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

Synchronization onset for contrarians with higher-order interactions in multilayer systems

We investigate the impact of contrarians (via negative coupling) in multilayer networks of phase oscillators having higher-order interactions. We report that the multilayer framework facilitates synchronization onset in the negative pairwise coupling regime. The multilayering strength governs the onset of synchronization and the nature of the phase transition, whereas the higher-order interactions dictate the backward critical coupling. Specifically, the system does not synchronize below a critical value of the multilayering strength. The analytical calculations using the mean-field Ott-Antonsen approach agree with the simulations. The results presented here may be useful for understanding emergent behaviors in real-world complex systems with contrarians and higher-order interactions, such as the brain and social system.

Catalytic feed-forward explosive synchronization in multilayer networks

Inhibitory couplings are crucial for the normal functioning of many real-world complex systems. Inhibition in one layer has been shown to induce explosive synchronization in another excitatory (or positive) layer of duplex networks. By extending this framework to multiplex networks, this article shows that inhibition in a single layer can act as a catalyst, leading to explosive synchronization transitions in the rest of the layers feed-forwarded through intermediate layer(s). Considering a multiplex network of coupled Kuramoto oscillators, we demonstrate that the characteristics of the transition emergent in a layer can be entirely controlled by the intra-layer coupling of other layers and the multiplexing strengths. The results presented here are essential to fathom the synchronization behavior of coupled dynamical units in multi-layer systems possessing inhibitory coupling in one of its layers, representing the importance of multiplexing.

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

The hair follicle is a biological oscillator that alternates growth, regression, and rest phases driven by the sequential activation of the proliferation/differentiation programs of resident stem cell populations. The activation of hair follicle stem cell niches and subsequent entry into the growing phase is mainly regulated by Wnt/β-catenin signalling, while regression and resting phases are mainly regulated by Tgf-β/Bmp/Smad activity. A major question still unresolved is the nature of the molecular switch that dictates the coordinated transition between both signalling pathways. Here we have focused on the role of Endoglin (Eng), a key co-receptor for members of the Tgf-β/Bmp family of growth factors. Using an Eng haploinsufficient mouse model, we report that Eng is required to maintain a correct follicle cycling pattern and for an adequate stimulation of hair follicle stem cell niches. We further report that β-catenin binds to the Eng promoter depending on Bmp signalling. Moreover, we show that β-catenin interacts with Smad4 in a Bmp/Eng-dependent context and both proteins act synergistically to activate Eng promoter transcription. These observations point to the existence of a growth/rest switching mechanism in the hair follicle that is based on an Eng-dependent feedback cross-talk between Wnt/β-catenin and Bmp/Smad signals.

Inhibition-induced explosive synchronization in multiplex networks

To date, explosive synchronization (ES) in a network is shown to be originated from considering either degree-frequency correlation, frequency-coupling strength correlation, inertia, or adaptively controlled phase oscillators. Here we show that ES is a generic phenomenon and can occur in any network by multiplexing it with an appropriate layer without even considering any prerequisite for the emergence of ES. We devise a technique which leads to the occurrence of ES with hysteresis loop in a network upon its multiplexing with a negatively coupled (or inhibitory) layer. The impact of various structural properties of positively coupled (or excitatory) and inhibitory layers along with the strength of multiplexing in gaining control over the induced ES transition is discussed. Analytical prediction for the spread of phase distribution of each layer is provided, which is in good agreement with the numerical assessment. This investigation is a step forward in highlighting the importance of multiplex framework not only in bringing phenomena which are not possible in an isolated network but also in providing more structural control over the induced phenomena.

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

According to the growth state of hair follicles, the hair cycle is divided into the anagen, catagen and telogen phases. A number of biological factors have been shown to synchronize with the hair cycle. As an important component of the hair follicle, the extracellular matrix is regulated by matrix metalloproteinases (MMPs) and their inhibitors (tissue inhibitor of matrix metalloproteinases; TIMPs). It has been reported that MMP-2, MMP-9 and TIMP-1 are associated with the hair cycle; however, their expression levels during the hair cycle have not been fully elucidated. Reverse transcription-polymerase chain reaction and ELISA analysis in the present study demonstrated that, during the hair cycle in mice, mRNA and protein expression levels of MMP-2 and MMP-9 were elevated in the anagen phase, and decreased during the catagen and telogen phases. Furthermore, SDS-PAGE gelatin zymography demonstrated that their activities fluctuated in the hair cycle. Additionally, it was observed that the mRNA and protein expression levels of TIMP-1 and TIMP-2 were negatively correlated with MMP-9 and MMP-2, respectively. Immunohistochemical examination demonstrated that MMP-2 and TIMP-2 were present in all structures of the hair follicle. However, MMP-9 and TIMP-1 were locally expressed in certain areas of the hair follicle, such as in the sebaceous gland at the anagen, catagen and telogen phases, and in the inner root sheath at the catagen phase. These results suggested that MMP-2 and MMP-9 may serve an important role in the hair growth cycle.

Advances in Understanding Hair Growth

In this short review, I introduce an integrated vision of human hair follicle behavior and describe opposing influences that control hair follicle homeostasis, from morphogenesis to hair cycling. The interdependence and complementary roles of these influences allow us to propose that the hair follicle is a true paradigm of a "Yin Yang" type, that is a cold/slow-hot/fast duality. Moreover, a new promising field is emerging, suggesting that glycans are key elements of hair follicle growth control.