Abstract
AbstractMany important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally.
Highlights
Molecular systems biology is a field that is concerned with understanding the processes in a cell as a unit rather than as the sum of its parts (Ideker et al, 2001; Kitano, 2002)
As observed in the MinDE localization studies in Escherichia coli (Shih et al, 2002), the membrane-bound MinE.MinDm ATP dimers appear to be lagging behind MinDm ATP molecules when they migrate from one pole to the other
We developed a new lattice-based Monte Carlo method called Spatiocyte that can perform RD in and between volume and surface compartments at single molecule resolution
Summary
Molecular systems biology is a field that is concerned with understanding the processes in a cell as a unit rather than as the sum of its parts (Ideker et al, 2001; Kitano, 2002). Methods for computational modeling correspond to the level of abstraction or specificity of a system (Ideker and Lauffenburger, 2003). At a lower level of abstraction, where quantitative information of the system is more relevant, hidden Markov models (Riley et al, 2008) can probabilistically model the creation, removal and interconversion of molecular species and states, whereas when we are concerned with the rates of biochemical reactions, ordinary differential equations (ODE) (Bever, 2008; Boyce, 2008) can be used. At the bottom level abstraction, the structural information of the system and the dynamic localization of molecules, resulting from diffusion and intracellular transport, can be modeled using spatial modeling methods such as partial differential equations (PDEs), spatial introduction
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