We establish the statistical mechanics framework for a bundle of Nf parallel uncrosslinked actin filaments in a solution of free monomers pressing against a mobile wall subject to an external compressive force; the free monomer density ρ1 is larger than the critical value ρ1c upon which the filaments tend to grow by free monomer aggregation at the barbed end (supercritical conditions: ρˆ1 = ρ1/ρ1c = 1). The filaments are anchored normally to a planar surface at their pointed ends, while the growing ends hit the obstacle, depicted as a second planar surface, parallel to the previous one. In order to make contact with the experimental measurement of the polymerization force of an actin bundle in an optical trap set-up (M. J. Footer et al., Proc. Natl. Acad. Sci. USA,104,2181,(2007)), we consider the obstacle to be subjected to a compressing load proportional to the distance L between the grafting plane and the obstacle. We model the grafted living filaments as discrete Wormlike chains (d-WLC) with F-actin persistence length subject to discrete contour length variations ±d (the monomer size) to model single monomer (de)polymerization steps. For an ideal solution of reactive filaments and free monomer at fixed free monomer chemical potential μ1, we obtain the general expression for the grand potential from which we derive averages and distributions of several physical properties of the systems (i.e. the bundle polymerization force or the obstacle position). At equilibrium, the average force exerted by the bundle is a few percents larger than the expected stalling force NfkBT/dlnρˆ1, and the average wall position if also slightly larger than the expected value, two correlated consequences of filament flexibility. For situations where the equilibrium trap length ⟨L⟩ remains below the threshold for lateral escaping filaments to appear, Lmax ≈ 60÷90d depending on the value of μ1, the force exerted by the bundle turns out to be produced by a suitable number of buckled filaments under compression N0 < Nf , the remaining Nf − N0 filaments being inactive as their contour lengths is shorter than L. Since the filament buckling force decreases as 1/L2c ∼ 1/L2 when L increases, the average number ⟨N0⟩ of recruited filaments at stalling increases as L2, to maintain the total force L–independent. We further discuss the domain of validity of this regime at L = Lmax(ρˆ1) where the possibility for filaments to escape laterally becomes relevant. Our development allows us to critically discuss published experimental results on the polymerization force under new perspectives.

On the properties of a bundle of flexible actin filaments in an optical trap

PIERLEONI, CARLO;
2016-01-01

Abstract

We establish the statistical mechanics framework for a bundle of Nf parallel uncrosslinked actin filaments in a solution of free monomers pressing against a mobile wall subject to an external compressive force; the free monomer density ρ1 is larger than the critical value ρ1c upon which the filaments tend to grow by free monomer aggregation at the barbed end (supercritical conditions: ρˆ1 = ρ1/ρ1c = 1). The filaments are anchored normally to a planar surface at their pointed ends, while the growing ends hit the obstacle, depicted as a second planar surface, parallel to the previous one. In order to make contact with the experimental measurement of the polymerization force of an actin bundle in an optical trap set-up (M. J. Footer et al., Proc. Natl. Acad. Sci. USA,104,2181,(2007)), we consider the obstacle to be subjected to a compressing load proportional to the distance L between the grafting plane and the obstacle. We model the grafted living filaments as discrete Wormlike chains (d-WLC) with F-actin persistence length subject to discrete contour length variations ±d (the monomer size) to model single monomer (de)polymerization steps. For an ideal solution of reactive filaments and free monomer at fixed free monomer chemical potential μ1, we obtain the general expression for the grand potential from which we derive averages and distributions of several physical properties of the systems (i.e. the bundle polymerization force or the obstacle position). At equilibrium, the average force exerted by the bundle is a few percents larger than the expected stalling force NfkBT/dlnρˆ1, and the average wall position if also slightly larger than the expected value, two correlated consequences of filament flexibility. For situations where the equilibrium trap length ⟨L⟩ remains below the threshold for lateral escaping filaments to appear, Lmax ≈ 60÷90d depending on the value of μ1, the force exerted by the bundle turns out to be produced by a suitable number of buckled filaments under compression N0 < Nf , the remaining Nf − N0 filaments being inactive as their contour lengths is shorter than L. Since the filament buckling force decreases as 1/L2c ∼ 1/L2 when L increases, the average number ⟨N0⟩ of recruited filaments at stalling increases as L2, to maintain the total force L–independent. We further discuss the domain of validity of this regime at L = Lmax(ρˆ1) where the possibility for filaments to escape laterally becomes relevant. Our development allows us to critically discuss published experimental results on the polymerization force under new perspectives.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/91194
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