Supplementary Material : Linking Cellular and Mechanical Processes - PDF document

Supplementary Material : Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model Georgi I. Kapitanov*, Xiayi Wang, Bruce P. Ayati, Marc J. Brouillette, James A. Martin *Correspondence: Author Name: Georgi I. Kapitanov georgi-kapitanov@uiowa.edu 1 SUPPLEMENTARY TABLES AND FIGURES 1.1 Figures t=0 t=1 1 1 0.8 0.8 0.6 0.6 cm cm 0.4 0.4 0.2 0.2 Healthy cells CE 0 0 0 0.5 1 0 0.5 1 cm cm t=7 t=14 1 1 500 7500 2000 0.8 1000 0.8 5000 500 0.6 0.6 cm cm 2000 0.4 0.4 1000 0.2 0.2 5 0 0 0 0 0 0.5 1 0 0.5 1 cm cm Figure S1. A contour graph of the density of the C E cells in the 2D model at 0, 1, 7, and 14 days. The units are cells/cm 3 . 1

Kapitanov Supplementary Material t=0 t=1 1 1 0.8 0.8 0.6 0.6 cm cm 0.4 0.4 0.2 0.2 Catabolic cells SA 0 0 0 0.5 1 0 0.5 1 cm cm t=7 t=14 1 1 100 1000 50 0.8 0.8 200 100 0.6 0.6 cm cm 5 0 0.4 0.4 0.2 0.2 0 0 0 0.5 1 0 0.5 1 cm cm Figure S2. A contour graph of the density of the S A cells in the 2D model at 0, 1, 7, and 14 days. The units are cells/cm 3 . t=0 t=1 1 1 0.0002 0.8 0.8 0.0001 0.6 0.6 cm cm 0.4 0.4 0.2 0.2 DAMPs 0 0 0 0.5 1 0 0.5 1 cm cm t=7 t=14 1 1 0.0002 0.0005 0.8 0.8 0.6 0.6 cm cm 0.0001 0.4 0.4 0.2 0.2 0.0002 0 0 0 0.5 1 0 0.5 1 cm cm Figure S3. A contour graph of the concentration of DAMPs in the 2D model at 0, 1, 7, and 14 days. The units are nanomolar. 2

Kapitanov Supplementary Material t=0 t=1 × 10 4 × 10 4 10 10 8 8 cells/cm 3 cells/cm 3 6 6 4 4 2 2 Healthy cells CU 0 0 0 0.5 1 0 0.5 1 cm cm × 10 4 t=7 × 10 4 t=14 10 10 8 8 cells/cm 3 cells/cm 3 6 6 4 4 2 2 0 0 0 0.5 1 0 0.5 1 cm cm Figure S4. Average density of C U cells along the radius of the model cylinder at 0, 1, 7, and 14 days. The C U cells are less dense near the area of contact. t=0 t=1 8000 8000 cells/cm 3 6000 cells/cm 3 6000 4000 4000 Pre-catabolic cells CT 2000 2000 Healthy cells CE 0 0 0 0.5 1 0 0.5 1 cm cm t=7 t=14 8000 8000 cells/cm 3 cells/cm 3 6000 6000 4000 4000 2000 2000 0 0 0 0.5 1 0 0.5 1 cm cm Figure S5. Average density of C T and C E cells along the radius of the model cylinder at 0, 1, 7, and 14 days. The density of C E cells is higher near the contact area, while the density of the C T cells is more evenly distributed. Frontiers 3

Kapitanov Supplementary Material t=0 t=1 2000 2000 1500 1500 cells/cm 3 cells/cm 3 1000 1000 500 500 Catabolic cells ST Catabolic cells SA 0 0 0 0.5 1 0 0.5 1 cm cm t=7 t=14 2000 2000 1500 1500 cells/cm 3 cells/cm 3 1000 1000 500 500 0 0 0 0.5 1 0 0.5 1 cm cm Figure S6. Average density of S T and S A cells along the radius of the model cylinder at 0, 1, 7, and 14 days. The densities of both cell states are higher near the contact area. × 10 -3 t=0 × 10 -3 t=1 1.5 1.5 nanomolar 1 nanomolar 1 PIC 0.5 0.5 DAMPs EPO 0 0 0 0.5 1 0 0.5 1 cm cm × 10 -3 t=7 × 10 -3 t=14 1.5 1.5 1 1 nanomolar nanomolar 0.5 0.5 0 0 0 0.5 1 0 0.5 1 cm cm Figure S7. Average concentrations of EPO, DAMPs, and PIC along the radius of the model cylinder at 0, 1, 7, and 14 days. DAMPs and particularly EPO concentrations are higher near the contact area. PIC concentrations are more evenly spread, although their concentrations are also somewhat higher near the area of contact. 4

Kapitanov Supplementary Material t=0 t=1 0.1 0.1 0.08 0.08 nanomolar nanomolar 0.06 0.06 0.04 0.04 0.02 0.02 ROS 0 0 0 0.5 1 0 0.5 1 cm cm t=7 t=14 0.1 0.1 nanomolar 0.08 nanomolar 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0 0 0 0.5 1 0 0.5 1 cm cm Figure S8. Average concentrations of ROS along the radius of the model cylinder at 0, 1, 7, and 14 days. The concentrations are higher near the area of contact. t=0 t=1 30.05 30.05 30 30 mg/cm 3 mg/cm 3 29.95 29.95 ECM 29.9 29.9 0 0.5 1 0 0.5 1 cm cm t=7 t=14 30.05 30.05 30 30 mg/cm 3 mg/cm 3 29.95 29.95 29.9 29.9 0 0.5 1 0 0.5 1 cm cm Figure S9. Average ECM density along the radius of the model cylinder at 0, 1, 7, and 14 days. The pressure applied is not enough to produce high deterioration of the ECM. Frontiers 5