Physics of biomolecules and cells

xxxiv

1.8	How to do it twice . . . . . . . . . . . . . . . . . . . . . . . . . . .	449
1.9	The care and proofreading of knots . . . . . . . . . . . . . . . . . .	451
1.10	Suppression of supercoils . . . . . . . . . . . . . . . . . . . . . . . .	453
1.11	Problems and outlook . . . . . . . . . . . . . . . . . . . . . . . . .	455
1.12	Disquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	457
2 Gene expression networks. Methods for analysis
of DNA chip experiments		457
2.1	The regulation of gene expression . . . . . . . . . . . . . . . . . .	457
2.2	Gene expression arrays . . . . . . . . . . . . . . . . . . . . . . . . .	460
2.3	Analysis of array data . . . . . . . . . . . . . . . . . . . . . . . . .	463
2.4	Some simplifying assumptions . . . . . . . . . . . . . . . . . . . . .	464
2.5	Probeset analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .	466
2.6	Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	470
3 Neural and gene expression networks: Song-induced gene
expression in the canary brain		471
3.1	The study of songbirds . . . . . . . . . . . . . . . . . . . . . . . . .	472
3.2	Canary song . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	473
3.3	ZENK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	474
3.4	The blush . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	476
3.5	Histological analysis . . . . . . . . . . . . . . . . . . . . . . . . . .	476
3.6	Natural vs. artificial . . . . . . . . . . . . . . . . . . . . . . . . . .	479
3.7	The Blush II: gAP . . . . . . . . . . . . . . . . . . . . . . . . . . .	480
3.8	Meditation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	481

Course 11. Thinking About the Brain
	by W. Bialek	485
1	Introduction	487
2	Photon counting	491
3	Optimal performance at more complex tasks	501
4	Toward a general principle?	518
5	Learning and complexity	538
6	A little bit about molecules	552
7	Speculative thoughts about the hard problems	564

Seminars by participants

579

Preface

Matter has many states, including soft condensed, inert or alive. The latter is far from thermodynamic equilibrium, and apparently has an agenda of its own. Yet the same physical laws apply to all matter. The difference is in the complexity to which living systems have evolved, to states that gather and process information, replicate themselves, etc.

Molecular and cell biology have dramatically expanded our knowledge about this complexity in the last decades. This knowledge is the foundation of biological physics, which is currently expanding rapidly and is itself adding to this knowledge. Its role in biology is a wonderful challenge: to draw the line between necessity and possibility, between results of immutable physical laws and results of evolution that may be specific to the one natural history we have access to. The study of life is, after all, similar to reverse engineering1. What fascinating engineering it describes, however! The deeper one gets into the details, the more captivating the study becomes: these systems were “designed” bottom-up, so answers to some of the biggest questions about Life are hidden in their smallest parts.

The 75th Les Houches summer school addressed the physics of biomolecules and cells. In biological systems ranging from single biomolecules to entire cells and larger biological systems, it focused on aspects that require concepts and methods from physics for their analysis and understanding. The school opened with two parallel lecture series by Robijn Bruinsma and Jonathon Howard. Physics of Protein-DNA Interaction by Robijn Bruinsma started from the structure of DNA and associated proteins, and lead to discussions of electrostatic interactions between proteins and DNA, and the diffusive search for specific binding sites. Joe Howard’s lectures on Mechanics of Motor Proteins discussed mechanical properties of individual proteins and motors, and of complex cytoskeletal structures. Simultaneously, Evan Evans’ shorter series

Using Force to Probe Chemistry of Biomolecular Bonds and Structural Transitions explored the rich dynamic behaviors of rupturing individual biomolecular bonds. These lectures were followed by Erich Sackmann’s discussion of Micro-rheometry of Actin Networks and Cellular Scaffolds. He gave an introduction to membranes and the cytoskeleton and discussed the mechanical properties of cells and the physics of cell adhesion. Robijn Bruinsma

1 Reverse engineering: “the process of analysing a subject system to identify the system’s components and their interrelationships and create representations of the system in another form or at a higher level of abstraction”. (E.J. Chikofsky and J.H. Cross, II. IEEE Software 7 (1990) 13-17.)

