Affiliation: University of Nebraska
- On the relationship of steady states of continuous and discrete models arising from biologyAlan Veliz-Cuba
University of Nebraska Lincoln, Lincoln, NE 68505, USA
Bull Math Biol 74:2779-92. 2012..Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics...
- Reduction of Boolean network modelsAlan Veliz-Cuba
Department of Mathematics, University of Nebraska Lincoln, USA
J Theor Biol 289:167-72. 2011..In particular, we use the reduction method to study steady states of Boolean networks and apply our results to models of Th-lymphocyte differentiation and the lac operon...
- Boolean models can explain bistability in the lac operonAlan Veliz-Cuba
Department of Mathematics, University of Nebraska Lincoln, Lincoln, Nebraska, USA
J Comput Biol 18:783-94. 2011..This work suggests that the key to model qualitative dynamics of gene systems is the topology of the network and Boolean models are well suited for this purpose...
- Modeling stochasticity and variability in gene regulatory networksDavid Murrugarra
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061 0123, USA
EURASIP J Bioinform Syst Biol 2012:5. 2012..We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex...
- Polynomial algebra of discrete models in systems biologyAlan Veliz-Cuba
Virginia Bioinformatics Institute, Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
Bioinformatics 26:1637-43. 2010..There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation...