# A kinetic model of copper homeostasis in Saccharomyces cerevisiae

## TL;DR

This paper presents a kinetic model to explain how yeast cells manage copper levels by importing excess copper and using metallothionein to store it, even when copper is abundant.

## Contribution

The study introduces a novel kinetic model with 25 reactions to explain copper homeostasis in yeast under varying copper concentrations.

## Key findings

- A MAC1-independent copper importer is necessary for sufficient copper uptake under Cu-excess conditions.
- Twenty-one rate-constants remained constant, while four increased, suggesting regulation not captured by initial rate laws.
- The model predicts that the MAC1-independent importer is likely FET4, which also imports iron.

## Abstract

Rather than inhibiting copper entry when grown on high Cu, yeast cells import excessive Cu while simultaneously increasing expression of metallothionein CUP1 which then sequesters excess Cu. An ordinary-differential-equations-based kinetic model was developed to investigate this unusual behavior. The assumed reaction network included 25 reactions and 10 components in the cytosol of yeast cells growing in media supplemented with a series of increasing nutrient COPPER concentrations. Published concentrations of copper proteins and coordination complexes that constitutes the low-molecular-mass (or labile) Cu pool were assumed. Other components included transcription factors MAC1 and ACE1, the MAC1-dependent copper importer CTR1, and other copper proteins considered collectively. A second MAC1-independent importer was required for sufficient Cu to enter the cell under Cu-excess conditions. The mathematical system was initially solved at steady state for each condition in the series. The null-space of the stoichiometric matrix was evaluated using the basic pathways approach. Steady-state rates and rate-constants were calculated for each reaction and each condition of the series. Twenty-one rate-constants remained relatively constant across the series, while 4 trended higher, indicating that cells regulate those latter reactions in ways that were not included in their assumed rate-law expressions. This behavior was simulated by augmenting those expressions with logistical functions that sensed labile Cu and/or nutrient COPPER. The resulting integrated dynamical system approximately generated observed component concentrations over the series and was stable to both intracellular and extracellular perturbations. The MAC1-independent importer is predicted to be FET4, a nonspecific importer of both Cu and Fe. Cells may tolerate excessive Cu import to import sufficient iron.