16 research outputs found
Reverse-engineering of polynomial dynamical systems
Multivariate polynomial dynamical systems over finite fields have been
studied in several contexts, including engineering and mathematical biology. An
important problem is to construct models of such systems from a partial
specification of dynamic properties, e.g., from a collection of state
transition measurements. Here, we consider static models, which are directed
graphs that represent the causal relationships between system variables,
so-called wiring diagrams. This paper contains an algorithm which computes all
possible minimal wiring diagrams for a given set of state transition
measurements. The paper also contains several statistical measures for model
selection. The algorithm uses primary decomposition of monomial ideals as the
principal tool. An application to the reverse-engineering of a gene regulatory
network is included. The algorithm and the statistical measures are implemented
in Macaulay2 and are available from the authors
Network Topology as a Driver of Bistability in the lac Operon
The lac operon in Escherichia coli has been studied extensively and is one of
the earliest gene systems found to undergo both positive and negative control.
The lac operon is known to exhibit bistability, in the sense that the operon is
either induced or uninduced. Many dynamical models have been proposed to
capture this phenomenon. While most are based on complex mathematical
formulations, it has been suggested that for other gene systems network
topology is sufficient to produce the desired dynamical behavior.
We present a Boolean network as a discrete model for the lac operon. We
include the two main glucose control mechanisms of catabolite repression and
inducer exclusion in the model and show that it exhibits bistability. Further
we present a reduced model which shows that lac mRNA and lactose form the core
of the lac operon, and that this reduced model also exhibits the same dynamics.
This work corroborates the claim that the key to dynamical properties is the
topology of the network and signs of interactions.Comment: 15 pages, 13 figures, supplemental information include