Non-genetic inheritance restraint of cell-to-cell variation
11 Non-genetic inheritance restraint of cell-to-cell variation
Harsh Vashistha , Maryam Kohram , and Hanna Salman Department of Physics and Astronomy, The Dietrich School of Arts and Sciences Department of Computational and Systems Biology, School of Medicine University of Pittsburgh, Pittsburgh, PA * Correspondence should be addressed to: [email protected]
Genetically identical cells exhibit large heterogeneity in their physical and functional characteristics even under constant homogenous environmental conditions. This heterogeneity proliferates among population members originating from a single mother 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 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 of about 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.
One of the main challenges in biological physics today is to quantitatively predict the change in cells’ physical and functional characteristics over time. Cellular characteristics are regulated by genetic and non-genetic (proteins, RNA, chemicals, etc.) factors that interact in order to determine the state of the cell at all times. While genetic information passed from generation to the next is the main scheme, by which cells conserve their characteristics, non-genetic cellular components are also transferred between consecutive generations and thus influence the state of the cell in future generations . The mechanism of genetic information transfer between generations, as well as how this information is expressed, are mostly understood – . This information can be altered by rare occurring processes such as mutations, lateral gene transfer, or gene loss . Therefore, changes resulting from genetic alterations emerge over very long timescales (several 10s 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 – . 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. This requires understanding and quantitatively characterizing 1) how intrinsic and extrinsic sources of variation contribute to the proliferation of heterogeneity in a population, and 2) how non-genetic inheritance contributes to the maintenance of cellular properties along time. While our understanding of variation sources have increased significantly over the past two decades – , 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 – . However, since the state of the cell (or its phenotype) is determined by the integration of multiple processes, the inheritance dynamics of most cellular phenotypes cannot be predicted by characterizing the effect of individual inheritance mechanisms separately. Instead, there is a need to measure and characterize the inheritance dynamics of the phenotype directly. Progress in this research has been drastically hindered by the limited experimental techniques that can provide reliable quantitative measurements. The recent development of the microfluidic device known as the “mother machine”, has allowed us to trap single bacterial cells and follow their growth and division, as well as their protein expression dynamics for hundreds of generations . These measurements have been used by several groups to gain insight into non-genetic inheritance and cellular memory of different cellular properties. The results obtained have consistently showed that non-genetic memory in bacteria is almost completely erased within one generation . This consensus 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 autocorrelation function, measurements of cells from different traps of the mother machine are averaged together. These cells might experience slightly different environments at different times resulting from thermal fluctuations and their dynamic interaction with their surroundings. As a result of the individuality of the cell-environment interaction, different microniches can be created in different traps . Thus, averaging over many traps erases 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 new 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 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 sister cells, for example, diverge immediately after division, but re-converge towards 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” (Fig. 1a), is similar to the mother machine used in earlier studies . It consists of 30µm long narrow trapping channels (1µm × × –
160 generations. Images of the cells in both DIC and fluorescence modes were acquired every 3 minutes and 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:
