# How to plot and simulate reaction networks in Mathematica?

I am trying to simulate reaction networks like it's done in the Simulation methods in this paper. They used Xcellerator, so I after installing on Mathmatica 11.2 and trying to run their Belousov-Zhabotinski Reaction example I got errors on obsolete functions.

What is the modern way to simulate their dynamic model, for example the one depicted here:

For example in their case they wrote down these equations:

Hence, we can write 4 equilibrium relations involving the macroscopic CaM states and 8 relations involving the microscopic CaM states (see below). This yields 12 equations relating the 4 microscopic equilibrium constants to the 4 macroscopic equilibrium constants. There are 12 unknown concentrations of CaM states we would like to eliminate. Eight variables can be eliminated among the 12 equations. Conservation of atoms between the microscopic and macroscopic states (3 equations) plus conservation of mass (one equation) provide the necessary constraints to do so. Explicitly, for given constant [Ca2+] and [CaM] one may solve the following equations for the equilibrium dissociation constants:

$$[CaM0][Ca^(2+)]=K_D^1 [CaM1] \\ [CaM1][Ca^(2+)]=K_D^2 [CaM2] \\ [CaM2][Ca^(2+)]=K_D^3 [CaM3] \\ [CaM3][Ca^(2+)]=K_D^4 [CaM4] \\$$

$$[CaM0][Ca^(2+)]=K_D^1C [CaM1C] \\ [CaM0][Ca^(2+)]=K_D^1N [CaM1N] \\ [CaM1C][Ca^(2+)]=K_D^2C [CaM2C] \\ [CaM2C][Ca^(2+)]=K_D^1N [CaM1N2C] \\ [CaM1N2C][Ca^(2+)]=K_D^2N [CaM2N2C] \\ [CaM2N1C][Ca^(2+)]=K_D^2C [CaM2N2C] \\ [CaM2N][Ca^(2+)]=K_D^1C [CaM2N1C] \\ [CaM1N1C][Ca^(2+)]=K_D^2N [CaM2N1C] \\ [CaM1N0C]+[CaM0N1C]=[CaM1] \\ [CaM1N1C]+[CaM0N2C]+[CaM2N0C]=[CaM2] \\ [CaM1N2C]+[CaM2N1C]=[CaM3] \\$$ $$∑_{(n=0)}^4[CaMn]=[CaM_TOTAL]$$

• Is there a question? If so, it will require the actual Mathematica code, in copy-pastable form, if some sort of diagnosis is being requested. – Daniel Lichtblau Jun 9 '19 at 19:59
• – 0x90 Jun 10 '19 at 0:47
• I'm not familiar with the Xcellerator package, but I installed it on v12.0 and tried the BZ demo. I also got the warnings General::obspkg -- PlotLegends is now obsolete and Arrays:shdw -- Symbol Arrays appears in multiple contexts {Global, System}, but the rest appears to basically work. – Chris K Jun 10 '19 at 8:37
• Since the authors of the paper you’re interested in used Mathematica and xcellerator, you could email them and ask for their code. – Chris K Jun 10 '19 at 10:38