Stochastic effects in mean-field population growth: The quasi-Gaussian approximation to the case of a Taylor’s law-distributed substrate

Khalin, Andrey A.; Postnikov, Eugene B.; Ryabov, Alexey

doi:10.1016/j.physa.2018.07.052

Cited by 3 publications

(7 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These factors can both amplify sensitivity to, and obscure the role of, extrinsic physiochemical variables. [34][35][36][37][38] Therefore, even slight differences in experimental parameters can have a large effect on the measured properties, especially in multicellular systems such as biofilms. Even with accurate analytical chemistry tools such as FTIR, bioanalytical studies can suffer from poor measurement repeatability, which strongly limits reliable analysis and transferability to other studies.…”

Section: Discussionmentioning

confidence: 99%

Linear Scanning ATR-FTIR for Chemical Mapping and High-Throughput Studies of Pseudomonas sp. Biofilms in Microfluidic Channels

et al. 2018

View full text Add to dashboard Cite

A fully automated linear scanning attenuated total reflection (ATR) accessory is presented for Fourier transform infrared (FTIR) spectroscopy. The approach is based on the accurate displacement of a multi-bounce ATR crystal relative to a stationary infrared beam. To ensure accurate positioning and to provide a second sample characterization mode, a custom-built microscope was integrated into the system and the computerized work flow. Custom software includes automated control and measurement routines with a straightforward user interface for selecting parameters and monitoring experimental progress. This cost-effective modular system can be implemented on any research-grade spectrometer with a standard sample compartment for new bioanalytical chemistry studies. The system was validated and optimized for use with microfluidic flow cells containing growing Pseudomonas sp. bacterial biofilms. The complementarity among the scan positioning accuracy, measurement spatial resolution and the microchannel dimensions paves the way for parallel biological assays with real-time control over environmental parameters and minimal manual labor. By rotating the channel orientation relative to the beam path, the system could also be used for acquisition of linear biochemical maps and stitched microscope images along the channel length.

show abstract

Section: Discussionmentioning

confidence: 99%

Linear Scanning ATR-FTIR for Chemical Mapping and High-Throughput Studies of Pseudomonas sp. Biofilms in Microfluidic Channels

et al. 2018

View full text Add to dashboard Cite

show abstract

“…On the contrary, it has been recently revealed [15] that the stochasticity in the growth rates, under quite general assumptions on their probability density distribution, results in the replacement of the semilogarithmic linearity with the quadratic logarithmic growth function log(N/N 0 ) = rt + (σ 2 /2)t 2 . Namely, a similar curve shape is detected in the experimental observations in Figure 1A, and the details will be given in the section Data Description.…”

Section: Discussionmentioning

confidence: 99%

“…Following [15], let us consider the growing mycobacterial culture as consisting of multiple sub-populations N P (individual bacteria, bacterial colonies, or even groups of colonies) parametrized by the variable P, each of which grows exponentially within the chosen time interval between the lag-phase and the start of saturation:…”

Section: Data Discussion With Respect To the Stochastic Growth Modelmentioning

confidence: 99%

“…Note that we have taken negative k = P, which corresponds to a possible presence of initial bacteria, which become extinct during the experiment. In fact, more complex dependencies of the growth rate on the substrate consumption described by more complicated functions k(P), e.g., Jacob-Monod's (Holling II), as well as more complex probability distributions p(P) observable in population dynamics, can be reduced to the same Gaussian-based form (2) within the considered characteristic time interval, introducing an effective mean growth rate µ and an effective acceleration σ 2 ; see [15] for details.…”

Section: Data Discussion With Respect To the Stochastic Growth Modelmentioning

confidence: 99%

“…They represent four possible combinations of initial conditions for the mycobacterial cultures: two different initial dilutions determined the initial population density (found optically before placing the culture into the microplate kit) and two different generations cultured previously. To avoid possible bias, the data presented in Columns 1-8, [9][10][11][12][13][14][15][16], and 17-20 in the Supplementary Data (the sheet "Raw data"), and referred to as "sample #" in the plots and discussions below, originate from experiments separated by two-month intervals between them; their initial seeds were prepared separately as well. Table 1.…”

Section: Data Descriptionmentioning

confidence: 99%

See 2 more Smart Citations

Resazurin Assay Data for Mycobacterium tuberculosis Supporting a Model of the Growth Accelerated by a Stochastic Non-Homogeneity

Postnikov

Khalin

Lavrova

et al. 2019

Data

View full text Add to dashboard Cite

Tuberculosis is one of the most widespread worldwide diseases heavily affecting society. Among popular modern laboratory tests for mycobacterial growth, the resazurin assay has certain advantages due to its effectiveness and relatively low cost. However, the high heterogeneity of the mycobacterial population affects the average growth rate. This fact must be taken into account in a quantitative interpretation of these tests’ output—fluorescence growth curves—related to the population growth of viable mycobacteria. Here, we report the spectrophotometric data obtained via the resazurin assay for the standard reference strain of Mycobacterium tuberculosis H37Rv for different initial dilutions and generation numbers of the culture, as well as their primary processing from the point of view of the stochastic multiplicative growth model. The obtained data, which indicate an accelerated (instead of linear) growth of the population density logarithm between the end of the lag phase and the saturation, provide evidence of the importance of the growth rates’ stochasticity. An analysis of the curve fits resulted in an estimation of the first two moments of the growth rates’ probability distributions, showing its relevance to vital processes for mycobacterial culture.

show abstract

Ensemble density-dependent synchronization of mycobacterial growth: BACTEC MGIT 960 fluorescence-based analysis and mathematical modelling of coupled biophysical and chemical processes

et al. 2022

Self Cite

View full text Add to dashboard Cite

<abstract> <p>This study presents an analysis of <italic>M. tuberculosis</italic> growth data obtained using the BACTEC MGIT 960 system and respective mathematical models. The system is based on the detection of a decrease in oxygen level in the broth due to the bacterial respiration. It is shown that recordings sampled with a 1 hour rate provide an opportunity to distinguish between the oxygen consumption of growing cells and active cells division when the density of micro-organisms is sufficient to enter into the synchronized division mode. More specifically, the growth of culture is continuous only with large initial dilutions; otherwise, there are jumps between different growth stages with a time interval of 13–15 h. The combination of the oxygen-quenching kinetics for an analytic reagent and the population growth kinetics resulted in a mathematical model, which consists of mixing Verhulst's and Gompertz's models. The parameters of such mixing and switching between the models' prevalences are discussed with respect to oxygen uptake reactions reflected in the changes in the experimentally registered fluorescence level.</p> </abstract>

show abstract

Stochastic effects in mean-field population growth: The quasi-Gaussian approximation to the case of a Taylor’s law-distributed substrate

Cited by 3 publications

References 30 publications

Linear Scanning ATR-FTIR for Chemical Mapping and High-Throughput Studies of Pseudomonas sp. Biofilms in Microfluidic Channels

Linear Scanning ATR-FTIR for Chemical Mapping and High-Throughput Studies of Pseudomonas sp. Biofilms in Microfluidic Channels

Resazurin Assay Data for Mycobacterium tuberculosis Supporting a Model of the Growth Accelerated by a Stochastic Non-Homogeneity

Ensemble density-dependent synchronization of mycobacterial growth: BACTEC MGIT 960 fluorescence-based analysis and mathematical modelling of coupled biophysical and chemical processes

Contact Info

Product

Resources

About