Genetics and biochemistry have defined the components and wiring of the signaling pathways that pattern the embryo. Among them, the transforming growth factor β (TGF-β) pathway has the potential to behave as a morphogen: invitro experiments established that it can dictate cell fate in a concentration-dependent manner. How morphogens convey positional information in a developing embryo, when signal levels change with time, is less understood.

Cells send and receive signals through pathways that have been defined in great detail biochemically, and it is often presumed that the signals convey only level information. Cell signaling in the presence of noise is extensively studied but only rarely is the speed required to make a decision considered. However, in the immune system, rapidly developing embryos, and cellular response to stress, fast and accurate actions are required.

Early T-cell activation is selected by evolution to discriminate a few foreign peptides rapidly from a vast excess of self-peptides, and it is unclear in quantitative terms how this is possible. We show that a generic proofreading cascade supplemented by a single negative feedback mediated by the Src homology 2 domain phosphatase-1 (SHP-1) accounts quantitatively for early T-cell activation, including the effects of antagonists.

Quantitative models of development that consider all relevant genes typically are difficult to fit to embryonic data alone and have many redundant parameters. Computational evolution supplies models of phenotype with relatively few variables and parameters that allows the patterning dynamics to be reduced to a geometrical picture for how the state of a cell moves. The clock and wavefront model, that defines the phenotype of somitogenesis, can be represented as a sequence of two discrete dynamical transitions (bifurcations).

The computational evolution of gene networks functions like a forward genetic screen to generate, without preconceptions, all networks that can be assembled from a defined list of parts to implement a given function. Frequently networks are subject to multiple design criteria that cannot all be optimized simultaneously. To explore how these tradeoffs interact with evolution, we implement Pareto optimization in the context of gene network evolution.

A temperature independent period and temperature entrainment are two defining features of circadian oscillators. A default model of distributed temperature compensation satisfies these basic facts yet is not easily reconciled with other properties of circadian clocks, such as many mutants with altered but temperature compensated periods. The default model also suggests that the shape of the circadian limit cycle and the associated phase response curves (PRC) will vary since the average concentrations of clock proteins change with temperature.

The TGF-β pathway plays a vital role in development and disease and regulates transcription through a complex composed of receptor-regulated Smads (R-Smads) and Smad4. Extensive biochemical and genetic studies argue that the pathway is activated through R-Smad phosphorylation; however, the dynamics of signaling remain largely unexplored. We monitored signaling and transcriptional dynamics and found that although R-Smads stably translocate to the nucleus under continuous pathway stimulation, transcription of direct targets is transient.

Developmental signaling networks are composed of dozens of components whose interactions are very difficult to quantify in an embryo. Geometric reasoning enumerates a discrete hierarchy of phenotypic models with a few composite variables whose parameters may be defined by in vivo data. Vulval development in the nematode Caenorhabditis elegans is a classic model for the integration of two signaling pathways; induction by EGF and lateral signaling through Notch.

During vertebrate embryogenesis, the expression of Hox genes that define anterior-posterior identity follows general rules: temporal colinearity and posterior prevalence. A mathematical measure for the quality or fitness of the embryonic pattern produced by a gene regulatory network is derived. Using this measure and in silico evolution we derive gene interaction networks for anterior-posterior (AP) patterning under two developmental paradigms.