*3.2. Different Phases of Hair Growth Cycle and Spatial Distribution of HS and GPC1 Determined by IR Spectral Imaging Analysis*

3.2.1. *k*-Means Clustering Identifies the Hair Follicle Structures in the Different Phases Based on the Protein and HSPG Spectral Information

The IR images obtained from HFs in different phases of the hair growth cycle were analyzed by common *k*-means clustering in the 1800–800 cm−<sup>1</sup> range (Figure 4). The protein, HSPG, and GAG contribution varied within HFs forming five different clusters (each associated with a pseudo-color) corresponding to different parts of the HF (the CTS, the ORS, the IRS, the bulb (germinative matrix and differentiation zone), and the hair shaft), independently of the phase of the hair growth cycle (Figure 4A–C). The five other clusters (1, 3, 5, 6, and 10) were attributed to the OCT spectral signatures and formed a separate group. The dendrogram constructed on centroid spectra illustrated the correlation between clusters and histological structures (Figure 4D,E).

**Figure 4.** Discrimination of hair follicle structures at different phases of hair growth cycle by *k*-means clustering. (**A**–**C**) Representative color-coded *k*-means clustering images using 10 classes in the 1800–800 cm−<sup>1</sup> spectral range for hair follicles in anagen A1 (**A**), catagen C1 (**B**), and telogen T1 (**C**) phases. (**D**) Centroid spectra corresponding to each cluster. (**E**) Dendrogram of centroid spectra and assignment of corresponding hair follicle structures. CTS, connective tissue sheath; IRS, inner root sheath; ORS, outer root sheath. Scale bar: 100 µm.

IRSI combined with *k*-means clustering allows separating the five principal structures of HFs using the protein, HSPG, and GAG spectral signatures and the OCT embedding.

3.2.2. IR Correlation Maps Highlight Spatial Distribution of HS and GPC1 in the Different Phases

In order to investigate the impact of HS and GPC1 in each phase of the hair growth cycle, IR correlation maps were calculated using their representative spectra (Figure 5). The spectra of HS and GPC1 used for the correlation maps are presented in Figure 5A. HS was mostly detected in the ORS in the anagen phase, and in the ORS and IRS in the catagen and telogen phases (see arrowheads in Figure 5B–D). HS correlation coefficient seems to be lower in the ORS in the anagen phase of the HF. GPC1 was majorly distributed in the differentiation zone and less in the hair shaft and in the germinative matrix without any significant differences between the three phases. The presence of GPC1 in the ORS was specifically detected in the catagen phase in agreement with immunohistochemical labeling (see Figure 3). In addition, the spectrum of HA was also used for the correlation map (Figure S2A). HA is detected in the IRS and the hair shaft in the anagen and catagen phases but not in the ORS and the differentiation zone (Figure S2B,C). A faint correlation is observed in the lower part of the differentiation zone in the telogen phase (Figure S2D).

**Figure 5.** Contribution of the heparan sulfate GAG chain and glypican-1 in a hair follicle. (**A**) Mean spectra of standard HS (continuous line) and GPC1 (dashed line). (**B**–**D**) IR correlation maps of hair follicles in the anagen A1 (**B**), catagen C1 (**C**), and telogen T1 (**D**) phases using mean spectra from standard heparan sulfate (left) and human recombinant glypican-1 (right). HS, heparan sulfate; GPC1, glypican-1. Arrowheads indicate high level of correlation. Scale bar: 100 µm.

> These correlation maps inform on the HS-type GAG and GPC1 distribution within the HF. The results suggest that GPC1, mainly detected in the differentiation zone and hair shaft, does not exhibit HS chains in contrast to HS, which is detected in the ORS and IRS. Based on this GPC1 distribution, at this stage, it is not possible to differentiate the different phases of the hair growth cycle. However, GPC1 correlation in the ORS (Figure 5C) requires further studies to eventually validate GPC1 as a spectral biomarker of the catagen phase. In contrast, the anagen phase, corresponding to a growing phase of the HF, is identified using IRSI as it is associated to a decreased HS correlation coefficient. However, the catagen phase is characterized by an increase in HS correlation. Moreover, HA, the non-sulfated GAG, exhibits a different distribution in the HF as compared to HSPG independently of the phases of the hair growth cycle. Malgouries et al. have previously described the capacity to discriminate the phases of the hair growth cycle by the distribution of several HSPGs using immunofluorescence [21].

> The differences observed in the distribution of HS and GPC1 in the three phases may partly account for the different classes obtained by *k*-means clustering.
