO 63110, USA
| | - Kathleen B. Hall
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, MO 63110, USA
| | - Martin Gruebele
- Center for Biophysics and Computational Biology, University of Illinois at Urbana-Champaign, IL 61801, USA
- Department of Chemistry, University of Illinois at Urbana-Champaign, IL 61801, USA
- Department of Physics, University of Illinois at Urbana-Champaign, IL 61801, USA
| |
Collapse
|
16
|
Zamparo M, Pelizzola A. Nearly symmetrical proteins: folding pathways and transition states. J Chem Phys 2009; 131:035101. [PMID: 19624233 DOI: 10.1063/1.3170984] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The folding pathways of the B domain of protein A have been the subject of many experimental and computational studies. Based on a statistical mechanical model, it has been suggested that the native state symmetry leads to multiple pathways, highly dependent on temperature and denaturant concentration. Experiments, however, have not confirmed this scenario. By considering four nearly symmetrical proteins, one of them being the above molecule, here we show that, if contact energies are properly taken into account, a different picture emerges from kinetic simulations of the above-mentioned model. This is characterized by a dominant folding pathway, which is consistent with the most recent experimental results. Given the simplicity of the model, we also report on a direct sampling of the transition state.
Collapse
Affiliation(s)
- Marco Zamparo
- Dipartimento di Fisica, CNISM Unità di Torino and INFN, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
| | | |
Collapse
|
17
|
Cobos ES, Iglesias-Bexiga M, Ruiz-Sanz J, Mateo PL, Luque I, Martinez JC. Thermodynamic Characterization of the Folding Equilibrium of the Human Nedd4-WW4 Domain: At the Frontiers of Cooperative Folding. Biochemistry 2009; 48:8712-20. [DOI: 10.1021/bi9007758] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Eva S. Cobos
- Department of Physical Chemistry and Institute of Biotechnology, Faculty of Sciences, University of Granada, 18071 Granada, Spain
| | - Manuel Iglesias-Bexiga
- Department of Physical Chemistry and Institute of Biotechnology, Faculty of Sciences, University of Granada, 18071 Granada, Spain
| | - Javier Ruiz-Sanz
- Department of Physical Chemistry and Institute of Biotechnology, Faculty of Sciences, University of Granada, 18071 Granada, Spain
| | - Pedro L. Mateo
- Department of Physical Chemistry and Institute of Biotechnology, Faculty of Sciences, University of Granada, 18071 Granada, Spain
| | - Irene Luque
- Department of Physical Chemistry and Institute of Biotechnology, Faculty of Sciences, University of Granada, 18071 Granada, Spain
| | - Jose C. Martinez
- Department of Physical Chemistry and Institute of Biotechnology, Faculty of Sciences, University of Granada, 18071 Granada, Spain
| |
Collapse
|
18
|
Downhill versus Barrier-Limited Folding of BBL. J Mol Biol 2009; 387:993-1001. [DOI: 10.1016/j.jmb.2009.02.014] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2008] [Revised: 02/03/2009] [Accepted: 02/04/2009] [Indexed: 11/18/2022]
|
19
|
Abstract
We investigate the structures of the major folding transition states of nine proteins by correlation of published Phi-values with inter-residue contact maps. Combined with previous studies on six proteins, the analysis suggests that at least 10 of the 15 small globular proteins fold via a nucleation-condensation mechanism with a concurrent build-up of secondary and tertiary structure contacts, but a structural consolidation that is clearly nonuniformly distributed over the molecule and most intense in a single structural region suggesting the occurrence of a single folding nucleus. However, on average helix- and sheet-forming residues show somewhat larger Phi-values in the major transition state, suggesting that secondary structure formation is one important driving force in the nucleation-condensation in many proteins and that secondary-structure forming residues tend to be more prominent in folding nuclei. We synthesize the combined information on these 10 of 15 proteins into a unified nucleation-condensation mechanism which also accounts for effects described by the framework, hydrophobic collapse, zipper, and funnel models.
Collapse
Affiliation(s)
- Bengt Nölting
- Department of Biochemistry and Biophysics, University of California, San Francisco, California 94158-2517, USA
| | | |
Collapse
|
20
|
Badasyan A, Liu Z, Chan HS. Probing possible downhill folding: native contact topology likely places a significant constraint on the folding cooperativity of proteins with approximately 40 residues. J Mol Biol 2008; 384:512-30. [PMID: 18823994 DOI: 10.1016/j.jmb.2008.09.023] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2008] [Revised: 09/06/2008] [Accepted: 09/10/2008] [Indexed: 10/21/2022]
Abstract
Experiments point to appreciable variations in folding cooperativity among natural proteins with approximately 40 residues, indicating that the behaviors of these proteins are valuable for delineating the contributing factors to cooperative folding. To explore the role of native topology in a protein's propensity to fold cooperatively and how native topology might constrain the degree of cooperativity achievable by a given set of physical interactions, we compared folding/unfolding kinetics simulated using three classes of native-centric C(alpha) chain models with different interaction schemes. The approach was applied to two homologous 45-residue fragments from the peripheral subunit-binding domain family and a 39-residue fragment of the N-terminal domain of ribosomal protein L9. Free-energy profiles as functions of native contact number were computed to assess the heights of thermodynamic barriers to folding. In addition, chevron plots of folding/unfolding rates were constructed as functions of native stability to facilitate comparison with available experimental data. Although common Gō-like models with pairwise Lennard-Jones-type interactions generally fold less cooperatively than real proteins, the rank ordering of cooperativity predicted by these models is consistent with experiment for the proteins investigated, showing increasing folding cooperativity with increasing nonlocality of a protein's native contacts. Models that account for water-expulsion (desolvation) barriers and models with many-body (nonadditive) interactions generally entail higher degrees of folding cooperativity indicated by more linear model chevron plots, but the rank ordering of cooperativity remains unchanged. A robust, experimentally valid rank ordering of model folding cooperativity independent of the multiple native-centric interaction schemes tested here argues that native topology places significant constraints on how cooperatively a protein can fold.
