Figure 2. Local trafficking rates determine the spatial distribution of biomolecules by a simple kinetic relationship.
(A) The mass action transport model for a simple branched morphology. (B) Demonstration of how trafficking rates can be tuned to distribute cargo to match a demand signal. Each pair of rate constants (, ) was constrained to sum to one. This constraint, combined with the condition in Equation (4), specifies a unique solution to achieve the demand profile. (C) A model of a CA1 pyramidal cell with 742 compartments adapted from (Migliore and Migliore, 2012). Spatial cargo demand was set proportional to the average membrane potential due to excitatory synaptic input applied at the locations marked by red dots. (D) Convergence of the cargo concentration in the CA1 model over time, (arbitrary units).
Figure 2—figure supplement 1. Equation 4 specifies the relative distribution of cargo, changing the total amount of cargo scales this distribution.
(A) Inspired by ion channel expression gradients observed in hippocampal cells (Hoffman et al., 1997; Magee, 1998), we produced a linear gradient in cargo distribution in an unbranched cable. By Equation 4, the trafficking rate constants satisfy (where indexes on increasing distance to the soma). Starting from a uniform distribution of cargo in the cable ( a.u.), the desired linear profile emerges over time. (B) Changing the amount of cargo in the cable (the sum of across all compartments, see legend) does not disrupt the steady-state linear expression profile, but scales its slope.