Damage dynamics and the role of chance in the timing of E. coli cell death

Genetically identical cells in the same stressful condition die at different times. The origin of this stochasticity is unclear; it may arise from different initial conditions that affect the time of demise, or from a stochastic damage accumulation mechanism that erases the initial conditions and instead amplifies noise to generate different lifespans. To address this requires measuring damage dynamics in individual cells over the lifespan, but this has rarely been achieved. Here, we used a microfluidic device to measure membrane damage in 635 carbon-starved Escherichia coli cells at high temporal resolution. We find that initial conditions of damage, size or cell-cycle phase do not explain most of the lifespan variation. Instead, the data points to a stochastic mechanism in which noise is amplified by a rising production of damage that saturates its own removal. Surprisingly, the relative variation in damage drops with age: cells become more similar to each other in terms of relative damage, indicating increasing determinism with age. Thus, chance erases initial conditions and then gives way to increasingly deterministic dynamics that dominate the lifespan distribution.


REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): In this manuscript, Yang et al. investigated why isogenic cells under the same stress conditions die at different times.This is a longstanding, fundamental question in our understanding of stress resistance and aging.To address this question, the authors quantified the dynamics of damage accumulation in single E.coli cells by measuring the uptake of PI as an indicator of cell membrane damage.It remains challenging to monitor the dynamics of damage accumulation as the direct upstream step to cell death, and this work represents one of the first studies to accomplish that.Based on these measurements, the authors found that the initial conditions or cell cycle phase of cells cannot account for the variation in their final lifespans.Instead, the authors developed a simple mathematical model based on the data, which suggests a linearly increased production of damage coupled with a saturated removal can amplify white noise in the system and account for the observed heterogeneity in lifespan.Specifically, the model is comprised of an age-dependent linear increase in the damage production rate and a damage removal rate that can be saturated by the damage level.This model can nicely capture the experimental data and impressively reproduce a series of nontrivial, characteristic statistics of aging dynamics.In addition, both the data and model reveal a surprising drop in the cellto-cell variation of damage level with age, indicating that damage levels become relatively more uniform among aged cells preceding death.I find this work convincing and thought-provoking.The effort toward a unified model of aging is fundamental and important.Therefore, I recommend the acceptance of this manuscript for publication with minor revisions.
Below are a couple of minor concerns: 1.The damage removal term in the MP-SR model is notably different from that in the previous SR model for mice aging by Karin et al.Although both can be saturated, they differ in the kinetics -one is sigmoidal (MP-SR) whereas the other is Michaelis-Menten (SR).It is straightforward to understand why Michaelis-Menten kinetics can be applied to damage removal, but the sigmoidal kinetics of damage removal is less intuitive.It would be very helpful if additional discussions can be provided.For example, (1) What are the potential biological processes underlying the sigmoidal kinetics of damage removal?(2) Why do bacterial aging and mammalian cell senescence need different damage removal term, whereas the damage production is the same?(3) Do these two damage removal terms have different impacts on "twilight"? 2. It would be helpful to show, in a supplemental figure, the raw data for time-series of PI fluorescence and the deduced PI uptake time traces for all the single cells sorted by lifespan, in heatmaps.This will help readers to better appreciate the experimental results that the model is based on.
Nan Hao, PhD Professor of Molecular Biology, UCSD Reviewer #2 (Remarks to the Author): This is a fantastic study by the group of Uri Alon that addresses a very fundamental and unsolved problem in biology: Is cellular aging and death predetermined or subject to stochasticity?The authors have beautiful experimental evidence to support their claims that as cells age, stochasticity becomes less dominant, and cell-to-cell variation in lifespan diminishes with age.It would be great if the authors could perhaps provide just a few additional experiments.I also like to point out that these requests are not "requirements", but rather suggestions to provide a little more data to help readers and strengthen their work.Specifically, 1. Unless I missed something, the authors use only Propidium iodide to quantify membrane integrity.It would be great to have one set of measurements with another fluorescent dye, such as Sytox (another cell death reporter).I am not asking the authors to repeat all the experiments using Sytox, just to provide some control that the PI results are consistent with another well-established dye. 2. The authors present a model that explains their observations.It would be great if the authors could perform a "forward experiment" to test if their model can also predict the outcome of a perturbation (new data that was not used to inform the model).For example, what would happen if the cells are exposed to a toxin (an antibiotic or radicals etc)?Since the authors use a microfluidic device, it seems straightforward to expose cells to an agent and determine the effect and compare the outcome to modeling predictions.3. Along these lines, how does temperature or presence of certain nutrients in the growth media effect their results?Increasing temperature could speed up the aging and also reduce the stochasticity.I thought it would be great if the authors could experimentally reduce the stochasticity in cells and determine its effect on aging and the "shortening twilight".4. Could the authors please include some images of cells?Since they use a microfluidic device that is optically accessible, it would be helpful for readers like me see just a few actual images of cells in the device and at different time points of the experiment.

