Fundamental limits on the suppression of randomness in biology

Monday, May 12, 2008 - 10:30am - 11:30am
EE/CS 3-180
Johan Paulsson (Harvard Medical School)
Living cells contain such low numbers of active genes, RNAs
and proteins that random fluctuations in concentrations arise
spontaneously. Because many biological processes require reliability and
precision, cells are thought to deal with this problem by using negative
feedback control loops, correcting perturbations by increasing synthesis
at high concentrations and decreasing it at low concentrations. Negative
feedback has been systematically studied in control theory, but focus
has been on macroscopically large systems subject to external
perturbations - like airplanes in random gusts of wind - while other
principles arise in discrete molecular-scale probabilistic processes.
Many biological control loops are also strongly nonlinear, and crucial
aspects are often unknown. Such systems are typically considered
impossible to analyze: how can we make quantitative statements about
strongly nonlinear stochastic systems if we do not even know the nature
of the nonlinearities? By combining exact analytical tools from
functional analysis, information theory and statistical physics, I will
show that seemingly mild constraints, such as short delays or finite
numbers of control molecules, can place fundamental limits on noise
suppression that no arbitrarily elaborate feedback system could ever
overcome - hard physical bounds that can be derived explicitly. Using
approximate methods for families of feedback systems, I will also show
how the limits arise because different types of noise are suppressed
according to incompatible principles, generating frustration trade-offs
where reducing one type of variation inevitably amplifies another.
Finally I discuss partial loopholes in the general laws where
counterintuitive mechanisms can circumvent the trade-offs to some
extent. The general results are illustrated by bacterial plasmids, where
large fluctuations promote extinction and where numerous mechanisms have
evolved to approach the physical limits. I will emphasize intuitive
reasoning and physical observables throughout, and show some preliminary