DOCSLIB.ORG

Behind the Folding Funnel Diagram

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Behind the Folding Funnel Diagram commentary Behind the folding funnel diagram Martin Karplus This Commentary clarifies the meaning of the funnel diagram, which has been widely cited in papers on protein folding. To aid in the analysis of the funnel diagram, this Commentary reviews historical approaches to understanding the mechanism of protein folding. The primary role of free energy in protein folding is discussed, and it is pointed out that the decrease in the configurational entropy as the native state is approached hinders folding, rather than guiding it. Diagrams are introduced that provide a less ambiguous representation of the factors governing the protein folding reaction than the funnel diagram. nderstanding the mechanism fewer) generally fold in times on the order to that shown in Figure 1. It is a schematic by which proteins fold to their of milliseconds to seconds (except in cases representation of how the effective Unative state remains a problem of with special factors that slow the folding, potential energy, implicitly averaged fundamental interest in biology, in spite of such as proline isomerization), there was over solvent interactions (in the vertical the fact that it has been studied for many indeed a paradox. The ultimate statement direction), and the configurational entropy years1. Moreover, now that misfolding has of the paradox was given in the language (in the horizontal direction) of a protein been shown to be the source of a range of of computational complexity5. Many decrease as the native state is approached; diseases, a knowledge of the factors that phenomenological models were proposed picturesque three-dimensional funnels are determine whether a polypeptide chain to show how the conformational space that also being used11. Both the two- and three- will fold to its native state or aggregate has has to be searched is restricted to reduce dimensional diagrams have a funnel-like become all the more important. the folding time to the experimental range. shape because the number of accessible The folding funnel diagram (see Fig. 1), Examples include the nucleation-growth or configurations, which determine the introduced by Wolynes, Onuchic and nucleation-condensation mechanism6,7, the configurational entropy, decreases as the Thirumalai2, is intended to provide diffusion-collision model8 and the jigsaw- energy decreases. Such funnel diagrams a pictorial representation of how the puzzle model9. are very appealing images from which Levinthal paradox3, which had dominated In the late 1980s, the focus of approaches many readers have concluded that folding discussion of protein folding for many to the protein folding problem shifted a protein is like “funneling wine into a © 2011 Nature America, Inc. All rights reserved. All rights Inc. America, Nature © 2011 years, is resolved. Since the original from phenomenological models to a bottle.” A typical statement of this type publication, funnel diagrams have become consideration of the general characteristics appears in a study of the folding of PDZ a fixture in papers on protein folding, of the energy surface of a polypeptide chain. domains12; in the introduction, it is stated and they are now being introduced in The new focus is eminently reasonable, as that “Free energy landscapes of many discussions of other problems, such as the energy surface is one of the fundamental proteins appear to resemble the shape of ligand binding4. Unfortunately, the funnel determinants of any reaction1, whether a a funnel that guides the folding process diagram has created a misconception in small-molecule reaction or protein folding. toward the native state.” Although Wolynes many readers. The change made explicit a concept that is et al.2 were aware that the occurrence of The concept introduced by Levinthal is implicit in the phenomenological models— that the appropriate point of reference for for any of the models to work, there must protein folding is a random search problem. be energetic factors that bias the folding Configurational entropy Taken literally, as it has been by many process. For example, only if a nucleus is people, this means that all conformations stable, relative to the random coil structures, of the polypeptide chain (except the native can it play a role in folding. In an insightful state) are equally probable, so that the native paper, Zwanzig et al.10 used a simplified state can be found only by an unbiased model to demonstrate that if there is a bias e energy random search. For such a search, the in the potential energy such that it decreases time to find the native state is given by the relatively smoothly toward the native state, Effectiv number of configurations of the polypeptide only a limited number of configurations