P. F. Verhulst's “notice sur la loi que la populations suit dans son accroissement” from correspondence mathematique et physique. Ghent, vol. X, 1838

Vogels, Maurice; Zoeckler, Rita; Stasiw, D.M.; Cerny, L.C.

doi:10.1007/bf02309004

Cited by 88 publications

(49 citation statements)

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“…where μ is the constant specific growth rate. Among all models describing a bounded sigmoidal growth curve, one of the simplest is the logistic model (Vogels et al, 1975). This model requires a maximum carrying capacity ( S max ) and an initial cell-covered surface ( S 0 ) to be solved, and is expressed by a nonlinear differential equation (Shuler & Kargi, 1992), where C max is a growth constant:…”

Section: Methodsmentioning

confidence: 99%

Selection and Tuning of a Fast and Simple Phase-Contrast Microscopy Image Segmentation Algorithm for Measuring Myoblast Growth Kinetics in an Automated Manner

2013

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Acquiring and processing phase-contrast microscopy images in wide-field long-term live-cell imaging and high-throughput screening applications is still a challenge as the methodology and algorithms used must be fast, simple to use and tune, and as minimally intrusive as possible. In this paper, we developed a simple and fast algorithm to compute the cell-covered surface (degree of confluence) in phase-contrast microscopy images. This segmentation algorithm is based on a range filter of a specified size, a minimum range threshold, and a minimum object size threshold. These parameters were adjusted in order to maximize the F-measure function on a calibration set of 200 hand-segmented images, and its performance was compared with other algorithms proposed in the literature. A set of one million images from 37 myoblast cell cultures under different conditions were processed to obtain their cell-covered surface against time. The data were used to fit exponential and logistic models, and the analysis showed a linear relationship between the kinetic parameters and passage number and highlighted the effect of culture medium quality on cell growth kinetics. This algorithm could be used for real-time monitoring of cell cultures and for high-throughput screening experiments upon adequate tuning.

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Section: Methodsmentioning

confidence: 99%

Selection and Tuning of a Fast and Simple Phase-Contrast Microscopy Image Segmentation Algorithm for Measuring Myoblast Growth Kinetics in an Automated Manner

2013

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“…Verhulst (Vogels et al 1975 ) developed the first logistic equation to describe population growth based on the work of Thomas Malthus. Verhulst added an extra term, K , called the overall saturation constant to the first model of Malthus to represent the resistance to growth up to a certain limit value of biomass concentration as shown in the equation describing logistic growth.…”

Section: Macroscopic Kinetic Modelsmentioning

confidence: 99%

Macroscopic modeling of mammalian cell growth and metabolism

Yahia

Malphettes

Heinzle

2015

Appl Microbiol Biotechnol

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We review major modeling strategies and methods to understand and simulate the macroscopic behavior of mammalian cells. These strategies comprise two important steps: the first step is to identify stoichiometric relationships for the cultured cells connecting the extracellular inputs and outputs. In a second step, macroscopic kinetic models are introduced. These relationships together with bioreactor and metabolite balances provide a complete description of a system in the form of a set of differential equations. These can be used for the simulation of cell culture performance and further for optimization of production.

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“…This model is based on a generalized logistic (Verhulst) growth model (Vogels et al 1975) as already done by Moejes et al (2017) to model the dynamics of a culture embedding P. tricornutum and a complex microbial community. Additionally, as P. haloplanktis is feeding on DOM released by P. tricornutum as the only carbon source, we included a Monod-type kinetic (Monod 1949) to reflect this dependency.…”

Section: Resultsmentioning

confidence: 99%

Scaling down the microbial loop: data-driven modelling of growth interactions in a diatom-bacterium co-culture

Daly

Perrin

Viti

et al. 2021

Preprint

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An intricate set of interactions characterizes marine ecosystems. One of the most important is represented by the so-called microbial loop, which includes the exchange of dissolved organic matter (DOM) from phototrophic organisms to heterotrophic bacteria. Here, it can be used as the major carbon and energy source. Arguably, this interaction is one of the foundations of the entire ocean food-web. Carbon fixed by phytoplankton can be redirected to bacterial cells in two main ways; either i) bacteria feed on dead (eventually lysed) phytoplankton cells or ii) DOM is actively released by phytoplankton cells (a widespread process that may result in up to 50% of the fixed carbon leaving the cell). In this work, we have set up a co-culture of the model diatom Phaeodactylum tricornutum and the model chemoheterotrophic bacterium Pseudoalteromonas haloplanktis TAC125 and used this system to study the interactions between these two representatives of the microbial loop. We show that the bacterium can indeed thrive on diatom-derived carbon and that this growth can be sustained by both diatom dead cells and diatom-released compounds. These observations were formalized in a network of putative interactions between P. tricornutum and P. haloplanktis and implemented in a mathematical model that reproduces the observed co-culture dynamics, suggesting that our hypotheses on the interactions occurring in this two-player system can accurately explain the experimental data.

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P. F. Verhulst's “notice sur la loi que la populations suit dans son accroissement” from correspondence mathematique et physique. Ghent, vol. X, 1838

Cited by 88 publications

References 0 publications

Selection and Tuning of a Fast and Simple Phase-Contrast Microscopy Image Segmentation Algorithm for Measuring Myoblast Growth Kinetics in an Automated Manner

Selection and Tuning of a Fast and Simple Phase-Contrast Microscopy Image Segmentation Algorithm for Measuring Myoblast Growth Kinetics in an Automated Manner

Macroscopic modeling of mammalian cell growth and metabolism

Scaling down the microbial loop: data-driven modelling of growth interactions in a diatom-bacterium co-culture

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