A quantitative model of cellular elasticity based on tensegrity

Area of Science:

• Cellular mechanics
• Biophysics
• Biomaterials

Background:

• Cellular mechanical properties are crucial for understanding cell function and behavior.
• The cytoskeleton, composed of microtubules and actin filaments, significantly influences cell elasticity.
• Previous models have simplified the complex interplay of cytoskeletal components.

Purpose of the Study:

• To develop a quantitative tensegrity model for predicting the steady-state elastic response of cells.
• To establish relationships between model parameters (tension, compression, length) and cell Young's modulus (E0).
• To predict upper and lower bounds for cellular E0 and compare with experimental data.

Main Methods:

• A tensegrity structure with six struts (microtubules) and 24 elastic cables (actin filaments) was employed.
• The model was subjected to uniaxial stretching to determine E0 from the stress-strain curve.
• E0 was related to cable tension and strut compression, and cable/strut length was linked to probe diameter in mechanical tests.

Main Results:

• Cellular E0 is directly proportional to pre-existing tension/compression and inversely proportional to strut/cable length squared.
• Predicted E0 bounds were established using actin yield force and microtubule buckling force.
• Experimental data for probe diameters ≥ 3 microns align closer to the lower bound, suggesting microtubules bear significant compression.

Conclusions:

• The tensegrity model provides a framework for understanding cell elasticity based on cytoskeletal mechanics.
• Microtubules likely experience compression exceeding their buckling force, while actin filaments are under tension below their yield force.
• Discrepancies at smaller probe sizes (< 2 microns) suggest limitations in the current model or experimental conditions.