An age-dependent feedback control model of calcium dynamics in yeast cells

Bifurcations and limit cycles in cytosolic yeast calcium

Calcium homeostasis is a fundamental cellular process in yeast. The regulation of the cytosolic calcium concentration is required for volume preservation and to regulate many vital calcium dependent processes such as mating and response to stress. The homeostatic mechanism is often studied by applying calcium pulses: sharply changing the calcium concentration in the yeast environment and observing the cellular response. To address these experimental investigations, several mathematical models have been proposed to describe this response. In this article we demonstrate that a previously studied model for this response predicts the presence of limit point instabilities and limit cycles in the dynamics of the calcium homeostasis system. We discuss the ways in which such dynamic characteristics can be observed with luminometric techniques. We contrast these predictions with experimentally observed responses and find that the experiments reveal a number of features that are consistent with modeling predictions. In particular, we find that equilibrium cytosolic concentrations have a sharp change in behavior as pulse size changes in the micromolar range. We show that such change is consistent with the presence of limit point instabilities. Additionally, we find that the response of synchronized yeast cells to millimolar range pulses is non-monotonic in its late stages. This response has characteristics similar to those associated with limit cycles.

Hydrogen peroxide induced loss of heterozygosity correlates with replicative lifespan and mitotic asymmetry in Saccharomyces cerevisiae

Cellular aging in Saccharomyces cerevisiae can lead to genomic instability and impaired mitotic asymmetry. To investigate the role of oxidative stress in cellular aging, we examined the effect of exogenous hydrogen peroxide on genomic instability and mitotic asymmetry in a collection of yeast strains with diverse backgrounds. We treated yeast cells with hydrogen peroxide and monitored the changes of viability and the frequencies of loss of heterozygosity (LOH) in response to hydrogen peroxide doses. The mid-transition points of viability and LOH were quantified using sigmoid mathematical functions. We found that the increase of hydrogen peroxide dependent genomic instability often occurs before a drop in viability. We previously observed that elevation of genomic instability generally lags behind the drop in viability during chronological aging. Hence, onset of genomic instability induced by exogenous hydrogen peroxide treatment is opposite to that induced by endogenous oxidative stress during chronological aging, with regards to the midpoint of viability. This contrast argues that the effect of endogenous oxidative stress on genome integrity is well suppressed up to the dying-off phase during chronological aging. We found that the leadoff of exogenous hydrogen peroxide induced genomic instability to viability significantly correlated with replicative lifespan (RLS), indicating that yeast cells' ability to counter oxidative stress contributes to their replicative longevity. Surprisingly, this leadoff is positively correlated with an inverse measure of endogenous mitotic asymmetry, indicating a trade-off between mitotic asymmetry and cell's ability to fend off hydrogen peroxide induced oxidative stress. Overall, our results demonstrate strong associations of oxidative stress to genomic instability and mitotic asymmetry at the population level of budding yeast.

Spatial Quantification of Cytosolic Ca²⁺ Accumulation in Nonexcitable Cells: An Analytical Study

Calcium ions act as messengers in a broad range of processes such as learning, apoptosis, and muscular movement. The transient profile and the temporal accumulation of calcium signals have been suggested as the two main characteristics in which calcium cues encode messages to be forwarded to downstream pathways. We address the analytical quantification of calcium temporal-accumulation in a long, thin section of a nonexcitable cell by solving a boundary value problem. In these expressions we note that the cytosolic Ca(2+) accumulation is independent of every intracellular calcium flux and depends on the Ca(2+) exchange across the membrane, cytosolic calcium diffusion, geometry of the cell, extracellular calcium perturbation, and initial concentrations. In particular, we analyse the time-integrated response of cytosolic calcium due to i) a localised initial concentration of cytosolic calcium and ii) transient extracellular perturbation of calcium. In these scenarios, we conclude that i) the range of calcium progression is confined to the vicinity of the initial concentration, thereby creating calcium microdomains; and ii) we observe a low-pass filtering effect in the response driven by extracellular Ca(2+) perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios.

Store-operated calcium entry could prevent continuous spiking of membrane potential to sustain normal intracellular calcium oscillations and normal potential bursting in pancreatic β-cells

We propose a dynamical store-operated calcium entry (SOCE) model to analyze the complex role of SOCE in modulating calcium oscillations and electrical activity in pancreatic β-cells and provide a new mathematical insight. Using this model, we simulate the SOCE role in a number of cases with different SOCE conductances. When the SOCE conductance is set to 0 or very small (5 pS), our numerical simulation conforms to the experimental observation that endoplasmic reticulum (ER) calcium can sustain normal calcium oscillations and the depletion of ER calcium transforms the normal calcium oscillations into a sustained calcium increase with oscillations of much higher frequency and much smaller amplitude, and transforms the normal membrane potential oscillations to a pattern of continuous spiking. When the SOCE conductance is increased to 20 pS and the ER calcium is depleted, our numerical simulation conforms to the other experimental observation that the normal calcium and potential oscillations are sustained and augmented a little bit. Moreover, the oscillation frequency is increased a very little bit. A further increase of the conductance to 35 pS slows down the oscillation a little bit. This numerical evidence suggests that a sufficiently large SOCE can prevent the continuous spiking of membrane potential to sustain the normal calcium oscillations and the normal membrane potential bursting. A careful examination of our simulated dynamics of the ATP/ADP ratio, the ATP-sensitive outward K(+) current, and the voltage-gated inward Ca(2+) current reveals that intracellular periodic Ca(2+) peaks perhaps resulted from SOCE might play a role in stabilizing the membrane potential at its resting level (avoiding the continuous spiking) for a certain period of time by accelerating ATP consumption, reducing the ratio ATP/ADP, opening the ATP-sensitive potassium channel, and repolarizing the membrane potential.

Designing dynamical output feedback controllers for store-operated Ca²+ entry

Store-operated calcium entry (SOCE) has been proposed as the main process controlling Ca²+ entry in non-excitable cells. Although recent breakthroughs in experimental studies of SOCE have been made, its mathematical modeling has not been developed. In the present work, SOCE is viewed as a feedback control system subject to an extracellular agonist disturbance and an extracellular calcium input. We then design a dynamic output feedback controller to reject the disturbance and track Ca²+ resting levels in the cytosol and the endoplasmic reticulum (ER). The constructed feedback control system is validated by published experimental data and its global asymptotic stability is proved by using the LaSalle's invariance principle. We then simulate the dynamic responses of STIM1 and Orai1, two major components in the operation of the store-operated channels, to the depletion of Ca²+ in the ER with thapsigargin, which show that: (1) Upon the depletion of Ca²+ in the ER, the concentrations of activated STIM1 and STIM1-Orai1 cluster are elevated gradually, indicating that STIM1 is accumulating in the ER-PM junctions and that the cytosolic portion of the active STIM1 is binding to Orai1 and driving the opening of CRAC channels for Ca²+ entry; (2) after the extracellular Ca²+ addition, the concentrations of both STIM1 and STIM1-Orai1 cluster decrease but still much higher than the original levels. We also simulate the system responses to the agonist disturbance, which show that, when a sequence of periodic agonist pulses is applied, the system returns to its equilibrium after each pulse. This indicates that the designed feedback controller can reject the disturbance and track the equilibrium.