Damage Repair Versus Aging in Biofilms

The extent of senescence due to damage accumulation (or aging) is evidently evolvable as it varies hugely between species and is not universal, suggesting that its fitness advantages depend on life history and environment. In contrast, repair of damage is present in all organisms studied. Repair and segregation of damage have not always been considered as alternatives, despite the fundamental trade-off between investing resources into repair or growth. For unicellular organisms, unrepaired damage could be divided asymmetrically between daughter cells, leading to aging of one and rejuvenation of the other. Repair of unicells has been shown to be advantageous in well-mixed environments such as chemostats. However, most microorganisms live in spatially structured systems such as biofilms with gradients of environmental conditions and cellular physiology as well as clonal population structure. We asked whether this clonal structure might favor aging by damage segregation as this can be seen as a division of labor strategy, akin to the germline soma division in multicellular organisms. We used an individual-based model with a newly developed adaptive repair strategy where cells respond to their current intracellular damage levels by investing into repair machinery accordingly. We found that the new adaptive repair strategy was advantageous whenever efficient and optimal, both in biofilms and chemostats. Thus, biofilms do not favor a germline soma-like division of labor between daughter cells in terms of damage segregation. We suggest that damage segregation is only beneficial when active and effective, extrinsic mortality is high and a degree of multicellularity is present. IMPORTANCE Damage is an inevitable consequence of life, leading to a trade-off between allocating resources into damage repair or into growth whilst allowing aging, i.e., segregation of damage upon cell division. Few studies considered repair as an alternative to aging. Moreover, all previous studies merely considered well-mixed environments, although the vast majority of unicellular organisms live in spatially structured environments, exemplified by biofilms, and fitness advantages in well-mixed systems often turn into disadvantages in spatially structured systems. We compared the fitness consequences of aging versus damage repair in biofilms with an individual-based model implementing an adaptive repair mechanism based on sensing damage. We found that aging is not beneficial. Instead, it is useful as a stress response to deal with damage that failed to be repaired when (i) clearly asymmetric cell division is feasible; (ii) extrinsic mortality is high; and (iii) a degree of multicellularity is present.

or the decision to submit the work for publication. 36 gradients of environmental conditions and cellular physiology as well as clonal population 48 structure. We asked whether this clonal structure might favor aging by damage segregation 49 as this can be seen as a division of labor strategy, akin to the germline soma division in 50 multicellular organisms. We used an individual-based model with a newly developed adaptive 51 repair strategy where cells respond to their current intracellular damage levels by investing 52 into repair machinery accordingly. We found that the new adaptive repair strategy was 53 advantageous whenever efficient and optimal, both in biofilms and chemostats. Thus, biofilms 54 do not favor a germline soma-like division of labor between daughter cells in terms of damage 55 segregation. We suggest that damage segregation is only beneficial when active and effective, 56 extrinsic mortality is high and a degree of multicellularity is present. 57 Senescence is all around us, yet it is not obvious why it has evolved in many taxa as it would 74 appear to be detrimental to the fitness of individuals. Importantly, the extent of senescence, 75 manifesting in decreasing fecundity and/or increasing mortality with age, is clearly evolvable 76 as it varies hugely between species and is not universal. For example, several taxa of simple 77 multicellular organisms can fully regenerate and for several taxa of complex multicellular 78 organisms, fecundity does not simply decrease with age and/or mortality does not simply 79 increase with age (1-3). An evolutionary explanation for the various extents of senescence 80 present in different organisms is challenging, particularly for unicellular organisms that divide 81 apparently symmetrically, such as most prokaryotes and some eukaryotic unicells, in contrast 82 to multicellular animals with a clear division of labor between germline and soma (4, 5). 83 However, the first single-cell study of division asymmetry in Escherichia coli highlighted that 84 morphological symmetry does not exclude functional asymmetry as daughter cells inheriting 85 the old cell pole were shown to grow a little slower than the mother cell while the new cell 86 pole daughters grew a little faster (6). Ironically, Caulobacter crescentus, the bacterium first 87 studied in terms of aging (7), as it has substantial morphological and functional asymmetry in 88 cell division, has been shown in more recent high-throughput microfluidic studies to maintain 89 a constant growth rate over cell divisions under benign conditions (8) and to divide protein 90 aggregates symmetrically between mother and daughter cells (9). 91 92 Following the first single-cell studies that suggested the existence of aging in unicellular 93 prokaryotes (7, 10, 11) and unicellular eukaryotes (12), there has been a gold rush of studies 94 eager to demonstrate aging in further unicells, such as bacteria (13-15) and eukaryotic algae 95 (16)(17)(18)(19). However, the loss of fecundity (10) or increase of mortality (20) with age, demonstrated in some of these unicells, are rather small effects compared with the resource 97 limitations of growth and high external mortality in most environments. The effects are also 98 much smaller than in the budding yeast, which has long been known to have a limited 99 replicative lifespan (21), supported by several recent high-throughput single-cell studies (22-100 28). However, it may be misleading to regard the budding yeast as a unicellular organism as 101 wild relatives are capable of dimorphic growth (29) and domesticated strains rapidly evolve 102 multicellularity (30, 31). Crucially, a number of recent experimental results have led to a 103 reinterpretation of aging, primarily in the sense of segregating protein aggregates, as a stress 104 response rather than an evolved characteristic of growth under benign conditions (9, 20, 32-105 38). 106

