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Fig. 7.
The figure (cropped for better illustration) shows the end result of the simulation for one
hour with 1200 actin-agents and 30 Arp2/3-agents. The black points mimic the free actin, the
blue the agents bind to the filamental structure.
simulation. The logarithmic curve on can be explained by the decreased number of free
molecules and the spatial phenomena, by which the simulated filament is growing close
to the boundary of the environment. The number of reachable free molecules close to
this boundary is then much lower. The difference in the speed of elongation is related
to two reasons:
1. Actin filaments can growth on both side, whereas the simulation allows only the
growth at the barbed end.
2. Actin can build small motile fragments, which then elongate the filament [25]. This
increases the speed of polymerisation significantly.
3.2
Branching Process
Figures 8(a) and 8(b) show the time plots for the actin and arp agents respectively. Both
time curves are sigmoidal with an inflection point around 1300 seconds.
Adding a new agent for the Arp2/3 protein, we simulated the actin polymerisation
with the branching process. To visualise this, Figure 7 shows a snapshot of the spa-
tial distribution at the end of one hour. In this simulation an overall filament length of
1
μm
was reached after 578 seconds. At the end of one hour, nearly all agents were
involved in the filament structure, 1121 actin agents were fully bound. Additionally 28
Arp2/3 agents are fully bound, two of them had an open binding side. In contrast to the
filament formation, solely with actin, the branching process accelerate the elongation
significantly. The snapshot in Figure 7 shows the spatial consideration and is in good
agreement with previously published simulations [2, Figure 17].
3.3
Disassembly Process
To model the disassembly of actin and Arp2/3 molecules from the filamental structure,
we added a new probability for each agent.
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