Rheological properties of living cells play a key role in the control of cell shape, growth, movement, and contractility, yet little is known about how these properties are governed. Past approaches to understanding cell mechanics focused on the contributions of membranes, the viscous cytoplasm, and the individual filamentous biopolymers that are found within the cytoskeleton. In contrast, recent work has revealed that the dynamic mechanical behavior of cells depends on generic system properties, rather than on a single molecular property of the cell. In this paper, we show that a mathematical model of cell mechanics that depicts the intracellular cytoskeleton as a tensegrity structure composed of a prestressed network of interconnected microfilaments, microtubules, and intermediate filaments, and that has previously explained static cellular properties, also can predict fundamental dynamic behaviors of living cells.
Tensegrity structures represent a special class of tendon space structures, whose members may simultaneously perform the functions of strength, sensing, actuating and feedback control. Thus, these structures ideally match the definition of smart structures. This paper introduces the concept of controllable tensegrity as a new class of smart structures capable of large displacement. The kinematics and nonlinear dynamics of one element of this class is derived and analyzed. Prestressability conditions are given and a particular equilibrium identified. The equations of motion are then linearized about this equilibrium and linear parametric models (the parameter being the pretension coefficient) generated. These are next used for controller design. For control system design some of the tendons are chosen as actuators and some as sensors and a family of dynamic controllers designed such that the control energy is minimized while requiring output variance constraints to be satisfied. Another family of controllers is designed such that the output variance is minimized while requiring input variance constraints to be satisfied. The performances of these controllers are evaluated.
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