DOCSLIB.ORG

The Potential Energy Landscape

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Potential Energy Landscape Computer simulations of glasses: the potential energy landscape Zamaan Raza, Björn Alling and Igor Abrikosov Linköping University Post Print N.B.: When citing this work, cite the original article. Original Publication: Zamaan Raza, Björn Alling and Igor Abrikosov, Computer simulations of glasses: the potential energy landscape, 2015, Journal of Physics: Condensed Matter, (27), 29, 293201. http://dx.doi.org/10.1088/0953-8984/27/29/293201 Copyright: IOP Publishing: Hybrid Open Access http://www.iop.org/ Postprint available at: Linköping University Electronic Press http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120738 Topical Review Computer simulations of glasses: the potential energy landscape Zamaan Raza1, Bj¨ornAlling1 and Igor A. Abrikosov1;2;3 1 Department of Physics, Biology and Chemistry (IFM), Link¨opingUniversity, SE-581 83, Link¨oping,Sweden 2 Materials Modeling and Development Laboratory, NUST \MISIS", 119049 Moscow, Russia 3 LOCOMAS Laboratory, Tomsk State University, 634050 Tomsk, Russia E-mail: [email protected] Abstract. We review the current state of research on glasses, discussing the theoretical background and computational models employed to describe them. This article focuses on the use of the potential energy landscape (PEL) paradigm to account for the phenomenology of glassy systems, and the way in which it can be applied in simulations and the interpretation of their results. This article provides a broad overview of the rich phenomenology of glasses, followed by a summary of the theoretical frameworks developed to describe this phenomonology. We discuss the background of the PEL in detail, the onerous task of how to generate computer models of glasses, various methods of analysing numerical simulations, and the literature on the most commonly used model systems. Finally, we tackle the problem of how to distinguish a good glass former from a good crystal former from an analysis of the PEL. In summarising the state of the potential energy landscape picture, we develop the foundations for new theoretical methods that allow the ab initio prediction of the glass-forming ability of new materials by analysis of the PEL. Keywords: Glasses, Potential Energy Landscape, Computer Simulation PACS numbers: 61.43.-j,61.43.Fs,64.70.kj,64.70.Q- Submitted to: J. Phys.: Condens. Matter 2 1. Introduction 1 Introduction2 1.1. Motivation 1.1 Motivation................2 One of the biggest challenges in condensed matter 1.2 Definition of a glass...........3 physics is the modelling of amorphous solids, which 1.3 Strong and fragile liquids........4 lack the long range order characteristic of crystalline 1.4 The glass transition...........5 solids. When modelling bulk crystals, it is possible 1.5 The Kauzmann paradox.........6 to exploit the translational symmetry of the system, 2 Models of glasses7 allowing the construction of a unit cell subject to 2.1 Mode-coupling theory (MCT)......7 periodic boundary conditions, i.e. the translation of 2.2 Random first-order transition theory a basis along lattice points. This method does not (RFOT)..................8 trivially map to amorphous phases which contain no 2.3 The potential energy landscape (PEL).9 such symmetries, although a large enough unit cell 2.4 The free energy landscape........ 12 will capture to some extent the short and medium 2.5 Discussion................. 12 range disorder in spite of the artificial periodic boundary conditions. This, however, comes at great 3 Theoretical background 13 computational expense. For example, first principles 3.1 Thermodynamic formalism....... 13 calculations in the framework of density functional 3.2 Density of configurational states and theory scale as N 3 for a unit cell containing N atoms, entropy.................. 14 while the scaling of higher level quantum mechanical 3.3 Basin free energy............. 15 methods is even worse. For reasons elucidated below, interest in glasses is increasing, and with it the need 4 Sampling schemes 15 for a complete theoretical model, which is not currently 4.1 Reverse Monte Carlo (RMC)...... 15 available. 4.2 Molecular dynamics: aging versus equi- One such reason is the new class of materials librium................... 15 called bulk metallic glasses. Metal atoms have 4.3 Density of states Monte Carlo...... 18 weak orientational constraints in the solid state, and 4.4 Continuous Random Networks (CRN). 