## FL #51 C/P

mshah
Posts: 18
Joined: Mon Aug 28, 2017 4:21 pm

### FL #51 C/P

Assuming a 95% yield for each coupling step, what would be the final yield for synthesizing a 10 amino-acid length peptide?

(.95)^10= Apprx. 60%

Are we supposed to know how to do this calculation for the exam?
NS_Tutor_Andrew
Site Admin
Posts: 520
Joined: Mon May 23, 2016 1:47 pm

### Re: FL #51 C/P

Hi mshah,

Yes and no. Tackling that calculation the direct way by calculating 0.95^10 would be prohibitively difficult to do in your head -- but you are expected to be able to very familiar w/ manipulating exponents, decimals, and fractions, as well as to be able to use strategies to estimate calculations that would be difficult to perform. The explanation to this question gives you one way of thinking about it, but here's another one: 95% efficiency means 5% loss. 5% loss incremented over 10 steps would be 50%. But that can't be quite right, because with every step, your 'starting point' shrinks. (To illustrate this point with simple numbers, imagine that we were dealing with a 90% efficiency [10% loss] at every step and repeated that for 3 steps. Applying the guesstimation technique outline above, we'd guess that the final outcome will be about 70% of the original. Now let's actually do the math. We start off with 100 units. 90% of 100 units [a 10% loss] is 90 units. Now we repeat the step. 90% of 90 units [a 10% loss] is 81 units. We repeat the step again. 90% of 81 units [a 10% loss] is 81 - 8.1 units = 72.9 units). Now, returning to this problem, we know that we need an answer slightly greater than 50% based on the above reasoning, and the choice of 60% is definitely more likely than 80%, so that's the best choice.

Hope this helps! This is a difficult calculation problem but it highlights the importance of thinking flexibly about what calculations 'mean' and applying estimations to the level of precision necessary to pick out the right answer choice, rather than get the precise numerical answer.
Andrew D.
Content Manager, Next Step Test Prep.
jangyong90
Posts: 1
Joined: Tue Dec 12, 2017 9:41 pm

### Re: FL #51 C/P

Although I am pretty sure I wont be able to perform this mathematical skill, I understood the logic.
The thing is... question stem stats, "Assuming a 95% yield for each coupling step, what would be the final yield for synthesizing a 10 amino-acid length peptide?" When it says each coupling step yield 95 %, why is that we do 0.95^10. Shouldn't it be 0.95^9? Though, answer is going to be around 60. I wanted make sure... Maybe I am over complicating myself. Could someone please help me with this problem?!

o-o-o-o-o-o-o-o-o-o

o:represent amino acid
-:represent coupling (linkage)