Protein Concentration Fluctuations in the High Expression Regime: Taylor’s Law and Its Mechanistic Origin

Sassi, Alberto Stefano; Garcia-Alcala, Mayra; Aldana, Maximino; Tu, Yuhai

doi:10.1103/physrevx.12.011051

Cited by 7 publications

(39 citation statements)

References 45 publications

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“…Previous work has argued for Gaussian-like division time distributions that collapse by scaling (24,28,29), and can be reconstructed by models with deterministic exponential accumulation rates (25,39). While this framework holds for some bacterial data-sets, others exhibit a much broader variability in accumulation rates (11,(18)(19)(20)37). Our analysis suggests that different experiments, possibly due to slightly different conditions or culture details, span a range of behaviors from highly uniform to highly varying accumulation rates.…”

Section: Discussionmentioning

confidence: 64%

“…5 compares the data with the two predicting curves. This may seem surprising at first, but can be understood once we recall the strong correlations between accumulation rates of different highly expressed proteins and cell size across cycles (18)(19)(20).…”

Section: Discussionmentioning

confidence: 99%

“…These dynamics define a different threshold crossing problem, in which smooth exponential accumulation needs to reach a threshold. Previous work considered such a process with white noise on top of a fixed exponential accumulation rate, and a constant threshold (20,(24)(25)(26), or a constant accumulation rate and a stochastic threshold (27). Thus in practically all previous models and analyses, the basic rate of exponential accumulation was considered fixed.…”

mentioning

confidence: 99%

“…This was motivated by single-cell measurements in E. coli that showed a narrow distribution of exponential rates (24,28,29). However, other data-sets in similar experiments on the same bacteria shows a more significant variability (18)(19)(20). It is therefore crucial to develop a theoretical framework that covers this range of behaviors and considers both the stochastic threshold and cycle-to-cycle variability in accumulation rate.…”

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confidence: 99%

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Universality of phenotypic distributions in bacteria

Biswas

Brenner

2022

Preprint

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For cell division to occur, proteins that carry it out must accumulate to a functional threshold. Most of these divisome proteins are highly abundant in the cell and accumulate smoothly and approximately exponentially throughout the cell cycle. In this threshold-crossing process, stochastic components arise from variation from one cycle to the next in accumulation rate and division fraction and from fluctuations of the threshold itself. How these combine to determine the statistical properties of division times is still not well understood. Here we formulate this stochastic process and calculate the statistical properties of cell division times by using first passage time (FPT) techniques. We find that the distribution shape is determined by a ratio between two coefficient of variations (CVs), interpolating between Gaussian-like and long-tailed. Mean, variance and skewness of division times are predicted to follow well-defined relationships with model parameters. Publicly available single-cell data span a broad range of values in parameter space; the measured distribution shape and moment scaling agree well with the theory over the entire range. Because of balanced biosynthesis, the accumulation dynamics of any abundant protein and cell size predict division time statistics equally well using our model. These results suggest that cell division is a multi-variable emergent process, which is nevertheless predictable by a single variable thanks to coupling and correlations inside the system.

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Section: Discussionmentioning

confidence: 64%

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Universality of phenotypic distributions in bacteria

Biswas

Brenner

2022

Preprint

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“…In small biological systems such as a cell, protein concentration can fluctuate in time and vary from cell to cell [24][25][26][27][28][29]. Here, we study how the positional error σ depends on the molecule (protein) concentration by varying the total molecule number N in the 3-state model with a fixed length L. Intuitively, since the overall noise level (fluctuation) scales as N −1/2 , increasing N is expected to lead to a higher spatial accuracy.…”

Section: Free Energy Dissipation Enhances the Robustness Of Turing Pa...mentioning

confidence: 99%

Free energy dissipation enhances spatial accuracy and robustness of Turing pattern in small reaction-diffusion systems

Zhang¹,

Zhang²,

Ouyang³

et al. 2022

Preprint

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Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Alan Turing proposed an elegant mechanism for pattern formation based on spontaneous breaking of the spatial translational symmetry in the underlying reaction-diffusion system. Much is understood about dynamics and structure of Turing patterns. However, little is known about the energetic cost of Turing pattern. Here, we study nonequilibrium thermodynamics of a small spatially extended biochemical reactiondiffusion system by using analytical and numerical methods. We find that the onset of Turing pattern requires a minimum energy dissipation to drive the nonequilibrium chemical reactions. Above onset, only a small fraction of the total energy expenditure is used to overcome diffusion for maintaining the spatial pattern. We show that the positioning error decreases as energy dissipation increases following the same tradeoff relationship between timing error and energy cost in biochemical oscillatory systems. In a finite system, we find that a specific Turing pattern exists only within a finite range of total molecule number, and energy dissipation broadens the range, which enhances the robustness of the Turing pattern against molecule number fluctuations in living cells. These results are verified in a realistic model of the Muk system underlying DNA segregation in E. coli, and testable predictions are made for the dependence of the accuracy and robustness of the spatial pattern on the ATP/ADP ratio. In general, the theoretical framework developed here can be applied to study nonequilibrium thermodynamics of spatially extended biochemical systems.

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Free energy dissipation enhances spatial accuracy and robustness of self-positioned Turing pattern in small biochemical systems

Zhang

Ouyang

et al. 2023

J. R. Soc. Interface.

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Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Turing proposed a general mechanism for pattern formation exemplified by a reaction–diffusion model with two chemical species in a large system. However, in small biological systems such as a cell, the existence of multiple Turing patterns and strong noise can lower the spatial order. Recently, a modified reaction–diffusion model with an additional chemical species is shown to stabilize the Turing pattern. Here, we study non-equilibrium thermodynamics of this three-species reaction–diffusion model to understand the relationship between energy cost and the performance of self-positioning. By using computational and analytical approaches, we show that beyond the onset of pattern formation the positioning error decreases as energy dissipation increases. In a finite system, we find that a specific Turing pattern exists only within a finite range of total molecule number. Energy dissipation broadens this range, which enhances the robustness of Turing pattern against molecule number fluctuations in living cells. The generality of these results is verified in a realistic model of the Muk system underlying DNA segregation in Escherichia coli , and testable predictions are made for the dependence of the accuracy and robustness of the spatial pattern on the ATP/ADP ratio.

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Protein Concentration Fluctuations in the High Expression Regime: Taylor’s Law and Its Mechanistic Origin

Cited by 7 publications

References 45 publications

Universality of phenotypic distributions in bacteria

Universality of phenotypic distributions in bacteria

Free energy dissipation enhances spatial accuracy and robustness of Turing pattern in small reaction-diffusion systems

Free energy dissipation enhances spatial accuracy and robustness of self-positioned Turing pattern in small biochemical systems

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