Why can't I extrapolate the Bradford Assay graph if the Beer-Lambert Law applies?

If you would like to test your skills in working with the Beer-Lambert Law, you might like to take the Spectrophotometry tests at Maths4Biosciences.

One question I have been asked several times after the feedback on a practical is if the Beer-Lambert Law, A = ε . c . l, gives a straight line, then why can't I extrapolate the data to find the answer for one of my unknown proteins?

The Bradford Assay is an indirect (or colorimetric) method for estimating protein concentrations. The assay is based on a shift in the absorbance of a dye, Coomassie Brilliant Blue G-250, from 465 nm to 595 nm when it binds a protein under acidic conditions. The Bradford assay measures the amount of bound dye and NOT the amount of protein present (although the two are connected until the dye is all used). As the dye is limiting (i.e. you only put in a set amount), you can reach a point when all the dye is bound, and no matter how much more protein you put in, you will not see a change in absorbance. You can increase the protein level to a point where available dye becomes exhausted so the graph would plateau.

Standard Curve for a Bradford Protein Assay

Any value that falls in the yellow area of the graph (i.e. a concentration of more than 15 µg/ml or an absorbance greater than 1.02) cannot be used as the graph is no longer linear and is starting to plateau. Any absorbance that gives a protein concentration below 15 µg/ml can be used as this is in the linear portion of the graph (i.e. blue area), and the Beer-Lambert Law applies as the dye is not limiting.

In the experiment, you are working in the linear portion of the graph above (the blue area), so the line is straight, i.e., it hasn't plateaued. Therefore, we can say that between 0 and x µg/ml (or 15 µg/ml above), we have a certain absorption range, say 0 to y (where y is about 1.01 in the above figure). However, once we get above x µg/ml, or above the maximum absorbance y, we cannot say whether or not the graph has plateaued, so all we can say is the value is greater than x µg/ml. This may seem somewhat limiting (pardon the pun), but the Bradford assay can, in fact, detect protein concentrations over a 10-fold concentration range.

By the way, if we were measuring the protein directly, say at 280 nm, then we could apply the Beer-Lambert Law. In fact, if we knew the extinction coefficient, we wouldn't even have to do a standard curve.

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Additional Resources 

• 📗 - Maths and Chemistry Refresher for Life and Biomedical Scientists
• 📗 - Catchup Chemistry (affiliate link)
• 📗 - Catchup Maths and Stats (affiliate link)

The Beer-Lambert Law, a straight line and the units of the extinction coefficient

If you would like to test your skills working with the Beer-Lambert Law, you might like to look at the Spectrophotometry tests at Maths4Biosciences.

Some students struggle to understand the relationship between the Beer-Lambert Law and a straight line and work out the units of the extinction coefficient (ε).

You may also find the following two videos helpful.

The Beer-Lambert Law states:

A = ε . c . l

Where:

A = absorbance 

ε = extinction coefficient 

c = concentration 

l = path length (i.e. the distance the light travels through the sample)

So, what is the connection between this and a straight line, and what are the units of the extinction coefficient?

The units of the extinction coefficient

In my opinion, the extinction coefficient has some of the craziest units out there.
Absorbance (A) has no units, so the units of the extinction coefficient (ε) are determined by how the concentration (c) and path length (l) are being measured. That is, the units of the extinction coefficient must cancel out the concentration and path length units so that the absorbance can have no units!

A worked example.

A = ε . c . l

A = absorbance, units - so put in 1 

ε = extinction coefficient, units - unknown 

c = concentration, units - milli-Molar, mM 

l = path length (i.e. the distance the light travels through the sample), units - cm

So...

A = ε . c . l

And, with units:

[1] = ε . [mM] . [cm]
Rearranging...
[1] / ε = [mM] . [cm] 
ε = 1 / ([mM] . [cm]) 
or 
ε = [mM]^-1 . [cm]^-1

So, the units are mM^-1 . cm^-1

This can be checked by putting it all back together:


A = ε . c . l 
A = ([mM]^-1 . [cm]^-1) . [mM] . [cm]
This gives:


A = [mM]/[mM] . [cm]/[cm]
So, the mM and the cm cancel each other out, leaving no units for absorbance A.

