A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Satya Arjunan,Masaru Tomita

doi:10.1038/npre.2009.3845.1

Satya Arjunan, Masaru Tomita

Open Access

https://doi.org/10.1038/npre.2009.3845.1

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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 established 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

Computational models are valuable to both theoretical and experimental biologists to rapidly analyze and test their predictions about qualitative or quantitative behavior of complex cellular processes (Ideker and Lauffenburger 2003)
Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and cellular processes, are supported
For the irreversible reaction A þ B Àk!AB C, it can be seen in Fig. 3a and b that the survival probabilities of A from simulations are in excellent agreement with the predicted previously reported in (Ridgway et al 2008), mass action fails to correctly reproduce the predicted survival probability of A for volume reversible reactions (Fig. 3c) because it assumes A, B and C to be homogeneously distributed (HD) species

Summary

Introduction

Computational models are valuable to both theoretical and experimental biologists to rapidly analyze and test their predictions about qualitative or quantitative behavior of complex cellular processes (Ideker and Lauffenburger 2003). Processes that are strongly dependent on the cell morphology, multicompartmental interaction and dynamic localization of molecules such as cell signaling (Rangamani and Iyengar 2008; Neves et al 2008), bacterial cell division. The processes rely on intricately controlled reaction and diffusion of molecules in and between cytoplasm (or nucleoplasm) and membrane compartments to perform their functions. Since some of the species involved in the processes comprise small number of molecules, stochasticity in the reactions can dominate over the law of mass action (Gillespie 1976; Gomez-Uribe and Verghese 2007), and affecting the macroscopic behavior of the processes (Fange and Elf 2006; Rangamani and Iyengar 2008; Hansen et al 2008)

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