1. Cell Biology
  2. Physics of Living Systems
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Non-genetic inheritance restraint of cell-to-cell variation

  1. Harsh Vashistha
  2. Maryam Kohram
  3. Hanna Salman  Is a corresponding author
  1. Department of Physics and Astronomy, The Dietrich School of Arts and Sciences, University of Pittsburgh, United States
  2. Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, United States
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Cite this article as: eLife 2021;10:e64779 doi: 10.7554/eLife.64779

Abstract

Heterogeneity in physical and functional characteristics of cells (e.g. size, cycle time, growth rate, protein concentration) proliferates within an isogenic population due to stochasticity in intracellular biochemical processes and in the distribution of resources during divisions. Conversely, it is limited in part by the inheritance of cellular components between consecutive generations. Here we introduce a new experimental method for measuring proliferation of heterogeneity in bacterial cell characteristics, based on measuring how two sister cells become different from each other over time. Our measurements provide the inheritance dynamics of different cellular properties, and the ‘inertia’ of cells to maintain these properties along time. We find that inheritance dynamics are property specific and can exhibit long-term memory (∼10 generations) that works to restrain variation among cells. Our results can reveal mechanisms of non-genetic inheritance in bacteria and help understand how cells control their properties and heterogeneity within isogenic cell populations.

eLife digest

All the different forms of life on our planet – including animals, plants, fungi and bacteria – tend to grow, multiply and expand. This happens through a process called cell division, where one cell becomes two; two cells become four; four cells become eight; and so on. Each dividing cell passes on the same set of genetic instructions to its two daughter cells in the form of DNA. Its remaining contents, made up of a mixture of proteins, RNA and other chemicals, also get divided up equally between the two new cells.

This division of cellular assets establishes a form of 'cellular memory', where daughter cells retain very similar properties to their ancestors, which helps them remain stable over time. Yet this memory can fade, and small changes in how a cell looks or acts can appear over many generations of cell division. This happens even when the exact same set of DNA-based genetic instructions have been passed down to daughter cells, confirming that other factors aside from DNA do influence cellular properties and can act to maintain them or introduce variation over time.

Here, Vashistha, Kohram and Salman set out to understand how long cellular memory could be maintained in dividing E. coli bacteria. To do this, they created a technique to track cellular memory as it passed down from a single mother cell to two daughter cells over dozens of generations. Using this technique, Vashistha, Kohram and Salman found that some inherited elements, including cell size and the time cells took to divide, were maintained between mother and daughter cells for almost 10 generations. Other elements, such as the density of proteins inside each cell, started changing almost immediately after daughter cells were formed, and only remained similar for about two generations.

These findings suggest that cellular memory may be long, but is not infinite, and that inheritance of non-genetic elements can help maintain cellular memory and reduce variation among new-born cells for considerable number of generations. Building on this research to achieve a better understanding of cellular memory may allow researchers to harness these insights to direct the evolution of different cellular properties over time. This could have a wide range of potential applications, such as designing new infection control measures for viruses or bacteria; enhancing our ability to grow working organs for tissue transplant; or improving the texture and consistency of cultured, lab-grown meat.

Introduction

One of the main challenges in biological physics today is to quantitatively predict the change over time in cells’ physical and functional characteristics, such as cell size, growth rate, cell-cycle time, and gene expression. All cellular characteristics are determined at all times by the interaction of genetic and non-genetic factors. While genetic information passed from generation to the next is the main scheme, by which cells conserve their characteristics, non-genetic cellular components, such as all proteins, RNA, and other chemicals, are also transferred between consecutive generations and thus influence the state of the cell’s characteristics (or its phenotype) in future generations (Lambert et al., 2014; Robert et al., 2010). The mechanism of genetic information transfer between generations, as well as how this information is expressed, is mostly understood (Casadesús and Low, 2006; Chen et al., 2017; Turnbough, 2019). This information can be altered by rare occurring processes such as mutations, lateral gene transfer, or gene loss (Bryant et al., 2012; Robert et al., 2018). Therefore, changes resulting from genetic alterations emerge over very long timescales (several 10 s of generations). On the other hand, inheritance of non-genetic cellular components, which are subject to a considerable level of fluctuations, can influence cellular characteristics at shorter timescales (Casadesús and Low, 2013; Huh and Paulsson, 2011; Norman et al., 2013; Veening et al., 2008).

Here we focus on understanding how robust cellular characteristics are to intrinsic sources (stochastic gene expression and division noise) and extrinsic sources (environmental fluctuations) of variation, and how cells that emerge from a single mother develop distinct features and over what time scale. While our understanding of variation sources has increased significantly over the past two decades (Ackermann, 2015; Avery, 2006; Elowitz et al., 2002), progress in understanding non-genetic inheritance and its contribution to restraining the proliferation of heterogeneity has been extremely limited. Extensive studies have been dedicated to revealing the different non-genetic mechanisms that influence specific cellular processes and how they are inherited over time (Chai et al., 2010; Govers et al., 2017; Mosheiff et al., 2018; Sandler et al., 2015; Wakamoto et al., 2005). However, the cell’s phenotype is determined by the integration of multiple processes. Thus, to predict the inheritance dynamics of a cellular phenotype, we need to measure the inheritance dynamics directly rather than characterizing the effect of individual inheritance mechanisms separately. Progress in this research has been drastically hindered by the limited experimental techniques that can provide reliable quantitative measurements.

The recent development of the ‘mother machine’ (Brenner et al., 2015; Wang et al., 2010) has provided valuable data of growth and division, as well as protein expression dynamics. These data have been used to gain insight into non-genetic inheritance and cellular memory. The results obtained have consistently showed that non-genetic memory in bacteria is almost completely erased within two generation (Susman et al., 2018; Tanouchi et al., 2015; Wang et al., 2010). This has also been the conclusion of theoretical calculations of cell size autocorrelation (Ho et al., 2018; Susman et al., 2018), which are based on the adder model (Amir, 2014; Taheri-Araghi et al., 2015; Si et al., 2019) for size homeostasis. The consensus of previous experimental studies is founded on the calculation of the autocorrelation function (ACF) for the different measurable cellular properties, such as cell size, growth rate, cell-cycle time, and protein content. It is important to note that in calculating the ACF, measurements of cells from different traps of the mother machine are averaged together. However, small variation in the trap sizes can manifest during the fabrication process, which can lead to distinct environments in different traps (Yang et al., 2018). In addition, cells might experience slightly different environments at different times resulting from thermal fluctuations and their dynamic interaction with their surroundings, i.e. environmental fluctuations can influence the cell’s growth and division dynamics, which in turn can change the cell’s micro-environment through consumption of nutrients and/or secretion of other chemicals. As a result of the individuality of the cell–environment interaction, different micro-niches can be created in different traps (as we demonstrate later in the Results section), which give rise to diverse patterns of growth and division dynamics and therefore distinct ACFs (Figure 1—figure supplement 1) (see also Susman et al., 2018; Yang et al., 2018; Tanouchi et al., 2015). Averaging over many traps, with such various ACFs, will thus erase the dynamics of cellular memory.

