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Mean quantities in the regime of non-progressive gel front.
(a) Status of actin filaments during the whole simulation time. For this system the attachment rate is constant, ka = 1 s−1, and the force-free detachment rate is . We have 25 filaments in the system which are shown in the horizontal axis. The blue and the black color represent the detached and attached status of the filaments, respectively. (b) The mean number of attached and detached filaments versus time. (c) The average force that attachment and detachment filaments apply on the membrane as a function of time. (d) The mean attachment and detachment time of the filaments versus time.</p
Mean quantities for the case of progressive gel front.
(a) Actin filaments status during the whole evolution for the case of active gel. We have 25 filaments in the system which are shown in the horizontal axis. The blue color shows the detached status of the filament and the black shows the attached status. (b) The average force exerted by attached and detached filaments on the membrane as a function of simulation time. (c) The mean attachment and detachment time of the filaments versus time.</p
List of parameters used in our simulations.
List of parameters used in our simulations.</p
Final steady state configuration of the membrane is reached faster in the case of non-progressive gel for different values of edge tension.
The dynamics of membrane’s middle point versus time for different values of edge tension Fe = [4, 8, 12, 16, 20] pN, with filaments polymerization rate equal to . (a) Non-progressive versus (b) progressive gel boundary with .</p
Snapshots of membrane’s protrusion with a wider actin brush underneath the membrane.
Upon distribution of actin filaments on a larger region, we obtain lamellipodium-like protrusions for (a) non-progressive and (b) progressive gel boundary. Total number of filaments is 101 and the parameters are , Fe = 12 pN, and na = 0.02 nm−1.</p
Comparison of membrane deformations between progressive versus non-progressive gel boundary.
(a) In the case of non-progressive gel front, the final steady configuration is established much earlier and the final membrane elongation is smaller than a progressive gel front. Here , Fe = 12 pN and for progressive gel scenario.</p
Filament distribution in the system with non-progressive gel boundary.
The probability distribution of (a) detached and (b) attached filaments for the early state and also the probability distribution of (c) detached and (d) attached filaments for the late stage of the whole movement. This is the result for a system of na = 0.1 nm−1, Fe = 12 pN and . The total number of filaments is constant and equal to 25 during the whole process. Here μ and σ are the mean value and standard deviation of a normal distribution fitted to the data.</p
Model scheme.
(a) Schematic representation of semiflexible region and actin gel in the model. (b) Magnification of three neighboring beads on the membrane plus the shaded area used for energy minimization. The faded filled circle represents the new position of the bead and defines the displacement vector . (c, d) Stretched and compressed configurations of an attached filament exerting pulling or pushing forces on the membrane. (e) An unattached filament is bent under the membrane and exert entropic force fd.</p
Membrane deformation in the regime of progressive gel.
(a) Initial (b) early and (c) late configuration of the membrane and gel for na = 0.1 nm−1, Fe = 12 pN, and . The insets in panels (a)-(c) show the filaments status underneath the membrane. The blue lines represent the free fluctuating filaments while the black lines show the attached filaments. (d) Behavior of the middle-point of the membrane versus time. The little arrows show the points where the data for the (a)-(c) plots are collected.</p
Force distribution in the system with non-progressive gel front.
Force distribution of detached actin filaments in (a) early stages, (b) late stages of the protrusion. The attached force distribution of actin in (c) early stages and (d) late stages of the total movement. Here μ and σ are mean value and standard deviation of a normal distribution fitted to the data.</p
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