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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. Dr. 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 ignore the complexities of cell biology. Dr. Siggia’s group has recently developed mathematical descriptions for embryonic patterning, which 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.

An example is a phenotypic model for vulva patterning in C. elegans, which requires a parameter for each new allele but then can predict the matrix of crosses between all pairs of alleles. Ongoing experiments with Rockefeller’s Shai Shaham aim to test predictions of this theory.

Vertebrate signaling pathways are another area where pathway dynamics in single cells has lagged behind the genetic and biochemical findings. In collaboration with Rockefeller’s Ali Brivanlou, Dr. Siggia’s group has found that the TGF-β pathway is adaptive: In response to a step increase in ligand, the transcriptional response of the pathway turns off; however, this is not due to the known negative feedbacks that operate at the receptor level. By adapting a microfluidic cell, developed at Stanford University, Dr. Siggia and his collaborators uncovered an important corollary of adaption in the embryo: that 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 (hESCs). All three germ layers can be induced by the two classes of TGF-β ligands, and the group has focused on the space-time development of the earliest fates. 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. With colleagues at McGill University, Dr. Siggia has developed computational evolutionary methods to discover them. These 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. Experiments motivated by this theory are in progress with Rockefeller’s Michael Young. In a related project with Rockefeller’s Fred Cross, Dr. Siggia’s group has demonstrated phase locking of the yeast cell cycle 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. With colleagues at UC San Diego, Dr. Siggia has recently shown that simple networks can perform close to the mathematical optimum for this problem.