I'm studying enzymati kinetics for a non-soluble substrate, which means that I need to work at a really low substrate concentration, and I am not able to find the right ratio between the enzyme amount and different substrate concentrations, how do you usually define it?
I define it experimentally by first testing a range of enzyme concentrations at one substrate concentration, and collecting evenly-spaced time points. You are looking for an enzyme concentration that will give you a linear progress curve over the period of time you wish to monitor (initial rate conditions), and with the steepest slope (i.e. maximal signal). Cover a wide range of enzyme concentrations by testing about 12 2-fold serial dilutions, covering a 1000-fold range, unless you already have a rough idea of the concentration needed.
Once you have done this initial experiment, you will be able to judge how long to run the reaction at various enzyme concentrations to get the largest signal under initial rate conditions at that specific substrate concentration. Long reaction times at low enzyme concentrations can be more practical for measuring reaction rates than short reaction times at high enzyme concentrations.
If you start with the highest feasible substrate concentration, you will most likely find that the initial rate conditions last for a shorter time with lower substrate concentrations, unless you lower the enzyme concentration. If you start with a substrate concentration at the low end of its range, however, all of the progress curves at higher substrate concentrations will also most likely be linear when using the same enzyme concentration and reaction time.
These experiments can be completed very quickly if you have an assay with a continuous readout and if you can run the reactions in a plate reader. In fact, under those conditions, you can vary enzyme concentration and substrate concentration in a matrix format and get enough data in one run to fully define the kinetics.
Remember that Michaelis-Menten kinetic analysis requires that the rate of reaction is measured at the initial rate, and that the concentration of the ES complex should be negligible compared to the total enzyme concentration. (This usually means that the substrate concentration should be much higher than the enzyme concentration.)
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