Mouse Hair Cycle Expression Dynamics Modeled as Coupled Mesenchymal and Epithelial Oscillators

Abstract

The hair cycle is a dynamic process where follicles repeatedly move through phases of growth, retraction, and relative quiescence. This process is an example of temporal and spatial biological complexity. Understanding of the hair cycle and its regulation would shed light on many other complex systems relevant to biological and medical research. Currently, a systematic characterization of gene expression and summarization within the context of a mathematical model is not yet available. Given the cyclic nature of the hair cycle, we felt it was important to consider a subset of genes with periodic expression. To this end, we combined several mathematical approaches with high-throughput, whole mouse skin, mRNA expression data to characterize aspects of the dynamics and the possible cell populations corresponding to potentially periodic patterns. In particular two gene clusters, demonstrating properties of out-of-phase synchronized expression, were identified. A mean field, phase coupled oscillator model was shown to quantitatively recapitulate the synchronization observed in the data. Furthermore, we found only one configuration of positive-negative coupling to be dynamically stable, which provided insight on general features of the regulation. Subsequent bifurcation analysis was able to identify and describe alternate states based on perturbation of system parameters. A 2-population mixture model and cell type enrichment was used to associate the two gene clusters to features of background mesenchymal populations and rapidly expanding follicular epithelial cells. Distinct timing and localization of expression was also shown by RNA and protein imaging for representative genes. Taken together, the evidence suggests that synchronization between expanding epithelial and background mesenchymal cells may be maintained, in part, by inhibitory regulation, and potential mediators of this regulation were identified. Furthermore, the model suggests that impairing this negative regulation will drive a bifurcation which may represent transition into a pathological state such as hair miniaturization.

A role for the Tgf-β/Bmp co-receptor Endoglin in the molecular oscillator that regulates the hair follicle cycle

“…This result was broadly confirmed by the analysis of the Eng protein expression and localization pattern in the skin (Figure 1B and Supplementary Figure S2). Interestingly, such expression pattern perfectly fits with the profile of master feedback target regulators of the hair follicle cycle predicted by a robust mathematical model that describes hair follicle dynamics as the result of coupled mesenchymal and epithelial oscillators, and that, in fact, identifies Eng as one of those potential targets (Tasseff et al, 2014).…”

The Kuramoto model in complex networks

“…Other aspects of dynamical criticality in human brain functional networks were studied in [400] by comparing times series generated with the Kuramoto model and fMRI data recorded from normal subjects under resting conditions. Other recent works have investigated further aspects of the relation between structure and dynamics of phase oscillators in anatomical and functional cortical networks [214,378,[401][402][403][404][405][406], which includes studies on the effects of remote synchronization [407][408][409], a toolbox for large-scale simulations of brain dynamics using different models [410] and discussions about the limitations of the above mentioned approaches [411].…”

Expression of matrix metalloproteinases and tissue inhibitor of matrix metalloproteinases in the hair cycle

“…3 and 4 , the mRNA and protein expression levels of the enzymes were similar and detectable throughout the hair cycle. The expression of each protein fluctuated, with a peak at 5 and 10 weeks, and a decrease at 7 and 12 weeks, as is expected in the hair cycle ( 29 ).…”