1. Alex Mogilner, UC Davis Leah Keshet, UBC, Canada Actin dynamics and the regulation of cell motility

2. Brief introduction to the cytoskeleton

3. PolymerActinMicrotubule Intermediate filament SubunitActin monomer Tubulin dimer  helical Elongate byPolymeriz. ? Bound nucleotide ATPGTPNone TreadmillingVery slowSlowNo Track for motors Yes, 20 myosins Yes, dynein, kinesin No Fluorescence micrograph in cells TD Pollard (2003) Nature 422: 741

4. Heath & Holifeld (1993) in: Cell Behaviour, Adhesion, and Motility, Jones, Wigley, Warn, eds Soc Exp Biol Symp 47

5. Ridley AJ. (2001)J Cell Sci.:114(Pt 15):2713-22

6. Cell motility is a complex process involving adhesion to the surrounding substrate, forward extension (protrusion), and contraction that retracts the rear portion of the cell. Here we will consider only protrusion. The main component implicated in protrusion is ACTIN.

7. GOAL: To relate the protrusion of the cell front to the underlying biochemistry of actin. To derive some connection between the biochemical parameters* and the cell velocity. * Binding rates, reaction rate constants, etc

8. Brief review of properties of actin

9. cell membrane Front edge of cell Actin cytoskeleton Actin filament “barbed end” “pointed end”

10. Keratocyte: Top view Side view 1 µm Svitkina & Borisy (1999) J. Cell Biol., 145(5): 1009-1026. lamellipod

11. Svitkina & Borisy (1999) J. Cell Biol., 145(5): 1009-1026. 1 µm

12. v v v v v Actin filament Pointed end Barbed end monomers

13. v v v v v Polymerization kinetics On rate: k on a Off rate: k off Barbed end grows rapidly k on a > > k off

14. v v v v v Barbed end capped quickly to prohibit explosive growth cappers Control of polymerization by capping

15. v v v v v Depolymerization dominates at pointed end Polymerization kinetics cont’d

16. v v v v v The actin monomers are modified by attached nucleotides (ATP, ADP) ADP-actin ATP-actin ATP-actin polymerizes fastest at barbed end

17. v v v v v As the filament ages, the ATP attached to its monomers is gradually hydrolized new old

18. v ADP-actin v v v v Cofilin chops and fragments actin filaments, preferentially at older (ADP-actin) parts of an actin filament

19. v v v v v There are mechanisms for converting “spent” ADP-actin monomers into their active form ADP-actin ATP-actin Recycling mechanism

20. ADP-actin ATP-actin Profilin facilitates conversion of “spent” ADP-actin to “new” ATP-actin, preparing the monomers for polymerization Recycling actin monomers “spent” “new”

21. Thymosin “sequesters” actin monomers I.e. acts as a reservoir for spare actin, to avoid excessive polymerization A reservoir for actin monomers

22. Total profilin10  M Total thymosin200  M Total Cofilin10  M Total F-Actin200  M Total G-actin~50  M Typical concentrations in lamellipod

23. F-Actin Cofilin-actin Profilin-actin (ADP) Profilin-actin (ATP) Thymosin actin

24. Filaments Spent monomers Activated monomers Reservoir

25. Filaments s pa 

26. Rate constants for all these biochemical events (values known from the literature), will enter into the model.

27. Actin filament dynamics

28. Actin-binding proteins cap barbed end, cut, or degrade a filament crosslink filaments into bundles or networks nucleate new filaments by branching off a pre-existing filament

29. Arp2/3 (when activated) forms branch points and nucleates new, growing barbed ends. T. M. Svitkina and G.G. Borisy, J. Cell Biol., 145(5): 1009-1026, 1999 v v v v v v v v v Arp2/3 actin

30. We’ll be interested in the number of actin filament barbed ends that are at the cell edge pushing on the membrane. We’ll take into account the nucleation of new ends by Arp2/3, as well as the (rapid) capping of loose ends inside the lamellipod.

