Résumé |
The problem of irreversible polymerization is fundamental for its many applications to
different fields, from material science to biology. In living cells, cytoskeletal
filaments grow and bundle together, forming complex networks. Since the assembly and
bundling of these filaments often involve energies of the order of hundreds or
thousands of $k T$, the final structure of the network will be heavily influenced by
the kinetics of these processes (Kayser et al., Soft Matter, 2012, 8, 8873).
Approaches based on equilibrium physics are therefore bound to fail when studying the
structural and mechanical properties of such networks, and approaches that explicitly
considers the kinetics are necessary.
We extend a previously developed theoretical framework (De Gennes, J. Chem. Phys.,
1982, 76, 3316) to study how the average length $L$ of a system of semiflexible
filaments that anneal irreversibly via end-to-end reactions increases with time. We
find that filament assembly is controlled by the short-time transversal fluctuations,
which lead to a linear growth of $L$ with time. We perform the same calculations also
for perfectly rigid rods, which have no transversal fluctuations modes, showing that
in this case L increases only as the square root of time. Finally, we compare our
theoretical predictions with molecular dynamics simulations of particles that
aggregate irreversibly into semiflexible filaments with a tunable persistence length,
finding an excellent agreement with the theoretical predictions.
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