Selective benefits of damage partitioning in unicellular systems and its effects on aging

Results

Modeling Growth and Cell Division.

To simulate the proliferation of a simple entity consisting of 2 types of molecules (e.g., diffusible proteins), intact and damaged ones, we constructed a mathematical model based on ordinary differential equations (see Eqs. 1–6), describing the accumulation of the intact (P_int) and damaged (P_dam) proteins, such as oxidatively carbonylated proteins, during the cell cycle and successive cell generations. The sum (P) of intact (P_int) and damaged (P_dam) proteins determines the total size of the entity. The temporal dynamics of P_int are given by a production term (rate of protein synthesis; maximal rate k₁/k_s), that depends on the current amount of total protein in the cell, the rate of intact protein degradation (rate constant k₂), and the conversion of intact proteins to irreversibly damaged proteins (rate constant k₃) (ref. 1; see Materials and Methods). The constant k_s represents the protein concentration leading to half-maximal protein production rate. The dynamics of P_dam are ruled by the conversion of intact proteins to damaged proteins (k₃) and the rate of degradation of damaged proteins (rate constant k₄). Initially, the number of intact and damaged molecules increase until production and degradation is balanced (Fig. S1 A and B). It has been estimated that as much as one-third of every protein in some organisms may be damaged by carbonylation, a specific irreversible oxidative modification (17). Based on this information and taking other noxious modifications into consideration, we tested P_dam damaging rates generating up to 66% damage (of total protein). The half-life of proteins in unicellular systems has been shown to range from minutes to days depending on the specific protein analyzed, but most bulk proteins display half-lives markedly longer than a generation time (see ref. 18). Therefore, in the present study we simulated between 5% and 35% degradation of total proteins within 1 generation. Protein and RNA syntheses in S. pombe have been shown to increase exponentially during the cell cycle (19), whereas volume increase is biphasic linear (20). The model has therefore been tested for both types of growth, yielding comparable results (Fig. S1 A and B).

To trigger cell division in the growing entity, we introduced a critical value P_div that defines the number of intact proteins required for cytokinesis, including all checkpoints from initiation of cell division to completion of cytokinesis. We made the assumption that the critical cell size reflects the accumulation of key proteins and that these proteins are, on average, as susceptible to damage as bulk protein. The damaged proteins exhibit no intrinsic value of toxicity, but their accumulation increases the generation time by affecting the time it takes for the cell to reach the critical, functional, and undamaged size required for cytokinesis (P_div) (Eq. 1). When P_div has been reached, the system can divide in a symmetrical or asymmetrical fashion with respect to size and damaged proteins (Fig. 1 A and C and Fig. S2 A and C). A set of transition equations determines the size of the cells produced and how the proteins are distributed between progenitor and progeny during cytokinesis (see Materials and Methods).

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Fig. 1.

Damage segregation prevents clonal senescence of a symmetrically dividing system. (A and C) Schematic representation of a symmetrically dividing system, the sibling lineages analyzed, and the distribution of intact (blue) and damaged (red) proteins in a system without (A) and with (C) damage segregation. (B and D) Simulations of divisions, accumulation of intact (blue), damaged (red), and total (green) proteins during progressive cell cycles in the sibling lineages 1 and 2 at different rates of damage production (k₃). Simulations were performed without (B) and with (D) segregation of damage. The temporal dynamics of cytokinesis, damaged, intact, and total proteins at low (k₃ = 0.6; Top), moderate (k₃ = 1.2; Middle), and high damage (k₃ = 1.7; Bottom) production rates are shown. The retention coefficient used in D is 0.875.

Effects of Asymmetry on Clonal Senescence.