To overcome this hurdle, we have developed a new measurement technique, which enables us to separate environmental effects from cellular ones. The technique is based on a new microfluidic device that allows trapping two cells immediately after they divide from a single mother simultaneously and sustain them right next to each other for extended time. Thus, with this technique, we track the lineages of the two sister cells (SCs) from the time of their birth and follow them as they age together for tens of generations. This enables us to measure how two cells that originate from the same mother become different over time, while experiencing exactly the same environment. Thus, we are able to measure the non-genetic memory of bacterial cells for several different traits. Our results reveal important features of cellular memory. We find that different traits of the cell exhibit different memory patterns with distinct timescales. While the cell-cycle time and cell size exhibit slow exponential decay of their memory that extends over several generations, other cellular features exhibit complex memory dynamics over time. The growth rates of two SCs, for example, diverge immediately after division, but re-converge toward the end of the first cell cycle and subsequently persist together for several generations. In comparison, the mean fluorescence intensities, reporting gene expression, are identical in both cells immediately after they separate but diverge within two cell cycles.

Results

Our new microfluidic device, dubbed the ‘sisters machine’ (Figure 1A), consists of 30 μm long narrow trapping channels (1 μm—1 μm) open at one end to a wide channel (30 μm—30 μm), through which fresh medium is continuously pumped to supply nutrients to cells in the traps and wash away cells that are pushed out of them. Here however, every two neighboring trapping channels are joined on the closed end through a v-shaped connection of the same width and height. The tip of the v-shaped connection is made 0.5 μm narrower than the rest of the channel to reduce the likelihood of cells passing from one side to the other (Figure 1B). Therefore, once it happens, the cells at the tip will remain there, while we track their growth and division events, and measure their size and protein expression (Figure 1C,D), until the next cell passage occurs, which can take 10 s of generations (see Figure 1—video 1). The environment in this setup is identical for both cells at the tip of the v-shaped connection, as they are kept in close proximity to each other. This ensures that differences observed between the two cells are due to internal cellular factors only. A comparison of the growth patterns of two pairs of SCs measured in the same experiment, where each pair shares a common trap, reveals that while the growth dynamics of SCs are strikingly similar, they are significantly different between the two pairs (Figure 2A). This is further confirmed by comparing the distribution of the difference between the average growth rates of SCs to that of pairs of cells residing in different channels (Figure 2B). These results highlight the significance of the contribution of environmental fluctuations to cellular growth dynamics and support the existence of different environmental micro-niches within our, and similar, microfluidic setups as mentioned earlier. Note, however, that cell division in the new v-shaped channels does not alter the statistics of SCs’ relative sizes, growth rates, or generation times, in comparison to that observed in the case of division in straight channels (Figure 3).

Figure 1 with 2 supplements see all
Scheme of the experimental setup for tracking sister cells.

(A) Long (30 μm) narrow traps (1 μm—1 μm) are connected on one end and open on the other to wide (30 μm—30 μm) perpendicular flow channels through which fresh medium is pumped and washes out cells that are pushed out of the traps. (B) Illustration of SCs being born from a single mother cell at the tip of the trap, as can also be seen in real fluorescence images of the cells in the trap (C), which are then followed for a long time (see Figure 1—video 1). (D) Section of example traces of two sister cells from the time they are born, which shows how they become different over time.

Individuality of cellular growth dynamics in different microenvironments.

(A) Depicts the cell length of two pairs of SCs measured in two different V-shaped traps as a function of time. The length of each cell is presented in a ‘stitched’ form, where the length of the cell in each cell cycle is adjusted to start from the length of the cell at the end of the previous cycle, ignoring by this the division events. This is done by dividing the length in each cycle by the starting length and multiplying it by the length of the cell at the end of the previous cycle. This presentation emphasizes the difference in the average growth rates measured in different traps. Note, however, that each pair of SCs exhibits similar average growth rate. (B) Probability distribution function (PDF) of the absolute difference in the average growth rate of two SCs is compared with the absolute difference in the average growth rate of two randomly paired cells (RPs) growing in separate traps in the same device (see Figure 4A for further elaboration on random pairing of cells). The standard deviation of the difference for SCs (σSCs) is almost half of the calculated value for RPs (σRPs). This shows that cells grow with different average growth rates in different traps and supports the idea of micro-niche formation in the microfluidic device.

The effect of the v-shaped channel on the distribution of the different cellular characteristics between SCs during division.

(A) Probability distribution Function (PDF) of the difference in the first cell-cycle time of two sister cells after separation relative to the population’s average cycle time under the same experimental conditions. (B) PDF of the difference in cell length between the sister cells immediately after division relative to the population’s average length at the start of the cell cycle. (C) PDF of the difference in the growth rate of the two sister cells after separation relative to the population’s average growth rate. The difference measured in the straight channels here is larger than that measured in the v-shaped channels. This could be due to the fact that the two cells in the mother machine trap are at different distance from the nutrients diffusing from the flow channel into the traps. This has been shown before to result in variation in the cells growth rate (Yang et al., 2018). In all graphs, the blue curves represent the distributions measured in our new device with the v-shaped channels using 194 pairs, while the brown curves were measured in the straight channels of the mother machine using 198 pairs.

Using this setup, we successfully trapped pairs of cells next to each other for 20−160 generations. Images of the cells in both Differential Interference Contrast (DIC) and fluorescence modes were acquired every 3 min. Under our experimental conditions (cells growing in LB medium at 32°C), the average generation time was 34 ± 7 min, which provided ~11 images every generation. The acquired images were used to measure various cellular characteristics as a function of time, including cell size, protein concentration, growth rate, and generation time. To measure cellular memory, we replace the ACF, used in previous studies, with the Pearson correlation function (PCF) between pairs of cells:

(1) PCF(y)(t)=1σy(1)σy(2)i=1n(yi(1)(t)-<y(1)>).(yi(2)(t)-<y(2)>)

where y is the cellular property of interest, t is the measurement time, n is the number of cell pairs measured, σy is the population standard deviation of y, and (1) and (2) represent the two cells being considered. PCF(y)(t) is therefore a measure of the correlation between the values of a specific cellular property at time t. We use this correlation function to compare three types of cell pairs (Figure 4A): (1) SCs are cells that originate from the same mother at time 0, and therefore, the value of PCF at time 0 is 1. (2) Neighbor cells (NCs) are cells that reside next to each other at the tip of the v-shaped connection. However, NCs are cells that do not originate from the same mother. They are cells that happen to enter into both sides of the same v-shaped channel from the start of the experiment. We initiate their tracking though, only when they happen to divide at the same time, such that at time 0, they are both at the start of a new cell cycle, and if their length is almost identical at that point in time. This choice is to ensure that any long-term correlation measured in SCs does not stem from a size homeostasis mechanism, which would maintain the size of both cells similar for several generations if they start similar. (3) Random cell pairs (RPs) are cells that reside in different traps and their lineages are aligned artificially even though they can be measured at different times. In this case, t is measured relative to the alignment point, which is chosen to be at the start of the cell cycle for both cells. Since NCs and RPs do not originate from the same mother at time 0, the PCF is measured from the first generation only, and we set it to be 1 at time 0. Comparing the correlation of NCs, which experience the same environmental conditions at the same time, with that of RPs allows us to determine the effect of the environment on the correlation. On the other hand, the comparison of SCs with NCs provides the effect of cellular factors (i.e. epigenetics) that are shared between SCs, on the correlation function. This in turn allows us to determine the cellular memory of a specific property resulting from shared information passed on from the mother to the two sisters (see Appendix for the mathematical relationship between the different measures).

Figure 4 with 5 supplements see all
PCF of cell-cycle time and cell size measured in cell pairs as a function of number of generations.

