The mechanistic origin of incomplete enzyme saturation in vivo and the generalization of intracellular kinetic formalisms for in vivo enzymology

Classical enzyme kinetics measures parameters such as $K_M$, $V_{\max}$ and $k_{cat}$ in diluted in vitro assays whose conditions differ sharply from the interior of living cells. Castaño-Cerezo et al. (2024) introduced an in vivo enzymology pipeline — synthetic strain series with graded substrate supply, combined with absolute metabolomics, fluxomics and proteomics — and measured in vivo Michaelis–Menten parameters for carotenoid-pathway enzymes in Saccharomyces cerevisiae, finding incomplete enzyme saturation and parameters that differ from in vitro values. They left open four linked issues: the mechanistic origin of incomplete saturation in vivo (subcellular substrate heterogeneity versus genuinely low affinity versus overflow/export, alternative sinks, or toxicity); the generalization of the kinetic formalism beyond irreversible, substrate-excess, zero-product Michaelis–Menten conditions; extension of the pipeline to in vivo inhibition/activation constants and time-course responses; and the dependence of in vivo parameters on the microenvironment and growth conditions. No published work resolves these four strands.

Background

Enzyme kinetics has been quantified for over a century with the Michaelis–Menten formalism: for the reaction $S \rightarrow P$ catalyzed by enzyme $E$, the rate is $v = V_{\max}\,[S]/(K_M+[S])$, where $K_M$ is the substrate concentration at half-maximal rate and $V_{\max}=k_{cat}[E]$, with the turnover number $k_{cat}$ setting the maximal catalytic rate per enzyme molecule. This framework was derived for dilute in vitro assays in which substrate is in large excess over enzyme, the product concentration is initially zero, and the reaction is effectively irreversible. The cytoplasm of a living cell violates all of these conveniences to various degrees: it is a crowded, spatially heterogeneous gel; substrates partition among compartments and membranes; enzymes and their substrates can be present at comparable concentrations; products accumulate; and growth-coupled regulation, toxicity and overflow phenomena (export or relocation of excess metabolites) reshape the effective substrate pool. A long line of work therefore asked how far classical parameters are physiologically meaningful: genome-scale comparisons found that in vivo enzyme catalytic rates derived from flux and proteomics data often disagree with in vitro $k_{cat}$ values (Davidi et al. 2016), while kinetic profiling across specialists found apparent in vivo turnover numbers to be condition-dependent yet internally consistent (Heckmann et al. 2020). These inference-based studies, however, did not measure full saturation curves inside cells.

Castaño-Cerezo et al. (2024) provided such measurements with a synthetic-biology design: in yeast strains carrying a heterologous carotenoid pathway, they graded the expression of GGPP synthase — the enzyme producing geranylgeranyl diphosphate (GGPP), the C20 isoprenoid building block — to span intracellular GGPP concentrations over a factor of about 38, then combined absolute quantification of GGPP, phytoene (the colorless C40 carotene first formed from two GGPP molecules), downstream carotenoids, $^{13}$C-based metabolic fluxes and targeted proteomics to fit in vivo Michaelis–Menten parameters ($K_{1/2}^{cell}$, $V_{\max}^{cell}$, $k_{cat}^{cell}$) for the GGPP-consuming phytoene synthase PaCrtB and several phytoene desaturases (CrtI enzymes, which introduce double bonds into phytoene). The in vivo parameters differed from in vitro values, and, strikingly, enzymes did not reach complete saturation even when total intracellular GGPP was high (around 20 µM). The authors argued that the classical assumptions are only partially satisfied in vivo (the substrate/enzyme ratio ranged from 2 to 2500 depending on the enzyme, and product concentrations are non-zero), listed several candidate explanations for incomplete saturation — heterogeneous subcellular distribution of GGPP with only a fraction accessible to the enzyme, substrate or product toxicity, overflow mechanisms that relocate substrate to other compartments or export it, alternative metabolic sinks that activate above concentration thresholds, and systemic homeostatic properties that reduce production fluxes as products accumulate — and stated that dedicated studies would be required to clarify the effects of cell compartments on enzyme efficiency. They further noted that new kinetic formalisms will be required to account for in vivo conditions (presence of products, similar enzyme and substrate concentrations, local concentration variations, and molecular fluxes within the cell), proposed but did not demonstrate extensions to in vivo inhibition and activation parameters and to time-course data, and emphasized that enzymatic parameters should not be treated as constants because they depend on the microenvironment (pH, ion concentration, temperature, membrane composition, lipid droplet formation). The unresolved question is thus both mechanistic (why saturation is incomplete in the cell) and theoretical (which kinetic formalism correctly describes intracellular enzyme behavior), and both answers are prerequisites for the source paper's stated goal of broadly generalizing in vivo parameters for predictive metabolic engineering.

Problem Statement

As posed by Castaño-Cerezo et al. (2024), establish the mechanistic and theoretical basis required for in vivo-measured enzyme kinetic parameters to be mechanistically interpretable and predictive, in four linked parts. (1) Determine the mechanistic origin of incomplete enzyme saturation in vivo — specifically for GGPP-consuming enzymes such as phytoene synthase in S. cerevisiae that fail to saturate despite total intracellular GGPP of around 20 µM — by discriminating among the candidate mechanisms: genuinely lower in vivo enzyme affinity, heterogeneous subcellular distribution of the substrate (compartmentation or sequestration into lipid droplets leaving only a fraction of substrate accessible to the enzyme), substrate overflow or export, alternative metabolic sinks that become active above concentration thresholds, and product- or substrate-toxicity-driven physiological perturbation. (2) Generalize the in vivo kinetic formalism beyond the classical irreversible Michaelis–Menten equation, which assumes zero product concentration, substrate in large excess over enzyme, and homogeneous substrate availability, to a framework that accounts for non-negligible product concentrations, enzyme and substrate concentrations of similar magnitude, local concentration gradients, and molecular fluxes within the cell, and that reduces to the classical Michaelis–Menten equation in the limits of excess substrate, absence of product and homogeneous substrate availability and states which additional parameters it introduces. (3) Establish experimentally whether the in vivo pipeline can measure inhibition and activation parameters and transient, time-course responses to metabolic or genetic perturbations, as proposed but not demonstrated in the source. (4) Quantify how the measured in vivo parameters depend on microenvironmental variables (membrane composition, lipid droplet formation, pH, ionic strength, temperature) and growth conditions. Strands (1) and (2) jointly constitute the interpretive core — the measured parameters cannot be given a mechanistic meaning until it is known why saturation is incomplete and which formalism applies — and strands (3) and (4) extend the range of variables and conditions over which the source seeks to generalize in vivo enzyme parameters for predictive metabolic engineering.

References

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