Effects of Nonequilibrium Processes on Actin Polymerization and Force Generation

Transcription

1 Effects of Nonequilibrium Processes on Actin Polymerization and Force Generation Anders Carlsson Washington University in St Louis Biological cells constantly utilize the influx of energy mediated by ATP and related energy carriers Our goals: Understand how ATP hydrolysis affects dynamics of actin polymerization and ratchetbased force generation Evaluate the relation between macroscopic contractile stress and the molecular-level properties of myosin with Frank Brooks

2 Dynamics of Actin Polymerization in Vitro Actin in cells responds dynamically to stimuli such as uncapping, branching, and severing We try to understand dynamics of this response by using in vitro polymerization as a model system In vitro studies have been very important in understanding control of actin polymerization by actin-binding proteins

3 Rate-Equation Simulations of Branching Polymerization of Actin Intensity (arbitrary units) Curves approach asymptotic values smoothly Increasing CP slows polymerization Time 14.3 nm activated Arp2/3 complex, varying armounts of capping protein (BPJ 2004) 3

4 Actin Polymerization as Measured by Pyrene Fluorescence 2.5 mm actin, 100 nm Arp2/3 complex Fluorescence measures polymerized actin - approximately When polymerization is fastest, fluorescence reaches a peak, then drops This has often been viewed as an artifact (Tehrani and Cooper 2007) 4

5 ATP Hydrolysis Reduces Actin Polymerization Actin ATP in filaments khyd, kphos on monomers knex G-actin monomers are charged with ATP by nucleotide exchange Newly polymerized actin subunits have same state as monomers Barbed ends can have ATP cap, but pointed end is more ADP-like because of slower kinetics khyd 0.3 s -1, kphos 0.002s -1, knex 0.01s -1 in vitro Gc (ATP) 0.1 μm, Gc(ADP) 2 μm Actin ADP How does this affect actin polymerization dynamics? 5

6 Stochastic-Growth Simulations of in Vitro Actin Polymerization All filament subunits are tracked over time, along with their nucleotide states (ATP, ADP-Pi, ADP) Capping and branching states of filaments are also tracked Polymerization/depolymerization, capping/uncapping, branching/ debranching occur stochastically Rates taken from direct measurements of filament growth, or fits to previous and current polymerization data (F Brooks + AEC, Biophys. J. in press)

7 Parameter Symbol Value Barbed end G-ATP on rate k BT Barbed end G-ADP+P i on rate k BP i Barbed end G-ADP on rate k BD Pointed end G-ATP on rate k P T Pointed end G-ADP+P i on rate k P P i Pointed end G-ADP on rate k P D Barbed end F-ATP off rate k BT Barbed end F-ADP+P i off rate k BP i Barbed end F-ADP off rate k BD Pointed end F-ATP off rate k P T Pointed end F-ADP+P i off rate k P P i Pointed end F-ADP off rate k P D on 11.6µM 1 s 1 on 0 on 2.9µM 1 s 1 on 1.3µM 1 s 1 on 0 on 0.13µM 1 s 1 off 1.4s 1 off 1.4s 1 off 5.4s 1 off 0.8s 1 off 0.8s 1 off 0.25s 1 Pointed end Arp2/3 uncapping rate k un 0 Filament branching rate per subunit k µ 3 s 1 G-ATP hydrolysis rate k G hyd 0 G-ADP+P i inorganic phosphate release rate k G phos F-ATP hydrolysis rate F-ADP+P i inorganic phosphate release rate khyd acc kphos acc 0.3s s 1 F-ATP hydrolysis range k hyd s 1 F-ADP+P i inorganic phosphate release range k phos s 1 Nucleotide exchange rate k ex 0.01s 1

8 Pyrene Fluorescence Intensity Depends on Hydrolysis State 8

9 Polymerized Actin Peaks Early, Then Drops Polymerized actin from simulation Fluorescence intensity Overshoot in actual polymerized actin is greater than overshoot in fluorescence intensity Overshoot occurs because actin polymerization exhausts reserves of ATP-actin Overshoot behavior results from sudden jump in number of free barbed ends 9

10 If the Concentration B of Free Barbed Ends is Large, Actin is Primarily ADP at Long Times 2.5 G-actin (µm) G-ADP G-ATP G-ATP Time (s) B=12 nm knex=0.01s - 1 knex/kon T B=

