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

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Abstract

The functional decline of selected proteins or organelles leads to aging at the intracellular level. Identification of these proteins or organelles is usually challenging to traditional single-factor approaches since these factors are inter-connected via feedback or feedforward controls. Establishing a feedback control model to simulate the interactions of multiple factors is an insightful approach to guide the search for proteins involved in aging. However, there are only a few mathematical models describing the age-dependent accumulation of DNA mutations, which are directly or indirectly induced by deterioration of the intracellular environment including alteration of calcium homeostasis, a contributor of aging. Thus, based on Cui and Kaandorp’s model, we develop an age-dependent mathematical model for the calcium homeostasis in budding yeast Saccharomyces cerevisiae. Our model contains cell cycle-dependent aging factors and can qualitatively reproduce calcium shocks and calcium accumulations in cells observed in experiments. Using this model, we predict calcium oscillations in wild type, pmc1Δ, and pmr1Δ cells. This prediction suggests that Pmr1p plays a major role in regulating cytosolic calcium. Combining the model with our experimental lifespan data, we predict an upper-limit of cytosolic calcium tolerance for cell survival. This prediction indicates that, for aged cells (>35 generations), no pmr1 Δ can tolerate the cytosolic calcium concentration of 0.1 μM while a very small fraction (1%) of aged wild type cells (>50 generations) can tolerate a high cytosolic calcium concentration of 0.5 μM.

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References

  • Aiello DP, Fu L, Miseta A, Bedwell DM (2002) Intracellular Glucose 1-Phosphate and Glucose 6-Phosphate levels modulate Ca2+ homeostasis in Saccharomyces cerevisiae. J Biol Chem 277(48): 45751–45758

    Article  Google Scholar 

  • Ashrafi K, Sinclair D, Gordon JI, Guarente L (1999) Passage through stationary phase advances replicative aging in Saccharomyces cerevisiae. Proc Natl Acad Sci USA 96(16): 9100–9105

    Article  Google Scholar 

  • Bagnat M, Keranen S, Shevchenko A, Shevchenko A, Simons K (2000) Lipid rafts function in biosynthetic delivery of proteins to the cell surface in yeast. Proc Natl Acad Sci USA 97(7): 3254–3259

    Article  Google Scholar 

  • Baran I (1996) Calcium and cell cycle progression: possible effects of external perturbations on cell proliferation. Biophys J 70(3): 1198–1213

    Article  Google Scholar 

  • Belde PJ, Vossen JH, Borst-Pauwels GW, Theuvenet AP (1993) Inositol 1,4,5-trisphosphate releases Ca2+ from vacuolar membrane vesicles of Saccharomyces cerevisiae. FEBS Lett 323(1–2): 113–118

    Article  Google Scholar 

  • Bonilla M, Nastase KK, Cunningham KW (2002) Essential role of calcineurin in response to endoplasmic reticulum stress. EMBO J 21: 2343–2353

    Article  Google Scholar 

  • Boustany LM, Cyert MS (2002) Calcineurin-dependent regulation of Crz1p nuclear export requires Msn5p and a conserved calcineurin docking site. Genes Dev 16: 608–619

    Article  Google Scholar 

  • Chen KC, Csikasz-Nagy A, Gyorffy B, Val J, Novak B, Tyson JJ (2000) Kinetic analysis of a molecular model of the budding yeast cell cycle. Mol Biol Cell 11: 369–391

    Google Scholar 

  • Chen KC, Calzone L, Csikasz-Nagy A, Cross FR, Novak B, Tyson JJ (2004) Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell 15: 3841–3862

    Article  Google Scholar 

  • Cho JH, Ko KM, Singaravelu G, Ahnn J (2005) Caenorhabditis elegans PMR1, a P-type calcium ATPase, is important for calcium/manganese homeostasis and oxidative stress response. FEBS Lett 579(3): 778–782

    Article  Google Scholar 

  • Choi J, Chiang A, Taulier N, Gros R, Pirani A, Husain M (2006) A calmodulin-binding site on cyclin E mediates Ca2+-sensitive G1/s transitions in vascular smooth muscle cells. Circ Res 98(10): 1273–1281

    Article  Google Scholar 

  • Ciapa B, Pesando D, Wilding M, Whitaker M (1994) Cell-cycle calcium transients driven by cyclic changes in inositol trisphosphate levels. Nature 368(6474): 875–878