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In concert with the gold rush for experimental evidence for aging, there has also been one of 108 mathematical modelling studies eager to find evolutionary advantages of aging. Some of these 109 models did not consider extrinsic mortality (39-41), although it favors rapid and early 110 reproduction and thus tilts the evolutionary trade-off towards investment of resources into 111 growth and reproduction, rather than maintenance and repair (1, 42). Some also did not 112 consider repair as an alternative (40,41,43,44) or did not consider the cost of repair (39). 113

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Repair is present in all organisms studied and evidence for the evolution of mechanisms that 115 repair damage, such as misfolded and aggregated proteins (9), is beyond doubt. Of the few 116 models that consider both extrinsic mortality and costly repair, the model of Ackermann et al. 117 (2007) (45) was the first. It found that asymmetric damage segregation outperformed repair. 118 In contrast, our previous study, Clegg et  None of these studies considered the fitness effects of aging and repair in spatially structured 136 environments such as biofilms, although biofilms are prevalent in nature and important for 137 ecosystem function. For humans, they have many advantages in biotechnology but also cause 138 big problems in industry and health. Biofilms are heterogeneous in both time and space (49) 139 and cells that are growing within them are therefore exposed to varying, and often limiting, 140 nutrient regimes (50). This leads to gradients in growth rate and the presence of an active 141 layer in biofilms, where active growth only occurs close to the boundary of the biofilm, due to 142 slow nutrient diffusion (51). Growth within biofilms has also been shown to confer tolerance 143 to damage-inducing agents, such as antibiotics (49, 52-54) and UV radiation (55, 56), and it is 144 therefore likely that these gradients of growth rate and stress could make the evolutionary 145 benefits of aging and repair different from spatially uniform environments, such as 146 chemostats. Moreover, biofilms have a clonal population structure unless the cells remain 147 motile (57-59). This can have strong effects on the evolution of division of labor (60). Damage 148 segregation can be seen as a division of labor akin to the germline soma differentiation in 149 multicellular animals (61). Thus, we hypothesized that biofilms might favor damage 150 segregation over repair. 151

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To test this hypothesis, we developed a new individual-based model with adaptive repair, 153 whereby cells were able to sense and respond to their current intracellular damage levels. 154 This enables an appropriate response to gradients of stress and damage in biofilms. We found 155 that adaptive repair rather than damage segregation or a fixed rate of repair was the optimal 156 strategy for unicells growing in a biofilm, but only when the rate of damage accumulation was 157 proportional to the cells' specific growth rate. 158

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Characteristics of adaptive repair. We developed a new repair strategy where allocation of 160 newly synthesized protein into repair machinery, denoted by " , rather than growth 161 machinery, depends on the current level of damage in the cell and compared this with 162 previous strategies (Fig. 1). The idea was that the cell can sense and appropriately respond to 163 its damage level. This adaptive repair is more appropriate than a fixed repair strategy when 164 rates of growth and damage accumulation vary in time or space, e.g. in fluctuating or spatially 165 structured environments, such as biofilms. Adaptive repair is therefore meant to replace the 166 previous strategy of a fixed allocation into repair machinery at an optimal level, , which is 167 appropriate for constant or chemostat environments, where growth and damage 168 accumulation rates are in a steady state, like in our previous study, Clegg et al. (2014) (46). 169 There, we estimated the optimal, fixed investment into repair (here simply referred to as fixed 170 repair) by examining the mean specific growth rates of cells with different investments into 171 repair and found that for a damage accumulation rate of 0.1 h -1 , an investment into repair of 172 = 0.07 was optimal for both asymmetric and symmetric strategies (for the case where 173 damage is toxic, that we focus on here). The purpose of this section is to examine the 174 consequences of the new adaptive repair strategy and to test whether it is equivalent to the 175 previous optimal repair strategy in steady state environments. 176 FIG 1 General schematic of division and repair strategies used in this study, giving rise to 6 combinations: (i) symmetric division with no repair (NR) (ii) symmetric division with fixed repair (FR); (iii) symmetric division with adaptive repair (AR); (iv) asymmetric division (damage segregation) without repair (DS); (v) asymmetric division with fixed repair (DSFR); and (vi) asymmetric division with adaptive repair (DSAR). 178