𝑃𝐶𝐹 (𝑦) (𝑡) = 1𝜎 𝑦 (1) 𝜎 𝑦 (2) ∑(𝑦 𝑖(1) (𝑡) − 〈𝑦 (1) 〉) ∙ (𝑦 𝑖(2) (𝑡) − 〈𝑦 (2) 〉) 𝑛𝑖=1 where 𝑦 is the cellular property of interest, t is the measurement time, n is the number of cell pairs measured, 𝜎 𝑦 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 (Fig. 2a): 1) Sister cells (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, and are chosen to be at the start of the cell cycle at time 0, and almost identical in size. 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. We measured the correlations between the different pair types for cell cycle time (T) (Fig. S1 and S2) . We find that T of SCs remain strongly correlated for up to 8 successive cell divisions (Fig. 2b) regardless of the environmental conditions (Fig. S3), while the NCs correlation decays to zero within 3 generation (Fig 2c). 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 (Fig. 2b and c). Next, we applied our method to cell size. Also here, our measurements show that SCs correlation decays slowly over ~7 generations (Fig. 2d), while the correlation of NCs exhibit fast decay to zero within 2 generations similar to the ACF (Fig. 2e). Note that RPs exhibit no correlation from the start of the measurement (Fig.2d and 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 (Fig. S5 and S6). Thus, we have measured the relative fluctuations in the exponential elongation rate of the cell pairs 𝛿𝛼 , defined as: 𝛿𝛼(𝑡) = 𝛼 (1) (𝑡) − 𝛼 (2) (𝑡) where 𝛼(𝑡) = 𝑑 ln 𝐿(𝑡)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 (Fig. S7a-c). As expected, 𝛿𝛼 for all pairs of lineages is randomly distributed with < 𝛿𝛼 >=0 (Fig. S7d), 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 ( 𝜎 𝛿𝛼 𝑅𝑃𝑠 (𝑡) ) and NCs ( 𝜎 𝛿𝛼 𝑁𝐶𝑠 (𝑡) ), was found to be constant over time and is similar for both types of cell pairs (Fig. 3a). However, the variance of 𝛿𝛼 for SCs ( 𝜎 𝛿𝛼 𝐶𝑆𝑠 (𝑡) ) exhibits a complex pattern (Fig. 3b), which eventually converges to the same value as 𝜎 𝛿𝛼 𝑅𝑃𝑠 (𝑡) and 𝜎 𝛿𝛼 𝑁𝐶𝑠 (𝑡) . The time it takes for 𝜎 𝛿𝛼 𝑆𝐶𝑠 (𝑡) to reach saturation extends over almost 10 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 minutes throughout the cell cycle, and compared the results between SCs. Our comparison clearly shows that a 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 (Fig. 3b 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. 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 . 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 Fig. S8 for details). Upon division, soluble proteins are partitioned symmetrically with both daughters receiving almost the same protein concentration. As expected, 𝜎 𝛿𝑓 𝑆𝐶𝑠 starts from zero initially, and diverges to reach saturation within 2 generations (Fig. 3c). On the other hand, NCs and RPs exhibit constant variance throughout the whole time. 𝜎 𝛿𝑓 𝑅𝑃𝑠 is twice as large as 𝜎 𝛿𝑓 𝑁𝐶𝑠 , 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 (Fig. S8), 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 ~10 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.
METHODS SUMMARY Device fabrication.
The master mold of the microfluidic device was fabricated in two layers. Initially, the growth channels for the cells were printed on a 1mm x 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 . 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.
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 . 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 (cid:79) -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 1g/l casamino acids and 4g/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 (cid:113) C, in either LB or M9CL medium depending on the intended testing 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.
Images of the channels were acquired every 3 minutes (in LB medium) or 7 minutes (in M9CL medium) in DIC and fluorescence modes using a Nikon eclipse Ti2 microscope with a 100x objective. The size and protein content of the sister cells were measured from these images using the image analysis software Oufti . The data were then used to generate traces such as in Fig. 1d, and for further analysis as detailed in the main text. Single-cell measurements were analyzed using MATLAB. Sample autocorrelation functions, Pearson correlation coefficients, sample distributions and curve fitting were all calculated by their implementations in MATLAB toolboxes. Acknowledgments:
We thank Naama Brenner for helpful discussions and comments on the manuscript. This work was supported in part by the US-Israel Binational Science Foundation.
References
1. Lambert, G. & Kussell, E. Memory and Fitness Optimization of Bacteria under Fluctuating Environments.
PLoS Genet. , e1004556 (2014). 2. Robert, L. et al. Pre‐dispositions and epigenetic inheritance in the
Escherichia coli lactose operon bistable switch.
Mol. Syst. Biol. , 357 (2010). 3. Casadesus, J. & Low, D. Epigenetic Gene Regulation in the Bacterial World. Microbiol. Mol. Biol. Rev. (2006). doi:10.1128/mmbr.00016-06 4. Turnbough, C. L. Regulation of Bacterial Gene Expression by Transcription Attenuation.
Microbiol. Mol. Biol. Rev. (2019). doi:10.1128/mmbr.00019-19 5. Chen, C. et al.
Convergence of DNA methylation and phosphorothioation epigenetics in bacterial genomes.
Proc. Natl. Acad. Sci. U. S. A. (2017). doi:10.1073/pnas.1702450114 6. Bryant, J., Chewapreecha, C. & Bentley, S. D. Developing insights into the mechanisms of evolution of bacterial pathogens from whole-genome sequences.