xxii

complemented Erich Sackmann’s lectures with theoretical lectures on Statistical Mechanics and Bioadhesion. The second half of the school contained two long, parallel lecture series by Thomas Duke and Bill Bialek. Tom Duke complemented Joe Howard’s course with Modelling Motor Protein Systems, which focused more on theoretical approaches. Starting with physical models for motor proteins, he discussed physical aspects of cilia and flagella and showed that active physical phenomena on the cellular scale are important in hearing. Another example of motion generation was discussed in Jacques Prost’s lectures Physics of Listeria Propulsion, which provided a general description of how the controlled polymerization of an actin gel can be used for propulsion. Bill Bialek’s long series of lectures Thinking About the Brain gave an introduction to the principles governing sensory and nervous systems. Starting from simple examples of information processing in the visual system of the fly, he moved to fundamental questions on how nervous systems process information. In

Bioinformatics and Statistical Mechanics Eric Siggia reviewed decoding of genetic information obtained from genome projects. It was followed by Bob Austin’s lectures on Microand Nanotechnology-Physics in Biotechnology, new technologies which make it possible to study and manipulate biomolecules in artificial arrays and structures. Marcelo Magnasco wrapped up the school excellently with his Three Lectures on Biological Networks, which covered the unknotting of DNA, the analysis of gene chip data, and studies of gene expression in learning canaries, all in a style that kept the attention of the audience to the last minute of four weeks.

The lectures were complemented by invited seminars given by Albert Libchaber (RecA Polymerization on Single-Stranded DNA and Directed Evolution: A Molecular Study) and Marileen Dogterom (Polymerization Forces). Two public lectures were given in the town of Les Houches, by Albert Libchaber (Qu'est-ce que la vie ?) and Thomas Duke (Les moteurs de la vie). Furthermore, Phil Williams gave an invited lecture within Evan Evan's series, and Tom McLeish and Chris Wiggins contributed with seminars: The Mysterious Case of Too Many β-Sheets and Into Physical Models of Biopolymers, respectively. During a study period, Tom McLeish gave a well-attended tutorial on thermally activated barrier crossing, on the school's lawn, with Mt. Blanc as a backdrop and most illustrative barrier. We also organized sixteen short student presentations over four evenings, and two poster sessions with a total of seventeen posters; see titles and presenters at the end of this volume. The students had great energy and enthusiasm, and, amazingly in view of their schedule, kept it up till the very end.

This school had three times as many applicants as there are seats in the lecture hall, and we had to turn down many strong applicants. We hope this book to some extent makes up for this unfortunate restriction on admission.

xxiii

The relative isolation of the Les Houches Physics School on the mountain side vis-à-vis Mt. Blanc is perfect for learning and interacting. As are long hikes in the mountains on weekends. Life-long friendships are formed, we know: Two of this school’s organizers first met as students in a Les Houches summer school. If the present school has taught and inspired its participants as much as that school did years ago, we have done well.

Acknowledgements

The four weeks spent in Les Houches went smoothly, thanks to the staff of the school: Ghislaine D'Henry, Isabel Lelièvre and Brigitte Rousset. The school was sponsored by NATO as an Advanced Study Institute, by the EU as a

Eurosummerschool, by CNRS as an École Théematique, and by the Danish Research Agency through its Graduate School of Biophysics. NSF covered travel costs for some US residents. We thank them all for making the school possible. We are convinced that this book presents outstanding examples of biological physics, and thank the contributors again for their great efforts of lecturing and writing.

