2018/02/27 by Marcelo S. Reis, Reis, Marcelo S.
Biochemistry, Genetics and Molecular Biology · Chemistry · Engineering · #Advanced Control Systems Optimization #Computational Complexity (cs.CC) #Enzyme Catalysis and Immobilization #FOS: Computer and information sciences #Mass Spectrometry Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1803.00618
openalex publication_date 2018/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of modeling of cell signaling pathways, a relevant step is finding steady-state solutions for ODE systems that describe the kinetics of a set of chemical reactions, especially sets composed of zero, first, and second-order reactions. To compute a steady-state solution, one must set the left-hand side of each ODE as zero, hence obtaining a system of non-negative, quadratic polynomial equations. If all second-order reactions are homogeneous in respect to their reactants, then the obtained quadratic polynomial equation system will also have univariate monomials. Although it is a well-known fact that finding a root of a quadratic polynomial equation system is a NP-hard problem, it is not so easy to find a readily available proof of NP-hardness for special cases like the aforementioned one. Therefore, we provide here a self-contained proof that finding a root of non-negative, with univariate monomials quadratic polynomial equation system (NUMQ-PES) is NP-hard. This result implies that finding steady-state solutions for ODE systems of zero, first and homogeneous second-order chemical reactions is a NP-hard problem; hence, it is not a feasible approach to approximate non-homogeneous second-order reactions into homogeneous ones.