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McBride JM, Tlusty T. Slowest-first protein translation scheme: Structural asymmetry and co-translational folding. Biophys J 2021; 120:5466-5477. [PMID: 34813729 PMCID: PMC8715247 DOI: 10.1016/j.bpj.2021.11.024] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Revised: 09/30/2021] [Accepted: 11/17/2021] [Indexed: 11/19/2022] Open
Abstract
Proteins are translated from the N to the C terminus, raising the basic question of how this innate directionality affects their evolution. To explore this question, we analyze 16,200 structures from the Protein Data Bank (PDB). We find remarkable enrichment of α helices at the C terminus and β strands at the N terminus. Furthermore, this α-β asymmetry correlates with sequence length and contact order, both determinants of folding rate, hinting at possible links to co-translational folding (CTF). Hence, we propose the "slowest-first" scheme, whereby protein sequences evolved structural asymmetry to accelerate CTF: the slowest of the cooperatively folding segments are positioned near the N terminus so they have more time to fold during translation. A phenomenological model predicts that CTF can be accelerated by asymmetry in folding rate, up to double the rate, when folding time is commensurate with translation time; analysis of the PDB predicts that structural asymmetry is indeed maximal in this regime. This correspondence is greater in prokaryotes, which generally require faster protein production. Altogether, this indicates that accelerating CTF is a substantial evolutionary force whose interplay with stability and functionality is encoded in secondary structure asymmetry.
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Affiliation(s)
- John M McBride
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan, South Korea.
| | - Tsvi Tlusty
- Center for Soft and Living Matter, Institute for Basic Science, Ulsan, South Korea; Departments of Physics and Chemistry, Ulsan National Institute of Science and Technology, Ulsan, South Korea.
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Dai W, Sengupta AM, Levy RM. First Passage Times, Lifetimes, and Relaxation Times of Unfolded Proteins. PHYSICAL REVIEW LETTERS 2015; 115:048101. [PMID: 26252709 PMCID: PMC4531052 DOI: 10.1103/physrevlett.115.048101] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2015] [Indexed: 06/04/2023]
Abstract
The dynamics of proteins in the unfolded state can be quantified in computer simulations by calculating a spectrum of relaxation times which describes the time scales over which the population fluctuations decay to equilibrium. If the unfolded state space is discretized, we can evaluate the relaxation time of each state. We derive a simple relation that shows the mean first passage time to any state is equal to the relaxation time of that state divided by the equilibrium population. This explains why mean first passage times from state to state within the unfolded ensemble can be very long but the energy landscape can still be smooth (minimally frustrated). In fact, when the folding kinetics is two-state, all of the unfolded state relaxation times within the unfolded free energy basin are faster than the folding time. This result supports the well-established funnel energy landscape picture and resolves an apparent contradiction between this model and the recently proposed kinetic hub model of protein folding. We validate these concepts by analyzing a Markov state model of the kinetics in the unfolded state and folding of the miniprotein NTL9 (where NTL9 is the N-terminal domain of the ribosomal protein L9), constructed from a 2.9 ms simulation provided by D. E. Shaw Research.
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Affiliation(s)
- Wei Dai
- Department of Physics and Astronomy, Rutgers the State University of New Jersey, Piscataway, New Jersey 08854, USA
| | - Anirvan M Sengupta
- Department of Physics and Astronomy, Rutgers the State University of New Jersey, Piscataway, New Jersey 08854, USA
| | - Ronald M Levy
- Center for Biophysics and Computational Biology and Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122-1801, USA and Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122-1801, USA
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3
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Rollins GC, Dill KA. General mechanism of two-state protein folding kinetics. J Am Chem Soc 2014; 136:11420-7. [PMID: 25056406 DOI: 10.1021/ja5049434] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We describe here a general model of the kinetic mechanism of protein folding. In the Foldon Funnel Model, proteins fold in units of secondary structures, which form sequentially along the folding pathway, stabilized by tertiary interactions. The model predicts that the free energy landscape has a volcano shape, rather than a simple funnel, that folding is two-state (single-exponential) when secondary structures are intrinsically unstable, and that each structure along the folding path is a transition state for the previous structure. It shows how sequential pathways are consistent with multiple stochastic routes on funnel landscapes, and it gives good agreement with the 9 order of magnitude dependence of folding rates on protein size for a set of 93 proteins, at the same time it is consistent with the near independence of folding equilibrium constant on size. This model gives estimates of folding rates of proteomes, leading to a median folding time in Escherichia coli of about 5 s.