chain (on the order of 1070 for a 100-residue would be visited in the folding reaction, protein) multiplied by the time required to and the configurational search (Levinthal) find one configuration (say, 10−11 seconds). problem would be solved. Figure 1 | A schematic folding funnel diagram. This leads to an enormously long folding The required energy bias is embodied The effective energy is plotted vertically and the time (say, 1059 seconds or about 1052 years). in the two-dimensional funnel diagram, configurational entropy horizontally. Adapted from Given that small proteins (100 residues or the most widely used of which is similar reference 2. NATURE CHEMICAL BIOLOGY | VOL 7 | JULY 2011 | www.nature.com/naturechemicalbiology 401 commentary a to microseconds and more recently to b 14 −55 nanoseconds . An important result of such studies is the finding that the folding −40 −60 reaction of many small proteins follows an exponential time course. This is interpreted −65 −60 to mean, as in chemical reactions1, that there are only two significantly populated −70 −80 states, the denatured state and the native Average energy −75 state, and that there is a barrier separating −100 the two that is larger than a few kilocalories. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 However, it has so far not been possible to determine experimentally the detailed c d folding trajectories even for a simple −85 protein—that is, a complete description of the conformations that are sampled in going −65 −90 from the multiconfiguration denatured state to a well-defined native state. Consequently, −95 −70 a range of theoretical methods continues to be used to supplement the experimental Free energy −100 data. Models that go beyond the −75 phenomenological approaches mentioned −105 above by focusing on the structural and 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Q Q thermodynamic parameters include lattice models1,13, coarse-grained models15 and Figure 2 | Folding of a lattice polymer. (a–d)The effective energy a( ,b) and free energy (c,d) calculated as atomistic simulations with implicit (see, a function of the fraction of native contacts for the 27-mer lattice polymer: a and c at a low temperature; for example, ref. 16) and explicit (see, and b and d at a high temperature. Adapted with permission from reference 22. for example, ref. 17) representations of the solvent. Also, unfolding simulations in explicit solvent, combined with such “guiding” is a misconception, as can the mechanism, such as those making use experimental data, have been used to be seen from their original paper, they of NMR1 and protein engineering7. Also, propose folding pathways for small proteins have not emphasized this point, and the it has become possible to rapidly trigger (see, for example, ref. 7). misconception concerning the funnel folding and unfolding so that measurements The first concrete demonstration of diagram has continued to proliferate. can be extended from milliseconds down how the Levinthal paradox can be resolved The essence of the misconception is that the decrease in configuration entropy, a b which gives the diagram its funnel-like −100 −100 shape, aids the polypeptide chain in finding 270 K 390 K ) the native state. In fact, exactly the opposite –1 −110 −110 © 2011 Nature America, Inc. All rights reserved. All rights Inc. America, Nature © 2011 is true; that is, the decrease in the number of available configurations, as the native −120 −120 state is approached, actually tends to slow −130 −130 folding. The difficulty of finding these configurations is essentially the origin of −140 −140 the Levinthal paradox. To understand the Average energy (kcal mol −150 −150 folding process it must be realized that the 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 major determinant of the folding rate is the free-energy surface (often referred to as a c d “landscape”) of the polypeptide chain1,2,7,13, 4 4 rather than the energy shown in the funnel ) diagram. The free energy is the sum of the –1 2 2 potential energy, which decreases as the native state is approached and therefore 0 0 favors folding, and the unfavorable contribution of the decrease in the −2 −2 configuration entropy. The delicate balance Free energy (kcal mol −4 −4 between the two generally leads to a free- 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 energy barrier that results in the two-state Q Q folding behavior observed for most small proteins (see ref. 7 and references therein). Figure 3 | Folding of a designed α-helical peptide. (a–d) The effective energy a( ,b) and free energy (c,d) The developing understanding of protein calculated as a function of the fraction of native hydrogen bonds for a designed α-helical peptide: a and folding has been aided by experiments c at a low temperature (270 K); b and d at a high temperature (390 K).