(A) Three types of pairs used for calculating PCF. (B) PCF of cell-cycle time for SCs (122 pairs from three separate experiments) exhibit memory that extends for almost nine generations (half lifetime ∼ 4.5 generations). This is ∼3.5× longer than the half lifetime of NCs PCF (calculated using a 100 pairs from three separate experiments) (C), which is comparable to the ACF (half lifetime ∼1 generation). (D) Similarly, SCs exhibit strong cell size correlation that decays slowly over a long time (half lifetime ∼3.5 generations), while (E) NCs show almost no correlation in cell size similar to ACF of initial sizes (half lifetime ∼1 generation). For details of the cell-cycle time PCF and errors calculation see SI and Figure 4—figure supplements 1 and 2. PCF values for cell size were calculated in similar way to cell-cycle time and were then averaged over a window of six consecutive time frames (15 min time window) (See Figure 4—figure supplement 4 for raw data). Shaded area represents the standard deviation of the average. The equations in the graphs represent the best fit to the PCF depicted in each graph with g is generation number.

We measured the correlations between the different pair types for cell-cycle time (T). We find that T of SCs remain strongly correlated for up to eight successive cell divisions (Figure 4B also see Figure 4—figure supplements 1 and 2) regardless of the environmental conditions (Figure 4—figure supplement 3), while the NCs correlation decays to zero within three generations (Figure 4C). These results clearly reveal the effects of epigenetics and environmental conditions on cellular memory when compared to the RPs correlation, which as expected decays to zero within one generation similar to the ACF (Figure 4B,C).

Next, we applied our method to cell size. Also here, our measurements show that SCs correlation decays slowly over ∼7 generations (Figure 4D), while the correlation of NCs exhibit fast decay to zero within two generations similar to the ACF (Figure 4E). Note that RPs exhibit no correlation from the start of the measurement (Figure 4D,E). These results further demonstrate the existence of strong non-genetic memory that restrains the variability of cell size between SCs for a long time. Unlike the cell-cycle time however, the effect of both epigenetic factors and environmental conditions on the cellular memory appears to extend for a slightly shorter time.

To quantify the increase in variability among cells along time differently, we measured the change in the variance of a cellular property as time advances, which is expected to reach an equilibrium saturation value at long timescales. Measuring how the variance reaches saturation provides information about cellular memory and the nature of forces acting to restrain variation. The cellular memories of cell-cycle time and length, measured using this method, agree well with our previous PCF results (Figure 5—figure supplements 1 and 2). Thus, we have measured the relative fluctuations in the exponential elongation rate of the cell pairs δα defined as:

(2) δα(t)=α(1)(t)-α(2)(t)

where α(t)=(dlnL/dt) is the exponential elongation rate of the cell, L(t) is the cell length at time t, and (1) and (2) distinguish the cell pair (Figure 5—figure supplement 3). As expected, δα for all pairs of lineages is randomly distributed with δα = 0 (Figure 5—figure supplement 3), as the elongation rate of all cells fluctuate about a fixed value identical for all cells in the population and depends on the experimental conditions. The variance of δα for both RPs (σδαRPs2) and NCs (σδαNCs2) was found to be constant over time and is similar for both types of cell pairs (Figure 5A). However, the variance of δα for SCs (σδαSCs2) exhibits a complex pattern (Figure 5B), which eventually converges to the same value as RPs (σδαRPs2) and NCs (σδαNCs2). The time it takes for (σδαSCs2) to reach saturation extends over almost eight generations, which again reflects a long memory resulting from epigenetic factors. These results show that, unlike cell-cycle time and cell length, elongation rates of SCs immediately after their division from a single mother exhibit the largest variation. This variation decreases to its minimum value within a single cell-cycle time (∼30 min). To understand the source of this large variation immediately following separation, we have measured the growth rate over a moving time window of 6 min throughout the cell cycle and compared the results between SCs. Our comparison clearly shows that an SC that receives a smaller size-fraction from its mother exhibits a larger growth rate immediately after division. The growth rate difference between the small and large sisters decreases to almost zero by the end of the first cell cycle after separation (Figure 5B inset). This result reveals that the exponential growth rate of a cell immediately after division inversely scales with the size-fraction the cell receives from its mother (see also Kohram et al., 2020). It also demonstrates that the difference in the growth rates between SCs changes during the cell cycle, indicating that they are not constant throughout the whole cycle as has been accepted so far (Godin et al., 2010; Soifer et al., 2016; Wang et al., 2010). Note that similar results have been reported recently for Bacillus subtilis (Nordholt et al., 2020), where it was observed that the growth rate is inversely proportional to the cell size at the start of the cell cycle and changes as the cell-cycle advances.

Figure 5 with 4 supplements see all
Variance (σδα2) as a function of the time.

(A) σ2 of the growth rate difference (δα) between cell pairs for NCs and RPs as a function of time (see Figure 5—figure supplement 3 for the details of the calculation). The variance for both pair types does not change over time. (B) δα of SCs, on the other hand, exhibits large variance immediately after separation (∼50%) higher than NCs and RPs and rapidly drops to its minimum value within one generation time (∼30 min), and increases thereafter for 4 hr (∼8 generations) until saturating at a fixed value equivalent to that observed for NCs and RPs. Each point in A and B is the average over three frames moving window, and the shaded area represents the standard deviation of that average. (C) Unlike δα, δf of SCs increases to its saturation value within ∼2 generations (see Figure 5—figure supplement 4 for the details of the calculation). Here, each point represents the average of three different experiments, and the shaded part represents the standard deviation.

We have also examined how the protein concentration varies over time between the two cells by measuring the concentration of GFP (green fluorescent protein), via its fluorescence intensity, expressed from a constitutive promoter in a medium copy-number plasmid. The variance of fluorescence intensity difference between cell pairs δf was calculated as for the growth rate (see Figure 5—figure supplement 4 for details). Upon division, soluble proteins are partitioned symmetrically with both daughters receiving almost the same protein concentration. As expected, σδfSCs2 starts from ∼0 initially, and diverges to reach saturation within two generations (Figure 5C). On the other hand, NCs and RPs exhibit constant variance throughout the whole time, with σδfRPs2 twice as large as σδfNCs2, which reflects the influence of the shared environment resulting in additional correlations between NCs. The relatively short-term memory in protein concentration may be protein specific (Figure 5—figure supplement 4), or it could reflect the fact that in this case the protein is expressed from a plasmid. Nevertheless, this result indicates that cellular properties are controlled differently and can exhibit distinct memory patterns. It is important therefore to distinguish between different cellular characteristics and to examine their inheritance patterns individually.

Discussion

There has been a rising interest over the past two decades in understanding the contribution of epigenetic factors to cellular properties and their evolution over time. Here, we introduce a new measurement technique that can separate environmental fluctuations from cellular processes. This allows for quantitative measurement of non-genetic memory in bacteria and reveals its contribution to restraining the variability of cellular properties. Our results show that the restraining force dynamics vary significantly among different cellular properties, and its effects can extend up to sim10 generations. In addition, the growth rate variation emphasizes the effect of division asymmetry, which can help in understanding the mechanism that controls cellular growth rate. The slow increase in the growth rate variance that follows reflects the effect of inheritance. Since both cells inherit similar content, which ultimately determines the rate of all biochemical activities in the cell and thus its growth rate, it is expected that both cells would exhibit similar growth rates once they make up for the uneven partitioning of size acquired during division. The short memory we see in the protein concentration, on the other hand, suggests that cells are less restrictive of their protein concentration. This might be protein specific, or for proteins that are expressed from plasmids only. Nevertheless, these results highlight the importance of such studies, and how this new method can help answer fundamental questions about non-genetic memory and variability in cellular properties.