Collapse
Affiliation(s)
- Artem Badasyan
- Department of Biochemistry, Faculty of Medicine, University of Toronto, Toronto, Ontario, Canada M5S 1A8
| | | | | |
Collapse
|
21
|
Imparato A, Pelizzola A. Mechanical unfolding and refolding pathways of ubiquitin. PHYSICAL REVIEW LETTERS 2008; 100:158104. [PMID: 18518158 DOI: 10.1103/physrevlett.100.158104] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2007] [Indexed: 05/26/2023]
Abstract
Mechanical unfolding and refolding of ubiquitin are studied by Monte Carlo simulations of a Gō model with binary variables. The exponential dependence of the time constants on the force is verified, and folding and unfolding lengths are computed, with good agreement with experimental results. Furthermore, the model exhibits intermediate kinetic states, as observed in experiments. Unfolding and refolding pathways and intermediate states, obtained by tracing single secondary structure elements, are consistent with simulations of previous all-atom models and with the experimentally observed step sizes.
Collapse
Affiliation(s)
- A Imparato
- Dipartimento di Fisica and CNISM, INFN Sezione di Torino, Politecnico di Torino, c. Duca degli Abruzzi 24, Turin, Italy
| | | |
Collapse
|
22
|
Ting CL, Makarov DE. Two-dimensional fluorescence resonance energy transfer as a probe for protein folding: A theoretical study. J Chem Phys 2008; 128:115102. [DOI: 10.1063/1.2835611] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
23
|
An experimental survey of the transition between two-state and downhill protein folding scenarios. Proc Natl Acad Sci U S A 2008; 105:2369-74. [PMID: 18268349 DOI: 10.1073/pnas.0711908105] [Citation(s) in RCA: 130] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A kinetic and thermodynamic survey of 35 WW domain sequences is used in combination with a model to discern the energetic requirements for the transition from two-state folding to downhill folding. The sequences used exhibit a 600-fold range of folding rates at the temperature of maximum folding rate. Very stable proteins can achieve complete downhill folding when the temperature is lowered sufficiently below the melting temperature, and then at even lower temperatures they become two-state folders again because of cold denaturation. Less stable proteins never achieve a sufficient bias to fold downhill because of the onset of cold denaturation. The model, considering both heat and cold denaturation, reveals that to achieve incipient downhill folding (barrier <3 RT) or downhill folding (no barrier), the WW domain average melting temperatures have to be >/=50 degrees C for incipient downhill folding and >/=90 degrees C for downhill folding.
Collapse
|
24
|
Nelson ED, Grishin NV. Folding domain B of protein A on a dynamically partitioned free energy landscape. Proc Natl Acad Sci U S A 2008; 105:1489-93. [PMID: 18230738 PMCID: PMC2234171 DOI: 10.1073/pnas.0705707105] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2007] [Indexed: 11/18/2022] Open
Abstract
The B domain of staphylococcal protein A (BdpA) is a small helical protein that has been studied intensively in kinetics experiments and detailed computer simulations that include explicit water. The simulations indicate that BdpA needs to reorganize in crossing the transition barrier to facilitate folding its C-terminal helix (H3) onto the nucleus formed from helices H1 and H2. This process suggests frustration between two partially ordered forms of the protein, but recent varphi value measurements indicate that the transition structure is relatively constant over a broad range of temperatures. Here we develop a simplistic model to investigate the folding transition in which properties of the free energy landscape can be quantitatively compared with experimental data. The model is a continuation of the Muñoz-Eaton model to include the intermittency of contacts between structured parts of the protein, and the results compare variations in the landscape with denaturant and temperature to varphi value measurements and chevron plots of the kinetic rates. The topography of the model landscape (in particular, the feature of frustration) is consistent with detailed simulations even though variations in the varphi values are close to measured values. The transition barrier is smaller than indicated by the chevron data, but it agrees in order of magnitude with a similar alpha-carbon type of model. Discrepancies with the chevron plots are investigated from the point of view of solvent effects, and an approach is suggested to account for solvent participation in the model.
Collapse
Affiliation(s)
- Erik D. Nelson
- Howard Hughes Medical Institute and University of Texas Southwestern Medical Center, 6001 Forest Park Boulevard, Room ND10.124, Dallas, TX 75235-9050
| | - Nick V. Grishin
- Howard Hughes Medical Institute and University of Texas Southwestern Medical Center, 6001 Forest Park Boulevard, Room ND10.124, Dallas, TX 75235-9050
| |
Collapse
|
25
|
Imparato A, Pelizzola A, Zamparo M. Protein mechanical unfolding: A model with binary variables. J Chem Phys 2007; 127:145105. [DOI: 10.1063/1.2776271] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|