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.
At this site IÕm trying to collect the current versions of all the
pieces, each section of the book corresponding roughly to one of the lectures
in the course. 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 (usually in different typeface) about what is
missing. I am past my
deadline, so hopefully if you revisit this site youÕll see progress. If something catches your eye as
problematic (or especially interesting), please donÕt hesitate to drop me a
note. If youÕd 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
(2009).
Please
note that, at the moment, my referencing of the original literature is somewhat
haphazard; the absence of references thus is not a claim of originality! Also, even the sections which are
written and posted are not necessarily well–balanced; I will wait until
there is a complete draft before going back to fix this. Stay tuned for
updates, or ask me specifically for links to the relevant papers.
1. Photon counting in vision (full chapter, except
perspective at the end)
Sitting quietly in a dark room, we can detect the
arrival of individual photons at our retina. This observation has a beautiful history, with its roots in
a suggestion by Lorentz in 1911. Tracing through the steps from photon arrival
to perception we 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. We will look at photon counting not just for its intrinsic interest, but also as a way
of motivating some more general questions. The problem of photon counting also introduces us to methods
and concepts of much broader applicability.
1.3 Dynamics of biochemical networks
1.4 Signal processing at the first synapse
1.5 Pointers to higher level issues
1.6
Perspectives
2. Noise isn't negligible (full chapter, except
perspective at the end)
The great poetic images of classical physics are those
of determinism and clockwork.
Strikingly, life operates far from this limit. Interactions between molecules involve energies of just a
few times the thermal energy, and biological motors, including the molecular
components of our muscles, move on the same scale as Brownian motion. Biological signals 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 a 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? Are there ways in which noise can be
productive, rather than a nuisance?
2.1 Molecular fluctuations and chemical reactions
2.2 Molecule counting and chemotaxis
2.3 Molecule counting more generally
2.4 More about noise in perception
2.5 Proofreading and active noise reduction
2.6
Perspectives
3. Fine tuning vs. robustness (full chapter, except
perspective at the end)
Imagine making a model of all the chemical reactions
that occur inside a cell. Surely this model would have many thousands of
variables, so we would have 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 (that is,
what we get by solving the equations) 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 ŌgenericĶ 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 cellÕs 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. Our goal in this chapter is to look at
several examples, from single molecules to brains, hoping to see the common
themes. [Note: these are the newest and hence roughest of the roughly drafted
sections; they need much work to fill in details and problems!]
3.1 Sequence ensembles and protein folding
3.2 Ion channels and neuronal dynamics
3.3 Long time scales in neural networks
3.4 Adaptation and the states of cells
3.5 Reproducibility in morphogenesis
3.6
Perspectives
4. Efficient representation (full chapter, except
perspective at the end)
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.
There is, of course, some difficulty in translating the colloquial
notion of information into something mathematically precise. Indeed, almost all statistical
mechanics textbooks note that the entropy of a gas measures our lack of information
about the microscopic state of the molecules, but often this connection is left
a bit vague or qualitative. Shannon proved a theorem that makes the connection
precise: entropy 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 section of the course we'll explore
the possibility that biological systems in fact form efficient representations,
maximizing the amount of relevant information that they can transmit and
process, subject to fundamental physical constraints. WeÕll see that these ideas have the potential to tie
together phenomena ranging from the control of gene expression in bacteria to
learning in the brain.
4.2 Entropy lost and information gained
4.3 Does biology care about bits?
4.4 Optimizing information flow
4.5 Gathering information and learning rules
4.6
Perspectives
5.
Outlook: How far can we go?
Appendices
The goal of these Appendices is to collect some
background and technical asides.
In some cases I will review things that students might have learned in
earlier courses. In other cases, I
will develop in more detail ideas that seem important, but are off to the side
of the main points I am trying to make.
I am not sure of exactly which topics will be covered, and suspect that
this will solidify only on reading through a full draft of the main text. So, this is a bit more plastic than the
rest!