CEMB summer school. Intro to cell and tissue mechanics July 10, 2017 Paul Janmey janmey@mail.med.upenn.edu Soft Stiff
Motivation Soft tissues have well-defined and controlled elastic moduli Cells in vitro do not: their stiffness depends on environment Physical properties of tissues and cells provide signals that are as strong and specific as chemical stimuli Tumors are often (not always) stiffer than surrounding normal tissue. What are the physical principles that define tissue mechanics?
A bit of history: Early cell and tissue mechanics at Penn, Berlin, and Cambridge
Lewis V. Heilbrunn, Dept. of Zoology, Penn 1929-1960 In any attempt to interpret the machinery of a living cell, it is essential to know something about the mechanical properties of the protoplasm in the cell that is being investigated. AN OUTLINE OF GENERAL PHYSIOLOGY, Philadelphia, W.B. Saunders, 1937 (second edition 1943; third edition 1952)
First measurement of microrheology in gels and calls William Seifriz, Dept. of Botany, Penn 1925-1955 Z. physikal. Chem. 104, 235 264; 1923 Must watch this http://www.youtube.com/watch?v=xaatcqstdc4
25 years later.. Experimental Cell Research 1, (1950): 37-80 Finally we would plead that the evidence we have presented for elasticity, and therefore a structure in the cytoplasm will not be regarded as evidence for some cytoskeleton in the chick cell.
Normal tissues have well-defined stiffness characterized by an elastic modulus* Tissue Stiffness Shear storage modulus, G (Pa) < 5% strain; ~ 1s Changes in stiffness often accompany disease * time and strain-dependent Levental et al Soft Matter, 20 Kothapalli et al. Cell Rep 2013
Hepatic stellate cells spontaneously activate on pathologically stiff substrates Rebecca Wells Olsen et al, Am. J. Physiol. 2011
Hydrogel systems to study effects of substrate mechanics 1-5 nm 100 µm E = 50-50,000 Pa ECM protein cadherin, etc PAA or HA gel Glass
Stiffness responses are not always monotonic. Cardiac myocytes on collagen-i and FN-coated PA gels have optimal stiffness F-actin a-actinin Anant Chopra, Erdem Tabdanov, J. Yasha Kresh Chopra et al. Am J. Physiol. 2011
Two ways to measure soft material viscoelasticity Oscillatory shear Compression or indentation Shear modulus G Young s modulus E
Brief intro to mechanical measurements: rheology Apply force (F) to a the surface of a material with area (A); calculate stress (σ); σ = F/A Measure the resulting deformation; quantified by strain (γ) Stiffness, quantified as elastic modulus Emod= σ/γ σ = F/h 2 γ=δx/h here ~ 20% strain
Elastic modulus: (G) ratio of stress (Pa) to strain (dimensionless) L 0 F Leads to L f or ~ 50% strain in elongation or shear Strain (g) = (L f -L 0 )/L 0 (usually shown as a dimensionless percentage) Stress (s) = F/area (typically given in Pascals=N/m 2 ) Elastic modulus (E) = Stress/Strain
Basic terms in cell (soft matter) mechanics Stress: Force per unit area. The direction at which a force is applied to a surface defines whether it is a shear stress (parallel to the surface), compressive stress or elongational stress (perpendicular to the surface). The SI unit for stress is the Pascal (Pa) = N/m2. Strain: A quantitative measure of the amount by which a material is deformed. This unit-less quantity is calculated from changes in the dimensions of a piece of material before and after the application of a force and it depends on the size and shape of the original material. Elastic: A response to force in which the material deforms instantaneously by an amount proportional to the stress, maintains this deformation independent of duration, and recovers to its original unstrained shape when the stress is removed. Elastic modulus: The ratio of stress to strain, representing a kind of spring constant for a material. Because strain has no units, the SI unit for elastic moduli is the Pascal.
Viscous: A response to force in which the material deforms without limit at a rate proportional to the stress, increases its deformation in proportion to the duration that the stress is applied, and remains in its fully strained state when stress is released Viscosity: The ratio of stress to strain rate. Strain rate has units of s -1 so the SI unit for viscosity is the Pascal-second. Viscoelastic: A combination of elastic and viscous responses. Because most soft materials have both elastic and viscous responses, their deformation changes over time but not at a rate that is proportional to the stress, and their strain is partially recoverable when the stress is removed. Mechanosensing: The ability of a cell or tissue to detect the imposition of a force. Examples of such forces include gravitational pressures, shear stresses caused by fluid flow, acoustic waves and contractile forces exerted from one cell to another.
Biologically relevant forces Fluid shear stress blood vessels Stretch/tension circumferential dilation, muscle contraction Substrate stiffness environmentdependent tissue compliance Compression - bone
Shear stress in pathophysiology Cardiovascular disease / atherosclerosis movie Image Mike Plank
Endothelial cells align in the direction of laminar flow Galbraith et al, Cell Motil Cytosk 1998 Static Laminar flow Turbulent flow PF Davies, PNAS 1986
Stereocilia and Trp channels Nature Reviews - Neuroscience
What controls tissue stiffness? The cell interior and the ECM are filled with semiflexible filaments Cortical actin gel JH Hartwig Fibroblasts in collagen ECM (T. Nishida et al. Invest. Ophthalmol. Vis.)
The cell interior and the ECM are filled with semiflexible filaments Cortical actin gel JH Hartwig Fibroblasts in collagen ECM (T. Nishida et al. Invest. Ophthalmol. Vis.)
