Cell-matrix adhesion is a central mechanical function to a large number of phenomena in physiology and disease, including morphogenesis, wound healing, and tumor cell invasion. Today, how single cells respond to different extracellular cues has been comprehensively studied. However, how the mechanical behavior of the main individual molecules that form an adhesion complex cooperatively responds to force within the adhesion complex is still poorly understood. This is a key aspect of cell adhesion because how these cell adhesion molecules respond to force determines not only cell adhesion behavior but, ultimately, cell function. To answer this question, we develop a multi-scale computational model for adhesion complexes mechanics. We extend the classical clutch hypothesis to model individual adhesion chains made of a contractile actin network, a talin rod, and an integrin molecule that binds at individual adhesion sites on the extracellular matrix. We explore several scenarios of integrins dynamics and analyze the effects of diverse extracellular matrices on the behavior of the adhesion molecules and on the whole adhesion complex. Our results describe how every single component of the adhesion chain mechanically responds to the contractile actomyosin force and show how they control the traction forces exerted by the cell on the extracellular space. Importantly, our computational results agree with previous experimental data at the molecular and cellular levels. Our multi-scale clutch model presents a step forward not only to further understand adhesion complexes mechanics but also to impact, e.g., the engineering of biomimetic materials, tissue repairment, or strategies to arrest tumor progression.

One of the most important steps in obtaining a relational model from legacy systems is the extraction of functional dependencies (FDs) through data mining techniques. Several methods have been proposed for this purpose and most use direct search methods that traverse the search space in exponential time in the number of attributes of the relation. As it is not uncommon to find in practice relations with tens of attributes, a need exists to further develop more efficient techniques to find FDs. The method studied here finds the minimal set of minimal FDs using algorithms that solve the hypergraph duality problem applied on the complement of the refutation hypergraph of the relation without going through the exponential search space. After showing that the extraction of FDs can be reduced to the hypergraph duality problem, experimental results are given as verification and characterization of the correctness and time complexity of the proposed tool.