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Article |
Address correspondence to V.D. Longo, Andrus Gerontology Center and Dept. of Biological Sciences, University of Southern California, 3715 McClintock Ave., Los Angeles, CA 90089-0191. Tel.: (213) 740-6212. Fax: (213) 821-5714. email: vlongo{at}usc.edu
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Abstract |
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Key Words: apoptosis; adaptive regrowth; programmed aging; superoxide; oxidtive stress
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Introduction |
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Analogously to C. elegans and some hibernating mammals, yeast enter different phases based on the availability of nutrients. After growing to the maximum density by using the glucose and other nutrients available on rotting fruit, yeast populations can enter a low metabolism stationary phase and survive for weeks or generate dormant spores that can remain viable for years (Phaff et al., 1966). Moreover, when incubated in medium containing a high concentration of glucose (2% synthetic dextrose complete [SDC] medium) yeast can enter a third survival phase characterized by high metabolic rates and a shorter life span (Longo and Fabrizio, 2002; Fabrizio et al., 2003). We termed survival in these low and high metabolism phases "chronological life span" (Longo, 1997; Fabrizio and Longo, 2003). Saccharomyces cerevisiae wild-type strains DBY746 and SP1 grown in SDC medium have a mean survival of 6 d (see Fig. 1 A; Longo et al., 1996, 1997). Survival in SDC medium provides a model for natural environments such as fruits that contain a high level of glucose (rotting figs), from which ancestors of the wild-type yeast strains used in our experiments were isolated (Mortimer and Johnston, 1986). Because the death of a yeast population is mediated in part by mitochondrial superoxide (Fabrizio et al., 2001, 2003) and is delayed by overexpression of superoxide dismutases (Sods) or the human antiapoptotic protein Bcl-2, we hypothesized that it may represent a form of programmed death (Longo et al., 1997). Apoptosis has been shown to occur in yeast after treatment with hydrogen peroxide or acetate (Madeo et al., 1997, 1999; Ludovico et al., 2001; Skulachev, 2002). Analogously to mammalian cells, a caspase-related protease regulates hydrogen peroxideinduced programmed cell death in yeast (Madeo et al., 2002). Although markers of apoptosis have been detected in yeast cells undergoing replicative or chronological senescence (Laun et al., 2001; Herker et al., 2004), the existence programmed or altruistic aging has not been demonstrated in any organism.
Here, we study several yeast strains isolated from grapes and three different laboratory wild-type strains under conditions that model natural environments and provide evidence for the role of superoxide in an altruistic aging and death program that kills over 90% of a yeast population to release nutrients that promote the growth of a small better-adapted mutant subpopulation.
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Results |
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Budding yeast isolated from grapes undergo age-dependent death and adaptive regrowth
To determine if "programmed aging" may be limited to laboratory yeast strains, we isolated yeast cells from organically grown California red grapes. We selected cells that grew within 48 h in YPD medium, generated colonies similar to those formed by S. cerevisiae, and divided by asymmetric budding (Fig. 2 A). The survival of populations generated from cells derived from three different wild colonies was similar to that of wild-type laboratory strains (Fig. 2 B). After 9099% of the "wild" population died (day 311), the number of viable cells in the culture increased, suggesting that adaptive regrowth is occurring. In contrast, incubation in water prevented age-dependent death and regrowth (Fig. 2 C). As observed in the laboratory wild-type strains, the pH of wild yeast grown in SDC medium decreases to approximately pH 3 by day 1. Adjustment of the extracellular pH from 3 to 6.5 prevented age-dependent death (Fig. 2 D). These data confirm our results with laboratory strains and suggest that programmed aging occurs in wild strains isolated from natural environments.
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In contrast to wild-type and sod1 mutants, long-lived yeast overexpressing antioxidant enzymes (SOD2ox, SOD1ox SOD2ox, and SOD1ox CTT1ox), lacking RAS2 (ras2
) or lacking SCH9 (sch9
), exhibited a major reduction of regrowth frequency (Fig. 3 A and Table I). Adaptive regrowth was not observed in any of the cultures overexpressing both SOD1 and catalase (SOD1ox CTT1ox; Fig. 3 A, and Table I, 13 cultures) and was reduced from a 48 to 31% frequency by the overexpression of SOD1 (19 cultures; Table I). Overexpression of SOD1 also caused a major adaptive regrowth disadvantage in another parental strain (SP1; Fig. 3 D and Table I).