Thos softest filament in the cytoskeleton, intermediate filaments, are pulled straight to form a continuous meshwork that interconnects cytoskeletons of neighboring cells
Elastic filaments (e.g. elastin, collagen) form the matrix that surrounds blood vessels and other soft structures
Mechanical properties of matrix determined by fiber properties as well as crosslinks
Cells are usually linked to each other and to the extracellular matrix. They also apply tension to all of these junction sites.
When the cell exerts a stress by contraction of the actomyosin network (1000 Pa = 300 myosins / 1 µm 2 ), the resulting deformation will depend on the stiffness of both the cytoskeleton and the ECM (whichever is softer will deform). The tissue will deform passively if its modulus is smaller than the stress, and remodel actively if the stress activates a signal Cytoskeletal and soft tissue stiffness: 100 20,000 Pa
Forces at the cell membrane are distributed among several molecular springs in series. 5 7 1 2 3 4 * apply force * *
Cytoskeletal and extracellular matrix filaments are all approximately semiflexible polymers Filament contour is slightly curved: countour length > but not >> end-to end distance, or distance between crosslinks Thermal motions are sufficient to bend the filament at least a little. 28
MTs collagen fibers F-actin Intermediate filaments Uniquely extended conformation of biopolymers determines their rheologic properties SW carbon nanotubes Wen et al, Curr. Opin. Coll. 2011 ds-dna (also e.g. alginate, HA) polyethylene in theta solvent
Both cytoskeletal and ECM networks are strain stiffening Shear modulus, G or G' (Pa) plat G (Pa ) 1000 100 10 Strain stiffening of semiflexible biopolymer networks [biopolymers] 0.1 to 0.3 % [polyacrylamide] 5% Actin Fibrin 0.01 0.1 1 Shear Strain Strain Collagen polyacrylamide Vimentin Non-linear elasticity allows cytoskeletal and ECM networks to stiffen by internal stress, without increasing polymer mass or XLs. NF Storm et al. Nat. 2005 Gardel et al. Sci 2005
Biopolymer gels show non-linear shear stress and negative normal stress Shear or normal stress (Pa) 50 0-50 Polyacrylamide 0 50 100 Shear strain (%) Flexible polyacrylamide gel has small positive normal stress
Why are networks of biopolymers strain-stiffening? 1. Intrinsic non-linear force-extension relation of thermally fluctuating semi-flexible polymer entropic, affine 2. Orientition of stiff fibers in network under shear shift from bending to stretching enthalpic, non-affine, fiber need not have non-linear elasticity 32
Origin of strain-stiffening: Non-linear force-extension from theory of Fred MacKintosh, Kees Storm, Tom Lubensky u(z) z τ energy : force-extension : force φ 0 φ = normalized force = τl c2 /κπ 2 0 extension PRL, 1995:75:4425-8 Nature 2005: 435:191-194
The (non-linear) force-extension relation for semi-flexible polymers predicts increasing stiffness with increasing strain Model needs as input: mesh size,bending stiffness Assumes that network is isotropic and the persistence length is similar to mesh size. MacKintosh 1995; Storm 2005
Strain stiffening of rigid filament networks can occur by filament alignment, something contractile cells do very well. P. R. Onck, et al. PRL 95, 178102 (2005).
Semiflexible polymers and strain stiffening
Methods to measure single cell viscoelastic properties Atomic Force Microscopy (AFM) Cell aspiration Whole cell rheology and microrheology Optical tweezers Magnetic tweezers
Cell poking by microindenters or atomic force microscope
Atomic force microscopy measures local cell and substrate stiffness cantilever deflection (nm) 300 200 E = 4.2 kpa 100 0 1300 1800 2300 Cantilever position (nm) cantilever deflection (nm) 300 200 E = 4.4 kpa 100 0 1300 1800 2300 cantilever position (nm) cantilever deflection (nm) 300 200 E = 3.2 kpa 100 0 500 1000 1500 2000 2500 cantilever position (nm) Fit deflection curves to Hertz Model of conical deformable solid indenting into another deformable solid k 1 ' k $ kδz Δd = + Δz + % " + 4 4A 2 & A # A 2 2 E A = tan( α) 2 π 1 ν k = bending rigidity and Dz = vertical indentation of the cantilever E = Young s modulus, a = cone tip angle, and n =Poisson ratio.
Fibroblasts become softer and more uniform on gels 1 µm 2 µm 2 µm 0 µm 1 µm
Microaspiration of a red blood cell Fig. 5. Aspiration of a flaccid (a) and swollen (b) red cell into a pipette. The diameter of the flaccid red cell is approximately 8 µm and that of the swollen cell is about 6 µm. The scale bars indicate 5 µm.
Cell micro-rheology
Optical trap
Magnetic Tweezers
How might mechanosensing work? The cytoskeleton is in an initial configuration that surrounds the nucleus and is attached to the cell membrane by a linker protein (e.g. talin, vinculin or a actinin), which is attached to a transmembrane protein (e.g. integrin or cadherin), which in turn is bound at its extracellular domain to an extracellular matrix protein (e.g. fibronectin, collagen or laminin. When a force is applied possible changes include stretching of the extracellular matrix protein to activate a new receptor, activation of the transmembrane receptor that is linked to the cytoskeleton, stretching of the intracellular protein that links the cytoskeleton to the transmembrane protein, and transmission of the force directly to the nucleus.