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

9627047首席研究员马哈菲继续他对造血和细胞控制系统的研究。一项研究考察了红细胞生成的年龄结构模型，并与具有两个延迟的更简单的模型进行了比较。分支分析预测的振荡与自身免疫溶血性兔的研究有相当好的相关性。数学研究调查了导致在一些严重的血液系统疾病中观察到的振荡的关键建模元素。对红细胞生成模型的研究延伸到与血小板生成相关的系统，已观察到更多的临床问题。这项研究改进了目前的年龄结构模型，以便更好地匹配采血后的实验数据，包括血浆再生、红细胞加速成熟和主动破坏在红细胞老化中的影响。数学分析检验了在简化的年龄结构模型和参数敏感度中状态依赖延迟的重要性。与J·W·齐斯金德博士合作继续研究在大肠杆菌中启动DNA复制的建模。数学模型被开发来支持当前关于DNA复制周期开始的最重要的生化事件的理论。人们的兴趣集中在稳定蛋白Dna A的作用上，实验证明它发挥了关键作用。这些模型考虑了起始后DNAA mRNA合成的阴影期的重要性，最近发现的使DNAA失活的未知蛋白质的存在，以及与生长依赖蛋白FIS结合重要激活位点的竞争。数学研究继续对指数增长的细胞中的细胞控制系统进行研究，并扩展到研究当细胞经历饥饿时会发生什么。这两个拟议的研究领域都使用数学模型来更好地了解重要生物系统中的基本控制。由于担心血液供应被HIV病毒污染，从而导致艾滋病，导致许多外科患者为手术提供自己的血液。这项建议中的数学模型允许研究红细胞再生的最佳方案，这可能表明增加这种供应的方法。这导致对一般血液供应的需求较低，并提高了自我献血者的血液供应安全。此外，还有几种严重的血液病(与不同类型血细胞的形成有关的疾病)对此知之甚少。提出的模型提供了一种非侵入性的方法来检查这个复杂的生物控制系统的哪些方面最有可能导致观察到的问题。这为临床医生提供了更多关于可能的治疗方法的信息，并缩小了对疾病主要原因的搜索范围。在细菌中启动DNA复制的数学模型再次为更好地理解一个重要的生物过程提供了一种非实验的方法。在这种情况下，这项研究检查了细菌细胞周期的控制，这是细胞生长和繁殖的基础。生物技术的许多实验和产品在很大程度上依赖于细菌--大肠杆菌，因此，更好地了解细胞周期有助于该行业，并为细胞生物学的基本问题提供一些答案。

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.