Bunow B, Colton C K
Biosystems. 1975 Jul;7(1):160-71. doi: 10.1016/0303-2647(75)90054-4.
The collective kinetic behavior of a linear array of cells containing a substrate inhibited enzyme is studied with a model in which each cell is considered a well-stirred compartment surrounded by a semipermeable membrane. At large values of a reaction-permeation modulus, wherein substrate access to interior cells is limited, plots of total reaction rate versus concentration of the external reservoir show sharp projections which correspond to dominant reaction occurring in a pair of symmetrically placed cells. Over prescribed ranges of reservoir concentration, multiple stable steady states can occur, some of which are characterized by asymmetric profiles of concentration and reaction rate across the array. A simple stability criterion is proposed and applied to arrays with arbitrary numbers of cells.
利用一个模型研究了包含底物抑制酶的线性细胞阵列的集体动力学行为，在该模型中，每个细胞被视为一个由半透膜包围的充分搅拌的隔室。在反应渗透模量的较大值下，其中底物进入内部细胞受到限制，总反应速率与外部储库浓度的关系图显示出尖锐的凸起，这对应于在一对对称放置的细胞中发生的主导反应。在储库浓度的规定范围内，可能会出现多个稳定的稳态，其中一些稳态的特征是整个阵列中浓度和反应速率的不对称分布。提出了一个简单的稳定性判据，并将其应用于具有任意数量细胞的阵列。