    Article  Google Scholar 

  • Courchesne WE, Ozturk S (2003) Amiodarone induces a caffeine-inhibited, MID1-depedent rise in free cytoplasmic calcium in Saccharomyces cerevisiae. Mol Microbiol 47(1): 223–234

    Article  Google Scholar 

  • Crabtree GR (2001) Calcium, calcineurin, and the control of transcription. J Biol Chem 276(4): 2313–2316

    Article  Google Scholar 

  • Cronin SR, Rao R, Hampton RY (2002) Cod1p/Spf1p is a P-type ATPase involved in ER function and Ca2+ homeostasis. J Cell Biol 157(6): 1017–1028

    Article  Google Scholar 

  • Cui J, Kaandorp JA (2006) Mathematical modeling of calcium homeostasis in yeast cells. Cell Calcium 39: 337–348

    Article  Google Scholar 

  • Cui J, Kaandorp JA, Ositelu OO, Beaudry V, Knight A, Nanfack YF, Cunningham KW (2009) Simulating calcium influx and free calcium concentrations in yeast. Cell Calcium 45: 123–132

    Article  Google Scholar 

  • Cunningham KW, Fink GR (1994) Calcineurin-dependent growth control in Saccharomyces cerevisiae mutants lacking PMC1, a homolog of plasma membrane Ca2+ ATPases. J Cell Biol 124(3): 351–363

    Article  Google Scholar 

  • Cunningham KW, Fink GR (1996) Calcineurin inhibits VCX1-dependent H+/Ca2+ exchange and induces Ca2+ ATPases in Saccharomyces cerevisiae. Mol Cell Biol 16(5): 2226–2237

    Google Scholar 

  • Cyert MS (2001) Genetic analysis of calmodulin and its targets in Sacchromyces cerevisiae. Annu Rev Genet 35: 647–672

    Article  Google Scholar 

  • Denis V, Cyert MS (2002) Internal Ca2+ release in yeast is triggered by hypertonic shock and mediated by a TRP channel homologue. J Cell Biol 156(1): 29–34

    Article  Google Scholar 

  • Díaz J, Martínez-Mekler G (2005) Interaction of the IP3-Ca2+ and MAPK signaling systems in the Xenopus blastomere: a possible frequency encoding mechanism for the control of the Xbra gene expression. Bull Math Biol 67(3): 433–465

    Article  MathSciNet  Google Scholar 

  • Dunn T, Gable K, Beeler T (1994) Regulation of cellular Ca2+ by yeast vacuoles. J Biol Chem 269: 7273–7278

    Google Scholar 

  • Flanagan WM, Corthesy B, Bram RJ, Crabtree GR (1991) Nuclear association of a T-cell transcription factor blocked by FK-506 and cyclosporin A. Nature 352: 803–807

    Article  Google Scholar 

  • Förster C, Kane PM (2000) Cytosolic Ca2+ homeostasis is a constitutive function of the V-ATPase in Saccharomyces cerevisiae. J Biol Chem 275(49): 38245–38253

    Article  Google Scholar 

  • Foster TC (2007) Calcium homeostasis and modulation of synaptic plasticity in the aged brain. Aging Cell 6(3): 319–325

    Article  Google Scholar 

  • Funakoshi M, Kajiwara R, Goda T, Nishimoto T, Kobayashi H (2000) Isolation and characterisation of a mutation in the PMR1 gene encoding a Golgi membrane ATPase, which causes hypersensitivity to over-expression of Clb3 in Saccharomyces cerevisiae. Mol Gen Genet 264(1–2): 29–36

    Google Scholar 

  • Gillespie CS, Proctor CJ, Boys RJ, Shanley DP, Wilkinson DJ, Kirkwood TB (2004) A mathematical model of ageing in yeast. J Theor Biol 229(2): 189–196

    Article  MathSciNet  Google Scholar 

  • Gourlay CW, Ayscough KR (2005) The actin cytoskeleton: a key regulator of apoptosis and ageing? Nat Rev Mol Cell Biol 6(7): 583–589

    Article  Google Scholar 

  • Iida H, Sakaguchi S, Yagawa Y, Anraku Y (1990) Cell cycle control by Ca2+ in Saccharomyces cerevisiae. J Biol Chem 265(34): 21216–21222

    Google Scholar 

  • Jain J, McCaffrey PG, Miner Z, Kerppola TK, Lambert JN, Verdine GL, Curran T, Rao A (1993) The T-cell transcription factor NFATp is a substrate for calcineurin and interacts with Fos and Jun. Nature 365: 352–355

