Reaction kinetics + Gillespie algorithm: Propensity function?

[maistral]

TL;DR Summary

What is a propensity function? And some other questions.

I'm trying to simulate a simple series reaction stochastically using Gillespie's algorithm. I found this file:

1. What is this 'propensity function'? Say for example I have the simple reactions:
   
   A --(k₁)--> R
   R--(k₂)--> S
   
   are these 'propensity functions' the rates (a wild guess)? I mean;
   α₁ = k₁[A]
   α₂ = k₂[R],
   
   where [A] and [R] are the number of molecules of A and R?
2. I am assuming that these 'rate constants' are based on the number of molecules themselves, and not the 'molarity'. I also read from an article (Stochastic chemical kinetics by Lecca) that they're supposed to be different (the rate constants based on the molarity are 'continuous' or something). How do I convert the rate constants from the molarity-based ones to the number of molecules-based ones?
3. With regards to the updating of the numbers of reactants and products, assuming the simple reactions
   
   A --(k₁)--> R
   R--(k₂)--> S
   
   are taken into consideration, and that the first reaction is supposed to be occurring, am I correct to assume that I subtract one molecule A and add one molecule R?

Thank you very much.

 

[nbryan5]

Yes, the propensity functions are the rates (or rate constants) k1 and k2 for your two reactions. They are based on the number of molecules present in the system and not the molarity. To convert from the molarity-based rate constants to the number of molecules-based ones, you will need to know the volume of the system and the number of molecules of the reactant/product in question.The updating of the numbers of reactants and products is correct. For the reaction A --(k1)--> R, you would subtract one molecule of A and add one molecule of R when it occurs.