The model was initially simulated for low damage rates k₃ (see Materials and Methods), with an equal inheritance of damaged proteins (Fig. 1A). Under these conditions the system was characterized by constant initial and final concentrations of intact and damaged proteins during successive generations and the population was immortal (Fig. 1B). At moderate damage rates, cells still divided indefinitely but displayed longer generation times (Fig. 1B). At high damage rates, the cells went through a finite number of divisions characterized by progressively longer generation times and a pronounced accumulation of damaged proteins at the expense of intact ones, eventually preventing P_div from being attained (Fig. 1B). Because division, in this simulation, was perfectly symmetrical and all cells in the population were identical, the outcome was clonal senescence. That is, the model predicted that, at high damage rates, the entire population would eventually reach a “dead end,” reminiscent of the Hayflick limit (21).

We next asked whether an unequal distribution of damaged proteins during cytokinesis (Fig. 1C) among individuals affects the damage rate at which clonal senescence is reached. We therefore introduced the retention coefficient into the model (see Eqs. 7 and 8 in Materials and Methods); such that equal-sized siblings were distinguishable by the amount of damaged proteins they inherited. The system then showed signs of sibling-specific replicative senescence; the cells that retained more of the damage displayed progressively longer generation times, whereas the “low-damage” sibling lineage propagated indefinitely (Fig. 1D). In addition, damage segregation (Fig. 1D) allowed the population to propagate at damage rates, which caused clonal senescence of a perfectly symmetric system (Fig. 1B).

This analysis was followed by testing whether a difference only in size between a large progenitor and a smaller offspring (Fig. S2A) was sufficient to prevent clonal senescence. At low to moderate damage, the system showed signs of a sibling-specific replicative senescence, typical of asymmetrical dividing systems such as budding yeast. The larger parent lineage (mother cell) displayed increasingly longer generation times (Fig. S2B) until eventually the persistent titration of intact proteins by damaged proteins prevented it from dividing again. In contrast, at the same damage rate, the smaller progeny lineage continued to divide indefinitely (Fig. S2B). Also, a system of different-sized progeny can proliferate ad infinitum even without damage segregation at damage rates giving rise to clonal senescence in the perfectly symmetrical system (Fig. 1B and Fig. S2B). When damage was segregated such that the larger mother cells received an even higher load than expected from their size (Fig. S2C), the system could withstand even higher levels of damage before entering clonal senescence (Fig. S2D).

The model also suggested that, to prevent clonal senescence, the degree of damage segregation (or size asymmetry) needed to increase as the damage production rate was elevated (Fig. 2 A and B). The tradeoff for this beneficial effect of damage retention or size asymmetry on clonal senescence is sibling-specific aging at progressively lower damage rates (Fig. 2 A and B). Interestingly, even very low retention coefficients (re = 0.125; 1 sibling effectively retaining 58% of the overall P_dam) were sufficient to prevent a symmetrically dividing population from reaching a dead end at moderate damage rates (Fig. 2A).

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Fig. 2.

Damage segregation and size asymmetry causes sibling-specific aging but increases the robustness of the system. (A) Effect of damage segregation (y axis) on damage levels (k₃; x axis) triggering clonal senescence and replicative aging. Green bars indicate that both siblings produced during cytokinesis are immortal but exhibit longer generation times with increasing damage. Red bars indicate that the sibling retaining more damage at the time of cytokinesis undergoes replicative senescence; i.e., can only perform a finite number of new generations, whereas the other sibling is immortal. Empty bars indicate that the system has reached clonal senescence; i.e., a damage rate at which both siblings display a finite ability to produce new cells. (B) Effect of size asymmetry (y axis) on damage levels (k₃; x axis) triggering clonal senescence and replicative aging. Color-coding is as described in A.

Effects of Asymmetry on Population Fitness.

If we define fitness as the number of entities produced in total per time unit, the population fitness of the different systems can be calculated at different damage production rates. When doing so for a system that divided symmetrically size-wise, damage segregation surprisingly improved population fitness at all damage rates analyzed (Fig. 3A). Different models by Ackerman et al. (22) and Watve et al. 23) describing the effects of differentiation between an aging parent and rejuvenated offspring in a population of unicellular organisms also suggested benefits of damage segregation at least at one fixed level of damage.

