Advances in modeling cellular mechanical perceptions and responses via the membrane-cytoskeleton-nucleus machinery.

Mechanical models offer a quantitative framework for understanding scientific problems, predicting novel phenomena, and guiding experimental designs. Over the past few decades, the emerging field of cellular mechanobiology has greatly benefited from the substantial contributions of new theoretical tools grounded in mechanical models. Within the expansive realm of mechanobiology, the investigation of how cells sense and respond to their microenvironment has become a prominent research focus. There is a growing acknowledgment that cells mechanically interact with their external surroundings through an integrated machinery encompassing the cell membrane, cytoskeleton, and nucleus. This review provides a comprehensive overview of mechanical models addressing three pivotal components crucial for force transmission within cells, extending from mechanosensitive receptors on the cell membrane to the actomyosin cytoskeleton and ultimately to the nucleus. We present the existing numerical relationships that form the basis for understanding the structures, mechanical properties, and functions of these components. Additionally, we underscore the significance of developing mechanical models in advancing cellular mechanobiology and propose potential directions for the evolution of these models.