Asymmetrical Cell Division With Exponential Growth

Zaidi, Ali Ashher; Brunt, Bruce van

doi:10.1017/s1446181121000109

Cited by 5 publications

(11 citation statements)

References 25 publications

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“…Analogues of ( 5) have been used in biophysics to model the size distribution of a population of dividing cells [48][49][50]. Other contexts for pantograph-type functional equations are discussed in [51,52].…”

Section: B Derivation Of the Steady-state Distribution From The Panto...mentioning

confidence: 99%

An advection-diffusion process with proportional resetting

Pierce¹

2022

Preprint

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This paper presents a diffusion process with a novel resetting mechanism in which the amplitude of the process is instantaneously converted to a proportion of its value at random times. This model is described by a Langevin equation with both additive Gaussian white noise and multiplicative Poisson shot noise terms. The distribution function obeys a pantograph equation, a functional partial differential equation evaluated at two amplitudes simultaneously. From this equation the exact statistical moments and steady-state distribution of the process are calculated. The distribution interpolates between exponential and Gaussian extremes depending on the proportion of the amplitude lost in each reset. These results will be useful for applications in which stochastic quantities are suddenly reduced in proportion to their values due to random events.

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Section: B Derivation Of the Steady-state Distribution From The Panto...mentioning

confidence: 99%

An advection-diffusion process with proportional resetting

Pierce¹

2022

Preprint

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“…where the coefficients c k,l are given in appendix B 2 and C is a normalization constant. For exponential growth, we find that this lineage distribution is related to the population distribution ψ(x) obtained in [31] by…”

Section: Exact Lineage Distributions For Deterministic Partitioningmentioning

confidence: 78%

“…Exact population solutions to eq. ( 3) have been obtained in the particular case of exponential and noiseless (D = 0) growth, for deterministic symmetric [28] and asymmetric [31] partitioning. The same methods can be used to derive the lineage distribution, for which the hypothesis of exponential growth can even be relaxed and replaced by power-law growth rates, still in the absence of noise.…”

Section: Exact Lineage Distributions For Deterministic Partitioningmentioning

confidence: 99%

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

Genthon¹

2022

Preprint

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Solving population balance equations, we derive analytical steady-state cell size distributions for single-lineage experiments, such as the mother machine. These experiments are fundamentally different from batch cultures where populations of cells grow freely, and the statistical bias between them is obtained by comparing our results to cell size distributions measured in population. 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. 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 E. 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 smallsize tails of the lineage size distributions, and show that they respectively do not depend on the partitioning of volume and on the size control strength. 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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“…After 1 week the meristems were removed from solution and final length of the germinating meristems were calculated. Using following formula exponential growth rate was calculated to evaluate anti-proliferative potency of the candidate drugs [27].…”

Section: Anti-proliferative Assaymentioning

confidence: 99%

An Anti-radical, Cytoprotective, Anti-proliferative, Anti-inflammatory and Toxicological Assessment of Metallo-porphyrins Isolated from Fresh Leaves of Spinacia oleracea L.

Das

Patil

Gajbhiye

2021

JPRI

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Aim: Synthetic lead molecules are associated with host of adverse effects while medicinal molecules isolated from natural sources are blessed with both safety as well as efficacy. The ancient doctrine of Ayurveda ardently advocates the therapeutic virtues contained in green leaves of Spinacia oleracea L. The principal constituent of the leaves is the class of metalloporphyrin chlorophyll, which is also the floral counterpart of faunal heme. Chlorophyll-a (Chl-a) and chlorophyll-b (Chl-b) are the cardinal members of the chlorophyll family. Study design: Herein, we have explored the anti-radical, cytoprotective, anti-inflammatory and anti-proliferative efficacy of Chl-a and Chl-b in reference to standard drug and crude extract of Spinacia leaves. The current study is aimed to establish, naturally mined metaloporphyrins as safe and efficacious replacement of synthetic leads that are associated with a wide range of toxicological issues. Methodology: Using a combination of Silica Gel-G column chromatography and preparative thin layer chromatography, the two principal green metallo-porphyrins (Chl-a and Chl-b) were sequentially extracted and isolated from crude extract of Spinacia oleracea L leaves. Antiradical efficacy, of the isolated green porphyrins was quantified by DPPH and Hydrogen peroxide radical scavenging assay. Cytoprotective efficacy was evaluated using ex-vivo hemolysis assay and anti-inflammatory potency was attested employing carrageenan induced paw edema bioassay. To enumerate on the anti-proliferative potency, MTT assay was employed, while toxicology of the isolates was evaluated employing OECD 420 acute toxicity guidelines. Findings: The study confirmed that isolated green porphyrins Chl-a and Chl-b as well as crude extract all exerts significant anti-radical, cytoprotective, anti-inflammatory and anti-proliferative efficacy however while potency of Chl-a was at par with that of reference standard and superior to the crude extract, Chl-b clocked in a value inferior to both. Furthermore, acute toxicity study indicated that even at p.o. dose of 2000mg/Kg b.w, no toxicity was manifested in either of the metalloporpyrin treated groups thus ascertaining the safe nature of the naturally mined metalloporphyrin entities. Also naturally mined Chl-a is not only a safer alternative to synthetic medicine but it is more potent and safe than its parent extract popularly used in herbal medicine. Conclusion: The results of the study indicates that Chl-a having a more profound structural resemblance to heme than Chl-b can be further modulated as a cost-effective and safe anti-radical alternative to synthetic leads in inhibiting inflammation and untoward cell proliferative while extending cyto-protection from pathological ROS generated in diseased states.

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Asymmetrical Cell Division With Exponential Growth

Cited by 5 publications

References 25 publications

An advection-diffusion process with proportional resetting

An advection-diffusion process with proportional resetting

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

An Anti-radical, Cytoprotective, Anti-proliferative, Anti-inflammatory and Toxicological Assessment of Metallo-porphyrins Isolated from Fresh Leaves of Spinacia oleracea L.

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