Session H43: Invited Session: Physics of Systems Biology

Robustness of Biological Circuits

In responding to inputs biological systems do many types of calculations, some of which serve to maximize the signal and suppress noise. Physiology faces similar requirements and to fulfill these many sensory systems such as vision and hearing are designed to respond logarithmically to the fold change over initial conditions, a property known as ``Weber's Law.'' Mathematical modeling of the ancient Wnt signaling circuit suggested that a key design feature of that pathway was to provide a robust logarithmic output and as a consequence it does not respond robustly in a linear or hyperbolic way. We confirmed this behavior in Xenopus embryos and in human colorectal cells in culture. However, to read a robust logarithmic output from the Wnt pathway in the form of fold change in the levels of beta catenin, the responding transcriptional circuit must be able to compare initial and final levels of beta catenin accurately. This is exactly what we found in Xenopus embryos. What kind of transcriptional pathway has this property? Examination of the detailed promoter of a classic wnt responsive gene showed that two domains contribute to the calculation: the well known TCF/LEF sites that bind beta catenin near the coding sequence and a functional DNA feature upstream, which is unresponsive to beta catenin. The TCF/LEF sites on their own respond in a linear mode to the beta catenin concentration. The upstream functional feature confers the logarithmic response. Knowledge of the pathway structure should allow us to define a ``Weber's Law'' circuit that allows transcriptional systems to suppress noise by responding to fold change rather than to simple saturation.   

Epigenetic switches and network transitions

We investigate dynamics of gene networks which are regulated by both the fast binding/unbinding of transcription factors to/from DNA and the slow processes of chromatin structural change or histone modification. This heterogeneous dynamics consisting of different time scales is analyzed by the mean-field approximation and the stochastic simulation to show that the network exhibits multiple metastable states and is characterized by transitions among them. We discuss distribution and fluctuation of states of the core gene network of embryonic stem cells as an example of such heterogeneous dynamics and the simulated transitions are compared with the experimental data on the distribution of stem cell states.   

Landscape and Flux Framework for Non-Equilibrium Networks: Kinetic Paths and Rate Dynamics

We developed a general framework to quantify three key ingredients for dynamics of nonequilibrium systems through path integrals in length space. First, we identify dominant kinetic paths as the ones with optimal weights, leading to effective reduction of dimensionality or degrees of freedom from exponential to polynomial so large systems can be treated. Second, we uncover the underlying nonequilibrium potential landscapes from the explorations of the state space through kinetic paths. We apply our framework to a specific example of nonequilibrium network system: lambda phage genetic switch. Two distinct basins of attractions emerge. The dominant kinetic paths from one basin to another are irreversible and do not follow the usual steepest descent or gradient path along the landscape. It reflects the fact that the dynamics of nonequilibrium systems is not just determined by potential gradient but also the residual curl flux force, suggesting experiments to test theoretical predictions. Third, we have calculated dynamic transition time scales from one basin to another critical for stability of the system through instantons. Theoretical predictions are in good agreements with wild type and mutant experiments.We further uncover the correlations between the kinetic transition time scales and the underlying landscape topography: the barrier heights along the dominant paths. We found that both the dominant paths and the landscape are relatively robust against the influences of external environmental perturbations and the system tends to dissipate less with less fluctuations. Our theoretical framework is general and can be applied to other nonequilibrium systems.   

Experimental evolution in budding yeast

I will discuss our progress in analyzing evolution in the budding yeast, Saccharomyces cerevisiae. We take two basic approaches. The first is to try and examine quantitative aspects of evolution, for example by determining how the rate of evolution depends on the mutation rate and the population size or asking whether the rate of mutation is uniform throughout the genome. The second is to try to evolve qualitatively novel, cell biologically interesting phenotypes and track the mutations that are responsible for the phenotype. Our efforts include trying to alter cell morphology, evolve multicellularity, and produce a biological oscillator.