    Article  Google Scholar 

  • Kaeberlein M, Kennedy BK (2005) Large-scale identification in yeast of conserved ageing genes. Mech Ageing Dev 126(1): 17–21

    Article  Google Scholar 

  • Kaeberlein M, Kirkland KT, Fields S, Kennedy BK (2004) Sir2-independent life span extension by calorie restriction in yeast. PLoS Biol 2(9): E296

    Article  Google Scholar 

  • Kaeberlein M, Powers RW 3rd, Steffen KK, Westman EA, Hu D, Dang N, Kerr EO, Kirkland KT, Fields S, Kennedy BK (2005) Regulation of yeast replicative life span by TOR and Sch9 in response to nutrients. Science 310(5751): 1193–1196

    Article  Google Scholar 

  • Keizer J, De Young GW (1992) Two roles for Ca2+ in agonist stimulated Ca2+ oscillations. Biophys J 61: 649–660

    Article  Google Scholar 

  • Kellermayer R, Aiello DP, Miseta Aa, Bedwell DM (2003) Extracellular Ca2+ sensing contributes to excess Ca2+ accumulation and vacuolar fragmentation in a pmr1 Δ mutant of S. cerevisiae. J Cell Sci 116: 1637–1646

    Article  Google Scholar 

  • Klemm RW, Ejsing CS, Surma MA, Kaiser HJ, Gerl MJ, Sampaio JL, de Robillard Q, Ferguson C, Proszynski TJ, Shevchenko A, Simons K (2009) Segregation of sphingolipids and sterols during formation of secretory vesicles at the trans-Golgi network. J Cell Biol 185(4): 601–612

    Article  Google Scholar 

  • Kowald A, Kirkwood TB (2000) Accumulation of defective mitochondria through delayed degradation of damaged organelles and its possible role in the ageing of post-mitotic and dividing cells. J Theor Biol 202(2): 145–160

    Article  Google Scholar 

  • Kuepfer L, Peter M, Sauer U, Stelling J (2007) Ensemble modeling for analysis of cell signaling dynamics. Nat Biotechnol 25(9): 1001–1006

    Article  Google Scholar 

  • Li Y, Camacho P (2004) Ca2+-dependent redox modulation of SERCA 2b by ERp57. J Cell Biol 164(1): 35–46

    Article  Google Scholar 

  • Liu W, Tang F (2008) Modeling a simplified regulatory system of blood glucose at molecular levels. J Theor Biol 252: 608–620

    Article  Google Scholar 

  • Locke EG, Bonilla M, Liang L, Takita Y, Cunningham KW (2000) A homolog of voltage-gated Ca2+ channels stimulated by depletion of secretory Ca2+ in yeast. Mol Cell Biol 20(18): 6686–6694

    Article  Google Scholar 

  • Mao L, Zabel C, Wacker MA, Nebrich G, Sagi D, Schrade P, Bachmann S, Kowald A, Klose J (2006) Estimation of the mtDNA mutation rate in aging mice by proteome analysis and mathematical modeling. Exp Gerontol 41(1): 11–24

    Article  Google Scholar 

  • Matsuura I, Kimura E, Tai K, Yazawa M (1993) Mutagenesis of the fourth calcium-binding domain of yeast calmodulin. J Biol Chem 169: 13267–13273

    Google Scholar 

  • Merz AJ, Wickner WT (2004) Trans-SNARE interactions elicit Ca2+ efflux from the yeast vacuole lumen. J Cell Biol 164(2): 195–206

    Article  Google Scholar 

  • Miseta A, Kellermayer R, Aiello DP, Fu L, Bedwell DM (1999a) The vacuolar Ca2+/H+ exchanger Vcx1p/Hum1p tightly controls cytosolic Ca2+ levels in S. cerevisiae. FEBS Lett 451: 132–136

    Article  Google Scholar 

  • Miseta A, Fu L, Kellermayer R, Buckley J, Bedwell DM (1999b) The Golgi apparatus plays a significant role in the maintenance of ca2+ homeostasis in the vps33Δ vacuolar biogenesis mutant of Saccharomyces cerevisiae. J Biol Chem 274(9): 5939–5947

    Article  Google Scholar 

  • Miyakawa T, Mizunuma M (2007) Physiological roles of calcineurin in Saccharomyces cerevisiae with special emphasis on its roles in G2/M cell-cycle regulation. Biosci Biotechnol Biochem 71(3): 633–645