Future Microbiology (2012). doi:10.2217/fmb.12.108 7. Robert, L. et al.
Mutation dynamics and fitness effects followed in single cells.
Science (80-. ). (2018). doi:10.1126/science.aan0797 8. Casadesús, J. & Low, D. A. Programmed heterogeneity: Epigenetic mechanisms in bacteria.
Journal of Biological Chemistry (2013). doi:10.1074/jbc.R113.472274 9. Huh, D. & Paulsson, J. Non-genetic heterogeneity from stochastic partitioning at cell division.
Nature Genetics (2011). doi:10.1038/ng.729 10. Veening, J.-W. et al.
Bet-hedging and epigenetic inheritance in bacterial cell development.
Proc. Natl. Acad. Sci. , 4393 – Nature , 481 –
486 (2013). 12. Elowitz, M. B., Levine, A. J., Siggia, E. D. & Swain, P. S. Stochastic gene expression in a single cell.
Science (80-. ). (2002). doi:10.1126/science.1070919 13. Avery, S. V. Microbial cell individuality and the underlying sources of heterogeneity.
Nature Reviews Microbiology (2006). doi:10.1038/nrmicro1460 14. Ackermann, M. A functional perspective on phenotypic heterogeneity in microorganisms.
Nature Reviews Microbiology (2015). doi:10.1038/nrmicro3491 15. Mosheiff, N. et al.
Inheritance of Cell-Cycle Duration in the Presence of Periodic Forcing.
Phys. Rev. X (2018). doi:10.1103/PhysRevX.8.021035 16. Sandler, O. et al.
Lineage correlations of single cell division time as a probe of cell-cycle dynamics.
Nature (2015). doi:10.1038/nature14318 17. Chai, Y., Norman, T., Kolter, R. & Losick, R. An epigenetic switch governing daughter cell separation in Bacillus subtilis.
Genes Dev. (2010). doi:10.1101/gad.1915010 18. Wakamoto, Y., Ramsden, J. & Yasuda, K. Single-cell growth and division dynamics showing epigenetic correlations.
Analyst , 311 –
317 (2005). 19. Govers, S. K., Adam, A., Blockeel, H. & Aertsen, A. Rapid phenotypic individualization of bacterial sister cells.
Sci. Rep. , 8473 (2017). 0 20. Wang, P. et al. Robust growth of escherichia coli.
Curr. Biol. (2010). doi:10.1016/j.cub.2010.04.045 21. Brenner, N. et al.
Single-cell protein dynamics reproduce universal fluctuations in cell populations.
Eur. Phys. J. E. Soft Matter , 102 (2015). 22. Tanouchi, Y. et al. A noisy linear map underlies oscillations in cell size and gene expression in bacteria.
Nature , 357 –
360 (2015). 23. Susman, L. et al.
Individuality and slow dynamics in bacterial growth homeostasis.
Proc. Natl. Acad. Sci. U. S. A. , (2018). 24. Yang, D., Jennings, A. D., Borrego, E., Retterer, S. T. & Männik, J. Analysis of Factors Limiting Bacterial Growth in PDMS Mother Machine Devices.
Front. Microbiol. , 871 (2018). 25. Godin, M. et al. Using buoyant mass to measure the growth of single cells.
Nat. Methods , 387 –
390 (2010). 26. Soifer, I., Robert, L. & Amir, A. Single-cell analysis of growth in budding yeast and bacteria reveals a common size regulation strategy.
Curr. Biol. , 356 –
361 (2016). 27. Jenkins, G. Rapid prototyping of PDMS devices using su-8 lithography.
Methods Mol. Biol. (2013). doi:10.1007/978-1-62703-134-9_11 28. Rodrigo Martinez-Duarte and Marc J. Madou.
Microfluidics and Nanofluidics Handbook . Microfluidics and Nanofluidics Handbook (CRC Press, 2016). doi:10.1201/b11188 29. Lutz, R. & Bujard, H. Independent and tight regulation of transcriptional units in Escherichia coli via the LacR/O, the TetR/O and AraC/I1-I2 regulatory elements.
Nucleic Acids Res. , 1203 –
10 (1997). 30. Paintdakhi, A. et al.
Oufti: An integrated software package for high-accuracy, high-throughput quantitative microscopy analysis.