31. Geometry and spatial aspects of actin dynamics

32. Keratocyte: shape does not change as cell moves adhesion/contraction relatively constant as cell moves. actin filaments stationary relative to substrate

33. close to front edge, geometry “1D”: i.e., lamellipod is a thin sheet, most gradients into the cell (normal to edge)

34. x=L x=0 Simplified geometry X=0 at cell edge; moving coordinate system; Note direction of positive x into the cell

35. Abraham, Krishnamurthi, Taylor, Lanni (1999) Biophys J 77: 1721-1732

36. Length of actin monomer2.72 nm Abraham et al 1999 length of lamellipod~ 10  Abraham et al 1999 thickness of lamellipod0.1  Abraham et al 1999 Typical size scales:

37. TD Pollard (2003) Nature 422: 741

38. Spatial features: Extracellular signals activate WASp at cell membrane. This then activates Arp2/3 Arp2/3 nucleates new branches off actin filaments close to the cell membrane, creating new barbed ends that can grow & push. uncapping is enhanced, and capping is inhibited close to cell membrane. depolymerization dominates at older parts of filament, away from the cell membrane

39. Thus it is safe to assume that new barbed ends are mainly generated close to the front edge of the cell.

40. When a filament grows at the front edge, it has to push against a load force (e.g. membrane resistance).

41. Mogilner & Oster (1996) Biophys J, 71: 3030-3045 We use results of the thermal ratchet model for the extension of an actin filament under a load force.

42. Thermal fluctuations occasionally create a gap between the cell membrane and the tips of actin filaments. Monomers can fill in this gap to cause the displacement to persist. Mogilner/Oster Thermal Ratchet Model:

43. Force per filament, f protrusion velocity, V Thermal Ratchet Model Mogilner & Oster v v v v v

44. Work done to create gap Thermal energy An important ratio for thermal ratchets:

45. Probability of a gap forming on rate off rate (very small) Speed of motion of one filament barbed end

46. Neglecting depolymerization: To know the velocity of barbed end, we need to know the local actin monomer conc. Compare with “free polymerization velocity”:

47. Force per filament, f protrusion velocity, V Load-Velocity relation for single filament Free polymerization velocity Monomer size Load force Thermal energy v v v v v

48. Actin monomers are the fuel that cause extension of the cytoskeleton, and drive the edge of the cell forward. Our (1D) model aims to determine how much of that fuel is available at the front edge, and how this amount is controlled biochemically.

49. “ This system has several advantages for modeling: It runs at steady state, the inventory of core proteins is small, the structures and concentrations of these proteins are known, and biophysicists have measured many of the rate and equilibrium constants for the reactions.” T.D. Pollard (2003) Nature 422, 741-5

50. Diffusion coeff actin30  2 /sMogilner/LEK 2002 thermal energy kT4.1 pN nmPeskin et al 1993 actin monomer on-rate11.6 /  M /sPollard 1986 capping rate4 /sSchafer et al 1996 Arp2/3 attachment rate1-10 /s speculative Arp2/3 diffusion coef3  2 /scalculated monomers in 1  M actin600/  3 conversion factor Examples of representative parameters

51. Assembling a 1D model for the protrusion of the cell based on actin filaments. X=0 front edge x=L rear of lamellipod direction of motion L a m e l l i p o d

52. Ingredients of the model: nucleation of barbed ends by Arp2/3 at front edge actin monomer exchange between various forms (with realistic values of biochemical rate- constants) diffusion of monomers across lamellipod assembly at front edge leading to protrusion

53. How does the protrusion velocity depend on the number of barbed ends ? Main question addressed:

54. B(t) = density barbed ends at edge x=0 motion Arp2/3 nucleation capping nucleation of barbed ends at front edge:

55. Filaments s pa  actin monomer exchange:

56. exchange & activation diffusion of monomers across lamellipod s p a  a(x,t) = conc. actin monomers (ATP form) s(x,t) = conc “spent” monomers (ADP form) Source From depolym Similar terms + Etc..

