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Inferring intra-cellular mechanics using geometric metamorphosis: A preliminary study

Mechanotransduction plays an important role in sub-cellular processes and is an active area of research. Determining the forces/strains that the intra-cellular structures experience is vital for developing quantitative models of cellular behavior. Established techniques such as traction force microscopy, digital image correlation etc. track surface forces and kinematics of intra-cellular structures. However, difficulties arise when cells cannot be seeded on micro-patterned substrates or the intra-cellular structures vary (unstable landmarks). Here, we applied geometric metamorphosis, a global image registration method, to determine the kinematic profile of a cell during cell division. The method does not require stable landmarks, the registration is non-local in nature and constraints such as volume conservation can be enforced. The cell wall was tracked over time and a sequence of transformations relating the cell wall at the start of cytokinesis to the configuration prior to the daughters completely separate was determined. These transformations are associated with a scalar metric and a statistical atlas describing the wall kinematics from multiple tracking's of the wall shape is constructed. Using these transformations, the cellular kinematics can be described using a Lagrangian frame of reference and the evolution of a material point property can be easily modeled. To demonstrate this, we use the kinematic data derived from the atlas along with a model of stress-fiber (de)formation dynamics to simulate the stress-fiber configuration as the cell domain deforms.