now that we've seen how the michaelis-menten equation relates the kinetic constants of km and v-max to reaction velocity let's try to get a better idea of the significance of these constants recall from an earlier lesson that when the velocity is at 1/2 v-max the substrate concentration represents the value of km what does this have to do with what happens inside a living cell if you think about it another way it means that if the substrate concentration is much less than this value less than the km the enzyme is not working very efficiently we find then
that the value of km often gives us a good estimate of substrate concentration in vivo we've talked about km as being an equilibrium dissociation constant let's see if we can prove that mathematically looking at our expression for km we see that it is a ratio of the rate constants from our simple reaction scheme the rate constant k1 is the rate of the formation of es k minus 1 is the rate of es dissociation and k2 is the rate of product formation if the rate of es dissociation that is K minus 1 is much greater than
that of product formation k2 then the value of k2 has little effect on km and our expression simplifies to the ratio of K minus 1 to K 1 in other words it is the rate at which es dissociates as compared to the rate it forms a true dissociation constant perhaps this will help us better understand that km is a true measure of substrate affinity one of our assumptions in this simple model is that there was only one irreversible catalytic step and one rate constant for that step k2 at levels of saturating substrate initial velocity or
v-0 is equal to the value of the max which is simply k2 times the total concentration of enzyme the constant k2 is also called the catalytic rate constant or k-kat substituting this into our expression and rearranging it slightly we see that the cake hat is equal to the value of V Max divided by enzyme concentration we call this the turnover number and it is simply the moles of product formed per mole of enzyme per second remember the v-max is simply an average maximum speed for all of the molecules in solution if we divide by the
amount of enzyme present then we're looking at the speed of each enzyme molecule if we compare k-kat and km values for some enzymes we might see quite a difference let's compare the enzymes carbonic anhydrase and lysosome if we consider k-kat or to know turnover number we see from our table that carbonic anhydrase is orders of magnitude faster than lysozyme on the other hand by comparing km values we see that lysozyme has an affinity for its substrate 500 times that of carbonic anhydrase for its substrate yet these very characteristics are perfectly suited to their respective functions
recall that carbonic anhydrase converts co2 to carbonic acid the concentration of co2 and our blood and tissues is very high so it doesn't really need a high binding affinity it does however need to rapidly convert to product in order to maintain blood pH in neutral lysozyme is an enzyme that degrades bacterial cell walls having a very low km means that it will find bacterial invaders at very low concentrations this is a good thing the speed at which it accomplishes the reaction is not so critical hopefully from this you can see the power of knowing the
kinetics of an enzyme they can tell us a lot about what enzymes do as well as how and why