Growth under starvation condition was not observed in any of the 29 independent cultures of the long-lived ras2 and sch9
(Table I). This effect of mutations in the RAS2 or SCH9 genes on stationary phase regrowth may be mediated, in part, by decreased superoxide and hydrogen peroxide levels. In fact, deletion mutations in RAS2 or SCH9 increase resistance to both superoxide and hydrogen peroxide (Fig. 1 E), decrease the level of superoxide, and extend longevity by inducing the expression of Sod2 and other stress resistance genes (Fabrizio et al., 2001, 2003).
In summary, regrowth was observed in 90% of the cultures of short-lived mutants deficient in SOD1, in 50% of wild-type cultures, but in <10% of long-lived yeast overexpressing antioxidant enzymes (Table I). The strong inverse correlation between mean life span and the ability to grow in stationary phase (r = 0.90; Fig. 3 E) is consistent with a role for superoxide and hydrogen peroxide in a death program that increases the chance of adapting to a nutrient-poor environment. These results are also consistent with the initiation of caspase-dependent apoptosis in yeast exposed to hydrogen peroxide (Madeo et al., 2002). However, a major increase in longevity may not be required to prevent adaptive growth. In fact, the overexpression of SOD1CTT1 or SOD1SOD2 prevents growth in stationary phase cultures but only causes a 1030% increase in life span.
Adaptive regrowth in media that model natural environments
To test whether or not the age-dependent adaptive regrowth may be an artifact of the laboratory medium, we monitored viability in yeast cultures aged in medium obtained by processing organic red grapes or in medium containing 10% of the ammonium sulfate compared with the standard SDC medium. This decrease in ammonium sulfate can serve to model the low levels of nitrogen, characteristic of certain natural environments (e.g., grapes). The S. cerevisiae DBY746 strain grown in grape extracts died at rates similar to those observed in SDC medium (Fig. 4 A). A leveling off in mortality and then adaptive regrowth was observed after day 15 (Fig. 4 A and not depicted). In contrast, adaptive regrowth in sod1 cultures maintained in "grape extracts" was observed much earlier (day 3; Fig. 4 A).
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Competition experiments in mixed cultures
To test further if cytosolic superoxide and hydrogen peroxide can provide an adaptive regrowth advantage, we mixed in the same flasks wild-type yeast with mutants either lacking SOD1 or overexpressing both SOD1 and CTT1. To distinguish between the wild-type and mutant populations, we monitored the presence of specific biosynthetic markers present on the SOD1 and CTT1 overexpression plasmids (Fabrizio et al., 2003), which do not affect either survival or adaptive regrowth (unpublished data). Although the SOD1CTT1 population initially survived better than wild-type yeast, after day 13 only wild-type organisms grew back by using nutrients released by dead cells (Fig. 5 A and not depicted). By day 21, the ratio between SOD1CTT1 overexpressors and wild-type yeast in the flasks was 1:10,000, confirming that overexpressors of Sod1 and catalase have an adaptive growth disadvantage compared with wild-type yeast. We also monitored the survival of mixed cultures of wild-type yeast and sod1 mutants. Because sod1
mutants die very rapidly (Longo et al., 1996), to avoid an early takeover of the culture by wild-type yeast, we used sod1
mutants that have acquired additional mutations that reverse the initial survival defects. These mutants were isolated during chronological survival and maintain viability comparable to that of wild-type yeast during the first 2 d in culture. The ratio between sod1
mutants and wild type was low during the initial 9 d, but the sod1
mutants slowly took over the culture and reached a 1,000:1 ratio by day 14 (Fig. 5 B). These results confirm that superoxide provides an adaptive regrowth advantage but a survival disadvantage. To determine whether or not the mutation that reverses survival defects in sod1
mutants (Fig. 5 B) causes an adaptive regrowth advantage, we tested if yeast lacking the PMR1 gene regrow early compared with wild type. We determined the mutation that reverses the survival defects of our sod1
mutant isolated after regrowth to be in the PMR1 gene after determining that the mutants (Fig. 5 B) grow in the absence of lysine and are sensitive to manganese (not depicted; Lapinskas et al., 1995). The two major mutations that reverse the lysine and methionine auxotrophies of sod1
mutants are in the BSD2 and PMR1 genes (Lapinskas et al., 1995). It is possible to distinguish between these mutations by testing for sensitivity to 5 mM MnCl2, which is only associated with the accumulation of cytosolic manganese caused by loss of Pmr1 activity. The pmr1
mutation did not cause an early adaptive regrowth, suggesting that increased superoxide levels and not "survival mutations" are responsible for the adaptive advantage of sod1
mutants in mixed sod1
/wildtype cultures (unpublished data).
