Phenotype Switching in a Self-Regulating Gene

Michael Assaf, Elijah Roberts, Zaida Luthey-Schulten, and Nigel Goldenfeld,

Extrinsic noise
Extrinsic noise
In a new collaborative direction between Luthey-Schulten and Goldenfeld, the work is primarily analytical, and will help us understand the emergence of heterogeneous cell populations in initially clonal bacterial populations. Biological systems are of great interest to statistical physicists, because they contain a large number of strongly fluctuating degrees of freedom, but not enough that they are in the thermodynamic limit.  Accordingly the noise characteristics and the dynamical behavior of such systems pose a unique challenge to theory that is rarely encountered in other areas of physics, leading to important biological phenomena.  A population of clonal cells can become phenotypically differentiated as a result of environmental (i.e. extrinsic) noise and intrinsic noise, such as number fluctuations. These phenomena are now well understood in the case where intrinsic gene expression stochasticity is the key noise source.  But what is the role of extrinsic noise, arising from cell-to-cell variations in (e.g.) ribosome or RNA polymerase number, thus equally affecting each gene within the cell?  How do mean switching times between allowed states depend on the extrinsic noise?

To address this, Goldenfeld and Luthey-Schulten have solved the problem of phenotype switching due to a single self-regulating gene with positive feedback.  The technical advance that they and their CPLC associated postdocs introduced in this context was to use WKB and Hamilton-Jacobi methods to go beyond simple mass-action results.  The key result was that the different phenotypes' lifetime is significantly altered, with increased parameter range for bistability.  The mean switching time is lowered by many orders of magnitude even for a very moderate amount of extrinsic noise, which is important for bacterial communities that exploit heterogeneity in order to inhabit new ecological niches, for example.  The semi-analytical results were validated through state of the art stochastic simulations available through the Luthey-Schulten’s Lattice Microbe software (E. Roberts et al. JCC (2013)).

The intire article can be viewed at Phys. Rev. Lett., 2013, Volume  111, Pages 058102.