The initial elastic modulus of hydrogels was characterized with unconfined compression tests using a mechanical tester (5848 MicroTester, Instron). Stress relaxation tests were performed using both unconfined and confined compression tests. Alginate gel disks (a diameter of 6 mm, a thickness of 2 mm) were formed and equilibrated in DMEM for 24 hours. The alginate gel disks were placed on the machine and compressed to a strain of 10% at a deformation rate of 1 mm mm−1. The slope of the stress-strain curve up to a strain of 5 to 10% was measured as the initial elastic modulus (obtained on the time scales of ~0.2 s). Subsequently, stress relaxation tests were conducted. A 10% strain was held constant while measuring stress over time. The stress relaxation time was quantified as the time at which the initial modulus of the gels was relaxed to half of its initial value. To remove the noise and select an appropriate value for the initial and half moduli, a Savitzky-Golay filter was used with a polynomial order of 20 and a window length of 421 points. We note that the values of relaxation time from unconfined and confined compression tests were similar. While the time scales from unconfined compression tests were used to describe the hydrogels to be consistent with previous literatures, confined compression tests may be more relevant to the physiological context of cells expanding within a hydrogel. Creep tests of alginate gels in shear were conducted using an AR-G2 stress-controlled rheometer (TA Instruments) equipped with the 25-mm-diameter top and bottom plates (42, 55). Alginate solution was directly deposited on the bottom plate of the rheometer immediately after mixing with calcium sulfate, and the top plate was lowered into contact with the solution immediately before gelation. Mineral oil (Sigma-Aldrich) was deposited around the exposed gel surface between the rheometer plates to avoid dehydration of the alginate. The storage modulus was monitored at a strain of 0.01 and a frequency of 1 rad/s during the gelation of alginate. Creep tests were conducted once the storage modulus of alginates reached an equilibrium value, typically around 45 to 60 min. In creep tests, a constant shear stress of 100 Pa was applied for 2 hours, while strain in response to the stress was recorded over time.

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