Mathematical modelling of human hematopoiesis

人类造血是研究细胞增殖、分化和成熟的一个美丽的完整器官系统。少数长期造血干细胞(HSCs)驻留在骨髓中，可能每10个月分裂一次，它们位于一个巨大的生产网络的中心，每天生产超过1011个血细胞。这个过程需要多次细胞分裂，从长期HSC的初始分化到所产生的成熟细胞出现在循环中需要几个星期的时间。值得注意的是，所有不同的血细胞类型，包括中性粒细胞、单核细胞、红细胞和血小板等，都是通过这种方式从一小群表面上相同的HSC中产生的。尽管产量巨大，系统的成熟延迟很大，需要产生不同数量的各种子代细胞，但几乎所有个体的造血在几十年里都进行得无懈可击，这意味着存在微调的控制机制和反馈回路。大多数的生产过程发生在骨髓中，在那里直接观察明显比在循环中更难。因此，我们对发生在骨髓中的动力学和过程进行了数学建模，通过观察成熟细胞循环中浓度的变化来验证模型。使用这样的模型，我们将以一种非侵入性的方式阐明骨髓中发生的过程。我们的主要目标是了解正常造血的调节，为此，我们将研究主要的细胞因子和由它们的动力学和动力学形成的控制环。我们已经详细地模拟了G-CSF的动力学和动力学，G-CSF是粒细胞生成的主要细胞因子，并演示了它是如何调节中性粒细胞的产生的。我们将扩展我们的模型，以包括单核细胞和红细胞及其相关的细胞因子。对人类HSC生理学的最新见解将被转化为HSC调控的数学模型，该模型区分长期、中期和短期HSC，并包括对称和不对称细胞分裂。我们的数学模型是机械性的，每个变量、系数和函数代表一个特定的细胞类型或过程。它们通常被描述为延迟-微分方程组，其中延迟是由于完成细胞周期的时间或由于成熟时间而产生的。由于造血通常被很好地调节，为了深入了解它的控制机制，有必要在不处于内稳态的情况下考虑该系统。来自不同来源的数据，包括给健康受试者或接受化疗或自体外周干细胞移植的患者注射合成形式的细胞因子，将被用来指导我们的建模并揭示控制造血的反馈回路的细节。

Human hematopoiesis is a beautiful full organ system for studying cellular proliferation, differentiation and maturation. A small number of long term hematopoietic stem cells (HSCs) which reside in the bone marrow and may divide as rarely as once every 10 months, sit at the heart of a vast web of production which produces more than 1011 blood cells per day. This process requires many cellular divisions and takes several weeks from the initial differentiation of a long term HSC until resulting mature cells appear in circulation. Remarkably, all the different blood cell types including neutrophils, monocytes, erythrocytes and platelets among others are created from a small pool of apparently homogeneous HSCs in this way. Despite the tremendous production rate, significant maturation delays in the system, and need to produce different quantities of various daughter cells, for nearly all individuals hematopoiesis proceeds flawlessly over many decades, implying the existence of finely tuned control mechanisms and feedback loops. Most of the production process occurs in the bone marrow where direct observation is markedly more difficult than in the circulation. Consequently, we mathematically model the dynamics and processes occurring in the bone marrow, using observations of the changing circulating concentrations of mature cells to validate the models. Using such models we will elucidate the processes taking place in the bone marrow in a non-invasive manner. Our main objective is to understand the regulation of normal hematopoiesis, and to do this we will study the principal cytokines and the control loops formed by their kinetics and dynamics. We already modelled in detail the kinetics and dynamics of G-CSF, the main cytokine acting in granulopoiesis, and demonstrated how it regulates the production of neutrophils. We will extend our modelling to include monocytes and erythrocytes and their associated cytokines. Recent insights into human HSC physiology will be translated into a mathematical model for HSC regulation that distinguishes between long, intermediate and short term HSCs, and includes both symmetric and asymmetric cell division. Our mathematical models are mechanistic with each variable, coefficient and function representing a specific cell type or process. They are typically stated as systems of delay-differential equations, where delays arise due to the time to complete the cell cycle or due to maturation times. Because hematopoiesis is usually so well regulated, to gain insight into its control mechanisms it is necessary to consider the system when not at homeostasis. Data from various sources, including administering synthetic forms of cytokines to healthy subjects, or to patients undergoing chemotherapy or autologous peripheral blood stem cell transplantation, will be used to guide our modelling and reveal the details of the feedback loops that control hematopoiesis.