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An increasing number of studies have demonstrated the significant roles of the interplay between microenvironmental mechanics in tissues and biochemical-genetic activities in resident tumor cells at different stages of tumor progression. Mediated by molecular mechano-sensors or -transducers, biomechanical cues in tissue microenvironments are transmitted into the tumor cells and regulate biochemical responses and gene expression through mechanotransduction processes. However, the molecular interplay between the mechanotransduction processes and intracellular biochemical signaling pathways remains elusive. This paper reviews the recent advances in understanding the crosstalk between biomechanical cues and three critical biochemical effectors during tumor progression: calcium ions (Ca 2+ ), yes-associated protein (YAP), and microRNAs (miRNAs). We address the molecular mechanisms underpinning the interplay between the mechanotransduction pathways and each of the three effectors. Furthermore, we discuss the functional interactions among the three effectors in the context of soft matter and mechanobiology. We conclude by proposing future directions on studying the tumor mechanobiology that can employ Ca 2+ , YAP, and miRNAs as novel strategies for cancer mechanotheraputics. This framework has the potential to bring insights into the development of novel next-generation cancer therapies to suppress and treat tumors.

Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creates ambiguity and can lead to many different interpretations of the same set of classes. One approach to solving this problem is to optimize the choice of representative against some measure that is meaningful in the context of the data. In this work, we provide a study of the effectiveness and computational cost of several ℓ 1 minimization optimization procedures for constructing homological cycle bases for persistent homology with rational coefficients in dimension one, including uniform-weighted and length-weighted edge-loss algorithms as well as uniform-weighted and area-weighted triangle-loss algorithms. We conduct these optimizations via standard linear programming methods, applying general-purpose solvers to optimize over column bases of simplicial boundary matrices. Our key findings are: 1) optimization is effective in reducing the size of cycle representatives, though the extent of the reduction varies according to the dimension and distribution of the underlying data, 2) the computational cost of optimizing a basis of cycle representatives exceeds the cost of computing such a basis, in most data sets we consider, 3) the choice of linear solvers matters a lot to themore »computation time of optimizing cycles, 4) the computation time of solving an integer program is not significantly longer than the computation time of solving a linear program for most of the cycle representatives, using the Gurobi linear solver, 5) strikingly, whether requiring integer solutions or not, we almost always obtain a solution with the same cost and almost all solutions found have entries in { ‐ 1,0,1 } and therefore, are also solutions to a restricted ℓ 0 optimization problem, and 6) we obtain qualitatively different results for generators in Erdős-Rényi random clique complexes than in real-world and synthetic point cloud data.« less

Given the pleiotropic nature of coding sequences and that many loci exhibit multiple disease associations, it is within non-coding sequence that disease-specificity likely exists. Here, we focus on joint disorders, finding among replicated loci, thatGDF5exhibits over twenty distinct associations, and we identify causal variants for two of its strongest associations, hip dysplasia and knee osteoarthritis. By mapping regulatory regions in joint chondrocytes, we pinpoint two variants (rs4911178; rs6060369), on the same risk haplotype, which reside in anatomical site-specific enhancers. We show that both variants have clinical relevance, impacting disease by altering morphology. By modeling each variant in humanized mice, we observe joint-specific response, correlating withGDF5expression. Thus, we uncouple separate regulatory variants on a common risk haplotype that cause joint-specific disease. By broadening our perspective, we finally find that patterns of modularity atGDF5are also found at over three-quarters of loci with multiple GWAS disease associations.