Statistics and simulation of growth of single bacterial cells: illustrations with B. subtilis and E. coli

Heerden, Johan van; Kempe, Hermannus; Doerr, Anne; Maarleveld, Timo; Nordholt, Niclas; Bruggeman, Frank J.

doi:10.1038/s41598-017-15895-4

Cited by 48 publications

(34 citation statements)

References 49 publications

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“…The specific growth rate ( k ) for each substrate was calculated from the following equation:

K (h^{‐ 1}) = 2.303 (\log_{10} X 2 ‐ \log_{10} X 1) / (t_{2} ‐ t_{1})

where, X1 and X2 were cell counts at times t 1 and t 2 , respectively (Cogan, 1978). The reciprocal of specific growth rate was recorded as generation time (van Heerden et al., 2017).…”

Section: Methodsmentioning

confidence: 99%

Low‐calorie synbiotic yoghurt from indigenous probiotic culture and combination of inulin and oligofructose: Improved sensory, rheological, and textural attributes

Chand

Kumar

Singh

et al. 2021

J. Food Process. Preserv.

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Skim milk served as the base for the production of low‐calorie synbiotic yoghurt (LCSY) and four randomly selected indigenous LAB probiotic strains namely, Lactobacillus acidophilus (NCDC 13), Lactobacillus paracasei ssp. paracasei (NCDC 627), Lactobacillus rhamnosus (NCDC 610), and Lactobacillus plantarum (NCDC 344) were evaluated for their growth characteristics in skim milk. Lactobacillus rhamnosus with S. thermophilus 74 (LR_74) exhibited desirable pH (4.60 ± 0.01), acidity, significantly highest acidification rate (4.23 ± 0.03 × 10−3 pH units min‐), probiotic count (9.10 ± 0.10 log cfu/ml), and specific growth rate (0.47 ± 0.08 hr−1). Also, Power law model fitted best for skim milk inoculated with LR_74. Further, evaluation of prebiotics namely, inulin and oligofructose at different levels revealed that the combination of inulin and oligofructose at 2% significantly improved the viscosity (13.75 ± 0.33 Pa s), sensory, textural properties, and probiotic count (9.67 ± 0.02 log cfu/ml) of LCSY. Practical applications The results of our study reveal a suitable and compatible combination of yoghurt culture and probiotic culture which could further be exploited for the development of inulin/oligofructose or combination thereof, based synbiotic beverages and other fermented dairy products.

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“…The specific growth rate ( k ) for each substrate was calculated from the following equation:

K (h^{‐ 1}) = 2.303 (\log_{10} X 2 ‐ \log_{10} X 1) / (t_{2} ‐ t_{1})

where, X1 and X2 were cell counts at times t 1 and t 2 , respectively (Cogan, 1978). The reciprocal of specific growth rate was recorded as generation time (van Heerden et al., 2017).…”

Section: Methodsmentioning

confidence: 99%

Low‐calorie synbiotic yoghurt from indigenous probiotic culture and combination of inulin and oligofructose: Improved sensory, rheological, and textural attributes

Chand

Kumar

Singh

et al. 2021

J. Food Process. Preserv.

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“…Results from single-cell experiments are generally close to theoretical expectations (van Heerden et al . 2017 ).…”

Section: Foundational Principlesmentioning

confidence: 99%

Searching for principles of microbial physiology

Bruggeman

Planquè

Molenaar

et al. 2020

FEMS Microbiology Reviews

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Why do evolutionarily distinct microorganisms display similar physiological behaviours? Why are transitions from high-ATP yield to low(er)-ATP yield metabolisms so widespread across species? Why is fast growth generally accompanied with low stress tolerance? Do these regularities occur because most microbial species are subject to the same selective pressures and physicochemical constraints? If so, a broadly-applicable theory might be developed that predicts common microbiological behaviours. Microbial systems biologists have been working out the contours of this theory for the last two decades, guided by experimental data. At its foundations lie basic principles from evolutionary biology, enzyme biochemistry, metabolism, cell composition, and steady-state growth. The theory makes predictions about fitness costs and benefits of protein expression, physicochemical constraints on cell growth, and characteristics of optimal metabolisms that maximise growth rate. Comparisons of the theory with experimental data indicates that microorganisms often aim for maximisation of growth rate, also in the presence of stresses; they often express optimal metabolisms and metabolic proteins at optimal concentrations. This review explains the current status of the theory for microbiologists; its roots, predictions, experimental evidence, and future directions.

