I am using Trypsin to determine its Km and Vmax values against casein from bovine milk. I know higher enzyme concentrations increase the Vmax value, but does more trypsin also affect the Km value?
No, enzyme concentration does not influence Km, as long as the measurements are done under proper conditions for Michaelis-Menten kinetic analysis. That means that the enzyme concentration is far below the substrate concentration and the initial rate is measured.
If the enzyme concentration is too high, it becomes difficult to measure the initial rate because the reaction goes too fast. If the enzyme concentration is not much lower than the substrate concentration, the free substrate concentration may be significantly reduced due some of it binding to the enzyme, so the free substrate concentration does not match the total substrate concentration.
Based on the typical MM reaction scheme involving E and S, the mathematical expression of Km is a combination of rate constantes only (Km = (kcat+k-1)/k1) therefore it doesn't depend on any concentration whatsoever. Unlike Vm which is not actually a constant as its value depends on enzyme concentration.
While I agree with both Adam B Shapiro & Dominique Liger, enzyme concentration could influence its Km by at least two mechanisms:-
1) proteins could associate: e.g., at higher concentrations monomers could become for example dimers and tetramers, which could exhibit different kinetics (allosteric regulation).
2)Effects of proteolysis on the proteins activity, partially digested enzymes are frequently still active (sometimes even more so than the original) so as the enzyme does it job and ages, or auto-digests it km value is likely to change.