Editors Dionys Baeriswyl Institut fur Theoretische Physik, ETH ZSrich HSnggerberg, CH-8093 ZLirich, Switzerland Michel Droz Andreas Malaspinas DPT, Universit~ de Gen~ve 24, quai E.-Ansermet, CH-1211 Gen~ve 4, Switzerland Piero Marfinoli Inetitut de Physique, Universit~ de Neuch&tel 1, rue A.-L. Breguet, CH-2000 Neuch&tel, Switzerland IS BN 3-540-18192-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18192-X Springer-Verlag NewYork Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specificallyt he rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisionso f the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 198"7 Printed in Germany Printing: Druckhaus Beltz, Hemsbach/Bergstr.; Bookbinding: J. Sch&ffer GmbH & Co. KG., GrOnstadt 2153/3140-543210 PREFACE Physicists have always been fascinated by the puzzling world of biological phenomena, but recently the temptation of applying physical ideas and methods to living matter has increased dramatically. This is not only a result of improved experimental techniques and data analysis but also of a growing interest in complex structures and dynamics. The improved ability of dealing with many degrees of freedom allows us to study theoretically the emergence of structures and patterns on a scale which is typically much larger than the size of the microscopic constituents. Viscous fingering and the roughening transition are prom- inent examples. Topological defects, which play an important role in solid state physics and field theory, also belong to this class. Often these structures do not represent the true thermodynamic equilibrium; they can grow and decay in time or even freeze out. Thus nontrivial spatial patterns are frequently associated with interesting time evo- lutions. The possible impact of physics in life sciences is twofold. On the one hand the powerful experimental and theoretical techniques devel- oped for studying complex physical phenomena can certainly be very useful in the biological context. On the other hand certain physical concepts such as symmetryand symmetry breaking, linear and nonlinear stability, frustration and constrained dynamics are likely to be equal- ly useful. It was the aim of the tenth workshop in Gwatt to elucidate this double role of physics in the study of living matter. Since it was obviously impossible to cover exhaustively such a wide subject we tried to make an exemplary selection of topics. Part I deals with the structural and functional building blocks, the biomolecules, and their role in the evolution process. H. Frauen- felder's contribution can serve as a clear illustration of the general theme of the workshop. Part II is devoted to symmetry and structure. Y. Bouligand shows that symmetries observed in biological systems are strikingly similar to those observed in certain physical systems, in particular in liquid crystals. He also suggests that symmetry break- ing is intimately connected to the emergence of life.W. Braun, U. Aebi and P. B~siger explain experimental techniques for investigating the structure of proteins, cells and organs, especially nuclear magnetic IV resonance and electron microscopy. It becomes clear that careful image processing is essential for extracting detailed structural information from raw data. Part III is concerned with thermodynamics and transport properties of living matter, in particular of biomembranes. O. Mourit- sen demonstrates that mathematical modeling can provide new insight into the relation between structure and biological function, whereas E. Neher describes a refined experimental technique which allows one to detect electrical currents flowing through single tiny channels across membranes. Part IV is devoted to neural networks. K. Hepp and V. Henn describe the ne~ralpathways associated with visual perception and subsequent eye movements. H.R. L~scher attributes the transfer of stimuli to muscles to the cooperative action of a random neural network. Models for the processes of learning, storage and retrieval of information in the central nerve system are described by R.M.J. Cotterill and W. Kinzel. We are grateful to E. Kellenberger (Biozentrum Basel), K. Hepp (ETH ZHrich) and H.R. Zeller (Brown Boveri Research Center Baden) for their advice in establishing the scientific program. The meeting was finan- cially supported by the Swiss National Science Foundation, the Swiss Physical Society, the chemical industry in Basel (Ciba-Geigy, Hoffmann- La Roche, Lonza and Sandoz) and the research laboratories of Brown Boveri Baden, IBM ZHrich and RCA ZOrich. We also thank the Evangeli- sche Heimst~tte Gwatt for providing a comfortable housing which great- ly facilitated fruitful conversations. We hope that the present