Load more

Recommended publications
  • Chapter 6 Protein Structure and Folding
    Chapter 6 Protein Structure and Folding 1. Secondary Structure 2. Tertiary Structure 3. Quaternary Structure and Symmetry 4. Protein Stability 5. Protein Folding Myoglobin Introduction 1. Proteins were long thought to be colloids of random structure 2. 1934, crystal of pepsin in X-ray beam produces discrete diffraction pattern -> atoms are ordered 3. 1958 first X-ray structure solved, sperm whale myoglobin, no structural regularity observed 4. Today, approx 50’000 structures solved => remarkable degree of structural regularity observed Hierarchy of Structural Layers 1. Primary structure: amino acid sequence 2. Secondary structure: local arrangement of peptide backbone 3. Tertiary structure: three dimensional arrangement of all atoms, peptide backbone and amino acid side chains 4. Quaternary structure: spatial arrangement of subunits 1) Secondary Structure A) The planar peptide group limits polypeptide conformations The peptide group ha a rigid, planar structure as a consequence of resonance interactions that give the peptide bond ~40% double bond character The trans peptide group The peptide group assumes the trans conformation 8 kJ/mol mire stable than cis Except Pro, followed by cis in 10% Torsion angles between peptide groups describe polypeptide chain conformations The backbone is a chain of planar peptide groups The conformation of the backbone can be described by the torsion angles (dihedral angles, rotation angles) around the Cα-N (Φ) and the Cα-C bond (Ψ) Defined as 180° when extended (as shown) + = clockwise, seen from Cα Not
    [Show full text]
  • Protein Misfolding in Human Diseases
    Linköping Studies in Science and Technology Dissertation No. 1239 Protein Misfolding in Human Diseases Karin Almstedt Biochemistry Department of Physics, Chemistry and Biology Linköping University, SE-581 83 Linköping, Sweden Linköping 2009 The cover shows a Himalayan mountain range, symbolizing a protein folding landscape. During the course of the research underlying this thesis, Karin Almstedt was enrolled in Forum Scientium, a multidisciplinary doctoral program at Linköping University, Sweden. Copyright © 2009 Karin Almstedt ISBN: 978-91-7393-698-9 ISSN: 0345-7524 Printed in Sweden by LiU-Tryck Linköping 2009 Never Stop Exploring 83 ABSTRACT The studies in this thesis are focused on misfolded proteins involved in human disease. There are several well known diseases that are due to aberrant protein folding. These types of diseases can be divided into three main categories: 1. Loss-of-function diseases 2. Gain-of-toxic-function diseases 3. Infectious misfolding diseases Most loss-of-function diseases are caused by aberrant folding of important proteins. These proteins often misfold due to inherited mutations. The rare disease carbonic anhydrase II deficiency syndrome (CADS) can manifest in carriers of point mutations in the human carbonic anhydrase II (HCA II) gene. One mutation associated with CADS entails the His107Tyr (H107Y) substitution. We have demonstrated that the H107Y mutation is a remarkably destabilizing mutation influencing the folding behavior of HCA II. A mutational survey of position H107 and a neighboring conserved position E117 has been performed entailing the mutants H107A, H107F, H107N, E117A and the double mutants H107A/E117A and H107N/E117A. We have also shown that the binding of specific ligands can stabilize the disease causing mutant, and shift the folding equilibrium towards the native state, providing a starting point for small molecule drugs for CADS.
    [Show full text]
  • Evolution, Energy Landscapes and the Paradoxes of Protein Folding
    Biochimie 119 (2015) 218e230 Contents lists available at ScienceDirect Biochimie journal homepage: www.elsevier.com/locate/biochi Review Evolution, energy landscapes and the paradoxes of protein folding Peter G. Wolynes Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA article info abstract Article history: Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem Received 15 September 2014 involved in folding however has been simplified through the evolution of folding energy landscapes that are Accepted 11 December 2014 funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal Available online 18 December 2014 frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy Keywords: landscape ideas also have allowed successful protein structure prediction algorithms to be developed. Folding landscape The selection constraint of having funneled folding landscapes has left its imprint on the sequences of Natural selection Structure prediction existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signaling a beautiful confluence of ge- nomics and chemical physics. © 2014 Elsevier B.V. and Societ e française de biochimie et biologie Moleculaire (SFBBM). All rights reserved. Contents 1. Introduction . ....................... 218 2. General evidence that folding landscapes are funneled . ....................... 221 3. How rugged is the folding landscape e physicochemical approach . ....................... 222 4.
    [Show full text]
  • 50+ Years of Protein Folding
    ISSN 0006-2979, Biochemistry (Moscow), 2018, Vol. 83, Suppl. 1, pp. S3-S18. © Pleiades Publishing, Ltd., 2018. Original Russian Text © A. V. Finkelstein, 2018, published in Uspekhi Biologicheskoi Khimii, 2018, Vol. 58, pp. 7-40. REVIEW 50+ Years of Protein Folding A. V. Finkelstein Institute of Protein Research, Russian Academy of Sciences, 142290 Pushchino, Moscow Region, Russia; E-mail: afinkel@vega.protres.ru Received May 25, 2017 Revision received July 10, 2017 Abstract—The ability of proteins to spontaneously form their spatial structures is a long-standing puzzle in molecular biol- ogy. Experimentally measured rates of spontaneous folding of single-domain globular proteins range from microseconds to hours: the difference – 10-11 orders of magnitude – is the same as between the lifespan of a mosquito and the age of the Universe. This review (based on the literature and some personal recollections) describes a winding road to understanding spontaneous folding of protein structure. The main attention is given to the free-energy landscape of conformations of a protein chain – especially to the barrier separating its unfolded (U) and the natively folded (N) states – and to physical the- ories of rates of crossing this barrier in both directions: from U to N, and from N to U. It is shown that theories of both these processes come to essentially the same result and outline the observed range of folding and unfolding rates for single-domain globular proteins. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control, and explain the observed maximal size of “foldable” protein domains.
