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Ask not what physics can do for biology—ask what biology can do for physics
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Phys. Biol. 11 053004 (http://iopscience.iop.org/1478-3975/11/5/053004) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 131.91.169.193 This content was downloaded on 22/05/2015 at 11:50
Please note that terms and conditions apply.
Physical Biology Phys. Biol. 11 (2014) 053004 (4pp)
doi:10.1088/1478-3975/11/5/053004
Perspective
Ask not what physics can do for biology— ask what biology can do for physics Hans Frauenfelder Los Alamos National Laboratory, USA E-mail: [email protected]
Abstract
Stan Ulam, the famous mathematician, said once to Hans Frauenfelder: ‘Ask not what Physics can do for biology, ask what biology can do for physics’. The interaction between biologists and physicists is a two-way street. Biology reveals the secrets of complex systems, physics provides the physical tools and the theoretical concepts to understand the complexity. The perspective gives a personal view of the path to some of the physical concepts that are relevant for biology and physics (Frauenfelder et al 1999 Rev. Mod. Phys. 71 S419–S442). Schrödinger’s book (Schrödinger 1944 What is Life? (Cambridge: Cambridge University Press)), loved by physicists and hated by eminent biologists (Dronamraju 1999 Genetics 153 1071–6), still shows how a great physicist looked at biology well before the first protein structure was known. Keywords: biophysics, physics–biology interface, interdisciplinary, protein structure
Biology and physics
The interaction between physics and biology has for the most part been one-way. Physics has provided experimental tools such as the microscope, x-rays, NMR, lasers and computers, and theoretical tools such as the quantum theory and statistical physics. When biology impacts physics, biology often provides the facts on which physics builds theoretical constructs as for instance network theory [4]. Physics and biology are intrinsically different. Equations with predictive power such as Newton’s or Schrödinger’s or Dirac’s quantitatively explain a huge number of phenomena. In biology, to my knowledge, similar laws with predictive power do not yet exist. On the other hand, biology provides an infinite amount of data that call for unifying concepts. A physicist moving into biology can select a subset with which he or she can wrestle with the tools of physics to find such concepts. My own research started in 1947 as a nuclear physicist at the ETH in Zurich, mainly using perturbed angular correlation of nuclear radiation. I continued this work after moving to the University of Illinois in 1952. The direction changed in 1960 after Mössbauer’s discovery of the effect named after him. An accidental social interaction with a famous biochemist, I C Gunsalus (‘Gunny’) led to a collaboration with biochemists to use the Mössbauer effect for studying proteins. The first major discovery that we made was that biologists and physicists use different languages. To establish a bridge between the two cultures we instituted joint lunches and seminars, sometimes at midnight. Equally important we worked together in the lab. The Mössbauer work led to a number of spectroscopic results at Illinois and in other laboratories. In 1969, the first Mössbauer conference dedicated to biological systems was held at the University of Illinois [5]. It was at this conference that Cyrus Levinthal presented his famous paradox. Most of the other talks presented static Mössbauer spectra. In the final discussion session I asked: ‘Proteins must move. Why are there no motion studies?’ The answer was 1478-3975/14/053004+04$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
Phys. Biol. 11 (2014) 053004
Perspective
‘Too difficult’. We considered this statement a challenge and searched for ways to study protein motions. The technique that we finally adapted was flash photolysis in which a reaction is initiated by a flash of light and observed optically. Take myoglobin (Mb), the protein that carries dioxygen (O2) in muscles and that also binds carbon monoxide (CO) to form MbCO. Hitting MbCO with a laser flash breaks the MbCO bond. The CO moves away and returns and rebinds. Around 1970 Mb was considered to be fully understood [6]. It was the prototype of a simple protein with unique structure, no conformational motion, no Bohr’s effect, no allostery. Oxygen binding was a one-step reaction with the temperature dependence given by the Arrhenius equation. These claims were shown to be wrong by experiments over broad ranges of time, temperature, pressure, pH, and viscosity [7–12]. Even simple proteins are exceedingly complex. A quantitative understanding with predictive power will require interaction and collaboration among biologists, chemists, computer scientists, mathematicians and physicists. All disciplines will gain.
