麻省理工大学：《生物工程》教学讲义（英文版）lec 19 slides

Sliding Filament Model Myosin head Myosin filament Actin binding site Actin filament As the actin filament sin filament. the Rate constants k myosin head can bind to it at the red triangle k When it does, the springs are either stretched or compressed and a force cts at the bind Equations governing the probability n(, tthat a cross-bridge is attached dn(x, t) an(, t) an(x, t) =[1-m(x,1)]k(x)-m(x,D)k(x) Formation of new Detachment of existing bonds At steady state n =n(x) I-n(x]k(x)-n(x).(x) k= attachment rate:k= k detachment rate probability of attachment

Sliding Filament Model Myosin filament Myosin head Actin binding site Actin filament x k Rate constants + k- x As the actin filament moves past the (fixed) myosin filament, the myosin head can bind to it at the red triangle. When it does, the springs are either stretched or compressed and a force x acts at the binding site. Equations governing the probability n(x,t) that a cross-bridge is attached dn( x,t) = n( x,t) − v n(x,t) = [1− n( x,t)]k+ ( x) − n(x,t)k−( x) dt t x Formation of new Detachment of existing bonds bonds At steady state [n = n(x)] − v dn(x) = [1− n(x)]k+ ( x) − n(x)k−(x) dx k+ k+ = attachment rate; k- = k￾detachment rate; n = probability of attachment x h 1

The sliding filament model Since both k+ and k are zero, no binding occurs If binding is to occur, it has to do so(according to this simple model)within this narrow region where the binding rate constant is large, described by the equation d k k so 0<x<h-x0 Both the attachment and detachment rate constants are zero, so the myosin head can n(x)=n(-xo/ ≤0 As the complex moves into the region x < 0, the force of interaction sustained at the myosin bond changes sign and its probability of attachment begins to fall, described by the equa dh kx

The sliding filament model x > h: In this region the actin binding site is approaching the free myosin head, unoccupied. Since both k+ and k- are zero, no binding occurs: n(x) = n(h) = 0 h-x0 < x <h: If binding is to occur, it has to do so (according to this simple model) within this narrow region where the binding rate constant is large, described by the equation: −v dn = (1− n)k+ 0 dx k+ k- 0 ⎛ k+ x0 ⎞ n(h − x0 ) = 1− exp⎜− ⎟ ⎝ v ⎠ x h 0 < x < h-x0 Both the attachment and detachment rate constants are zero, so the myosin head can neither bind to nor detach from an actin filament, and the probability of attachment remains constant: n(x) = n(h-x0) = constant x < 0 As the complex moves into the region x < 0, the force of interaction sustained at the actin-myosin bond changes sign and its probability of attachment begins to fall, as described by the equation: −v dn =− k− 0 n k+ k- ⎛ k− x ⎞ ⎡ ⎛ k+ 0 x0 ⎞⎤ ⎛ k− x ⎞ dx 0 0 n(x) = n(0)exp⎜ ⎟ = ⎢1− exp⎜− ⎟⎥ exp⎜ ⎟ ⎝ v ⎠ ⎣ ⎝ v ⎠⎦ ⎝ v ⎠ x h 2

Work done by a single cross-bridge that attaches at x=a and detaches at x=-b w=]kxdx=K(a2-b2) oLA=(n(x)p, As /2)xdr SK 21A 川(x)xa=P4 21A n(O)xex +]n(O)xdx p skh Predicted force-velocity curve from cross- bridge model 1-(F/ 1+C 0.2 D.4 V/Vmax F k: max

W = xdx = 2 a 2 − b 2 ( ) −b a ∫ Work done by a single cross-bridge that attaches at x=a and detaches at x=-b: n(x) [ s As /2 −∞ ∞ lA = ∫ ] xdx n(x)xdx = 2lA n(0)x exp k− 0 x v ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −∞ 0 ∫ dx + n(0)xdx 0 h ∫ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 2lA −∞ ∞ ∫ s As s As = s s h2 4l 1− 2 v hk− 0 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1− exp − k+ 0 x0 v ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ = ⎥ max = ss h2 4l max = 1− v vmax ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1− exp − k+ 0 x0 v ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ vmax = hk− 0 2 Predicted force-velocity curve from cross￾bridge model F Fmax = 1 − v vmax ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1 − exp − k+ 0 x0 v ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ -0.2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 V/Vmax F/Fmax 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 v/vmax F/Fmax or P/Pmax v vmax = 1− ( ) F Fmax 1+ C F F ( ) max Hill’s equation 3

Introduction to Cellular Biomechanics References:RD. Kamm ch 1, 2.2(handed out) Molecular Cell Biology, Lodish et al. Goals for today Why is cell mechanics important Important structural components of the cell Plasma Membrane Models Length scales and details Lumped parameters(Kelvin, Voight, Maxwell Coarse Grained Continuum Mechanics Statistical Mechanical Models Single Molecule