Finally, in order to understand and characterize the evolution of population growth rate as it reflects its fitness, there is a need to incorporate inheritance effects, which has been thus far assumed to be short lived. This study confirms that cellular memory can persist for several generations, and therefore limits the variation in certain cellular characteristics, including growth rate. Such memory should be considered in future studies and has the potential of changing our perception of population growth and fitness.

Materials and methods

Key resources table
Reagent type (species)
or resource
DesignationSource or referenceIdentifiersAdditional information
Strain, strain
background
(Escherichia coli)
MG1655Coli Genetic Stock
Center (CGSC)
6300F-, λ-, rph-1
Recombinant
DNA reagent
pZA3R-GFPLutz and Bujard, 1997https://academic.oup.com/nar/article/25/6/1203/1197243GFP expressed from
the λ Pr promoter
Recombinant
DNA reagent
pZA32wt-GFPLutz and Bujard, 1997https://academic.oup.com/nar/article/25/6/1203/1197243GFP expressed from
the LacO promoter
Software, algorithmMATLABMathWorksN/A
Software, algorithmOuftiPaintdakhi et al., 2016http://oufti.org/

Device fabrication

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The master mold of the microfluidic device was fabricated in two layers. Initially, the growth channels for the cells were printed on a 1 mm × 1 mm fused silica substrate using Nanoscribe Photonic professional (GT). The second layer, containing the main flow channels that supply nutrients and wash out excess cells, was formed using standard soft lithography techniques (Jenkins, 2013; Martinez-Duarte and Madou, 2016). SU8 2015 photoresist (MicroChem, Newton, MA) was spin coated onto the substrate to achieve a layer thickness of 30 μm and cured using maskless aligner MLA100 (Heidelberg Instruments). Following a wash step with SU8 developer, the master mold was baked and salinized. The experimental setup described in the main text was then prepared using this master mold, from PDMS prepolymer and its curing agent (Sylgard 184, Dow Corning) as described in previous studies.

Cell culture preparation

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The wild-type MG1655 E. coli bacteria were used in all experiments described. Protein content was measured through the fluorescence intensity of green fluorescent protein (GFP) inserted into the bacteria on the medium copy-number plasmid pZA (Lutz and Bujard, 1997). The expression of GFP was controlled by one of two different promoters, the Lac Operon (LacO) promoter was used to measure the expression level of a metabolically relevant protein, while the viral λ-phage Pr promoter was used to measure the expression level of a constitutive metabolically irrelevant protein.

Two testing media were used in our experiments. M9 minimal medium supplemented with 1 g/l casamino acids and 4 g/l lactose (M9CL) was used for measuring the expression level from the LacO Promoter, and LB medium was used for all other experiments. The cultures were grown over night at 30°C, in either LB or M9CL medium depending on the intended conditions. The following day, the cells were diluted in the same medium and regrown to early exponential phase, optical density (OD) between 0.1 and 0.2. When the cells reached the desired OD, they were concentrated into fresh testing medium to an OD∼0.3 and loaded into a microfluidic device. Once enough cells were trapped in the channels, fresh testing medium was pumped through the wide channels of the device to supply the trapped cells with nutrients and wash out extra cells that are pushed out of the channels. The cells were allowed to grow in this device for days, while maintaining the temperature, using a microscope top incubator (Okolab, H201-1-T-UNIT-BL).

Image acquisition and data analysis

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Images of the channels were acquired every 3 min (in LB medium) or 7 min (in M9CL medium) in DIC and fluorescence modes using a Nikon eclipse Ti2 microscope with a 100× objective. The size and protein content of the SCs were measured from these images using the image analysis software Oufti (Paintdakhi et al., 2016). The data were then used to generate traces such as in Figure 1D, and for further analysis as detailed in the main text. Single-cell measurements were analyzed using MATLAB. Sample ACFs, Pearson correlation coefficients, sample distributions, and curve fitting were all calculated by their implementations in MATLAB toolboxes.

Appendix 1

Mathematical framework

Assuming that x(t) is a measurable cellular property, such as cells size, growth rate, etc. We can present it as:

x(t)=x+δx(t)

where x is the average of x(t) over time, and δx is its fluctuations around x. The difference of this measured property between two cells:

(4) Δx(t)=x1(t)-x2(t)

where 1 and 2 represent the two different cells, will average to zero, that is, <Δx0. Its variance on the other hand will be:

(5) σΔx2(t)=<Δx(t)2>-<Δx(t)>2=2<δx2(t)>-2<δx1(t)δx2(t)>

where <δx2>=<δx12>=<δx22> is the variance of x, which is the same for all cells, and <δx1(t)δx2(t)> is the covariance of the fluctuations in both cells, which when normalized by σδx1. σδx2 would give the correlation, that is, the PCF, between the two variables. On the other hand, if we assume that x is determined by two factors, internal cellular composition (I(t)) and external environmental conditions (E(t)), such that:

(6) x(t)=I(t)+E(t)

Then σΔx2(t)=<[(I1-I2)+(E1-E2)]2> would depend on whether the two cells share the same environment and/or the same cellular compositions. Therefore, random pair of cells (RPs), which reside in different channels and thus do not share neither the environment nor the internal composition would exhibit a variance:

(7) RPs:σΔx2(t)=2σI2+2σE2+4cov(I,E)

where σI2=<I2>-<I>2 is the variance in the internal composition of the cell (similar for all cells and constant over time), σE2=<E2>-<E>2 is the variance in the environmental conditions (also the same for all cells in the same experiment), and cov(I,E) is the covariance of the environment and the internal composition of the cell, which as discussed earlier can influence each other in a trap-specific manner. However, averaging many measurements from different traps erases this effect as clear from Figure 1—figure supplement 1 (see also Susman et al., 2018). On the other hand, for cells that share the environment but not their internal composition, that is, neighboring cells (NCs), the variance would be:

(8) NCs:σΔx2(t)=2σI2

Note that when the NCs are chosen to have similar size and divide simultaneously at time zero, this variance for cell size would be small initially and its increase would not be constrained by the epigenetic similarity between the two cells as in the case of sister cells (SCs). And finally, for SCs, which share both the environment and their internal composition, which means that I1 and I2 can be correlated, then:

(9) SCs:σΔx2(t)=2σI2-2cov(I1,I2)

where cov(I1,I2) is the covariance of the internal states of the cells as a function of time, that is, the non-genetic memory of the cell. Using the definitions above, it is easy to see the relationship between the variance and the PCF. It is also clear that the difference between NCs and RPs variances would provide the contribution of the environment, while the difference between SCs and NCs variances would give the contribution of the internal composition of the cell to the variance, or the epigenetic memory.

Appendix 1—table 1
The calculated values of the PCF for SCs were verified by calculating the slopes of best fits to the plots of TimeA vs TimeB graphs (Figure 4—figure supplement 2).
GenerationPCF ±σPCFSlope of best fit line (Figure 4—figure supplement 2)
1st0.86 ± 0.020.87
2nd0.65 ± 0.050.69
3rd0.54 ± 0.060.44
4th0.36 ± 0.070.42
5th0.28 ± 0.080.25
6th0.23 ± 0.080.25
7th0.12 ± 0.090.11
8th0.23 ± 0.090.25
9th0.00 ± 0.090.00

Appendix 2

Supplementary material

PCF and error calculation

The PCF was calculated using following equation:

(3) PCF(y)(t)=1σy(1)σy(2)i=1n(yi(1)(t)-<y(1)>).(yi(2)(t)-<y(2)>)

and the standard deviation (Bowley, 1928):

(4) σPCF=(1-PCF2)n

where n is the number of cell pairs considered in the calculation.