Consequences of adaptive repair on the fraction of repair protein in single cells. The adaptive 179
repair strategy leads to an allocation into repair that responds to current levels of damage and 180 therefore lags behind the ideal level of repair machinery, unless damage levels reach a steady 181 state due to symmetric division (Fig. S1). Since asymmetric division causes sudden changes in 182 damage levels, the current investment into repair tracks the changing damage levels ( Fig. 2A). 183 Damage levels then change as a result of repair, which in turn changes allocation into repair. 184 As a result, the level of repair machinery never reaches ideal levels in asymmetrically dividing 185 cells, in contrast to symmetrically dividing cells ( Fig. 2A and S1). To approach ideal levels of 186 repair machinery more quickly, a high turnover of repair protein would be required. Since 187 cellular proteins that are not involved in regulation have a long half-life of more than one 188 generation (62), it seems more realistic to assume that repair protein does not turn over; 189 turnover would also be costly and unnecessary. Investment into repair varies greatly over the 190 cell cycle for cells with asymmetric segregation of damage but is always at approximately the 191 same level immediately before division. The investment into repair immediately before 192 division is approximately the same as the fixed optimal investment into repair. Investment into repair ( " on the y axis) for the new adaptive repair strategy following the old pole cell over many divisions. In asymmetric divisions, the old pole cell inherits all damage, leading to a jump in allocation into repair following division and then decreasing steadily until the next division. In symmetric divisions, damage, and therefore investment into repair, reaches a steady state. (B) Specific growth rate of a single cell over consecutive cell divisions. Numbers in the panel label generations and each generation is shown with a new line (for asymmetric strategies). The specific growth rate of an asymmetrically dividing cell with no repair (red, = 0) drops quickly to zero. For a cell with fixed optimal repair (magenta, = 0.07), it decreases more slowly over time but also reaches zero. For a cell with adaptive repair (yellow, " variable), it decreases only initially towards a see saw pattern, as in (A). Specific growth rates do not change at division for symmetric strategies (blue, cyan, and green) and there is no difference between daughter cells. Symmetric strategies show an initial decrease in specific growth rate before reaching a steady state, with similar values for fixed and adaptive repair and lower without repair. (C) Distribution of specific growth rates in populations at steady state (snapshot taken at 100 days) for asymmetrically dividing cells. Specific growth rates of cells with adaptive repair are between those with fixed repair and those without repair. The medians and inter-quartile ranges for adaptive and fixed repair are close and higher than for symmetrically dividing cells. Data are reproduced with permission from Fig. 4A,B in (46), with the new adaptive repair strategy added. Specific growth rate was 0.6 h -1 and aging rate was 0.22 and dependent upon specific growth rate for all strategies. Replicate simulations are similar, see Fig. S2. repair, specific growth rate declined rapidly towards zero. With fixed repair, specific growth 199 rates likewise declined towards zero, albeit more slowly. For symmetric strategies, specific 200 growth rates were similar for all strategies while damage levels were low. Later, cells with 201 repair maintained substantially higher specific growth rates than cells without repair (Fig. 2B).  (old ages) of other strategies. For symmetric strategies, adaptive repairers were marginally 208 older than fixed repairers, but much younger than cells without repair. Growth rates in 209 populations of asymmetrically dividing cells had a multimodal distribution with marked 210 differences between generations (Fig. 2C). There were fewer cells with very high and very low 211 specific growth rates in populations using either fixed or adaptive repair. The growth rate 212 distribution of the new adaptive repair strategy was in between the fixed and no repair 213 strategies. The medians for each population confirm that the population specific growth rates 214 were highest for cells using the fixed repair strategy, though the adaptive repair strategy was 215 only slightly lower and showed less variation between cells (Fig. 2C). Symmetrically dividing 216 cells all had the same specific growth rate as the single cells in Fig. 2B with the fixed repairers 217 having a slight specific growth rate advantage again. In summary, the new adaptive repair 218 strategy led to growth rates that were very similar to fixed repair at the population level, but 219 on the individual level, there were fewer old cells. 220 221