Dear Editors,
Thank you for the reviewer comments and for your positive consideration of our manuscript.We were delighted that the reviewers found the work important and convincing, and that they valued the new insights it carries to the understanding of cell aging and death.We have now addressed the reviewers comments.In particular we add new data that repeats the experiment on a mutant strain with reduced repair, new control data with a different viability stain and additional microscopy images, movies and data heat maps.We detail our point-by-point responses below in blue.We believe these revisions make the manuscript stronger, clearer and more rigorous.
We detail our point-by-point responses below.

Sincerely, Uri Alon and Yifan Yang
Response to reviewer 1: In this manuscript, Yang et al. investigated why isogenic cells under the same stress conditions die at different times.This is a longstanding, fundamental question in our understanding of stress resistance and aging.To address this question, the authors quantified the dynamics of damage accumulation in single E.coli cells by measuring the uptake of PI as an indicator of cell membrane damage.It remains challenging to monitor the dynamics of damage accumulation as the direct upstream step to cell death, and this work represents one of the first studies to accomplish that.Based on these measurements, the authors found that the initial conditions or cell cycle phase of cells cannot account for the variation in their final lifespans.Instead, the authors developed a simple mathematical model based on the data, which suggests a linearly increased production of damage coupled with a saturated removal can amplify white noise in the system and account for the observed heterogeneity in lifespan.Specifically, the model is comprised of an age-dependent linear increase in the damage production rate and a damage removal rate that can be saturated by the damage level.This model can nicely capture the experimental data and impressively reproduce a series of nontrivial, characteristic statistics of aging dynamics.In addition, both the data and model reveal a surprising drop in the cell-to-cell variation of damage level with age, indicating that damage levels become relatively more uniform among aged cells preceding death.I find this work convincing and thought-provoking.The effort toward a unified model of aging is fundamental and important.Therefore, I recommend the acceptance of this manuscript for publication with minor revisions.shape of damage distributions, as described in Method sections "Marginal damage distributions" and "Derivation of the MP-SR model".
Despite the empirical origin, the functional form of f(X) has a natural physical interpretation: it is the partition function of a two-state system.If the damage repair system has two states, inactive and active, and the free energy differential between the two states depends on the level of damage X, then () =  ,-/( ,-+  ,. ) gives the fraction of the repair system in its active state.The exponential terms are interpreted as Boltzmann factors exp(ΔG/kT).An example is ATP synthase whose energy states depend on proton gradients.
We accordingly revised the 2nd paragraph of page 9 (in the results section entitled "Damage dynamics indicate a saturated-repair stochastic model") as follows (changes highlighted) (line 223-229): Notably, this model is in the same class as the saturated repair (SR) model established for aging in mice 20 , in the sense that the production rate of damage rises linearly with age and damage inhibits or saturates its own removal.The only difference is that the mouse SR model used a different saturating removal function, () = /( + ).Hence we call the model of Eq. 1 the membrane-potential-SR model or MP-SR model.We note that the MP-SR removal function () =  ,-/( ,-+  ,. ) can be interpreted as a two-state partition function that senses the loss of membrane potential X.
(2) Why do bacterial aging and mammalian cell senescence need different damage removal terms, whereas the damage production is the same?
