Crossbridge model Crossbridge biophysics Force generation Energetics

Crossbridge Cycle ATP Pi ADP Shape change Animation: Graham Johnson & Ron Vale

Myosin physics Globular head – Actin binding – ATP binding Filamentous neck – Flexible – Light chain binding Filamentous tail – Dimerization – Oligomerization Actin Binding ATP cleft Hinge Neck S-1 Fragment Native Myosin

Laser Trap Photon momentum = E/c Refraction changes momentum 3D Position control

Measuring myosin steps Compliant traps Low ATP Record position Position data: Many steps: Brownian Motion “Step”

Actin-myosin chemical scheme State/compartment model Actin-myosin bound/unbound ATP bound/unbound ATP/ADP+P i Hidden states

Crossbridge Cycle Actin catalyzes Pi release ATP catalyzes A release AMAMT AMDPAMD AM MTMDPMTMDM T TP PD D AMDPAMD AM MTMDPM T PPDD AActin MMyosin T ATP DADP PPi Shape Changes Lymn & Taylor 1971 First cycle: Repeatable:

Quenched-flow chemistry Reactions in moving medium – Steady-state relation btw time and distance – Measure very fast reactions Reagent 1Reagent 2 Mix ATP  Pi by o Actin-myosin Myosin alone o AM + ATP  AMADP + Pi M+ATP  MADP + Pi Quench After an initial burst, actin accelerates reaction Initial ATP hydrolysis independent of actin, sustained Rx catalyzed by actin

Actin-myosin dissociated by ATP Stopped-flow measurements Light scattering by A-M filaments – ie, turbidity AM + ATP  A + M●ATP Turbidity Reagent 1Reagent 2 Mix Quench Detector Lymn & Taylor (1971) AMAMT MT T

Phosphate release catalyzed by actin Pi release by fluorescence More actin  faster release Heeley & al (2002) AMAMT AMDPAMD MTMDPMD TP P Add actin 75 s s -1

Chemical summary Myosin is an ATPase with large shape differences – M-MATP – MATP-MADP – MADP-M Filamentous actin facilitates P i release ATP facilitates f-actin release

Relate chemistry to force AF Huxley 1957 Crossbridge model Two states: myosin attached or myosin not attached Force results from elasticity of individual crossbridges Myosin interacts with actin at discrete sites Attachment and detachment rates are position dependent

Cartoon: capture the minimal process Modeling crossbridge attachment – Imagine Pi release & power stroke instantaneous – A + M  AM + Force with rate constant f – AM  A + M●ATP with rate constant g Think about behavior of single crossbridge Imagine many crossbridges spanning all configs Thick filament Thin filament Rigor State x=0 Max Attachment length x=h

Mathematics Two states: myosin attached (n) or myosin not attached (1-n) Force results from elasticity of individual crossbridges – Individual: F b =kx – All:

Mathematical features First order: exponential Steady state – dn/dt  0 – – n(x) = f/(f+g)

Crossbridge attachment rate Relate crossbridge physics to x Energy released by binding Energy required for deformation Position (X) Binding Deformation “Energy” An unbound myosin is positioned just at “x=1” and can drop onto actin without any bending 0 h 0.0 f1f1 Position (X) f Prohibit attachment x>h

Crossbridge detachment rate Release deformation energy Release conformation energy – Discrete change x< Position (X) Binding Deformation“Energy” 0h 0.0 g1g1 g3g3 Position (X) g A bound myosin is positioned just at “x=0” and any displacement requires bending

Steady state crossbridge attachment n(x) = f/(f+g) x h  n=0 – 0<x<h  n=f 1 /(f 1 +g 1 ) Force=∫k∙n∙xdx – k(f 1 /(f 1 +g 1 ))(h 2 /2) – Crossbridge stiffness – Ratio of f:g 0h 0.0 g1g1 g3g3 Position (X) 0 h 0.0 f1f1 Position (X) f 1 /(f 1 +g 1 )

Crossbridge behavior during shortening Since n=n(x), dn/dt depends on dx/dt Crossbridge moving in from x>>h – No chance to attach until x=h – High probability to attach, but limited time – Probability to attach decreases to x=0, but time rises – Rapid detachment x<0

Crossbridge distribution V=0 – Uniform attachment – Mean x = h/2 V= V max /3 – No saturation – Mean x x n x n x>0  force > 0 x>0  force < 0 These crossbridges resist shortening

Dynamic response

Transition to lengthening Fully attached crossbridges get over-stretched Unattached crossbridges dragged in from left

Faster lengthening

Fully attached crossbridged get compressed Unbound crossbridges dragged in from right Transition to shortening

Faster shortening

Damping without viscosity Qualitative (and quantitative) results of crossbridge and Hill models similar – Even the math: dL/dt = F/b - k/b L – dn/dt = f - (f+g)n Mechanisms behind the models are very different – Crossbridge predicts/validated by biochemistry

Energy prediction Energy liberation – Power from P*v – Heat from dn/dt: increased by shortening x n Shortening V opt Accelerated binding Accelerated release Total energy rate – Hill’s data o Huxley’s model

Issues Fast length changes – < 2 ms (500 s -1 ) – Violates “one process” assumption Lengthening – Too many very long x-bridges Residual force enhancement Double-hyperbolic F-V 100 ms T0T0 T1T1 T2T2 Model Data

Summary Crossbridge cycle: – AM+T  A+MT  A+MDP  AMDP  AMD  AM Attachment of elastic crossbridges explains force-velocity relationship – Reduced attachment during shortening – Shorter length of attachment Higher state models fit better