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Fig. 3.

Effects of asymmetries on population fitness upon increasing rates of damage production. Fitness, defined by the population size produced within one time unit (y axis), is plotted as a function of increasing damage rate (k₃; x axis). The different retention coefficients modeled are color-coded and shown in the graph. (A) Fitness of symmetrically dividing systems (by size) displaying different degrees of damage segregation as indicated. (B) Fitness of an asymmetrically dividing system (by size) displaying no retention (green) and retention (red). (C) Fitness of a symmetrically dividing system without damage retention (black) compared with an asymmetrically dividing system without damage retention (green). (D) Fitness of a symmetrically dividing system with damage retention (blue) and an asymmetrically dividing system with the same degree of damage retention (red).

In a system with different-sized progeny, damage partitioning (based on the model and assumptions made) is only beneficial at high damage propagation rates (Fig. 3B). On the other hand, a population dividing asymmetrically will present a substantial fitness advantage over one dividing symmetrically at all damage rates (Fig. 3C). However, if damage is segregated, an asymmetrical system is favored at low damage but looses out at high damage (Fig. 3D) due to the fact that larger parent cells will reach the size for division (P_div) much faster than their symmetrically dividing counterparts (Fig. 1 and Fig. S2). The fact that the smaller progeny have a longer generation time does not outweigh the parents' rate as long as the proportion of intact constituents is sufficiently high. However, as the damage rate increases, the progenitor lineage slows down, making the fitness largely dependent on the smaller offspring. At this point, the beneficial effect of retention allows a symmetrically dividing population with retention to be equally well off, or overtake, an asymmetrically propagating population (Fig. 3D).

Damage Segregation in a System Dividing by Binary Fission.

Our simulations suggest that a system dividing symmetrically by size displays an increased fitness at all damage propagation rates when partitioning its damage during cytokinesis. This suggestion raises the possibility that segregation is more common than previously anticipated, which prompted us to analyze the in situ distribution of carbonylated proteins in the fission yeast, S. pombe. Although the volume of the 2 siblings is equal, previous landmarks of division (birth scars) will remain confined to one-half of the growing cell and be inherited by one “sib” only (20) (Fig. 4A). When we followed birth scars and protein carbonyls during the cell cycle in synchronized cells, we found that carbonylated proteins were inherited asymmetrically between the 2 siblings such that the one with the previous birth scar was always left with more damage (Fig. 4B). After completion of cytokinesis, the newborn cells displayed most of their damage at the new end (Fig. 4 B and C).

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Fig. 4.

Damaged proteins are segregated during binary fission of S. pombe in a Sir2p- and Tea1p-dependent way. (A) Localization of septum and birth scar(s), visualized with calcofluor white, in cells of S. pombe during progression through the cell cycle. Arrows indicate the birth scar. (B) Distribution of carbonylated proteins during the cell cycle. In situ preparation and detection of carbonyls was carried out as described in Material and Methods and the cells placed such that the pole displaying the birth scar was on top. The cells were synchronized by centrifugal elutriation, resuspended in YES media and subsequently allowed to grow at 30 °C. After synchronization, ≈30–40 cells were analyzed at each state in the cell cycle. Carbonyls were detected and quantified in situ as described in Material and Methods. Blue and purple denote the highest concentration of carbonyls followed by red and yellow. (C) Quantification of carbonyls from pole to pole in newborn wild-type cells (Upper) and cells immediately before cell division (Lower). The spatial intensity of the carbonyl signal was obtained by drawing a line along the longitudinal axis of the cells and deriving the corresponding intensity plot profile. Approximately 30–40 cells were analyzed at each state in the cell cycle. (Lower) The red arrow points to the site of the septum. (D) Quantification of carbonyls from pole to pole in newborn tea1Δ cells (Upper) and cells immediately before cell division (Lower). (E) Quantification of carbonyls from pole to pole in newborn wild-type (Upper) and cells immediately before cell division (Lower) transiently treated with Lantranculin-A as described in Materials and Methods. (F) Quantification of carbonyls from pole to pole in newborn wild-type (Upper) and cells immediately before cell division (Lower) transiently treated with Benomyl as described in Materials and Methods. (G and H) Quantification of carbonyls from pole to pole during the cell cycle of wild-type (G) and sir2Δ (H) cells. Representative micrographs of cells at the different stages of the cell cycle are depicted next to the quantification graphs. The red arrow points to the site of the septum.

