Force and polymerization: Breaking symmetry

1. Force and polymerization: Breaking symmetry We will start with demonstrating a relationship and then demonstrating significant biological importance Marc W. Kirschner Lecture IV April 5, 2005

2. Effect of actin polymerization on lipid vesicles coated with Act A Sickle cell Anemia control ActA Proc Natl Acad Sci U S A. 2003 May 27;100(11):6493-8. Epub 2003 May 8.

3. Even without nucleotide hydrolysis polymers like actin and microtubules can exert force and do work. We consider the situation where the thermodynamic work that is done is pushing with a force, F, over a distance of one subunit that is inserted (l0 = L/N). For a microtubule which is 13 strands l0 is 8nm/ 13 = 0.615nm F We assume that the force obeys Hooke’s law where F = a(l - l0) l = F/a +l0

4. The chemical potential m is given by • dm = - ldF (at constant temperature) • dm = - (F/a + l0)dF • On integrating: • = m0 - {l0F + (F2/2a)}; for small F m = m0 - l0F Extension F>0 m < 0 m = 0 Hill TL, Kirschner MW. Proc Natl Acad Sci U S A. 1982 Jan;79(2):490-4. Subunit treadmilling of microtubules or actin in the presence of cellular barriers: possible conversion of chemical free energy into mechanical work. m > 0

5. Now considering the free monomers in solution. At equilibrium their chemical potential is given by: m0 = ms0 + kT ln ce0 m0 - l0F = ms0 + kT ln ce Combining these we get that: lnce = lnce0 - (m0 - l0F) L(solution) F Ja = ac - a¢ + end J LLLLLLLLLLL a a’ Jb = bc - b¢ ce0 ce - end -b¢ b¢ b

6. The reciprocal effect of force on the rate constants • Consider the situation at equilibrium. • ce0 = a0’/a0 • ce = a’/a • kTln(a0/a0’) = ms0 -m0 • kTln(a/a’)= ms0 -m0 +l0F • There is a relationship between the rate constants • a’/a = a0/a0’ elF/kT • The difference in free energy is sharedbetween the two rates • = a0eflF/kT a’ = a0ef-lF/kT’ F + end LLLLLLLLLLL a a’ Capped b=b’=0 We might expect that f is itself a function of F. In any case compressive force should make it difficult to add subunits; the higher the force the more difficult. Experimental studies show that compressive force only affects on-rate.

7. Does polymerization and depolymerization do important work? The first case was the demonstration that the depolymerization of microtubules can pull chromosomes. Other materials bound to motor proteins could also be shown to move in the absence of ATP. Movement caused by microtubule depolymerization in the absence of ATP or GTP. Coue, et al., (1991) J. Cell biol 147, 355

8. Koshland DE, Mitchison TJ, Kirschner MW. Nature. 1988 Feb 11;331(6156):499-504. Polewards chromosome movement driven by microtubule depolymerization in vitro.

9. Koshland DE, Mitchison TJ, Kirschner MW. Nature. 1988 Feb 11;331(6156):499-504. Polewards chromosome movement driven by microtubule depolymerization in vitro.

10. This led to statistical mechanical models to ask whether the thermodynamic feasibility could be achieved. Since the process depends on the diffusion of the filament away from the wall, the process could either be diffusion limited or reaction limited. By diffusion limited, one assumes that there are a high concentration of subunits ready to jump into the gap but they wait for a rare movement. By reaction limited, the fluctuations are high but not every fluctuation inserts a subunit. This process is called a Brownian Ratchet after the machine described by Richard Feynman. Theriot JA.Traffic. 2000 Jan;1(1):19-28.The polymerization motor.

11. Pulling the microtubules by microtubule depolymerization: The Dam 1 Ring complex. Formation of a dynamic kinetochore-microtubule interface through assembly of the Dam1 ring complex. Westermann S, Avila-Sakar A, Wang HW, Niederstrasser H, Wong J, Drubin DG, Nogales E, Barnes G. Mol Cell. 2005 Jan 21;17(2):277-90 From Moldotsov et al. PNAS, (2005) 102, 4353

12. Following the GTP subunits

13. Force-dependent growth and Symmetry Breaking The listeria assay for polymerization driven motility. The active protein in listeria, ActA, can be adsorbed to beads and actin will assembly. Initially there is a cloud of actin around the bead which establishes no strong polarity. Suddenly within a few seconds it becomes asymmetrical and becomes motile. van Oudenaarden A, Theriot JA. Nat Cell Biol. 1999 Dec;1(8):493-9. Cooperative symmetry-breaking by actin polymerization in a model for cell motility.