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Mutation frequency in sod1 and long-lived mutants
To determine if genes that regulate aging and protection against superoxide/hydrogen peroxide toxicity may affect adaptive regrowth by also regulating mutation rates, we monitored the age-dependent frequency of mutations in the CAN1 gene (Huang et al., 2003). At day 3, the frequency of canR mutations was approximately fivefold higher in sod1 mutants compared with DBY746 wild-type controls (Fig. 7 A). These results are consistent with those published by Gralla and Valentine (1991) and Huang et al. (2003) for sod1
mutants. Notably, a genomewide screen of 4,870 yeast gene deletion mutants identify sod1
mutants as one of the top 25 mutator strains (Huang et al., 2003). In contrast, the age-dependent increase in canR mutation frequency was delayed by
24 d in SOD1CTT1 overexpressors and by
10 d in sch9
mutants compared with DBY746 controls (Fig. 7, B and C). These results are consistent with a role for the rate of spontaneous mutations in adaptive regrowth.
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Isolation of regrowth mutants
The death of Escherichia coli populations maintained in stationary phase is followed by growth of a better-adapted mutant subpopulation, which rapidly takes over the culture (Zambrano et al., 1993). To test if the yeast population undergoes programmed death to favor the growth of a mutant sub-population, we isolated regrown organisms and compared their survival and regrowth to that of wild type. In six studies with four independent clones (adr-1, adr-3, adr-4, and adr-5), we observed that organisms isolated after regrowth would adapt and grow back earlier than wild-type organisms during survival in stationary phase (Fig. 8, AC), suggesting that the subpopulations that regrow have acquired a mutation that improves adaptation to the new environment containing nutrients released by dead cells. To confirm the presence of a "regrowth mutation," we generated diploid cells by mating the adr-1 mutant with the wild-type DBY747 strain. The diploid strain maintained the ability to regrow early, suggesting that the regrowth mutation is dominant (Fig. 8 D). After sporulation of the adr-1/+, diploid tetrads were dissected and cultures from individual spores were generated and monitored for their survival/regrowth phenotype. 48 spores derived from 12 tetrads were analyzed. Although the adaptive regrowth phenotype is difficult to monitor, the survival pattern of the 48 cultures is consistent with the presence of a single regrowth mutation as suggested by a higher age-dependent viability in 50% of the cultures (unpublished data). Therefore, the altruistic behavior of the population favors organisms that are not genetically identical to the dying population, but that have evolved to adapt to the changing environment.
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Computational simulation of adaptation to changing environments in S. cerevisiae undergoing programmed or "stochastic" aging
We describe a computational model and simulation to compare the ability of yeast cells that undergo either programmed or stochastic aging and death to adapt to changing environments. We have coded and run two models for two situations: (1) We modeled the early death and higher mutation frequency of a population of 109 wild-type DBY746 cells (based on our experiments with 109 cells/flask; Fig. 9 A). (2) We modeled the longer life span and lower mutation frequency of sch9 mutants (Fig. 9 B). For the simulation of programmed aging in wild-type cells we assumed that the population follows survival Eq. 1:
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From this function we find that between days 0 and 5 each living yeast cell has one chance in 109 to have undergone a mutation, and between days 0 and 11 this chance has increased by 2.6-fold, and then it remains stable until death (Fig. 7).
We did not use the frequency of mutations in the CAN1 gene (2 x 106) based on the observation that 50% of the wild-type DBY746 cultures do not regrow (Table I). In fact, based on the simulations described in the following paragraphs, a frequency of adaptive mutations above 108 is expected to cause regrowth in nearly all cultures.
When a yeast cell dies, it releases its nutrients into the environment in the new form we call type B. Based on the leveling off of the viability of regrowth mutants (R) after regrowth at a sixth of the initial (day 1) maximum viability (unpublished data), we assumed that R requires the B nutrients released by six wild-type yeast after death to reproduce and generate a young R. Based on the slope of regrowth we calculated that the R population doubles every 13.5 h. For these simulations, we assumed that R no longer follows the programmed death pattern of DBY746 because it switches to a growth mode.
