MONTE-CARLO ANALYSIS OF OBSTRUCTED DIFFUSION IN 3 DIMENSIONS - APPLICATION TO MOLECULAR-DIFFUSION IN ORGANELLES

Molecular transport in the aqueous lumen of organelles involves diffus ion in a confined compartment with complex geometry. Monte Carlo simul ations of particle diffusion in three dimensions were carried out to e valuate the influence of organelle structure on diffusive transport an d to relate experimental photobleaching data to intrinsic diffusion co efficients. Two organelle structures were modeled: a mitochondria-like long closed cylinder containing fixed luminal obstructions of variabl e number and size, and an endoplasmic reticulum-like network of interc onnected cylinders of variable diameter and density. Trajectories were computed in each simulation for >10(5) particles, generally for >10(5 ) time steps. Computed time-dependent concentration profiles agreed qu antitatively with analytical solutions of the diffusion equation for s imple geometries. For mitochondria-like cylinders, significant slowing of diffusion required large or wide single obstacles, or multiple obs tacles. In simulated spot photobleaching experiments, a similar to 25% decrease in apparent diffusive transport rate (defined by the time to 75% fluorescence recovery) was found for a single thin transverse obs tacle occluding 93% of lumen area, a single 53%-occluding obstacle of width 16 lattice points (8% of cylinder length), 10 equally spaced 53% obstacles alternately occluding opposite halves of the cylinder lumen , or particle binding to walls (with mean residence time = 10 time ste ps). Recovery curve shape with obstacles showed long tails indicating anomalous diffusion. Simulations also demonstrated the utility of meas urement of fluorescence depletion at a spot distant from the bleach zo ne. For a reticulum-like network, particle diffusive transport was mil dly reduced from that in unobstructed three-dimensional space. In simu lated photobleaching experiments, apparent diffusive transport was dec reased by 39-60% in reticular structures in which 90-97% of space was occluded. These computations provide an approach to analyzing photoble aching data in terms of microscopic diffusive properties and support t he paradigm that organellar barriers must be quite severe to seriously impede solute diffusion.