A straight line

The Beer-Lambert Law:

A = ε . c . l

Where:

A = absorbance 

ε = extinction coefficient 

c = concentration, units 

l = path length

The equation for a straight line is:

y = mx + c

Where:

m = the gradient 

c = the y-intercept

If you plot concentration against absorbance, then x = concentration and y = absorbance. Plus, from the Beer-Lambert Law, we know that if the concentration is zero, then absorbance must be zero.

A = ε . c . l A = ε . 0 . l A = 0  So...

y = mx + c absorbance = m . concentration + c

From above, if concentration = 0, then absorbance = 0, hence c must be zero
y = mx + c absorbance = m . concentration + c* 0 = m . 0 + c  c = 0
(* note, this c is the y-intercept and not the concentration)

Therefore...
y = mx + c absorbance = m . concentration + 0 or y = mx


Comparing:

y = mx absorbance = m . concentration
With (and rearranging):

A = ε . c . l 
A = (ε . l) . c 
y = m . x If y = absorbance, and x = concentration, then m (the gradient) must equal extinction coefficient (ε) multiplied by the path length, l, or ε . l. As l is typically 1 cm, the gradient, m, must equal the extinction coefficient (ε).

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Additional Resources

• 📗 - Maths and Chemistry Refresher for Life and Biomedical Scientists
• 📗 - Catchup Chemistry (affiliate link)
• 📗 - Catchup Maths and Stats (affiliate link)

Plagiarism: Three tips to help you avoid plagiarism

Here is an interesting question with an interesting answer...

At what age do children see plagiarism as wrong?

Blog Bonus: Free flowchart to help you decide if something is plagiarised - download.

Over at Plagiarism Today, I read an article about the age at which children start to know plagiarism is wrong—it turns out the answer is around 5 years old.

One point in the article caught my attention:

"Generational Gap: It is interesting that students as young as 5 and 6 see the moral issues of plagiarism in this capacity but, according to research of college students, many seem to lose that moral qualm with plagiarism later on. Could this be a shift in thinking over generations or do many students lose that view over time?"

Plus, a recent (August 1st, 2010) New York Times article (cited in a blog post at Plagiarism Today) pointed out there is a problem with plagiarism at Universities and Colleges and that it is widespread. So, this does raise the question: If children as young as 5 know copying is wrong, how come students in their late teens and early 20s think it is OK? When, where, and why does this shift happen?

From talking to students who have plagiarised and talking to students who are 'sailing close to the wind' (i.e. their work shows some characteristics when scanned with TurnItIn which hint that they may be using 'unsafe' academic practice), three things are commonly mentioned, and if these could be avoided a lot of potential cases of plagiarism would fade away:

1. Time

It sounds odd, but this is often a reason given for copying: I didn't have the time to put it in my own words. I forgot the deadline, panicked, and copied straight from X.

Solution: Watch your time, don't panic and put things in your own words.

2. Citation

This is one of the most common reasons for plagiarising, but I cited (referenced) the paper.

Well, citation (referencing) is not a licence to copy. The function of citation is to say where the information came from so the reader can check the original report/data/experiments and/or expand on their own reading. Think of references as links on a web page - both take you to additional information.

Solution: Don't think that citation is a licence to copy.

3. Best example

This links up with citation - but I couldn't write it any better

Generally, if you find yourself with this problem, that is, you can't think of how else something could be written, then you need to do more reading and understand what you are writing about.

Solution: Read more papers, understand the subject, and use your own words.

So, three handy little hints (besides the usual and often unhelpful - Don't copy) that may help you avoid plagiarism.

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Blog Bonus: Free flowchart to help you decide if something is plagiarised - download.

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Original post - What Age Do Children See Plagiarism As Wrong?

Original paper - ‘No fair, copycat!’: what children’s response to plagiarism tells us about their understanding of ideas

New York Times Article - Plagiarism Lines Blur for Students in Digital Age

What is a Unit of enzyme?

What is a 'Unit' of enzyme.... this always seems to give problems.

1 Unit of enzyme is defined as "an amount of protein that produces 1 µmole of product per minute". The thing that causes the problem is the word "amount".

The "amount" is not a mass; it is, for want of a better word, a 'blob'. You can buy enzymes in 'Units'. You buy a vial that will contain a number of Units of enzyme. You then know that if you dissolve the contents of the vial in a solution, how many µmoles of product per minute will be produced. If you buy 1 Unit of a particular enzyme from two different suppliers you may have vials that contain different weights of powder, but the work that can be done (i.e. the amount of product produced) will be the same.

