科研之友
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摘要
We consider a single living semi-flexible filament with persistence length l(p), in chemical equilibrium with a solution of free monomers at fixed monomer chemical potential mu(1) and fixed temperature T. While one end of the filament is chemically active with single monomer (de)polymerization steps, the other end is grafted normally to a rigid wall to mimic a rigid network from which the filament under consideration emerges. A second rigid wall, parallel to the grafting wall, is fixed at distance L << l(p) from the filament seed. In supercritical conditions where monomer density rho(1) is higher than the critical density rho(1c), the filament tends to polymerize and impinges onto the second surface which, in suitable conditions (non-escaping filament regime), stops the filament growth. We first establish the grand-potential Omega(mu(1), T, L) of this system treated as an ideal reactive mixture, and derive some general properties, in particular the filament size distribution and the force exerted by the living filament on the obstacle wall. We apply this formalism to the semi-flexible, living, discrete Wormlike chain model with step size d and persistence length l(p), hitting a hard wall. Explicit properties require the computation of the mean force (f) over bar (i)(L) exerted by the wall at L and associated potential (f) over bar (i)(L) = -dW(i)(L)/dL on a filament of fixed size i. By original Monte-Carlo calculations for few filament lengths in a wide range of compression, we justify the use of the weak bending universal expressions of Gholami et al. [Phys. Rev. E 74, 041803 (2006)] over the whole non-escaping filament regime. For a filament of size i with contour length L-c = (i - 1)d, this universal form is rapidly growing from zero (non-compression state) to the buckling value f(b)(L-c, l(p)) = pi(2)k(B)Tl(p)/4L(c)(2) over a compression range much narrower than the size d of a monomer. Employing this universal form for living filaments, we find that the average force exerted by a living filament on a wall at distance L is in practice L independent and very close to the value of the stalling force F-s(H) = (k(B)T/d)ln((rho) over cap (1)) predicted by Hill, this expression being strictly valid in the rigid filament limit. The average filament force results from the product of the cumulative size fraction x = x(L, l(p), (rho) over cap (1)), where the filament is in contact with the wall, times the buckling force on a filament of size L-c approximate to L, namely, F-s(H) = X f(b)(L; l(p)). The observed L independence of F-s(H) implies that x proportional to L-2 for given (l(p), (rho) over cap (1)) and x proportional to ln (rho) over cap (1) for given (l(p), L). At fixed (L, (rho) over cap (1)), one also has x proportional to l(p)(-1) which indicates that the rigid filament limit l(p) -> infinity is a singular limit in which an infinite force has zero weight. Finally, we derive the physically relevant threshold for filament escaping in the case of actin filaments.
- 出版日期2015-10-14