18 therefore tend to crystallise easily. Certain alloy 4.5 Stochastic Quenching (SQ)....... 18 compositions, such as Cu64Zr36 have a much lower 4.6 Activation-Relaxation Technique (ART) 19 tendency to crystallise, i.e. a good glass-forming ability 4.7 Discussion................. 19 [1], while others, such as Ni64Zr36 tend to form ordered structures [2]. Bulk metallic glasses are currently 5 Theoeretical characterisation 19 of particular interest due to their unique physical 5.1 Structure and packing.......... 20 properties, such as high elastic moduli or plasticity [3] 5.2 Density of states............. 21 and the potential for surface smoothness not limited 5.3 Normal mode analysis.......... 21 to crystal facets. They lack an intrinsic length scale 5.4 Activated dynamics........... 22 (grain size in the case of crystalline structures, or chain 5.5 Network topology............. 23 length in the case of polymer glasses), and can in 5.6 Discussion................. 24 principle be shaped at the atomic level [4]. Finding compositions with good glass forming ability is a time- 6 Model Systems 25 intensive task, with one composition taking around a 6.1 The binary Lennard-Jones (BLJ) glass. 25 day to fabricate; this trial-and-error process could be 6.2 Amorphous silica............. 27 greatly streamlined using modelling methods [4]. 6.3 Hard sphere model............ 28 Another reason is the development of physical 6.4 Discussion................. 28 vapour deposition as a technique for synthesising glasses with extraordinary thermodynamic and kinetic 7 Ab initio models 29 stability [5{8]. Until recently, such ultrastable glasses 8 Glass-forming ability 29 were limited to complex molecular and polymer glasses; more recently however, vapour deposition has allowed 9 Conclusions 30 the preparation of ultrastable metallic glasses [9]. When formed from the liquid phase, the properties of a glass depend strongly on its thermal history, i.e. its cooling rate, and it cannot be assumed to be at equilibrium, since glasses are known to \age", or find more thermodynamically favourable states as 3 time passes. Recent developments in vapour deposition energy (the forces) are zero. The minima correspond techniques have allowed the synthesis of ultrastable to stable and metastable atomic configurations, and glasses occupying equilibrium states equivalent to a the saddle points to transition states between minima. supercooled liquid aged for thousands of years or cooled Common atomistic calculations examine local features at a rate 19 orders of magnitude slower than current of the landscape, such as a minimum (zero temperature methods allow [10]. Although aging is believed to structure optimisation) or a limited region determined allow a glass to find more stable states, experimental by the temperature (molecular dynamics), but our aim determinations of the enthalpies of ultrastable metallic is to link collective and statistical features of the PEL glasses formed by vapour deposition suggests that with the properties of amorphous materials and glasses. their stability is not necessarily a result of being This review is organised as follows. In section1 in the lowest thermodynamic state [9]. There are we introduce the topic of computational modelling of many empirical measures of glass forming ability (see glasses and the problems therein, setting some basic section8), but there is not coherent microscopic defintions. In section2, we introduce the theoretical structural explanation that accounts for the differences frameworks most commonly used to model glasses, between compositions. Furthermore, it is possible to with an emphasis on the potential energy landscape. synthesise stable glasses from compositions with low In section3 we discuss the construction of the potential phenomenological glass forming ability such as Fe1-xCx energy landscape paradigm in a more rigorous way, using thin film vapour deposition techniques[11]. This focusing on the statistical mechanics required to suggests that there is something missing in the various link microscopic computer models to thermodynamic empirical measures of glass forming ability, and a more quantities. In section4, we summarise the methods fundamental description is required. for sampling the potential energy landscape, i.e. how An example of a good glass former is B2O3.A to generate atomistic models of glasses. In section5 B2O3 melt does not crystallise even when seeded with we describe the methods by which such structural a crystallite of the stable phase, as a result of the models can be analysed. Simple empirical models low driving force and slow kinetics; its crystallisation of glasses are discussed in section6, followed by can only be induced at high pressure, when enthalpic an extension to the use of first principles electronic considerations force the structure to adopt an optimal structure calculations for higher quality models in packing [12]. This leads to the question of which section7. Finally, we discuss possible methods parameters define a good glass former. In general, and parameters for distinguishing good crystal-formers we describe a material that has a high tendency
