Asymmetric cell division with stochastic growth rate. Dedicated to the memory of the late Spartak Agamirzayev

Efendiev, Messoud; Brunt, Bruce van; Zaidi, Ali Ashher; Shah, Shitanshu

doi:10.1002/mma.5269

Cited by 7 publications

(2 citation statements)

References 22 publications

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“…To our knowledge, exact solutions to the steady-state version of equation (2.3) were obtained for deterministic partitioning and for specific growth rates ν ( x ), division rates r ( x ) and diffusion coefficients D ( x ) only. For instance, it was solved for constant functions ν ( x ), r ( x ) and D ( x ), both for deterministic symmetric [45] and asymmetric [46] partitioning; and for deterministic asymmetric partitioning, exponential growth ν ( x ) = νx , multiplicative noise D ( x ) = Dx 2 and quadratic division rate r ( x ) = rx 2 [23]. In this last case, the solution is a series of modified Bessel functions, generalizing the Dirichlet series obtained when there is no diffusion and arising from the quadratic division rate which turns equation (2.3) into a modified Bessel equation.…”

Section: Noisy Single-cell Exponential Growthmentioning

confidence: 99%

Analytical cell size distribution: lineage-population bias and parameter inference

Genthon

2022

J. R. Soc. Interface.

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We derive analytical steady-state cell size distributions for size-controlled cells in single-lineage experiments, such as the mother machine, which are fundamentally different from batch cultures where populations of cells grow freely. For exponential single-cell growth, characterizing most bacteria, the lineage-population bias is obtained explicitly. In addition, if volume is evenly split between the daughter cells at division, we show that cells are on average smaller in populations than in lineages. For more general power-law growth rates and deterministic volume partitioning, both symmetric and asymmetric, we derive the exact lineage distribution. This solution is in good agreement with Escherichia coli mother machine data and can be used to infer cell cycle parameters such as the strength of the size control and the asymmetry of the division. When introducing stochastic volume partitioning, we derive the large-size and small-size tails of the lineage distribution and show that the lineage-population bias only depends on the single-cell growth rate. These asymptotic behaviours are extended to the adder model of cell size control. When considering noisy single-cell growth rate, we derive the large-size lineage and population distributions. Finally, we show that introducing noise, either on the volume partitioning or on the single-cell growth rate, can cancel the lineage-population bias.

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Section: Noisy Single-cell Exponential Growthmentioning

confidence: 99%

Analytical cell size distribution: lineage-population bias and parameter inference

Genthon

2022

J. R. Soc. Interface.

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“…There is no general method available to solve (1.4) subject to conditions (1.2) and (1.3). However, the second-order generalization of the first-order PDE (1.4) has been solved for constant coefficients [2] and has been discussed for certain variable coefficients [15]. The presence of two nonlocal terms in the problem complicates the analysis used in the solution technique developed for the constant coefficient case G(x, t) = g and B(x, t) = b, where g and b are positive numbers, for the symmetric division problem (1.1)- (1.3) [14].…”

Section: Introductionmentioning

confidence: 99%