Mechanical Behavior in Living Cells Consistent with the Tensegrity Model

Ning Wang et al. PNAS 2001; 98:7765-7770

Presented by: David L. Simpson

ARTNews- February 1981

Outline

• Background and Introduction

• Methods

• Results

• Strengths and Limitations

• Discussion Topics

Current Models of Cell Mechanics

• Simple Mechanical Continuum

• Porous Filament Gel

• Tensed Cortical Membrane

• Tensegrity Model

Tensegrity Model

• Continuous and intricate network of tensed and compressed filaments

• Deformability Depends on level of prestress

• Prestress dependent on active (actomyosin contractile apparatus) and passive (distension by cell adhesions to the ECM) elements

Intent of Selected Paper

• Demonstrate that the cytoskeleton (CSK) behaves as a discrete network of filaments

• Demonstrate that microtubules behave as compression struts

• Demonstrate that CSK prestress is a major determinant of cell deformability

• Experimental confirmation of the a priori predictions of model

Motivation for Study

• In vitro experimentation inadequate

• Limitations of other models suggest the need for a more accurate model which links mechanics to microstructure and molecular biochemistry

Oscillatory Magnetic Twisting Cytometry

• Bead Rotation and oscillatory pattern resisted by intrinsic stresses developed by the cell

• Ratio of specific torque and angular rotation of bead define Complex Elastic Modulus a. G(f) = T(f)/φ(f) b. G(f) = G’(f) + G”(f) Real and imaginary parts

J. Appl. Physiol. Vol. 89, Issue 4, 1619-1632, October 2000

Traction Force Microscopy

• Cells cultured on flexible ECM-coated, PA gels with fluorescent beads inside

• Traction at the cell-gel interfaced obtained by solving the problem of Boussinesq using a Fourier transform

MLC Phosphorylation and Intracellular Calcium

• Immunoblotting with MLC mAbs

• Microfluormetric quantitation of intracelluar calcium

Fig 3. PNAS 2001; 98:7765-7770

Internal Cell Deformation Depends on Molecular Connectivity

Closed circles: RGD Beads

Open circle: AcLDL Beads

Fig 1. PNAS 2001; 98:7765-7770

Microtubules Bear Compression in Living Cells

Fig 2. PNAS 2001; 98:7765-7770

Microtubules Bear Compression in Living Cells

Prestress is transferred to external adhesions which increases traction.

Fig 5. PNAS 2001; 98:7765-7770

Quantitative Measurements Support the Tensegrity Model

Prestress as a function of histamine and colchicine concentration

Shear Modulus as a function of histamine concentration

Shear modulus as a function of prestress. Notice the linear relationship over specified range

Fig 4. PNAS 2001; 98:7765-7770

An a priori Prediction

• Tensegrity predicts that the cells dynamic shear modulus can be decomposed into the product of a prestress-dependent component and a frequency-dependent component

• Models confirms prediction in that both the storage and loss moduli increase by 70% while hysteresivity coefficient remained constant with increased prestress (J. of Appl. Physiol. 2000; 89:1619-1632)

Strengths and Limitations

• Model is able to accurately model a priori prediction offered by the authors

• Models and defines prestress as a major player in cell mechanics

• Tensegrity does not consider viscoelastic forces, thermal motions and polymer. Dynamics

• Authors find ways to test there predictions buy offer no alternatives to observations– For example, the mitochondria moves away from and toward

induced forced– Is it possible that signaling plays a role as well as polymerization

dynamics• Focus of this paper is mainly surrounded around

microtubules. Not much on other the CSK elements

Let’s Discuss

• Let’s look at the most obvious: Is tensegrity a reasonable model?– Prestress is a major part of this model, is it accounted

for in other models?– Are there alternatives for the predictions verified by

this model?– Adam Smith may describe such a situation by the

distribution of labor• How would divide the tensegrity model• Could more than one model be combined to achieve a final

product

• Critics to tensegrity indicate that only local responses occur w/ an induced forced– If an advocate, why might these responses be

occurring– If a critic why does this hurt the concept of tensegrity

• Referring to the famous engineer Rene Descartes, he found the concept of “seeking certainty in an uncertain world.” In other words always ask questions, so…ANY QUESTIONS?

Let’s Discuss

AND I’M SPENT…THANKS FOR YOUR ATTENTION