Single-celled organisms dividing by binary fission were thought not to age []. A 2005 study by Stewart et al. [] reversed the dogma by demonstrating that Escherichia coli were susceptible to aging. A follow-up study by Wang et al. [] countered those results by demonstrating that E. coli cells trapped in microfluidic devices are able to sustain robust growth without aging. The present study reanalyzed these conflicting data by applying a population genetic model for aging in bacteria []. Our reanalysis showed that in E. coli, as predicted by the model, (1) aging and rejuvenation occurred simultaneously in a population; (2) lineages receiving sequentially the maternal old pole converged to a stable attractor state; (3) lineages receiving sequentially the maternal new pole converged to an equivalent but separate attractor state; (4) cells at the old pole attractor had a longer doubling time than ones at the new pole attractor; and (5) the robust growth state identified by Wang et al. corresponds to our predicted attractor for lineages harboring the maternal old pole. Thus, the previous data, rather than opposing each other, together provide strong evidence for bacterial aging.

Results and Discussion

7 Chao L. A model for damage load and its implications for the evolution of bacterial aging. 8 Lindner A.B.

Madden R.

Demarez A.

Stewart E.J.

Taddei F. Asymmetric segregation of protein aggregates is associated with cellular aging and rejuvenation. The population genetic model used for our study was originally constructed to provide a predictive framework for studying the evolution of bacterial aging []. Because bacterial aging was attributed to the accumulation of nongenetic (e.g., oxidative) damage in aging cells [], the model was designed to describe the partitioning of such damage by a mother bacterium to her daughters. The model revealed that a mother that partitions asymmetrically more damage to one daughter has a higher evolutionary fitness. Asymmetry is advantageous because it creates fitness variance for natural selection. The daughter receiving less damage is rejuvenated and the one receiving more ages.

The model also tracked the partitioning of damage in relation to the two poles of a bacterial cell. E. coli cells divide by cleaving their long axis with a division plate. Because two new poles are formed at the plate, poles distal to the plate are the old poles and every bacterium has a new and an old pole. Whenever a mother bacterium divides, one daughter receives the maternal old pole and the other receives the maternal new pole. The model found that if bacterial lineages receiving sequentially the maternal old pole were tracked, their doubling times converged onto a stable attractor state. The doubling times of lineages receiving likewise the maternal new pole converged onto an equivalent but different attractor state. More importantly, the bacteria at the old pole attractor were more aged and had a longer doubling time. If bacteria were symmetrical, old and new poles would converge to a single attractor and aging would not be evident. Thus, bacterial aging evolves because natural selection favors bacteria that partition damage asymmetrically.

