Molecular, Cellular & Tissue Biomechanics Goal: Develop a fundamental understanding of biomechanics over a wide range of length scales. Patrick Doyle (ChemE), Roger Kamm (ME & BE) Maxine Jonas (BE) I Biomolecules and intermolecular forces II Single molecule biopolymer mechanics III Formation and dissolution of bonds IV Motion at the molecular/macromolecular level MOLECULAR MECHANICS I Structure/function/properties of the cell II Biomembranes III The cytoskeleton IV Cell adhesion and aggregation V Cell migration VI Mechanotransduction CELLULAR MECHANICS TISSUE MECHANICS I Molecular structure --> physical properties II Continuum, elastic models (stress, strain, constitutive laws) III Viscoelasticity IV Poroelasticity V Electrochemical effects on tissue properties Typical Length Scales in Biology 10 -9 10 -7 10 -5 10 -3 10 -1 10 1 meters human typical animal cell nucleus DNA width microtubule width length of DNA contained in a typical human cell chromatin width histone proteins length of DNA in a chromosome Similar spectra exist in time scales or energy scales. Muscles: Spanning from Macro to Nano molecular motor semiflexible polymer Actin: semiflexible polymer Myosin: molecular motor Titin: resting elasticity Cardiovascular mechanics Computational fluid mechanics used to study shear stresses in the carotid artery Peak flow Maximum deceleration 108 bpm 72 bpm Macro-scale applications Image removed due to copyright considerations. Image removed due to copyright considerations. Image removed due to copyright considerations. Image removed due to copyright considerations. …or tissue stresses in the wall of a diseased vessel Stress (Pa) Histological section obtained from surgery Computational mesh for finite element analysis Image removed due to copyright considerations. Image removed due to copyright considerations. Image removed due to copyright considerations. Boundary data (x,y,z) IGES boundary : Quilting / Knitting MRI images Vessel cross-sections 3D model Finite element mesh ParaSolid Model ? Modeling Complex Material Properties? Continuum Microstructural? bending plate entangled polymer force balance Constitutive relations and Viscoelastic or poroelastic strut model solid t 21 (t) Typical Eukaryotic Cell? 10-30 mm 1 mm = 10 -6 m? 1 nm = 10 - 9 m? 1 ? = 10 -10 m? Plasma Membrane? Plasma Membrane ~5 nm 2-D Elastic Plate Cytoskeleton? TEM cytoskeleton photograph, J. Hartwig, Harvard University. Cytoskeletal fibers “rigidity” Diameter (nm) actin 6-8 microtubule 10 intermediate 20-25 filament Persistence Length (mm) 15 60,000? 1-3 Courtesy of J. Hartwig. Used with permission. TEM cytoskeleton photograph, J. Hartwig, Harvard University. When stressed, cells form stress fibers, mediated by a variety of actin-binding proteins. Structure of actin.? Image courtesy of Dr. Willy Wriggers. Used with permission. ? Courtesy of John Hartwig. Used with permission. Measuring Complex Material Properties? Aspiration Cell Poking? Thermal tracers? 4 2 0 -2 -4 -6 -6 -4 -2 0 2 4 Cell Adhesion? Physical forces effect bond association/dissociation Finite contact times Cell deformation After Orsello, Lauffenburger and Hammer, 2001. Dynamic Processes: Cell Migration Fluorescently marked actin Cell Motility ? Actin is a polymer ? The cytoskeleton is active ? Coordinated processes: adhesion, (de-) polymerization Active Cell Contraction Cardiac myocyte (Jan Lammerding) Courtesy of Jan Lammerding, Harvard Medical School. Used with permission. Cytoskeletal Mechanics Probed by External Force Fibroblast with fluorescent mitochondria forced by a magnetic bead D. Ingber, P. LeDuc Image removed due to copyright considerations. Mechanotransduction: Hair cell stimulation stereocilium tip link tension in tip link increases SEM of the stereocilia on the surface of a single hair cell (Hudspeth) Tension in the tip link activates a stretch-activated ion channel, leading to intracellular calcium ion fluctuations. Image removed due to copyright considerations. Image removed due to copyright considerations. Molecular dynamics simulation of channel regulation by membrane tension But other evidence suggests that the pore increases to >20 angstroms! Images removed due to copyright considerations. See Figures 1 and 9 in Gullingsrud, Justin, Dorina Kosztin, and Klaus Schulten. "Structural Determinants of MscL Gating Studied by Molecular Dynamics Simulations." Biophys J, Vol. 80, No. 5 (May 2001), p. 2074-2081. http://www.biophysj.org/cgi/content/full/80/5/2074 Steered molecular dynamics of fibronectin Constant applied force = 500 pN Unfolding has been thought to be important in exposing buried cryptic binding sites. Images removed due to copyright considerations. See Figures 2 and 3 in Gao, Mu, David Craig, Viola Vogel, and Klaus Schulten. "Identifying unfolding intermediates of FN-III10 by steered molecular dynamics." Journal of Molecular Biology, 323:939-950 (2002). The Orders of Magnitude in DNA Organization Compaction of a stretched DNA after histones are introduced. Image removed due to copyright considerations. See Figure 1 in Ladoux, B., P. Doyle et al. "Fast kinetics of chromatin assembly revealed by single-molecule videomicroscopy and scanning force microscopy." Proc Natl Acad Sci U S A. 97(26):14251-6 (2000 Dec 19). Image removed due to copyright considerations. Diagram showing range of size magnitudes, from metaphase chromosome (1400 nm) down to short region of DNA double-helix (2 nm). Dynamic Processes: Molecules Single T4-phage DNA in solution Doyle Group ? Thermal forces are important (kT/ 1 nm ~ 4 x 10 -12 N ) ? Entropic & enthalpic effects ? Generic/specific mechanical responses ? Single molecule experiments are possible Bustmante 1996 Stretching a Single DNA Image removed due to copyright considerations. Motor Proteins Mechanochemical (Enzyme) Engines ATP hydrolysis->conformation change Actin filament Linear Motor Myosin II Rotary Motor (F 0 F 1 ) Yanagida 1999 Image removed due to copyright considerations. Image removed due to copyright considerations. Motor Proteins Reoccurring Themes in Biomechanics ? Multiple length/time/energy scales ? Polymers play an important role ? Thermal energy is important ? Interplay of chemical, electrical, mechanical interactions ? Quantitative (single molecule) experiments ? Scaling arguments ? Mechanical models (polymer physics) ? Experimental techniques ? Importance of the stochastic nature of biology Biology is soft, wet & dynamic Molecular, Cellular & Tissue Biomechanics Using Engineering/Physics to Unravel & Manipulate Biology Readings There is no single text which covers all of this material ! Texts: Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues, 2 nd Edition, Springer -Verlag, 1993R. Nossal and L. Lecar, Molecular and Cellular Biophysics, Wiley, 1990.H. Lodish, D. Baltimore, L. Zipurksy, P. Matsudaira, Molecular Cell Biology, 1996. K. Dill and S. Bromberg, Molecular Driving Forces, 2003 Manuscript Drafts: P.C. Nelson, Biological Physics: Energy, Information Life A. Grodzinksy, R. Kamm, L. Mahadevan: BEH 410 Research Articles: Posted/linked on the web Notes: Periodically posted