Additive and dominance gene effects described by a logistic function in concentration-limited metabolic pathways at steady state out of equilibrium
- 1Departamento de Ciencias Biologicas, Facultad de Ciencias Agrarias y Forestales. Universidad Nacional de La Plata - IBBM-CONICET
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.
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BibTeX
@misc{melgarejo2026additive,
title = {{Additive and dominance gene effects described by a logistic function in concentration-limited metabolic pathways at steady state out of equilibrium}},
author = {A. Melgarejo and A. R. Roig and B. S. Ramirez and A. R. Lodeiro},
howpublished = {bioRxiv},
year = {2026},
month = oct,
doi = {10.64898/2026.10.22.761079},
url = {https://www.biorxiv.org/content/10.64898/2026.10.22.761079v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Additive and dominance gene effects described by a logistic function in concentration-limited metabolic pathways at steady state out of equilibrium
AU - A. Melgarejo
AU - A. R. Roig
AU - B. S. Ramirez
AU - A. R. Lodeiro
PY - 2026
DA - 2026/10/22
PB - bioRxiv
DO - 10.64898/2026.10.22.761079
UR - https://www.biorxiv.org/content/10.64898/2026.10.22.761079v1
AB - 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.
ER -