1 and T 2 , respectively) are graphed against the doubling time of their mother cell (T 0 ) ( Figure 1 Graphical Prediction for Aging and Rejuvenation in Bacteria Show full caption 7 Chao L. A model for damage load and its implications for the evolution of bacterial aging. 1 and T 2 as a function of T 0 . T 1 and T 2 are the doubling times of daughters 1 and 2, which receive the new and old poles, respectively, of the mother cell. T 0 is the doubling time of the mother cell. The predicted relationships are represented as two solid lines (lower, T 1 ; upper, T 2 ). The dashed line is the identity line. The intercept of the identity line and the T 1 and T 2 graph lines corresponds to attractor states to which the new and old pole lineages converge ( , ). To illustrate the convergence, consider a mother cell with a doubling time of 29.5 min. Projecting upwards from T 0 = 29.5 (▴) to the two solid lines identifies the two points ○ and , which are the predicted T 1 and T 2 values for the mother cell's two daughters. In preparation for a later discussion, we denote ○ as T ˜ 1 . Following only the new pole lineage, let the T ˜ 1 become a mother by projecting its doubling time onto the T 0 axis (▵). T ˜ 1 's daughters will have the doubling times T′ and T″ (□, ■). By tracking T ˜ 1 and T′, the new pole lineage progresses downwards along the T 1 graph line (rightmost arrow). Because T ˜ 1 is greater than T′, the progression corresponds to rejuvenation. If the T′ daughter and its subsequent daughters are likewise projected in turn onto the T 0 axis as mothers, the resulting new pole lineage converges to the lower attractor ( ). If the initial mother cell had a T 0 = 26.2 min (▾), a similar convergence occurs, albeit from the left of the attractor (leftmost arrows), and the increase in doubling times corresponds to aging. Note that the old pole graph line also has its own attractor point ( ). These attractors are stable equilibrium points and are hereafter denoted T ˆ 1 and T ˆ 2 , respectively. A bacterial population consists of a dynamical network of cells connected by cell division. Some cells reside at the attractor states, but others emanate from them and their lineages and converge to the alternate attractor. Note that the points in this figure illustrate qualitatively that the relationships T ˆ 2 > T″ > T ˜ 1 > T′ and [ T ˆ 2 – T″] > [ T ˜ 1 – T′], which will be used in Unless otherwise specified, black and white symbols refer respectively to old and new poles in this and subsequent figures. Predictions based on model of Chao [] and are presented on a phase plot of Tand Tas a function of T. Tand Tare the doubling times of daughters 1 and 2, which receive the new and old poles, respectively, of the mother cell. Tis the doubling time of the mother cell. The predicted relationships are represented as two solid lines (lower, T; upper, T). The dashed line is the identity line. The intercept of the identity line and the Tand Tgraph lines corresponds to attractor states to which the new and old pole lineages converge (). To illustrate the convergence, consider a mother cell with a doubling time of 29.5 min. Projecting upwards from T= 29.5 (▴) to the two solid lines identifies the two points ○ and, which are the predicted Tand Tvalues for the mother cell's two daughters. In preparation for a later discussion, we denote ○ as. Following only the new pole lineage, let thebecome a mother by projecting its doubling time onto the Taxis (▵).'s daughters will have the doubling times T′ and T″ (□, ■). By trackingand T′, the new pole lineage progresses downwards along the Tgraph line (rightmost arrow). Becauseis greater than T′, the progression corresponds to rejuvenation. If the T′ daughter and its subsequent daughters are likewise projected in turn onto the Taxis as mothers, the resulting new pole lineage converges to the lower attractor (). If the initial mother cell had a T= 26.2 min (▾), a similar convergence occurs, albeit from the left of the attractor (leftmost arrows), and the increase in doubling times corresponds to aging. Note that the old pole graph line also has its own attractor point (). These attractors are stable equilibrium points and are hereafter denotedand, respectively. A bacterial population consists of a dynamical network of cells connected by cell division. Some cells reside at the attractor states, but others emanate from them and their lineages and converge to the alternate attractor. Note that the points in this figure illustrate qualitatively that the relationships> T″ >> T′ and [– T″] > [– T′], which will be used in Figure 3 for data testing. The attractor states and temporal dynamics of bacterial aging and rejuvenation predicted by the model can be visualized graphically on a phase plane onto which the doubling times of daughter cells harboring the new and maternal old poles (Tand T, respectively) are graphed against the doubling time of their mother cell (T) ( Figure 1 ). Hereafter, daughters 1 and 2, or simply new and old pole cells, will be used as notations for the daughters harboring the new and maternal old poles. Besides demonstrating the old and new pole attractors, the phase plane also shows that not all cells reside at the two attractors. For example, if a mother cell resides at the old pole attractor, its daughter 2 is expected to have the doubling time of the attractor, but its daughter 1 will be far away from the new pole attractor. The lineage descending from this daughter 1, as all other new pole lineages, should then converge to the new pole attractor.

5 Stewart E.J.

Madden R.

Paul G.

Taddei F. Aging and death in an organism that reproduces by morphologically symmetric division. 1 and T 2 attractors [ 7 Chao L. A model for damage load and its implications for the evolution of bacterial aging. By fitting the data of Stewart et al. [] to our model, we had previously confirmed the locations of the predicted Tand Tattractors []. However, those results were based solely on a static snapshot of bacterial doubling times on a phase plane. To test the model more completely and rigorously, it would be desirable to determine whether the additional temporal dynamics predicted by the model are realized. To achieve such a goal, we used our model to make new and explicit predictions and tested them against novel data extracted from previously published data.