Data availability

All data generated or analyzed during this study, are available on Zenodo at http://doi.org/10.5281/zenodo.4476617.

The following data sets were generated
    1. Vashistha H
    2. Kohram M
    3. Salman H
    (2021) Zenodo
    Non-genetic inheritance restraint of cell-to-cell variation.
    https://doi.org/10.5281/zenodo.4476617

References

  1. Book
    1. Martinez-Duarte R
    2. Madou MJ
    (2016)
    Microfluidics and Nanofluidics Handbook
    CRC Press.

Decision letter

  1. Petra Anne Levin
    Reviewing Editor; Washington University in St. Louis, United States
  2. Aleksandra M Walczak
    Senior Editor; École Normale Supérieure, France
  3. Sattar Taheri-Araghi
    Reviewer; California State University, Northridge, United States
  4. Minsu Kim
    Reviewer; Emory University, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

[Editors’ note: the authors submitted for reconsideration following the decision after peer review. What follows is the decision letter after the first round of review.]

Thank you for submitting your work entitled "Non-genetic inheritance restraint of cell-to-cell variation" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Minsu Kim (Reviewer #2).

Our decision has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife at this time. However, if you feel you can satisfy the reviewers' comments, we encourage you to resubmit.

As you will see from the reviews which are copied below, all three reviewers as well as the Reviewing Editor were enthusiastic about your innovative microfluidic device and its ability to assess sister cell development and the impact of microenvironment on cell fate. However, in addition to specific concerns listed below, there was consensus that the data themselves represent a more modest advance over previous work. This was unfortunate, as reviewer 2 noted, as the set-up has the potential to permit disentangling of the effect of micro-environment and inheritance, a thorny and important problem that has not yet been solved.

Given the dichotomy of opinion about the potential impact of the approach versus the included results, we would encourage you to consider obtaining additional, data specifically addressing the relative effect of microenvironment and inheritance on cell fate. If you are amenable to this idea, eLife would be happy to consider the manuscript as a new submission at a later date. At the same time, we recognize that obtaining additional data is time consuming and completely understand if you would prefer to publish elsewhere.

Reviewer #2:

This article describes correlation timescale of various cellular properties. The experimental design is ingenious, and findings shed new light on epigenetic inheritance. I believe that this article warrants publication in eLife.

There are two points that are not clear to me.

1) The first is the disagreement with previous ACF measurements with mother machine data for similar traits. The author argues "These cells might experience slightly different environments at different times resulting from thermal fluctuations and their dynamic interaction with their surroundings […] Thus, averaging over many traps erases the dynamics of cellular memory". I find it hard to imagine that significant variation in tiny microfluidic traps that are flushed actively by fresh medium. In principle, this could be easily checked by performing ACF for each trap (rather than averaging over many traps)?

2) Figure 3C. What is the dashed line for? What does it means that the correlation drops below the dash line immediately within a one generation, before it slowly goes back?

Reviewer #3:

This is an interesting paper introducing a microfluidics system, the "sister machine", that traps two Escherichia coli sister cells in a v-shaped ending, which allows to study the progeny of each sister over future generations. This is a novel approach and the device, in fact, allows certain measurements that were not possible with previous microfluidics systems. The widely-used mother machine traps one mother cell in each channel, hence the sister cell is eventually pushed away from the channel within several generations.

With this new device, authors performed live cells microscopy experiments and proceeded with detailed image and statistical analysis of individual cells in three different pairing categories: (1) Sister cells (SCs), (2) Neighbor cells (NCs), and (3) Random cell pairs (Rps). The sister cells are form the same mother cells. The neighbor cells are from random mothers but positioned next to each other similar to two sister cells. And the random pairs are cells from random mothers in different channels. Comparison between these three categories reveals long-term memory in specific cellular characteristic (size, generation time, growth rate, protein expression, etc) that may arise only in sister cells progenies.

The quantities that were measured in this work are (1) cell size, (2) generation time, (3) elongation rate, (4) fluorescent intensity (a proxy for protein expression). Authors presented Pearson- and auto-correlation of each pairing category to show there are long-term effects (up to ~9 generations) among sister cells that are not found in random pairs or non-sister neighbor cells.

Overall, this is an interesting manuscript mainly due to the introduction of the v-shaped microfluidics device and I do recommend it for publication. However, I am concerned that the focus of the results in the main text are on the cells size and generation time, which are somehow predictable from our prior knowledge on cell size (as I explain below in 3e). As such, the data does not fully reveal the potential of the device. Perhaps focus on protein expression data is a better choice for demonstrating sister cell correlations which in fact show distinct feature as depicted in Figure 3C.

Below I have detailed point-by-point comments. Most of the items blow concerned with presentations and are rather suggestions.

1) Abstract

a) The authors mention that they "introduce a new experimental method" and discuss the findings and results of using the device. But unfortunately there is not mentioned of the new experimental method, which I think is the single most important part of this work. I suggest including a short description of sisters cells trapping early in the Abstract.

b) I also suggest adding a few words to elucidate "physical and functional characteristics" term in the Abstract.

2) Introduction

a) The opening paragraph contains many terms that need to defined or elucidated such as "physical and functional characteristics", "cellular characteristics", "the state of the cell", and "non-genetic cellular components."

b) The statement "… non-genetic memory in bacteria is almost completely erased within one generation" does not apply to every parameter. Cell-size is known to have a long-term memory as authors discuss later.

c) Because of the small size, this is not clear how much "different environment" cells may experience in a microfluidics system. Thus, the statement "These cells might experience slightly different environments at different times resulting from.…", needs to be backed by data or references.

d) Again, more important than the environmental fluctuation, the significance of the device is that it allows a certain tracking of the lineage which was not possible with mother machine. I believe this needs to be emphasized more clearly.

3) Results

a) Is there any side-effects from physical confinement and bending of the mother cell at the v-shaped end? This needs detailed discussion.

b) Since number of generations and imaging interval is mentioned, it helps if authors add the cells' average generation time too. The explanation of NCs and the difference between them and SCs is not very clear in the text. The figure made it clear though.

c) "Since NCs and RPs do not originate from the same mother at time 0, the PCF is measured from the first generation only, and we set it to be 1 at time 0." Why is the correlation set to 1? If they are from different mother cells, isn't that expected to be zero?

d) Figure 2 has number of issues.

– With no panel title it is not clear what quantity is plotted without reading the caption.

– Axes limit need adjustment. Some error bars span outside the border.

– The variable “g” is not defined. Is it the generation number?

– The grid lines are not necessary.

e) The E. coli cell-size is known to have long-term memory based on the adder model. Thus, the progeny of each sister cell will retain the correlation with the mother cell for a number of generations. Thus it is not a surprise to see stronger Pearson correlation between the progenies of a sister pair that random pairs. The same goes with the generation time. Perhaps similar data for protein expression shows something that has not been studied before?

f) Presentation of all panels of Figure 3 can be improved by eliminating grid lines and using a solid line with shades to depict error bars.

