|The physical structure of a cell is largely determined by the expression level of each of its genes. These levels are governed by complicated transcriptional and translational processes that form proteins, whose presence can then alter those processes and hence influence the expression levels of the very genes that produced them. At its deepest level, this complex physical structure can be represented as a network of interactions among genes -- a network that governs the progression of the cell through an abstract space of gene expression patterns. Together with Stuart Kauffman (U. of Calgary) and collaborators in the Duke Center for Systems Biology, I am conducting research addressing the dynamical properties of such complex networks. The mathematical networks we study are selected specifically for their relevance to the biology of gene expression.||
Cartoon of a Boolean network with two inputs per node. Colors represent the state of a node ("on" or "off"). At each time step, the each color is updated according to the node's truth table and the states of its input nodes.
Our research aims to develop useful models of the complex regulatory
networks that determine the activities of all of the genes in a
eukaryotic cell. Recent advances in experimental technique have
prompted an explosion of activity in functional genomics, dominated at
present by efforts to deduce particular substructures of a network by
analyzing correlations in gene expression patterns. We are focusing
on a complementary set of questions regarding the generic properties
of complex Boolean and continuous networks, with the goal of elucidating the
functional implications of different types of network architecture.
The working hypothesis is that certain classes of network architecture
illustrate principles of organization that underlie the structure of
This work is being supported by NSF.
Scaling of the number of dynamically relevant nodes with system size in a Kauffman net. Blue and green points are for networks in the ordered regime; purple points are for critical networks.