Biophysics:  Searching for Principles

 

William Bialek

 

For several years I have been teaching PHY 562 at Princeton, which is a Biophysics course for PhD students in Physics, and I have the ambition of turning my lecture notes into a book, to be published by Princeton University Press.  This site has the current draft of the book, downloadable all at once or chapter by chapter.  I hope this is useful.

 

I should emphasize that things still are a bit rough.  The course changes every time I teach it, and whole sections have never been written up.  I try, in spots, to give a hint (in red) about what is missing.   I have given the current draft to my editor, but this is just the start of a process, so there is plenty of time for input, and I would appreciate any help you are willing to offer!  Please don’t hesitate to drop me a note.  If you’d like to cite any of the things you find here, I think you can use:

 

W Bialek, Biophysics: Searching for Principles.  http://www.princeton.edu/~wbialek/PHY562.html (2011).

 

For a complete draft, click on the title at the top the page.  For the individual chapters, click on the items below.

 

Data you will need for the problems can be found here.

 

For Spring 2012:  I will teach the course once again.  We have twelve weeks of lectures, and so the plan is to spend three weeks on each of the main topics, as indicated by the dates next to the chapter titles.  We will choose problems from the text, with one substantial assignment each week.   Grades will be based 50% on homework and 50% on the final exam.

 

Introduction (Lecture M 6 Feb)

 

              A.  About our subject

                  B.  About this book

                  C.  About this draft

                  Acknowledgments

 

1. Photon counting in vision (Lectures W 8 Feb through W 22 Feb 2012)

 

In this Chapter, we will see that humans (and other animals) can detect the arrival of individual photons at the retina.  Tracing through the many steps from photon arrival to perception we will see a sampling of the physics problems posed by biological systems, ranging from the dynamics of single molecules through amplification and adaptation in biochemical reaction networks, coding and computation in neural networks, all the way to learning and cognition.  For photon counting some of these problems are solved, but even in this well studied case many problems are open and ripe for new theoretical and experimental work.  The problem of photon counting also introduces us to methods and concepts of much broader applicability.  We begin by exploring the phenomenology, aiming at the formulation of the key physics problems.  By the end of the Chapter I hope to have formulated an approach to the exploration of biological systems more generally, and identified some of the larger questions that will occupy us in Chapters to come.

 

                  A.  Posing the problem

                  B.  Single molecule dynamics

                  C.  Dynamics of biochemical networks

                  D.  The first synapse, and beyond

                  E.  Perspectives

 

2. Noise isn't negligible (Lectures M 27 Feb through W 14 Mar 2012)

 

In this Chapter, we will take a tour of various problems involving noise in biological systems. Interactions between molecules involve energies of just a few times the thermal energy.  Biological motors, including the molecular components of our muscles, move in elementary steps that are on the nanometer scale, driven forward by energies that are larger than the thermal energies of Brownian motion, but not much larger.  Crucial signals inside cells often are carried by just a handful of molecules, and these molecules inevitably arrive randomly at their targets.   Human perception can be limited by noise in the detector elements of our sensory systems, and individual elements in the brain, such as the synapses that pass signals from one neuron to the next, are surprisingly noisy. How do the obviously reliable functions of life emerge from under this cloud of noise? Are there principles at work that select, out of all possible mechanisms, the ones that maximize reliability and precision in the presence of noise?   I should admit up front that this is a topic that always has fascinated me, and I firmly believe that there is something deep to be found in exploration of these issues.  We will see the problems of noise in systems ranging from the behavior of individual molecules to our subjective, conscious experience of the world.  In order to address these questions, we will need a fair bit of mathematical apparatus, rooted in the ideas of statistical physics.   I hope that, armed with this apparatus, you will have a deeper view of many beautiful phenomena, and a deeper appreciation for the problems that organisms have to solve.

 

                  A.  Molecular fluctuations and chemical reactions

                  B.  Molecule counting

                  C.  More about noise in perception

                  D.  Proofreading and active noise reduction

                  E.  Perspectives

 

3. No fine tuning (Lectures M 26 Mar through W 11 Apr 2012)

 

Imagine making a model of all the chemical reactions that occur inside a cell.  Surely this model will have many thousands of variables, described thousands of differential equations.  If we write down this many differential equations with the right general form but choose the parameters at random, presumably the resulting dynamics will be chaotic.  Although there are periodic spurts of interest in the possibility of chaos in biological systems, it seems clear that this sort of “generic” behavior of large dynamical systems is not what characterizes life.  On the other hand, it is not acceptable to claim that everything works because every parameter has been set to just the right value---in particular these parameters depend on details that might not be under the cell's control, such as the temperature or concentration of nutrients in the environment.  More specifically, the dynamics of a cell depend on how many copies of each protein the cell makes, and one either has to believe that everything works no matter how many copies are made (within reason), or that the cell has ways of exerting precise control over this number; either answer would be interesting.  This problem—the balance between robustness and fine tuning—arises at many different levels of biological organization.  In this section we will look at several examples of the fine tuning problem, starting at the level of single molecules and then moving “up” to the dynamics of single neurons, the internal states of single cells more generally, and networks of neurons.  As noted at the outset, these different biological systems are the subjects of non-overlapping literatures, and so part of what I hope to accomplish in this Chapter is to highlight the commonality of the physics questions that have been raised in these very different biological contexts.

 

                  A.  Sequence ensembles

                  B.  Ion channels and neuronal dynamics

                  C.  The states of cells

                  D.  Long time scales in neural networks

                  E.  Perspectives

 

4. Efficient representation (Lectures M 16 Apr through W 2 May 2012)

 

The generation of physicists who turned to biological phenomena in the wake of quantum mechanics noted that, to understand life, one has to understand not just the flow of energy (as in inanimate systems) but also the flow of information.  In 1948, Shannon proved a theorem stating that entropy, which we know and love from statistical physics, is the unique measure of available information consistent with certain simple and plausible requirements.   Further, entropy also answers the practical question of how much space we need to use in writing down a description of the signals or states that we observe.   This leads to a notion of efficient representation, and in this Chapter we'll explore the possibility that biological systems in fact form efficient representations, maximizing the amount of relevant information that they transmit and process, subject to fundamental physical constraints. The idea that a mathematically precise notion of “information” would be useful in thinking about the representation of information in the brain came very quickly after Shannon's original work.  There is, therefore, a well developed set of ideas about the how many bits are carried by the responses of neurons, in what sense the encoding of sensory signals into sequences of action potentials is efficient, and so on.  More subtly, there is a body of work on the theory of learning that can be summarized by saying that the goal of learning is to build an efficient representation of what we have seen.  In contrast, most discussions of signaling and control at the molecular level has left “information” as a colloquial concept.  One of the goals of this Chapter, then, is to bridge this gap.  Hopefully, in the physics tradition, it will be clear how the same concepts can be used in thinking about the broadest possible range of phenomena. We begin, however, with the foundations.

 

                  A.  Entropy and information

                  B.  Does biology care about bits?

                  C.  Optimizing information flow

                  D.  Gathering information and making models

                  E.  Perspectives

 

5. Outlook: How far can we go?  (not much here)

 

Appendix

 

1.      Poisson process

2.        Correlations, power spectra and all that

3.        Electronic transitions in large molecules

4.        Cooperativity

5.        X-ray diffraction and biomolecular structure

6.        Berg and Purcell, revisited

7.        Dimensionality reduction

8.        Maximum entropy

9.        Measuring information transmission