Life is motion
At present the protein data bank contains the structure of more than 100 000 proteins [13]. These structures are static snapshots that show the stage but not the action. To understand the function, movies are needed that show the structure as it evolves. Free-electron lasers permit shooting such movies, but such research is in an early stage [14]. However, while a protein structure can be obtained within a very short time, movies will take much more time and it is difficult to imagine that 100 000 movies will be produced and analyzed. It is therefore important to search for concepts that are valid for a broad range of biological processes. In the following I sketch some concepts that have emerged in the past half-century. Conformational substates (CS)
Proteins could not function if they existed in only one structure; they must be able to assume many different conformations, called conformational substates. Substates because proteins have usually different states such as oxy- and deoxy or bound and unbound, each of these states contains substates. The fact that biomolecules must be able to have multiple conformations had been anticipated by Schrödinger [2] and by Linderstrom-Lang and Schellman [15]. An unambiguous proof for the existence of substates came from low-temperature flash photolysis experiments because the binding process is highly non-exponential in time [7]. Non-exponential processes can be explained in two ways. Either all proteins have the same non-exponential time dependence or binding is exponential in each protein, but proteins in different substates have different rate coefficients. Multiple flash experiments eliminated the first alternative; a protein sample thus must consist of proteins in many different conformational substates. Biologists were not convinced and said: ‘Look at the beautiful x-ray structures; they prove that proteins have unique structures!’ The fallacy in this argument is obvious. The published structures are averages, selected by the computer [16]. CS are here to stay; they are necessary for proteins to move and function. As an aside we note that the use of a logarithmic time scale is still not universally accepted; a text says: if one exponential does not fit, use two. The resistance may be overcome by explaining that log t is just pt, where p has the same meaning as p in pH. The free-energy landscape (FEL)
Proteins in different CS have different structures and energies. In nuclei and atoms states are drawn in energy level diagrams. In proteins the number of different CS is 2
Phys. Biol. 11 (2014) 053004
Perspective
so gigantic that diagrams are inadequate; the CS are described in the FEL [17]. At any instance of time, the structure of a protein is described by the set of the coordinates of all its atoms, a point in a gigantic hyperspace. A conformational transition is a leap from one point to another one. One or two-dimensional cross sections through the energy landscape give some insight into the FEL. Such cross sections indicate that the FEL is organized in a hierarchy of different tiers [18]. The existence of the FEL and its organization into tiers has been confirmed by computation and experiments, for instance [19–22]. Reactions
Proteins such as enzymes often perform chemical reactions. In this field collaboration among biologists, chemists, and physicists can be particularly productive. Traditionally chemical reactions have been evaluated using the transition state theory (TST). This theory has at least two weak points: (i) deviations of a reaction rate from the canonical value of approximately 1012 s−1 are blamed on entropy. The deviation is, however, more convincingly explained by the Kramers theory as being caused by friction [23]. Thus the TST can lead to wrong information about the entropy changes in biological reactions. (ii) The conventional approach pictures the reaction as a motion over a static potential barrier, but conformational motions are essential for many reactions. The reaction can then be pictured as the passage of a molecule through a fluctuating gate [8]. Motions and fluctuations
These terms do not appear in most biological and biophysical texts, but life would be impossible without motions. The study of motions caused by fluctuations may be where biologists and theoretical and experimental physicists can collaborate profitably. Protein folding is a case where the function is described by the folding funnel, a clear case of an FEL [24] and where without motions the protein could not reach its working structures. The binding of CO and O2 to Mb is another case where motions are crucial for function as pointed out earlier. The binding process is actually very complicated. Flash photolysis and Laue diffraction techniques [14, 25, 26] demonstrate that the ligand performs a carefully choreographed dance among many positions inside the protein before covalently binding to the iron [27, 28]. The dance would not be possible without fluctuating conformations. The structural fluctuations imply fluctuations in the FEL. The protein motions are