Abstract
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.
Highlights
Interaction between components is a fundamental feature of biological systems
While a simple system of independent subunits is completely defined by its subunits, a complex system with interactions is more than the sum of its parts
A classical example of a small biological system with non-trivial interaction is hemoglobin with its four binding sites for oxygen (Bohr et al 1904; Barcroft 1913; Hill 1913)
Summary
Interaction between components is a fundamental feature of biological systems. While a simple system of independent subunits is completely defined by its subunits, a complex system with interactions is more than the sum of its parts. A classical example of a small biological system with non-trivial interaction is hemoglobin with its four binding sites for oxygen (Bohr et al 1904; Barcroft 1913; Hill 1913). The sigmoidal shape implies that the extremal states of full and zero saturation are more stable than the intermediate states of partial saturation. This phenomenon is commonly referred to as cooperativity, named after the intuition that bound ligands affect, either positively or negatively, the chances of new ligands binding to the still open sites (see Stefan and Le Novère 2013 for a review and interpretations). It is an essential trait for transport molecules, and its importance in the formation of multi-protein complexes (Roy et al 2017), in general signal transduction processes (Salakhieva et al 2016; Lenaerts et al 2009; Martini et al 2016b) and in the regulation of noise (Gutierrez et al 2009; Monteoliva et al 2013) has been discussed
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