Calendar

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.

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.

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.

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.)

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.

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).

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;

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).

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.

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.

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.

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.