Biological materials such as bone, tooth, and nacre are load-bearing nanocomposites composed of mineral and protein. Since the mineral crystals often have slender geometry, the nanocomposites are susceptible to buckle under the compressive load. In this paper, we analyze the local buckling behaviors of the nanocomposite structure of the biological materials using a beam-spring model by which we can consider plenty of mineral crystals and their interaction in our analysis compared with existing studies. We show that there is a transition of the buckling behaviors from a local buckling mode to a global one when we continuously increase the aspect ratio of mineral, leading to an increase of the buckling strength which levels off to the strength of the composites reinforced with continuous crystals. We find that the contact condition at the mineral tips has a striking effect on the local buckling mode at small aspect ratio, but the effect diminishes when the aspect ratio is large. Our analyses also show that the staggered arrangement of mineral plays a central role in the stability of the biological nanocomposites.
Collective cells are organized to form specific patterns which play important roles in various physiological and pathological processes, such as tissue morphogenesis, wound healing, and cancer invasion. Compared to single cell behaviors, which has been intensively studied from many aspects (cell migration, adhesion, polarization, proliferation, etc.) and at various scales (molecular, subcellular, and cellular), the multiple cell behaviors are relatively less understood, particularly in a quantitative manner. In this paper, we will present our recent studies of collective polarization and orientation of multiple cells through both experimental measurement and theoretical modeling, including those cell behaviors on/in 2D and 3D substrate/tissue. We find that the collective cell behaviors, including polarization, alignment and migration are closely related to local stress states in cell layer or tissue, which demonstrate the crucial roles of mechanical forces in the living organisms. Specifically, the cells prefer to polarize and align along the maximum principal stress in the cell layer, and the aspect ratio of cell increases with the in-plane maximum shear stress, suggesting that the maximum shear stress is the underlying driving force of cell polarization and orientation. This theory of stress-driven cell behaviors of polarization and orientation provides a new perspective for understanding cell behaviors in living organisms and the guideline for tissue engineering in biomedical applications.
The stiffness and strength of extracellular （EC） region of cadherin are proposed to be two important mechanical properties both for cadherin as a mechanotransductor and for the formation of cell-cell adhesion. In this study, we quantitatively characterized the stiffness and strength of EC structure when it binds with different types of ions by molecular dynamics simulations. Resuits show that EC structure exhibits a rod-like shape with high stiffness and strength when it binds with the bivalent ions of calcium or magnesium. However, it switches to a soft and collapsed conformation when it binds with the monova- lent ions of sodium or potassium. This study sheds light on the important role of the bivalent ions of calcium in the physiological function of EC.
