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We would like to thank Dr. B. de Crombrugghe (University of Texas, Houston, TX) for providing us with the 4X48-p89Luc reporter gene, pcDNA3-hSox9, and p309i(182X2)βgeoCol2a1. Also, we thank Dr. R. Davis (University of Massachusetts Medical School, Worcester, MA) for pcDNA3-p38α-Flag, Dr. J. Han (The Scripps Research Institute, La Jolla, CA) for pcDNA3-p38β2-Flag, and Dr. I. Skerjanc (University of Western Ontario) for pcDNA3-HA-MKK6E. The primary rat articular chondrocytes were provided by Dr. S. Bernier and C. Sequin (University of Western Ontario), and the C5.18 cells were a gift from Dr. J. Aubin (University of Toronto, Toronto, Ontario, Canada). We are grateful for the technical assistance provided by Matthew Cowan, Linsay Drysdale, and Julie Ruston.

Download (@Sigma Top Tech TeL)Fig rar

Protein was extracted from hESCs grown on matrigel (1:100 in KO-DMEM), using 100 μl lysis bufferX1 (Promega) with a 1 % protease inhibitor cocktail (Sigma). Cell lysates were incubated for 20 min on ice, centrifuged, and the supernatants were separated on 7.5 % SDS-polyacrylamide gel electrophoresis (SDS-PAGE), followed by transfer to nitrocellulose membranes (0.2 μm, BIO-RAD) using BIO-RAD Mini Trans-Blot Cell. The membranes with the proteins were subjected to blocking solution (0.001 % TWEEN-20 in phosphate buffered solution (PBS) with 5 % low fat milk, Sigma). They were then incubated with primary antibody overnight at 4 C, and washed with 0.001 % TWEEN-20 in PBS, followed by incubation for 1 h at room temperature with horseradish peroxidase-conjugated secondary antibody. After washing, the membranes were exposed to enhanced chemiluminescence detection analysis (EZ-ECL, Biological Industries). The antibodies used were: rabbit anti β-catenin, Santa Cruz Biotechnology; mouse anti-β-actin, Abcam; peroxidase-conjugated goat anti-rabbit and peroxidase-conjugated goat anti-mouse, Jackson Immune Research.

In natural systems, a series of activities (events) is observed for some duration followed by prolong inactivity. This intermittent increase or decrease in the occurrence of events is termed as burstiness (Karsai et al. 2018). Based on the measure introduced by (Goh and Barabási 2008), the burstiness parameter is defined by the coefficient of variation \(r\equiv \frac\sigma \langle \tau \rangle \) of interevent times as follows:

For a regular process with equal interevent times, B is -1 as \(\sigma =0\). The value of B is 0 for random, Poisson process where \(\sigma =\langle \tau \rangle\). For heterogenous interevent times other than Poisson process, the parameter B is positive and it takes a value 1, when the process is extremely bursty with \(\sigma \to \infty\). It is observed that the parameter is B is severely impacted by finite-size effect of the sample with n number of events (Kim and Jo 2016). It is difficult to be certain about the similarity in burstiness of two processes with different n despite of having same value of B (Kim and Jo 2016) corrected the parameter B by incorporating the sample size n as follows:

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