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Mouse hair cycle expression dynamics modeled as coupled mesenchymal and epithelial oscillators.

Tasseff R, Bheda-Malge A, DiColandrea T, Bascom CC, Isfort RJ, Gelinas R - PLoS Comput. Biol. (2014)

Bottom Line: Furthermore, we found only one configuration of positive-negative coupling to be dynamically stable, which provided insight on general features of the regulation.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.

View Article: PubMed Central - PubMed

Affiliation: Institute for Systems Biology, Seattle, Washington, United States of America.

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.

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Summary schematic of the hair oscillator.Synchronization (red line, corresponds to Figure 2B) is shown to follow the temporal trajectory of the hair follicle. Rough predictions of relative size for expanding matrix cell and background dermal papillae populations are indicated at specific times in the cycle by green and blue ovals, respectively (similar to figure 4). The arrow and bar indicate positive and negative coupling to the mean field, respectively. The symbol is shown in bold when corresponding genes reach there maximum as estimated in Figure 1C.
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pcbi-1003914-g008: Summary schematic of the hair oscillator.Synchronization (red line, corresponds to Figure 2B) is shown to follow the temporal trajectory of the hair follicle. Rough predictions of relative size for expanding matrix cell and background dermal papillae populations are indicated at specific times in the cycle by green and blue ovals, respectively (similar to figure 4). The arrow and bar indicate positive and negative coupling to the mean field, respectively. The symbol is shown in bold when corresponding genes reach there maximum as estimated in Figure 1C.

Mentions: In this study, we focused on potentially periodic gene expression patterns in whole skin that changed on the same time-scale as cyclical hair growth. We identified two distinct clusters consistent with synchronized, out-of-phase gene expression (Figure 1 and 2). Through nonlinear-dynamic analysis, we proved that a simple, coupled oscillator model was mathematically sufficient to recapitulate this observed synchronization, and that the coupling scheme involves both positive and negative coupling (Figure 3A). We go on to show that these clusters can be associated with either static or expanding cell populations (Figures 4 and 5), and that the size of the expanding population, determined by gene expression data, was consistent with the population dynamics of follicle epithelial cells (Figure 4). Follow-up experimental and enrichment analyses indicated that the corresponding genes (provided as Supplementary Information File S3) were strongly associated with biologically distinct cell-types, such as MX or DP cells (Figures 6 and 7, Supplementary Table S1). Taken together, these results were consistent with regulatory mechanisms involving negative feedback from background mesenchymal cells to the expanding epithelial cells (see summary Fig 8). Finally, we identified a subset of genes that could potentially communicate the inhibitory signal to the follicle (provided as Supplementary Information File S5). Other aspects of the study provided interesting, but speculative, insights on possible alternative hair cycle states that are similar to those of miniaturized hair follicles (Figure 3B).


Mouse hair cycle expression dynamics modeled as coupled mesenchymal and epithelial oscillators.

Tasseff R, Bheda-Malge A, DiColandrea T, Bascom CC, Isfort RJ, Gelinas R - PLoS Comput. Biol. (2014)

Summary schematic of the hair oscillator.Synchronization (red line, corresponds to Figure 2B) is shown to follow the temporal trajectory of the hair follicle. Rough predictions of relative size for expanding matrix cell and background dermal papillae populations are indicated at specific times in the cycle by green and blue ovals, respectively (similar to figure 4). The arrow and bar indicate positive and negative coupling to the mean field, respectively. The symbol is shown in bold when corresponding genes reach there maximum as estimated in Figure 1C.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4222602&req=5

pcbi-1003914-g008: Summary schematic of the hair oscillator.Synchronization (red line, corresponds to Figure 2B) is shown to follow the temporal trajectory of the hair follicle. Rough predictions of relative size for expanding matrix cell and background dermal papillae populations are indicated at specific times in the cycle by green and blue ovals, respectively (similar to figure 4). The arrow and bar indicate positive and negative coupling to the mean field, respectively. The symbol is shown in bold when corresponding genes reach there maximum as estimated in Figure 1C.
Mentions: In this study, we focused on potentially periodic gene expression patterns in whole skin that changed on the same time-scale as cyclical hair growth. We identified two distinct clusters consistent with synchronized, out-of-phase gene expression (Figure 1 and 2). Through nonlinear-dynamic analysis, we proved that a simple, coupled oscillator model was mathematically sufficient to recapitulate this observed synchronization, and that the coupling scheme involves both positive and negative coupling (Figure 3A). We go on to show that these clusters can be associated with either static or expanding cell populations (Figures 4 and 5), and that the size of the expanding population, determined by gene expression data, was consistent with the population dynamics of follicle epithelial cells (Figure 4). Follow-up experimental and enrichment analyses indicated that the corresponding genes (provided as Supplementary Information File S3) were strongly associated with biologically distinct cell-types, such as MX or DP cells (Figures 6 and 7, Supplementary Table S1). Taken together, these results were consistent with regulatory mechanisms involving negative feedback from background mesenchymal cells to the expanding epithelial cells (see summary Fig 8). Finally, we identified a subset of genes that could potentially communicate the inhibitory signal to the follicle (provided as Supplementary Information File S5). Other aspects of the study provided interesting, but speculative, insights on possible alternative hair cycle states that are similar to those of miniaturized hair follicles (Figure 3B).

Bottom Line: Furthermore, we found only one configuration of positive-negative coupling to be dynamically stable, which provided insight on general features of the regulation.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.

View Article: PubMed Central - PubMed

Affiliation: Institute for Systems Biology, Seattle, Washington, United States of America.

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.

Show MeSH
Related in: MedlinePlus