Improved Asymptotic Expansions in High- and Low-Dose Ranges for Generalized Multi-Hit Model of Radiation-Induced Cell Survival.

By considering an upper bound on the number of radiation-induced potential lethal damages that can be repaired in a cell, we have proposed the generalized multi-hit (GMH) model with a closed-form solution, which can better fit various radiation-induced cell survival curves. Recent analysis shows that the asymptotic expansions that we gave before can be used to approximate the generalized single-hit single-target (GSHST) model rather than the GMH model. To illustrate the asymptotic trends of radiation-induced cell survival curves, in this study, we improve the asymptotic expansions of the GMH model in low- and high-dose ranges based on the limit formula of the incomplete gamma function in the corresponding dose ranges. When the upper limit of the number of radiation-induced potential lethal damages is one, the improved expansions of the GMH model can be reduced to the previous expansions of the GSHST model, and the improved asymptotic expansions of the GMH model also indicate that the GMH model has the generalized linear-quadratic-linear (LQL) feature. The numerical simulations indicate that the improved asymptotic expansions in high- and low-dose ranges agree well with the non-linear fitting of the GMH model in six kinds of cell lines under the corresponding dose ranges. In addition, we analyze the relative errors of the improved expansions of the GMH model in high- and low-dose ranges to demonstrate the accuracy and effectiveness of the improved expansions. Based on the error analysis, we further give the reasonable ranges of radiation dose applicable to the improved asymptotic expansions of the GMH model.

Generalized Multi-Hit Model of Radiation-Induced Cell Survival with a Closed-Form Solution: An Alternative Method for Determining Isoeffect Doses in Practical Radiotherapy.

The standard linear-quadratic (LQ) model is currently the preferred model for describing the ionizing radiation-induced cell survival curves and tissue responses. And the LQ model is also widely used to calculate isoeffect doses for comparing different fractionated schemes in clinical radiotherapy. Despite its ubiquity, because the actual dose-response curve may appear linear at high doses in the semilogarithmic plot, the application of the LQ model is greatly challenged in the high-dose region, while the dose employed in stereotactic body radiotherapy (SBRT) is often in this area. Alternatively, the biophysical models of radiation-induced effects with a linear-quadratic-linear (LQL) characteristic can well fit the dose-survival curve of cells in vitro. However, most of these LQL models are phenomenological and have not fully considered the biophysical mechanism of radiation-induced damage and repair, and the fitting quality decreases in some high-dose ranges. In this work, to provide an alternative model to describe the cell survival curves in high-dose ranges and predict the biologically effective dose (BED) for SBRT, we propose a novel generalized multi-hit model with a closed-form solution by considering an upper bound on the number of lethal damages induced by radiation that can be repaired in a cell. This model has a clear biophysical basis and a simple expression, and also has the LQL characteristic under low- and high-dose approximate conditions. The experimental data fitting indicated that compared to the standard LQ model and our previously generalized target model, the current model can better fit the radiation-induced cell survival curves in the high-dose ranges (P < 0.05). The current model parameters and parameter ratios were determined from the fits in different kinds of cell lines irradiated with various dose rates and linear energy transfer (LET), which indicates that the model parameters significantly depend on the dose rate and LET. Based on the current model, we derived two equivalence formulae for the BED calculations in the low- and high-dose ranges, and then calculated the BED for the clinical data of SBRT from 17 selected studies. The correlation analysis showed that there were significant linear correlations between the BED at isocenter and planning target volume (PTV) edge calculated by this model and the LQ model (R > 0.86, P < 0.001). In conclusion, the generalized multi-hit model proposed in this work can be used as an alternative tool to handle in vitro radiation-induced cell survival curves in high-dose ranges, and calculate the in vivo BED for comparing the dose fractionation schemes in clinical radiotherapy.

Comparison of the transcriptome between two cotton lines of different fiber color and quality.

To understand the mechanism of fiber development and pigmentation formation, the mRNAs of two cotton lines were sequenced: line Z128 (light brown fiber) was a selected mutant from line Z263 (dark brown fiber). The primary walls of the fiber cell in both Z263 and Z128 contain pigments; more pigments were laid in the lumen of the fiber cell in Z263 compared with that in Z128. However, Z263 contained less cellulose than Z128. A total of 71,895 unigenes were generated: 13,278 (20.26%) unigenes were defined as differentially expressed genes (DEGs) by comparing the library of Z128 with that of Z263; 5,345 (8.16%) unigenes were up-regulated and 7,933 (12.10%) unigenes were down-regulated. qRT-PCR and comparative transcriptional analysis demonstrated that the pigmentation formation in brown cotton fiber was possibly the consequence of an interaction between oxidized tannins and glycosylated anthocyanins. Furthermore, our results showed the pigmentation related genes not only regulated the fiber color but also influenced the fiber quality at the fiber elongation stage (10 DPA). The highly expressed flavonoid gene in the fiber elongation stage could be related to the fiber quality. DEGs analyses also revealed that transcript levels of some fiber development genes (Ca(2+)/CaM, reactive oxygen, ethylene and sucrose phosphate synthase) varied dramatically between these two cotton lines.