# Lineweaver burk plot km and vmax relationship

### The Equations of Enzyme Kinetics - Chemistry LibreTexts

Use of equation () involves the determination of the initial rate of reaction ( b) Eadie-Hofstee plot of v against v/[S]0 giving intercepts at Vmax and Vmax/Km. However, Vmax can be accurately determined if the Michaelis-Menten equation is transformed into one that gives a straight-line plot. Taking the reciprocal of. To be analytically useful we need to write Equation $$\ref{}$$ in terms of the reactants . Tthe Lineweaver–Burk plot (or double reciprocal plot) is a graphical Km = slope × Vmax = molimM × mol = mM.

But, first, lets review the idea that enzyme catalysis can be divided into two steps. First, the binding of enzyme to substrate, and second, the conversion of substrate to product. And using this idea you can derive the Michaelis-Menten equation, which is useful for quantitatively looking at how enzymes behave kinetically.

## Enzyme Kinetics

Also remember that within that equation, we have the Km or Michaelis constant, which is defined as the substrate concentration where the speed of product formation is at one-half of its max value. So the first thing that I'm going to talk about is something called a Lineweaver-Burke plot, and how it allows us to look at the Michaelis-Menten equation in a different way.

So what I'm going to do is take the Michaelis-Mentin equation, but then take the inverse of both sides of the equation, so one over everything. Now if we cancel out the two S values, then we are left with the equation that I've just drawn out. And conveniently we can use this equation to describe a linear function.

We can make one over V O our Y or dependent variable, Km over V max our coefficient m, or the slope, one over S our X, or independent variable, and then one over V max our b, or Y-intercept.

We can then plot this on a graph, with our Y-axis being one over V O, and our X-axis being one over S, and if we draw out the corresponding line, the slope of our line will be equal to Km over V max, and our Y-intercept will be equal to one over V max. And we call this plot a Lineweaver-Burke plot. And it gives us another way to look into the Michaelis-Menten equation.

So let's take a step away from this idea for a moment, and talk about the three types of enzyme inhibitors. So our first type of inhibitor is called the competitive inhibitor, and it works by binding to free enzyme, or E, to form EI, or enzyme inhibitor complex. The intersections are separately ranked in order of increasing value of both Km and Vmax and the median values taken as the best estimates for these parameters.

The error in these estimates can be simply determined from sub-ranges of these estimates, the width of the sub-range dependent on the accuracy required for the error and the number of data points in the analysis. In this example there are 7 data points and, therefore, 21 estimates for both Km and Vmax. The ranked list of the estimates for Km mM is 0. The Km must lie between the 4th 1. The list of the estimates for Vmax mM. The Vmax must lie between the 4th 3.

It can be seen that outlying estimates have little or no influence on the results. This is a major advantage over the least-squared statistical procedures where rogue data points cause heavily biased effects. Three ways in which the hyperbolic relationship between the initial rate of reaction and the initial substrate concentration can be rearranged to give linear plots.

Again, originally this was done subjectively. Later, computers permitted least-squares fit of linear models to data linear regression ; this statistical process removed the subjective component. Today, people use either linear regressions on Lineweaver-Burk transformed data or they do non-linear regression of raw data to fit to the Michaelis-Menten function. In our laboratory exercise, we will use this much finer method for finding the best-fit parameters for the untransformed Michaelis-Menten relationship.

Lineweaver Burk plot data analysis

Enzyme catalyzed reactions can be inhibited competitively Enzymes can be altered in various ways. One way, is by competition between the substrate and a molecular analog called a competitive inhibitor. The competitive inhibitor is so similar to the substrate that it binds at the active site and accomplishes some kind of induced fit with the enzyme. However, the competitive inhibitor is different enough that it cannot react in the same way as the substrate.

So no chemical reaction occurs, no product is formed, the inhibitor is released unchanged, as is the enzyme. This relationship can be depicted as: The enzyme-inhibitor complex falls apart without forming a product.

This competitive inhibition does not occur in isolation. Generally the reaction system looks more like this: Obviously the frequency that the substrate occupies the site will be determined by how abundant the substrate is compared to the inhibitor. If the substrate is present in relative abundance then the rate of the reaction will be the same as if the inhibitor were absent.

In other words, the presence of a competitive inhibitor does not change the Vmax. It takes more substrate to reach half of Vmax.

Again, if one measures the rates of reaction systems with various substrate concentrations and repeats those in the presence of the inhibitor, then a plot like the one above can be made. If the Vmax is the same in the presence and absence of the inhibitor, and the Km increases in the presence of the inhibitor, then you have great evidence for a competitive inhibitor.

## Enzymatic inhibition and Lineweaver Burk plots

An example of an enzyme regulated by competitive inhibition in plants perhaps to the benefit of people is 5-enolpyruvylshikimatephosphate EPSP synthase. This enzyme is critical in the synthesis of aromatic amino acids phenylalanine and tyrosine. Without these amino acids, a plant cannot translate complete proteins. Severe symptoms of yellowing, wilting, and death follow. Thus glyphosate can be used as an herbicide vegetation killer.

Because humans do not have EPSP synthase, it is "safe" to use compared to most other herbicides. Biologists have inserted extra copies of EPSP synthase genes into the genome of crop plants behind a constitutive promoter.

This causes the transformed plants to over-produce EPSP synthase, swamping out the effect of any glyphosate sprayed on them.

This way the engineered crop plants can be grown in a weed-free field using a relatively safe herbicide. Of course if the crop plant has wild relatives nearby, the genes for this herbicide resistance could be passed to the wild relatives producing herbicide resistant weeds. Enzyme catalyzed reactions can be inhibited non-competitively Another way to inhibit a enzyme-catalyzed reaction is by use of a non-competitive inhibitor.

### Untitled Document

This kind of molecule binds to the enzyme somewhere besides at the active site. This binding therefore does not interfere with the affinity and therefore Km of the enzyme for the substrate.

• Lineweaver–Burk plot
• Structural Biochemistry/Enzyme/Michaelis and Menten Equation
• 10.2: The Equations of Enzyme Kinetics

What inhibitor binding does is to alter the effectiveness of the other functional groups of the enzyme in catalyzing the reaction through poorer induced fit. This will, of course, reduce the Vmax possible.

### Determination of Vmax and Km

This kind of relationship is depicted below. Enzymes that are allosterically regulated often work in this non-competitive way. Once an enzyme has been "deactivated" this way, no amount of substrate will increase the rate of reaction back to normal. The only solution is to metabolize the inhibitor, thereby restoring normal conformation of the enzyme and normal rates of reaction.

Enzyme activity is pH sensitive As a protein, made of some 20 different amino acids in primary structure that end up producing the secondary, tertiary and quaternary structure, its conformation is pH dependent.

Some of the amino acids have R groups with imidazole hiscarboxyl asp, glu or amino lys, arg.

This change in charge will, very likely, alter the conformation and thereby activity.