Table 2 Predictions of the one-state model

From: Neurons exploit stochastic growth to rapidly and economically build dense dendritic arbors

Parameter

Formula

Steady-state dendrite number density (\(N\))

\(N={2k}_{{{{\rm{b}}}}}/(\alpha \bar{v})\)

Steady-state dendrite length density (\(\rho\))

\(\rho=(\sqrt{2{k}_{{{{\rm{b}}}}}/\bar{v}})/\alpha\)

Average branch length (\(\bar{l}\))

\(\bar{l}\equiv \rho /N=\sqrt{\bar{v}/2{k}_{{{{\rm{b}}}}}}\)

Number-length parabola

\(N=\alpha {\rho }^{2}\)

Expansion rate (\(c\)), decay length \((\lambda )\)

\(c=\bar{v}/2\), \(\lambda=0\)

  1. See Table 1 for definitions of parameters. \(\alpha=0.75\) is the collisional prefactor for the one-state model calculated from simulations (Methods). The factors of 2 in length and density reflect correction for internal branches.
Back to article page