14. Symmetry Breaking from van Oudenaarden Lab http://web.mit.edu/biophysics/movies/bead4.mov

15. The utility of rigid mechanical structures in symmetry breaking. Symmetry breaking or large distances (e.g. in eggs and embryos) is difficult. It is hard to repress local autonomy. In the case of a bead of Act A, how is one side to be repressed and the other activated? B A Polymerization is nucleated by Act A on the bead so if the filament too far from the bead polymerization is low (A) but if it is too close to the bead the force on the actin polymerization slows the polymerization (B).

16. The effect of the bead is to correlate the forces. For example, two filaments next to each other will stimulate the polymerization, since the force acting on one will decrease the force acting on the other. For filaments on opposite sides of the bead the actions will be anticorrelated. As we saw earlier the on-rate is diminished by : a’/a = exp(-f d/kT)

17. The model also explains the large lag (over one hour) before symmetry is broken. In the first stage actin filaments assemble there is little force exerted. In the next stage, force builds up symmetrically on the bead. This increases the off-rate. At a critical off-rate, the stochastic nature of the assembly is magnified. Correlated unidirectional growth follows.

18. Breaking symmetry on a cellular level: the egg and the organism • Eggs are simple cells, often no more complex than somatic cells • The complexity of the organism is built up by several processes of self-organization which increase asymmetry • The egg often uses the cytoskeleton to break asymmetry

20. There is an initial animal vegetal asymmetry which corresponds to one axis of the embryo (equivalent to delineating latitudes). The other axis is induced by sperm penetration. How does sperm penetration cause the egg to become asymmetric?

21. Vincent JP, Gerhart JC. Dev Biol. 1987 Oct;123(2):526-39. Subcortical rotation in Xenopus eggs: an early step in embryonic axis specification.

22. The importance of cortical rotation in the later embryology

23. What powers the cortical rotation and what determines the orientation?

24. Movement begins before appreciable orientation

26. Dorsal/Ventral Polarity in Drosophila-geometric bistability and microtubules Roth S. Philos Trans R Soc Lond B Biol Sci. 2003 Aug 29;358(1436):1317-29; discussion 1329. The origin of dorsoventral polarity in Drosophila.

30. Relaying the initial nuclear asymmetry in the oocyte to the follicle cells and then back to the oocyte Gurken secreted by the oocyte near the nucleus Pipe and kekkon are turned on in the ventral and dorsal regions in response to gurken

31. There is a further relay of the Pipe signal which is an extracellular matrix component in liberating an autoactivating circuit leading to the nuclear localization of dorsal

32. This in turn will activate target genes:

33. Geometric bistability utilizes arbitrary features of the environment amplified by self organizing systems with positive feedback • In Xenopus the sperm aster biases a process of microtubule self-organization that is amplified by the rotation process itself • In Drosophila the nucleus follows one of an infinite number of paths in migrating to the anterior side. Mutual activations lead to D/V differences • In other eggs (e.g. chicken) gravity is used to bias a symmetric process • In other cases (e.g. Ascidian) there is spontaneous actin based collapse to a point

34. In mammals, the basic geometry of spheres inside of spheres seems to be the clue for a unique point determining the D/V axis. • In many organisms, one of the unique axes is determined by the nuclear-centrosome axis within the cell itself, which may or may not be aligned with external factors. • All of these assure collapse to a single point or single axis--the orientation may be arbitrary or unimportant. • The problem that is solved is to use local organization to achieve a single overall polarity--to break symmetry on a large scale (up to millimeters).

35. Hill TL, Kirschner MW. Proc Natl Acad Sci U S A. 1982 Jan;79(2):490-4. Subunit treadmilling of microtubules or actin in the presence of cellular barriers: possible conversion of chemical free energy into mechanical work. Koshland DE, Mitchison TJ, Kirschner MW. Nature. 1988 Feb 11;331(6156):499-504. Polewards chromosome movement driven by microtubule depolymerization in vitro. Theriot JA. Traffic. 2000 Jan;1(1):19-28. The polymerization motor. van Oudenaarden A, Theriot JA. Nat Cell Biol. 1999 Dec;1(8):493-9. Cooperative symmetry-breaking by actin polymerization in a model for cell motility. Vincent JP, Gerhart JC. Dev Biol. 1987 Oct;123(2):526-39. Subcortical rotation in Xenopus eggs: an early step in embryonic axis specification. Roth S. Philos Trans R Soc Lond B Biol Sci. 2003 Aug 29;358(1436):1317-29; discussion 1329. The origin of dorsoventral polarity in Drosophila. References