Noise-driven growth rate gain in clonal cellular populations Mikihiro Hashimotoa, Takashi Nozoea, Hidenori Nakaokaa, Reiko Okuraa, Sayo Akiyoshia, Kunihiko Kanekoa,b, Edo Kussellc,d, and Yuichi Wakamotoa,b,1 aDepartment of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Tokyo 153-8902, Japan; bResearch Center for Complex Systems Biology, University of Tokyo, Tokyo 153-8902, Japan; cDepartment of Biology, Center for Genomics and Systems Biology, New York University, New York, NY 10003; and dDepartment of Physics, New York University, New York, NY 10003 Edited by Daniel L. Hartl, Harvard University, Cambridge, MA, and approved February 5, 2016 (received for review October 19, 2015) Cellular populations in both nature and the laboratory are com- equal the mean generation time when no variability of genera- posed of phenotypically heterogeneous individuals that compete tion time exists at the single-cell level. Population growth rate with each other resulting in complex population dynamics. Predicting is determined not only by an average of single cells but also by population growth characteristics based on knowledge of heteroge- the details of heterogeneity within a population. Therefore, un- neous single-cell dynamics remains challenging. By observing groups derstanding how population growth rates and other properties of cells for hundreds of generations at single-cell resolution, we arise from single-cell heterogeneity poses a fundamental chal- reveal that growth noise causes clonal populations of Escherichia coli lenge to single-cell biology. to double faster than the mean doubling time of their constituent A classical study of theoretical and experimental microbiology single cells across a broad set of balanced-growth conditions. We attempted to reveal the discrepancies between mean cellular show that the population-level growth rate gain as well as age struc- generation times and population doubling times in real bacterial turesofpopulationsandofcelllineages in competition are predict- populations (13). Experimental methods and techniques avail- able. Furthermore, we theoretically reveal that the growth rate gain able at that time, however, hampered reliable tests. Recently, the can be linked with the relative entropy of lineage generation time techniques of single-cell time-lapse microscopy have advanced to distributions. Unexpectedly, we find an empirical linear relation a great extent, revealing the heterogeneous and stochastic nature between the means and the variances of generation times across of single-cell dynamics quantitatively (14). With the aid of conditions, which provides a general constraint on maximal growth microfluidic platforms, tracking single cells over many genera- rates. Together, these results demonstrate a fundamental benefit of tions in controlled constant or changing environments has also noise for population growth, and identify a growth law that sets a become feasible, providing insights into the mechanisms of cell “speed limit” for proliferation. size homeostasis and stress responses (3, 6, 7, 9, 15–22). In this study, through microfluidics time-lapse microscopy and growth noise | age-structured population model | cell lineage analysis | single-cell analysis on large-scale, single-cell lineage trees, we growth law | microfluidics reveal that clonal populations of Escherichia coli indeed grow BIOPHYSICS AND with a doubling time that is smaller than the mean doubling time COMPUTATIONAL BIOLOGY ell growth is an important physiological process that under- of their constituent cells under broad, balanced-growth condi- Clies the fitness of organisms. In exponentially growing cell tions. We show that the observed growth rate gains and pop- populations, proliferation is usually quantified using the bulk ulation age structures are predictable from cellular generation population growth rate, which is assumed to represent the av- time distributions based on a simple age-structured population erage growth rate of single cells within a population. In addition, model. Furthermore, we reveal unique features of long single- basic growth laws exist that relate ribosome function and meta- cell lineages within populations in competition, and provide a bolic efficiency, macromolecular composition, and cell size of the culture as a whole to the bulk population growth rate (1–3). Population growth rate is therefore a quantity of primary im- Significance portance that reports cellular physiological states and fitness. However, at the single-cell level, growth-related parameters Differences between individuals exist even in the absence of such as the division time interval and division cell size are het- genetic differences, e.g., in identical twins. Over the last de- erogeneous even in a clonal population growing at a constant cade, experiments have shown that even genetically identical rate (4–9). Such “growth noise” causes concurrently living cells microbes exhibit large cell-to-cell differences. In particular, the to compete within the population for representation among its timing of