Developing Mathematical Models for Immune Interactions in Cancer, Cachexia, and the Microbiome

数学模型可以通过以受控的方式检查单个元素来梳理复杂生物相互作用的非线性动力学。由于种群的异质性和许多混杂的变量，很难通过传统的动物或细胞系模型来检验人类免疫和生理之间的相互作用。这项研究计划创建了描述免疫系统、正常组织和癌症之间相互作用的新数学模型，从而创建了新的模型配方，并提高了对生物系统的理解。 这项提议包含三个主要目标，都涉及创建新的多室微分方程式系统，以描述免疫系统与癌症或其他宿主组织的相互作用。第一个目标是研究免疫与癌症的关系，包括炎症和衰老对免疫功能的影响。第二个目标是研究癌症恶病质中肌肉或脂肪组织的丢失。而第三个目标是研究肠道微生物群、免疫系统和癌症之间的关系。新开发的基于微分方程式的模型将用一种可以计算分析的公式来描述细胞相互作用。基因组数据分析将被用来提出癌症存在导致细胞功能障碍的可能生物学机制。这些机制将被编码到模型公式中，在那里可以进行严格的研究。实验数据将用于模型构建和验证，确保创建高质量的预测工具。 目标三中创建的描述免疫-微生物-癌症相互作用的数学模型将是此类模型中的第一个。目标一和目标二中使用的配方是本研究计划所独有的，比现有模型更具生物学准确性，值得进一步研究和开发。新创建的模型将把数学地图集扩展到数学生物学家、进化生态学家和其他研究非线性种群动力学的人。这项工作将通过将基因组数据提炼成可编码为模型形式和参数的基本生物学机制，将数据集成到数学建模的方法正式化。开发的模型可能会导致未来的实验或临床应用，在那里可以对人类健康和癌症治疗产生影响。事实上，通过数学建模，更好地理解免疫系统、宿主生理和癌症之间发生的非线性动力学，只会改善健康维护和疾病治疗的干预措施，包括免疫治疗和肠道微生物组操作。

Mathematical models can tease apart the nonlinear dynamics of complex biological interactions by examining individual elements in a controlled manner. Interactions between human immunity and physiology are difficult to examine through traditional animal or cell line models due to the heterogeneous populations and many confounding variables. This research program creates new mathematical models describing the interactions between the immune system, normal tissues, and cancer, resulting in the creation of new model formulations and improved understanding of the biological system. This proposal contains three main objectives that all involve the creation of novel multi-compartment systems of differential equations to describe the interactions of the immune system with cancer or other host tissues. The first objective examines the immune-cancer relationship, including inflammation and aging effects on immune function. The second objective examines the loss of muscle or adipose tissue in cancer cachexia. While the third objective examines the relationship between the gut microbiome, immune system, and cancer. Newly developed differential equation-based models will describe the cellular interactions in a formulation that can be analyzed computationally. Genomic data analyses will be used to suggest possible biological mechanisms responsible for the cellular dysfunctions resulting from cancer presence. These mechanisms will be encoded into the model formulations where they can be rigorously studied. Experimental data will be used for model construction and validation, guaranteeing the creation of good quality predictive tools. The mathematical models created in objective three, describing immune-microbiome-cancer interactions, will be the first of their kind. The formulations used in objectives one and two are unique to this research program, are more biologically accurate than existing models, and are worthy of further research and development. Newly created models will extend the mathematical atlas available to mathematical biologist, evolutionary ecologists, and others who study nonlinear population dynamics. This work will formalize methods of data integration into mathematical modelling by distilling genomic data into fundamental biological mechanisms that can be encoded into model forms and parameters. The developed models may lead to future experimental or clinical applications where implications to human health and cancer treatment can be made. Indeed, improved understanding of the nonlinear dynamics occurring between the immune system, host physiology, and cancer, through mathematical modelling, can only lead to improved interventions for health maintenance and disease treatment, including immunotherapy and intestinal microbiome manipulation.