    Article  Google Scholar 

  • Mouillac B, Balestre MN, Guillon G (1990) Positive feedback regulation of phospholipase C by vasopressin-induced calcium mobilization in WRK1 cells. Cell Signal 2: 497–507

    Article  Google Scholar 

  • Murchison D, Griffith WH (2007) Calcium buffering systems and calcium signaling in aged rat basal forebrain neurons. Aging Cell 6(3): 297–305

    Article  Google Scholar 

  • Norel R, Agur Z (1991) A model for the adjustment of the mitotic clock by cyclin and MPF levels. Science 251(4997): 1076–1078

    Article  Google Scholar 

  • Ohsumi Y, Anraku Y (1983) Calcium transport driven by a proton motive force in vacuolar membrane vesicles of Saccharomyces cerevisiae. J Biol Chem 258: 5614–5617

    Google Scholar 

  • Palmer CP, Zhou X, Lin J, Loukin SH, Kung C, Saimi Y (2001) A TRP homolog in Saccharomyces cerevisiae forms an intracellular Ca2+-permeable channel in the yeast vacuolar membrane. Proc Natl Acad Sci USA 98: 7801–7805

    Article  Google Scholar 

  • Pinton P, Pozzan T, Rizzuto1 R (1998) The Golgi apparatus is an inositol 1,4,5-trisphosphate-sensitive Ca2+ store, with functional properties distinct from those of the endoplasmic reticulum. EMBO J 17(18): 5298–5308

    Google Scholar 

  • Pozos TC, Sekler I, Cyert MS (1996) The product of HUM1, a novel yeast gene, is required for vacuolar Ca2+/H+ exchange and is related to mammalian Na+/Ca2+ exchangers. Mol Cell Biol 16(7): 3730–3741

    Google Scholar 

  • Putney JW Jr (1986) A model for receptor-regulated calcium entry. Cell Calcium 7: 1–12

    Article  Google Scholar 

  • Putney JW Jr (2007) Recent breakthroughs in the molecular mechanism of capacitative calcium entry (with thoughts on how we got here). Cell Calcium 42(2): 103–110

    Article  Google Scholar 

  • Putney JW Jr, McKay RR (1999) Capacitative calcium entry channels. Bioessays 21: 38–46

    Article  Google Scholar 

  • Ryu JH, Lee Y, Han SK, Kim HY (2003) The role of hydrogen peroxide produced by polychlorinated biphenyls in PMR1-deficient yeast cells. J Biochem 134(1): 137–142

    Article  Google Scholar 

  • Salazar C, Höfer T (2003) Allosteric regulation of the transcription factor NFAT1 by multiple phosphorylation sites: a mathematical analysis. J Mol Biol 327: 31–45

    Article  Google Scholar 

  • Schomerus C, Kntzel H (1992) CDC25-dependent induction of inositol 1,4,5-trisphosphate and diacylglycerol in Saccharomyces cerevisiae by nitrogen. FEBS Lett 307(3): 249–252

    Article  Google Scholar 

  • Shaw KT, Ho AM, Raghavan A, Kim J, Jain J, Park J, Sharma S, Rao A, Hogan PG (1995) Immunosuppressive drugs prevent a rapid dephosphorylation of transcription factor NFAT1 in stimulated immune cells. Proc Natl Acad Sci 92: 11205–11209

    Article  Google Scholar 

  • Shukla N, Rowe D, Hinton J, Angelini GD, Jeremy JY (2005) Calcium and the replication of human vascular smooth muscle cells: studies on the activation and translocation of extracellular signal regulated kinase (ERK) and cyclin D1 expression. Eur J Pharmacol 509(1): 21–30

    Article  Google Scholar 

  • Sible JC, Tyson JJ (2007) Mathematical modeling as a tool for investigating cell cycle control networks. Methods 41(2): 238–247

    Article  Google Scholar 

  • Sorin A, Rosas G, Rao R (1997) PMR1, a Ca2+-ATPase in yeast Golgi, has properties distinct from sarco/endoplasmic reticulum and plasma membrane calcium pumps. J Biol Chem 272(15): 9895–9901

    Article  Google Scholar 

  • Squier TC, Bigelow DJ (2000) Protein oxidation and age-dependent alterations in calcium homeostasis. Front Biosci 5: D504–D526

    Article  Google Scholar 

  • Starovasnik MA, Davis TN, Klevit RE (1993) Similarities and differences between yeast and vertebrate calmodulin: an examination of the calcium-binding and structural properties of calmodulin from the yeast Saccharomyces cerevisiae. Biochemistry 32: 3261–3270