    [Show full text]
  • The Protein Folding Problem
    The Protein Folding Problem Ken A. Dill,1,2 S. Banu Ozkan,3 M. Scott Shell,4 and Thomas R. Weikl5 1Department of Pharmaceutical Chemistry, 2Graduate Group in Biophysics, University of California, San Francisco, California 94143; email: dill@maxwell.ucsf.edu 3Department of Physics, Arizona State University, Tempe, Arizona 85287; email: banu.ozkan@asu.edu 4Department of Chemical Engineering, University of California, Santa Barbara, California 93106; email: shell@engineering.ucsb.edu 5Max Planck Institute of Colloids and Interfaces, Department of Theory and Bio-Systems, 14424 Potsdam, Germany; email: thomas.weikl@mpikg.mpg.de Annu. Rev. Biophys. 2008. 37:289–316 Key Words The Annual Review of Biophysics is online at structure prediction, funnel energy landscapes, CASP, folding biophys.annualreviews.org code, folding kinetics This article’s doi: 10.1146/annurev.biophys.37.092707.153558 Abstract Copyright c 2008 by Annual Reviews. The “protein folding problem” consists of three closely related puz- All rights reserved zles: (a) What is the folding code? (b) What is the folding mechanism? 1936-122X/08/0609-0289$20.00 (c) Can we predict the native structure of a protein from its amino acid sequence? Once regarded as a grand challenge, protein fold- ing has seen great progress in recent years. Now, foldable proteins and nonbiological polymers are being designed routinely and mov- ing toward successful applications. The structures of small proteins are now often well predicted by computer methods. And, there is now a testable explanation for how a protein can fold so quickly: A protein solves its large global optimization problem as a series of smaller local optimization problems, growing and assembling the native structure from peptide fragments, local structures first.
    [Show full text]
  • Shaping up the Protein Folding Funnel by Local Interaction: Lesson from a Structure Prediction Study
    Shaping up the protein folding funnel by local interaction: Lesson from a structure prediction study George Chikenji*†, Yoshimi Fujitsuka‡, and Shoji Takada*‡§¶ *Department of Chemistry, Faculty of Science, and ‡Graduate School of Science and Technology, Kobe University, Nada, Kobe 657-8501, Japan; †Department of Computational Science and Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan; and §Core Research for Evolutionary Science and Technology, Japan Science and Technology Agency, Nada, Kobe 657-8501, Japan Edited by R. Stephen Berry, University of Chicago, Chicago, IL, and approved December 30, 2005 (received for review September 22, 2005) Predicting protein tertiary structure by folding-like simulations is CASP6, our group Rokko (as well as the server Rokky) used the one of the most stringent tests of how much we understand the SIMFOLD software as a primary prediction tool, demonstrating principle of protein folding. Currently, the most successful method one of the top-level prediction performances in the new fold for folding-based structure prediction is the fragment assembly category (elite club membership by the assessor, B.K. Lee). (FA) method. Here, we address why the FA method is so successful In this work, we start with comparison of the structures and its lesson for the folding problem. To do so, using the FA predicted in the past. We then design a structure prediction test method, we designed a structure prediction test of ‘‘chimera of ‘‘chimera proteins,’’ where the local structural preference is proteins.’’ In the chimera proteins, local structural preference is that for the wild-type (WT) sequence and nonlocal interactions specific to the target sequences, whereas nonlocal interactions are are the only sequence-independent compaction force.
    [Show full text]
  • THEORY of PROTEIN FOLDING: the Energy Landscape Perspective
    P1: NBL/ary/dat P2: N/MBL/plb QC: MBL/agr T1: MBL July 31, 1997 9:34 Annual Reviews AR040-19 Annu. Rev. Phys. Chem. 1997. 48:545–600 Copyright c 1997 by Annual Reviews Inc. All rights reserved THEORY OF PROTEIN FOLDING: The Energy Landscape Perspective Jose´ Nelson Onuchic Department of Physics, University of California at San Diego, La Jolla, California 92093-0319 Zaida Luthey-Schulten and Peter G. Wolynes School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801 KEY WORDS: folding funnel, minimal frustration, lattice simulations, heteropolymer phase diagram, structure prediction ABSTRACT The energy landscape theory of protein folding is a statistical description of a protein’s potential surface. It assumes that folding occurs through organizing an ensemble of structures rather than through only a few uniquely defined structural intermediates. It suggests that the most realistic model of a protein is a minimally frustrated heteropolymer with a rugged funnel-like landscape biased toward the native structure. This statistical description has been developed using tools from the statistical mechanics of disordered systems, polymers, and phase transitions of finite systems. We review here its analytical background and contrast the phenom- ena in homopolymers, random heteropolymers, and protein-like heteropolymers that are kinetically and thermodynamically capable of folding. The connection between these statistical concepts and the results of minimalist models used in by University of California - San Diego on 07/02/07. For personal use only. computer simulations is discussed. The review concludes with a brief discus- sion of how the theory helps in the interpretation of results from fast folding experiments and in the practical task of protein structure prediction.