Load more

Recommended publications
  • DNA Energy Landscapes Via Calorimetric Detection of Microstate Ensembles of Metastable Macrostates and Triplet Repeat Diseases
    DNA energy landscapes via calorimetric detection of microstate ensembles of metastable macrostates and triplet repeat diseases Jens Vo¨ lkera, Horst H. Klumpb, and Kenneth J. Breslauera,c,1 aDepartment of Chemistry and Chemical Biology, Rutgers, The State University of New Jersey, 610 Taylor Rd, Piscataway, NJ 08854; bDepartment of Molecular and Cell Biology, University of Cape Town, Private Bag, Rondebosch 7800, South Africa; and cCancer Institute of New Jersey, New Brunswick, NJ 08901 Communicated by I. M. Gelfand, Rutgers, The State University of New Jersey, Piscataway, NJ, October 15, 2008 (received for review September 8, 2008) Biopolymers exhibit rough energy landscapes, thereby allowing biological role(s), if any, of kinetically stable (metastable) mi- biological processes to access a broad range of kinetic and ther- crostates that make up the time-averaged, native state ensembles modynamic states. In contrast to proteins, the energy landscapes of macroscopic nucleic acid states remains to be determined. of nucleic acids have been the subject of relatively few experimen- As part of an effort to address this deficiency, we report here tal investigations. In this study, we use calorimetric and spectro- experimental evidence for the presence of discrete microstates scopic observables to detect, resolve, and selectively enrich ener- in metastable triplet repeat bulge looped ⍀-DNAs of potential getically discrete ensembles of microstates within metastable DNA biological significance. The specific triplet repeat bulge looped structures. Our results are consistent with metastable, ‘‘native’’ ⍀-DNA species investigated mimic slipped DNA structures DNA states being composed of an ensemble of discrete and corresponding to intermediates in the processes that lead to kinetically stable microstates of differential stabilities, rather than DNA expansion in triplet repeat diseases (36).
    [Show full text]
  • Ruggedness in the Free Energy Landscape Dictates Misfolding of the Prion Protein
    Article Ruggedness in the Free Energy Landscape Dictates Misfolding of the Prion Protein Roumita Moulick 1, Rama Reddy Goluguri 1 and Jayant B. Udgaonkar 1,2 1 - National Centre for Biological Sciences, Tata Institute of Fundamental Research, Bengaluru 560065, India 2 - Indian Institute of Science Education and Research, Pashan, Pune 411008, India Correspondence to Jayant B. Udgaonkar: Indian Institute of Science Education and Research, Pashan, Pune 411008, India. [email protected] https://doi.org/10.1016/j.jmb.2018.12.009 Edited by Sheena Radford Abstract Experimental determination of the key features of the free energy landscapes of proteins, which dictate their adeptness to fold correctly, or propensity to misfold and aggregate and which are modulated upon a change from physiological to aggregation-prone conditions, is a difficult challenge. In this study, sub-millisecond kinetic measurements of the folding and unfolding of the mouse prion protein reveal how the free energy landscape becomes more complex upon a shift from physiological (pH 7) to aggregation-prone (pH 4) conditions. Folding and unfolding utilize the same single pathway at pH 7, but at pH 4, folding occurs on a pathway distinct from the unfolding pathway. Moreover, the kinetics of both folding and unfolding at pH 4 depend not only on the final conditions but also on the conditions under which the processes are initiated. Unfolding can be made to switch to occur on the folding pathway by varying the initial conditions. Folding and unfolding pathways appear to occupy different regions of the free energy landscape, which are separated by large free energy barriers that change with a change in the initial conditions.
