Additive and dominance gene effects described by a logistic function in concentration-limited metabolic pathways at steady state out of equilibrium

Abstract

Abstract Additive (a) and dominance (d) gene effects are key to phenotype manifestation. We investigated the relationship between these effects and gene-encoded enzyme rates in an n-step linear metabolic pathway with mass limitation at stationary state out of equilibrium, where internal flux depended on internal enzyme concentrations (Ei, i=1 to n) and external flux on input/output enzyme/transporter concentrations (Ee). Using coupled reversible Michaelis-Menten (MM) equations for Ei rates and irreverisble MM for Ee rates we found that stationary-state metabolite concentration (Si) was a logistic function of Ei. Its inflection point (S0i, E0i) depended on the total mass of the system ({Sigma} Si) and on Ee saturation, shifting from negative to positive values as reaction kinetics transitioned from first to mixed or zero order. Moreover, {Sigma} Si and Ee saturation explained negative, partial, and complete dominance in this metabolic system, provided phenotypic value of trait T is linearly dependent on Si at certain sink. The system was unstable when approaching closure (Ee=0). In this condition, asymptotic Smax equaled equilibrium concentration, being equilibrium displacement the driving force of flux. In pathways with n>1 reaction steps there was a change of regime in early reactions when increments in En passed E0n. This change of regime led to peaks raising at some Si previous to Sn and Sn+1 that were modeled by adding a Gaussian component to the logistic equation. Therefore, if T is determined by some of these Si, overdominance and dominance reversals may be explained. We obtained a good fit when applied this equation to Ei and Si data obtained from silicon-cell models developed with specific kinetic equations and experimentally determined kinetic parameters. In addition, we applied this framework to experimental data on amylose accumulation in starch granules catalyzed by granule-bound starch synthase I, and found that the logistic function fitted data from six plant species. This framework may contribute a partial explanation of the non-linearity between genotype and phenotype from the metabolic standpoint, which may be useful in the future for plant or animal breeding technologies.