**Dynamics and
computation in single cells and biochemical networks**

** **

William Bialek and
collaborators

Single cells have to solve many problems of computation and signal processing at the biochemical level. Many of the problems they face are analogous to those faced by the brain, but the physical constraints are even clearer. In particular, many critical phenomena of life depend on shockingly small numbers of molecules. How do cells achieve reliable function in the presence of the inevitable fluctuations associated with these small numbers? How much of the intricate machinery of the cell can be understood as a principled solution to these problems of noise and computation? These are some of the questions we have been exploring, both theoretically and more recently in connection with specific experiments.

Papers
are in inverse chronological order, most recent papers at the top. Numbers refer to a full list of publications.

[99.] Physical limits to biochemical
signaling. W Bialek & S Setayeshgar, physics/0301001.

In 1977 Berg and Purcell wrote a classic paper analyzing the physical constraints on bacterial chemotaxis. Their discussion inspired many people, including me, but they also had a decidedly idiosyncratic style of argument that left many loose ends. Many of their intuitive arguments can be made rigorous and generalized by noting that biochemical signaling depends on binding of signaling molecules to specific binding sites, and this interaction leads to equilibrium. This means that fluctuations in the occupancy of the binding sites are a form of thermal noise and can be treated using the standard methods of statistical mechanics. These tools allow us to compute not only the occupancy noise for a single site, but to understand how these fluctuations are changed by the diffusion of the signaling molecules and the resulting interactions with other sites. We find a minimum effective noise level that depends on physical parameters such as the diffusion constant and the size and geometrical arrangement of the relevant binding sites; this Ònoise floorÓ is independent of all the (often unknown) details of the chemical kinetics. Comparison with recent experiments on noise in the control of gene expression and the switching of the bacterial flagellar motor suggest that these intracellular signaling processes operate with a precision close to the fundamental physical limits.

[90.] Network information and connected
correlations. E Schneidman, S Still, MJ Berry II & W Bialek, *Phys
Rev Lett* **91,** 238701 (2003).

[88.] Computation in single neurons: Hodgkin and Huxley revisited. B
AgŸera y Arcas, AL Fairhall, & W Bialek, *Neural Comp* **15, **1715-1749 (2003).

[74.] Stability and noise in biochemical switches.
W Bialek, in *Advances in Neural Information Processing 13, *TK Leen, TG Dietterich & V
Tresp, eds, pp 103-109 (MIT Press, Cambridge, 2001).

[68.] Adaptation and optimal chemotactic strategy
for *E. Coli**.* SP Strong, B Freedman,
W Bialek & R Koberle, *Phys Rev E* **57,** 4604-4617 (1998).

Another paper that was inspired in part by Berg and
Purcell. Given that bacteria can measure
the time derivative of concentration along their trajectories, that this
measurement inevitably has a substantial noise level, and that the bacteria
cannot steer but only go straight (up to the limits set by their own rotational
diffusion) or tumble to choose a new direction at random, how can they use the
results of their measurements to guide their behavior? In particular, is there a strategy that
would maximize their progress along favorable concentration gradients? This problem of optimal behavioral
strategy turns out to be quite subtle.
I donÕt think we have a complete solution, but we said some interesting
things, in particular about the extent to which the decision to tumble can be
nearly deterministic and yet still consistent with the apparently stochastic
behavior observed for *E Coli. * I think
that subsequent measurements on the nearly switch-like input/output relation of
the bacterial motor are consistent with these results, but many questions
remain open.