A large number of biochemical systems show regulatory feedback mechanistic steps either at the cellular level, like in the HIV-Rev protein, or at the physiological level, like in the hypothalamous-pituitary-adrenal hormonal system. Our group has been studying the molecular basis of different chemical, biochemical and physiological mechanisms and has proposed several dynamic models to explain observed temporal and chaotic oscillation in the concentrations of relevant metabolites.
We have concentrated most of our effort in understanding chemical self-replication, where several chemical systems have been designed experimentally. For example, oligonucleotides have been considered by von Kiedrowski’s, Orgel’s and Nicolau’s groups, and peptides have been studied by Gadhiri’s and Chmielewski’s groups. More recently Joyce’s group designed a self-replicating and a cross-catalytic self-replicating ribozymes, which may be better suited for Darwiniam evolution than the oligonucleotide or peptide systems. In the case of cross-catalytic mechanisms, we have considered the dynamics of competitive systems and mutualistic hypercycles. We also continue studying and modeling the transport of incompletely spliced mRNAs across the nuclear membrane, which is regulated by HIV-Rev protein, and we have studied the behavior of an insect-predator-ant system, and we want to develop mathematical models that we will allow us to improve our understanding of species competition and coexistence.