Biophysics of Macromolecules

Transcription

1 Biophysics of Macromolecules Lecture 11: Dynamic Force Spectroscopy Rädler/Lipfert SS Forced Ligand-Receptor Unbinding - Bell-Evans Theory 22. Mai. 2014

2 AFM experiments with single molecules custom-built instrument (M. Rief, H. Gaub et al., Science 275, 1295 (1997)):" Deflection" Piezopath" intermolecular forces" (binding interactions)" intramolecular forces" (polymer elasticity)" Force [pn]" 600" 400" 200" 0" -200" -400" 0" 100" 200" 300" 400" Extension [nm]"

3 Measuring the binding strength of individual ligand-receptor pair commercial instrument designed for! high resolution imaging:! H.L. Florin, H. Gaub et al., " Science 264, " 415 (1994)" lense" laser! " diode" segmented! photodiode! biotin" avidin! agarose bead" sample" x-y-z-! piezo! tube" " Das Bild kann nicht angezeigt werden. Dieser Computer D verfügt möglicherweise über zu wenig Arbeitsspeicher, um das Bild D zu öffnen, oder das Bild ist beschädigt. Starten Sie den Computer neu, und öffnen Sie dann erneut die Datei. Wenn weiterhin das rote x angezeigt wird, müssen Sie das Bild möglicherweise löschen und dann erneut einfügen. cantilever with! integrated tip" " Counts " 200" 400" 600" 800" 1000" adhesion force [pn] Precision: position accuracy ~ 0.1 nm!! Sensitivity: measuring forces < 10 pn! adhesion force quantized! in integer multiples of ~160 pn!

4 Principle of the biomembrane force probe (BFP)! R. Merkel, Physics Reports 346, 343 (2001)"

5 The rupture force is loading rate dependent! Slow retraction (10 pn/sec ) Fast retraction (60000 pn/sec ) Evans, Annu. Rev. Biophys. Biomol. Struct :105 28

6 Biotin-streptavidin bond strength measured by BFP! Merkel et al., Nature 397, 50 (1999)"

7 Probing potential landscapes by dynamic force spectroscopy" R. Merkel et al., Nature 397, 50 (1999)" External force along the molecular coordinate, x " adds a mechanical potential to the energy landsscape" inner barrier dominates! when outer barrier falls! below k B T! sharp barriers (transition states) change little" in shape or location under force, while" shallow barriers may completely vanish"

8 Desorption of single polymer chains from a solid surface! F Kraft! L k off << F s F u Binding sites! Between polymer! and substrate Länge! k on k off 'Kraft! k off >> F s F u s L Länge!

9 Chemical bonds in equilibrium k S D 1 S 2 k A S 2 [ ] = k off [ S 1 ] [ S 1 ] = k on S 2 [ ] [ S 2 ] [ ] = k off S 1 k on S 1 and S 2 are different states, e.g.conformations of a protein Free energy landscape G = H TS S 2 [ S ] ΔG 2 [ S ] = e kt 1 = k off k on =: K eq S 1 Δx ΔG(0) Def.: equilibrium constant

10 The energy landscape tilts under external force ΔG(F) ΔG(0) FΔx Δx ΔG(0) [ S ] ΔG FΔx 2 [ S ] (F) = K kt eq (F) = e 1

11 Chemische Bindungen unter Kraft II: Nichtgleichgewicht Beispiel: Das Rezeptor-Ligand System Biotin-Avidin k off (F) BA A + B Die Polymeranker verhindern eine mögliche Rückbindung k on =0 Gaub/SS 2005 BPM

12 The rate of escape is force dependent k off k off (F) ΔG a * : Free activation energy ΔG a* ΔG (F) a* (F=0) Arrhenius: Δx a * k off = ν e ΔG a kt ν: attempt frequency Under external force: k off = ν e ΔG a * F Δx a kt FΔx k off (F) = k 0 kt off e The escape rate increases exponentially under force (Bell, 1978) Gaub/SS 2005 BPM

13 Rate of Escape Over an Idealized Barrier Kramer Theory (1956) k off = ν e ΔG a kt * k off The attempts are described as a diffusive motion in a potential ν = l c l st D Δx a l c represents the thermal spread in bound states ound states limited by the rise in ene l c = R dx exp[ 1E c (x)/k B T]. l c 2πkT /κ c l ST 2πkT /κ ST κ c curvature at the minimum κ ST curvature at the maximum ν = τ D 1 = κ c κ ST / 2πζ m Kramers formula

14 k off (F) BA A + B Bond rupture as a statistical prozess dn BA = k off n BA dt dp Z = P Ü k off (t) dt dp Z : Probability that a bond breaks in the time interval dt P Z : Probability that bond is broken at time t P ü : Probability that bond still exisits at time t ( ) k off (t) dt dp Z = 1 P Z P Ü =1 P Z Spring const. Loading rate f(t) = v P k C t with: dp Z df (F) dp Z (F) ΔF df P Z (T )= 1 e P Z (F)= 1 e T 0 1 v P k C k off (t ) dt k off (f ) df dp Z df (F)= 1 k v P k off (F) e C : Probability density of bond rupture. Gaub/SS 2005 BPM F 0 1 v P k C Probability that a bond ruptures in the force interval F 0 k off (f ) df

15 dp Z df (F)= 1 k off (F) e v P k C mit: 1 v P k C ( k off (F) = k 0 e ΔG * F Δx a ) k B T F 0 k off (f ) df ( ΔG* F Δx a ) 1 k dp Z df (F)= k B T 0 e v P k C * k, B T k 0, e v P k C Δx, a, + $ & ΔG * F Δx % a k B T ' ) ( ΔG* k e B T - / / / /. Maximum of the probability density yields most probable rupture force F A F A = kt $ ln Δx a k ' & c ) Δx a %& α 0 kt () + kt ln v Δx P a k 0 [ ] Gaub/SS 2005 BPM

16 F A = kt " % $ Δ x a k c ' ln$ ' + kt ln v P Δ x a # $ α 0 kt &' Δ x a k 0 [ ] Force [pn] Δ x=3å 1/ s 1/30000 s 1/3000 s 1/300 s 1/30 s Force [pn] k =1/30000 s 0 1Å 2Å 3Å 4Å 5Å Pulling Speed [m/s] Pulling Speed [m/s] Ratedependent force measurements yield information about the width of the energy landscape (Δx a ). Gaub/SS 2005 BPM

17 Die Verteilung der Entfaltungskräfte von Titindomänen spiegeln die Zufallsnatur des Bindungsbruchprozesses wider. Gaub/SS 2005 BPM

18 Schlußfolgerungen 1. Bindungsbrüche sind thermisch aktivierte statistische Prozesse und haben dementsprechend keinen scharfen Wert sondern eine charakteristische Verteilung 2. Die Bruchkräfte hängen von der Geschwindigkeit ab, mit der ein Experiment durchgeführt wird.