Introduction to Cellular Biomechanics References: R.D. Kamm Chapters 2.1, 2.2 (handed out) Molecular Cell Biology, Lodish et al. Goals for today: • Why is cell mechanics important ? • Important structural components of the cell. • Plasma Membrane. Models Length scales and details Lumped parameters (Kelvin, Voight, Maxwell..) Coarse Grained Continuum Mechanics Statistical Mechanical Models Single Molecule 4

Why is cell mechanics important Critical to function: red blood cells Migration Cell-Cell/Cell-Matrix Adhesion Division Mechanotransduction- respond to mechanical stimuli cell differentiation gene expression diseases (arthritis) Single Cell Mechanics: Aspiration by Micropipette What mechanical properties can we measure

Why is cell mechanics important ? Critical to function: red blood cells Migration Cell-Cell/Cell-Matrix Adhesion Division Mechanotransduction- respond to mechanical stimuli - cell differentiation - gene expression -diseases (arthritis) Single Cell Mechanics: Aspiration by Micropipette What mechanical properties can we measure ? 5

During blood clotting, platelets change shape due to changes in the actin cytoskeleton Images removed due to copyright consideration

During blood clotting, platelets change shape due to changes in the actin cytoskeleton 6 Images removed due to copyright considerations

Important Structural Components in Cells 1. Membrane 2. Cytoskeleton 3. Nucleus and other organelles 4. Cytosol (excluding the cytoskeleton) 5. Adhesion sites Plasma Membrane Extracellular Oligosaccharide G Periphera Peripheral proteins Intracellula

7 Important Structural Components in Cells 1. Membrane 2. Cytoskeleton 3. Nucleus and other organelles 4. Cytosol (excluding the cytoskeleton) 5. Adhesion sites Plasma Membrane

1. Acti 2. Microtubules 3. Intermediate Filaments Motility and the Cytoskeleton Actin filaments(or microfilaments)are one of the three protein filament systems that comprise the cytoskeleton Eukaryotic cells contain abundant amounts of highly conserved actin Images removed due to copyright considerations Figure 18-1

Cytoskeleton 1. Actin 2. Microtubules 3. Intermediate Filaments • Actin filaments (or microfilaments) are one of the three protein filament systems that comprise the cytoskeleton • Eukaryotic cells contain abundant amounts of highly conserved actin Figure 18-1 Motility and the Cytoskeleton 8 Image courtesy of J. Hartwig. Used with permission. Images removed due to copyright considerations. See Figure 18-1 in [Lodish]

Organelles of the eukaryotic cell Lysosomes Peroxisomes Image removed due to copyright considerations Chloroplasts the Endoplasmic Reticulum the Golgi complex the Nucleus the Cytosol Cytosol (excluding the cytoskeleton) Inclusion bodies Proteins(actin monomers) ons Viscosity=50-10 Valentine and Weitz 2003

Organelles of the eukaryotic cell • Lysosomes • Peroxisomes • Mitochondria • Chloroplasts • • the Golgi complex • the Nucleus • the Cytosol the Endoplasmic Reticulum Viscosity=50-104 cp (water : 1 cp) Valentine and Weitz 2003 microrheology Cytosol (excluding the cytoskeleton) • Inclusion bodies • Proteins (actin monomers) • Ions • Water Xenopus egg extracts: 9 Image removed due to copyright considerations Image removed due to copyright considerations. Image removed due to copyright considerations

Glycocalyx: Cell Coat, Furry Coat Image removed due to copyright considerations See Holland, N.B., et al. Biomimetic engineering of non-adhesive glycocalyx-like surfaces using oligosaccharide surfactant polymers Nature392(6678);:799-801(1998Apr23) In endothelial cells-compressible barrier from blood cells Case study Bacteria-2 Primary Roles 1)resisting phagocytosis 2)adhering to and colonizing environmental surfaces(rocks, he th.. Adhesion sites Cell-cell adhesions Cell-adhesion attachment protein Coupling to tissue Cell-surface Sens y

Case Study: Bacteria- 2 Primary Roles: 2) adhering to and colonizing environmental surfaces (rocks, hair, teeth…) In endothelial cells- compressible barrier from blood cells Adhesion sites Glycocalyx: ‘Cell Coat’, ‘Furry Coat’ 1) resisting phagocytosis •Coupling to tissue •Sensing •Migration •Communication 10 Image removed due to copyright considerations. See Holland, N.B., et al. Biomimetic engineering of non-adhesive glycocalyx-like surfaces using oligosaccharide surfactant polymers. Nature 392(6678):799-801 (1998 Apr 23)