    [Show full text]
  • Folding Proteins with Both Alpha and Beta Structures in a Reduced Model
    Folding Proteins with Both Alpha and Beta Structures in a Reduced Model Nan-Yow Chen Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China Advisor: Chung-Yu Mou Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China Advisor: Zheng-Yao Su National Center for High-Performance Computing, Hsinchu, Taiwan, Republic of China June, 2004 Contents Abstract iii 1 Introduction 1 2 Essentials of Proteins Structures and Numerical Methods 5 2.1 Building Blocks and Level of Protein Structures 5 2.2 Monte Carlo Method 9 3 Reduced Protein Folding Model (RPFM) 11 3.1 Coarse-Grained Representation of the Protein Molecules 12 3.1.1 Backbone Units 12 3.1.2 Side-chain Units 15 3.2 Interaction Potentials 19 3.3 Relative Energy Strengths and Conformation Parameters 34 3.3.1 Relative Energy Strengths 34 3.3.2 Conformation Parameters 36 i 4 Simulation Results and Analysis 39 4.1 Simulation Results 40 4.1.1 One Alpha Helix Case 40 4.1.2 One Beta Sheet Case 45 4.1.3 One Alpha Helix and One Beta Sheet Case 50 4.1.4 Effects of Dipole-Dipole Interactions and 56 Local Hydrophobic Interactions 4.2 Real Protein Peptides 59 5 Conclusions and Outlook 63 Bibliography 67 Appendix 71 ii Abstract A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same time can predict the three dimensional structure of a protein with a given sequence in reasonable time.
    [Show full text]
  • Folding Funnel J
    Proc. Natl. Acad. Sci. USA Vol. 92, pp. 3626-3630, April 1995 Biophysics Toward an outline of the topography of a realistic protein- folding funnel J. N. ONUCHIC*, P. G. WOLYNESt, Z. LUTHEY-SCHULTENt, AND N. D. SoccI* tSchool of Chemical Sciences, University of Illinois, Urbana, IL 61801; and *Department of Physics-0319, University of California, San Diego, La Jolla, CA 92093-0319 Contributed by P. G. Wolynes, December 28, 1994 ABSTRACT Experimental information on the structure other; thus, intermediates are not present at equilibrium (i.e., and dynamics ofmolten globules gives estimates for the energy a free thermodynamic energy barrier intercedes). In a type I landscape's characteristics for folding highly helical proteins, transition, activation to an ensemble of states near the top of when supplemented by a theory of the helix-coil transition in this free-energy barrier is the rate-determining step. Type I collapsed heteropolymers. A law of corresponding states transitions occur when the energy landscape is uniformly relating simulations on small lattice models to real proteins smooth. When the landscape is sufficiently rugged, in addition possessing many more degrees of freedom results. This cor- to surmounting the thermodynamic activation barrier, at an respondence reveals parallels between "minimalist" lattice intermediate degree of folding, unguided search again be- results and recent experimental results for the degree ofnative comes the dominant mechanism. At this point, a local glass character of the folding transition state and molten globule transition has occurred within the folding funnel. If the glass and also pinpoints the needs of further experiments. transition occurs after the main thermodynamic barrier, the mechanism is classified as type IIa.