    [Show full text]
  • Introducing the Levinthal's Protein Folding Paradox and Its Solution
    Article pubs.acs.org/jchemeduc Introducing the Levinthal’s Protein Folding Paradox and Its Solution Leandro Martínez* Department of Physical Chemistry, Institute of Chemistry, University of Campinas, Campinas, Saõ Paulo 13083-970, Brazil *S Supporting Information ABSTRACT: The protein folding (Levinthal’s) paradox states that it would not be possible in a physically meaningful time to a protein to reach the native (functional) conformation by a random search of the enormously large number of possible structures. This paradox has been solved: it was shown that small biases toward the native conformation result in realistic folding times of realistic-length sequences. This solution of the paradox is, however, not amenable to most chemistry or biology students due to the demanding mathematics. Here, a simplification of the study of the paradox and its solution is provided so that it is accessible to chemists and biologists at an undergraduate or graduate level. Despite its simplicity, the model captures some fundamental aspects of the protein folding mechanism and allows students to grasp the actual significance of the popular folding funnel representation of the protein energy landscape. The analysis of the folding model provides a rich basis for a discussion of the relationships between kinetics and thermodynamics on a fundamental level and on student perception of the time-scales of molecular phenomena. KEYWORDS: Upper-Division Undergraduate, Graduate Education, Biochemistry, Biophysical Chemistry, Molecular Biology, Proteins/Peptides,
    [Show full text]
  • Complex Energy Landscapes” (IPAM Program, Fall 2017)
    Whitepaper: “Complex Energy Landscapes” (IPAM program, fall 2017) Authors list (alphabetically) Nestor F. Aguirre, Chris Anderson, Lorenzo Boninsegna, Gábor Csányi, Mauricio del Razo Sarmina, Marco Di Gennaro, Florent Hédin, Graeme Henkelman, Richard G. Hennig, Jan Janßen, Tony Lelièvre, Hao Li, Mitchell Luskin, Noa Marom, Jörg Neugebauer, Feliks Nüske, Joshua Paul, Danny Perez, Giovanni Pinamonti, Petr Plechac, Biswas Rijal, Gideon Simpson, Justin C. Smith, Thomas Swinburne, Anne Marie Z. Tan, Mira Todorova, Dallas R. Trinkle, Stephen Xie, Ping Yang Abstract Recent advances in computational resources and the development of high-throughput frameworks enable the efficient sampling of complicated multivariate functions. This includes energy and electronic property landscapes of inorganic, organic, biomolecular, and hybrid ​ ​ materials and functional nanostructures. Combined with new developments in data science, this ​ leads to a rapidly growing need for numerical methods and a fundamental mathematical ​ ​ understanding of efficient sampling approaches, optimization techniques, hierarchical surrogate models, coarse-graining techniques, and methods for uncertainty quantification. The complexity of these energy and property landscapes originates from their simultaneous dependence on discrete degrees of freedom – i.e., number of atoms and species types – and continuous ones – i.e., the position of atoms. Moreover, dynamical behavior governed by complex landscapes involves a rich hierarchy of timescales and is characterized by rare events
    [Show full text]
  • Protein Functional Landscapes, Dynamics, Allostery 297
    Quarterly Reviews of Biophysics 43, 3 (2010), pp. 295–332. f Cambridge University Press 2010 295 doi:10.1017/S0033583510000119 Printed in the United States of America Protein functional landscapes,dynamics, allostery: a tortuouspathtowards a universal theoretical framework Pavel I. Zhuravlev and Garegin A. Papoian* Department of Chemistry and Biochemistry, Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA Abstract. Energy landscape theories have provided a common ground for understanding the protein folding problem, which once seemed to be overwhelmingly complicated. At the same time, the native state was found to be an ensemble of interconverting states with frustration playing a more important role compared to the folding problem. The landscape of the folded protein – the native landscape – is glassier than the folding landscape; hence, a general description analogous to the folding theories is difficult to achieve. On the other hand, the native basin phase volume is much smaller, allowing a protein to fully sample its native energy landscape on the biological timescales. Current computational resources may also be used to perform this sampling for smaller proteins, to build a ‘topographical map’ of the native landscape that can be used for subsequent analysis. Several major approaches to representing this topographical map are highlighted in this review, including the construction of kinetic networks, hierarchical trees and free energy surfaces with subsequent structural and kinetic analyses. In this review, we extensively discuss the important question of choosing proper collective coordinates characterizing functional motions. In many cases, the substates on the native energy landscape, which represent different functional states, can be used to obtain variables that are well suited for building free energy surfaces and analyzing the protein’s functional dynamics.
