ABSTRACT
Ordered polarity alignment of cell populations plays vital roles in biology, such as in hair follicle alignment and asymmetric cell division. Although cell polarity is uniformly oriented along a tissue axis in many tissues, its mechanism is not well understood. In this paper, we propose a theoretical framework to understand the generic dynamical properties of polarity alignment in interacting cellular units, where each cell is described by a reaction-diffusion system, and the cells further interact with one another through the contacting surfaces between them. Using a perturbation method under the assumption of weak coupling between cells, we derive a reduced model in which polarity of each cell is described by only one variable. Essential dynamical properties including the effects of cell shape, coupling heterogeneity, external signal and noise can be clarified analytically. In particular, we show that the anisotropicity of the system, such as oriented cell elongation and axial asymmetry in the coupling strength, can serve as a global cue that drives the uniform orientation of cell polarity along a certain axis. Our study bridges the gap between detailed and phenomenological models, and it is expected to facilitate the study of polarity dynamics in various nonequilibrium systems.
Subject(s)
Cell Polarity/physiology , Models, Biological , Algorithms , Animals , Anisotropy , DiffusionABSTRACT
Excitable media can develop spiral chaos, in which the number of spirals changes chaotically with time. Depending on parameter values in dynamical equations, spiral chaos may permanently persist or spontaneously arrive at a steady state after a transient time, referred to as the lifetime. Previous numerical studies have demonstrated that the lifetime of transient spiral chaos increases exponentially with system size to a good approximation. In this study, using the fact that the number of spirals obeys a Gaussian distribution, we provide a general expression for the system size dependence of the lifetime for large system sizes, which is indeed exponential. We confirm that the expression is in good agreement with numerically obtained lifetimes for both excitable and oscillatory media with parameter sets near the onset of transient chaos. The expression we develop for the lifetime is expected to be useful for predicting lifetimes in large systems.
ABSTRACT
PURPOSE: The purpose of this study was to analyze the difference in educational effect on students who experienced both lecture-based learning (LBL) and problem-based learning (PBL) in a complete denture course. The analysis focused on differences between the two methods concerning self study, ability to understand clinical inference, and appraisal of class contents and tutors. METHODS: In the complete denture preclinical course, the class of 2003 received LBL in 3rd grade and PBL in 4th grade. PBL was planned to present five cases in five consecutive classes. Group discussion was carried out for each case, and a summary was required to be produced two times as a group, two times as an individual report and one time by group presentation. A questionnaire regarding the educational effect of LBL and PBL and assessment of tutors was administered. Factor analysis was carried out to classify the questionnaire items and each item was analyzed between LBL and PBL (Paired-t test). RESULTS: Factor analysis revealed that the questionnaire items could be classified into four components. Comparing lecture type and PBL: "study attitude" (4 out of 7 items), "clinical inference ability" (all items), "class contents" (5 out of 7 items) and "tutor appraisal" (2 out of 5 items) showed significant assessment with PBL. Eighteen of 27 items (66.6%) indicated the significant usefulness of PBL. CONCLUSION: PBL improves the educational effect of self study and clinical inference ability, in comparison with LBL. However, since students are passive about taking the same system class repeatedly, a strategy to improve their attitude needs to be considered.