    Article  Google Scholar 

  • Strayle J, Pozzan T, Rudolph HK (1999) Steady-state free Ca2+ in the yeast endoplasmic reticulum reaches only 10 mM and is mainly controlled by the secretory pathway pump Pmr1. EMBO J 18(17): 4733–4743

    Article  Google Scholar 

  • Sudbrak R, Brown J, Dobson-Stone C, Carter S, Ramser J, White J, Healy E, Dissanayake M, Larrègue M, Perrussel M, Lehrach H, Munro CS, Strachan T, Burge S, Hovnanian A, Monaco AP (2000) Hailey-Hailey disease is caused by mutations in ATP2C1 encoding a novel Ca2+ pump. Hum Mol Genet 9(7): 1131–1140

    Article  Google Scholar 

  • Takita Y, Engstrom L, Ungermann C, Cunningham KW (2001) Inhibition of the Ca2+-ATPase Pmc1p by the v-SNARE Protein Nyv1p. J Biol Chem 276(9): 6200–6206

    Article  Google Scholar 

  • Tan Y, Bush JM, Liu W, Tang F (2008) Identification of longevity genes with systems biology approaches. Comput Biol Chem Adv Appl 2(2009): 49–56

    Google Scholar 

  • Tang F, Kauffman EJ, Novak JL, Nau JJ, Catlett NL, Weisman LS (2003) Regulated degradation of a class V myosin receptor directs movement of the yeast vacuole. Nature 422(6927): 87–92

    Article  Google Scholar 

  • Tang F, Watkins W, Bermudez M, Gray R, Gaban A, Portie K, Grace S, Kleve M, Craciun G (2008) A life span-extending form of autophagy employs the vacuole-vacuole fusion machinery. Autophagy 4(7): 874–886

    Google Scholar 

  • Tanida I, Hasegawa A, Iida H, Ohya Y, Anraku Y (1995) Cooperation of calcineurin and vacuolar H+-ATPase in intracellular Ca2+ homeostasis of yeast cells. J Biol Chem 270(17): 10113–10119

    Article  Google Scholar 

  • Thibault O, Gant JC, Landfield PW (2007) Expansion of the calcium hypothesis of brain aging and Alzheimer’s disease: minding the store. Aging Cell 6(3): 307–317

    Article  Google Scholar 

  • Tisi R, Belotti F, Wera S, Winderickx J, Thevelein JM, Martegani E (2004) Evidence for inositol triphosphate as a second messenger for glucose-induced calcium signalling in budding yeast. Curr Genet 45(2): 83–89

    Article  Google Scholar 

  • Ward JPT, Robertson TP, Aaronson PI (2005) Capacitative calcium entry: a central role in hypoxic pulmonary vasoconstriction? Am J Physiol Lung Cell Mol Physiol 289: L2–L4

    Article  Google Scholar 

  • Wei Y, Marchi V, Wang R, Rao R (1999) An N-terminal EF hand-like motif modulates ion transport by Pmr1, the yeast Golgi Ca2+/Mn2+-ATPase. Biochemistry 38: 14534–14541

    Article  Google Scholar 

  • Weisman LS, Wickner W (1988) Intervacuole exchange in the yeast zygote: a new pathway in organelle communication. Science 241(4865): 589–591

    Article  Google Scholar 

  • Zamponi GW (2003) The L-type calcium channe C-terminus: sparking interest beyond its role in calcium-dependent inactivation. J Physiol 552: 333

    Article  MathSciNet  Google Scholar 

  • Zinser E, Paltauf F, Daum G (1993) Sterol composition of yeast organelle membranes and subcellular distribution of enzymes involved in sterol metabolism. J Bacteriol 175(10): 2853–2858

    Google Scholar 

  • Zhou X-L, Batiza AF, Loukin SH, Palmer CP, Kung C, Saimi Y (2003) The transient receptor potential channel on the yeast vacuole is mechanosensitive. Proc Natl Acad Sci USA 100: 7105–7110

    Article  Google Scholar 

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  1. Department of Biology, FH 406, University of Arkansas at Little Rock, 2801 S. University Ave., Little Rock, AR, 72204-1099, USA

    Fusheng Tang

  2. Department of Mathematics, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR, 72035, USA

    Weijiu Liu

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  1. Fusheng Tang
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Tang, F., Liu, W. An age-dependent feedback control model of calcium dynamics in yeast cells. J. Math. Biol. 60, 849–879 (2010). https://doi.org/10.1007/s00285-009-0289-0

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