controlled by thermal fluctuations and two processes known from the physics of supercooled liquids and glasses [29, 30]. These are the α-fluctuations in the bulk solvent and the βh-fluctuations in the hydration shell of the protein [31]. Even the final step in the binding process, forming the covalent bond, is a combination of a transition over an enthalpic barrier and conformational motions [32]. The conclusion from even simple biological processes is clear: the interdisciplinary collaboration between biology and physics can lead to quantitative insight into biological processes and even produce new physics. References [1] Frauenfelder H, Wolynes P G and Austin R H 1999 Biological Physics Rev. Mod. Phys. 71 S419–42 [2] Schrödinger E 1944 What is Life? (Cambridge: Cambridge University Press) [3] Dronamraju K R 1999 Erwin schrödinger and the origins of molecular biology Genetics 153 1071–6 [4] Hopfield J J 1982 Neural networks and physical systems with emergent collective computational abilities Proc. Natl. Acad. Sci. USA 79 2554–8 [5] Debrunner P, Tsibris J C M and Münck E (ed) 1969 Mössbauer Spectroscopy in Biological Systems (Champaign, IL: University of Illinois Press) 3
Phys. Biol. 11 (2014) 053004
Perspective
[6] Antonini E and Brunori M 1971 Hemoglobin and Myoglobin in Their Reactions with Ligands (Amsterdam: North-Holland) [7] Austin R H et al 1975 Dynamics of ligand binding to myoglobin Biochemistry 14 5355–73 [8] Beece D et al 1980 Solvent viscosity and protein dynamics Biochemistry 19 5147–57 [9] Doster W et al 1982 Control and pH dependence of ligand binding to heme proteins Biochemistry 21 4831–9 [10] Frauenfelder H et al 1990 Proteins and pressure J. Phys. Chem. 94 1024–37 [11] Kleinert T et al 1998 Solvent composition and viscosity effects on the kinetics of co binding to horse myoglobin Biochemistry 37 717–33 [12] Frauenfelder H, McMahon B H, Austin R H, Chu K and Groves T 2001 The role of structure, energy landscape, dynamics, and allostery in the enzymatic function of myoglobin Proc. Natl. Acad. Sci. USA 98 2370–4 [13] www.wwpdb.org [14] Neutze R 2014 Opportunities and challenges for time-resolved studies of protein structural dynamics at x-ray free-electron lasers Phil. Trans. R. Soc. B 369 20130318 [15] Linderstrom-Lang K U and Schellman J A 1959 Enzymes 1 443 [16] Frauenfelder H, Petsko G A and Tsernoglou D 1979 Temperature-dependent x-ray diffraction as a probe of protein structural dynamics Nature 280 558–63 [17] Frauenfelder H, Sligar S G and Wolynes P G 1991 The energy landscapes and motions of proteins Science 254 1598–603 [18] Ansari A et al 1985 Protein states and proteinquakes Proc. Natl. Acad. Sci. USA 82 5000–4 [19] Kitao A, Hayward S and Go N 1998 Energy landscape of a native protein: jumping-amongminima model proteins: structure Funct., Genet. 33 496–517 [20] Hofmann C, Aartsma T J, Michel H and Köhler J 2003 Direct observation of tiers in the energy landscape of a chromoprotein: a single-molecule study Proc. Natl. Acad. Sci. USA 100 15534–8 [21] Zhuravlev P and Papoian G A 2010 Protein functional landscapes, dynmics, allostery: a tortuous path towards a universal theoretical framework Q. Rev. Biophys. 1–38 [22] Milanesi L et al 2012 Measurement of energy landscape roughness of folded and unfolded proteins Proc. Natl. Acad. Sci. USA 109 19563–8 [23] Hänggi P, Talkner P and Borkovec M 1990 Reaction-rate theory: fifty years after Kramers Rev. Mod. Phys. 62 251–341 [24] Bryngelson J D, Onuchic J N, Socci N D and Wolynes P G 1995 Funnels, pathways, and the energy landscape of protein folding: a synthesis Proteins 21 167–95 [25] Srajer V et al 2001 Protein conformational relaxation and ligand migration in myoglobin: a nanosecond to millisecond molecular movie from time-resolved laue x-ray diffraction. Biochemistry 40 13802–15 [26] Bourgeois D et al 2006 Extended subnanosecond structural dynamics of myoglobin revealed by Laue crystallography Proc. Natl. Acad. Sci. USA 103 4924–9 [27] Mourant J R et al 1993 Ligand binding to heme proteins: II. transitions in the heme pocket of myoglobin Biophys. J. 65 1496–507 [28] Lamb D C et al 2002 Structural dynamics of myoglobin J. Biol. Chem. 277 11636–44 [29] Donth E 2001 The Glass Transition (Berlin: Springer) [30] Frauenfelder H et al 2009 A unified model of protein dynamics Proc. Natl. Acad. Sci. USA 106 5129–34 [31] Lubchenko V, Wolynes P G and Frauenfelder H 2005 Mosaic energy landscapes in liquids and the control of protein conformational dynamics by glass-forming solvents J. Phys. Chem. B 109 7488–99 [32] McMahon B H et al 2000 Microscopic model of carbon monoxide binding to myoglobin J. Chem. Phys. 113 6831–50
4
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My IOPscience
Ask not what physics can do for biology—ask what biology can do for physics
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Phys. Biol. 11 053004 (http://iopscience.iop.org/1478-3975/11/5/053004) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 131.91.169.193 This content was downloaded on 22/05/2015 at 11:50
Please note that terms and conditions apply.
