In various cellular processes, bio-filaments like F-actin and F-tubulin are able to exploit chemical energy associated with polymerization to perform mechanical work against an obstacle loaded with an external force. The force-velocity relationship quantitatively summarizes the nature of this process. By a stochastic dynamical model, we give, together with the evolution of a staggered bundle of Nfrigid living filaments facing a loaded wall, the corresponding force-velocity relationship. We compute the evolution of the model in the infinite wall diffusion limit and in supercritical conditions (monomer density reduced by critical density ρ^1>1), and we show that this solution remains valid for moderate non-zero values of the ratio between the wall diffusion and the chemical time scales. We consider two classical protocols: the bundle is opposed either to a constant load or to an optical trap setup, characterized by a harmonic restoring force. The constant load case leads, for each F value, to a stationary velocity Vstat(F;Nf,ρ^1) after a relaxation with characteristic time τmicro(F). When the bundle (initially taken as an assembly of filament seeds) is subjected to a harmonic restoring force (optical trap load), the bundle elongates and the load increases up to stalling over a characteristic time τOT. Extracted from this single experiment, the force-velocity VOT(F;Nf,ρ^1) curve is found to coincide with Vstat(F;Nf,ρ^1), except at low loads. We show that this result follows from the adiabatic separation between τmicroand τOT, i.e., τmicro≈ τOT.
On the force-velocity relationship of a bundle of rigid bio-filaments / Perilli, Alessia; Pierleoni, Carlo; Ciccotti, Giovanni; Jean-Paul Ryckaert, And. - In: THE JOURNAL OF CHEMICAL PHYSICS. - ISSN 0021-9606. - 148:9(2018), p. 095101. [10.1063/1.5001124]
On the force-velocity relationship of a bundle of rigid bio-filaments
Alessia Perilli
;Carlo Pierleoni;Giovanni Ciccotti;
2018
Abstract
In various cellular processes, bio-filaments like F-actin and F-tubulin are able to exploit chemical energy associated with polymerization to perform mechanical work against an obstacle loaded with an external force. The force-velocity relationship quantitatively summarizes the nature of this process. By a stochastic dynamical model, we give, together with the evolution of a staggered bundle of Nfrigid living filaments facing a loaded wall, the corresponding force-velocity relationship. We compute the evolution of the model in the infinite wall diffusion limit and in supercritical conditions (monomer density reduced by critical density ρ^1>1), and we show that this solution remains valid for moderate non-zero values of the ratio between the wall diffusion and the chemical time scales. We consider two classical protocols: the bundle is opposed either to a constant load or to an optical trap setup, characterized by a harmonic restoring force. The constant load case leads, for each F value, to a stationary velocity Vstat(F;Nf,ρ^1) after a relaxation with characteristic time τmicro(F). When the bundle (initially taken as an assembly of filament seeds) is subjected to a harmonic restoring force (optical trap load), the bundle elongates and the load increases up to stalling over a characteristic time τOT. Extracted from this single experiment, the force-velocity VOT(F;Nf,ρ^1) curve is found to coincide with Vstat(F;Nf,ρ^1), except at low loads. We show that this result follows from the adiabatic separation between τmicroand τOT, i.e., τmicro≈ τOT.File | Dimensione | Formato | |
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