Quantitative Analysis of Forces in Cells

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1 Quantitative Analysis of Forces in Cells Anders Carlsson Washington University in St Louis Basic properties of forces in cells Measurement methods and magnitudes of particular types of forces: Polymerization forces Osmotic forces Forces from whole cells and cell aggregates

2 Fundamental Cell Mechanobiology Fact: Net Forces Are Very Small in Comparison to Individual Force Contributions Moving/accelerating cell: Fnet=ma=(2000 µm 3 )(1gm/cm 3 ) (0.01µm/s 2 )= 2x10-20 N 0 Fnet = 0 = Fstatic + Fdrag Fdrag = (6πηR)v = 6π (0.01Pa-s) (20µm) (0.1µm/s) = 2x10-13 N 0 So Fstatic = 0: Force balance Also, Fgrav = mg = (4πR 3 /3)(ρcell - ρwater)g =[4π(20µm) 3 /3](0.05gm/cm 3 )(10m 2 /s) = 2x10-13 N 0

3 Force Balance We always speak of forces between different entities, like tension or stress: Tension (or compression) T T Shear stress and tensile stress Pressure is an isotropic compressive stress

4 Force Balance in cells (Baum lab Dev Bio 2015)

5 Basic Units Facts kt = 4.1 pn-nm 1 Mpa = 1 pn/nm 2 = 10 atm = 147 psi

6 Biological Force Measurements Require a Reference Mechanical Scale, Like Temperature or Stiffness of a Filament/Rod Persistence length Lp quantifies the stiffness of a biopolymer filament. It is (roughly) the distance it takes a filament to bend 90 degrees by thermal fluctuations Thermal fluctuations of two bundled actin filaments (Dogic group Nat Matls 2015) Filament Type DNA Actin Microtubule Lp 75 nm 10 µm 2 mm

7 Biological Force Measurements Require a Reference Mechanical Scale, Like Temperature or Stiffness of a Filament/Rod Persistence length Lp quantifies the stiffness of a biopolymer filament. It is (roughly) the distance it takes a filament to bend 90 degrees by thermal fluctuations Thermal fluctuations of two bundled actin filaments (Dogic group Nat Matls 2015) Filament Type DNA Actin Microtubule Spaghetti Lp 75 nm 10 µm 2 mm 100 light years

8 Polymerization Forces - the Brownian Ratchet Membrane (AEC PRE 2000) Growth velocity is predicted to slow exponentially with 8 opposing force

9 Measuring Polymerization Force of a Single Actin Filament Green end is attached to formin, red end is anchored by inactive myosin Initial straight length is about 0.7 µm Buckling force is π 2 ktlp/4l 2 =0.8 pn So the growing filament could exert a force of at least 0.8 pn Kovar and Pollard PNAS

10 Microtubule Polymerization Forces ation Fig. 1. In vitro assay to study the force exerted by (Dogterom and Yurke 1997) Fig. 4. Average MT growth velocity as a function of force. Velocity and force were obtained from combining data such as shown in Fig. 3A (18). The lower x axis gives the value of the normalized force, f p /. The upper x axis gives the absolute value of the force, based on our measurement of Fig. 4. Average MT growth velocity as a function the flexural rigidity. The solid line gives the best fit of the data to an exponential decay. V decays exponentially, but too rapidly

11 Polymerization Forces of Small Number of Actin Filaments Growing from a Bundle Bead is held in keyhole trap of known stiffness Force is obtained from deflection of bead Growing actin filament bundle Measured forces of 1-2 pn are smaller than expected from a bundle of filaments 11 (Footer et al 2007)

12 Actin Comet Tail Forces Measured by Micromanipulation 1.5 V/V Bead with actin nucleator on surface Growing actin comet tail V0 = growth velocity at zero force F (nn) (Marcy et al 2004) Growth velocity drops gradually with opposing force Growth is accelerated by pulling force

13 Measuring Forces Generated by Whole Cells Cantilever approach Side view Front view of cantilever Since stiffness of cantilever is known, force can be obtained from measured displacement Prass et al, JCB 2006 Scale bar: 5 microns 13

14 Cell Exerting a Force on a Barrier 1) Initial contact 2) Deflection of lamellum 3) Contact with nuclear mound 4) Maximum force 5) Release (Prass et al 2006)

15 Quantifying Motion and Force Initial peak at 25s, 2.2 nn - lamellipodium (leading edge) Then lamellipodium sneaks around cantilever Later contact is with mound of the cell body Initial contact area is about 1 µm 2

16 Measurements of Force Distribution on Substrate (Traction Force) If the elastic properties of the gel are known, the bead displacement response to a given distribution of forces can be calculated This relationship is inverted to calculate the force distribution given from the bead displacements

17 Traction Forces of Cardiac Myocytes Scale bar = 10 microns Cells pull inward on substrate, in time with spontaneous contractions Strength of contraction increases with stiffness of substrate (Hoffmann group, Biology Open 2013)

18 Stresses and Forces in Layers Layer of cells or molecules with alternating displacement Stress σ Force f Stress is positive when cells/molecules pull on each other (tension) Force is largest where stress is changing most rapidly f dσ/dx

19 W EEVVIIEEW Measured Stresses and Forces in Cell Layers bb aa cc Scale bar = 50 microns ee Migrating kidney cells on elastic substrate containing fluorescent beads ff Displacements of beads are measured with (green) and without (red) forces from cells (Trepat lab, Nat Cell Biol 2017) gg

20 x-direction traction force density obtained from bead displacements Compressive (dark blue) and tensile (red/green/blue) stress corresponding to measured force density

21 Force Measurement Using Micropillars Micropillar array Forces from smooth muscle cell bend pillars inward Scale bar = 10 microns (C. S. Chen lab, PNAS 2003)

22 Molecular-Level Adhesion Forces Molecular Force Sensors Donor can emit green fluorescence Donor But by Förster resonance energy transfer (FRET), energy is instead transferred to the acceptor if is close to the donor Acceptor (Dunn group, Nano Letters 2015) For low force, FRET occurs and the green fluorescence is not seen For high force, FRET is prevented and green fluorescence is seen The protein paxillin is 22 concentrated in regions of high force

23 m m qq Stress Measurement Using Ablation Normal stress Normal stress(nn (nnµm µm 2 2) ) 00ss Scale bar = 10 microns nn rr Arrow indicates target of laser on a stress fiber (Ingber lab, Biophys. J. 2006) 1s 1s Ends of fiber retract immediately after laser pulse; initial rate is set by viscosity of medium o

24 o 55ss pp tt s Ends of stress fiber continue to move apart; final displacement is determined by elastic properties of medium Tension Tension Pressure Pressure 15s 15s

25 Measuring Osmotic Pressure Difference in Walled Cells Cell wall Cin Cout Osmotic pressure difference (turgor pressure) is Π= kt(cin - Cout) Chemical measurement of Π : increase external ion concentration by an amount ΔCout=(Cin - Cout) so that Π vanishes. Then collapse of membrane away from cell wall can be observed.

26 Cusp in volume variation occurs when membrane leaves cell wall Π= ktcp=0 (Klipp lab, Eur. Biophys. J. 2010) Budding Yeast Π= 0.5 MPa

27 Measuring Osmotic Pressure Difference in Walled Cells Nanoindentation Budding Yeast Cell wall (Klipp lab, Biophys. J. 2016) Physics analysis shows that (Boudaoud lab, JRSI 2011) Π=(spring constant k)/π(cell radius) = 0.2 Mpa

28 Conclusions We can only measure a limited range of forces in cells New technologies are pushing the field forward Measurement of stress inside cells remains a hard problem