Mathematical and numerical modelling of copper transport in yeast

Abstract

The transport and regulation of metals in eukaryotic cells is a complex process, dependent on protein transporters that respond to cell needs. The application of dynamic mathematical models can provide valuable insights into these transport mechanisms. Mathematical simulations of transport processes may not directly predict transport mechanisms but can guide experimental design or identify inconsistencies between observation and hypotheses. Copper is an essential metal in eukaryotic cells as a catalytic co-factor in metallochaperone proteins and is therefore tightly regulated in living systems, making it valuable for quantifying biological transport mechanisms. In order to test our modeling system, a culture of baker’s yeast (Saccharomyces cerevisiae) was grown, copper concentrations were obtained from the cells and growth media, and a mathematical model was developed to investigate transport mechanisms between the growth media and the cells. A model based on conservation of mass was presented as a system of equations upon which to develop. This system of equations was developed to include an active transport term that describes a homeostatic concentration that cells actively maintain through negative feedback, and with a delayed activation, the model was more accurate at predicting the experimental data. The hypothesis and dynamic model derived in this work provide a novel framework that may be applied to additional metals or used to describe other transport mechanisms in biological systems.