In a close collaboration with Shawn Little, we designed a FISH-based technique (Fluorescent In-Situ Hybridization) to measure transcriptional activity in the fruit fly embryo with single-molecule precision. We used it to demonstrate that the remarkable precision of the developmental program, previously documented at the protein level, arises already at the level of mRNA profiles. Although the transcriptional readout itself is indeed highly stochastic, simple physical mechanisms such as spatiotemporal averaging are sufficient to explain the observed noise reduction. Curiously, throughout most of the early patterning events, the developing embryo remains a single cell ("syncytium"): the dividing nuclei are not separated by membranes, and we have shown that the spatial averaging this affords does indeed have a measurable effect on noise reduction. In other words, the long syncytial stage improves the precision of the patterning program.
 

Information theory is gaining popularity as a tool to characterize performance of biological systems. However, information-theoretic quantities are easily misinterpreted if information is quantified without reference to whether or how a system could extract and use it. In this paper of primarily pedagogical intention, I discuss these pitfalls using the example of pattern-forming developmental systems, which are commonly structured as cascades of sequential gene expression steps. Such a multi-tiered structure appears to constitute sub-optimal use of the positional information provided by the input morphogen because noise is added at each tier. However, what matters is not the total information content of a morphogen, but the information it can usefully transmit to downstream elements.

Biological networks are characterized both by their topology and a multitude of adjustable parameters (the "numbers on the arrows"). Network-level properties can be quite sensitive to such parameters, but this sensitivity can be partially alleviated by special topological features conferring greater "robustness". Characterizing statistical properties of the topologies of real-life networks is a very active field.

The two extremes are clear: certain topologies can be very robust, while others are very sensitive. But real networks presumably lie somewhere in between. It would be useful if the relative roles of topology and parameters could be quantified; however, the task is non-trivial. Changing a parameter and changing the topology are qualitatively different operations, and seem impossible to compare without introducing ad hoc penalties describing how much "harder" it is for a system to add (remove) a link as opposed to changing its strength. In this project with William Bialek, we showed how the problem can be resolved - at least in a particular class of perceptron-like models.