Physical Biology Phys. Biol. 11 (2014) 053004 (4pp)
doi:10.1088/1478-3975/11/5/053004
Perspective
Ask not what physics can do for biology— ask what biology can do for physics Hans Frauenfelder Los Alamos National Laboratory, USA E-mail: [email protected]
Abstract
Stan Ulam, the famous mathematician, said once to Hans Frauenfelder: ‘Ask not what Physics can do for biology, ask what biology can do for physics’. The interaction between biologists and physicists is a two-way street. Biology reveals the secrets of complex systems, physics provides the physical tools and the theoretical concepts to understand the complexity. The perspective gives a personal view of the path to some of the physical concepts that are relevant for biology and physics (Frauenfelder et al 1999 Rev. Mod. Phys. 71 S419–S442). Schrödinger’s book (Schrödinger 1944 What is Life? (Cambridge: Cambridge University Press)), loved by physicists and hated by eminent biologists (Dronamraju 1999 Genetics 153 1071–6), still shows how a great physicist looked at biology well before the first protein structure was known. Keywords: biophysics, physics–biology interface, interdisciplinary, protein structure
Biology and physics
The interaction between physics and biology has for the most part been one-way. Physics has provided experimental tools such as the microscope, x-rays, NMR, lasers and computers, and theoretical tools such as the quantum theory and statistical physics. When biology impacts physics, biology often provides the facts on which physics builds theoretical constructs as for instance network theory [4]. Physics and biology are intrinsically different. Equations with predictive power such as Newton’s or Schrödinger’s or Dirac’s quantitatively explain a huge number of phenomena. In biology, to my knowledge, similar laws with predictive power do not yet exist. On the other hand, biology provides an infinite amount of data that call for unifying concepts. A physicist moving into biology can select a subset with which he or she can wrestle with the tools of physics to find such concepts. My own research started in 1947 as a nuclear physicist at the ETH in Zurich, mainly using perturbed angular correlation of nuclear radiation. I continued this work after moving to the University of Illinois in 1952. The direction changed in 1960 after Mössbauer’s discovery of the effect named after him. An accidental social interaction with a famous biochemist, I C Gunsalus (‘Gunny’) led to a collaboration with biochemists to use the Mössbauer effect for studying proteins. The first major discovery that we made was that biologists and physicists use different languages. To establish a bridge between the two cultures we instituted joint lunches and seminars, sometimes at midnight. Equally important we worked together in the lab. The Mössbauer work led to a number of spectroscopic results at Illinois and in other laboratories. In 1969, the first Mössbauer conference dedicated to biological systems was held at the University of Illinois [5]. It was at this conference that Cyrus Levinthal presented his famous paradox. Most of the other talks presented static Mössbauer spectra. In the final discussion session I asked: ‘Proteins must move. Why are there no motion studies?’ The answer was 1478-3975/14/053004+04$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
Phys. Biol. 11 (2014) 053004
Perspective
‘Too difficult’. We considered this statement a challenge and searched for ways to study protein motions. The technique that we finally adapted was flash photolysis in which a reaction is initiated by a flash of light and observed optically. Take myoglobin (Mb), the protein that carries dioxygen (O2) in muscles and that also binds carbon monoxide (CO) to form MbCO. Hitting MbCO with a laser flash breaks the MbCO bond. The CO moves away and returns and rebinds. Around 1970 Mb was considered to be fully understood [6]. It was the prototype of a simple protein with unique structure, no conformational motion, no Bohr’s effect, no allostery. Oxygen binding was a one-step reaction with the temperature dependence given by the Arrhenius equation. These claims were shown to be wrong by experiments over broad ranges of time, temperature, pressure, pH, and viscosity [7–12]. Even simple proteins are exceedingly complex. A quantitative understanding with predictive power will require interaction and collaboration among biologists, chemists, computer scientists, mathematicians and physicists. All disciplines will gain.