Henrik Flyvbjerg

Frank Jülicher

Pál Ormos

François David

COURSE 1

PHYSICS OF PROTEIN-DNA INTERACTION

R.F. BRUINSMA

Department of Physics and

Astronomy, University of California, Los Angeles, CA 90024, USA,

and Instituut-Lorentz for Theoretical

Physics, Universiteit Leiden,

Postbus 9506, 2300 Leiden,

The Netherlands

Contents

1	Introduction		3
	1.1	The central dogma and bacterial gene expression . . . . . . . . . .	3
	1.2	Molecular structure . . . . . . . . . . . . . . . . . . . . . . . . . .	8
2	Thermodynamics and kinetics of repressor-DNA interaction		16
	2.1	Thermodynamics and the lac repressor . . . . . . . . . . . . . . . .	16
	2.2	Kinetics of repressor-DNA interaction . . . . . . . . . . . . . . . .	26
3	DNA deformability and protein-DNA interaction		34
	3.1	Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	34
	3.2	The worm-like chain . . . . . . . . . . . . . . . . . . . . . . . . . .	40
	3.3	The RST model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	50
4	Electrostatics in water and protein-DNA interaction		53
	4.1	Macro-ions and aqueous electrostatics . . . . . . . . . . . . . . . .	54
	4.2	The primitive model . . . . . . . . . . . . . . . . . . . . . . . . . .	56
	4.3	Manning condensation . . . . . . . . . . . . . . . . . . . . . . . . .	58
	4.4	Counter-ion release and non-specific protein-DNA interaction . . .	63

PHYSICS OF PROTEIN-DNA INTERACTION

R.F. Bruinsma

1 Introduction

1.1 The central dogma and bacterial gene expression

1.1.1 Two families

Life is based on a symbiotic relationship between two families of biopolymers: DNA and RNA, constituted of nucleic-acids, and proteins, constituted of amino-acids [1]. Proteins are the active agents of the cell. As enzymes, they control the rates of biochemical reactions taking place inside the cell. They are responsible for the transcription of the genetic code, i.e., the production of copies of short segments of the genetic code that are used as blue-prints for the production of new proteins, and for the duplication of the genetic code, i.e., the production of a full copy of the genetic code during cell division. Synthesis of other macromolecules, such as lipids and sugars, is carried out by proteins, the mechanical force of our muscles is generated by specialized proteins adept at “mechano-chemistry”, they detect light, sound, and smell, and maintain the structural integrity of cells.

If we view the cell as a miniature chemical factory that simultaneously runs many chemical processes, then the proteins form the control system of the factory, turning reactions on and o . The control system obeys orders from the central o ce: the cell nucleus. The DNA inside the nucleus can be considered as the memory of the computer system of the central o ce: it is the information storage system of the cell. Blueprints for the synthesis of proteins are stored in the form of DNA base-pair sequences, much like strings of zero’s and one’s store information in digital computers. A gene is the data string required for the production of one protein (actually, multiple variants of a protein can be produced from the same gene). The beginning and end points of a gene are marked by special “start” and a “stop” signals. When a protein has to be synthesized, a specialized copying protein, RNA polymerase, transcribes a copy of a gene beginning at the start signal and ending at the stop signal (see Fig. 1).

c EDP Sciences, Springer-Verlag 2002

4	Physics of Bio-Molecules and Cells

Fig. 1. Gene transcription.

This copy is in the form of an RNA strand known as mRNA (or “messenger” RNA). A huge molecular machine, the Ribosome, synthesizes the protein from the mRNA blueprint. Interestingly, these Ribosomes are compound constructs of RNA strands (known as rRNA) and proteins, with the active biochemistry carried out not by the protein part, as you might have expected, but by the RNA part. Indeed, unlike DNA, RNA strands are in fact capable to act as enzymes.

The information stream is strictly one way: DNA contains the information required for the synthesis of proteins. The genetic code is not altered by the transcription, and RNA strands do not insert their code into DNA. We call this basic principle of biochemical information flow the “central dogma”. We know next to nothing about how this elaborate relationship between the nucleic and amino acids developed. The basic chemical structure of the two families is quite di erent. The molecular biology of living organisms is all highly similar and based on the central dogma and we do not know of the existence of more primitive molecular information and control systems from which we could somehow infer a developmental history (though we suspect that once upon a time both information storage and enzymatic activity was based purely on RNA since RNA is able to carry out enzymatic activity as we saw). The central dogma applies to living organisms. Retroviruses are able to insert their RNA code into host DNA, using a special enzyme called “reverse transcriptase”. This looks like an exception to the central dogma but viruses are not considered living organisms since they are not able to reproduce themselves independently nor do they carry out metabolic activity, the two defining requirements of a living organism.