collection of papers together with the numerous references will help to stimulate the curiosity of physicists about biological problems. At the same time we hope that this small volume will further the goodwill of biologists towards the attempt of physicists to advance into the complex field of living matter. Geneva, March 1987 Dionys Baeriswyl Michel Droz Andreas Malaspinas Piero Martinoli TABLE OF CONTENTS I. Dynamics of Proteins and Evolution H. Frauenfelder: The Protein as a Physics Laboratory 1 M. Eigen: The Physics of Evolution 15 II. Symmetry and Structure Y. Bouligand: Symmetries in Biology 17 W. Braun: Calculation of Protein Structures from NMR Data 32 U. Aebi: Structural Analysis at Molecular Dimensions of Proteins and Protein Assemblies Using Electron Microscopy (EM) and Image Processing 5~ P. Boesiger: Magnetic Resonance Imaging in Medicine 62 M. Kunt: Digital Image Processing 73 III. Biomembranes and Nonequilibrium Phenomena O.G. Mouritsen: Physics of Biological Membranes 76 E. Neher: Transport and Signal Transfer Across Biomembranes 110 J. Ross: Chemical Instabilities and Applications of Biological Interest 119 IV. Neural Networks and Vision H.-R. LHscher: The Innervation of Skeletal Muscles: Properties Emerging from a Random Neural Network 123 R.J.M. Cotterill: Physics of the Brain 138 W. Kinzel: Models of Neural Networks 152 K. Hepp and V. Henn: Nonabelian Neurodynamics 163 List of Participants 178 THE PROTEIN AS A PHYSICS LABORATORY Hans Frauenfelder Department of Physics University of Illinois at Urbana-Champalgn iii0 West Green Street, Urbana, IL 61801 Why should physicists be interested in blomolecules? One reason is that physics and in particular physical techniques have had, and still have, a great impact on biological sciences. A prime example is X-ray diffraction which in the hands of Max Perutz and John Kendrew led to the elucidation of the three- dimensional structure of proteins. A second reason is the fact that proteins are beautifully designed laboratories in which many physics problems can be studied. A few years ago I had dinner with Stan Ulam at the Los Alamos Inn. After telling him about our work he said: "I understand what you are saying. Ask not what physics can do for biology, ask what biology can do for physics." In these notes I will discuss two areas, complexity and reactions, where experiments on proteins provide new information. Both of these areas llnk blomolecules to physics and chemistry and both contain many unsolved and challenging problems. I. PROTEINS Proteins are the structural elements and the machines of llfe; they form all the elements and perform the myriads of tasks that a living system needs. 1 A brief description of their construction can be found in ref. 2. Here only the most sketchy outline is given. Proteins are built from twenty different building blocks, amino acids. Details of the structure of the amino acids are not important here. In constructing a protein, nature covalently links of the order of i00 to 200 amino acids into a linar "polypeptide" chain. In the proper solvent the chain spontaneously folds into the working three-dlmenslonal "tertiary" structure. The arrangement of the amino acids in the primary sequence completely determines the tertiary structure and the function of the protein. A globular protein typically has a molecular weight of the order of 20,000 dalton, a linear dimension of a few nm, and it consists of a few thousand atoms. Proteins are therefore complex many-body systems, at the border between classical and quantum mechanics. They are also disordered in the sense of a Picasso painting or Beethoven's Grosse Fuge. One important aspect is the highly anlsotropic arrangement of the forces. Along the polypeptide chain or backbone, the bonds are covalent and are therefore not broken by thermal fluctuations. The three-dlmensionl structure is, however, stabilized by hydrogen bonds and Van der Waals forces. These '~eak" forces can be spontaneously broken by thermal fluctuations so that the protein is a very flexible and mobile system. We will consider a particular class, heme proteins. In these molecules, the folded polypeptlde chain or globln contains a small organic molecule, protoheme. Protoheme is a roughly spherical molecule of about 1 nm diameter, with an iron atom at the center. Heme proteins perform a wide variety of tasks, from storage and transport of matter and electricity to the catalysis of reactions. The best known hems protein is hemoglobin, the oxygen carrier. We will be concerned mainly with myoglobln, which stores oxygen in the muscles. Myoglobln (Mb) is built from 153 amino acids, has a molecular weight of about 18,000 dalton, contains about 1200 non-hydrogen atoms, and has dimensions of about 3 x 4 x 4 nm. 3 Fig. 1 shows f 3 °~n / ,,/ / Fig. 1 Schematic cross section through myoglobln. / li?o~.