11 Increase of ADP-G-Actin Causes Overshoot Behavior Concentration of free barbed ends B Concentration of F-actin Gc ATP ftgc ATP +fdgc ADP Total Actin F fd 1/[1+knex/kon T B] 1 kon T B 1 kon D B+knex Time Nucleotide exchange rate

12 Overshoot Behavior is a General Feature of Nonequilibrium Polymerization It occurs if nucleotide exchange is slow, or there is a high density of free barbed ends - overshoots are not artifacts! In vitro experiments can be in either the fast-exchange or slow-exchange limits In cells, exchange is probably accelerated 100-fold by profilin, but the density of barbed ends is also much higher than in vitro - overshoot behavior is a possibility Incorporating hydrolysis effects on pyrene intensity is crucial for interpreting polymerization data

13 Effects of ATP Hydrolysis on Ratchet-Based Force Generation Rigorous thermodynamic result valid in absence of hydrolysis (multiple internal states): ] Stall force = kta [ ] per filament ln GGc F eq = kt a ln [ kon (0) k off (0) kon(0) and koff(0) are on- and off-rates in absence of force, a is step size per subunit Gc is critical concentration How is stall force affected by multiple internal states resulting from hydrolysis? 13

14 Two-State Model of Actin Filament Ensemble Extended Brownian-ratchet model At each time step, subunits add and subtract according to known rate constants Tip switches between ADP (state 1) and ATP (state 2), at rates determined from polymerization data Obstacle held in optical trap of spring constant pn/nm Obstacle is assumed to be in thermal equilibrium relative to filaments Key idea: force reduces on-rate, which reduces or eliminates ATP cap

15 Measured Polymerization Velocity Shows Two-State Behavior State 2 Slope changes abruptly at G c Above G c tip is ATP-like (state 2), below G c it is ADP-like (state 1) ADP-like tip depolymerizes rapidly State 1 (Carlier et al 1986)

16 Rates in Model (L, 2) (L + 1, 2) : k 22,on = 11.6 s -1 µm -1 (L, 2) (L 1, 2) : k 22,off = 1.16 s -1 (L, 1) (L 1, 1) : k 11,off = 6.6 s -1 (L, 1) (L + 1, 2) : k 21,on = 11.6 s -1 µm -1 (L, 2) (L 1, 1) : k 12,off = k 21,on (G c - G) (for G < G c ) k 22,on and k 22,off known from electron microscopy data and critical concentration k 11,off obtained from measured depolymerization at G=0 Ratio of k 21,on to k 12,off obtained from fit to polymerization data below G c On-rates are reduced by opposing force according to Brownian-ratchet model Geff=Gexp(-Fa/kT)

17 Simulated Filament Growth and Obstacle Motion at G=1.67G c Obstacle Ten-filament ensemble Filament tip contacts obstacle only a small fraction of the time Single filament

18 Force per Filament Decreases with Filament Number G=1.67Gc F eq is equilibrium stall force for a single filament As number of filaments grows, asymptotic force is about 0.25F eq

19 Mechanism of Force Reduction When many filaments are present, the obstacle force exerted on a single filament fluctuates strongly During periods of high force, hydrolysis is enhanced Because off-rate constant is large, even a small amount of hydrolysis can significantly reduce the velocity

20 Force Measurement of Small Ensemble of Growing Actin Filaments Stall force per filament is only pn 0.2 Feq Force reduction is comparable to that seen in the simulations, as are obstacle fluctuations (Footer et a 2007)

21 Analytic theory: single filament contacting immobile obstacle Theory treats case in which excursions from obstacle are large Assumes force is Feq when filament is in vicinity of obstacle F = F eq 1 + (G c /G)[1 + (G c /G)(k 11 off /k22 off 1)] Large reduction in force occurs when off-rate in depolymerizing state greatly exceeds off-rate in polymerizing state and G is near G c

22 Force-Velocity Relation N=10 filaments Solid lines: Brownian-ratchet theory Circles: simulation Hydrolysis effects turn on suddenly, causing curves to bend down

23 Dependence of Hydrolysis Effect on Monomer Concentration F/F eq Analytic Theory Simulations F(G)/F(3G c ) G/G c B G/G c Effect disappears slowly at large G Measurement of stall force as a function of G could allow observation of effect 23