cell division events is highly variable between single future descendants. For example, if two sibling cells born from bacterial cells. The effect of this variability on long-term the same mother cell had different division intervals, the faster growth and survival of bacteria, however, remains elusive. dividing sibling is likely to have more descendants in the future Here, we present a striking finding showing that a bacterial population compared with its slower dividing sister, despite the population grows faster on average than its constituent cells. fact that progenies of both siblings may proliferate equally well To explain this counterintuitive result, we present a mathe- (Fig. 1). Intrapopulation competition complicates single-cell matical model that precisely predicts our measurements. Fur- thermore, we show an empirical growth law that constrains analysis because any growth-correlated quantities measured over the maximal growth rate of Escherichia coli. the population deviate from intrinsic single-cell properties (10– 12). In the case of the toy model described in Fig. 1, cells are Author contributions: M.H. and Y.W. designed research; M.H., T.N., H.N., R.O., K.K., E.K., assumed to determine their generation times (division interval) and Y.W. performed research; Y.W. contributed new reagents/analytic tools; M.H., R.O., randomly by roll of a dice. The mean of intrinsic cellular gen- S.A., and Y.W. analyzed data; and M.H., E.K., and Y.W. wrote the paper. eration time is thus ð1 + 2 + ⋯ + 6Þ=6 = 3.5 h, but population The authors declare no conflict of interest. doubling time, which is the time required for a population to This article is a PNAS Direct Submission. double the number of cells, is in fact 3.2 h. This counterintuitive 1To whom correspondence should be addressed. Email: [email protected]. result is a direct consequence of growth noise in a population. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. Indeed, as we will see, the population doubling time can only 1073/pnas.1519412113/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1519412113 PNAS | March 22, 2016 | vol. 113 | no. 12 | 3251–3256 Downloaded by guest on September 28, 2021 A Cellular generation time decorating the surface of a microfabricated glass coverslip with (interdivision time) biotin and membrane with streptavidin (23). The narrow and hr shallow growth channels can harbor 25 ∼ 40 cells at a time. A Mean generation time of cells small fraction of the cells within growth channels are constantly hr removed to the wide and deep flow channels, which maintains B the number of cells in the growth channels nearly constant. In Sibling cell 1 Descendants contrast to the “mother machine” (7), the width of the growth of sibling cell 1 channels is wider than a single-cell width, and both ends are open Expected ratio of descendant cells to flow channels. This configuration introduces competition among cells to remain within the growth channels, which is an important feature of this device for evaluating growth properties Descendants of both single cells and the population. Fresh medium is con- of sibling cell 2 stantly supplied to the cells both from the flows in the flow channels and above the membrane, allowing efficient environ- Sibling cell 2 mental control. Cellular growth rates in this device were indeed stable during the entire period of observation (SI Appendix, Fig. S2). Furthermore, the statistics of cellular growth were indis- Population doubling time tinguishable across different locations within the growth chan- C 4 nels (SI Appendix, Fig. S3), which confirms efficient control of 2 Population hr growth rate environmental conditions around the cells. Using this device, we 0 0 5 10 15 20 observed clonal proliferation processes of E. coli in constant Time, t environments by time-lapse microscopy, obtaining large-scale Fig. 1. Competition within a population caused by growth noise and its consequence to population growth rate. (A) Toy model of cell proliferation. Here, we consider a model of cell proliferation in which all of the cells in a A Cell D population determine their generation time (interdivision time) randomly Flow Flow by throwing a dice to learn the consequences of intrapopulation growth noise. In this setting, cells can take either of the six possible choices of generation time, τ = 1,2, ⋯, 6 h, with the equal probability of 1/6. The mean hτi = generation time is thus g 3.5 h. (B) Example of pedigree tree showing competition between sibling cells. In this tree, two sibling cells were born B Growth channel Flow channel from the common mother cell at t = 0 h, and divided with different gen- Cellulose membrane eration times (sibling cell 1: τs1 = 5 h; and sibling cell 2: τs2 = 2 h). The de- scendant cells from the both sibling cells follow the same rule of cell divisions irrespectively of the ancestral generation time. The difference of generation C time between the sibling cells 1 and 2 was caused just by chance, but the expected number of descendant cells becomes larger for the fast dividing sibling cell.