Lecture Notes

L1 Introduction: From Tissue Biomechanics to Molecular Nanomechanics (PDF - 1.1 MB)  
Molecular Mechanics
L2 Length, Time and Forces in Biology

Molecules of Interest: DNA, Proteins, Actin, Peptides, Lipids

Molecular Forces: Charges, Dipole, Van der Waals, Hydrogen Bonding

kT as Ruler of Molecular Forces

Thermal Forces and Brownian Motion

Life at Low Reynolds Number
L3 Thermodynamics and Elementary Statistical Mechanics

Review of Classical Thermodynamics: Entropy, Equilibrium, Open Systems, Ensembles, Boltzmann Distribution, Entropic Forces

Tutorial on Statistical Mechanics



L4 Ideal Polymer Chains and Entropic Elasticity

Statistics of Random Walks - Freely Jointed Chain - Origins of Elastic Forces

Extreme Extension of a FJC and Modeling Force as an Effective Potential Field
L5 Persistent Chain Model and Cooperativity

The Worm-like Chain Model - Persistence Length as a Measure of Rigidity - Cooperativity Modeled using Ising Models

Examples: Actin Length Fluctuations, Pulling on DNA and Synthetic Polymers
L6 Mechano-Chemistry

Reactions and Chemical Equilibrium - Kramers/Eyring Rate Theories - Effect of Forces on Chemical Equilibrium

Examples: Pulling on Titin, Bond Rupture Experiments
L7 Motility at the Macromolecular Level

Forces by Polymerization - Concept of Equilibrium Force - Motor Proteins - Molecular Springs

Examples: Listeria, Acto-myosin Motors, Kinesin, Vorticellid
L8 Linear Elasticity

Continuum Mechanics - Basis of Linear Elasticity: Stress, Strain vs. Strain-rate, Hooke's Law, Experiments to Measure the Moduli
(PDF - 1.5 MB)  
Tissue Mechanics
L9 Composition and Structure of the Extracellular Matrix (ECM)

Collagens, Proteoglycans, Elastin - Cellular Synthesis and Secretion of ECM Macromolecules - Cell-mediated Assembly of ECM
L10 Pushing and Pulling on Molecules

Guest Lecturer: Prof. Matt Lang
L11 Elastic (Time-Independent) Behavior of Tissues

Stress and Strain in Tissues Modeled via Hookian Constitutive Law - Homogeneous/NonHomogeneous - Isotropic/Anisotropic - Linear/Nonlinear Behavior of Tissues and Relation to the ECM - Relation between Molecular Constituents and Macroscopic Tensile, Compressive, and Shear Properties of Connective Tissues
L12 Examples

Isotropic Cross-linked Gels Compared to Fibrous Tissues such as Arterial Wall, Cornea (Relevant to Corneal Dystrophy), Tendon, Ligament, Cartilage, Bone, Lung
L13 Viscoelastic (Time-Dependent) Behavior of Tissues

Time-dependent Viscoelastic Behavior of Tissues as Single-phase Materials - Transient Behavior (Creep and Stress Relaxation) - Dynamic Behavior (Storage and Loss Moduli) - Lumped Parameter Models (Advantages and Limitations)

L14 Viscoelastic (Time-Dependent) Behavior of Tissues (cont.)   (PDF)
L15 Poroelastic (Time-Dependent) Behavior of Tissues

The Role of Fluid/Matrix Interactions in Tissue Biomechanics - Darcy's Law and Hydraulic Permeability, Continuity, Conservation of Momentum - Creep, Stress Relaxation, Dynamic Moduli Revisited - Poro-viscoelastic Behavior

Examples: Muscle and Soft Tissues in Health and Disease - e.g., Arthritis and Joint Degeneration
E1 Midterm Quiz    
L16 Poroelastic (Time-Dependent) Behavior of Tissues (cont.)   (PDF)
L17 Electromechanical and Physicochemical Properties of Tissues

Role of Electrical and Chemical Phenomena in Determining Tissue Biomechanical Behavior - Fluid Convection of Ions During Tissue Deformation and the Resulting "Electrokinetic" Phenomena - Electrostatic Interactions between Charged ECM

Molecules: Tissue Swelling and Donnan Osmotic Swelling Pressure

Examples: Bone, Muscle, Soft Connective Tissues - Streaming Potentials and Electro-osmosis - Tissue Swelling and Molecular Electromechanical Forces
L18 Muscle Constriction From the Molecular to Macro Scale

Characteristics of Contracting Muscle - Hill's Equation - Force-velocity Curves - Muscle Energetics, Activation - Cross-bridge Dynamics - Models for Muscle Behavior
Cell Mechanics
L19 Structure of the Cell

Cellular Anatomy, Cytoskeleton, Membrane, Types of Attachment to Neighboring Cells or the ECM, Receptors, Different Cell Types, Experimental Measurements of Mechanical Behavior
L20 Biomembranes

Stiffness and Role of Transmembrane Proteins - Equations for a 2-D Elastic Plate - Patch-clamp Experiments - Membrane Cortex - Vesicles: Model Systems
L21 The Cytoskeleton

Fiber Microstructure - Actin and Microtubule Dynamics, Methods of Visualizing Actin Diffusion and Polymerization - Rheology of the Cytoskeleton - Active and Passive Measures of Deformation - Storage and Loss Moduli and their Measurements - Models of the Cytoskeleton: Continuum, Microstructural - Tensegrity, Cellular Solids, Polymer Solution
L22 Cell Peeking and Poking

Guest Lecturer: Prof. Peter So
L23 The Cytoskeleton (cont.)   (PDF)
L24 Cell Adhesion and Aggregation

Cell Adhesion Assays, Cell-free Adhesion Assays - Receptor-ligand Interactions Mediated by the Cytoskeleton and the Cell Membrane - Focal Adhesions

L25/E2 Cell Migration and Mechanotransduction

Measurement of Cell Motility (Speed, Persistence, "Diffusivity") - Simple Models for Cell Migration - Actin Filament Assembly/Crosslinking and Disassembly - Intracellular Signaling Relating to Physical Force - Molecular Mechanisms of Force Transduction - Force Estimates and Distribution within the Cell