Simulating calcium influx and free calcium concentrations in yeast

Abstract

Yeast can proliferate in environments containing very high Ca(2+) primarily due to the activity of vacuolar Ca(2+) transporters Pmc1 and Vcx1. Yeast mutants lacking these transporters fail to grow in high Ca(2+) environments, but growth can be restored by small increases in environmental Mg(2+). Low extracellular Mg(2+) appeared to competitively inhibit novel Ca(2+) influx pathways and to diminish the concentration of free Ca(2+) in the cytoplasm, as judged from the luminescence of the photoprotein aequorin. These Mg(2+)-sensitive Ca(2+) influx pathways persisted in yvc1 cch1 double mutants. Based on mathematical models of the aequorin luminescence traces, we propose the existence in yeast of at least two Ca(2+) transporters that undergo rapid feedback inhibition in response to elevated cytosolic free Ca(2+) concentration. Finally, we show that Vcx1 helps return cytosolic Ca(2+) toward resting levels after shock with high extracellular Ca(2+) much more effectively than Pmc1 and that calcineurin, a protein phosphatase regulator of Vcx1 and Pmc1, had no detectable effects on these factors within the first few minutes of its activation. Therefore, computational modeling of Ca(2+) transport and signaling in yeast can provide important insights into the dynamics of this complex system.

Fig. 1

Schematic graph of the system and control block diagram. Panel A, A schematic graph of Ca²⁺ homeostasis/signaling system in yeast cells (for details, please see the text in Section 1). Transporter M is newly detected in this work and is assumed to open under extremely high extracellular Ca²⁺ concentration. Panel B, Control block diagram of our model. In yvc1 cch1 yeast cells, the cytosolic Ca²⁺ influx is through Transporter X and an assumed Transporter M, the cytosolic Ca²⁺ efflux is through Pmc1, Pmr1 and Vcx1. For yeast cells with fixed volume, the cytosolic Ca²⁺ concentration (i.e., x(t)) is the integral of the flux rate difference (i.e., influx rate subtracting efflux rate) divided by the cytosolic volume. The green lines describe the feedback loop: cytosolic Ca²⁺ concentration is sensed by the calmodulin and Ca²⁺-bound calmodulin is assumed to inhibit the activity of both transporters M and X. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 2

Experimental results. Panel A, the concentrations of CaCl₂ that caused a 50% inhibition of growth (i.e., the IC₅₀ for CaCl₂ ) were shown for pmc1 (filled circles), pmc1 vcx1 (open circles), pmc1 vcx1 cnb1 (filled triangles) and vcx1 cnb1 (open triangles) mutants after 24 h of growth standard YPD culture medium supplemented with 0–32 mM MgCl₂ . Panel B, A yvc1 cch1 double mutant expressing apo-aequorin from a plasmid was incubated with coelenterazine co-factor to reconstitute aequorin in situ. The cells bearing reconstituted aequorin were returned to growth medium for an additional 90 min, divided into equal aliquots, treated with varying amounts (0 mM, 0.3 mM, 3 mM, 30 mM, 90 mM) of MgCl₂ , placed into a tube luminometer, and monitored for luminescence before and after injection of 800 mM CaCl₂ . Panel C, the corresponding aequorin luminescence curves for vcx1 yvc1 cch1 mutant.

Fig. 3

Steady state analysis and flux analysis of the system. Panel A, the steady state value of x(t) as a function of parameter [Mg_ex ] for simulated yvc1 cch1 mutant in extracellular medium with high calcium concentration (parameter [Ca_ex ] = 800 mM). The simulated cytosolic calcium level of our model yvc1 cch1 mutant rests within 0.173–0.212 μM (regardless of the initial conditions) as the media Mg²⁺ level (parameter [Mg_ex ]) ranges from 0 mM to 90 mM. Panel B, the simulated flux proportion of Transporter M in the total cytosolic Ca²⁺ influx as a function of t for yvc1 cch1 mutant under hypertonic shock (at t = 0, parameter [Ca_ex ] suddenly increases from 0 mM to 800 mM and at the same time parameter [Mg_ex ] suddenly increases from 0 mM to various concentrations (0 mM, 0.3 mM, 3 mM, 30 mM, 90 mM)). Please note that the blue, green and yellow curves coincide with the red curve in this graph. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 4

Simulated response curves and volume evolution curves. Panel A, the simulated response curves of the best fit using two transporters model for yvc1 cch1 mutant. The black, blue, green, yellow and red curves depict the simulated x(t) curves for parameter [Mg_ex ] suddenly increasing from 0 mM to various concentrations (0 mM, 0.3 mM, 3 mM, 30 mM, 90 mM) at t = 0, respectively (please note that at the same time t = 0 parameter [Ca_ex ] suddenly increases from 0 mM to 800 mM in these simulations). Panel B, the corresponding simulated response curves using two transporters model for vcx1 yvc1 cch1 mutant. Panel C, the simulated response curves of the best fit using one Mg²⁺-sensitive transporter model (i.e., in this case we assume that Transporter X is the sole influx pathway) for yvc1 cch1 mutant. The black, blue, green, yellow and red curves depict the simulated x(t) curves for parameter [Mg_ex ] suddenly increasing from 0 mM to various concentrations (0 mM, 0.3 mM, 3 mM, 30 mM, 90 mM) at t = 0, respectively (please note that at the same time t = 0 parameter [Ca_ex ] suddenly increases from 0 mM to 800 mM in these simulations). Panel D, the simulated volume evolution curves using the two transporters model for yvc1 cch1 mutant under hypertonic shock (step increase of [Ca_ex ] from 0 mM to 800 mM with simultaneous step increase of [Mg_ex ] to various concentrations). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 5

Simulated cytosolic Ca²⁺ level (i.e., x(t)) for yvc1 cch1 mutant increases upon extracellular Mg²⁺ depletion or extracellular Ca²⁺ challenge. Panel A, the simulated x(t) response curve (the black curve) for parameter [Mg_ex ] (the red curve) suddenly decreasing from 1 mM to 0 mM at t = 0 and being reset to 1 mM after 90 s (please note that in this simulation, parameter [Ca_ex ] = 150 mM). Panel B, the simulated x(t) response curve (the black curve) for parameter [Ca_ex ] (the red curve) suddenly increasing from 150 mM to 200 mM at t = 0 and being reset to 150 mM after 90 s (please note that in this simulation, parameter [Mg_ex ] = 0 mM). The basal level of [Ca_ex ] in these two simulations is set to be 150 mM instead of 2 mM as in Wiesenberger’s paper [49] because our model is only valid for hypertonic shock (extracellular Ca²⁺ >132 mM). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)