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Hydrogels are widely used as substrates to investigate interactions between cells and their microenvironment as they mimic many attributes of the extracellular matrix. The stiffness of hydrogels is an important property that is known to regulate cell behavior. Beside stiffness, cells also respond to structural cues such as mesh size. However, since the mesh size of hydrogel is intrinsically coupled to its stiffness, its role in regulating cell behavior has never been independently investigated. Here, we report a hydrogel system whose mesh size and stiffness can be independently controlled. Cell behavior, including spreading, migration, and formation of focal adhesions is significantly altered on hydrogels with different mesh sizes but with the same stiffness. At the transcriptional level, hydrogel mesh size affects cellular mechanotransduction by regulating nuclear translocation of yes-associated protein. These findings demonstrate that the mesh size of a hydrogel plays an important role in cell-substrate interactions. 

We study economic incentives provided by space-time dynamics of day-ahead and real-time electricity markets. Specifically, we seek to analyze to what extent such dynamics promote decentralization of technologies for generation, consumption, and storage (which is essential to obtain a more flexible power grid). Incentives for decentralization are also of relevance given recent interest in the deployment of small-scale modular technologies (e.g., modular ammonia and biogas production systems). Our analysis is based on an asset placement problem that seeks to find optimal locations for generators and loads in the network that minimize profit risk. We show that an unconstrained version of this problem can be cast as an eigenvalue problem. Under this representation, optimal network allocations are eigenvectors of the space-time price covariance matrix while the eigenvalues are the associated profit variances. We also construct a more sophisticated placement formulation that captures different risk metrics and constraints on types of technologies to systematically analyze trade-offs in expected profit and risk. Our analysis reveals that space-time market dynamics provide significant incentives for decentralization and strategic asset placement but that full mitigation of risk is only possible through simultaneous investment in generation and loads (which can be achieved using batteries or microgrids). 

Abstract Strain gradients widely exist in development and physiological activities. The directional movement of cells is essential for proper cell localization, and directional cell migration in responses to gradients of chemicals, rigidity, density, and topography of extracellular matrices have been well‐established. However; it is unclear whether strain gradients imposed on cells are sufficient to drive directional cell migration. In this work, a programmable uniaxial cell stretch device is developed that creates controllable strain gradients without changing substrate stiffness or ligand distributions. It is demonstrated that over 60% of the single rat embryonic fibroblasts migrate toward the lower strain side in static and the 0.1 Hz cyclic stretch conditions at ≈4% per mm strain gradients. It is confirmed that such responses are distinct from durotaxis or haptotaxis. Focal adhesion analysis confirms higher rates of contact area and protrusion formation on the lower strain side of the cell. A 2D extended motor‐clutch model is developed to demonstrate that the strain‐introduced traction force determines integrin fibronectin pairs' catch‐release dynamics, which drives such directional migration. Together, these results establish strain gradient as a novel cue to regulate directional cell migration and may provide new insights in development and tissue repairs.