A Fractional Order Standard Linear Solid Model for Extracting the Elastic Moduli of Internal Cell Structures

As the mechanomarker of cellular behavior, the elastic moduli of internal cell structures can be measured through complex experimental procedure operated on micro or nano scale. Herein, a fractional-order standard linear solid model consisting of nucleus, cytoskeleton, and cytoplasm as the load-bearing components, is proposed. By fitting this model to the cell creep curves obtained by atomic force microscope (AFM), the elastic moduli of nucleus, intermediate filaments, microtubules and membrane-cytoplasm-actin cortex composite element can be extracted. The validity of this model is supported by the appropriate magnitude of order of fitted elastic moduli of internal cell structures and their independence of loading magnitudes, the good fitting (R²: 0.95-0.98) with experimental data in references, and lower Akaike Information Criterion (AIC) values than traditional Prony models. This proposed method eliminates the need for the complicated experimental procedure and can also be used to monitor the dynamic response of internal cell structures to physical and chemical stimuli.