Reviewer #4:

The paper by Vashistha et al. presents a new method to investigate the inheritance and memory of cellular characteristics in bacteria, such as cell cycle properties (cell size, division time…), protein content or growth rate. This method is based on the development of a new microfluidic device, that the authors name the "sisters machine", that allows keeping sister cells created from a single mother close to one another in a v-shaped channel, for tens of generation. These sister cells and their descendants therefore share the same microenvironment. The authors can then compute the correlation between the characteristics of the two sister cells and their progeny as a function of time. They can then compare this correlation function to the same correlation obtained on non-related cells sharing the same microenvironment, or on non-related cells in different channels/microenvironment. In doing so they aim at disentangling the effect of epigenetic memory and micro-environment fluctuations.

I think introducing a new tool to disentangle environment fluctuations and epigenetic memory is very interesting, and this new microfluidic chip offers great possibilities in that regard. Given the small dimensions of the chip and the precision that is probably needed for the tip of the v-shaped channels (so that sister cells can be trapped for generations), the development of this sisters machine represents an impressive technical achievement. The data produced in this work is new and very interesting. However, I think this paper does not present the theoretical foundations that are required to interpret the results and quantify inheritance of cellular characteristics. I will list below several issues that are completely unclear for me and that would probably all be resolved by defining a clear theoretical framework.

– I do not understand why the autocorrelation functions (ACF) vanish so fast (Figure 2B and C). The authors say (l.60-61) that averaging over many channels erases the memory. But I do not see why/how this would be the case. I believe there are several models in which this is not true. For simplicity let's take a non-normalized form for the ACF of X(t), i.e. E(X(t)X(t+tau)) and assume all the variables are of average 0. Let's say that the random variable of interest at time t X(t) (for example cell cycle time) is the sum of an environment-dependent noise N(t) and an environment-independent variable Y(t). Then the ACF of X is the sum of the ACF of N(t) and the ACF of Y(t) (assuming independence of Y and N). So the inheritance of environmental fluctuations and the inheritance of epigenetic fluctuations are entangled, but the ACF does not vanish.

– From the definition of the PCF (Equation 1) I can see clearly why the PCF decreases with time for SC but I cannot understand why it is not constant for NC in Figure 2 (the only way I see to have a decreasing function for NC is that the environmental fluctuations are non-stationary, and their variance decreases with time)

– Likewise I understand the trends in Figure 3—figure supplement1 panel D, where the variance is constant for NC and RP and increases for SC. But why is it different in Figure 3—figure supplement 2 ?

To answer these questions and all the others that could be raised by this interesting data, I think a theoretical framework has to be clearly defined. Maybe the authors had such a framework in mind when interpreting the data. In this case I would recommend that they define it clearly in the paper. If on the contrary, the development of such a framework is beyond the scope of this work, then simulations should be provided and compared with the data. Otherwise it is very difficult to interpret the data and demonstrate the validity of the method.

Another important point that was unclear to me : how are NC pairs of cells defined? I understood that they are not sisters but how can the authors be sure that they are not cousins (1st, 2nd, 3rd, 4th cousins…)? In which case the NC cells at time 0 would be the same as the SC cells but at a larger generation (this would explain why the PCF of NC cells decrease in Figure 2). This should be clarified in the text.

[Editors’ note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Non-genetic inheritance restraint of cell-to-cell variation" for further consideration by eLife. Your revised article has been evaluated by Aleksandra Walczak (Senior Editor) and a Reviewing Editor.

The manuscript has been improved but there are a few small remaining issues that need to be addressed before acceptance. In particular, please note the comments from reviewer 1 regarding the need to clarify the tracking period in the appendix, from reviewer 2 requesting proper citation of relevant articles from the cell size literature, and from reviewer 3 requesting clarification of how your results compare with those of previous studies and a more thorough explanation of the data in Figure 1—figure supplement 1. See full reviewer comments below:

Reviewer #1:

The manuscript by Vashistha et al. is a revised manuscript. My concerns about the previous version were satisfyingly addressed in the present version and in the authors' answers. So I recommend this manuscript for publication

I just have a minor comment :

I now understand that NC cells are tracked from a point where they divide at the same time and have approximately the same lengths (this is now clearly stated in the present version, I hadn't understood from the previous one…). However in the appendix where the mathematical framework is presented (which I find very useful) it is not stated and I think it may be misleading. I think it could be useful to mention that in the appendix too

Reviewer #2:

Since cell size is discussed in the manuscript, I suggest authors to cite related and key publications in the field of cell-size too.

Reviewer #3:

I believe that Figure 1—figure supplement 1 is new. I like this graph, but it requires further explanation. The legend says "This presentation emphasizes the difference in the average growth rates measured in different traps. Note however, that each pair of SCs exhibits similar average growth rate." Can authors quantify the difference and similarity? It is hard to deduce that numbers from the graph. And also, do authors know whether this variation from different traps is also a problem in previous experimental set-up (mother machine)?

https://doi.org/10.7554/eLife.64779.sa1

Author response

[Editors’ note: the authors resubmitted a revised version of the paper for consideration. What follows is the authors’ response to the first round of review.]

Reviewer #2:

This article describes correlation timescale of various cellular properties. The experimental design is ingenious, and findings shed new light on epigenetic inheritance. I believe that this article warrants publication in eLife.

There are two points that are not clear to me.

1) The first is the disagreement with previous ACF measurements with mother machine data for similar traits. The author argues "These cells might experience slightly different environments at different times resulting from thermal fluctuations and their dynamic interaction with their surroundings […] Thus, averaging over many traps erases the dynamics of cellular memory". I find it hard to imagine that significant variation in tiny microfluidic traps that are flushed actively by fresh medium. In principle, this could be easily checked by performing ACF for each trap (rather than averaging over many traps)?

This is a good point, and we apologize for not including this information before. We have now added a new supplementary figure (Figure 1—figure supplement 1B) that depicts single traps ACFs and their average. As can be seen in the figure, each trap exhibits different behavior with distinct ACF, and the average ACF decays exponentially with a decay time of 2 generations. We address this in the text that describes Figure 2, where we also cite 2 other references that have presented similar calculations with the same result, namely references: Tanouchi et al., 2015, and Susman et al., 2018.

2) Figure 3C. What is the dashed line for? What does it means that the correlation drops below the dash line immediately within a one generation, before it slowly goes back?

We think that the reviewer means the dashed line in Figure 3B. In that case, the line represents the average variance (not correlation) measured for the NCs and RPs depicted in Figure 3A. The fact that the variance of SCs is higher at time zero and drops immediately below that line within one generation before it slowly goes back up reflects that immediately after separation, the sisters exhibit large growth rate variance (the variance is actually larger than the variance exhibited by unrelated cells, i.e. NCs and RPs represented by the dashed line), which means lower correlation. However, they become very similar towards the end of the first cell cycle, i.e. more correlated. After the first cell cycle, the growth rates of the SCs start to diverge again but very slowly until they exhibit similar variance to unrelated cells after ~7 generations. We explain this now in the main text addressing the figure. This is discussed in the second paragraph before the Discussion section.

Reviewer #3:

This is an interesting paper introducing a microfluidics system, the "sister machine", that traps two Escherichia coli sister cells in a v-shaped ending, which allows to study the progeny of each sister over future generations. This is a novel approach and the device, in fact, allows certain measurements that were not possible with previous microfluidics systems. The widely-used mother machine traps one mother cell in each channel, hence the sister cell is eventually pushed away from the channel within several generations.