Competitions of aging strategies in constant and chemostat environments. Competitions are 222
unambiguous and unbiased ways to measure fitness holistically. In the constant environment, 223 cells were removed at random, which modelled extrinsic mortality, and the strategy that was 224 left at the end had won. In the chemostat environment, cells were likewise removed 225 randomly, but they also competed for the substrate that entered the environment with a 226 given rate. This means that lineages that produced fewer offspring per time at the current 227 concentration of substrate were washed out. In other words, cells with the highest specific 228 growth rate (as dependent on substrate concentration) will emerge as the winner (on average, 229 as removal is stochastic). The damage segregation without repair strategy (DS) quickly lost 230 against either repair strategies (FR and AR) in both environments (Fig. 3). The winner took 231 much longer to emerge between the two repair strategies and there were large fluctuations 232 in the biomass ratios over the course of the simulations. In the constant environment, fixed 233 repairers (FR) had an advantage, whereas in the chemostat, the adaptive repairers (AR) won 234 in the end. Hence, the new adaptive repair strategy was slightly fitter than the fixed repair 235 strategy in those natural environments that are better approximated by chemostats than 236 constant environments, such as systems that are mixed on a reasonably short time scale and 237 that receive resource inputs and experience removal of biomass by various means. However, 238 more environments are spatially structured and are therefore better modelled by biofilms, so 239 we turn to these in the next section. for all). The two repair strategies were closer in fitness, as seen in Fig. 2B, and it took more than an order of magnitude longer before the final outcome was clear. FR was slightly fitter than AR in the constant environment (C; n=10; proportion test, p=0.00195), as expected from Fig. 2B, but not in the chemostat environment (F; n=10; proportion test, p=0.00195). Maximum specific growth rate was 0.6 h -1 , and aging rate was 0.22 h -1 and dependent upon specific growth rate for all strategies. 242 Generating realistic biofilm structures in the absence of damage accumulation. We first 243 identified which parameter set would give rise to typical, rough biofilm structures with 'finger' 244 formation (63-65), rather than flat biofilms, so that we could then study aging in biofilms using 245 realistic biofilm structures ( Fig. S4 and File S1). These simulations were without aging or repair. 246 The substrate concentration in the bulk liquid was varied in order to change the dimensionless 247 group ( that quantifies the extent to which biofilm growth is intrinsically limited (growth-248 limited regime, high ( ) or limited extrinsically by diffusional mass transport into the biofilm 249 Repair of damaged material is assumed to require resources, e.g., energy and some new 259 material to replace the damaged parts of the old material. These resources are assumed to be 260 supplied by endogenous metabolism of cellular material rather than the substrate, as the 261 latter is not always available. As a result, converting damaged material into undamaged, active 262 material comes at a loss of biomass (we assume a loss of 20% for reasons given in Clegg et al. 263 (2014) (46)). This loss leads to shrinking of cells (since the density of cells is assumed to be 264 constant), unless cells grow sufficiently fast to compensate, which is not the case in the lower 265 layers of a biofilm. Shrinking does not affect fitness in constant and chemostat environments 266 as only the numbers of organisms matters, but the shrinking of cells of the adaptive repair 267 strategy had profound effects on biofilm structure and reduced the fitness of this strategy in 268 biofilms (Fig. 4). In these competitions, the winner depended upon the initial cell density. 269 When the initial cell density was low, it appears that the winner depends more upon the initial, 270 random placement; cells of any strategy that happen to be placed furthest away from the 271 other strategies tend to win. When the initial cell density is higher, the winner is more 272 dependent upon the fitness of that strategy. Because cells of the adaptive repair strategy 273 shrink so much more than the other strategies, this effect is much greater for them. 274

