Modelling The Cancer Growth Process By Stochastic Delay Diffferential Equations Under Verhults And Gompertz's Law

In this paper, the uncontrolled environmental factors are perturbed into the intrinsic growth rate factor of deterministic equations of the growth process. The growth process under two different laws which are Verhults and Gompertz’s law are considered, thus leading to stochastic delay differential equations (SDDEs) of logistic and Gompertzian, respectively. Gompertzian deterministic model has been proved to fit well the clinical data of cancerous growth, however the performance of stochastic model towards clinical data is yet to be confirmed. The prediction quality of logistic and Gompertzian SDDEs are evaluating by comparing the simulated results with the clinical data of cervical cancer growth. The parameter estimation of stochastic models is computed by using simulated maximum likelihood method. We adopt 4-stage stochastic Runge-Kutta to simulate the solution of stochastic models

Potential Application of the <i>Oryza sativa</i> Monodehydroascorbate Reductase Gene (<i>OsMDHAR</i>) to Improve the Stress Tolerance and Fermentative Capacity of <i>Saccharomyces cerevisiae</i>

<div><p>Monodehydroascorbate reductase (MDHAR; EC 1.6.5.4) is an important enzyme for ascorbate recycling. To examine whether heterologous expression of <i>MDHAR</i> from <i>Oryza sativa</i> (<i>OsMDHAR</i>) can prevent the deleterious effects of unfavorable growth conditions, we constructed a transgenic yeast strain harboring a recombinant plasmid carrying <i>OsMDHAR</i> (p426GPD::OsMDHAR). <i>OsMDHAR</i>-expressing yeast cells displayed enhanced tolerance to hydrogen peroxide by maintaining redox homoeostasis, proteostasis, and the ascorbate (AsA)-like pool following the accumulation of antioxidant enzymes and molecules, metabolic enzymes, and molecular chaperones and their cofactors, compared to wild-type (WT) cells carrying vector alone. The addition of exogenous AsA or its analogue isoascorbic acid increased the viability of WT and <i>ara2Δ</i> cells under oxidative stress. Furthermore, the survival of <i>OsMDHAR</i>-expressing cells was greater than that of WT cells when cells at mid-log growth phase were exposed to high concentrations of ethanol. High <i>OsMDHAR</i> expression also improved the fermentative capacity of the yeast during glucose-based batch fermentation at a standard cultivation temperature (30°C). The alcohol yield of <i>OsMDHAR</i>-expressing transgenic yeast during fermentation was approximately 25% (0.18 g·g^-1) higher than that of WT yeast. Accordingly, <i>OsMDHAR</i>-expressing transgenic yeast showed prolonged survival during the environmental stresses produced during fermentation. These results suggest that heterologous <i>OsMDHAR</i> expression increases tolerance to reactive oxygen species-induced oxidative stress by improving cellular redox homeostasis and improves survival during fermentation, which enhances fermentative capacity.</p></div

Fermentative capacity and the survival of <i>OsMDHAR</i>-expressing yeast cells during batch fermentation.

<p>(A) Fermentative capacity was analyzed by measuring the alcohol (AC) and residual glucose (RG) concentrations in YG medium after fermentation for 72 h at 30°C. Upward triangles, AC of WT cells; circles, AC of TC cells; squares, RG of WT cells; diamonds, RG of TC cells. (B) Time-dependent <i>OsMDHAR</i> expression during batch fermentation was evaluated by western blotting. Tubulin (Tub) was used as a loading control. (C) Growth kinetics during fermentation was assessed by measuring the OD₆₀₀ at 2-h intervals for the indicated time. Squares, WT cells; circles, TC cells. (D) Cell viability during fermentation at 30°C was assessed by a spotting assay. Cells were harvested after 24 h (upper panel), 48 h (middle panel), and 72 h (lower panel) of fermentation and serially diluted to 10⁻⁹. A 5-μL aliquot of each diluted solution was spotted onto YPD agar plates. After incubation for 3 days, the plates were photographed. (E) Stress response to ethanol. Mid-log phase yeast cells (OD₆₀₀ ≈ 2.0) were exposed to different concentrations of ethanol (0, 15%, and 20%) for 1 h, serially diluted, and spotted onto YPD agar plates. WT, yeast cells with an empty vector; TC, <i>OsMDHAR</i>-expressing yeast cells.</p

Stress response related to ascorbate (AsA)-like molecules.

