[sameeralord]

I know how to get the answer for this question using hesselback equation but I don't understand the question. I have some questions about the questiuon.

1. The PKa value of the sulphydryl (-SH) group of cysteine is 8.33. Calculate the fraction of anion to free sulfhydryl group at PH 7.O.

So is this Pka value referring to

SH + H20 <---> H+ + S- reaction

Why is this reaction significant. How does getting the PH of the equlibrium constant of this reaction provide any meaningful value.

Also in this amino acid there is only one SH group(meaning two atoms) so how can an equilibrium reaction occur.

My question is related to PKa values. I don't understand how getting the PH of the equilibrium constant can be meaningful and that two atom problem.

Thank you so much

[renge ishyo]

In the future, if you have an additional question on an earlier question you have posted, it is probably a good idea to just reply to your own post with the additional question in the original thread. It's easier for people to see where your question is coming from if they can read the earlier reponse, and you might get a greater variety of responses 

The pKa lets you figure out in what "form" (either SH or S^-) the majority of your sulfhydral groups are in for a large group of similar molecules at a given pH.

Here's an idea of how it works with examples:

1. At pH = 4, pka = 8.33: the pH is lower than the pKa, so most of the molecules are in the SH form and only a small amount are in the S^- form at this pH.

2. At pH = 8.33, pka = 8.33:  the pH is equal to pKa so you have an exactly 50/50 mix of SH and S^- in solution at this pH. Note that this is a special point where both forms are in exactly equal numbers.

3. At pH = 10, pka = 8.33: the pH is higher than the pka, so most of the molecules are in the S^- form and only a small amount are in the SH form at this pH.

It is sort of like a "seesaw" between the two forms and the pKa is at the pivot point in the center. pKa is a very powerful tool to use in biochemistry. By just glancing at the pKa you can predict what the charges on the side groups would be at the pH of your solution. This further allows you to predict what interactions these side chains can (and cannot) participate in at a given pH.

[sameeralord]

Thanks a lot for your answer  . You are the only one who has helped so far. Yeah I'll post in the old topic next time. I now understand the 3 points you have stated. However I have a sight problem.

The pKa lets you figure out in what "form" (either SH or S^-) the majority of your sulfhydral groups are in for a large group of similar molecules at a given pH.

It is sort of like a "seesaw" between the two forms and the pKa is at the pivot point in the center. pKa is a very powerful tool to use in biochemistry. By just glancing at the pKa you can predict what the charges on the side groups would be at the pH of your solution. This further allows you to predict what interactions these side chains can (and cannot) participate in at a given pH.

In an amino acid there is only one molecule of SH. How can there be a large group SH molecules in one amino acid. Is the question talking about like one amino acid or mole of amino acid. I know I'm not understanding something obvious but please help
Thank you!!

[Yggdrasil]

You are correct that the sulfur on cysteine can either be protonated or deprotonated (there are no intermediate states), so it would seem like an equilibrium constant would not be useful for a single molecule.  However, you must remember that chemical systems are dynamic and equilibrium is dynamic.  What do I mean by that?

Let's say you are looking at a mole of cysteine molecules in water that has a pH of 8.33.  Now, from the Henderson-Hasselbach equation, you know that when the pH = pKa, half of the cysteine molecules will be protonated and half will be deprotonated.  If you take a snapshot of your mole of cysteine in water, you will see exactly that.

Now, let's zoom in on one of the protonated molecules (R-SH) and see what happens over time.  This cysteine will float around in solution bumping against water molecules and occasionally, during one of these collisions with a water molecule (or perhaps an OH^- ion) it's proton will fall off (attaching to the water molecule instead).  The cysteine is now deprotonated (R-S^-).  It will then spend some time randomly bumping into water molecules until one of the water's protons falls onto it, protonating the thiol again.  As you track this cysteine over time, you will see it randomly flipping back and forth between the protonated and deprotonated states.  Now, if you look for a long enough time, what do you think the ratio will be between the time spent in the protonated state versus the time spent in the deprotonated state?  The answer is 1:1... the equilibrium constant.  So, the equilibrium constant does give you information for a single molecule.  Instead of telling you about the relative concentrations of each form of the thiol, it tells you about the fraction of time that the thiol spends in each state.

This equivalence between the statistical behavior of a large number of particles at one particular instance and the statistical behavior of an individual over time is known as ergodicity, and it is a common and important property of many chemical systems.  Can systems be non-ergodic?  Sure, human gender is a common example.  If you look at a large number of people, you will see roughly an equal number of men and women.  If this system were ergodic, you would expect then that an individual would spend roughly half its life as a man and half its life as a woman.  Clearly, this is not the case (for most individuals), meaning that human gender is does not display ergodicity.

[sameeralord]

You are correct that the sulfur on cysteine can either be protonated or deprotonated (there are no intermediate states), so it would seem like an equilibrium constant would not be useful for a single molecule.  However, you must remember that chemical systems are dynamic and equilibrium is dynamic.  What do I mean by that?

Let's say you are looking at a mole of cysteine molecules in water that has a pH of 8.33.  Now, from the Henderson-Hasselbach equation, you know that when the pH = pKa, half of the cysteine molecules will be protonated and half will be deprotonated.  If you take a snapshot of your mole of cysteine in water, you will see exactly that.

Now, let's zoom in on one of the protonated molecules (R-SH) and see what happens over time.  This cysteine will float around in solution bumping against water molecules and occasionally, during one of these collisions with a water molecule (or perhaps an OH^- ion) it's proton will fall off (attaching to the water molecule instead).  The cysteine is now deprotonated (R-S^-).  It will then spend some time randomly bumping into water molecules until one of the water's protons falls onto it, protonating the thiol again.  As you track this cysteine over time, you will see it randomly flipping back and forth between the protonated and deprotonated states.  Now, if you look for a long enough time, what do you think the ratio will be between the time spent in the protonated state versus the time spent in the deprotonated state?  The answer is 1:1... the equilibrium constant.  So, the equilibrium constant does give you information for a single molecule.  Instead of telling you about the relative concentrations of each form of the thiol, it tells you about the fraction of time that the thiol spends in each state.

This equivalence between the statistical behavior of a large number of particles at one particular instance and the statistical behavior of an individual over time is known as ergodicity, and it is a common and important property of many chemical systems.  Can systems be non-ergodic?  Sure, human gender is a common example.  If you look at a large number of people, you will see roughly an equal number of men and women.  If this system were ergodic, you would expect then that an individual would spend roughly half its life as a man and half its life as a woman.  Clearly, this is not the case (for most individuals), meaning that human gender is does not display ergodicity.

WOW this is exactly what I wanted. How equilibrium constant relates to one molecule. So in this question equilibrium constant can give us an indication of time right (varies according to PH). Mole all the way!! Thank you 

Thanks for renge as well