Growth of S. pombe will first take place at the old end and subsequently also at the new end (damage-enriched). The latter growth period is called New End Take Off (NETO) (20, 24). NETO is characterized by the reorganization of the actin cytoskeleton and a redistribution of actin patches from the ends toward the equatorial plane of the cell (24), similar to the redistribution of damage shown here. We found that Tea1p, a protein required for establishing cell polarity (25, 26) and the redistribution of actin patches during NETO, is necessary also for the polar localization of damage and the redistribution of damage toward the equatorial plane before cytokinesis (Fig. 4D). In addition, as with budding yeast, the mechanism responsible for the asymmetric segregation of damaged proteins in S. pombe is cytoskeleton-, actin-, and microtubule-dependent (Fig. 4 E and F). Intriguingly, deleting SIR2, which has been shown to be a requirement for establishing damage asymmetry in budding yeast (10, 12, 13), resulted in the same loss of spatial control and retention of carbonylated proteins as treatment with cytoskeleton depolymerizing drugs (Fig. 4 G and H).

Because our model predicted that symmetrically dividing cells without protein damage retention would display a reduced fitness and run into clonal senescence at lower damage rates than cells partitioning their damage, we monitored growth of wild-type and sir2Δ mutant cells at different concentrations of hydrogen peroxide. Interestingly, whereas wild-type and sir2 mutant populations display the same fitness (growth rate) when cultured without stressors, hydrogen peroxide caused a much more pronounced fitness reduction in sir2 mutants than wild-type cells (Fig. S3). However, we cannot presently assign the fitness reduction and stress sensitivity of sir2 mutant cells to their inability to segregate damage because a number of other functions, including silencing at different loci, are severely affected in the mutant.

We next followed the replicative potential of both S. pombe sibling lineages, arising from a common parent cell, which had already completed 9 divisions and therefore accumulated damaged proteins (see Fig. 5A and Materials and Methods). We found that the sibling enriched for protein damage (“old” sib) displayed a shorter mean life span (12.5 generations) than the “young” sib (15.9 generations; see Fig. 5B), Moreover, the generation time of the damage-enriched cell was markedly longer; 4.5 h compared with 2.5 h for the new sib (Fig. 5C). This result points to a “sibling-specific” aging in S. pombe that correlates with the unequal inheritance of damaged proteins.

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Fig. 5.

S. pombe display sibling-lineage specific aging. (A) Schematic representation of the criteria used in discriminating between “old” (Sib-1) and “new” (Sib-2) siblings, derived from a common 9-generations-old progenitor (starting cell). Vertical bars indicate birth scars, present as bulges on the cell surface, and here represented chronologically by different colors. Upon division, the cell with more birth scars (i.e., more divisions) and rounder appearance was selected as the older sibling. These cells coincide with those inheriting more carbonylated proteins, as detected by immunofluorescence microscopy and here depicted by orange dots. The arrow denotes the generation time (g) as analyzed for the 2 siblings and presented in C. (B) Replicative life span of the old sibling (Sibling-1; filled squares; n = 75), and new sibling (Sibling-2; open squares; n = 75) derived from a common 9-generations-old progenitor cell. (C) Generation times for old (Sib-1) and new (Sib-2) siblings.