24 Hydrolysis and Actin Force Generation Hydrolysis-induced disassembly of actin filaments leads to large force reduction if filaments are stiff and actin concentration is low In cells, this effect is most likely to occur in filopodia where filaments are in a stiff aggregate and the tip monomer concentration is low

25 Possible Experimental Tests: Extending current experiments to measure force per filament as a function of filament number Measurement of force per filament as a function of free-actin concentration 25

26 Contractile Stress Generation by Actomyosin Structures Actin and myosin generate contractile forces in nonmuscle cells even though the filament arrangement is very different from that in muscle Why does myosin generate contractile stresses in disordered actin structures? How is the macroscopic tension related to the molecularscale forces? What is the role of actin network structure and dynamics?

27 Nonmuscle Myosin II Produces Contractile Forces Fibroblast cell placed on flexible posts Bending of posts indicated by color change (Sheetz lab, BPJ 2006) Scale bar: 10 μm

28 Nonmuscle Myosin Generates Retrograde Flow RPTP-control: wild type RPTP-C6: NMM-IIA knockdown (Sheetz lab, BPJ 2006)

29 Contractile Ring in Budding Yeast Ring contains actin, myosin, and numerous other proteins (Bi et al 1998) Contractile stress pinches off cell into two daughters

30 Myosin Occurs in Dipolar Minifilaments Myosins move toward actin filament barbed ends F -F d (Niederman and Pollard 1975) Model assumes m heads at each end in contact with an actin filament Each head exerts a force Fmyo, pulling the actin filament toward the center of the minifilament F=mFmyo Magnitude of force dipole is Fd, d 0.4 µm

31 Pull: to apply force so as to cause motion toward the source of the motion - occurs if myosin is near pointed end Push: the act of applying force to move something away - occurs if myosin is near barbed end

32 Actin Treadmilling is Needed for Continuous Generation of Tension Pulling Pushing After myosins move to filament barbed ends, they expand the network But if filaments treadmill faster than myosins move, myosins will stay near pointed ends Rate of network contraction will be limited by actin treadmilling rate

33 Actin Treadmilling is Needed for Continuous Generation of Tension Pulling Pushing After myosins move to filament barbed ends, they expand the network But if filaments treadmill faster than myosins move, myosins will stay near pointed ends Rate of network contraction will be limited by actin treadmilling rate

34 Actin Dynamics Accelerates Cytokinesis Jasplakinolide treated cell Epithelial control cell (Wadsworth lab, 2005)

35 Stress from Myosin Forces Can Be Amplified by Connecting to Filaments Bare myosin minifilament in elastic medium Myosin minifilament attached to actin filaments F -F d F -F strain Fd/Er 3 stress Fd/V deff Filament length = L stress Fdeff/V deff (d+l)

36 Contractile stress from a concentration cmyo of myosins is: σ=cmyofmyo(d+l)/2 Sensitive to actin network structure Stress per myosin is greatest in bundled structures

37 Cytokinesis Tension T (Yoneda and Dan 1972) Cytokinesis tension T is about 4 nn for fission yeast for an assumed membrane tension of 1.5 nn/µm

38 Calculation of Cytokinesis Tension Treat polymerized actin in contractile ring as a uniform homogeneous elastic medium Maximum tension is T = NrFmyo(d+L)/2C where N is the total number of myosin heads, r is the duty ratio, L is the filament length, and C is the circumference of the ring Thus T is reduced by a factor of (d+l)/c relative to simplest estimate NrFmyo/2

39 Calculation of Myosin-Induced Stress in Fission Yeast Using Realistic Duty Ratio and Contractile Ring Structure Assume L=0.6 µm, C=7 µm (late anaphase B) from Mabuchi group results (2005), and r=0.1 Result: T = 0.15 nn << 4 nn Possible reasons for underestimate: Duty ratio could be higher than 0.1 Force chains could result in larger deff Membrane tension could be less than assumed Actin depolymerization could be providing force

40 Conclusions ATP hydrolysis can lead to complex polymerization dynamics At low actin concentrations, ATP hydrolysis can greatly reduce the stall force of actin filament ensembles Contractile stresses generated by myosin depend strongly on the actin network structure and require actin filament treadmilling