# Cooperativity, Absolute Interaction, and Algebraic Optimization

## TL;DR

This paper introduces a measure of cooperativity based on minimal absolute interaction, formulates it as an algebraic optimization problem, and applies it to analyze hemoglobin binding behaviors under various conditions.

## Contribution

It presents a novel algebraic optimization approach to quantify cooperativity through minimal absolute interaction, using nonlinear algebra tools like SCIP.

## Key findings

- Minimal absolute interactions align with chemical modifications' expected outcomes.
- The measure ranks cooperativity differently than traditional Hill slope analysis.
- Application to hemoglobins demonstrates the method's practical utility.

## Abstract

We consider a measure of cooperativity based on the minimal absolute 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 \texttt{SCIP}. Moreover, we compute the minimal absolute interactions for various binding polynomials that describe the oxygen binding of various hemoglobins under different conditions. While calculated minimal absolute interactions are consistent with the expected outcome of the chemical modifications, it ranks the cooperativity of the molecules differently than the maximal Hill slope.