Vieira F M, Bisch P M
Centro Brasileiro de Pesquisas Fiscias, Rio de Janeiro, Brazil.
Eur Biophys J. 1994;23(4):277-87. doi: 10.1007/BF00213577.
The dynamic behavior of some non-linear extensions of the six-state alternating access model for active membrane transport is investigated. We use stoichio-metric network analysis to study the stability of steady states. The bifurcation analysis has been done through standard numerical methods. For the usual six-state model we have proved that there is only one steady state, which is globally asymptotically stable. When we added an autocatalytic step we found self-oscillations. For the competition between a monomer cycle and a dimer cycle, with steps of dimer formation, we have also found self-oscillations. We have also studied models involving the formation of a complex with other molecules. The addition of two steps for formation of a complex of the monomer with another molecule does not alter either the number or the stability of steady states of the basic six-state model. The model which combines the formation of a complex with an autocatalytic step shows both self-oscillations and multiple steady states. The results lead us to conclude that oscillations could be produced by active membrane transport systems if the transport cycle contains a sufficiently large number of steps (six in the present case) and is coupled to at least one autocatalytic reaction,. Oscillations are also predicted when the monomer cycle is coupled to a dimer cycle. In fact, the autocatalytic reaction can be seen as a simplification of the model involving competition between monomer and dimer cycles, which seems to be a more realistic description of biological systems. A self-regulation mechanism of the pumps, related to the multiple stationary states, is expected only for a combined effect of autocatalysis and formation of complexes with other molecules. Within the six-state model this model also leads to oscillation.
研究了主动膜运输六态交替访问模型的一些非线性扩展的动力学行为。我们使用化学计量网络分析来研究稳态的稳定性。通过标准数值方法进行了分岔分析。对于通常的六态模型，我们证明只有一个稳态，它是全局渐近稳定的。当我们添加一个自催化步骤时，我们发现了自振荡。对于单体循环和二聚体循环之间的竞争，以及二聚体形成步骤，我们也发现了自振荡。我们还研究了涉及与其他分子形成复合物的模型。添加两个步骤用于单体与另一个分子形成复合物，既不会改变基本六态模型稳态的数量，也不会改变其稳定性。将复合物形成与自催化步骤相结合的模型显示出自振荡和多个稳态。结果使我们得出结论，如果运输循环包含足够多的步骤（在当前情况下为六个）并且与至少一个自催化反应耦合，那么主动膜运输系统可能会产生振荡。当单体循环与二聚体循环耦合时，也预测会出现振荡。实际上，自催化反应可以看作是涉及单体和二聚体循环之间竞争的模型的简化，这似乎是对生物系统更现实的描述。仅对于自催化和与其他分子形成复合物的综合作用，才预期存在与多个稳态相关的泵的自我调节机制。在六态模型中，该模型也会导致振荡。