~eA ~- -~ . ~ ~ % a schematic cross section through Mb. The reversible storage of dloxygen (0 2 ) occurs at the hems iron; we represent it by the equation Mb + 0 2 ~ MbO 2. (I) This relation appears extremely simple, but it turns out that we know less now than when we started our work about 15 years ago. In fact, the closer one looks at the reactions involved in Eq. (I), the more one appreciates Bohr's favorite Schiller verse: "Nur die F~lle fHhrt zur Klarhelt, Und im Abgrund liegt die Wahrheit." 2. EXPERIMENTAL TECHNIQUES Biomolecular phenomena are so complex that every available physical and chemical tool must be used for the elucidation of structure and function. We sketch here only two techniques to at least provide some insight into the gathering of the essential experimental data. 2.1 Flash photolysis. Flash photolysis is simply a photodissociation experiment. In the standard approach in physics~ all one observes is the process of dissociation, as for instance in the photodisintegration of the deuteron. In biological physics, in contrast, both photodissociation and rebinding are observed. Consider for instance carbonmonoxymyoglobin, MbCO, where carbon monoxide is bound to the heme iron of Mb. A laser pulse breaks the bond between the iron atom and the CO molecule. The CO molecule then separates from the iron and at high temperatures from the Mb molecule. Ultimately, however, it will rebind so that the reaction cycle is y + HbCO + Mb + CO + MbCO. (2) The reaction can be followd for instance by observation of the optical spectrum near 440 nm, where Mb and MbCO have a very different extinction coefficient (Venous and arterial blood have different colorl). It is important to study the reaction (2) over wide ranges in time (fs to Ms), temperature (2-300 K), and pressure (to 2 kbar). The experimental arrangement is slmple3: A thin MbC0 sample is placed into a cryostat with windows. The Fe-CO bond is broken with a short laser flash and the subsequent dissociation and reassociation processes are followed optically. To observe the entire time range, different lasers and approaches are needed. 4-7 Since many protein phenomena are nonexponential in time and cover many orders of magnitude in time, results must nearly always be plotted versus log time. Fig. 2 shows typical rebinding data. The data describe log N(t) versus log t, where N(t) denotes the fraction of Mb molecules that have not rebound a CO molecule at the time t after photodissociation. id 2 _ io-6 io-S io-4 io-~ 16 z lo- ~ Time(s ) Fig. 2 Time dependence of the binding of carbon monoxide to myoglobin. N(t) is the fraction of Mb molecules that have not rebound a CO at the time t after photodlssociation. (The fit is from R.D. Young and S.F. Bowne, J. Chem. Phys. 81, 3730 (1984)). 2.2 X-ray dlffraction. As pointed out in the introduction, the determination of the electron density of myoglobin and hemoglobin by Kendrew and Perutz, respectively, was one of the truly fundamental steps in the exploration of blomolecules. A clear and beautiful description of many aspects of the structure determination is given in ref. 8. It turns out, however, that X-ray diffraction is capable of yielding considerably more information than Just the average structure. Two applications of particular importance to protein dynamics are the determination of the Debye-Waller factor and of the thermal expansion. (1) Debye-Waller Systems exhibiting nonexponentlal time dependencies have been treated by a wide variety of theoretical approaches, e.g. refs. 14, 16-18. The nonexponential time dependence can be explained by homogeneous or by inhomogeneous processes. Consider a system that consists of a number of subsystems, for instance the individual Mb molecules in a sample. In a homogeneous system~ all subsystems are identical and each subsystem exhibits nonexponential time dependence. In an inhomogeneous system, each subsystem can have exponential behavior, but with different rates. The ensemble then shows the nonexponentiallty. Remarkably enough, proteins show both types of behavior. The homogeneous case will be discussed somewhat later. In the binding of CO to Mb, we have shown conclusively by repeated photodissoclation ("hole burning in time") that the Mb sample must be inhomogeneous. 