Mathematical Modeling of the Vesicle Transport

All eukaryotic cells use vesicular trafficking to transport proteins and lipids. Vesicles bud from one compartment, taking along both soluble and membrane proteins as well as lipids, and fuse with another compartment. Transport in the anterograde direction must be counterbalanced by retrograde traffic to keep the size of compartments constant and reuse components of the transport machinery.

The bidirectional traffic would tend to equalize the composition of the compartments, yet most proteins and some lipids are concentrated in one organelle and define its identity. At issue here is a very general question: How can such nonuniform distributions be achieved?

One pioneering analysis has been done by Heinrich and Rapoport [1]. They provide an explanation for the generation of a small and fixed number of stable, nonidentical compartments and their size regulation, based on a minimal vesicular transport system comprising coat proteins and SNAREs as major variables. A second approach focuses on Rab GTPases as the major marker proteins on organelles [2]. Moreover, a recent analysis shows that Rab5 and Rab7 might be the key proteins to describe reasonably well the maturation switch from early to late endosomes [3].

The present work aims to combine the SNARE and Rab based approaches to retrieve a more accurate understanding of the experimental results gained in [1], [2] and [3]. This concerns time profiles of the two key proteins and the endosomes size during the transition from an early to a late endosome.

Our conceptual model (Fig. 1B), based on ODEs postulates the cooperative clustering of each of the two proteins for a successful Rab-driven fusion of vesicles as a necessary prerequisite for the maintenance of biochemical identity. The latter is defined by means of an exclusive accumulation of one marker protein on the organelle. As a by-product of the cooperative kinetics, one finds a bistable steady state situation for the protein numbers of the two endosomal marker proteins Rab5 and Rab7.



Fig. 1 Schematic model

The results are described in a bifurcation diagram in Fig. 2. The bifurcation parameter is the cluster affinity Kc of Rab7 proteins, which is decreased from left to right depicted on the horizontal axis. An identity switch from early (Rab5) to late endosome (Rab7) occurs at a critical value of Kc. A possible reason for the increase of clustering of Rab7 proteins might by initiated by a dropping pH value. in the lumen of the organelle.


Fig. 2 Bifurcation diagram. Maturation switch
from early to late endosome.

Our simple model comprises only membrane material and two decisive marker proteins. It may reflect a very basic vesicular transport system and identity switching machinery developed in evolutionary early times. Probably, more elaborated interactions between the Rab proteins, described in [3], developed later in evolution on top of this system, thereby, increasing already existing principles.

Researchers

Prof. Hermann-Georg Holzhütter
Dr. Bernd Binder
Dr. Andrean Goede

This project is part of the HepatoSys Network EndoSys.

Own Publications

Binder B, Goede A, Berndt N, Holzhütter HG. (2009) A conceptual mathematical model of the dynamic self-organisation of distinct cellular organelles. PLoS One, 4(12):e8295. [PubMed]

References

[1] Heinrich R, Rapoport TA. (2005) Generation of nonidentical compartments in vesicular transport systems. J Cell Biol., 168(2):271-80. [PubMed]

[2] Rink J, Ghigo E, Kalaidzidis Y, Zerial M. (2005) Rab conversion as a mechanism of progression from early to late endosomes. Cell., 122(5):735-49. [PubMed]

[3] Del Conte-Zerial P, Brusch L, Rink JC, Collinet C, Kalaidzidis Y, Zerial M, Deutsch A. (2008) Membrane identity and GTPase cascades regulated by toggle and cut-out switches. Mol Syst Biol., 4:206. [PubMed]