Deterministic and Stochastic Descriptions of Gene Expression Dynamics

Marathe, Rahul; Bierbaum, Veronika; Gomez, David; Klumpp, Stefan

doi:10.1007/s10955-012-0459-0

Cited by 17 publications

(49 citation statements)

References 49 publications

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“…E. coli , for instance, grows and replicates DNA continuously throughout its cell cycle, though for slow growth there are periods without replication activity [ 22 , 23 ]. Expression activity can be dependent on the cell cycle nonetheless, for example because the replication of a gene may double the transcriptional activity at a specific moment in time, as suggested by recent single-cell studies [ 17 , 24 , 25 ]. That doubling would then in turn affect enzyme concentration and could cause quasi-periodic fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Generation and filtering of gene expression noise by the bacterial cell cycle

2016

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BackgroundGene expression within cells is known to fluctuate stochastically in time. However, the origins of gene expression noise remain incompletely understood. The bacterial cell cycle has been suggested as one source, involving chromosome replication, exponential volume growth, and various other changes in cellular composition. Elucidating how these factors give rise to expression variations is important to models of cellular homeostasis, fidelity of signal transmission, and cell-fate decisions.ResultsUsing single-cell time-lapse microscopy, we measured cellular growth as well as fluctuations in the expression rate of a fluorescent protein and its concentration. We found that, within the population, the mean expression rate doubles throughout the cell cycle with a characteristic cell cycle phase dependent shape which is different for slow and fast growth rates. At low growth rate, we find the mean expression rate was initially flat, and then rose approximately linearly by a factor two until the end of the cell cycle. The mean concentration fluctuated at low amplitude with sinusoidal-like dependence on cell cycle phase. Traces of individual cells were consistent with a sudden two-fold increase in expression rate, together with other non-cell cycle noise. A model was used to relate the findings and to explain the cell cycle-induced variations for different chromosomal positions.ConclusionsWe found that the bacterial cell cycle contribution to expression noise consists of two parts: a deterministic oscillation in synchrony with the cell cycle and a stochastic component caused by variable timing of gene replication. Together, they cause half of the expression rate noise. Concentration fluctuations are partially suppressed by a noise cancelling mechanism that involves the exponential growth of cellular volume. A model explains how the functional form of the concentration oscillations depends on chromosome position.Electronic supplementary materialThe online version of this article (doi:10.1186/s12915-016-0231-z) contains supplementary material, which is available to authorized users.

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Section: Introductionmentioning

confidence: 99%

Generation and filtering of gene expression noise by the bacterial cell cycle

2016

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“…Although pioneering studies on molecular networks followed shortly after 40 , the coupling between those two types of theories is a much more recent development (e.g. 6,22,41,42 ). Current analytical theories of the two-way coupling between single-cell growth and molecular circuit dynamics (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…Current analytical theories of the two-way coupling between single-cell growth and molecular circuit dynamics (e.g. 22,40,42 ), generally deal with small circuits. Numerical simulations are therefore indispensable for making predictions in single-cell physiology.…”

Section: Discussionmentioning

confidence: 99%

Statistics and simulation of growth of single bacterial cells: illustrations withB. subtilisandE. coli

Heerden

Kempe

Doerr

et al. 2017

Preprint

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The inherent stochasticity of molecular reactions prevents us from predicting the exact state of singlecells in a population. However, when a population grows at steady-state, the probability to observe a cell with particular combinations of properties is fixed. Here we validate and exploit existing theory on the statistics of single-cell growth in order to predict the probability of phenotypic characteristics such as cell-cycle times, volumes, accuracy of division and cell-age distributions, using real-time imaging data for Bacillus subtilis and Escherichia coli. Our results show that single-cell growth-statistics can accurately be predicted from a few basic measurements. These equations relate different phenotypic characteristics, and can therefore be used in consistency tests of experimental single-cell growth data and prediction of single-cell statistics. We also exploit these statistical relations in the development of a fast stochastic-simulation algorithm of single-cell growth and protein expression. This algorithm greatly reduces computational burden, by recovering the statistics of growing cell-populations from the simulation of only one of its lineages. Our approach is validated by comparison of simulations and experimental data. This work illustrates a methodology for the prediction, analysis and tests of consistency of single-cell growth and protein expression data from a few basic statistical principles.Thousands of biochemical reactions are required for bacterial growth and division. Some of them operate in a regime where they are susceptible to stochastic fluctuations in the concentrations of their reactants and regulators 1,2 . These fluctuations can be amplified by molecular networks , where fluctuations at a cellular level can in turn cause cell-to-cell variations at the level of molecules and reaction activities. For instance, uneven cell division causes size differences between cells such that their protein content and reaction rates vary 4,6,7 . The fluctuating copy number of a particular molecule in a cell, over a time period of several bacterial cell cycles, is therefore the outcome of (stochastic) biochemical and cell-growth processes [8][9][10] . Coupled molecular and cellular fluctuations are associated with many surprising phenomena in single-cell biology [10][11][12][13][14] . This complex feedback circuitry generates cell-to-cell variability in a population of isogenic cells, which may result in individual cells transiting to different phenotypic states when conditions change [11][12][13]15,16 . Examples include adaptive phenotypic-diversification of populations of cells, e.g. the emergence of antibiotics-tolerant persister cells 2 and bacterial-cell differentiation 16 . Acquiring a predictive understanding of these phenomena is one of the current challenges in single-cell physiology 17 , with direct applications in biotechnology 18 and medical microbiology 19,20 . Disentangling causes and effects, using a stochastic framework, is a major challenge for single-cell physiology 21,22 an...

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“…In this paper, we have reviewed models for constitutive (unregulated) protein synthesis that we have studied previously [23] and presented some new results for protein synthesis with negative autoregulation. In both cases, different model variants were considered to disentangle different sources of stochasticity, specifically stochastic synthesis of the protein and stochastic partitioning during cell division.…”

Section: Discussionmentioning

confidence: 99%

“…When a cell divides, the partitioning of proteins among daughter cells also generates fluctuations. In our recent work [23], we analyzed these different sources in a systematic way to see which sources contribute to the observed noise and whether there is a dominant source. In this section, we briefly summarize some key results obtained with these models.…”

Section: Sources Of Stochasticity For Constitutive Gene Expressionmentioning

confidence: 99%

Sources of stochasticity in constitutive and autoregulated gene expression

Marathe¹,

Gomez²,

Klumpp³

2012

Phys. Scr.

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Gene expression is inherently noisy as many steps in the read-out of the genetic information are stochastic. To disentangle the effect of different sources of stochasticity in such systems, we consider various models that describe some processes as stochastic and others as deterministic. We review earlier results for unregulated (constitutive) gene expression and present new results for a gene controlled by negative autoregulation with cell growth modeled by linear volume growth.

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Deterministic and Stochastic Descriptions of Gene Expression Dynamics

Cited by 17 publications

References 49 publications

Generation and filtering of gene expression noise by the bacterial cell cycle

Generation and filtering of gene expression noise by the bacterial cell cycle

Statistics and simulation of growth of single bacterial cells: illustrations withB. subtilisandE. coli

Sources of stochasticity in constitutive and autoregulated gene expression

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