3'19 Each protein molecule can be characterized by a single rate coefficient. Assume that the rate coefficient k is determined by an Arrhenlus relation, k(H) = A exp(-H/k B T), (4) where H is the height of the barrier governing the reaction. The observed binding process can be fitted by a linear superposltion of exponential terms, N(t) - f dH g(H) exp{-k(H)/t}, (5) where g(H)dH is the probability of having a Mb molecule with barrier height between H and H + dH. Inverting the Laplace transform Eq. (5) (not trivial) with Eq. (4) yields the probability distribution g(H) and values of the preexponential A for each protein-ligand combination. Values of A are typically of the order of 10 9 s-i; g(H) is characteristic for the protein-ligand combination. 3'13 3.2 Conformational substates. Why do different protein molecules with the same primary sequence possess different activation enthalpies H at low temperatures? The simplest explanation is based on the complexity of protein folding and protein structure. Folding is unlikely to lead to a unique tertiary structure. The protein structure is so flexible and so complex that small changes in the structure and the arrangement of the weak bonds and of the water molecules on the outside of the protein are unlikely to change the total binding energy of the protein by mach. We therefore assume that a given protein~ say sperm whale myoglobin, can exist in a large number of conformatlonal substates (cs). 3'9-II All conformational substates have the same overall structure, but differ in smaller features. All cs perform the same function, e.g. binding of dioxygen, but may have different rates. The concept of conformational substates, introduced in 197320 , is analogous to the concept of energy valleys in spin glasses. 21 Each substate is a valley in the Gibbs energy surface, separated by high barriers from other valleys. At temperatures below about 180 K, a protein will remalu frozen in a particular cs; above about 200 Kj a protein will fluctuate from ca to c$. All present experi- mental evidence is consistent with the concept of substatea. Particularly striking evidence comes from the Debye-Waller factor. 9-II As pointed out above, different substates have different values of the activation enthalpy H for the binding of CO and 0 2. Different substates thus have different properties and this fact may be analogous to replica-symmetry breaking in the theory of spin glasses. 3.3 States and substates. The existence of conformatlonal substate8 leads to some new features. In order to perform a function~ a protein must be able to exist in more than one state. Myoglobin, for instance, can be in the llganded or the unliganded state, MbCO and Mb. Cytochrome c, an electron carrler~ can be in an oxidized and a reduced state. Since each of these states can assume a multitude of cs, we must distinguish two different types of motions, equilibrium fluctuations (EF) and nonequillbrlum motions. EF lead from one substate to another. The nonequilibrium motions lead from one state to another. Since they are involved in the function of the protein or enzyme, we call them functionally important motions, or fims. Equilibrium fluctuations and rims are related by fluctuation-dissipatlon theorems. 22-25 The theorem is, of course, only valid if fluctuations and dissipative motions cover essentially the same substates. 3.4 Noner~odiclty and time scales. 26 In the application of physical concepts to proteins and in the extraction of new concepts from blomolecular experiments, the time scales must be considered. Assume that a protein can hop from cs to cs with a rate k r = I/Tr~ where ~r is the hopping (relaxation) time. The response of the system to an experimental observation depends on T r and on the characteristic time Cob s of the observation. If T r << tobs, the system passes through all substaces during the observation and it appears as er~odic. If Tr >> tobs, each subsystem is frozen into a particular substate during the experiment and the system appears as noner~odic. In general T r is a strong function of temperature and the properties of the system as seen by a particular observation will depend on T. 3.5 Proteinquakes. 27 The shift of tectonic plates in the earth can lead to stress and the build-up of strain energy. An earthquake occurs when the stress is relieved and the strain energy dissipated, resulting in a permanent deformation and the emission of shear and pressure waves. In a protein, stress is established for instance when CO binds to the hems iron in Mb. When photodlssociation breaks the bond between the iron atom and the CO molecule, the stress is relieved and the protein changes from the liganded to the unliganded structure. We call the rearrangement after the bond breaking a proteinquake. Progress of the quake can be followed by monitoring suitable spectroscopic markers. The protelnquake following the photodlssoclatlon of MbCO, monitored by a number of techniques 27, implies that the release of the strain energy occurs in a