Analysis of Noise Mechanisms in Cell-Size Control

Abstract

At the single-cell level, noise arises from multiple sources, such as inherent stochasticity of biomolecular processes, random partitioning of resources at division, and fluctuations in cellular growth rates. How these diverse noise mechanisms combine to drive variations in cell size within an isoclonal population is not well understood. Here, we investigate the contributions of different noise sources in well-known paradigms of cell-size control, such as adder (division occurs after adding a fixed size from birth), sizer (division occurs after reaching a size threshold), and timer (division occurs after a fixed time from birth). Analysis reveals that variation in cell size is most sensitive to errors in partitioning of volume among daughter cells, and not surprisingly, this process is well regulated among microbes. Moreover, depending on the dominant noise mechanism, different size-control strategies (or a combination of them) provide efficient buffering of size variations. We further explore mixer models of size control, where a timer phase precedes/follows an adder, as has been proposed in Caulobacter crescentus. Although mixing a timer and an adder can sometimes attenuate size variations, it invariably leads to higher-order moments growing unboundedly over time. This results in a power-law distribution for the cell size, with an exponent that depends inversely on the noise in the timer phase. Consistent with theory, we find evidence of power-law statistics in the tail of C. crescentus cell-size distribution, although there is a discrepancy between the observed power-law exponent and that predicted from the noise parameters. The discrepancy, however, is removed after data reveal that the size added by individual newborns in the adder phase itself exhibits power-law statistics. Taken together, this study provides key insights into the role of noise mechanisms in size homeostasis, and suggests an inextricable link between timer-based models of size control and heavy-tailed cell-size distributions.

Analysis of Cell Size Homeostasis at the Single-Cell and Population Level

“…We also observe that an instability occurs for timer-like mechanisms as described previously [25,27]. Interestingly, this instability occurs for smaller values of a in the backward lineages than those previously reported for forward lineages.…”

“…These initial studies formulated sizer models based on the population balance equation, an integro-differential equation that is notoriously difficult to solve in practice [21][22][23][24]. With the advent of single-cell traps such as the mother machine [2], the theoretical focus moved toward describing single cells over many divisions [13,[25][26][27]. This path is more amenable to analysis because it considers only a single individual described by a discrete-time stochastic process or stochastic map [28].…”

Analysis of cell size homeostasis at the single-cell and population level

“…4d increases for the sizer mechanism with small division errors both in forward and backward lineages, but exhibits opposite dependencies for the adder and timer-like controls in the respective lineage statistics. We also observe that an instability occurs for timer-like mechanisms as described previously 22,24 . Interestingly, this instability occurs for smaller values of a in the backward lineages than those previously reported for forward lineages.…”

“…These initial studies formulated sizer models based on the population balance equation, an integro-differential equation that is notoriously difficult to solve in practice [19][20][21] . With the advent of single-cell traps such as the mother machine 2 , the theoretical focus moved towards describing single cells over many divisions 11,[22][23][24] . This path is more amenable to analysis because it considers only a single individual described by a discrete-time stochastic process or stochastic map 25 .…”

Microfluidic time‐lapse analysis and reevaluation of the Bacillus subtilis cell cycle

“…The classical model falls into a class of models sometimes called “Sizer,” in which the cell can sense its mass and use this information to control cell cycle events. An interesting alternative to this model, which has received considerable attention recently, is sometimes called “Incremental” or “Adder” and is based on the notion that the cell is oblivious to its starting mass but instead divides after the addition of a constant amount of new material (Amir, ; Campos et al, ; Fantes & Nurse, ; Modi, Vargas‐Garcia, Ghusinga, & Singh, ; Sauls et al, ). The two models both assume that the cell can somehow “measure” mass – Sizer measures the mass appropriate for division and Adder the amount of new growth.…”