With this new device, authors performed live cells microscopy experiments and proceeded with detailed image and statistical analysis of individual cells in three different pairing categories: (1) Sister cells (SCs), (2) Neighbor cells (NCs), and (3) Random cell pairs (Rps). The sister cells are form the same mother cells. The neighbor cells are from random mothers but positioned next to each other similar to two sister cells. And the random pairs are cells from random mothers in different channels. Comparison between these three categories reveals long-term memory in specific cellular characteristic (size, generation time, growth rate, protein expression, etc) that may arise only in sister cells progenies.

The quantities that were measured in this work are (1) cell size, (2) generation time, (3) elongation rate, (4) fluorescent intensity (a proxy for protein expression). Authors presented Pearson- and auto-correlation of each pairing category to show there are long-term effects (up to ~9 generations) among sister cells that are not found in random pairs or non-sister neighbor cells.

Overall, this is an interesting manuscript mainly due to the introduction of the v-shaped microfluidics device and I do recommend it for publication. However, I am concerned that the focus of the results in the main text are on the cells size and generation time, which are somehow predictable from our prior knowledge on cell size (as I explain below in 3e). As such, the data does not fully reveal the potential of the device. Perhaps focus on protein expression data is a better choice for demonstrating sister cell correlations which in fact show distinct feature as depicted in Figure 3C.

Below I have detailed point-by-point comments. Most of the items blow concerned with presentations and are rather suggestions.

1) Abstract

a) The authors mention that they "introduce a new experimental method" and discuss the findings and results of using the device. But unfortunately there is not mentioned of the new experimental method, which I think is the single most important part of this work. I suggest including a short description of sisters cells trapping early in the Abstract.

We have added a short description of the method as suggested.

b) I also suggest adding a few words to elucidate "physical and functional characteristics" term in the Abstract.

We have explained “physical and functional characteristics” better now.

2) Introduction

a) The opening paragraph contains many terms that need to defined or elucidated such as "physical and functional characteristics", "cellular characteristics", "the state of the cell", and "non-genetic cellular components."

We have now added definitions for all these terms.

b) The statement "… non-genetic memory in bacteria is almost completely erased within one generation" does not apply to every parameter. Cell-size is known to have a long-term memory as authors discuss later.

Previous measurements of cell-size autocorrelation function by the mother machine has consistently showed no memory, as seen in all the references we cite there including Wang et al., 2010, Tanouchi et al., 2015, and Susman et al., 2018. Indeed, our measurements do show that there is a long memory including in cell-size, however, this is a new result, and the statement the reviewer is referring to here is meant to convey what is the current state of the measurements available in order to emphasize the importance of our new results presented here.

c) Because of the small size, this is not clear how much "different environment" cells may experience in a microfluidics system. Thus, the statement "These cells might experience slightly different environments at different times resulting from.…", needs to be backed by data or references.

We have explained this better now, and added in addition to the references, a supplementary figure (Figure 1—figure supplement 1B), which shows the distinct ACFs measured in different traps, and their average that shows no memory.

d) Again, more important than the environmental fluctuation, the significance of the device is that it allows a certain tracking of the lineage which was not possible with mother machine. I believe this needs to be emphasized more clearly.

We emphasize now that we do track two lineages of sister cells simultaneously using this technique for tens of generations.

3) Results

a) Is there any side-effects from physical confinement and bending of the mother cell at the v-shaped end? This needs detailed discussion.

We thank the reviewer for reminding us of this important test. We now added a new supplementary figure (Figure 1—figure supplement 2) that compares the effect of division, in our V-shaped device to that in the mother machine, on different parameters. Our results show that there is almost no distinct difference between division in the straight traps of the mother machine and in the V-shaped ones. The largest difference is observed in the growth rate, where the division in the mother machine exhibits larger variation between the two cells than in our device. This could be due to the fact that in the mother machine, the daughter cell is always closer to the food source (diffusing from the flow channel into the trap) than its mother, whereas in the V-Shaped device, both cells are at the same distance from the food source. Therefore, the similarity in our device between the two cells immediately after division is either the same or larger than in the mother machine as expected.

b) Since number of generations and imaging interval is mentioned, it helps if authors add the cells' average generation time too. The explanation of NCs and the difference between them and SCs is not very clear in the text. The figure made it clear though.

The average generation time is now provided in the same paragraph. And the difference between NCs and SCs is clarified.

c) "Since NCs and RPs do not originate from the same mother at time 0, the PCF is measured from the first generation only, and we set it to be 1 at time 0." Why is the correlation set to 1? If they are from different mother cells, isn't that expected to be zero?

This is a good question that we should clarify more. We do that for reasons of comparing the decay time of the correlation between NCs with that of SCs. We choose the NCs such that their size at time 0 is almost identical similar to SCs, and setting the correlation at time 0 to 1, is like assuming that NCs originate from a single mother but they do not share the same epigenetic information. This comparison actually emphasizes that the correlation we measure between SCs is not due to the fact that they have similar size at time 0 like NCs, but rather due to the fact that they share epigenetic information. We explain this point more clearly now in the text.

d) Figure 2 has number of issues.

– With no panel title it is not clear what quantity is plotted without reading the caption.

– Axes limit need adjustment. Some error bars span outside the border.

– The variable “g” is not defined. Is it the generation number?

– The grid lines are not necessary.

All issues have been fixed.

e) The E. coli cell-size is known to have long-term memory based on the adder model. Thus, the progeny of each sister cell will retain the correlation with the mother cell for a number of generations. Thus it is not a surprise to see stronger Pearson correlation between the progenies of a sister pair that random pairs. The same goes with the generation time. Perhaps similar data for protein expression shows something that has not been studied before?

The prediction of the adder model is that the correlation time of size is ~2 generations. We now add two citations that show this calculation. Namely: Susman et al., 2018, and Ho et al., 2018. We also would like to point out that all measurements of the ACF for size decays over ~2 generation. This is much smaller than what our measurements show, and that is why we consider this result to be significant. We hope that the reviewer will agree to reconsider this point in light of the references we provide here.

f) Presentation of all panels of Figure 3 can be improved by eliminating grid lines and using a solid line with shades to depict error bars.

The suggestions have been included.

Reviewer #4:

The paper by Vashistha et al. presents a new method to investigate the inheritance and memory of cellular characteristics in bacteria, such as cell cycle properties (cell size, division time…), protein content or growth rate. This method is based on the development of a new microfluidic device, that the authors name the "sisters machine", that allows keeping sister cells created from a single mother close to one another in a v-shaped channel, for tens of generation. These sister cells and their descendants therefore share the same microenvironment. The authors can then compute the correlation between the characteristics of the two sister cells and their progeny as a function of time. They can then compare this correlation function to the same correlation obtained on non-related cells sharing the same microenvironment, or on non-related cells in different channels/microenvironment. In doing so they aim at disentangling the effect of epigenetic memory and micro-environment fluctuations.

I think introducing a new tool to disentangle environment fluctuations and epigenetic memory is very interesting, and this new microfluidic chip offers great possibilities in that regard. Given the small dimensions of the chip and the precision that is probably needed for the tip of the v-shaped channels (so that sister cells can be trapped for generations), the development of this sisters machine represents an impressive technical achievement. The data produced in this work is new and very interesting. However, I think this paper does not present the theoretical foundations that are required to interpret the results and quantify inheritance of cellular characteristics. I will list below several issues that are completely unclear for me and that would probably all be resolved by defining a clear theoretical framework.