    [Show full text]
  • Energy Landscape in Protein Folding and Unfolding
    Energy landscape in protein folding and unfolding Francesco Mallamacea,b,c,1, Carmelo Corsaroa,d, Domenico Mallamacee, Sebastiano Vasid, Cirino Vasia, Piero Baglionif, Sergey V. Buldyrevg, Sow-Hsin Chenb, and H. Eugene Stanleyc,1 aCNR-Istituto per i Processi Chimico Fisici Messina, I-98166 Messina, Italy; bDepartment of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; cCenter for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215; dDipartimento di Fisica e di Scienze della Terra, Università di Messina, I-98166 Messina, Italy; eConsorzio per lo Sviluppo dei Sistemi a Grande Interfase, Unità di Catania, I-95125 Catania, Italy; fDipartimento di Chimica, Università di Firenze and Consorzio per lo Sviluppo dei Sistemi a Grande Interfase, I-50019 Florence, Italy; and gDepartment of Physics, Yeshiva University, New York, NY 10033 Contributed by H. Eugene Stanley, December 22, 2015 (sent for review March 17, 2015; reviewed by Anders Nilsson and Michele Parrinello) We use 1H NMR to probe the energy landscape in the protein fold- simulation (9, 10) and different experimental techniques (11–16). ing and unfolding process. Using the scheme ⇄ reversible unfolded Whereas MD simulations directly model peptide conformational (intermediate) → irreversible unfolded (denatured) state, we study transitions in terms of the energy landscape, experiments supply the thermal denaturation of hydrated lysozyme that occurs when useful but limited information, revealing some details in the the
    [Show full text]
  • Theory of Protein Folding Jose´ Nelson Onuchic1,2, and Peter G Wolynes1,2,3
    Theory of protein folding Jose´ Nelson Onuchic1,2,Ã and Peter G Wolynes1,2,3 Protein folding should be complex. Proteins organize leave others to review the results of highly detailed all- themselves into specific three-dimensional structures, through atom simulation. a myriad of conformational changes. The classical view of protein folding describes this process as a nearly sequential Basic concepts series of discrete intermediates. In contrast, the energy The locations of atoms in proteins can be determined, in landscape theory of folding considers folding as the progressive favorable cases, to an accuracy of less than 3 A˚ using X-ray organization of an ensemble of partially folded structures crystallography. This specificity of structure arises from through which the protein passes on its way to the natively the heterogeneity of the protein chain. The differing folded structure. As a result of evolution, proteins have a rugged energies associated with positioning different residues funnel-like landscape biased toward the native structure. near or far from each other or from solvent enable some Connecting theory and simulations of minimalist models with structures to be more stable than others. If a sequence experiments has completely revolutionized our understanding is chosen at random, the specificity of structure is still of the underlying mechanisms that control protein folding. small — a variety of globally different structures have very low energies, but within a few kBT of each other. Addresses This mathematical observation has been the bane of 1Center for Theoretical Biological Physics, 2Department of Physics, computational protein structure prediction using energy 3 Department of Chemistry and Biochemistry, University of California functions.
    [Show full text]
  • Thermodynamics and Kinetics of Iso-1-Cytochrome C Denatured State
    University of Montana ScholarWorks at University of Montana Graduate Student Theses, Dissertations, & Professional Papers Graduate School 2009 Thermodynamics and Kinetics of Iso-1-cytochrome c Denatured State Franco Ollan Tzul The University of Montana Follow this and additional works at: https://scholarworks.umt.edu/etd Let us know how access to this document benefits ou.y Recommended Citation Tzul, Franco Ollan, "Thermodynamics and Kinetics of Iso-1-cytochrome c Denatured State" (2009). Graduate Student Theses, Dissertations, & Professional Papers. 1112. https://scholarworks.umt.edu/etd/1112 This Dissertation is brought to you for free and open access by the Graduate School at ScholarWorks at University of Montana. It has been accepted for inclusion in Graduate Student Theses, Dissertations, & Professional Papers by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact scholarworks@mso.umt.edu. THERMODYNAMICS AND KINETICS OF ISO-1-CYTOCHROME C DENATURED STATE By FRANCO OLLAN TZUL B. Sc. Chemistry & Biology, Regis University, Denver, CO, USA, 1997 Dissertation presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemistry & Biochemistry The University of Montana Missoula, MT March 2009 Approved by: Perry Brown, Associate Provost for Graduate Education Graduate School Dr. J.B. Alexander Ross, Committee Chairperson Department of Chemistry & Biochemistry Dr. Bruce E. Bowler, Committee Member Department of Chemistry & Biochemistry Dr. Klára Briknarová, Committee Member Department of Chemistry & Biochemistry Dr. Michael DeGrandpre, Committee Member Department of Chemistry & Biochemistry Dr. Michele A. McGuirl, Committee Member Division of Biological Sciences Tzul, Franco O., Ph. D., Spring 2009 Chemistry & Biochemistry Thermodynamics and Kinetics of Iso-1-cytochrome c Denatured State Chairperson: J.
    [Show full text]