7 Chao L. A model for damage load and its implications for the evolution of bacterial aging. 7 Chao L. A model for damage load and its implications for the evolution of bacterial aging. Figure 2 Observed Temporal Dynamics of Aging and Rejuvenation Tracked in Lineages of E. coli Descending from a Single Mother Cell Show full caption 5 Stewart E.J.

Madden R.

Paul G.

Taddei F. Aging and death in an organism that reproduces by morphologically symmetric division. is the attractor for old pole lineages or T ˆ 2 ; is the attractor for new pole lineages or T ˆ 1 . The positions of the attractors at 29.5 and 27.2 min are predicted by our previous analysis [ 7 Chao L. A model for damage load and its implications for the evolution of bacterial aging. For interpretation of the plot and definitions, see Figure 1 . These results provide the experimental complement of the projection described in Figure 1 for a new pole lineage. Data were extracted from Stewart et al. []. All lineages descended from a single mother cell that had a doubling time of 38 min (▴) and were tracked for eight generations.is the attractor for old pole lineages oris the attractor for new pole lineages or. The positions of the attractors at 29.5 and 27.2 min are predicted by our previous analysis [] of the data of Stewart et al. (A) Lineage nnnnnnnn (—○—○—) was tracked by following only the doubling times of cells receiving the new pole from a mother. Lineage ooonnnnn (—●—○—) was tracked for three generations by old pole cells and then crossed over to new poles. (B) Lineages oooooooo (—●—●—); nnnooooo (—○ —●—) were tracked by reversing the order of new and old poles in (A). From the results of Stewart et al., we first generated data to test the prediction that the new and old pole lineages should converge over time to two attractors. In our previous static analysis of their data, we had examined only the doubling times of 128 mother cells and their 256 daughters over two generations []. However, the data go back eight generations to the origin of the population from a single mother cell. Thus, longer and continuous temporal dynamics of a lineage could be extracted. Such lineage dynamics were obtained by recovering the doubling time of all new poles of the lineage descending from the original cell (see Supplemental Information available online), or what is termed an nnnnnnnn lineage over eight generations. Likewise, data for an old pole or oooooooo lineage were also extracted. For comparison, ooonnnnn and nnnooooo lineages, which harbored for the three initial generations the alternate pole, were also obtained. The results remarkably confirmed the temporal dynamics predicted by the model ( Figure 2 ). In each case, the lineages converged to the appropriate attractors, whose positions had been estimated in our previous study []. In the lineages that were switched after three generations, the tracking responded accordingly after the change. Because the lineages tracked from right to left, the ones converging onto the new pole attractor did not have sufficient time to encircle the attractor ( Figure 2 A). The old pole lineages clearly show dynamics encircling the corresponding attractor ( Figure 2 B). However, the trajectories around the old pole attractor were not well superimposed, which suggests that there is stochasticity and error to the process.

6 Wang P.

Robert L.

Pelletier J.

Dang W.L.

Taddei F.

Wright A.

Jun S. Robust growth of Escherichia coli. T ˜ 1 , T ˆ 2 , T′, and T″, where T ˜ 1 and T ˆ 2 were respectively daughters 1 and 2 of a cell at the old pole attractor and T′ and T″ were respectively daughters 1 and 2 of a T ˜ 1 cell. Two explicit predictions were made: (1) the doubling times should have the ranking T ˆ 2 > T″ > T ˜ 1 > T′, and (2) the difference [ T ˆ 2 – T″] should be greater than [ T ˜ 1 – T′]. T ˆ 2 > T″ > T ˜ 1 > T′ as 21.8 > 20.1 > 19.7 > 18.8 min. The ranking [ T ˆ 2 – T″] > [ T ˜ 1 – T′] was estimated as1.68 > 0.92 min. All predictions were found to be significantly different on the basis of nonoverlapping 95% confidence limits ( Figure 3 Observed Temporal Dynamics of Aging and Rejuvenation Emanating from Wang et al.'s Robust Stable State Show full caption , ○, □, and ■) represent observed estimates of T ˆ 2 , T ˜ 1 , T′, and T″, which are as defined in T ˆ 2 attractor and the daughter cells descending from it. Estimates were extracted from the data of Wang et al. [ 6 Wang P.