<p>(A) AsA-like content in yeast cells exposed to 20 mM H₂O₂ for 1 h was analyzed and is shown as nmol per mg protein. The ratio shown is that of the reduced form to oxidized form. (B) <i>ARA2</i> expression was evaluated by semi-quantitative RT-PCR. <i>PDA1</i> was used as a control. (C) Oxidative stress response of yeast cells in the absence and presence of <i>ARA2</i>. Mid-log phase cells were serially diluted, and 5 μL of the diluted solutions were spotted onto YPD agar plates containing 4 mM H₂O₂ (upper panels). Mid-log phase cells were treated with 20 mM H₂O₂ for 1 h with shaking, diluted with YPD medium, and spotted onto YPD agar plates. The plates were incubated for 2–3 days and photographed. (D) Stress sensitivity of <i>ara2Δ</i> yeast cells, in which the erythroascorbate (EAA) biosynthesis gene was deleted. Yeast cells (A₆₀₀ ≈ 1.0) were exposed to 10 mM H₂O₂ for 1 h at 28°C with shaking, serially diluted with YPD medium, spotted onto YPD agar plates, and incubated for 2–3 days. (E) The redox state of <i>ara2Δ</i> yeast cells under oxidative conditions. Yeast cells (OD₆₀₀ ≈ 1.0) were exposed to 10 mM H₂O₂ for 1 h after DCFHDA and DHAR 123 treatment for 30 min and washed twice with phosphate-buffered saline (PBS). Probe intensity was observed by fluorescence microscopy. BY, wild-type cells without an empty vector; <i>ara2Δ</i>, cells with a deletion of the EAA biosynthetic gene <i>ARA2</i>; WT, wild-type yeast cells with an empty vector; TC, yeast cells with p426GPD::OsMDHAR; WA, <i>ara2Δ</i> yeast cells with an empty vector; TA, <i>ara2Δ</i> yeast cells with p426GPD::OsMDHAR; N, normal conditions; S, in the presence of H₂O₂.</p

Analyses of cell rescue proteins, redox state, and protein oxidation under oxidative conditions.

<p>(A) Expression changes in antioxidant and metabolic enzymes in mid-log phase yeast cells exposed to 20 mM H₂O₂ for 1 h with shaking. Tubulin (Tub) was used as a loading control. (B) Hydroperoxide levels in TC cells in the absence (red bar) and presence (green bar) of 20 mM H₂O₂ were assessed using FOX reagent and were calculated relative to that in WT cells grown under normal conditions, which was set to 100%. (C) Mid-log phase yeast were exposed to 20 mM H₂O₂ for 1 h at 28°C with shaking. Redox state was analyzed by measuring DCFHDA oxidation as an indicator of cytosolic ROS. (D) Sensitivity of mutants (<i>sod1Δ</i>, <i>tsa1Δ</i>, <i>por1Δ</i>, and <i>por2Δ</i>) to oxidative stress. Yeast cells (OD₆₀₀ ≈ 1.0) were exposed to 10 mM H₂O₂ for 1 h at 28°C with shaking, serially diluted with YPD medium, spotted onto YPD agar plates, and incubated for 2–3 days. (E) Expression changes in molecular chaperones in mid-log phase yeast cells exposed to 20 mM H₂O₂ for 1 h with shaking. Tubulin (Tub) was used as a loading control. (F) Protein carbonylation in yeast cells exposed to 20 mM H₂O₂ for 1 h was calculated relative to that in WT cells under normal conditions, which was set to 100%. Red bar, normal conditions; green bar, H₂O₂ treatment; WT, yeast cells with an empty vector; TC, <i>OsMDHAR</i>-expressing yeast cells; N, normal conditions; S, H₂O₂ treatment.</p

Construction of an <i>OsMDHAR-</i>expressing yeast vector and the stress response of <i>OsMDHAR-</i>expressing yeast to hydrogen peroxide.

<p>(A) Schematic diagram of the p426GPD::OsMDHAR construct. The <i>OsMDHAR</i> gene (approximately 1.5 kbp) was subcloned to generate the p426GPD::OsMDHAR construct with <i>OsMDHAR</i> under the control of the constitutive <i>GPD</i> promoter. Semi-quantitative RT-PCR (B), immunoblotting (C), and an enzymatic assay (D) were performed to examine whether <i>OsMDHAR</i> is expressed in this yeast strain. <i>PDA1</i> and tubulin (Tub) were used as housekeeping controls for RT-PCR and western blotting, respectively. The molecular size of the PCR product and molecular weight of the detected band were approximately 494 bp and 47 kDa, respectively. Stress tolerance to hydrogen peroxide was evaluated by cell survival, growth kinetics, and spotting assays. (E) To monitor cell viability, yeast cells precultured in YPD medium were inoculated into fresh YPD medium and exposed to different concentrations of H₂O₂ for 16 h at 28°C. Then, the optical density at 600 nm (OD₆₀₀) was measured. Circles, cells transformed with p426GPD-<i>OsMDHAR</i> (TC cells); squares, wild-type (WT) cells transformed with an empty vector. (F) For the growth kinetics assay, precultured yeast cells were inoculated into YPD medium containing 5 mM H₂O₂, and the OD₆₀₀ was measured at 2-h intervals for 36 h. A streaking assay was also performed, in which mid-log phase yeast cells (OD₆₀₀ ≈ 2.0) were streaked onto YPD agar plates supplemented with 5 mM H₂O₂. WT (squares) and TC (circles) cells in the absence of 5 mM H₂O₂; WT (upward triangles) and TC (diamonds) cells in the presence of 5 mM H₂O₂. (G) Mid-log phase yeast cells were exposed to 20 mM H₂O₂ for 1 h with shaking, and serially diluted with YPD medium. A 5-μL aliquot of each dilution was spotted onto YPD agar plates.</p