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FIG 4 Damage segregation (DS, cold colors) versus adaptive repair (AR, warm colors) strategies in biofilms. Adaptive repairers are strongly affected by shrinking (top row) as they are much fitter when assumed not to shrink, i.e., when the material lost due to repair is replaced with inert and massless material of the same volume ('styrofoam', bottom row). Initial cell density increases from left to right (4, 8, 16 or 32 cells). Biofilm structures shown have all reached a height of 154 µm. Cells are colored by age with different color gradients for each species. Maximum specific growth rate was 1.2 h -1 and damage accumulation rate was 0.1 h -1 (not proportional to specific growth rate) for all. Results of replicate simulations, simulations which competed DS and AR against the fixed optimal repair strategy (FR) and controls are shown in File S1. See Fig. S5 for time courses of log biomass ratios. For simulations without styrofoam, DS tended to be fitter than AR at initial densities of 4 and 8 cells, but AR was fitter at the higher initial densities of 16 and 32 cells (top row). For competitions between DS and FR, FR was fitter at densities of 8, 16 or 32 cells (File S1 and Fig. S5). In the simulations with 'styrofoam', AR and FR were always fitter than DS (bottom row; File S1 and Fig. S5). For competitions between AR and FR, FR was fitter in simulations without 'styrofoam', while AR was fitter in simulations with 'styrofoam'. Control simulations that competed two cells of the same strategy always led to no clear winner. 276 How much of the disadvantage of adaptive repairers was due to shrinking can be seen by 277 comparing simulations with shrinking cells to identical simulations where, for the sake of 278 comparison, the lost material is assumed to continue to take up volume (i.e., the lost material 279 has no mass but keeps its original volume, dubbed 'styrofoam'). In the simulations without 280 styrofoam, AR was only fitter than DS at initial densities of above 8 cells, FR was fitter than DS 281 at initial densities above 4 cells and FR was fitter than AR in all simulations. In the simulations 282 with styrofoam the results were much clearer; AR and FR are fitter than damage segregating 283 cells and AR was fitter than FR, regardless of the cell density at the beginning of the simulation 284 The results caused by shrinking were thought to be unrealistic. Cells have not been observed 287 to shrink considerably, unless they have been starved for long periods of time, and biofilm 288 structures such as in Fig. 4 with a vanishing base due to endogenous metabolism have not, to 289 our knowledge, been observed, and would be mechanically unstable in the presence of shear 290 (66). Shrinking must therefore be either very limited in real cells, or the assumption that non-291 growing cells accumulate damage at the same rate as rapidly growing cells must be wrong 292 (which would only cause the non-growing cells to shrink as the growing cells can make up the 293 lost volume). We decided to avoid this unrealistic shrinking by assuming that cells that do not 294 grow also do not accumulate damage. The damage accumulation rate was therefore assumed 295 to be proportional to cellular specific growth rate (and was matched to the previous damage 296 accumulation rate; Fig. S6), to allow for the very low rates of growth of cells below the active 297 layer of the biofilm (the active layer is shown in Fig. 5). This means that shrinking is not 298 abolished, but that slowly growing cells will accumulate damage and shrink at a lower rate as 299 repair, leading to shrinking, is less necessary. See Materials and Methods for further 300 explanation of this proportional damage accumulation rate. We therefore continued with a 301 damage accumulation rate of 0.22 that is dependent upon specific growth rate and also 302 applied this to the earlier constant and chemostat environments. 303 304 AR performed better than FR in the biofilms with styrofoam (Fig. 4), and we therefore focus 305 on the two main alternative strategies, AR and DS, in the following section. 306 307 Biofilm simulations where the damage accumulation rate is proportional to specific growth 308 rate. When the damage accumulation rate was proportional to the specific growth rate, AR 309 was more competitive than DS (Figs. 5 and 6; Fig. S7 also shows the controls). The higher the 310 initial cell density, the stronger the advantage of AR and the earlier that they won. At the 311 highest initial cell density (32 cells), AR won in all 50 replicate simulations (p=0.00). At the 312 lowest cell density (4 cells), they won in the majority of the simulations (31 vs 19) but this 313 difference was not statistically significant (p=0.119). The advantage of adaptive repair became 314 statistically significant at initial cell densities of eight or higher (Table S1).  Table S1 and biofilm structures are plotted in Fig. 5 and File S1. Control time courses are shown in Fig. S7. Maximum specific growth rate was 1.2 h -1 and damage accumulation rate was set at 0.22 h -1 and dependent upon specific growth rate for all strategies. 318 We decided to use the log biomass ratios as the best measure of fitness after comparing the 319 performance of a range of different metrics when both strategies were identical (controls in 320 Table S1 and Fig. S7). The ideal fitness measure should not be time-dependent, such that 321 running simulations longer would not change outcomes. As the trends of the log biomass 322 ratios in Figs. 6 and S7 show, using biomass at the end of the simulations (approximately 250 323 h) was appropriate since outcomes would not have changed had the simulations continued. 324 Moreover, the fitness metric with its significance testing should never result in a statistically 325 significant result when the two competitors were identical, as was the case with final growth 326 rate (Table S1). Final growth rate was therefore not a suitable measure. Both biomass and 327 population size could be used; they are strongly coupled, but the biomass changes are 328 smoother than the cell numbers, hence, biomass was chosen as the fitness measure. 329

