Search arXiv⌕ Search

arXiv · 0708.1993

Dynamics of glucose-lactose diauxic growth in E. coli

Abstract

We present a mathematical model of glucose-lactose diauxic growth in Escherichia coli including both the postive and negative regulation mechanisms of the lactose operon as well as the inducer exclusion. To validate this model, we first calculated the time evolution of beta-galactosidase for only the lactose nutrient and compared the numerical results with experimental data. Second, we compared the calculated cell biomass of the glucose-lactose diauxic growth with the experimental optical density of the diauxic growth for a particular E. coli MG 1655. For both cases, the numerical calculations from this model are in good agreement with these two experiments' data. The diauxic growth pattern of a wild type E. coli was also investigated.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zhao Lu, Michael A Lee. 2011-01-28. Dynamics of glucose-lactose diauxic growth in E. coli. https://arxiv.org/abs/0708.1993

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

A mechanistic interpretation of mutation risk across biological scales

The allometry of cancer risk in mammals is scale-specific, as the inter-specific, intra-specific, and inter-organ patterns in cancer risk scaling are distinct from each other. While cancer risk barely changes with increasing body sizes across species, larger conspecifics are known to be at a higher risk of cancer. Cancer risk trends with age and lifespan have likewise been documented in humans and other species. Nevertheless, mammals broadly share developmental features, and the twin processes of cell division and differentiation are central to developmental dynamics. In this study, we suppose that a better understanding of these processes across biological scales could lead to a clearer understanding of cancer risk allometries. We develop an agent-based model in which a cell compartment grows from one cell to a target size. We assess how developmental dynamics scale with compartment size and influence mutation accumulation. Our data identify specific regions of the parameter space where the accumulation of neutral mutations increases with cell number, while providing a mechanistic explanation for such behavior. The accumulation of non-neutral mutations reveals an interesting antagonism in cell fitness between mutation and differentiation, which could change the viability of a given developmental strategy. Our model is able to produce a wide range of trends in cancer risk allometries in different parts of its parameter space, reflecting the observed heterogeneity across biological scales. Our results provide a theoretical framework that allows us to elucidate the conditions of mutation-differentiation balance under which having more cells does lead to higher cancer risk, and importantly, the conditions under which it does not.

q-bio.OT↗

2D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation

Once diagnosed, cancer requires a fast, reliable and preferably cost-efficient assessment of the current state and potential progression of the disease. A new method for estimating tumor cell diffusivity $D$ and proliferation rate $γ$ in the context of the mechanistic reaction-diffusion equation from single-point-in-time routine biopsies aims to deliver just that, and quantities computed from the parameter estimates have recently been tested as a new biomarkers for risk-stratification in radiotherapy. Here, we extend the findings of this previous work by providing a first theoretical validation. The method is applied to in-silico biopsies which are generated by solving the two-dimensional reaction-diffusion equation for different growth terms (exponential and logistic) with a Dirac-Delta initial condition, and transforming the continuous results into spatial point patterns via a form of reverse coarse-graining. If no information about tumor age is used, in short-term experiments the original dispersion length $\sqrt{D/γ}$ could be retrieved with a relative root mean squared error (RRMSE) of around 8% and an $\text{R}^2$-value of 0.97. In long-term experiments, the RRMSEs ranged from 8 to 14% and the $\text{R}^2$-values from 0.75 to 0.98. The scaled front velocity $\sqrt{D \cdotγ}$, which can only be estimated if information about tumor age is available, was retrieved with an RRMSE of 7% and an $\text{R}^2$ of 0.98 in both, the short-term and the long-term experiments.

q-bio.OT↗

Flash-Radiomics: A Scalable Hybrid CPU-CUDA Engine for Standardized Scalar Radiomics and Accelerated Spatial Mapping

Background and Objectives: Spatial mapping retains the spatial distribution of radiomic features, but computational cost and fragmented software limit its use. We developed Flash-Radiomics with scalar extraction and spatial mapping, a central processing unit (CPU) backend, a hybrid Compute Unified Device Architecture (CUDA) backend, consistent feature names, and Hierarchical Data Format version 5 (HDF5) storage. Methods: We evaluated Image Biomarker Standardisation Initiative (IBSI) compliance, CPU-CUDA concordance, and end-to-end processing time. Compliance testing included 825 chapter 1 (IBSI-1) tests covering 165 high-consensus features and 323 chapter 2 (IBSI-2) tests with numerical references. Concordance testing included 1,148 scalar pairs and 93 spatial-map pairs. End-to-end processing time was measured five times per input volume of interest (VOI) size. Comparisons included the Medical Image Radiomics Processor (MIRP) and PyRadiomics for 102 shared scalar features and PyRadiomics for 93 shared spatial maps. Results: Both backends passed all 1,148 IBSI tests, and all paired results were concordant. At the largest scalar input, CPU required 76.343 s and hybrid CUDA 81.915 s; CPU was 4.7 times faster than MIRP and 190.7 times faster than PyRadiomics. At the largest spatial input completed by both backends, hybrid CUDA reduced processing time by 68.6% relative to CPU (79.280 versus 252.791 s). At PyRadiomics' largest completed spatial input, hybrid CUDA was 84.9 times faster. Conclusions: Flash-Radiomics unified standardized scalar extraction, spatial mapping, concordant CPU-CUDA results, and HDF5 storage. CPU processing time was similar or shorter for scalar extraction, whereas hybrid CUDA was faster for spatial mapping under the tested conditions.

q-bio.OT↗