– I do not understand why the autocorrelation functions (ACF) vanish so fast (Figure 2B and C). The authors say (l.60-61) that averaging over many channels erases the memory. But I do not see why/how this would be the case. I believe there are several models in which this is not true. For simplicity let's take a non-normalized form for the ACF of X(t), i.e. E(X(t)X(t+tau)) and assume all the variables are of average 0. Let's say that the random variable of interest at time t X(t) (for example cell cycle time) is the sum of an environment-dependent noise N(t) and an environment-independent variable Y(t). Then the ACF of X is the sum of the ACF of N(t) and the ACF of Y(t) (assuming independence of Y and N). So the inheritance of environmental fluctuations and the inheritance of epigenetic fluctuations are entangled, but the ACF does not vanish.

This is an excellent point, which we now try to explain better in the manuscript. In short, fluctuations in the environmental conditions do influence the cell’s internal state such as growth rate, and in the mother machine or any microfluidic trap with such small dimensions, fluctuations in the growth rate can influence the concentration of nutrients in the cell’s surroundings. Therefore, the Y and N in the reviewer comment are not independent of each other. Their interaction though is distinct in different traps. This is what we observe in the ACF calculation, which we now present in Figure 1—figure supplement 1.

– From the definition of the PCF (Equation 1) I can see clearly why the PCF decreases with time for SC but I cannot understand why it is not constant for NC in Figure 2 (the only way I see to have a decreasing function for NC is that the environmental fluctuations are non-stationary, and their variance decreases with time)

– Likewise I understand the trends in Figure 3—figure supplement1 panel D, where the variance is constant for NC and RP and increases for SC. But why is it different in Figure 3—figure supplement 2 ?

We explain the NCs now better. The reviewer is right in expecting the NCs’ PCF to be zero in general, and now we add a supplemental figure to show that (Figure 2—figure supplement 5). However, as we try to explain now in reference to Figure 2, the NCs we use for comparison are cells that, at time zero, have size difference as small as that observed in SCs. The point of this choice is to emphasize that the long-term correlation observed between SCs is not simply due to the fact that they are similar in size and reside in the same environment, which is the case of NCs, but rather because they share epigenetic memory. If the observed long-term correlations in cell size between SCs was just due to the fact that they start from similar size at time zero and that they reside in the same environment, then the same correlation would be observed between NCs that start from a similar size.

To answer these questions and all the others that could be raised by this interesting data, I think a theoretical framework has to be clearly defined. Maybe the authors had such a framework in mind when interpreting the data. In this case I would recommend that they define it clearly in the paper. If on the contrary, the development of such a framework is beyond the scope of this work, then simulations should be provided and compared with the data. Otherwise it is very difficult to interpret the data and demonstrate the validity of the method.

We have added a mathematical appendix explaining the relationships between the different measures we use and how they relate to the nongenetic memory and restrain of variation. A more detailed explanation and a quantitative extraction of further information requires much more space and is beyond the scope of this study. We hope however, that the reviewer finds this additional information that we provide here sufficient to frame the problem for the readers and help them interpret the data properly.

Another important point that was unclear to me : how are NC pairs of cells defined? I understood that they are not sisters but how can the authors be sure that they are not cousins (1st, 2nd, 3rd, 4th cousins…)? In which case the NC cells at time 0 would be the same as the SC cells but at a larger generation (this would explain why the PCF of NC cells decrease in Figure 2). This should be clarified in the text.

We do know that these cells are not closely related because they are usually in the V-shaped channel from the start of the experiment, and we track them only from a point where their division occurs simultaneously. This usually happens after few divisions. Although some of the cells initially trapped in the channels can be indeed closely related, statistically this has a very low probability.

[Editors’ note: what follows is the authors’ response to the second round of review.]

Reviewer #1:

The manuscript by Vashistha et al. is a revised manuscript. My concerns about the previous version were satisfyingly addressed in the present version and in the authors' answers. So I recommend this manuscript for publication

I just have a minor comment :

I now understand that NC cells are tracked from a point where they divide at the same time and have approximately the same lengths (this is now clearly stated in the present version, I hadn't understood from the previous one…). However in the appendix where the mathematical framework is presented (which I find very useful) it is not stated and I think it may be misleading. I think it could be useful to mention that in the appendix too

We have added this text as requested in the appendix.

Reviewer #2:

Since cell size is discussed in the manuscript, I suggest authors to cite related and key publications in the field of cell-size too.

We have added citations of few important papers in the field of cell size homeostasis in the Introduction, as well as other studies of the growth rate in connection to size homeostasis in the Results section.

Reviewer #3:

I believe that Figure 1—figure supplement 1 is new. I like this graph, but it requires further explanation. The legend says "This presentation emphasizes the difference in the average growth rates measured in different traps. Note however, that each pair of SCs exhibits similar average growth rate." Can authors quantify the difference and similarity? It is hard to deduce that numbers from the graph.

We thank the reviewer for this important comment. We have now changed the figure and added a new figure, which presents the distributions of growth rates differences between sister cells and between random pairs. The distributions clearly show that the standard deviation of differences between sisters is almost half of that of random pairs occupying different traps. The old Figure 1-Figure 1A is now Figure 2A in the new format of the manuscript, and the new figure is Figure 2B, while the old Figure 1—figure supplement 1B is now Figure 1—figure supplement 1.

And also, do authors know whether this variation from different traps is also a problem in previous experimental set-up (mother machine)?

We think that this did occur in previous studies based on our own analysis of data published by other groups (see for example Susman et al., 2018). However, for the purpose of those studies, we don’t think that this effect changes their conclusions, since there was no distinction there between environmental fluctuations and molecular ones for the questions they were trying to address.

https://doi.org/10.7554/eLife.64779.sa2

Article and author information

Author details

  1. Harsh Vashistha

    Department of Physics and Astronomy, The Dietrich School of Arts and Sciences, University of Pittsburgh, Pittsburgh, United States
    Contribution
    Resources, Data curation, Software, Formal analysis, Validation, Investigation, Methodology, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-9411-5137
  2. Maryam Kohram

    Department of Physics and Astronomy, The Dietrich School of Arts and Sciences, University of Pittsburgh, Pittsburgh, United States
    Contribution
    Data curation, Investigation, Methodology
    Competing interests
    No competing interests declared
  3. Hanna Salman

    1. Department of Physics and Astronomy, The Dietrich School of Arts and Sciences, University of Pittsburgh, Pittsburgh, United States
    2. Department of Computational and Systems Biology, School of Medicine, University of Pittsburgh, Pittsburgh, United States
    Contribution
    Conceptualization, Supervision, Funding acquisition, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    hsalman@pitt.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-5847-524X

Funding

United States-Israel Binational Science Foundation (2016376)

  • Hanna Salman

National Science Foundation (2014116)

  • Hanna Salman

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank Naama Brenner for helpful discussions and comments on the manuscript. This work was supported by the National Science Foundation (Grant No. Phy-2014116), and the US-Israel Binational Science Foundation (Grant No. 2016376).

Senior Editor

  1. Aleksandra M Walczak, École Normale Supérieure, France

Reviewing Editor

  1. Petra Anne Levin, Washington University in St. Louis, United States

Reviewers

  1. Sattar Taheri-Araghi, California State University, Northridge, United States
  2. Minsu Kim, Emory University, United States

Publication history

  1. Received: November 10, 2020
  2. Accepted: January 28, 2021
  3. Accepted Manuscript published: February 1, 2021 (version 1)
  4. Version of Record published: March 4, 2021 (version 2)

Copyright

© 2021, Vashistha et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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