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The biofilms formed from these equal mixtures of DS and AR, initially placed randomly on the 331 substratum surface, show the spatial distribution of the strategies and the age and activity of 332 the cells (Fig. 5 and S7). First, it can be seen that there was limited mixing of cells where 333 neighboring 'fingers' touch (lines of different color standing out), consistent with our previous 334 work (67, 68). This is due to the assumption that cells embedded in the biofilm matrix are not 335 motile. Second, if finger-like cell clusters were similarly separated from other clusters, both 336 strategies reached a similar height, suggesting that shrinking was negligible ( Fig. 5; 4 cell initial 337 density). This was despite repair leading to loss of material and cellular volume as growth 338 could compensate for any losses when the rate of damage accumulation was proportional to 339 growth rate. Third, the effect of increasing the initial cell density can also be seen. When there 340 were only a few cells randomly placed on the substratum surface, it was likely that one cell 341 happened to be further away from competing cells than any of the other cells. This lineage 342 could therefore grow without much competition and became the highest finger producing the 343 highest biomass, regardless of which strategy it followed. Hence, results at low cell density were more dependent on the random initial cell positions determining the distance to 345 competitors than on competitiveness. The higher the initial density, the less influenced the 346 results were by the stochastic initial attachment of cells on the surface. In these cases, AR had 347 the advantage. Finally, comparing the distribution of young vs old cells with the distribution 348 of active vs inactive cells (Fig. 5) shows that AR were all young throughout the biofilm, while Here, we investigated two alternative strategies for unicells to deal with intracellular damage: 358 segregation or repair. Due to a trade-off between investing cellular resources into repair 359 machinery versus growth machinery that is fundamental to all living organisms, repair is costly 360 and therefore not obviously beneficial. This study is the first to compete these strategies in 361 biofilms, representing spatially structured environments. We began by developing a new 362 model for adaptive repair of cellular damage, whereby cells are able to sense and respond to 363 current damage levels by investing into repair machinery accordingly, enabling cells to deal 364 with spatial and temporal changes of conditions in biofilms. We found that in almost all 365 conditions tested, adaptive repair was fitter than the asymmetric segregation of damage at 366 division (Figs. 3 and 6). We also compared adaptive repair with our previous fixed optimal 367 repair strategy (46) -in well-mixed environments where both strategies are suitable. 368 Surprisingly, although cells with the adaptive repair mechanism had slightly lower growth 369 rates than those with fixed optimal repair at the level of the individual (Fig. 2B), they 370 outperformed them in the chemostat environment where there was competition for 371 resources (Fig. 3). The likely reason for this is that with adaptive repair, there are more cells 372 growing at the highest rate (Fig. 2C); as cells grow exponentially, any slight growth rate 373 advantage will increase over time, resulting in a higher chance of division before stochastic 374 removal from the chemostat. 375 376 When we initially applied the adaptive repair model to growth in biofilms we were surprised 377 that the bases of biofilm 'fingers' of adaptive repairers were disappearing (Fig. 4). Since we 378 assume that converting damaged into new material incurs a loss of 20% to account for the 379 energy requirement of repair, the slowly growing cells at the base of the biofilm are not able 380 to compensate for this 20% loss of biomass due to repair with new growth. Therefore, 381 repairers shrink. This could be considered a biofilm specific disadvantage of repair. However, 382 we think such extensive shrinking is unrealistic. First, to our knowledge, extensive shrinking of 383 the volume of starving or dormant cells other than by cell division has not been observed and 384 this may be due to the murein sacculus maintaining cell shape. Second, these biofilm 385 structures with completely disappearing bases are not realistic as the slightest shear stress 386 would detach these structures (66, 69, 70). Moreover, one would expect that the higher the 387 rate of metabolism such as protein folding or respiratory electron transport, the higher the 388 chance of damage arising such as protein misfolding or damage by reactive oxygen species 389 (19, 71, 72). Indeed, organisms that grow more rapidly have been shown to also accumulate 390 damage more rapidly (47, 73) and can have a higher rate of mortality (38). Therefore, we 391 decided to make the simplest assumption that the rate of damage accumulation should be 392 proportional to the specific growth rate of individual cells. In this case, biofilm fingers of 393 adaptive repairers no longer had shrinking bases (Fig. 5) and now performed better than the 394 damage segregators (Fig. 6 and Table S1), as may be expected when cell death is 395 predominantly intrinsic rather than extrinsic, as in the constant and chemostat environments. The evolved extent to which unicells segregate damage asymmetrically varies substantially 401 between species. This poses the question of whether this is due to differences in the 402 mechanism of cell growth and division, differences in the 'life span' of their habitats or the 403 degree to which these 'unicells' are actually multicellular with a clearer division of labor between germline and soma. The budding yeast, Saccharomyces cerevisiae, was the first 405 unicell shown to age (21) and, in fact, is the only unicell for which the evidence of aging under 406 benign conditions, rather than as a stress response, remains strong (9, 20, 32-38, 74-77). Its 407 habitat is very rich in sugars but short-lived (78), and we argued previously (46) that investing 408 resources into repairing the cell rather than reproduction is less advantageous when the 409 habitat is (reliably) transient. However, the fission yeast Schizosaccharomyces pombe lives in 410 the same kind of habitat (79). Also, the bacterium Caulobacter crescentus lives attached to 411 surfaces that are decaying or consumed by zooplankton and therefore similarly transient, yet 412 the evidence for senescence in C. crescentus has dwindled since our 2014 publication (9, 34, 413 80). This suggests that our previously proposed explanation -that morphologically 414 asymmetric cell division and high external mortality due to short-lived habitats are necessary 415 and sufficient conditions to see aging in unicells -needs to be revised as these conditions 416 appear necessary but not sufficient. A third condition, nascent multicellularity, needs to be 417 also met, see below. 418 419 Recent studies of the fission yeast, following single cells for many generations, provide clear 420 evidence that asymmetric damage segregation does not occur under benign conditions. 421 Instead, it appears to be a stress response to deal with misfolded proteins, which aggregate 422 and then fuse into fewer and larger aggregates, facilitating the segregation of the damage into 423 one aged daughter cell with a reduced growth rate and higher mortality (32, 33, 81). with age, instead, they found mortality to increase with growth rate. Moreover, they found 427 that aggregates can get lost from old pole cells during division so they can rejuvenate. 428 Remarkably, oxidative stress reduced growth rate only transiently and protein aggregates 429 present in the cell after stress did not affect growth. Apart from fission yeast, a recent study 430 Considering all evidence, the budding yeast appears to be the only studied 'unicell' where 447 aging occurs in the absence of stress. However, neither its asymmetric cell division mechanism 448 of budding, nor living in transient habitats, is sufficient to explain this difference. It seems to 449 us that the common view of the budding yeast as a unicell may be mistaken and the missing 450 ultimate reason why budding yeast ages is that it is, to some extent, a multicellular organism. Our study has several limitations. First, we have focused on the effect of damage on growth 464 rate rather than mortality. This is partly for simplicity and partly because some studies show 465 an increase of mortality with age (90) while others suggest mortality is random rather than 466 increasing with age (37, 38, 79). Second, we neglect damage that had not been repaired before 467 it became segregated or that would be prohibitively expensive to repair, since the work of Lin 468 Chao's group has covered this well. They showed that damage segregation under constant 469 environmental conditions leads to separate steady state levels of damage in old and young 470 lineage cells, meaning that growth rate and mortality of cells do not change over divisions (43,471 44, 91-94). (Since there is no trend of deterioration and the replication of young and old 472 lineages do not fit a soma germline distinction, it is probably better to refer to this as damage 473 homeostasis rather than aging). Third, we avoided specific assumptions on mechanisms of 474 damage repair or segregation that are organism specific as these are subject to evolution and 475 our interest is the evolution of general strategies. Fourth, we have simplified the biofilm system to growth on flat, inert surfaces without detachment. While our rough, finger like 477 biofilms capture typical aspects of biofilm structure, many processes and potential structures 478 could not be covered in this study as the number of possible combinations is huge. 479 Nonetheless, our study is the first to cover the extremes, from a perfectly mixed chemostat 480 to a simple biofilm without any mixing (no motility of cells and only diffusive transport of 481 substrate through boundary layer and biofilm). That the results were, surprisingly, essentially 482 the same for both extremes, suggests that the findings hold for environments in between 483 these extremes. (iii) a degree of multicellularity is present. Otherwise, aging is advantageous only as a stress 491 response to deal with damage that failed to be repaired. Here, we have expanded the scope 492 of this prediction substantially from previous work in constant and dynamic but spatially 493 uniform environments by exploring biofilms as an exemplar of spatially structured systems 494 thought to harbor the majority of microbes in the environment. In contrast to our original 495 hypothesis, we found that repair is also better than damage segregation in biofilms.