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Affiliation(s)
- Geoffrey C Rollins
- Department of Biochemistry and Biophysics, University of California , San Francisco, California 94143, United States
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Lane TJ, Schwantes CR, Beauchamp KA, Pande VS. Probing the origins of two-state folding. J Chem Phys 2014; 139:145104. [PMID: 24116650 DOI: 10.1063/1.4823502] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Many protein systems fold in a two-state manner. Random models, however, rarely display two-state kinetics and thus such behavior should not be accepted as a default. While theories for the prevalence of two-state kinetics have been presented, none sufficiently explain the breadth of experimental observations. A model, making minimal assumptions, is introduced that suggests two-state behavior is likely for any system with an overwhelmingly populated native state. We show two-state folding is a natural consequence of such two-state thermodynamics, and is strengthened by increasing the population of the native state. Further, the model exhibits hub-like behavior, with slow interconversions between unfolded states. Despite this, the unfolded state equilibrates quickly relative to the folding time. This apparent paradox is readily understood through this model. Finally, our results compare favorable with measurements of folding rates as a function of chain length and Keq, providing new insight into these relations.
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Affiliation(s)
- Thomas J Lane
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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5
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Klippenstein SJ, Pande VS, Truhlar DG. Chemical Kinetics and Mechanisms of Complex Systems: A Perspective on Recent Theoretical Advances. J Am Chem Soc 2014; 136:528-46. [DOI: 10.1021/ja408723a] [Citation(s) in RCA: 187] [Impact Index Per Article: 18.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Affiliation(s)
- Stephen J. Klippenstein
- Chemical
Sciences and Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Vijay S. Pande
- Department
of Chemistry and Structural Biology, Stanford University, Stanford, California 94305, United States
| | - Donald G. Truhlar
- Department
of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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6
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Abstract
We investigate the rate-length scaling law of protein folding, a key undetermined scaling law in the analytical theory of protein folding. Available data yield statistically significant evidence for the existence of a rate-length law capable of predicting folding times to within about two orders of magnitude (over 9 decades of variation). Unambiguous determination of the functional form of such a law could provide key mechanistic insight into folding. Four proposed laws from literature (power law, exponential, and two stretched exponentials) are tested against one another, and it is found that the power law best explains the data by a modest margin. We conclude that more data is necessary to unequivocally infer the rate-length law. Such data could be obtained through a small number of protein folding experiments on large protein domains.
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Affiliation(s)
- Thomas J. Lane
- Department of Chemistry, Stanford University, Stanford, California, United States of America
| | - Vijay S. Pande
- Departments of Chemistry, Computer Science, and Biophysics, Stanford University, Stanford, California, United States of America
- * E-mail:
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7
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Comparing a simple theoretical model for protein folding with all-atom molecular dynamics simulations. Proc Natl Acad Sci U S A 2013; 110:17880-5. [PMID: 24128764 DOI: 10.1073/pnas.1317105110] [Citation(s) in RCA: 83] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Advances in computing have enabled microsecond all-atom molecular dynamics trajectories of protein folding that can be used to compare with and test critical assumptions of theoretical models. We show that recent simulations by the Shaw group (10, 11, 14, 15) are consistent with a key assumption of an Ising-like theoretical model that native structure grows in only a few regions of the amino acid sequence as folding progresses. The distribution of mechanisms predicted by simulating the master equation of this native-centric model for the benchmark villin subdomain, with only two adjustable thermodynamic parameters and one temperature-dependent kinetic parameter, is remarkably similar to the distribution in the molecular dynamics trajectories.