Robert L.

Pelletier J.

Dang W.L.

Taddei F.

Wright A.

Jun S. Robust growth of Escherichia coli. T ˆ 2 , T″, T ˜ 1 , and T′ had values of 21.8, 20.1, 19.7, and 18.8 min. These averages and their plot confirm the prediction that T ˆ 2 > T″ > T ˜ 1 > T′. All averages were significantly different from each other. Error bars correspond to 95% confidence limits (n = 618), which never overlapped. Estimates from the data also supported the prediction that [ T ˆ 2 – T″] > [ T ˜ 1 – T′]. We estimated that [ T ˆ 2 – T″] = 1.68 and [ T ˜ 1 – T′] = 0.92 and found these average values to be significantly different (standard error of the mean = 0.101 and 0.136; n = 618; p < 0.0000005). The confirmation of the predictions shows that Wang et al.'s robust attractor is equivalent to the old pole attractor of our model. Solid lines are drawn through the four points to represent the possible relationship corresponding to our model. Extending the lower solid line to its intersection with the dashed identity line predicts that the unrecorded T ˆ 1 value in Wang et al.'s system is approximately 18 min ( ). For definitions, color code, and interpretation of the dynamics of the phase plot see Figure 1 . The four points (, ○, □, and ■) represent observed estimates of, T′, and T″, which are as defined in Figure 1 and correspond to the old pole orattractor and the daughter cells descending from it. Estimates were extracted from the data of Wang et al. [] by assuming that the robust state was the old pole attractor. Estimated averages for, T″,, and T′ had values of 21.8, 20.1, 19.7, and 18.8 min. These averages and their plot confirm the prediction that> T″ >> T′. All averages were significantly different from each other. Error bars correspond to 95% confidence limits (n = 618), which never overlapped. Estimates from the data also supported the prediction that [– T″] > [– T′]. We estimated that [– T″] = 1.68 and [– T′] = 0.92 and found these average values to be significantly different (standard error of the mean = 0.101 and 0.136; n = 618; p < 0.0000005). The confirmation of the predictions shows that Wang et al.'s robust attractor is equivalent to the old pole attractor of our model. Solid lines are drawn through the four points to represent the possible relationship corresponding to our model. Extending the lower solid line to its intersection with the dashed identity line predicts that the unrecordedvalue in Wang et al.'s system is approximately 18 min (). The data from Wang et al. [] provided the second test. As indicated above, these data reported stable and robust growth of trapped E. coli cells over hundreds of generations and were interpreted to be at odds with bacterial aging. However, our conjecture was that the robust state was simply the confirmation of the old pole attractor predicted by our model. Because any new pole remains a new pole for only one generation, all trapped cells harbor an old pole after one generation and eventually should converge onto the old pole attractor. We tested our conjecture by extracting new data from Wang et al.'s study and determining whether the doubling time of cells descending from their robust state matched values predicted by our model for cells emanating from an old pole attractor ( Supplemental Information ). Because the depth of the channels in Wang et al.'s microfluidic device retained cells for only three generations, the predictions were limited to that time horizon. Four types of cells were tracked. The cells and their doubling times were denoted, T′, and T″, whereandwere respectively daughters 1 and 2 of a cell at the old pole attractor and T′ and T″ were respectively daughters 1 and 2 of acell. Two explicit predictions were made: (1) the doubling times should have the ranking> T″ >> T′, and (2) the difference [– T″] should be greater than [– T′]. Figure 1 provides a graphical interpretation of the four cell types and the meaning of the rankings. Analytical proofs for the rankings are available as Supplemental Information . Data extracted from Wang et al. fully confirmed the two predictions ( Figure 3 ). Data values matched to our model yielded doubling times that ranked> T″ >> T′ as 21.8 > 20.1 > 19.7 > 18.8 min. The ranking [– T″] > [– T′] was estimated as1.68 > 0.92 min. All predictions were found to be significantly different on the basis of nonoverlapping 95% confidence limits ( Figure 3 ).