57. s p a  coordinate system moving with cell edge Monomer exchange Depolym. source

58. Boundary conditions cont’d: No flux of monomers at rear: da/dx =0, d  /dx =0 etc at x=L No flux of some forms of monomers at front: d  /dx =0 etc at x=0

59. assembly at front leading to protrusion (BC): Flux of actin monomers arriving at edge = Extension of barbed ends Conversion factor: monomer conc to filament length

60. Analysis of the model to investigate steady state propulsion, using realistic biochemical parameters

61. Over relevant spatial scale of lamellipod, diffusion dominates over the apparent convective flux: D > V L 30 > 0.3 (10 )  2 /s In the analytical realm, can neglect the first derivative terms for approx solns.

62. s p a  For steady-state motion with D>>VL

63. X=0 front edge x=L rear of lamellipod net polymerization balances total depolymerization da/dx = J p /D at x=0 (BC) For steady-state motion:

64.  a profiles of s, p nearly constant with x s p

65. Analysis of the model for steady-state motion: for given biochemical parameters, profiles of s, p nearly constant. Model reduces to 2 eqns Explicit analytical solutions found, and monomer concentration at edge, a(0) determined

66. Net polymerization equal to depolym flux (J p =JL)

67. From the model and biological parameter values, we determine the actin monomer concentration at membrane available to drive protrusion.

68. Total actin in all forms Amount not available for polymerization Time for monomer to depolymerize, become activated, and diffuse across lamellipod

70. Result: Protrusion velocity depends on kinetic rate constants and on the number of barbed ends (B) pushing the membrane

71. F=100 pN/  m F=300 pN/  m B, # /  m

72. The model predicts: There is an optimal barbed end density The protrusion drops very rapidly for barbed ends below their optimal density, but drops more gradually above the optimum

73. There is an optimal density of barbed ends at the leading edge: too few: force to drive protrusion insufficient. too many: competition for monomers depletes monomer pool too quickly, slowing growth.

74. Limiting case 1: Small barbed end density (B small) “available actin”

75. Limiting case 2: Large barbed end density (B large) Velocity inversely proportional to B

76. What did we learn from the model? BIOLOGICAL IMPLICATIONS

77. The model predicts: optimal barbed end density: suggests that careful regulation of the barbed ends is needed in the cell. means that there are optimal nucleation and capping rates

78. For biological parameter values, V ~ 0.1- 0.3  /s, in good agreement with experimental values Optimal barbed end density is roughly proportional to membrane resistance. For resistance force F~50-500 pN/  optimal barbed end density is B ~ 25-250 per  at this optimum density, V is roughly inversely proportional to membrane resistance.

79. A greater amount of total actin and a faster rate of actin turnover correlate positively with the rate of locomotion. (Evidence from McGrath et al. and by Loisel et al. who showed that there is a concentration of ADF/cofilin that is optimal for enhancing the rate of depolymerization.) Increasing the amount of thymosin slows down locomotion Further model predictions :

80. “ These models identify the variables that limit the rate of movement, such as the concentration of actin bound to profilin. In fact, when the concentration of unpolymerized actin is lowered by releasing an actin monomer sequestering protein in the cytoplasm, that part of a cell stops moving.” TD Pollard (2003) Nature 422: 741-5

81. “ The models raise a number of questions that can be answered by further experimentation.” profilin-actin really limiting? do interactions of filaments with membrane inhibit capping, biasing forward motion? how are filaments reshaped at rear? TD Pollard (2003) Nature 422: 741-5

83. Comet tails assembled by 0.5  bead with 37.5% of its surface area coated with ActA in 40% Xenopus egg extract Cameron,Svitkina,Vignjevic, Theriot, Borisy (2001) Current Biology 11(2),2001, 130-135Current Biology 11(2

84. Time sequence: phase-contrast and fluorescence microscopy images of an actin cloud that spontaneously breaks symmetry (a), and a bead propelled by polymerizing filaments after symmetry-breaking (b). The bead shown in b moves with a constant velocity of 0.12  m s – van Oudenaarden, Theriot (1999) Nat Cell bio 1(8) 493-499

85. Arp2/3 nucleation on and close to bead barbed ends B > B thresh at bead surface leads to motion direction of motion determined by direction of greatest force (from barbed ends) Adriana Dawes and Stan Maree Recent and ongoing work