    [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]
  • Chemical Physics of Protein Folding
    Chemical physics of protein folding Peter G. Wolynesa,1, William A. Eatonb, and Alan R. Fershtc aDepartment of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, TX 77005; bNational Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892; and cMedical Research Council Laboratory of Molecular Biology, Cambridge CB2 0QH, United Kingdom n 2008, to the consternation of some, logically distinct traps. In other words, the Many of the most intriguing questions of one of the editors of this special issue energy landscape of evolved proteins ap- mechanism can only be addressed feebly at on the “Chemical Physics of Protein pears to be funneled (6, 7). the level of ensemble-averaged experi- I ” “ Folding, was quoted as saying, What The overall funneled nature of the folding ments; thus, folding science has called forth was called the protein folding problem 20 landscape provides a first guess of how some extremely challenging experiments in years ago is solved” (1). One purpose of this folding begins and continues: Proteins fold which molecules are studied individually special issue is to drive home this point. The by assembling primarily native substructures, oneatatime(17–19). On the computa- other, more important purpose is to illus- whereas they only transiently sample mis- tional side, although effective theories of trate how workers on the protein folding folds. This insight explains the success of folding can often use simplified models that problem, by moving beyond their early ob- protein engineering in providing detailed make interesting and surprising predictions session with seeming paradoxes (2), are structural information on the transition state (20, 21), many questions of detail can developing a quantitative understanding ensemble, the so-called “φ-value analysis” now be answered satisfactorily with fully of how the simpler biological structures (8, 9).
    [Show full text]
  • Modeling the Free Energy Landscape of Biomolecules Via Dihedral Angle Principal Component Analysis of Molecular Dynamics Simulations
    Modeling the Free Energy Landscape of Biomolecules via Dihedral Angle Principal Component Analysis of Molecular Dynamics Simulations Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften vorgelegt beim Fachbereich Biochemie, Chemie und Pharmazie der Goethe-Universit¨at in Frankfurt am Main von Alexandros Altis aus Frankfurt am Main Frankfurt am Main 2008 (D 30) vom Fachbereich Biochemie, Chemie und Pharmazie der Goethe-Universit¨at Frankfurt am Main als Dissertation angenommen. Dekan: Prof. Dr. Dieter Steinhilber 1. Gutachter: Prof. Dr. Gerhard Stock 2. Gutachter: JProf. Dr. Karin Hauser Datum der Disputation: ............................................. Contents 1 Introduction 1 2 Dihedral Angle Principal Component Analysis 7 2.1 Introduction to molecular dynamics simulation . ........ 9 2.2 Definition and derivation of principal components . ......... 11 2.3 Circularstatistics ................................ 12 2.4 Dihedral angle principal component analysis (dPCA) . ....... 18 2.5 Asimpleexample-trialanine . 19 2.6 Interpretation of eigenvectors . ..... 22 2.7 ComplexdPCA ................................. 25 2.8 Energylandscapeofdecaalanine. 27 2.9 CartesianPCA ................................. 31 2.10 DirectangularPCA............................... 35 2.11 Correlationanalysis. 39 2.12 Nonlinear principal component analysis . ...... 42 2.13Conclusions ................................... 43 3 Free Energy Landscape 47 3.1 Introduction................................... 47 3.2 Clustering ...................................
    [Show full text]
  • Energy Landscapes for Proteins: from Single Funnels to Multifunctional Systems
    Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems K. R¨oder,1,† J. A. Joseph,1,† Brooke E. Husic1,2 and D. J. Wales1,∗ 1: Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW, Cambridge, UK 2: Current affiliation: Chemistry Department, Stanford University, 333 Campus Drive, Stanford, CA 94305, USA ∗ Corresponding author: [email protected] † These authors contributed equally. Article type: Progress Report Keywords: Energy landscapes, protein folding, multifunnel paradigm In this report we advance the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. We compare systems that exhibit single, double, and multiple competing structures, and contrast multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self-organising and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter. 1 Introduction The field of protein science underwent dramatic transformations with the groundbreaking ex- periments of Sanger[1] and Kendrew,[2] characterising the sequence of insulin and the three- dimensional structure of myoglobin,
    [Show full text]
  • Making the Best of a Bad Situation: a Multiscale Approach to Free Energy Calculation Arxiv:1901.04455V3 [Physics.Comp-Ph] 22 F
    Making the best of a bad situation: a multiscale approach to free energy calculation Michele Invernizzi∗,y,{ and Michele Parrinelloz,{ yDepartment of Physics, ETH Zurich c/o USI Campus, Lugano, Switzerland zDepartment of Chemistry and Applied Biosciences, ETH Zurich c/o USI Campus, Lugano, Switzerland {Facolt`adi Informatica, Instituto di Scienze Computationali, and National Center for Computational Design and Discovery of Novel Materials MARVEL, Universit`adella Svizzera italiana (USI), Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland E-mail: [email protected] Abstract Many enhanced sampling techniques rely on the identification of a number of col- lective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently and reconstruct the free energy landscape. In methods like metadynamics, the quality of these collective variables plays a key role in convergence efficiency. Unfortunately in many systems of interest it is not possible to identify an optimal collective variable, and one must deal arXiv:1901.04455v3 [physics.comp-ph] 22 Feb 2019 with the non-ideal situation of a system in which some slow modes are not accelerated. We propose a two-step approach in which, by taking into account the residual mul- tiscale nature of the problem, one is able to significantly speed up convergence. To do so, we combine an exploratory metadynamics run with an optimization of the free en- ergy difference between metastable states, based on the recently proposed variationally 1 enhanced sampling method. This new method is well parallelizable and is especially suited for complex systems, because of its simplicity and clear underlying physical picture.