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Braselmann E, Chaney JL, Clark PL. Folding the proteome. Trends Biochem Sci 2013; 38:337-44. [PMID: 23764454 DOI: 10.1016/j.tibs.2013.05.001] [Citation(s) in RCA: 88] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2012] [Revised: 05/01/2013] [Accepted: 05/02/2013] [Indexed: 02/07/2023]
Abstract
Protein folding is an essential prerequisite for protein function and hence cell function. Kinetic and thermodynamic studies of small proteins that refold reversibly were essential for developing our current understanding of the fundamentals of protein folding mechanisms. However, we still lack sufficient understanding to accurately predict protein structures from sequences, or the effects of disease-causing mutations. To date, model proteins selected for folding studies represent only a small fraction of the complexity of the proteome and are unlikely to exhibit the breadth of folding mechanisms used in vivo. We are in urgent need of new methods - both theoretical and experimental - that can quantify the folding behavior of a truly broad set of proteins under in vivo conditions. Such a shift in focus will provide a more comprehensive framework from which to understand the connections between protein folding, the molecular basis of disease, and cell function and evolution.
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Affiliation(s)
- Esther Braselmann
- Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, IN 46556 USA
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Stepwise protein folding at near amino acid resolution by hydrogen exchange and mass spectrometry. Proc Natl Acad Sci U S A 2013; 110:7684-9. [PMID: 23603271 DOI: 10.1073/pnas.1305887110] [Citation(s) in RCA: 143] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The kinetic folding of ribonuclease H was studied by hydrogen exchange (HX) pulse labeling with analysis by an advanced fragment separation mass spectrometry technology. The results show that folding proceeds through distinct intermediates in a stepwise pathway that sequentially incorporates cooperative native-like structural elements to build the native protein. Each step is seen as a concerted transition of one or more segments from an HX-unprotected to an HX-protected state. Deconvolution of the data to near amino acid resolution shows that each step corresponds to the folding of a secondary structural element of the native protein, termed a "foldon." Each folded segment is retained through subsequent steps of foldon addition, revealing a stepwise buildup of the native structure via a single dominant pathway. Analysis of the pertinent literature suggests that this model is consistent with experimental results for many proteins and some current theoretical results. Two biophysical principles appear to dictate this behavior. The principle of cooperativity determines the central role of native-like foldon units. An interaction principle termed "sequential stabilization" based on native-like interfoldon interactions orders the pathway.
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Lane TJ, Shukla D, Beauchamp KA, Pande VS. To milliseconds and beyond: challenges in the simulation of protein folding. Curr Opin Struct Biol 2012; 23:58-65. [PMID: 23237705 DOI: 10.1016/j.sbi.2012.11.002] [Citation(s) in RCA: 264] [Impact Index Per Article: 22.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2012] [Revised: 11/15/2012] [Accepted: 11/19/2012] [Indexed: 01/02/2023]
Abstract
Quantitatively accurate all-atom molecular dynamics (MD) simulations of protein folding have long been considered a holy grail of computational biology. Due to the large system sizes and long timescales involved, such a pursuit was for many years computationally intractable. Further, sufficiently accurate forcefields needed to be developed in order to realistically model folding. This decade, however, saw the first reports of folding simulations describing kinetics on the order of milliseconds, placing many proteins firmly within reach of these methods. Progress in sampling and forcefield accuracy, however, presents a new challenge: how to turn huge MD datasets into scientific understanding. Here, we review recent progress in MD simulation techniques and show how the vast datasets generated by such techniques present new challenges for analysis. We critically discuss the state of the art, including reaction coordinate and Markov state model (MSM) methods, and provide a perspective for the future.
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Affiliation(s)
- Thomas J Lane
- Department of Chemistry, Stanford University, United States
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11
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Rustad M, Ghosh K. Why and how does native topology dictate the folding speed of a protein? J Chem Phys 2012. [DOI: 10.1063/1.4767567] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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