Inferring time derivatives including cell growth rates using Gaussian processes

Swain, Peter S.; Stevenson, Keiran; Leary, Allen; Montaño-Gutierrez, Luis Fernando; Clark, Ivan B. N.; Vogel, Jackie; Pilizota, Teuta

doi:10.1038/ncomms13766

Cited by 108 publications

(128 citation statements)

References 22 publications

(35 reference statements)

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“…Individual growth curves were analyzed with the software deODorizer from (40). To extract the maximum growth rate, three or more repeats in the same condition were aligned by the chosen OD value (usually OD $ 0.4) using the growth curve that reached it first (in the given condition).…”

Section: Plate Reader Datamentioning

confidence: 99%

A General Workflow for Characterization of Nernstian Dyes and Their Effects on Bacterial Physiology

Mancini

Terradot

Tian

et al. 2020

Biophysical Journal

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The electrical membrane potential (V m) is one of the components of the electrochemical potential of protons across the biological membrane (proton motive force), which powers many vital cellular processes. Because V m also plays a role in signal transduction, measuring it is of great interest. Over the years, a variety of techniques have been developed for the purpose. In bacteria, given their small size, Nernstian membrane voltage probes are arguably the favorite strategy, and their cytoplasmic accumulation depends on V m according to the Nernst equation. However, a careful calibration of Nernstian probes that takes into account the tradeoffs between the ease with which the signal from the dye is observed and the dyes' interactions with cellular physiology is rarely performed. Here, we use a mathematical model to understand such tradeoffs and apply the results to assess the applicability of the Thioflavin T dye as a V m sensor in Escherichia coli. We identify the conditions in which the dye turns from a V m probe into an actuator and, based on the model and experimental results, propose a general workflow for the characterization of Nernstian dye candidates.

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Section: Plate Reader Datamentioning

confidence: 99%

A General Workflow for Characterization of Nernstian Dyes and Their Effects on Bacterial Physiology

Mancini

Terradot

Tian

et al. 2020

Biophysical Journal

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“…The operator h obs t interpolates the sparse observed composition data Y to arbitrary radii r t . To transform the scattered discrete dataset of composition observations into a continuous one, we interpolate the data using Gaussian process regression [9], which is widely used for prediction and optimization in practical fields [18,19]. If the normalization constant in the denominator of Eq.…”

Section: B Bayesian Formulationmentioning

confidence: 99%

“…The synthetic garnet grain grew according to the assumed diffusion-controlled grain-growth law [Eq. (18)] along the assumed P -T -t trajectory, as shown in Figs. 4(a)-4(c).…”

Section: Numerical Experiments a Problem Settingmentioning

confidence: 99%

“…The synthetic garnet grain grew according to the assumed diffusion-controlled grain-growth law [Eq. (18)] along the assumed P -T -t trajectory. The parameter values were taken from Okudaira's previous work [28]: the rate constant k was 6.29×10 −14 m 2 /s; the activation energyE a was 8.37×10 4 J/mol; and the gas constant R was 8.314 J/(mol K).…”

Section: Appendix B: Details Of Numerical Experimentsmentioning

confidence: 99%

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Recovering the past history of natural recording media by Bayesian inversion

et al. 2018

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Spatial growth patterns are natural recording media (NRMs) that preserve important historical information, which can be accessed and analyzed to reconstruct past environmental conditions and events. Here, we propose the Bayesian inversion method, which can reconstruct the evolution of target parameters from purely spatial data by extending data assimilation (DA), a method for integrating numerical simulations with time-series observations. Our method converts discrete spatial observation data to time-series data with the help of a law representing the NRM's time-evolution dynamics and Gaussian process regression, enabling us to directly compare the observations with a numerical simulation based on the DA framework. The method's effectiveness is demonstrated using a synthetic inversion problem, namely reconstructing the pressure-temperature-time (P-T-t) path of a metamorphic rock from chemical composition profiles of its zoned minerals. The proposed method is broadly applicable to a wide variety of NRMs.

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“…To describe and/or predict S-shaped growth curves, a number of mathematical models have been proposed, such as the Logistic (Verhulst, 1845; 1847) and Gompertz (Winsor, 1932) models, and revised and expanded repeatedly to better understand the biological process of bacterial growth under varied conditions (Fujikawa and Morozumi, 2005; Kargi, 2009; Koseki and Nonaka, 2012; Alonso et al, 2014; Desmond-Le Quemener and Bouchez, 2014; Hermsen et al, 2015). Although the growth curve of the most representative bacterium, Escherichia coli , has been examined since the 1930s (Winsor, 1932), the indescribable complexity of the growth dynamics of E. coli remain and are still under investigation with other models to understand the current differential growth dynamics (Swain et al, 2016; Tonner et al, 2017).…”

Section: Introductionmentioning

confidence: 99%