Mol. Microbiol. (2016). doi:10.1111/mmi.13264 Figures:
Fig. 1. Scheme of the experimental setup for tracking sister cells. (a) Long (3 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 be also seen in real fluorescence images of the cells in the trap (c), which are then followed for a long time (see Supplementary movie). (d) Section of example traces of two sister cells from the time they are born, which shows how they become different over time. Fig. 2 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 c ell cycle time for SCs (122 pairs) exhibit memory that extends for more than 8 generations (mean lifetime ~4.5 generations). This is ~3.5x longer than the mean lifetime of NCs PCF (calculated from a 100 pairs) (c), which is comparable to the ACF (mean lifetime ~1 generation). (d) Similarly, SCs exhibit strong cell size correlation that decays slowly over a long time (mean lifetime ~3.5 generations), while NCs show almost no correlation in cell size similar to ACF of initial sizes (mean lifetime ~1 generation). For details of the cell-cycle time PCF and errors calculation see SI and Figs. S1 and S2. 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 minutes time window) (See Fig. S4 for raw data). Error bars represent averaging window size for the x component, and the standard deviation of the average for the y component. The equations in the graphs represent the best fit to the PCF depicted in each graph with g is generation number. 𝑃𝐶𝐹
𝑆𝐶𝑠 = 𝑒 −0.23𝑔
𝑃𝐶𝐹
𝑁𝐶𝑠 = 𝑒 −0.77𝑔
𝑃𝐶𝐹
𝑆𝐶𝑠 = 𝑒 −0.29𝑔
𝑃𝐶𝐹
𝑁𝐶𝑠 = 𝑒 −0.88𝑔 Fig. 3 . Variance (𝛔 ) as a function of the time. (a) σ of the growth rate difference (𝛿𝛼) between cell pairs for NCs and RPs as a function of time (see Fig. S7 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 minutes), and increases thereafter for 4 hours (~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 3 frames moving window (6 minutes), and the error bars represent the standard deviation of that average. The inset depicts the growth rate difference between a cell and its larger sister calculated over a 3 frame moving window during the first generation after separation. The values are normalized by the average growth rate of two cells. Also here, we see that the difference between the two cells is largest immediately after separation but it degreases to almost zero by the end of the cell cycle. (c) Unlike 𝛿𝛼 , 𝛿𝑓 of SCs increases to its saturation value within ~2 generation (see Fig. S8 for the details of the calculation). Here, each point represents the average of three different experiments, and the error bars are their standard deviation. on-genetic inheritance restraint of cell-to-cell variation Harsh Vashistha , Maryam Kohram , and Hanna Salman Department of Physics and Astronomy, The Dietrich School of Arts and Sciences Department of Computational and Systems Biology, School of Medicine University of Pittsburgh, Pittsburgh, PA * Correspondence should be addressed to: [email protected]
Supplementary Information Supplementary movie
The movie shows an example series of trap images taken every 3 minutes in fluorescence mode. At time 1:03 one can see the mother cell at the tip of the V-shaped trap right before it splits into two sister cells at 1:12. Thereafter, the two sister cells remain trapped right next to each other for an extended time, allowing us to obtain measurements various characteristics for both cells at the same time and under the same conditions.
CF and error calculation
The PCF was calculated using following equation:
𝑃𝐶𝐹 (𝑦) (𝑡) = 1𝜎 𝑦 (1) 𝜎 𝑦 (2) ∑(𝑦 𝑖(1) (𝑡) − 〈𝑦 (1) 〉) ∙ (𝑦 𝑖(2) (𝑡) − 〈𝑦 (2) 〉) 𝑛𝑖=1 and the standard deviation : 𝜎 𝑃𝐶𝐹 = 1 − 𝑃𝐶𝐹 √𝑛 Where n is the number of cell pairs considered in the calculation Generation 𝑃𝐶𝐹 ± 𝜎
𝑃𝐶𝐹
Slope of best fit (Fig. S2) 1 st ± nd ± rd ± th ± th ± th ± th ± th ± th ± Table ST1.