For example:

Look at these two 'piles' ('blobs') of enzyme:

Pile 1 of Enzyme

Pile 2 of Enzyme

Both 'piles' contain the same number of red balls (i.e. 4), and if 4 red balls are needed to produce 1 µmole of product per minute (i.e. 1 Unit), then both piles can be said to contain 1 Unit of the enzyme, and yet, as you can see, there are many more balls in pile 2... Pile 1 is certainly more pure as there is less contaminant (yellow balls) around.

This is why the 'amount' in "an amount of protein that produces 1 µmole of product per minute" is not a weight; it is an 'amount'; it is a 'pile', a 'blob'.

If you have problems with 'Sciences Maths' then you might like to check out some of the courses over at Maths4Biosciences.

If you would like to support my blogging efforts, then please feel free to buy me a coffee at https://www.buymeacoffee.com/drnickm

Additional Resources

• 📗 - Biochemistry (Stryer) (affiliate link)
• 📗 - Principles of Biochemistry (Lehninger) (affiliate link)

Plagiarism: Reusing figures from papers and textbooks in your work

One question I get asked is how to correctly reuse figures from textbooks and papers.

Blog Bonus: Free flowchart to help you decide if something is plagiarised - download.

First, you will gain more marks IF you draw your own figures and do not recycle figures from other sources. However, having said that, it still does not mean you can redraw a figure you have found without stating from where it came, as that would be plagiarism.

Suppose you found the idea figure for your report/essay in a paper....

The figure you want to use...

and the paper in question is:

Mol Syst Biol. 2007;3:139. 2007 Oct 16.
PhosphoPep--a phosphoproteome resource for systems biology research in Drosophila Kc167 cells.
Bodenmiller B, Malmstrom J, Gerrits B, Campbell D, Lam H, Schmidt A, Rinner O, Mueller LN, Shannon PT, Pedrioli PG, Panse C, Lee HK, Schlapbach R, Aebersold R.

If you just used the figure shown above in Figure 1, that would be plagiarism. However, if you used the above figure and stated - 'Taken from the paper of Bodenmiller et al. 2007' - at the end of the figure legend and then gave the complete reference in the bibliography, that would not be considered plagiarism. (One possible problem here may be the figure legend. Some staff members may expect the legend to be rewritten in your own words, even though you have stated the figure source, and some staff members may not. So, to be safe, it is a good idea to re-write the legend.)

Therefore, the final figure will look like this:

Fig 1: Text describing the figure in your own words... Taken from the paper of Bodenmiller et al. 2007.

Now, if you changed the figure in some way, you added something to it (see below where a red circle has been added) but were still using the base figure, you would still have to state the source of the original figure. For example:

Fig 1: Text describing the figure in your own words... Adapted from the paper of Bodenmiller et al. 2007.

Now, to get the most marks, you should draw the figure yourself and add something relevant to it (don't forget to state where you got the information in the legend, that is, give the reference), but again, you should still state from where you got the original figure.

Fig 1: Text describing the figure in your own words... Adapted from the paper of Bodenmiller et al. 2007.

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Plagiarism: The art of referencing...

How do I reference a paper? If I reference a paper, can I copy it? "But that can't be plagiarised, I referenced the paper!!!"

Blog Bonus: Free flowchart to help you decide if something is plagiarised - download.

These are all common questions and misconceptions about referencing.

Referencing a paper

You have read a paper and wish to report the facts and findings in your report/essay, etc., but you need to reference the source. So, how do you reference?

There are many different styles of referencing. If you read papers from different journals, you will see a whole range of styles, such as the Harvard and Vancouver styles, to name but two.

No matter what style is used, the approach and idea of referencing are the same. You write some facts/information in your work and state where that information came from. For example, you have read a paper on an amine oxidase found in adipocytes and in your essay, you wish to talk about the protein. So, the full reference of the paper you read would be:

Morris NJ, Ducret A, Aebersold R, Ross SA, Keller SR, and Lienhard GE. (1997) Membrane amine oxidase cloning and identification as a major protein in the adipocyte plasma membrane. J Biol Chem. 272(14):9388-92. - link

In your essay, you state that:

The first membrane-bound amine oxidase was discovered in 1997 and was found in adipocyte plasma membranes (Morris et al., 1997).

