Simulate chemical reactions: how to include one polymerization step which consists of x reactions with identical rate constants?

Hi, I'm trying to kinetically simulate polymerization and decay of a biopolymer. The model should include influx of a monomer into the reaction compartment (the cell), a few hundred (but ideally a variable number) of enyzme-catalyzed polymerization steps (each step being irreversible and adhering to Michaelis-Menten kinetics), irreversible termination and irriversible (exponential) decay of the polymer back into monomers.

I tried Simbiology, which works great for everything except for the polymerization step (explicitely drawing hundreds of species is tedious , and even though programmatically adding hundreds of steps may work, this many steps likely would slow down the simulation).

Any advice? Eg I was thinking whether i can add a single step for the polymerization and then somehow change the rate law for this step (its probability density function adheres to a Gamma distribution with N steps, each with the same rate constant).

I am also open to totally different ways of simulation (Simulink, or stochasitc simulation with a chemical master equation) although I'd have 0 XP with the latter.

Any advice is welcome!

Answer 1

[Arthur Goldsipe]

I think SimBiology is most suited to modeling each degree of polymerization as a separate species. Building and simulating will take some time, but I think it is still a reasonable and practically feasible approach. My main suggestion for this approach is to do that work programmatically and from the command line rather than in the app. While it's possible to have hundreds of species in a diagram, it does become unweildy and noticeably slower at such sizes.

In fact, I helped another user with a similar problem several years ago. They published their work last year, and that publications includes sample code at the end that shows how to build the polymerization reactions programmatically. If you want to pursue that approach, feel free to reach out with followup questions.

Another alternative would be to model the distribution of the polymerized species. I am less familiar with this approach, so I can't offer much help on that front.

Good luck!

[felix MP]

Thanks, Arthur, for your suggestions.

In the meantime i graphically assembled ~10 sequential irreversible polymerizations steps (each as second order reactions) in simbiology. Using the standard solver I optained rubbish results, but maybe i should have used ssa?

Thanks for pointing out the preprint. I downloaded their code and will check out how they programmtically solved the problem (and then may get back with more questions...)

Thanks a bunch!

Felix

[Arthur Goldsipe]

Hmm... I'm not sure what to think of those rubbish results. I know stochastic solvers can more realistic when you only have a small number of molecules of particular species, which is likely to happen if you're modeling all degrees of polymerization as separate species. But I'd suggest a little more investigation before switching over to stochastic solvers. For one thing, you'd need to model everything with mass action kinetics. (This is a requirement of SimBiology's stochsatic solvers, primarily due to limitations of the published algorithms we're using.) For another, it would significantly slow down the simulations. It's all still technically possible, but it's just going to make things even more complicated.