The calculated values of the PCF for SCs were verified by calculating the slopes of best fits to the plots of Time A vs Time B graphs (Fig. S2). References
1. Bowley, A. L. The Standard Deviation of the Correlation Coefficient.
J. Am. Stat. Assoc. , 31 (1928). Fig. S1.
Distributions of different cell parameters . In order to avoid artifacts arising in calculations due to differences between experiments carried out on different days, raw data from these experiments was normalized by subtracting the mean (μ) and dividing by the standard deviation (σ) for each experiment separately.
Later, this normalized data was combined and used for calculating the PCF and variances for different parameters. (a-b) distributions of cell cycle times (T) before and after normalization. (c-d) distributions of elongation rate (α) before and after normalization. (e-f) distributions of mean fluorescence intensity ( f ) before and after normalization. ig. S2. Correlation in cell cycle times for SCs was verified by calculating slopes of best fits to the plots of normalized Time A vs Time B. (a-i) Slopes of the best fit lines for Time A vs Time B show that cell cycle times are strongly correlated for first few generations in SCs. This shows existence of non-genetic memory that restrains the divergence of the phenotypes in cells originating from the same mother cell. Fig. S3. The PCF of cell cycle time (T) for SCs in different growth conditions.
The PCF of SCs cell-cycle time in LB at 37 (cid:113)
C (a) and in M9CL at 32 (cid:113)
C (b). Existence of strong correlation between cell cycle duration in both (a) and (b) demonstrates the robustness of non-genetic restraint in different experimental conditions. The lines in both graphs are the best fits to the data depicted in the graphs. The decay rate of the correlation in both cases is very similar to that observed in LB medium at 32°C described in the main text ( 𝑦 = 𝑒𝑥𝑝(−0.23𝑔) . Fig. S4. The PCF of cell size as a function of time for SCs, NCs and RPs.
The cell size PCF for SCs (a) and for NCs (b) are compared in both graphs with the cell size ACF and PCF for RPs. Sister cells show strong cell size correlation that decays slowly over a long time. NCs show almost no correlation in cell size similar to ACF of initial sizes. For details of the PCF and errors calculations, refer to earlier SI.
Fig. S5.
Cell-cycle time variance ( 𝝈 ) as a function of time. (a-c) Individual traces showing difference in cell cycle times ( 𝛿𝑇 ) for SCs, NCs and RPs respectively. The variance ( 𝜎 ) of cell cycles times differences (𝛿𝑇) as a function of time (d) represent the variance of the plots in (a – c) calculated at different time points using 𝜎 (𝛿𝑇) =< (𝛿𝑇) > −< 𝛿𝑇 > . 𝜎 ( 𝛿𝑇 ) for SCs starts from a small value in first generation and saturate to a constant value after ~7 generations (similar to the timescale obtained from the PCF ~8 generations), while 𝜎 ( 𝛿𝑇 ) for NCs and RPs remain constant over time. Fig. S6. Cell size variance ( 𝝈 ) as a function of time . 𝜎 was calculated similarly to 𝜎 in Fig. S5. 𝜎 for SCs increase much slower than that of NCs and RPs, and reaches saturation at a fixed value after ~7 generations (mean lifetime ~3.5 generations) similar to the time scale observed in the PCF. Each point in the graph represent an average over a 6 frames window (15 minutes), and the error bars represent the window size for the x value and the standard deviation of the window average for the y value. The lines depict the best fits to the data described in the graphs. Fig. S7.
Exponential elongation rate variance ( 𝝈 ) as a function of time. Individual traces showing the difference between the exponential elongation rates ( 𝛿𝛼 ) for SCs (a), NCs (b), and RPs (c). (d) The mean of 𝛿𝛼 for all cell pairs remain zero along time as expected. For details of 𝛿𝛼 calculations, please refer to the main text. Fig. S8. Mean fluorescence variance ( 𝝈 ) as a function of time . Individual traces showing the difference in mean fluorescence intensity ( 𝛿𝑓 ) of gfp expressed in SCs (a), NCs (b), and RPs (c). (d) The variance ( 𝜎 , calculated similarly to 𝜎 in Fig. S5) of GFP expressed under the control of the Lac Operon promoter in lactose medium (metabolically relevant) is compared with that of GFP expressed under the control of the λ Pr promoter in LB medium (metabolically irrelevant). It is clear that both exhibit no significant difference and a very short memory ( ≤2 generations).