T ˆ 2 was greater than T″, T ˜ 1 , and T′ shows that Wang et al.'s robust state was likely the old pole attractor and that there was a second attractor at which the doubling times would be shorter. The T ˜ 1 cells were the first step away from Wang et al.'s robust state. Although old pole cells at the robust state do not age, new cycles of both aging and rejuvenation are triggered by T ˜ 1 cells and their T″ and T′ daughters. The fact that T ˜ 1 and T′ were the shortest doubling times demonstrates rejuvenation resulting from the allocation of less damage. The fact that T ˜ 1 > T′ shows that not only does T ˜ 1 escape the robust state, its daughter moves even farther away, presumably toward our second and predicted attractor for the new pole. The fact that T″ is the second longest doubling time shows that it, as an old pole, is beginning to converge back to the old pole attractor. Altogether, these results provide strong support that Wang et al.'s robust state is our old pole attractor. Additionally, the relationship T″ > T ˜ 1 is significant because it shows that the slope of T 2 as a function of T 0 (the T 2 graph line in T ˆ 2 – T″]/[ T ˆ 2 – T ˜ 1 ] and is less than one if [ T ˆ 2 – T ˜ 1 ] > [ T ˆ 2 – T″], which is true when T″ > T ˜ 1 . Finally, the second prediction that [ T ˆ 2 – T″] > [ T ˜ 1 – T′] results from the fact that the slope of the T 2 graph line should be greater than that of T 1 ( 1 graph line has a slope that is less than one and thus also intercepts the identity line to create the new pole attractor. Although the data of Wang et al. do not provide a measurement of the new pole attractor, our analysis predicts that it should have a value of approximately 18 min (see 1 and T 2 lines result because the mapping relationship between damage and doubling time in our model is not linear. This nonlinearity was not intentionally assumed or built into the model (see The rankings we tested are more than simple numerical relationships. They reflect fundamental temporal changes predicted by the model. The fact thatwas greater than T″,, and T′ shows that Wang et al.'s robust state was likely the old pole attractor and that there was a second attractor at which the doubling times would be shorter. Thecells were the first step away from Wang et al.'s robust state. Although old pole cells at the robust state do not age, new cycles of both aging and rejuvenation are triggered bycells and their T″ and T′ daughters. The fact thatand T′ were the shortest doubling times demonstrates rejuvenation resulting from the allocation of less damage. The fact that> T′ shows that not only doesescape the robust state, its daughter moves even farther away, presumably toward our second and predicted attractor for the new pole. The fact that T″ is the second longest doubling time shows that it, as an old pole, is beginning to converge back to the old pole attractor. Altogether, these results provide strong support that Wang et al.'s robust state is our old pole attractor. Additionally, the relationship T″ >is significant because it shows that the slope of Tas a function of T(the Tgraph line in Figure 1 ) is less than one. A slope of less than one is needed for the function to intercept the identity line and generate the old pole attractor ( Figure 1 ). The slope equals [– T″]/[] and is less than one if [] > [– T″], which is true when T″ >. Finally, the second prediction that [– T″] > [– T′] results from the fact that the slope of the Tgraph line should be greater than that of T Figure 1 ). If it is greater, then the Tgraph line has a slope that is less than one and thus also intercepts the identity line to create the new pole attractor. Although the data of Wang et al. do not provide a measurement of the new pole attractor, our analysis predicts that it should have a value of approximately 18 min (see Figure 3 ). It is noteworthy that the different slopes of the Tand Tlines result because the mapping relationship between damage and doubling time in our model is not linear. This nonlinearity was not intentionally assumed or built into the model (see Supplemental Information ). The manifestation of this nonlinearity in Wang et al.'s data shows that an emergent property of the model is confirmed in bacteria.