Life is motion
At present the protein data bank contains the structure of more than 100 000 proteins [13]. These structures are static snapshots that show the stage but not the action. To understand the function, movies are needed that show the structure as it evolves. Free-electron lasers permit shooting such movies, but such research is in an early stage [14]. However, while a protein structure can be obtained within a very short time, movies will take much more time and it is difficult to imagine that 100 000 movies will be produced and analyzed. It is therefore important to search for concepts that are valid for a broad range of biological processes. In the following I sketch some concepts that have emerged in the past half-century. Conformational substates (CS)
Proteins could not function if they existed in only one structure; they must be able to assume many different conformations, called conformational substates. Substates because proteins have usually different states such as oxy- and deoxy or bound and unbound, each of these states contains substates. The fact that biomolecules must be able to have multiple conformations had been anticipated by Schrödinger [2] and by Linderstrom-Lang and Schellman [15]. An unambiguous proof for the existence of substates came from low-temperature flash photolysis experiments because the binding process is highly non-exponential in time [7]. Non-exponential processes can be explained in two ways. Either all proteins have the same non-exponential time dependence or binding is exponential in each protein, but proteins in different substates have different rate coefficients. Multiple flash experiments eliminated the first alternative; a protein sample thus must consist of proteins in many different conformational substates. Biologists were not convinced and said: ‘Look at the beautiful x-ray structures; they prove that proteins have unique structures!’ The fallacy in this argument is obvious. The published structures are averages, selected by the computer [16]. CS are here to stay; they are necessary for proteins to move and function. As an aside we note that the use of a logarithmic time scale is still not universally accepted; a text says: if one exponential does not fit, use two. The resistance may be overcome by explaining that log t is just pt, where p has the same meaning as p in pH. The free-energy landscape (FEL)
Proteins in different CS have different structures and energies. In nuclei and atoms states are drawn in energy level diagrams. In proteins the number of different CS is 2
Phys. Biol. 11 (2014) 053004
Perspective
so gigantic that diagrams are inadequate; the CS are described in the FEL [17]. At any instance of time, the structure of a protein is described by the set of the coordinates of all its atoms, a point in a gigantic hyperspace. A conformational transition is a leap from one point to another one. One or two-dimensional cross sections through the energy landscape give some insight into the FEL. Such cross sections indicate that the FEL is organized in a hierarchy of different tiers [18]. The existence of the FEL and its organization into tiers has been confirmed by computation and experiments, for instance [19–22]. Reactions
Proteins such as enzymes often perform chemical reactions. In this field collaboration among biologists, chemists, and physicists can be particularly productive. Traditionally chemical reactions have been evaluated using the transition state theory (TST). This theory has at least two weak points: (i) deviations of a reaction rate from the canonical value of approximately 1012 s−1 are blamed on entropy. The deviation is, however, more convincingly explained by the Kramers theory as being caused by friction [23]. Thus the TST can lead to wrong information about the entropy changes in biological reactions. (ii) The conventional approach pictures the reaction as a motion over a static potential barrier, but conformational motions are essential for many reactions. The reaction can then be pictured as the passage of a molecule through a fluctuating gate [8]. Motions and fluctuations
These terms do not appear in most biological and biophysical texts, but life would be impossible without motions. The study of motions caused by fluctuations may be where biologists and theoretical and experimental physicists can collaborate profitably. Protein folding is a case where the function is described by the folding funnel, a clear case of an FEL [24] and where without motions the protein could not reach its working structures. The binding of CO and O2 to Mb is another case where motions are crucial for function as pointed out earlier. The binding process is actually very complicated. Flash photolysis and Laue diffraction techniques [14, 25, 26] demonstrate that the ligand performs a carefully choreographed dance among many positions