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We are following the standard ODD (Overview, Design concepts, and Details) protocol for 498 describing individual-based models to facilitate comparison and review (Grimm et al., 2006(Grimm et al., , 499 2010. 500 501 Purpose 502 The purpose of this study is to determine whether segregation or repair of damage is the 503 optimal unicellular strategy for dealing with cellular damage in spatially structured systems 504 such as biofilms. In order to do this, we expand upon our previous work in spatially uniform

1,000 as new cells randomly replace existing cells. 522
Chemostat environment: The simulation domain behaves like a chemostat of size 1 µm 3 . A 523 chemostat is a well-mixed system where fresh resources constantly flow in and cells and left-524 over resources constantly flow out, at the same dilution rate D (0.3 h -1 ; Table 1). 525 Biofilm environment: Only two dimensional simulations were used, to simplify analysis, 526 however, the addition of a third dimension would not be expected to change results because 527 both horizontal dimensions are equivalent (68). The domain size is (256 x 256) µm 2 , and the 528 spatial grid for solving the diffusion reaction equation has a resolution of (4 x 4) µm 2 . The Cell growth is exponential, as growth rate is proportional to the current mass of the cell (but 543 see about age dependence below). Cells divide once their total protein threshold, :AB (Table  544 1), is reached (randomized by drawing from a normal distribution with given mean ± standard 545 deviation; 0.5 ± 0.025). Cells are made of two types of biomass, referred to as protein: protein 546 invested into growth machinery, or protein invested into repair machinery, and protein may 547 be either active or damaged (Table 1). As cells grow, they make active protein that is invested 548 into growth. Active protein is damaged in one of two ways: at a constant rate (a), as in our 549 previous work (46), or at a rate that is proportional to the cellular specific growth rate ( ′). If 550 cells possess the ability to carry out repair, damaged protein is converted back to active 551 protein, at a rate proportional to both the concentration of damaged protein and the 552 concentration of active repair protein with rate constant , but with an efficiency, or repair 553 yield ( 9 ), of 80% (these processes are summarized in Fig. 1). 554 Individuals can differ in their strategy for dealing with cellular damage, but strategies are 555 strategies used in this study (Fig. 1). All six combinations of division and repair strategies were 568 used for initial, single-strategy investigations (i.e. Fig. 2), but only FR, AR and DS were used for 569 competitions. 570

