Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch

Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.Comment: 14 pages, 4 figure

Alpha shapes: Determining 3D shape complexity across morphologically diverse structures

Background. Following recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To utilise this data to address evolutionary and ecological questions, an array of tools has been developed to conduct 3D shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose the new ‘alpha-shapes’ method for quantifying 3D shape complexity. Methods. We apply alpha-shapes to quantify shape complexity in the mammalian baculum as an example of a morphologically disparate structure. Micro- computed-tomography (μCT) scans of bacula were conducted. Bacula were binarised and converted into point clouds. Following application of a scaling factor to account for absolute differences in size, a suite of alpha-shapes was fitted to each specimen. An alpha shape is a formed from a subcomplex of the Delaunay triangulation of a given set of points, and ranges in refinement from a very coarse mesh (approximating convex hulls) to a very fine fit. ‘Optimal’ alpha was defined as the degree of refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall shape ‘complexity’. Results Our results show that alpha-shapes can be used to quantify interspecific variation in shape ‘complexity’ within biological structures of disparate geometry. The ‘stepped’ nature of alpha curves is informative with regards to the contribution of specific morphological features to overall shape ‘complexity’. Alpha-shapes agrees with other measures of topographic complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as possessing the highest topographic complexity, contrasting with other shape metrics. 3D fractal dimension is found to be an inappropriate metric of complexity when applied to bacula. Conclusions. The alpha-shapes methodology can be used to calculate ‘optimal’ alpha refinement as a proxy for shape ‘complexity’ without identifying landmarks. The implementation of alpha-shapes is straightforward, and is automated to process large datasets quickly. Beyond genital shape, we consider the alpha-shapes technique to hold considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines