Large range parameter identification

Question

I have a model (ODE) of an enzymatic reaction, and I'd like to estimate four of its parameters to fit some available data. To obtain the model I am just using Mass-Action Kinetics.

Some more details:

• The model is of the form $S_1+2S_2+S_3+E\leftrightarrow C \leftrightarrow P_1+P_2+P_3+E$, where $S_i$ are substrates concentrations, $P_i$ products concentrations, $E$ enzyme concentration, and $C$ the complex concentration.
• $S_2$ is Hydrogen and $P_3$ is Ammonium ($NH_4$), so besides the aforementioned reaction I have one reaction for the buffer and one reaction for ammonium dissociation, however, the parameters involved are known.
• Substrate concentrations are in the range of $1-10mM$.
• Enzyme concentrations are in the range of $.1-10\mu M$.
• The parameters I want to estimate are the 4 reaction rates, say, $k_1,k_{-1},k_2,k_{-2}$.
• The available data (measurements) is only pH. Thus I have a simulation of the model where the final output is $pH=log_{10}(1/S_2)$.
• Then, I try to estimate the parameters from the data and the (simulated) pH.

To estimate the parameters I am using Matlab, more specifically the 'Identification Toolbox' and the 'lsqnonlin' function.

I set the initial guess "visually", that is, I move manually the parameters and whenever I assume the simulation is "close enough", I set the initial parameters guess.

The problem is that some of the parameter of he initial guess are of order $1E20$. I am thinking that because of the large value of the parameters, the algorithm cannot find any better parameter values. I have tried moving several optimisation options without any valuable result.

Q: Is there some specific software, or method that is commonly used to estimate parameters of biochemical reactions? Is the large values of kinetic rates a common problem in parameter identification for these type of systems?

I do not know any $P_i$ though, just pH as a function of time. In principle nor E neither C are constant, but I could assume quasi-steady state conditions, no problem. My feeling is that I am not using or setting up correctly the numerical tool...