癌症动力学中的数学和计算方法
A Review of Mathematical and Computational Methods in Cancer Dynamics
摘要：
癌症是一种复杂的适应性疾病，受遗传不稳定性、环境信号、细胞蛋白流和基因调控网络之间的非线性反馈系统调控。理解癌症的控制论需要跨多维时空尺度整合信息动力学，包括遗传、转录、代谢、蛋白质组、表观遗传和多细胞网络。然而，这些复杂网络的时间序列分析在癌症研究中仍然非常缺乏。随着细胞动力学的纵向筛选和时间序列分析，普遍观察到的与动力学系统有关的因果模式可以在癌症触发过程的信号传导或基因表达状态空间中自组织。这些模式中的一类，奇怪的吸引子，可能是癌症进展的数学生物标志物。细胞内混沌和混沌细胞种群动力学的出现仍然是系统肿瘤学中的一个新范式。因此，本文将混沌和复杂的动力学讨论为癌症细胞命运动力学的数学标志。鉴于时间分辨的单细胞数据集可用的假设，从复杂性理论的跨学科工具和算法的调查，在此审查调查癌症生态系统中的关键现象和混沌动力学。总之，该观点培养了计算系统肿瘤学在非线性动力学，信息论，逆问题和复杂性方面的直觉。我们强调了我们在统计机器学习领域看到的局限性，但将其与所探索的数学工具提供的符号计算能力相结合的机会。
英文摘要：
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems oncology. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