The SR model for senescent cells in mice described in Karin et al (2019), had a removal term that goes as f(X)=X/(K+X), whereas the present model has () =  ,-/( ,-+  ,. ).Both removal terms are saturated by damage.The main reason for the differences in functional forms of the removal term, in our view, has to do with the type of damage X.For mice, X is the amount of senescent cells, which is an extensive variable.In E. coli, X measures the loss of membrane integrity in terms of loss potential, which is an intensive variable, and hence Boltzmann-like terms as discussed above appear.It is our view that both models capture essentially the same dynamics.
In the discussion, page 14 paragraph 3, we add (line 359-368): The inferred stochastic mechanism in E. coli is similar to a mechanism inferred in the context of mice aging by Karin et al.Karin et al used stochastic trajectories of senescent cells in mice, cells which are growth arrested cells that cause inflammation, to infer a mechanism for senescent-cell accumulation 20 .This mechanism, called the saturating removal (SR) model, is a stochastic differential equation with a production rate that rises linearly with age and a removal rate that saturates, so that high senescent cell levels slow their own removal.The removal terms in the SR and MP-Sr models both saturate; the difference between them may stem from the type of damage: X is senescent cell abundance in the SR model, an extensive variable, whereas X is membrane integrity in the MP-SR model in units of potential, which is intensive and can enter the dynamics in terms of Boltzmann-like factors.
(3) Do these two damage removal terms have different impacts on "twilight"?
The two models do not differ in terms of the "shortening twilight" phenomenon.We are able to reproduce the "shortening twilight" phenomenon in simulations for both models (MP-SR in Figure S5, SR model simulations not included as it is not the subject of the present manuscript).Conceptually, individuals who cross the lower damage threshold at younger ages have smaller damage production term , thus have a longer remaining lifespan.This causes a negative correlation between time to cross the first threshold and remaining lifespan.The mechanistic details of damage removal are not necessary nor relevant to reach this conclusion.
We now modified the SI section entitled "Shortening twilight in the E. coli dataset" (S5) as follows: We follow the pioneering work of Stroustrup et al and explore the question of twilight, the time between a measurable age-related phenotype to the time of death 47 .Suppose there is an agerelated phenotype that is equivalent to damage crossing a threshold X1.If we define twilight 23 as the remaining lifespan after the threshold is crossed, the question is whether twilight shortens or lengthens with the age at which the threshold is crossed.
The SR and MP-SR models predict that twilight shortens with age on average (Fig. S5ABC).Equivalently, the time to first cross X1, denoted  1 , is positively correlated with time of death  (Fig 5SD), but with a correlation coefficient less than one (Fig. S5E).This prediction is borne out by the E. coli dataset (Fig. S5FG).A similar effect was observed in C. elegans 47 .The reason for shortening twilight in the model is that the damage production term  rises with age.Individuals that cross X1 at early times have a low production term.It takes them longer (on average) to reach the death threshold than those crossing X1 at late times (Fig 1A).Thus there is a negative correlation between  1 and remaining lifespan (Fig. S5EG).

2.
It would be helpful to show, in a supplemental figure, the raw data for time-series of PI fluorescence and the deduced PI uptake time traces for all the single cells sorted by lifespan, in heatmaps.This will help readers to better appreciate the experimental results that the model is based on.
We thank the reviewer for this suggestion and we have added to figure 1 G) PI uptake rate distributions and best-fit to a type-2 generalized beta distribution with the ratio between shape parameters p/(p+q), plotted versus age in (H), see Methods.

