Mathematical Sciences: RUI: Mathematical Modeling of Hematopoiesis and Cell Cycles in Escherichia coli

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9627047 Mahaffy The principal investigator continues his research on hematopoietic and cellular control systems. One study examines an age-structured model for erythropoiesis, which is compared to a simpler model with two delays. Bifurcation analyses predict oscillations that correlate reasonably well with studies on auto-immune hemolytic rabbits. Mathematical studies investigate the key modeling elements that lead to oscillations observed in some serious hematopoietic diseases. Study of the erythropoietic model extends to a related system for thrombopoiesis for which more clinical problems have been observed. This research improves a current age-structured model so as to match better experimental data following a phlebotomy, including the effects of plasma regeneration, the accelerated maturing and active destruction in the aging of erythrocytes. Mathematical analyses examine the significance of the state-dependent delays in the reduced age-structured model and parameter sensitivity. Research continues in collaboration with Dr. J. W. Zyskind on the modeling of initiation of DNA replication in Escherichia coli. Mathematical models are developed to support current theories on the most important biochemical events beginning the DNA replication cycle. Interest centers on the role of the stable protein DnaA, which experimentally has been shown to play a key role. The models consider the significance of an eclipse period for DnaA mRNA synthesis following initiation, the existence of an unknown protein recently discovered that inactivates DnaA, and the competition for binding important activation sites with a growth dependent protein, Fis. Mathematical studies continue on cellular control systems in exponentially growing cells and extend to examine what happens when cells experience starvation. Both proposed areas of study use mathematical models to provide a better understanding of the fundamental controls in important biological systems. The f ear of contamination of the blood supply by the HIV virus, which causes AIDS, results in many surgical patients providing their own blood for the operation. The mathematical models in this proposal allow the study of optimal schemes for regeneration of red blood cells, which could indicate ways for increasing this supply. This leads to a lower demand on the general blood supply and increased security of the blood supply for the self-donors. In addition, there are several serious hematopoietic diseases (diseases linked to the formation of different types of blood cells) that are poorly understood. The proposed models provide a non-invasive means to examine which aspects of this complicated biological control system are most likely to result in the observed problems. This gives clinicians more information on possible therapeutic treatments and narrows the search for the primary cause of the disease. The mathematical models for the initiation of DNA replication in bacteria again provides a non-experimental approach to better understand an important biological process. In this case, the study examines the control of the cell cycle in bacteria, which is fundamental to cell growth and reproduction. Biotechnology relies heavily on the bacterium, E. coli, for many of its experiments and products, so a better understanding of the cell cycle aids this industry as well as providing some answers to basic questions in cell biology.