In 52% of 100 independent realizations of the computational model described in the previous paragraphs, we observed the growth pattern shown in Fig. 9 A. In the simulations where regrowth was observed, the first young R was generated at day 1 and the viability of the R population surpassed that of wild-type cells by day 12 (Fig. 9 A). These simulations are consistent with the experimental data (Table I and Figs. 25). When we doubled the mutation frequency at all time points (2 x 109), regrowth was observed in 82% of the simulations. When we decreased mutation frequency by fivefold (2 x 1010), regrowth was observed in only 18% of the population. Thus, the combination of high mutation frequency mortality and release of nutrients promotes adaptive regrowth.
For the simulation of stochastic aging, we used the mean life span and mortality pattern of the long-lived sch9 mutants. We used Eq. 1, where T (mean life span) is taken to be 20 d and
is 0.0205/G (based on G = 0.0045; Fig. 9 D). For age-dependent mutation frequencies in populations of sch9
mutants, we used Eq. 2 with µ = 105 and ß = 4.34. These parameters are based on the lower age-dependent CAN1 mutation frequency for sch9
mutants (Fig. 7). For these simulations, we assumed that when a cell dies it releases nutrients, which are divided and used equally by the surviving population. Furthermore, we assumed that R, which is now aging stochastically, will continue to follow the death rate described in Eq. 1 even after acquiring the regrowth mutation.
In contrast to the aforementioned simulation for wild-type DBY746 mutants, regrowth occurred in only 4 of 1,000 independent realizations of the computational model for long-lived strains (Fig. 9, B and C). In the long-lived cultures, R mutants appeared as early as day 10 but died before generating a young R (Fig. 9 B, bottom). In the 0.4% of the cultures where regrowth occurred, the growth of R mutants was observed late, in 25-d-old cultures (Fig. 9 C). Thus, the computational simulations suggest that programmed aging and the consequent early death, together with a relatively high mutation frequency, can result in a major advantage in adaptation to changing environments.
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Discussion |
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The computational simulation of survival and regrowth based on the experimental age-dependent mutation frequency and death rate of the wild-type and long-lived cells is consistent with our theory that early death and high mutation frequency have evolved to promote early adaptation (Fig. 9 A). The simulations with population size equivalent to that used experimentally (1 billion/flask), confirm that the early aging, death, and nutrient release in wild-type cultures (programmed aging) cause an increase in mutation frequency and the generation of R mutants by day 5, which regrow in 52 of 100 realizations. In contrast, the simulation based on the lower mutation frequency and longer life span of sch9 mutants (stochastic aging) indicates that yeast that age slowly and attempt to survive as long as possible have a major adaptive disadvantage, assuming that the nutrients released by the dying population are redistributed equally to the survivors. The latter simulation also shows that some adaptive regrowth mutants are generated, but are too old and die before they can acquire sufficient nutrients to reproduce (Fig. 9 B). Notably, we do not know whether sch9
mutants age stochastically or simply activate the "aging program" at a later point. In either scenario, our data and simulations suggest that, as first hypothesized by Wallace, natural selection favors such races that die after they have successors. Mutations that increase longevity and antioxidant protection or the overexpression of Sods and catalase negatively affect adaptive regrowth, raising the possibility that natural selection has prevented alleles that confer longevity extension from becoming fixed. In fact, mutations that cause inactivation of Ras2 or higher levels of Sod and catalase, which do not cause detectable growth defects, are predicted to be frequent and could easily become fixed if they did not negatively affect adaptation to changing environments.
The simulations indicate that minor changes in mutation frequency can cause major changes in the ability of a population to adapt and regrow. The association between mutation frequency and adaptive regrowth in wild-type, SOD1CTT1 overexpressors, sch9, and sod1
mutants is consistent with the outcome of these simulations (Fig. 9). However, increased mutation frequency is not sufficient to explain the early adaptive regrowth of sod1
. In fact, yap1
and skn7
mutants have high mutation rates but do not adapt early (Fig. 7 D), suggesting that an early release of nutrients is also required to maximize regrowth. The central role of Sods in the aging and death of yeast and the ability of Sod1 to cause major changes in adaptive regrowth suggests that superoxide and possibly hydrogen peroxide are important mediators of the Ras2- and Sch9-dependent aging/adaptive regrowth program (Longo, 1997; Fabrizio et al., 2001, 2003). Notably, superoxide is an important mediator of mammalian apoptosis (Hockenbery et al., 1993).