R.F. Bruinsma: Physics of Protein-DNA Interaction

5

It is reasonable to ask why biopolymers should be of special interest to physicists. The physics of polymers – particular synthetic polymers – has been studied for decades and an elegant, general theoretical framework is available. The motivation behind a study of the interaction between DNA and proteins is quite di erent from that of a study of synthetic polymers. In polymer physics, we want to compute the free energy and correlation functions of a typical polymer in a solution or melt, with results that are as much as possible independent of the detailed molecular structure of the polymers. That philosophy does not apply to biopolymers where we are dealing with highly a-typical molecules that carry out certain functions. Their structure presumably evolved under the adaptive pressures exerted on micro-organisms that relied for their survival on e cient performance of the functions these molecules are involved with. A molecular biophysicist tries to shed light on how functional molecular devices work and how their design constraints are met. These are of course very complex systems, so it is a good strategy to focus as much as possible on basic principles of physics of general validity and relying as little as possible on assumptions concerning the detailed molecular structure. The hope is that this will provide us with constraints on the design and operation of functional biopolymers in the way that the Second Law of Thermodynamics constrains the maximum e ciency of steam engines.

In order to illustrate this approach, we will focus on two special cases that have been particularly important in the development of our understanding of protein-DNA interaction, the lac repressor and the Nucleosome Complex. These two systems have been studied in such detail that we may hope to understand how they “work” as molecular devices. In these lectures, we will see what insights thermodynamics, statistical mechanics, elasticity theory, and electrostatics can provide us in this respect.

1.1.2 Prokaryote gene expression

How does an organism “know” when to turn gene transcription on and when to turn it o ? We divide cells in two groups: eukaryotes and prokaryotes. The cells of animals and plants – the eukaryotes – have their DNA sequestered inside a nucleus and the cell has a complex set of internal “organs” called organelles. Gene expression of eukaryotic cells, the focus of much current research, is a complex a air, which we will discuss in a later section. Bacteria, prokaryotes, lack a nucleus and organelles and their gene expression is much better understood [3]. We will discuss a simple example: the expression of the “lac” gene of the bacterium Escirichia Coli (E.Coli for short) [4].

Large numbers of the E.Coli parasitic bacteria live inside your intestines (“colon”). When you drink a glass of milk, part of it will be metabolized

6	Physics of Bio-Molecules and Cells

not by you but by your E.Coli bacteria. The first step is the breakdown of lactose, sugar molecules consisting of two linked molecular rings. Lactose is broken down into two single-ring glucose molecules. This chemical reaction requires an enzyme, called “β Galactosidase”, to proceed because lactose does not dissociate spontaneously (an enzyme speeds up a reaction by lowering the activation energy barrier). First though, the lactose molecules must be transferred from the exterior of the bacterium to the cell interior (or “cytoplasm”) across the membrane that surrounds E.Coli. This is done by another protein, called “Permease”. Finally, a third protein, called “Transacetylase”, is required for chemical modification of the sugar molecules.

The DNA of E.Coli carries three separate genes for the production of these three enzymes: lacY, lacZ, and lacA. Expression of the three genes starts when the environmental lactose concentration rises, and it stops when the lactose concentration drops (to avoid wasteful use of precious macromolecular material). The three genes are located right behind each other on the DNA, and – sensibly – they are transcribed collectively. Such a cluster of functionally connected genes is called an “operon”. The lac operon also contains three regulatory sequences:

a)Promoter Sequence

This sequence is “recognized” by RNA Polymerase. By that we mean that RNA Polymerase molecules in solution bind to Promoter Sequences on the DNA but not to other sequences. From this start site, RNA polymerase can transcribe RNA in either direction. In one direction, “downstream”, it produces the RNA code of our three enzymes. In the other direction, “upstream”, it transcribes the neighboring “Regulator” sequence.

b)Regulator Sequence

The Regulator sequence is the code of a fourth protein: lac repressor. The lac repressor, which is not involved in the metabolic of lactose, plays a key regulatory role in turning the gene “on” or “o ”.

c)Operator Sequence

The operator sequence is a DNA sequence that is recognized by lac repressor. If lac repressor is bound to the operator sequence, then downstream gene expression is blocked. The Figure 2 shows how this “genetic switch” works.

First, assume that the concentration of lactose in the environment is high. Lactose molecules bind reversibly to the repressor protein. For high lactose concentrations, the lactose-bound form is favored under conditions of chemical equilibrium. In the lactose-bound (or “induced”) form, the repressor