Quantifying the biological effects of radiation is essential for radiotherapy and radiation protection. While research has centered on statistical analyses of experimental data, this approach often fails to elucidate underlying mechanisms, limiting the development of generalizable models. Describing time dependent phenomena, such as sub-lethal damage (SLD) recovery during fractionated irradiation, presents a particularly significant challenge for existing static models. To address this, we developed a mechanistic mathematical model that extends the classical multi-target, single-hit model by introducing explicit recovery transitions among damage states, allowing the simultaneous description of radiation-induced damage accumulation and biological recovery. We applied this model to Elkind and Sutton's classical split-dose experimental data to determine its parameters. The model reproduced the major features of split-dose survival curves for treatments with 0-, 2.5-, and 23-hour recovery intervals. We visualized the temporal changes in damage state distributions within the cell populations. These simulations provided a process-level interpretation of the characteristic shoulder-like response appearing after an inter-fraction recovery interval. Furthermore, the estimated recovery half-life was about 120 minutes, which is broadly consistent with reported timescales of DNA double-strand break repair in mammalian cells, supporting the biological interpretability of the model parameters. The proposed framework provides a simple, interpretable description of radiation-induced cell death dynamics, including SLD recovery, and may serve as a basis for the improved mechanistic modeling of radiobiological effects under different irradiation protocols.
Phenotypic plasticity can buffer environmental change, but its evolution depends on cue reliability, fitness costs, genetic variation, and the duration of selection. We developed an individual-based Trait-Environment Fitness Interaction (TEFI) model to examine how cultivation interruptions affect absolute fitness and reaction-norm evolution. During interruptions, selection, reproduction, and mutation ceased, while damage accumulated and decayed after cultivation resumed. Across 100 replicate populations per scenario, long interruptions produced substantially lower final fitness than continuous cultivation. Seed-matched analyses showed lower mean fitness after intermediate and long interruptions, whereas 95% paired intervals for short and recurrent interruptions included zero. None of the baseline interruption scenarios clearly increased mean or final plasticity. Duration experiments, mechanism ablation, genetic-correlation tests, environmental controls, and global sensitivity analysis showed that the fitness response was robust, whereas the plasticity response was conditional. Damage and incomplete recovery contributed to the long-interruption fitness decline, whereas the direct cost of evolved plasticity contributed little. A clear plasticity increase occurred only when long interruptions were combined with strong directional environmental change. Across seven crop datasets, normalized plasticity was lower in rice and wheat than in the other five crops (difference = 0.102, hierarchical-bootstrap 95% interval: 0.072–0.177; exact one-sided permutation P = 0.0476), with the direction robust to alternative metrics and leave-one-dataset-out analyses. This provides a quantitative consistency test, not crop-specific validation of TEFI. Our results identify interruption duration, environmental direction, and recovery opportunity as determinants of post-interruption fitness and caution against assuming that cultivation interruption universally promotes greater plasticity.
Cortical spreading depolarization (CSD) propagates across cortex at millimeters per minute and can slow in sulcal regions, but the contribution of folded geometry remains unresolved. We tested whether sulcal dipole alignment adds a measurable electrodiffusive delay in a reduced surface model in which extracellular diffusion remains the dominant transport process. The model included overlapping extracellular and intracellular surface compartments, explicit K+, Na+, and Cl- concentrations, Goldman–Hodgkin–Katz membrane voltage, activation-dependent membrane sources, Na+/K+ pump dynamics, dynamic extracellular-space restriction, and a quasi-static screened potential. A nonlocal dipole kernel coupled membrane-current deviations through geodesic distance and surface-normal opposition. We compared paired simulations with dipole alignment disabled or enabled in one representative folded surface, 12 synthetic folded geometries plus a flat control, and 8 sulcal versus 8 flatter fsaverage6 patches. In the representative simulation, cross-fold speed decreased from 2.609 to 2.537 mm/min and the region-of-interest E1–E2 delay increased from 128.0 to 131.6 s. Across the synthetic sweep, all folded geometries slowed, whereas the flat control did not. Mean slowdown was 0.136 mm/min (95% bootstrap CI 0.106–0.170), corresponding to a 4.88% speed reduction, and mean delay increased by 6.81 s (95% CI 5.31–8.26). Null kernels and atlas patches supported geometry specificity. In this reduced surface model, folded cortical anatomy adds an orientation-dependent electrodiffusive slowing term to diffusion-driven CSD propagation.