inside the protein before covalently binding to the iron [27, 28]. The dance would not be possible without fluctuating conformations. The structural fluctuations imply fluctuations in the FEL. The protein motions are controlled by thermal fluctuations and two processes known from the physics of supercooled liquids and glasses [29, 30]. These are the α-fluctuations in the bulk solvent and the βh-fluctuations in the hydration shell of the protein [31]. Even the final step in the binding process, forming the covalent bond, is a combination of a transition over an enthalpic barrier and conformational motions [32]. The conclusion from even simple biological processes is clear: the interdisciplinary collaboration between biology and physics can lead to quantitative insight into biological processes and even produce new physics. References [1] Frauenfelder H, Wolynes P G and Austin R H 1999 Biological Physics Rev. Mod. Phys. 71 S419–42 [2] Schrödinger E 1944 What is Life? (Cambridge: Cambridge University Press) [3] Dronamraju K R 1999 Erwin schrödinger and the origins of molecular biology Genetics 153 1071–6 [4] Hopfield J J 1982 Neural networks and physical systems with emergent collective computational abilities Proc. Natl. Acad. Sci. USA 79 2554–8 [5] Debrunner P, Tsibris J C M and Münck E (ed) 1969 Mössbauer Spectroscopy in Biological Systems (Champaign, IL: University of Illinois Press) 3
Phys. Biol. 11 (2014) 053004
Perspective
[6] Antonini E and Brunori M 1971 Hemoglobin and Myoglobin in Their Reactions with Ligands (Amsterdam: North-Holland) [7] Austin R H et al 1975 Dynamics of ligand binding to myoglobin Biochemistry 14 5355–73 [8] Beece D et al 1980 Solvent viscosity and protein dynamics Biochemistry 19 5147–57 [9] Doster W et al 1982 Control and pH dependence of ligand binding to heme proteins Biochemistry 21 4831–9 [10] Frauenfelder H et al 1990 Proteins and pressure J. Phys. Chem. 94 1024–37 [11] Kleinert T et al 1998 Solvent composition and viscosity effects on the kinetics of co binding to horse myoglobin Biochemistry 37 717–33 [12] Frauenfelder H, McMahon B H, Austin R H, Chu K and Groves T 2001 The role of structure, energy landscape, dynamics, and allostery in the enzymatic function of myoglobin Proc. Natl. Acad. Sci. USA 98 2370–4 [13] www.wwpdb.org [14] Neutze R 2014 Opportunities and challenges for time-resolved studies of protein structural dynamics at x-ray free-electron lasers Phil. Trans. R. Soc. B 369 20130318 [15] Linderstrom-Lang K U and Schellman J A 1959 Enzymes 1 443 [16] Frauenfelder H, Petsko G A and Tsernoglou D 1979 Temperature-dependent x-ray diffraction as a probe of protein structural dynamics Nature 280 558–63 [17] Frauenfelder H, Sligar S G and Wolynes P G 1991 The energy landscapes and motions of proteins Science 254 1598–603 [18] Ansari A et al 1985 Protein states and proteinquakes Proc. Natl. Acad. Sci. USA 82 5000–4 [19] Kitao A, Hayward S and Go N 1998 Energy landscape of a native protein: jumping-amongminima model proteins: structure Funct., Genet. 33 496–517 [20] Hofmann C, Aartsma T J, Michel H and Köhler J 2003 Direct observation of tiers in the energy landscape of a chromoprotein: a single-molecule study Proc. Natl. Acad. Sci. USA 100 15534–8 [21] Zhuravlev P and Papoian G A 2010 Protein functional landscapes, dynmics, allostery: a tortuous path towards a universal theoretical framework Q. Rev. Biophys. 1–38 [22] Milanesi L et al 2012 Measurement of energy landscape roughness of folded and unfolded proteins Proc. Natl. Acad. Sci. USA 109 19563–8 [23] Hänggi P, Talkner P and Borkovec M 1990 Reaction-rate theory: fifty years after Kramers Rev. Mod. Phys. 62 251–341 [24] Bryngelson J D, Onuchic J N, Socci N D and Wolynes P G 1995 Funnels, pathways, and the energy landscape of protein folding: a synthesis Proteins 21 167–95 [25] Srajer V et al 2001 Protein conformational relaxation and ligand migration in myoglobin: a nanosecond to millisecond molecular movie from time-resolved laue x-ray diffraction. Biochemistry 40 13802–15 [26] Bourgeois D et al 2006 Extended subnanosecond structural dynamics of myoglobin revealed by Laue crystallography Proc. Natl. Acad. Sci. USA 103 4924–9 [27] Mourant J R et al 1993 Ligand binding to heme proteins: II. transitions in the heme pocket of myoglobin Biophys. J. 65 1496–507 [28] Lamb D C et al 2002 Structural dynamics of myoglobin J. Biol. Chem. 277 11636–44 [29] Donth E 2001 The Glass Transition (Berlin: Springer) [30] Frauenfelder H et al 2009 A unified model of protein dynamics Proc. Natl. Acad. Sci. USA 106 5129–34 [31] Lubchenko V, Wolynes P G and Frauenfelder H 2005 Mosaic energy landscapes in liquids and the control of protein conformational dynamics by glass-forming solvents J. Phys. Chem. B 109 7488–99 [32] McMahon B H et al 2000 Microscopic model of carbon monoxide binding to myoglobin J. Chem. Phys. 113 6831–50
4
