# Why plot double reciprocal graph for Vmax and Km ?????? watch

1. I just learnt about Vmax and Km in relation to enzyme activity, and I understand how to find these values from an initial rate vs substrate concentration graph. But I don't understand why it is necessary to plot a double reciprocal graph at all. What would we use this for? Also I can't get my head around why -(1/Km) would be the x axis intercept on this double reciprocal graph mathematically as I can't see how an intercept would be related to half of the Vmax - you would expect at least a 2 somewhere right?
2. Hi,

When we plot the (double) reciprocal graph, it allows us to work out a value that is difficult to estimate with any degree of accuracy on a normal plot, in this case, the V would probably be tending to keep on rising within our set of results, and we cannot extrapolate the graph enough or with enough confidence to estimate its highest value - when we plot the reciprocal, that highest value [now being plotted as its reciprocal] will hit the y axis at some point [as the lowest value which will now be within reach!] - we read off this value, then calculate its reciprocal, to get the value of VMax.

I am confused.com with your 2nd Q, as I am not sure where your factor of 2 comes from - I am sure a maths nerd will be able to help you!

M (biology nerd!)
3. (Apologies if you already knew this, since this post is now a few days old, but my inner geek saw the mention of enzyme kinetics and got a bit excited..)

The relationship between the rate (v) and substrate concentration [S] is modelled by the Michaelis-Menten equation, v = Vmax*[S] / (Km+[S]), which when plotted would give a curve (a rectangular hyperbola). It would be difficult to assess by eye how well your experimentally measured data points fit onto this curve.

A double reciprocal plot (the Lineweaver-Burk plot) is a useful way to linearise the relationship, giving 1/v = (Km/Vmax)*(1/[S]) + 1/Vmax. From which it is then easy to find the values of the constants Km and Vmax, simply by fitting a straight line (linear regression) and reading off the intercepts.

The x-intercept is the point where 1/v = 0, thus (Km/Vmax)*(1/[S]) = -1/Vmax.
Dividing both sides by Km/Vmax gives 1/[S] = -1/Km.

I've included the names of the equations to make it easier to look up should you be interested
4. (Original post by randombiochemist)
(Apologies if you already knew this, since this post is now a few days old, but my inner geek saw the mention of enzyme kinetics and got a bit excited..)

The relationship between the rate (v) and substrate concentration [S] is modelled by the Michaelis-Menten equation, v = Vmax*[S] / (Km+[S]), which when plotted would give a curve (a rectangular hyperbola). It would be difficult to assess by eye how well your experimentally measured data points fit onto this curve.

A double reciprocal plot (the Lineweaver-Burk plot) is a useful way to linearise the relationship, giving 1/v = (Km/Vmax)*(1/[S]) + 1/Vmax. From which it is then easy to find the values of the constants Km and Vmax, simply by fitting a straight line (linear regression) and reading off the intercepts.

The x-intercept is the point where 1/v = 0, thus (Km/Vmax)*(1/[S]) = -1/Vmax.
Dividing both sides by Km/Vmax gives 1/[S] = -1/Km.

I've included the names of the equations to make it easier to look up should you be interested
Thanks! So is the only purpose of reciprocal plots to linearise curved graphs or are there any other useful applications?
5. (Original post by Fairly7Local)
Thanks! So is the only purpose of reciprocal plots to linearise curved graphs or are there any other useful applications?
Hi To linearise curved graphs, and thereby estimate parameters of the original function, yeah. And it should be noted that reciprocal plots (especially the classical double reciprocal plot) are not at all the ideal approach, due to the large errors associated with calculating inverses and extrapolating data. They're just the simplest way to analyse this type of data with pen and paper (without the aid of a computer programme which could e.g. do non-linear regression)..
6. (Original post by randombiochemist)
Hi To linearise curved graphs, and thereby estimate parameters of the original function, yeah. And it should be noted that reciprocal plots (especially the classical double reciprocal plot) are not at all the ideal approach, due to the large errors associated with calculating inverses and extrapolating data. They're just the simplest way to analyse this type of data with pen and paper (without the aid of a computer programme which could e.g. do non-linear regression)..
7. (Original post by Fairly7Local)
No problem

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 16, 2018
Today on TSR

### 2,657

students online now

Exam discussions

### Find your exam discussion here

Poll
Useful resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE