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.

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.

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).

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Figure 2

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Figure 3

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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:

where y is the cellular property of interest, t is the measurement time, n is the number of cell pairs measured, ${\sigma }_y$ is the population standard deviation of y, and (1) and (2) represent the two cells being considered. $PC{F}^{(y)}(t)$ 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).

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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 $\delta \alpha$ defined as:

where $\alpha (t)=(d\ln L/dt)$ 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, $\delta \alpha$ for all pairs of lineages is randomly distributed with ${\displaystyle ⟨\delta \alpha ⟩}$ = 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 $\delta \alpha$ for both RPs (${\sigma }_{\delta {\alpha }_{RPs}}^2$) and NCs (${\sigma }_{\delta {\alpha }_{NCs}}^2$) was found to be constant over time and is similar for both types of cell pairs (Figure 5A). However, the variance of $\delta \alpha$ for SCs (${\sigma }_{\delta {\alpha }_{SCs}}^2$) exhibits a complex pattern (Figure 5B), which eventually converges to the same value as RPs (${\sigma }_{\delta {\alpha }_{RPs}}^2$) and NCs (${\sigma }_{\delta {\alpha }_{NCs}}^2$). The time it takes for (${\sigma }_{\delta {\alpha }_{SCs}}^2$) 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.

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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, ${\sigma }_{\delta f_{SCs}}^2$ 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 ${\sigma }_{\delta f_{RPs}}^2$ twice as large as ${\sigma }_{\delta f_{NCs}}^2$, 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.

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.

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

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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

   "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

   "This ORCID iD identifies the author of this article:" 0000-0002-5847-524X

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