In your bibliography (references at the end of your work), you would write:

Morris NJ, Ducret A, Aebersold R, Ross SA, Keller SR, and Lienhard GE. (1997) Membrane amine oxidase cloning and identification as a major protein in the adipocyte plasma membrane. J Biol Chem. 272(14):9388-92

(By the way, please note that et al. should normally be in italics or underlined. Also, please note the full stop after the al. in et al.)

Now, depending on the referencing style you are using, there may be some rules governing how many authors you include in the references in the text and the bibliography, so that will have to be checked.

Finally, with 'names referencing,' there can be the problem of the same name publishing two papers in the same year. So, for example, imagine there were these two papers.

Morris NJ (2010) Everything you wanted to know about plagiarism. J. Plag. 123(10):992-999 

and

Morris NJ (2010) How to plagiarise and not get caught. J. Cheats 1(13):10-15

The way you would cite them in your text would be as (Morris, 2010a) and (Morris, 2010b), and in the bibliography as:

Morris NJ (2010a) Everything you wanted to know about plagiarism. J. Plag. 123(10):992-999
Morris NJ (2010b) How to plagiarise and not get caught. J. Cheats 1(13):10-15

If you were using a numbering style of referencing, it may look like this:

The first membrane-bound amine oxidase was discovered in 1997 and was found in adipocyte plasma membranes (12).

In your bibliography (references at the end of your work), you would write:

12. Morris NJ, Ducret A, Aebersold R, Ross SA, Keller SR, and Lienhard GE. (1997) Membrane amine oxidase cloning and identification as a major protein in the adipocyte plasma membrane. J Biol Chem. 272(14):9388-92

If I reference a paper, can I copy it?

No. Referencing does not mean you can copy the text from a paper. All referencing does is state where you got the data, idea, or hypothesis so that other scientists can check the facts, look up the method etc. Putting a reference in your text as a link on a webpage allows the reader to find additional information.

Referencing does 'protect' against ideas plagiarism because referencing the source states who originally had the idea and where it was published.

"But that can't be plagiarised, I referenced the paper!!!"

This is the most common comment I receive from students when discussing plagiarised work.

Just because you reference a paper does not mean you can copy from it.

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Plagiarism: What is plagiarism and how can I avoid it?

Plagiarism, a serious academic offense, is defined as the act of copying another person's work and presenting it as your own. The consequences of plagiarism can be severe, ranging from academic penalties to damage to one's professional reputation.

Blog Bonus: Free flowchart to help you decide if something is plagiarised - download.

Plagiarism can be split into four main types:

1. ‘Text’ - copying text from a book, paper, document etc.
2. ‘Diagrams’ - copying a diagram
3. ‘Idea’ - passing off another person's idea as your own
4. ‘Auto’ - copying from yourself!

Text Plagiarism: This is the easiest to understand and the most common form of plagiarism. Basically, it is the copying of text from some source (a paper, textbook, fellow student, internet) into your own work and then passing it off as your own. It should be noted that adding a reference (i.e. stating from where you copied the text) is no 'protection' and doesn't mean you can copy. If you find yourself reaching for the copy and paste keys on the computer, then there is a good chance it will be plagiarism.

Diagram Plagiarism: This is where you copy a diagram or figure from a textbook or paper and pass it off as your own (this can also be viewed as 'idea' plagiarism as someone has thought long and hard about constructing (and drawing) the figure). You can 'protect' against diagram plagiarism by simply stating from where you got the figure (see later post for more details).

Idea Plagiarism: This, in my opinion, is the worst form of plagiarism, as you would be attempting to pass off the hard work and intellectual property of a fellow scientist as your own. You can write about the ideas and thoughts of other scientists, but YOU MUST STATE FROM WHERE YOU GOT THE IDEA. Basically, this is one of the reasons why we reference sources of information; you are stating who had the original idea and how they came by it. Effectively, by referencing, you are acknowledging the hard work of the other scientists.

Auto-Plagiarism: This form of plagiarism is the one most people have difficulty understanding. After all, how can you plagiarise yourself? You 'own' the work and the intellectual property! Well, basically, auto-plagiarism would occur if you handed in the same piece of work for two different assignments and got two lots of marks for it. Put another way, it is like making one burger at McDonald's and selling it twice.

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