# Km and vmax relationship advice

### biochemistry - Does pH affect Michaelis constant? - Biology Stack Exchange Answer to Quantitative relationships between rate constants to calculate Km, kinetic efficiency (kcat/Km) and Vmax. (and how they're made). Km and Vmax. Enzymes whose kinetics obey this equation are called Michaelis-Menten enzymes. If you want a more detailed look . The Michaelis constant Km is the substrate concentration at which the reaction rate is at half-maximum,and is an There is no Kmax, there is Vmax as shown in the above equation. Hoping this will be helpful,. Rafik. 1 Recommendation.

Next I'll introduce a new idea and say that the total amount of enzyme available which we'll call ET or E total is equal to the free enzyme E plus the enzyme bound to substrate or ES. Using this equation I'm going to rewrite the E on the left side of our equation as the total E minus the ES which would be equal to the E we had there before. On the right side of the equation I just factored out the common term ES. Next I'm just going to expand the left side of the equation so take a moment to look at that. Now what I'm going to do is I'm going to divide both sides of the equation by K one. K one will disappear on our left side and on our right side I've put K one in with all the other rate constants. Now since all these rate constant are constant values I'm going to combine them in this expression of K minus one plus K two over K one into a new term KM which I'm going to talk a little bit more about later.

In this next line I've done two things. First I've thrown in that KM value that I just mentioned, but I've also added ES times S to both sides of the equations and thus moved it from the left side to the right. In the next line I've done two things. First I switched the left sides and right sides of the equation just to keep things clear, but I've also factored out the common term ES on our new left side.

### Determining Km and Vmax

Then what I'm gonna do is I'm gonna divide both sides of the equation by KM plus S so I can move that term to the right side. I'll make some more room over here and now what I'm gonna do is remind you that the speed of our whole process which I'll call Vo is equal to the rate of formation of our product which we called rate two before which is also equal to K two times ES. Now using our equation over here I'm gonna multiply both sides of the equation by K two.

Here's where it gets really tricky. Remember that if we're if at our max speed so our reaction speed Vo is equal to Vmax which happens when our substrate concentration is really high, then our total enzyme concentration is going to be equal to ES since all of our enzyme is saturated by substrate and there won't be any free enzyme left.

## Steady states and the Michaelis Menten equation

I'll make some room here and then sub in K two ES for Vo and K two E total for Vmax and then we finally get to our end equation which is called the Michaelis-Menten Equation and is super important when we talk about enzyme kinetics. Let's take a few steps back and talk about the Michaelis constant.

First I'll write out the Michaelis-Menten equation and if you remember we created this new term which I called KM, but we never really talked about what it meant. Let's get to that. Now if you bear with me for a moment and pretend that KM is equal to our substrate concentration then we can sub in that value into our Michaelis-Menten equation which would put two S on the bottom, the sum of S plus S and then the S will cancel out and will be left with Vmax over two.

What this means that KM which we call the Michaelis constant is defined as the concentration of substrate at which our reaction speed is half of the Vmax.

If we look at that on a graph from before you'd see that KM is a substrate concentration specific to our circumstances. Where our rate is at half of its max and the lower our KM, the better our enzyme is at working when substrate concentrations are small. We can use this KM term to quantify an enzyme's ability to catalyze reactions which we call Catalytic Efficiency. I'll rewrite the Michaelis-Menten Equation. Since it's a concentration it will be in units of molar or moles per liter. Now I'm going to throw a new term at you called Kcat which is equal to the maximum speed of a reaction divided by the total enzyme available. We call this the enzyme's turnover number. All these term is, is how many substrates and enzyme can turn into product in one second at its maximum speed.

We measure it in units of seconds minus one or per second as in reactions per second. We can define an enzyme's catalytic efficiency as a combination of KM and Kcat, and we do this by saying it's equal to Kcat over KM.

### Untitled Document

V0 is the initial velocity of the reaction. Vmax is the maximal rate of the reaction. Km is the Michaelis-Menten constant which shows the concentration of the substrate when the reaction velocity is equal to one half of the maximal velocity for the reaction. It can also be thought of as a measure of how well a substrate complexes with a given enzyme, otherwise known as its binding affinity. An equation with a low Km value indicates a large binding affinity, as the reaction will approach Vmax more rapidly. An equation with a high Km indicates that the enzyme does not bind as efficiently with the substrate, and Vmax will only be reached if the substrate concentration is high enough to saturate the enzyme.

As the concentration of substrates increases at constant enzyme concentration, the active sites on the protein will be occupied as the reaction is proceeding. When all the active sites have been occupied, the reaction is complete, which means that the enzyme is at its maximum capacity and increasing the concentration of substrate will not increase the rate of turnover.

Here is an analogy which helps to understand this concept easier. Vmax is equal to the product of the catalyst rate constant kcat and the concentration of the enzyme. Kcat is equal to K2, and it measures the number of substrate molecules "turned over" by enzyme per second.

The reciprocal of Kcat is then the time required by an enzyme to "turn over" a substrate molecule. The higher the Kcat is, the more substrates get turned over in one second. Km is the concentration of substrates when the reaction reaches half of Vmax. A small Km indicates high affinity since it means the reaction can reach half of Vmax in a small number of substrate concentration. 