We consider a measure of cooperativity based on the minimal interaction required to generate an observed titration behavior. We describe the corresponding algebraic optimization problem and show how it can be solved using the nonlinear algebra tool SCIP. Moreover, we compute the minimal interactions and minimal molecules for several binding polynomials that describe the oxygen binding of various hemoglobins under different conditions. We compare their minimal interaction with the maximal slope of the Hill plot, and discuss similarities and discrepancies with a view towards the shapes of the binding curves.

中文翻译：

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协同性、绝对交互和代数优化。

我们考虑了一种基于产生观察到的滴定行为所需的最小相互作用的协同性度量。我们描述了相应的代数优化问题，并展示了如何使用非线性代数工具SCIP来解决它。此外，我们计算了几个结合多项式的最小相互作用和最小分子，这些多项式描述了不同条件下各种血红蛋白的氧结合。我们将它们的最小相互作用与希尔图的最大斜率进行比较，并从结合曲线形状的角度讨论相似之处和差异。