Response to reviewer 2:
This is a fantastic study by the group of Uri Alon that addresses a very fundamental and unsolved problem in biology: Is cellular aging and death predetermined or subject to stochasticity?The authors have beautiful experimental evidence to support their claims that as cells age, stochasticity becomes less dominant, and cell-to-cell variation in lifespan diminishes with age.It would be great if the authors could perhaps provide just a few additional experiments.I also like to point out that these requests are not "requirements", but rather suggestions to provide a little more data to help readers and strengthen their work.
We thank the reviewer for this warm endorsement.Specifically, 1.
Unless I missed something, the authors use only Propidium iodide to quantify membrane integrity.It would be great to have one set of measurements with another fluorescent dye, such as Sytox (another cell death reporter).I am not asking the authors to repeat all the experiments using Sytox, just to provide some control that the PI results are consistent with another well-established dye.
We have now added to the revised manuscript control experiments with a second viability stain, AFH+TOPRO.This combined reagent stains both damaged proteins (AFH) and DNA (TOPRO), and thus extends our main dye PI which only stains DNA.We find good agreement between lifespan measured by PI in our microfluidic experiment and conventional FACS assay at a single time point of fraction surviving using AFH+TOPRO.We now add this to a new SI section S3, quoted below:

Lifespan based on PI agrees with viability using a different viability stain, AFH+TOPRO.
We compared the present lifespan measurements using PI to viability using a different stain, AFH+TOPRO 45 .This combined reagent stains both damaged proteins (AFH) and DNA (TOPRO), and thus extends our main dye PI which only stains DNA.We find good agreement between lifespan measured by PI in our microfluidic experiment and conventional single timepoint (day 7) FACS assay of fraction surviving using AFH+TOPRO (Fig. S3) We used PI in our experiments because of previous validation in E. coli 4,46 as a non-toxic dye to track cell viability longitudinally.Longitudinal experiments have different requirements than single-time-point experiments on cell viability -for example, uniformity of maximum intensity across cells might be more important in the latter.Longitudinal analysis allows imaging transients and end-stages for each cell, and thus avoids some of the concerns inherent in singletime point studies.

Figure
Figure S5 E. coli shows shortening twilight at old age as redacted by the MP-SR model.(A) Examples of two MP-SR model simulation trajectories.Wildtype parameters were used.Thresholds are X1=10 for twilight onset and Xc=20 for death.Triangles and squares symbolize first-passage times ( 1 ,  4 ) to cross the X1 and Xc respectively.(B) Durations of health ( 1 , shown in red) and twilight ( 4 − 1 , shown in yellow) for 2000 simulated cells ranked by lifespan.(C) Fraction of lifespan spent in health and twilight for the cells, ranked by fraction of time in health.(D) Time to first cross the two thresholds is correlated with slope less than 1 (Regression line y=0.39x+62.9) in MP-SR simulations.(E) Remaining lifespan drops with time to cross threshold 1 in MP-SR simulations.(F) E. coli lifespan versus the time to cross a damage threshold of normalized PI uptake rate=6 (Regression line is y=0.89x+23.3).(G) Remaining lifetime versus time to cross a damage threshold of normalized PI uptake rate =6.
heat maps of the raw PI data and the membrane damage computed from the PI rate of change.The new panels are Fig 1 CD.

Figure 1 .
Figure 1.Damage dynamics in starving E. coli cells.(A) Individual E. coli cells were placed in microfluidic channels with medium flow.Propidium iodide (PI) added to the medium crosses the membrane and stains DNA when membrane integrity is compromised.(B) Membrane damage was measured by the temporal derivative of PI fluorescence, as shown for two individual bacteria.Top: fluorescence signal, bottom: derivative (uptake rate) in 7h time windows.(C) Colormaps of normalized fluorescence time-series, with individual cells ranked by lifespan.(D) Colormaps of membrane damage computed from the PI rate of change, with individual cells ranked by lifespan.(E) Cumulative risk of death as a function of age shows an exponential

Figure S3
Figure S3Lifespan measurements using PI in microfluidic experiments correlate well with single-time point longevity measurements using AFH+TOPRO in batch culture.Each marker in orange corresponds to one E. coli strain (all based on MG1655 backgrounds).For each strain, we have performed microfluidic experiments 4 similar to those performed in the present study, in order to measure their survival curves.Plotted on the x-axis are median lifespan of these strains in microfluidic experiments.We also performed conventional batch-culture experiments to test cell viability, in conditions similar to those in microfluidics, and tested cell viability with AFH+TOPRO staining and FACS.Each train was tested three times.Plotted on the y-axis are the average fluorescence signal at day 7, normalized by cell size (estimated by forward scatter).