The directed polymerization of dendritic actin networks is an essential element of many biological processes, including cell migration. Different theoretical models for the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction which is first (autocatalytic) versus zeroth order in filament density . Here we introduce a unifying framework from which these two models emerge as limiting cases for low and high filament density, respectively . A smooth transition between these cases is found at intermediate conditions. We also derive a threshold for the capping rate, below which zeroth order characteristics are predicted to dominate the dynamics of the network for all accessible filament densities. For capping rates above this threshold, autocatalytic growth is predicted at sufficiently low filament density .
The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments . Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament number . A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate, above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, this allows cells to grow stable actin networks over a large range of different conditions .
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