    [Show full text]
  • Mapping Transiently Formed and Sparsely Populated Conformations on a Complex Energy Landscape Yong Wang, Elena Papaleo, Kresten Lindorff-Larsen*
    RESEARCH ARTICLE Mapping transiently formed and sparsely populated conformations on a complex energy landscape Yong Wang, Elena Papaleo, Kresten Lindorff-Larsen* Structural Biology and NMR Laboratory, Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark Abstract Determining the structures, kinetics, thermodynamics and mechanisms that underlie conformational exchange processes in proteins remains extremely difficult. Only in favourable cases is it possible to provide atomic-level descriptions of sparsely populated and transiently formed alternative conformations. Here we benchmark the ability of enhanced-sampling molecular dynamics simulations to determine the free energy landscape of the L99A cavity mutant of T4 lysozyme. We find that the simulations capture key properties previously measured by NMR relaxation dispersion methods including the structure of a minor conformation, the kinetics and thermodynamics of conformational exchange, and the effect of mutations. We discover a new tunnel that involves the transient exposure towards the solvent of an internal cavity, and show it to be relevant for ligand escape. Together, our results provide a comprehensive view of the structural landscape of a protein, and point forward to studies of conformational exchange in systems that are less characterized experimentally. DOI: 10.7554/eLife.17505.001 Introduction *For correspondence: lindorff@ Proteins are dynamical entities whose ability to change shape often plays essential roles in bio.ku.dk their function. From an experimental point of view, intra-basin dynamics is often described via con- Competing interests: The formational ensembles whereas larger scale (and often slower) motions are characterized as authors declare that no a conformational exchange between distinct conformational states.
    [Show full text]
  • Energy Landscape Underlying Spontaneous Insertion and Folding of an Alpha-Helical Transmembrane Protein Into a Bilayer
    ARTICLE DOI: 10.1038/s41467-018-07320-9 OPEN Energy landscape underlying spontaneous insertion and folding of an alpha-helical transmembrane protein into a bilayer Wei Lu1,2, Nicholas P. Schafer1,3 & Peter G. Wolynes1,2,3,4 Membrane protein folding mechanisms and rates are notoriously hard to determine. A recent force spectroscopy study of the folding of an α-helical membrane protein, GlpG, showed that 1234567890():,; the folded state has a very high kinetic stability and a relatively low thermodynamic stability. Here, we simulate the spontaneous insertion and folding of GlpG into a bilayer. An energy landscape analysis of the simulations suggests that GlpG folds via sequential insertion of helical hairpins. The rate-limiting step involves simultaneous insertion and folding of the final helical hairpin. The striking features of GlpG’s experimentally measured landscape can therefore be explained by a partially inserted metastable state, which leads us to a reinter- pretation of the rates measured by force spectroscopy. Our results are consistent with the helical hairpin hypothesis but call into question the two-stage model of membrane protein folding as a general description of folding mechanisms in the presence of bilayers. 1 Center for Theoretical Biological Physics, Rice University, Houston 77005 TX, USA. 2 Department of Physics, Rice University, Houston 77005 TX, USA. 3 Department of Chemistry, Rice University, Houston 77005 TX, USA. 4 Department of Biosciences, Rice University, Houston 77005 TX, USA. These authors contributed equally:
    [Show full text]