Mortality (intrinsic and extrinsic) 572
In all environments, cells may be considered dead when their age reaches 1, signifying that 573 there is no longer any active protein within the cell (intrinsic mortality). Such 'dead' cells are 574 assumed to remain physically intact and to continue to occupy space (only relevant for 575 biofilms) since cell wall degradation is presumably a slow process (taking many residence 576 times in the chemostat and longer than the times we simulate in biofilms). The simulation is entirely time stepped rather than event driven. The order in which agents 614 are called in each time step is randomized. 615

Design concepts 617
Adaptation 618 Within this model, only those cells with the adaptive repair mechanism are able to adapt to 619 their environment. These cells are able to sense their current cellular damage levels and invest 620 into producing repair protein appropriately. Repair protein is assumed to be stable rather than 621 turned over. In other words, repair protein is not converted back into growth protein if it is no 622 longer needed. Almost all system and agent parameters are specified in an xml input file called 'protocol' file. 650 Example input files can be found at https://github.com/R-Wright-1/iDynoMiCS_1.5. 651 652

Mathematical skeleton 654
The following equations are for modeling growth, aging, and repair of individual cells. They 655 are ordinary differential equations (ODEs). Their solution depends on conditions prescribed at 656 one end of the interval of interest (Lick, 1989). 657 658

Individual Model Equations 659
The population is not modelled directly, but summary statistics are gathered and rates 660 summed over all individuals. The substrate consumption rates of all individuals are gathered 661 and summed and this total rate of substrate consumption enters the standard equation for 662 chemostat substrate dynamics (+ inflow − outflow − consumption). Note that the net specific 663 growth rate of an individual is also the sum of the rates of change for all four components of 664 the cell. We give the differential equations for the change of the cell's components below. 665 Individuals do not have access to population level information and their behavior depends 666 only on local conditions. 667 The biofilm environment consists of substrate concentration fields and a representation of 668 the current biofilm structure (substratum surface, biofilm, biofilm boundary-layer interface 669 and boundary-layer bulk-liquid interface). The environment is modelled as a continuum using  Since adaptive repair has a variable fraction of repair machinery, the previously used /;< and 676 :/. have each to be split into two fractions: 677 7,/ , 9,/ , 7,: and 9,: , referring to growth machinery, active; repair machinery, 678 active; growth machinery, damaged; and repair machinery, damaged, respectively 679 (as in Table 1). 680 Thus, the total 'protein' of the cell (representing all biomass) is <>< = 7,: + 9,: + 7,/ + 681 9,/ . 682 We assume that damage is always toxic, i.e., specific growth rate, due to some inhibitory effect 683 of damaged material, decreases with the fraction of damaged protein, , equivalent to the 684 age of the cell: 685 = 7,: + 9,: Toxic damage led to more pronounced differences between the strategies in our previous 687 study, whilst not changing the fitness ranking of strategies apart from one case, at the lowest 688 damage accumulation rate and only in the constant environment, where the differences 689 between strategies were minute (46). (2) 697 where f /;< represents the proportion of active biomass that is dedicated to repairing 698 damaged biomass and a placeholder for the value actually used depending on the repair 699 strategy. For fixed repair, it becomes the fixed fraction of active protein /;< that is repair 700 machinery f /;< = /;< . For adaptive repair, it is replaced by the currently active repair 701 machinery f /;< = 9,/ , which is produced as a fraction of growth " calculated for each 702 individual at every time step depending on its current fraction of damage (age ) from the 703 For ( ) in eq. 3, we do not take the gross specific growth rate according to eq. (1), but the 708 net specific growth rate each individual cell calculates from its change of total mass from one 709 iteration to the next, which due to inefficient repair could be less. 710 This gives the following differential equations for the four components of each individual cell 711 for the case of toxic damage that is being repaired: actively growing. It therefore makes sense to assume that non-growing cells that do not 753 produce proteins or respire do not accumulate damage (19, 71, 72). Thus, the damage 754 accumulation rate was assumed to be proportional to cellular specific growth rate. 755 In order to compare strategies across environments, we need to apply the same damage 756 accumulation rate in all three environments. Hence, the new damage accumulation rate that 757 is proportional to specific growth rate, ′, must be calculated to match the fixed damage 758 accumulation rate in the spatially uniform environments ( = 0.1 h -1 ) where the specific 759 growth rate is constant or predictable for a steady state. In the steady state of the chemostat, 760 the net specific growth rate, µ~, is equal to the dilution rate, D, which was set to 0.3 h -1 . In 761 iDynoMiCS, the gross specific growth rate, \ , is calculated with the Monod equation and 762 depends on substrate concentration, S. However, how much the net specific growth rate is 763 lower than the gross specific growth rate depends on the age of the cell, its rate of repair and 764 its current level of investment into repair. It is therefore difficult to work out analytically so 765 we had to run a number of simulations with different ratios of aging rates to specific growth 766 rates to find that a value of 0.22 (dimensionless) would match the previously used constant 767 aging rate for chemostats (Fig. S6). 768 769

Diagram of processes 770
A diagram containing a brief overview of all cellular processes is in Fig. 1.