I used to work on inhibitor discovery for NAD-dependent DNA ligase, an enzyme whose reaction involves 2 substrates and 3 products:
nicked DNA + NAD+ ligated DNA + AMP + nicotinamide mononucleotide
ATP-dependent DNA polymerase also has 2 substrates and 3 products:
nicked DNA + ATP ligated DNA + AMP + pyrophosphate
When studying product inhibition kinetics of NAD-dependent DNA ligase, I could not find in the literature or books full steady-state rate equations including products for reactions with 2 substrates and 3 products, so I had to derive it myself for DNA ligase, which has a Ping-Pong mechanism beginning with formation of adenylated enzyme, and substrate inhibition by nicked DNA.
I suddenly realized that another enzyme I later used as a coupling enzyme in a reaction to detect methionine, S-adenosylmethionine synthetase, also has 2 substrates and 3 products:
ATP + methionine S-adenosylmethionine + pyrophosphate + phosphate
Does anyone know of other enzymes with 2 substrates and 3 products? If so, have you seen the full kinetic rate equation including products for their reactions?
There must be thousands. Among them, there are a lot of dehydrogenases that conduct reaction of the following type:
substrate + NAD+ -> product + CO2 + NADH + H+
Such reactions are central to the Krebs cycle, so their kinetics should have been pretty well studied.
You should consider using DynaFit to fit your rate equations for your Bi-Ter systems. In Dynafit you construct the model, estimate the kinetic parameters, and the program solves the differential equations that describe the model you provided. Dynafit calculates more accurate kinetic parameters within errors than the initial velocity equations solved by linear regression for the same model.
You can try it yourself and see: http://www.biokin.com/dynafit/
For an ordered-BA system rapid equilbrium system in which enzyme binds substrate B first and then A, and then releases products P and Q, you would write an incomplete script like so:
[task]
task = fit
data = rates
model = ordered_BA?
approximation = rapid-equilibrium
[mechanism]
E + B EB : Km-b dissoc.
EB + A EAB : Km-a dissoc.
EAB ---> E + P + Q : kcat-for [constants]
Km-a = 3.85 ? ; An initial guess
Km-b = 105 ? ; A guess for this parameter
kcat-for = 0.764 ? ; A guess for this parameter
[concentrations]
E = 0.100 ; The enzyme concentration in uM
[responses]
P = 0.0154 ; The product concentration in uM
[equil]
directory ./mydirectory/my_data
sheet mydata.csv ... and you provide the data, and where you want the output files.
This is equivalent to the these equations (1). At no point did I need to know these equations to get good estimates.
1) Lillehaug, J. R., & Kleppe, K. (1975). Kinetics and specificity of T4 polynucleotide kinase. Biochemistry, 14(6), 1221-1225.
Thank you, Andrew Jenkins and Adron Ung.
A specific example of the type of enzyme Andrew Jenkins mentioned is isocitrate dehydrogenase. As written, this enzyme reaction has 4 products, but perhaps the H+ product can be treated as constant if the pH is buffered.
I have not used DynaFit, but I have used Global Kinetic Explorer (Kintek) in a similar way. With that program, the kinetic model is entered as text. The data consists of reaction progress curves.
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