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“…GFP fluorescence images (1 second exposure at 25% power) were acquired every 10 min. Time-lapse data were processed with custom MATLAB functions developed within our group 4 . Briefly, an automated pipeline segmented every image, identifying individual cells and calculating their spatial features.…”

Section: Methodsmentioning

confidence: 99%

“…Under constant conditions, isogenic populations of bacteria maintain time-invariant distributions of cell size, generation time and macromolecular composition. This growth mode is called balanced growth 1,2,3,4 . Yet, individual cells display molecular fluctuations that are the source for non-genetic heterogeneity within an isogenic population 5,6,7,8,9 and influence single cell growth behaviour 10 .…”

Section: Introductionmentioning

confidence: 99%

Integrated biphasic growth rate, gene expression, and cell-size homeostasis behaviour of singleB. subtiliscells

Nordholt

Heerden²,

Bruggeman³

2019

Preprint

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Integrated biphasic growth rate, gene expression, 1 and cell-size homeostasis behaviour of single B. 2 subtilis cells 3 Niclas Nordholt 1,2+ 7 2 Current affiliation: Bundesanstalt für Materialforschung und 8 -prüfung, Running title: Biphasic growth behaviour of single B. subtilis cells 12 1 Biphasic growth behaviour of single B. subtilis cells ABSTRACT 13The growth rate of single bacterial cells is continuously disturbed by random fluctu-14 ations in biosynthesis rates and by deterministic cell-cycle events, such as division, 15 genome duplication, and septum formation. It is not understood whether, and 16 how, bacteria reject these disturbances. Here we quantified growth and consti-17 tutive protein expression dynamics of single Bacillus subtilis cells, as a function 18 of cell-cycle-progression. Variation in birth size and growth rate, resulting from 19 unequal cell division, is largely compensated for when cells divide again. We anal-20 ysed the cell-cycle-dynamics of these compensations and found that both growth 21 and protein expression exhibited biphasic behaviour. During a first phase of vari-22 able duration, the absolute rates were approximately constant and cells behaved 23 as sizers. In the second phase, rates increased and growth behaviour exhibited 24 characteristics of a timer-strategy. This work shows how cell-cycle-dependent rate 25 adjustments of biosynthesis and growth are integrated to compensate for physio-26 logical disturbances caused by cell division. 27 28 IMPORTANCE 29 Under constant conditions, bacterial populations can maintain a fixed average 30 cell size and constant exponential growth rate. At the single cell-level, however, 31 cell-division can cause significant physiological perturbations, requiring compen-32 satory mechanisms to restore the growth-related characteristics of individual cells 33 toward that of the average cell. Currently, there is still a major gap in our under-34 standing of the dynamics of these mechanisms, i.e. how adjustments in growth, 35 metabolism and biosynthesis are integrated during the bacterial cell-cycle to com-36 pensate the disturbances caused by cell division. Here we quantify growth and 37 constitutive protein expression in individual bacterial cells at sub-cell-cycle reso-38 lution. Significantly, both growth and protein production rates display structured 39 and coordinated cell-cycle-dependent dynamics. These patterns reveal the dy-40 namics of growth rate and size compensations during cell-cycle progression. Our 41 findings provide a dynamic cell-cycle perspective that offers novel avenues for the 42 interpretation of physiological processes that underlie cellular homeostasis in bac-43 teria. 44 Under constant conditions, isogenic populations of bacteria maintain time-invariant 46 distributions of cell size, generation time and macromolecular composition. This 47growth mode is called balanced growth 1,2,3,4 . Yet, individual cells display molec-48 ular fluctuations that are the source for non-genetic heterogeneity within an iso-49 geni...

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Statistics and simulation of growth of single bacterial cells: illustrations with B. subtilis and E. coli

Cited by 48 publications

References 49 publications

Low‐calorie synbiotic yoghurt from indigenous probiotic culture and combination of inulin and oligofructose: Improved sensory, rheological, and textural attributes

Low‐calorie synbiotic yoghurt from indigenous probiotic culture and combination of inulin and oligofructose: Improved sensory, rheological, and textural attributes

Searching for principles of microbial physiology

Integrated biphasic growth rate, gene expression, and cell-size homeostasis behaviour of singleB. subtiliscells

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