Although it is not known whether or not higher eukaryotes would benefit from an altruistic aging and death program, the role of similar genes and pathways in the regulation of longevity in organisms ranging from yeast to mice (Longo and Finch, 2003) raises the possibility that aging is also programmed in mammals.
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Materials and methods |
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Isolation of regrowth mutants and wild yeast
We considered a population "regrown" (adaptive regrowth) if the viability increased by at least 100% and remained at that level or higher for at least two data points. The "frequency of regrowth" refers to the number of cultures in which regrowth was observed compared with the total number of cultures studied for a particular strain.
To obtain regrowth mutants adr-1, adr-3, adr-4, and adr-5, a small aliquot of cells was isolated at day 34 from four different DBY746 cultures (during the regrowth phase) and frozen. A new study was started with the regrown populations and, at day 25 (during another regrowth phase), four single colonies were isolated and frozen. Isolation of the clones after two cycles of survival and regrowth should favor the selection of better-adapted mutants.
Wild yeast strains (13) were isolated by plating a few drops of unfiltered grape extract onto YPD plates. Several colonies grew after 23 d. Those that most resembled budding yeast colonies were frozen for further analysis. To observe the morphology and budding pattern of the wild strains, cells were fixed with 70% ethanol, stained with Calcofluor (25 µM in water), and observed by fluorescence microscopy.
Chronological survival and apoptotic markers detection
Chronological lifespan of cells incubated in both SDC medium and water was measured as described previously (Longo et al., 1996; Fabrizio et al., 2001). Viability was measured every 2 d starting at day 13.
Experiments in medium containing low nitrogen were performed by incubating yeast in an SDC medium containing 1/10 of the standard ammonium sulfate concentration. Chronological life span of yeast incubated in filtered extracts obtained from organically grown California red grapes was also measured.
For nuclear staining, yeast cells were fixed with 70% ethanol, washed with water, incubated in 50 ng/ml DAPI in water, and examined by fluorescence microscopy. Exposed phosphatidylserine was detected by reaction with a GFP-coupled annexin V (ApoAlert Annexin V Apoptosis Kit; CLONTECH Laboratories, Inc.) as described previously (Madeo et al., 1997). Yeast were simultaneously stained also with 0.5 mg/ml propidium iodide to identify damaged/dead cells.
The effect of cytosolic alkalinization on cell death was studied by increasing the extracellular pH from the normal pH at day 13 (3 4) to pH 6.5. The increase in extracellular pH causes intracellular alkalinization.
Fluorescence microscopy
For image acquisition, we used a fluorescence microscope (model DM IRB; Leica) equipped with a PL fluotar100x/1.30 objective, a high-resolution digital camera (SPOT RT slider), and SPOT RT software v3.4.
Stress resistance assays and Sod measurements
Heat-shock resistance was tested by spotting serial dilutions of cells removed from day 3 SDC postdiauxic phase cultures onto YPD plates and incubating at 55°C (heat-shocked) or at 30°C (control) for 90 min. Pictures were taken after 34 d of incubation at 30°C.
For oxidative stress resistance assays, day 3 postdiauxic cells were diluted to an OD600 of 0.1 in K-phosphate buffer, pH 7.4, and treated with 200250 µM of menadione for 60 min. Viability was measured by plating the cells onto YPD plates before and after treatment. Alternatively, serial dilutions of untreated and menadione-treated cells were spotted onto YPD plates and incubated at 30°C. Pictures were taken after 34 d.
Sod activity was measured according to the method of auto-oxidation of 6-hydroxydopamine (Heikkila and Felicitas, 1976). For separate measurements of mitochondrial Sod activity, 1 mM NaCN, which inhibits 95% of the cytoplasmic Sod, was added to the reaction mix.
Competition studies
For wild type/SOD1ox CTT1ox competition study, 100-µl aliquots of yeast cells of the two strains were removed from day 20 cultures and frozen. The frozen aliquots were later expanded by growing the cells in SDC medium for 3 d and mixed at a ratio of 1:1. The viability of the mixed culture was measured every 2 d by plating onto SDC plates. To distinguish between the wild type and the overexpressors, we monitored the ability of cells to grow in the absence of leucine and uracil or on SDC plates (the YEp352-SOD1 and YEp351-CTT1 overexpression plasmids contain, respectively, the URA3 and LEU2 genes). Control plasmids expressing uracil and leucine biosynthetic enzymes did not affect either survival or adaptive regrowth.
