20.310J | Spring 2015 | Undergraduate

Molecular, Cellular, and Tissue Biomechanics


Instructor Key

RK = Roger Kamm
AG = Alan Grodzinsky

Molecular Mechanics

Length, Time, & Molecular-scale Forces in Biology

Overview of mechanics across all scales. Learning objectives for the term. Scales of force, displacement, time, and energy relevant to biological structures. Molecular forces and bond energies; kT as an energy ruler. Examples drawn from DNA folding, peptide assembly, protein binding, cytoskeletal strain, and tissue compliance.


Single Molecule Mechanics

Thermal forces and Brownian motion. Diffusion, viscous drag, shear forces at low Reynolds numbers. Statistical mechanics and entropy; rubber elasticity and freely jointed chain; Worm-like chain; Force-extension curves; Applications to DNA, proteins, actin filaments; rigidity of DNA.


Energy Landscapes and Transition States

Energy landscapes and reaction coordinates; transition state theory in thermodynamics; attempt rate and estimation of kinetics; Examples in Antiobody-antigen binding, DNA unfolding, hemoglobin.


Mechanochemistry at the Molecular Scale

Molecular networks as force versus displacement transducers; exampes of myosin in myofibers and fibronectin unfolding; Inside-out and Outside-in mechanical signaling. Example of mechanochemistry in connective tissues and their constituent matrix macromolecules.


Kramers’ and Bell’s Models of Reversible Binding

Effects of force on binding equilibrium; examples in reaction kinetics of ligands and receptors; applications to molecular adhesion. Eyring, Kramers, and Bell’s effect of applied force on reaction rate constants.


Experimental Methods in Single Molecule Mechanics

Examples of molecular imaging techniques and molecular force probes: Atomic force microscopy, optical tweezers, optical FRET techniques to quantify forces and displacements relevant to Molecular-scale health and disease. Applications to extracellular macromolecules: Collagens, proteoglycans, mechanochemistry of ECM.

Tissue Mechanics

Composition of Extracellular Matrix Constituents of Tissues; Relevance to Elastic (Time-independent) Behavior of Tissues

Different length scales in tissues. Composition of tissues as assemblies of cells within an extracellular matrix composed of collagens, proteoglycans, glycoproteins and elastin. Force balance in tissues: Stress and strain in the elastic region of behavior. Experiments to measure simple extension, shear, confined and unconfined compression. Examples from musculoskeletal system.


Elastic (Time-independent) Behavior of Tissues (cont.)

Stress-strain relations for tissues formalized using an elastic Hookean constitutive law: Stress and strain tensors, notation and book keeping. Experiments and applications involving tendons, ligaments, intervertebral disc and muscle. Relation between Nano-molecular constituents and macroscopic mechanical behaviors of connective tissues.


Elastic (Time-independent) Behavior of Tissues (cont.)

Homegeneous / nonhomogeneous; isotropic / anisotropic; linear / nonlinear behavior of tissues and relation to the Molecular-level properties of the extracellular matrix. Examples of models and experiments to measure the complex behavior of biological tissues in tension, shear and compression.

Time-dependent Tissue Behavior (Viscoelasticity and Poroelasticity)

Finish Topics on Tissue Elasticity; Begin Viscoelasticity

Summarize key features of tissue elastic behavior. Time-dependent viscoelastic behavior of tissues and molecules as single phase materials; molecular mechanisms for viscoelastic behavior; experiments demonstrating transient creep of tissues and the “Spring-dashpot” lumped parameter ‘Voigt’ model (advantages and limitations).

  Quiz 1: Molecular Mechanics  

Time-dependent Viscoelasticity of Tissues

Creep and stress relaxation of tissues: Experimental evidence and the lumped parameter models of Time-dependent viscoelastic behavior of tissues;


Dynamic (Frequency-dependent) Viscoelasticity

Dynamic tissue behavior: The oscillator complex modulus (storage and loss moduli) using the ‘Standard 3-Element Linear Solid’ viscoelastic model as an example.


Poroelastic (Time-dependent) Behavior of Tissues

The role of Fluid-matrix interactions in time- and Frequency-dependent behavior of biological tissues. Examples of poroelastic behavior: Soft tissues in health and disease. Darcy’s law for hydraulic permeability combined with continuity, conservation of momentum, and Stress-strain constitutive law gives the poroelastic “diffusion equation.” Creep and stress relaxation of isotropic Cross-linked gels compared to fibrous tissues, e.g., meniscus, cornea (relevant t ocorneal dystrophy), tendon, ligament, cartilage, bone (relevant to joint injuries).


Poroelastic (Frequency-dependent) Behavior of Tissues

Dynamic (storage and loss) moduli revisited in the poroelastic context; examples of oscillatory poroelastic behavior of tissues. Fluid flow through porous tissues (e.g., cartilage) and hydrogels in confined compression; combined Poro-viscoelastic behavior.


Dynamic Nanomechanical Behavior of Extracellular Matrix Macromolecules

Connections between the elastic, viscoelastic and poroelastic behavior of tissues and Time-dependent behavior of their constituent extracellular matrix molecules.


Time-and Frequency-dependent Behavior of Intracellular Networks

Does the Time-and Frequency-dependent behavior associated with cell deformation reflect the poroelastic behavior that is now well known and quantified at the tissue level? Controversies in the literature: A lead-in to Cell Mechanics.

Cell Mechanics

Cell Mechanics: Structure of the Cell

A brief overview of cell anatomy. Experimental measurements of cell elasticity. Micro versus macro perspectives. Data interpretation using scaling and approximation. Cytoskeletal microstructure and a reconsideration of the HILE assumptions.


Visco / Poroelasticity, Large Amplitude Deformations

Normal cell deformations. Active generation of internal tension. Need for experiments on gel systems. Comparison with exisiting viscoelastic and poroelastic models. Nonlinear elastic behavior. Fluidization.


Microstructural Models of the Cytoskeleton

Tensegrity, cellular solids, and biopolymer models of cytoskeletal elasticity. Scaling analyses to ‘derive’ basic predictions. Comparison to measurements.

  Quiz 2: Tissue Biomechanics  

The Cell Membrane

Membrane composition. Stretch, bending, and shear. Equations that govern membrane mechanics. Membrane tension versus bending. Relative importance of membrane and cytoskeleton.


Cell Motility and Mechanotransduction

Measurement of cell motility (speed, persistence, “diffusivity”). Migration in 2D and 3D; the critical differences. Simple models for cell migration. Actin filament assembly / crosslinking and disassembly. Cells sensing their external microenvironment. Protein conformational changes and cellular activation. Bell’s equation revisited. The role of matrix in cell motility and stiffness sensing.

Capstone Problems

The Physics of Cancer

In disease contexts, effects of matrix stiffness on the molecular, cellular, and tissue level processes related to cell adhesion and migration. Measurement of molecular binding kinetics and cell migration as influenced by Naturally-occurring forces. Discussion of the metastatic cascade and the role of mechanics in invasion, adhesion to the endothelium, and the transcendothelial migration.

  Term Project Group Presentations  
  Term Project Group Presentations (cont.)  

Molecular Electromechanics: Electromechanical and Physicochemical Properties of Tissues

Role of electrostatic and osmotic interactions between charged ECM molecules and resulting macroscopic tissue biomechanical properties and function. Measurement and modeling of Electro-mechanical forces at the molecular level.

24 Muscle from the Molecular, Cellular and Tissue Perspectives RK
  Quiz 3