Scaling laws governing stochastic growth and division of single bacterial cells

Iyer‐Biswas, Srividya; Wright, Charles S.; Henry, Jonathan T.; Lo, Klevin; Burov, Stanislav; Lin, Yihan; Crooks, Gavin E.; Crosson, Sean; Dinner, Aaron R.; Scherer, Norbert F.

doi:10.1073/pnas.1403232111

Cited by 222 publications

(371 citation statements)

References 53 publications

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“…The exponential accumulation of protein during a cell cycle suggests that protein production reflects a coherent integration of many correlated processes in the cell. Exponential growth of the cell size between divisions, as well as negative correlation analogous to the one reported here, were measured in several recent experiments [10,11,13,25]. Moreover, results on trapped bacteria show explicitly that the exponents of cell size growth and protein accumulation are strongly correlated on a cycle-by-cycle basis [8].…”

Section: Discussionsupporting

confidence: 83%

“…Another possibility consistent with our model is that both σ and α are fixed. At the moment, experimental perturbations -for example, changing medium or temperature -can change the mean, for example by modifying the mean cell cycle time; but their effect on the variance of exponents is unknown [10].…”

Section: Discussionmentioning

confidence: 99%

“…• The time T i of the i th generation (i.e., the time between cell division at the (i − 1) st generation and that at the i th ) is also random [9][10][11][12][13].…”

Section: Model Without Feedbackmentioning

confidence: 99%

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Universal protein distributions in a model of cell growth and division

Brenner¹,

Newman²,

Osmanović³

et al. 2015

Phys. Rev. E

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Protein distributions measured under a broad set of conditions in bacteria and yeast were shown to exhibit a common skewed shape, with variances depending quadratically on means. For bacteria these properties were reproduced by temporal measurements of protein content, showing accumulation and division across generations. Here we present a stochastic growth-and-division model with feedback which captures these observed properties. The limiting copy number distribution is calculated exactly, and a single parameter is found to determine the distribution shape and the variance-to-mean relation. Estimating this parameter from bacterial temporal data reproduces the measured distribution shape with high accuracy, and leads to predictions for future experiments.

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Section: Discussionsupporting

confidence: 83%

Section: Discussionmentioning

confidence: 99%

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Universal protein distributions in a model of cell growth and division

Brenner¹,

Newman²,

Osmanović³

et al. 2015

Phys. Rev. E

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“…Indeed, cell size at birth and generation time are weakly correlated negatively (Pearson correlation coefficient, −0.48 ∼ −0.22; SI Appendix, Fig. S12), and this effect must be considered to account for cell size stability (3,(31)(32)(33)(34)(35). Nevertheless, our results suggest that, as far as age-related parameters and population growth rates are concerned, cell size information does not play a predominant role in E. coli over a broad set of culture conditions.…”

Section: Discussionmentioning

confidence: 82%

“…A similar idea has been proposed in several recent studies. For example, Iyer-Biswas et al (31,36) proposed that the distributions of generation time normalized by their means collapses onto the universal curve based on their experiments with Caulobacter crescentus cultured under various temperature conditions, and that an autocatalytic cycle model for cell cycle control might account for this scaling property. Similarly, Taheri-Araghi et al (3) proposed the scaling of generation time distribution based on their single-cell analysis on E. coli growth under different nutrient conditions at a fixed temperature, and presented the adder model, which assumes that cells achieve cell size homeostasis by adding a constant size between birth and division irrespective of birth size.…”

Section: Discussionmentioning

confidence: 99%

Noise-driven growth rate gain in clonal cellular populations

Hashimoto

Nozoe

Nakaoka

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

167

205

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Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a "speed limit" for proliferation.growth noise | age-structured population model | cell lineage analysis | growth law | microfluidics C ell growth is an important physiological process that underlies the fitness of organisms. In exponentially growing cell populations, proliferation is usually quantified using the bulk population growth rate, which is assumed to represent the average growth rate of single cells within a population. In addition, basic growth laws exist that relate ribosome function and metabolic 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 importance that reports cellular physiological states and fitness.However, at the single-cell level, growth-related parameters such as the division time interval and division cell size are heterogeneous even in a clonal population growing at a constant rate (4-9). Such "growth noise" causes concurrently living cells to compete within the population for representation among its future descendants. For example, if two sibling cells born from the same mother cell had different division intervals, the faster dividing sibling is likely to have more descendants in the future population compared with its slower dividing sister, despite the fact that progenies of both siblings may proliferate equally well (Fig. 1). Intrapopulation competition complicates single-cell analysis because any growth-correlated quantities measured over the population deviate from intrinsic single-cell properties (10-12). In the case of the toy model described in Fig. 1, cells are assumed to determine their generation times (division interval) randomly by roll of a dice. The mean of intrinsic cellular generation time is thus ð1 + 2 + ⋯ + 6Þ=6 = 3.5 h, but population doubling time, which is...

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First‐Passage Processes in Cellular Biology

Iyer‐Biswas

Zilman

2016

Advances in Chemical Physics

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We first review fundamentals of the theory of stochastic processes. The system dynamics are specified by the set of its states, {S}, and the transitions between them, S → S , where S, S ∈ {S}. For example, the state S can denote the position of a Brownian particle, the numbers of molecules of different chemical species, or any other variable that characterizes the state of the system of interest. Here we restrict ourselves to processes for which the transition rates depend only on the system's instantaneous state, and not the entirety of its history. Such memoryless processes are known as Markovian and are applicable to a wide range of systems. We also assume that the transition rates do not explicitly depend on time, a condition known as stationarity. In this review we make the standard assumption that the transitions between the states are Poisson distributed random processes. In other words, the probability of transitioning from state S to state S in an infinitesimal interval, dt, is α(S, S )dt, where α(S, S ) is the transition rate.Examples. For a Brownian particle diffusing along a line, the state S is defined by the particle position; the transition rate is 2D/d 2 , where D is the diffusion coefficient and d is the step length. For a set of radioactive atoms undergoing decay with rate κ per atom, the state S is defined by the number, n, of atoms that have not decayed yet, and the transition rate from state n to state n − 1 is κ n. For a system with N reacting chemical species, the system state is defined by the concentrations of each reactant, (x 1 . . . x N ), and the transition rates are functions of these concentrations.B. Time evolution equation(s) for the system.We now summarize the equations that govern the dynamical evolution of the probability that the system is in state S at time t, which we denote by P (S, t). Typically, such equations are written in one of three formalisms: the Master Equation, the Fokker-Planck Equation, or the Stochastic Differential Equation; each is summarized below in turn. Details of the

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Scaling laws governing stochastic growth and division of single bacterial cells

Cited by 222 publications

References 53 publications

Universal protein distributions in a model of cell growth and division

Universal protein distributions in a model of cell growth and division

Noise-driven growth rate gain in clonal cellular populations

First‐Passage Processes in Cellular Biology

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