The wild type/sod1 competition study was performed analogously to the previous one except that, at day 20, postdiauxic sod1
population was mixed with a nonpreselected wild-type population. This was done to avoid the early takeover of the sod1
mutants, which die very rapidly, by the wild-type yeast. sod1
mutants isolated at day 20 survive similarly to the wild type.
Spontaneous mutation frequency
To measure spontaneous mutation frequency, overnight inoculations were diluted in 25 ml of liquid SDC medium and incubated at 30°C. Cell viability was measured during the exponential growth phase and every 2 d starting at day 3 by plating appropriate dilutions onto YPD plates. To identify the canavanine resistant mutants (canR) in the liquid culture, an appropriate number of cells was harvested by centrifugation, washed once with sterile water, and plated on selective medium (SD-ARG, 60 mg/l L-canavanine sulfate). Colonies were counted after 34 d.
Computational simulations for the growth of yeast
We have coded and run two similar models for two different situations described in this section.
Both of our models start with 109 original (O) yeast cells at day 0, each of which holds and retains one nutrient unit of type A for the duration of its lifetime. The simulation proceeds by advancing the time by steps of units of t = 1/16 of a day (the value of 1/16 d or 1.5 h represents the doubling rate of a wild-type yeast cell and was chosen because it is the fastest possible biological process we consider in this model). During each time step, each yeast cell may undergo death, a mutation, or may continue living as it is.
The cellular data
The computer simulation maintains a list of the living cells present in the population for both the original (O) and the mutant (R) population. This population list is structured and changes by forming, updating, and eventually removing sub-lists organized by generation. At time t our list has the following general form:
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Death
We assume that our yeast cells follow a survival equation f (t,T,t) given in Eq. 1. This equation allows us to derive and compute the expected number of cells of age t that will have died over the next time step. This is found by differentiating f (t,T,t) with respect to time and multiplying this by the time step t. From this, we deduce that if we start with N(t) alive wild-type cells at time t, then the expected number of deaths D(N(t)) during the following time step is
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Using Eq. 3 above, we compute the expected number of dying cells for each generation. If this number is larger than 30 then the number of cells removed is computed by generating a random integer variable with mean and variance of D(N(t)) taken from a negative exponential distribution. Otherwise, we use this expectation to compute the probability for each cell to die. Therefore, by generating 30 uniform random variables in the range of 0 and 1 and comparing these to the computed probability, we stochastically remove the cells.
Once an original (O) yeast cell dies, it releases its nutrients back to the environment in the new form we call type B. It requires the death of six original yeast cells to produce one unit of nutrient B. Likewise, the death of one mutant R releases the one unit of nutrient B it retained for its life span.
Mutation
Each of the original O yeast cells has a chance to mutate to cell form R during its life span. This mutation occurs with a time-dependent probability. We use a cumulative logistic probability function given in Eq. 2, with a mean of µ and scaling parameter ß to mimic the real mutation frequency observed experimentally. This function is only used up to and including the day for which the mutations were experimentally recorded. After this time, we impose there to be no more additional mutations. If n mutations take place for a cell belonging to the (i+1)th generation, we modify the related sub-list by subtracting n to numO(tti) and adding n to numR(tti).
Reproduction
The ability for reproduction is also determined by an age-dependent function. In both our models, the mutant yeast cell R requires to be fit and young enough in order to start reproducing. If the mutation occurs very late in life, the mutant is likely not to be fit enough to use its nutrients for reproduction. This fitness function is also determined via the function f (t,T,t) with the same parameters that determine its survival chance.
The conditions for a mutant cell to reproduce depends on the availability of nutrient of type B. Here, the two models described differ.
In the first model, which starts off with an original population of the programmed aging yeast type, once the mutant R is formed and absorbs one unit of nutrient B, it is from then on active to reproduce and every 13.5 h. This is because, in this model, our original yeast cell does not use any of the nutrients of type B.
In the second model, which starts off with an original population of long-lived yeast type, once the mutant R is formed it will need to wait until the average amount of released nutrients B per total number of present cells increases to one (or six deaths). In this model, we assume that both the original long-lived yeast cell and its mutant consume nutrients of type B. Thus, when six original O cells die producing one unit of nutrient B, this gets equally shared between all the cells in the population (regrowth mutants or original cells).
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Acknowledgments |
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This work was supported in part by an American Federation for Aging Research grant and by National Institutes of Health grant AG 20642 to V.D. Longo.
Submitted: 1 April 2004
Accepted: 5 August 2004
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