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Developmental genetics has furnished the parts list for vertebrate development, but it is not remotely possible to reassemble those parts and predict the outcome. Embryonic stem cells can recapitulate slices of development and thus provide a rich readout of the signaling pathways that pattern the embryo. Siggia wishes to quantify the genetic signals that define morphogenesis.

Genetics and genome sequencing have supplied an extensive parts list for how to create an embryo, yet it is still impossible to construct a precise description of the process from genome-scale data. Existing models of signaling pathways have too many parameters to fit experimentally, and they ignore the complexities of cell biology. Siggia’s group recently developed mathematical descriptions for embryonic patterning that encapsulate how a field of cells can react to an external signal and choose between three discrete fates. The resulting mathematics is geometric and naturally meshes with the phenomenological concepts from the pre-molecular era of embryology.

To test this model, Siggia’s group worked with Shai Shaham to develop a microfluidic device for long-term imaging of larval development in C. elegans. The device permits the timed application of genetic stimuli, offering a sensitive test of dynamical models of development.

Vertebrate signaling pathways are another area where pathway dynamics in single cells has lagged behind genetic and biochemical findings. In collaboration with Ali H. Brivanlou, Siggia’s group found that the TGF-β pathway is adaptive: in response to a step increase in ligand, the transcriptional response of the pathway turns off and the output varies with the time derivative of the ligand. In the embryo, positional information can be conveyed by the rate of ligand changes, not merely its level.

To take a step closer to the embryo, the Siggia lab has begun investigating early differentiation in human embryonic stem cells confined on micropatterned substrates. In response to the ligand at the top of the signaling hierarchy uniformly mixed in solution, all three germ layers emerge in reproducibly ordered patterns. Because cell communication via secondary signals is an essential part of morphogenesis, stem cell differentiation provides a quantitative assay for this process.

Geometric descriptions of biodynamics are not always evident by inspection, and Siggia, together with colleagues at McGill University, has developed computational evolutionary methods to discover them. These findings have led to proposals for how circadian oscillators can both have a temperature-independent period and the ability to entrain and phase lock to a temperature oscillation. Together with Michael W. Young, Siggia conducted experiments motivated by this theory. In a related project, his group worked with Frederick R. Cross to demonstrate that the yeast cell cycle is phase locked to a periodic cyclin signal.

The phosphorylation networks in cells have the potential to act as analogue computers when cells are confronted with discovering changes within a temporal stream of noisy data. Together with colleagues at University of California San Diego, Siggia recently showed that simple networks can perform close to the mathematical optimum for this problem.