Thermodynamic cost-controllability tradeoff in metabolic currency coupling

TL;DR

The paper develops a minimal coarse-grained model of metabolic currency coupling to quantify how the charged/uncharged states of currency metabolites are coordinated. By modeling two currency metabolites A and B with driving and coupling reactions, it derives steady-state ratios $\Gamma_A^{st}$ and $\Gamma_B^{st}$, elasticity measures $e^\pm_{XY}$, and the entropy production rate $\sigma_{cpl}^{st}$. A key finding is a fundamental tradeoff: increasing the system's controllability—via more balanced currency pools—generally increases the thermodynamic cost (entropy production). The authors further connect this tradeoff to evolutionary patterns in nucleotide-pool balance and genomic GC content, offering a testable hypothesis linking metabolism, evolution, and genome composition.

Abstract

Cellular metabolism is globally regulated by various currency metabolites such as ATP, GTP, and NAD(P)H. These metabolites cycle between charged (high-energy) and uncharged (low-energy) states to mediate energy transfer. While distinct currency metabolites are associated with different metabolic functions, their charged and uncharged forms are generally interchangeable via biochemical reactions such as ${\rm ATP{\,+\,}GDP{\,\rightleftharpoons\,}ADP{\,+\,}GTP}$ and $\rm NADP^+{\,+\,}NADH{\,\rightleftharpoons\,}NADPH{\,+\,}NAD^+ $. Thus, their energetic states are generally coupled and influence each other, which would hinder the independent regulation of different currency metabolites. Despite the extensive knowledge of the molecular biology of individual currency metabolites, it remains poorly understood how the coordination of various coupled currency metabolites shapes metabolic regulation, efficiency, and ultimately the evolution of organisms. Here, we present a minimal theoretical model of metabolic currency coupling and reveal a fundamental tradeoff relationship between metabolic controllability and thermodynamic cost: increasing the capacity to independently regulate multiple currency metabolites generally requires comparable abundances of those metabolites, which in turn incurs a higher entropy production rate. The tradeoff suggests that in complex environments, organisms evolutionarily favor an equal abundance of currency metabolites to enhance metabolic controllability at the expense of a higher thermodynamic cost; conversely, in simple environments, organisms evolve to have imbalanced amounts of them to reduce heat dissipation. These considerations also offer a hypothesis regarding evolutionary trends in nucleotide-pool balance and genomic GC content.

Figures (6)

• Figure 1: Metabolic currency coupling. (A) Examples of transferases and their associated currency coupling reactions. (B) Model of the coupling of currency metabolites. All reactions are reversible. Table \ref{['table:Symbols']} collects all the notation in one place. (C) Schematics of how the balance in currency metabolite pools affects metabolic controllability and thermodynamic cost. Coupling reactions cause the ratios $[A^\ast]/[A]$ and $[B^\ast]/[B]$ to shift in the same direction. The former strongly influences the latter when ${[A]_\mathrm{tot}}\gg{[B]_\mathrm{tot}}$. Conversely, a large ${[A]_\mathrm{tot}}/{[B]_\mathrm{tot}}$ ratio reduces the entropy production rate required to maintain the metabolic currency coupling, which is analogous to the "friction" between different currency metabolites. (D) A theoretical connection between organismal or habitat complexity and pool sizes of multiple currency metabolites.
• Figure 2: Elasticity of the charged/uncharged ratios with metabolic currency coupling. (A) Dependence of charged/uncharged ratio $\Gamma_X^{\mathrm{st}}\,(X{\,=\,}A,B)$ on $\kappa_B^+$. Colored lines show the cases with ${k_\mathrm{cpl}}{\,=\,}1,{[B]_\mathrm{tot}}{\,=\,}1$ and different ${[A]_\mathrm{tot}}$, while gray line shows the no coupling case. (B) Dependence of self-elasticity $e^+_{BB}$ on ${[A]_\mathrm{tot}}\kappa_A^+ / {[B]_\mathrm{tot}}\kappa_B^+$. Colored lines show different coupling strength ${k_\mathrm{cpl}}$ and black line shows the large coupling limit, $\tilde{e}^+_B$ (Eq. \ref{['eq:e_XY_k_large']}). (C) Relationship between ${[A]_\mathrm{tot}}/{[B]_\mathrm{tot}}$ and mean elasticity $e$. The black line shows the strong coupling limit. In panels (B) and (C), $\kappa_B^+{\,=\,}1/3$ and ${[A]_\mathrm{tot}}{\,+\,}{[B]_\mathrm{tot}}{\,=\,}2$ are fixed. The other parameters are set as $\kappa_A^+{\,=\,}2/3$, $\kappa_A^-{\,=\,}1/3$, and $\kappa_B^-{\,=\,}2/3$.
• Figure 3: Thermodynamic cost of currency coupling. (A) Dependence of ${k_\mathrm{cpl}}\sigma_{\mathrm{cpl}}^{\mathrm{st}}$ on ${[A]_\mathrm{tot}}/{[B]_\mathrm{tot}}$ with relatively strong currency coupling. The black curve represents the strong coupling limit, Eq. \ref{['eq:EPR_approx_largek']}. For a consistent comparison, the system size is kept constant by setting ${[A]_\mathrm{tot}}{\,+\,}{[B]_\mathrm{tot}}{\,=\,}2$ while ${[A]_\mathrm{tot}}/{[B]_\mathrm{tot}}$ is varied; parameters are set as $\kappa_A^+{\,=\,}2/3,\kappa_A^-{\,=\,}1/3$, $\kappa_B^+{\,=\,}1/3,\kappa_B^-{\,=\,}2/3$. (B) Relationship between the scaled EPR of the coupling reaction, $\frac{{k_\mathrm{cpl}} \sqrt{\kappa_A^+\kappa_A^- \kappa_B^+\kappa_B^-} }{(\kappa_A^-\kappa_B^+ - \kappa_A^+\kappa_B^-)^2} \sigma^{\mathrm{st}}_{\mathrm{cpl}}$, and mean elasticity $e$. ${k_\mathrm{cpl}}{\,=\,}10$. The parameters $\kappa_X^\pm$ and ${[X]_\mathrm{tot}}$ are randomly sampled from a uniform distribution within the range $[0,1]$. The black curve represents the strong coupling limit, Eq. \ref{['eq:tradeoff_k_large2']}.
• Figure 4: Statistical relationship between organismal complexity and GC content. (A) Correlation between genomic properties (genome size or the number of coding genes) and GC content. (B) Correlation between proteomic properties (the number of protein families or domains) and GC content. The data are obtained from dataset madin2020synthesis and Pfam mistry2021pfam for $496$ bacteria and archaea.
• Figure 5: Dependence of $\sigma_{\mathrm{cpl}}^{\mathrm{st}}/{k_\mathrm{cpl}}$ on the ${[A]_\mathrm{tot}}/{[B]_\mathrm{tot}}$ ratio with relatively weak currency coupling (colored points). The gray curve represents \ref{['eq:EPR_approx1']}. For a consistent comparison, the system size is kept constant by setting ${C_\mathrm{tot}}{\,=\,}{[A]_\mathrm{tot}}{\,+\,}{[B]_\mathrm{tot}}{\,=\,}2$ while varying ${[A]_\mathrm{tot}}/{[B]_\mathrm{tot}}$; parameters are set as $\kappa_A^+{\,=\,}2/3,\kappa_A^-{\,=\,}1/3$, $\kappa_B^+{\,=\,}1/3,\kappa_B^-{\,=\,}2/3$.