AbstractThis paper studies differential equation-based mathematical models
and their numerical solutions for genetic regulatory network
identification. The primary objectives are to design, analyze,
and test a general variational framework and numerical methods for seeking its
approximate solutions for reverse engineering genetic regulatory
networks from microarray datasets. In the proposed variational
framework, no structure assumption on the genetic network is presumed,
instead, the network is solely determined by the microarray profile
of the network components and is identified through a well chosen
variational principle which minimizes an energy functional.
The variational principle serves not only as a selection criterion
to pick up the right solution of the underlying differential
equation model but also provides an effective mathematical characterization
of the small-world property of genetic regulatory networks which
has been observed in lab experiments. Five specific models
within the variational framework and efficient numerical methods
and algorithms for computing their solutions are proposed and
analyzed. Model validations using both synthetic
network datasets and subnetwork datasets of
Saccharomyces cerevisiae (yeast) and E. coli are
performed on all five proposed variational models and
a performance comparison versus some existing genetic regulatory network
identification methods is also provided.
Parameter identification of genetic regulatory network with time-varying delays via adaptive synchronization method
