Spatial modeling of vesicle transport and the cytoskeleton: the challenge of hitting the right road

Abstract

The membrane trafficking machinery provides a transport and sorting system for many cellular proteins. We propose a mechanistic agent-based computer simulation to integrate and test the hypothesis of vesicle transport embedded into a detailed model cell. The method tracks both the number and location of the vesicles. Thus both the stochastic properties due to the low numbers and the spatial aspects are preserved. The underlying molecular interactions that control the vesicle actions are included in a multi-scale manner based on the model of Heinrich and Rapoport (2005). By adding motor proteins we can improve the recycling process of SNAREs and model cell polarization. Our model also predicts that coat molecules should have a high turnover at the compartment membranes, while the turnover of motor proteins has to be slow. The modular structure of the underlying model keeps it tractable despite the overall complexity of the vesicle system. We apply our model to receptor-mediated endocytosis and show how a polarized cytoskeleton structure leads to polarized distributions in the plasma membrane both of SNAREs and the Ste2p receptor in yeast. In addition, we can couple signal transduction and membrane trafficking steps in one simulation, which enables analyzing the effect of receptor-mediated endocytosis on signaling.

Figure 1. Modularity and Interactions of Vesicle Transport.

A: Each transport step between two compartments (or the plasma membrane) can be seen as an individual module. Each module contains the budding, transport, and fusion step. B: Vesicle fusion is mediated by tethering factors and SNAREs. These molecules can only interact if the vesicle is in close vicinity of the target compartment. C: The budding process involves the formation of a coat (cf. [46]) and the loading of the desired cargo and SNARE molecules into the vesicle. D: Interactions between the molecules of the vesicle machinery. Each class of molecules/interactions can also be linked to a distinct function (see also Table S1). For each interaction a set of kinetic parameters has to be assigned. The total set of interactions between different subtypes of ‘coats’, ‘snare’, ‘cargo’, and ‘motors’ can be broken into the subset of subspecies and interactions governing a given membrane trafficking connection between two compartments. In the principle of the Heinrich and Rapoport model ‘coat A’ binds to ‘compartment 1’, selects ‘cargo 1’ and ‘snare X’ into a vesicle which fuses via the strong ‘snare X-Y’ interaction to Ôcompartment2’. A second module, responsible for the reverse transport, is respectively set on the strong ‘compartment 2’-‘coat B’-cargo 2′-snare V′-‘snare U-V’ interaction. The directed transport with motor proteins requires adding ‘motor 1’ going from ‘compartment 1’ towards ‘compartment 2’ and the reverse ‘motor 2’ accordingly. These ‘motors’ represent for instance Kinesin and Dynein that walk along microtubules in different directions.

Figure 2. Spatial Aspects of Vesicle Transport in a Two Compartment System.

Spatial aspects of vesicle transport in a two compartment system: Comparison of diffusion and transport with motor proteins in different cytoskeleton structures. Vesicles and their paths are shown in similar colours as the donor compartment. Orange vesicles bud from the orange compartment 1, targeted for the green compartment 2. Green vesicles go into the opposite direction. Parameters are given in Text S2.

Figure 3. Spatial Aspects of Vesicle Transport in Endo- and Exocytosis.

Spatial aspects of vesicle transport in endo- and exocytosis: Comparison of A diffusion and B transport with motor proteins (red: endocytic vesicles; green: recycling vesicles from the big green endosome in the centre).

Figure 4. Embeding the Vesicle Transport Network in the Cytoskeleton.

The connection from ER to Golgi, Golgi to plasma membrane and Plasma membrane to the lysosomes can be aligned with the radial structure of the microtubule network, which then has to be tri-partitioned. The challenge is the bridging of these partitions to fully connect the vesicle network. Note, that in this structure transcytosis requires changing the motor direction in the centre.

Figure 5. Mathematical Description.

A: Interactions and rate constants between the molecules of the vesicle machinery function (cf. Table S1 for a description of the molecule species in the present model). Note that all rate constants are actually a matrix where the number of lines/columns depends on the number of coat/snare/motor/cargo-species as indicated in B and C. The coloured species are bound to the vesicle, while the grey species are located in the cytoplasm. This figure also shows the interaction with cytosolic proteins (e.g. the activation of signalling molecules by endocytosed receptors), as well as the binding/dissociation of cytosolic coats and motors to the vesicle surfaces. The subfigure exemplifies the simplified depolymerization function used to describe the degradation of the coat shell upon budding.

Figure 6. Recycling.

Coat molecules are recycled via a cytoplasmic pool of unbound molecules. Motor proteins can be recycled via recycling vesicles or a cytoplasmic pool. Snares can only be recycled via recycling vesicles. Figure S1 shows this process in the data of a simulation.

Figure 7. Reduced Model of Receptor Mediated Endocytosis Coupled with Signalling.

The signalling cascade is reduced to one stage for simplicity. Endocytosis is driven by the molecular interactions of the vesicle machinery, i.e. Coat, SNARE, cargo (here the receptors), and motor molecules as indicated in the subfigure. The parameters are given in Additional material, Text S2.

Figure 8. Combined Membrane Trafficking and Signaling Dynamics.

(a) The receptors (R) are activated by the binding of the ligand (RL = receptor ligand complex) and subsequently transported from the plasma membrane (PM) via transport vesicles (iT = in transit) to the endosome (E). The excerpt of the receptor ligand complex (RL) on the right shows single budding events from which the budding frequency and the cargo load of the endocytic vesicles can be derived. (RL) is deactivated in the endosome. Therefore the number of inactive receptors (R) in (E) is increased. The number of active receptor ligand complexes (RL) is reduced due to the endocytosis and deactivation reactions. (b) Accordingly, also the number of active MAPKp signalling molecules is reduced.

Figure 9. Cell Polarization.

Molecules, vesicle paths and cytoskeleton structure. SNAREs (blue) and Receptors (red) accumulate on the left. Endocytic vesicle tracks are shown in red, recycling paths in green. The polarization of the cell is in agreement with the findings of Valdez-Taubas and Pelham for the SNARE Snc1. The microscope image is reprinted from (Valdez-Taubas and Pelham, 2003) with permission from Elsevier.

Figure 10. Endocytosis Process in the Simulation: visualized at a section from the plasma membrane.

Coat (yellow), snare (green), and cargo (red, here a membrane bound receptor) molecules cluster together and eventually form a vesicle (large red sphere). This is pushed into the cell by the actin boost (path shown in light blue) and can subsequently bind to a cytoskeleton for transport with motor proteins (path during diffusion and motor protein transport is shown in red).