Combining Simulation Techniques to Create a Model

3 May 2007

JULIAN SHILLCOCK

Reading Professor Bhalla's comment, it is clear that there are already several simulation codes that can model aspects of signaling pathways. It seems that the existence of multiple internal states of proteins (phosphorylation states, etc), which result in extremely large numbers of coupled differential equations, is a significant problem with some of these simulation types. Also, the need to follow the behaviour of small numbers of molecules and to capture the fluctuations in populations of proteins is essential. I propose that mesoscopic simulation techniques, such as coarse-grained Molecular Dynamics (MD), Brownian Dynamics (BD), and Dissipative Particle Dynamics (DPD), may be combined to model different aspects of a cell signaling pathway, resulting in a model that can represent the pathway in its normal operation and allow it to be perturbed in clinically-relevant ways.

My background is in physics, so I am not an expert in this field, but I think that in order to construct a useful and predictive model of a signaling pathway it is necessary to represent each particle as an "Object" in the simulation code (Tolle et al. 2006). Objects have identity, position, and internal states. There is no combinatorial explosion of populations in such a model, as only the particles (proteins, ions, monomers,...) present in the pathway need to be represented. In such a simulation, there may be various physical phenomena occurring (ion diffusion, bulky-protein diffusion, tethered proteins floating around a filament, a membrane gently undulating) each of which provides a possible target for physical intervention.

Such a model requires capturing the behaviour of various transport processes: Free particle diffusion, tethered-particle oscillations, cytoskeletal filament assembly and disassembly, protein-protein binding that depends on the proteins' internal states, etc. Each of these processes will have natural length- and time-scales, and combining these different scales in one simulation is quite a challenge. Particularly, the presence of solvent in most MD and DPD simulations of membranes limits them to systems of the order of (100 nm)³. BD can go to much larger systems, but has then to be somehow integrated into the more detailed techniques.

If such a simulation can be constructed, one could explore the dependence of the signaling pathway on generic perturbations and then specialise it to particular pathways. If diffusion of protein A until it binds with protein B is part of the pathway, the effects of such diffusion occurring near a cytoskeletal filament can be tested; the filaments can be spatially distributed in various ways, from a regular 3-D lattice to a fractal network, and the variation of the signal transit time measured (Shafrir et al. 2000). Physical effects, such as depletion layers, occlusion of binding sites when several proteins approach each other, crosstalk between different pathways, will appear naturally in this model. It may be possible to test proposals for how signals are transmitted by proteins bound to the cytoskeleton (Park et al. 2003).

A problem that will then arise is the sheer volume of data that such a detailed simulation will produce. Recent work using DPD simulations to model tension-driven vesicle fusion (Shillcock and Lipowsky 2005), which used vesicles of 30-nm diameter and planar membranes of (100 nm)², produced about 1 GB of particle-coordinate data per fusion event. If such a simulation were to be scaled up to 1 micron, each event would generate 1 TB of data. Most of this is just the solvent coordinates, but these would be required if a simulation were to be restarted. Discarding the coordinate data requires that analysis must be performed "on the fly", which in turn means that one must anticipate the observables that one wants to measure. But the great benefit of simulations is that they can reveal unexpected effects, which would be missed if only expected observables were monitored. Retaining enough detail in the simulation to represent all relevant physical phenomena, while still being able to handle the data generated, is a nontrivial hurdle.

References

• D. P. Tolle, N. Le Novere, Particle-based stochastic simulation in systems biology. Current Bioinformatics 1, 315 - 320 (2006).
  [Online Journal]

• Y. Shafrir, D. ben-Avraham, G. Forgacs, Trafficking and signaling through the cytoskeleton: a specific mechanism. J. Cell. Sci. 113, 2747 -2757 (2000). [Abstract] [PDF]

• S-H. Park, A. Zarrinpar, W. A Lim, Rewiring MAP kinase pathways using alternative scaffold assembly mechanisms. Science 299, 1061- 1064 (2003). [Abstract] [Full Text]
• J. C. Shillcock, R. Lipowsky, Tension-induced fusion of bilayer membranes and vesicles. Nat. Mater. 4, 225-228 (2005). [PubMed]