Bronk B V, Dienes G J, Johnson R A
Biophys J. 1970 Jun;10(6):487-508. doi: 10.1016/S0006-3495(70)86315-9.
A theoretical model for the cooperative control of cellular kinetics is investigated. A critical substance A is produced by the cells whose concentration in a given cell determines whether that cell can divide. The substance A can leak out of the cells into the surrounding medium as well as be reabsorbed by the cells. This feature then implies communication between the cells since all concentrations will be functions of the population density. The substance A also has a lifetime, i.e. decays, for example, by denaturation. This system can be described by three coupled nonlinear differential equations which can be solved analytically in certain limiting cases and can, of course, be studied in detail by computer techniques. Our investigations have shown that (a) there is a critical initial cell population density below which cell proliferation will not occur, (b) cell proliferation can be stimulated by supplying substance A to the medium and there is a critical initial concentration in the medium for initiating proliferation when the cell population density is subcritical, and (c) a well-defined induction period prior to exponential growth may exist whose length depends on the system parameters and initial conditions.
研究了一种用于细胞动力学协同控制的理论模型。关键物质A由细胞产生，给定细胞中该物质的浓度决定该细胞是否能够分裂。物质A可以从细胞泄漏到周围介质中，也可以被细胞重新吸收。由于所有浓度都将是种群密度的函数，因此该特征意味着细胞之间存在通讯。物质A也有一个寿命，例如通过变性而衰变。该系统可以由三个耦合的非线性微分方程描述，这些方程在某些极限情况下可以解析求解，当然也可以通过计算机技术进行详细研究。我们的研究表明：（a）存在一个临界初始细胞种群密度，低于该密度细胞增殖将不会发生；（b）通过向培养基中供应物质A可以刺激细胞增殖，当细胞种群密度低于临界值时，培养基中存在一个用于启动增殖的临界初始浓度；（c）在指数生长之前可能存在一个明确的诱导期，其长度取决于系统参数和初始条件。
