nanoHUB-U Principles of Nanobiosensors/Lecture 3.5: Potentiometric Sensors Why are Biomolecules Charged?
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[Slide 1] Welcome back. We are discussing potentiometric sensors, and if you remember that we started with this basic notion that a potentiometric sensor should-- this response should scale linearly with an aniline concentration, that if we increase aniline concentration by a factor of 100 your current goes up by a factor of 100. That was our hope. Turned out that salt was a necessary evil. Necessary because it allowed the DNA to stay together, the protein and the antibody to bind, salt was essential through screening. However, it was evil in the sense that it, for the price it required to-- for the salt to be there was that essentially it took away 90 percent or more of the charges for itself, remaining-- allowing very little to be available for the sensor. And in fact this quote unquote tax went up as the aniline density increased, and therefore hence the log dependence. Now in the last lecture we talked about the second problem associated with the-- with the fluid like water, and that had to do with pH. Now in the last lecture we said that how that dependence, the surface charge dependence on pH could be used for a positive purpose, which is to use it as a pH meter. But, in this lecture I want to come back and show that pH also plays a sort of a negative role in terms of biomolecule detection. And this is very important because many times experiments are misinterpreted if you are not careful. Now at this point you might say that Professor, I'm not going to use-- put any orange juice in my experiments. I'll be really careful. But it doesn't matter because even pure water has pH of seven, and that itself can cause trouble. So that's the introduction. Let's get started.
[Slide 2] I'll begin by explaining how the DNA charges depend on the pH. We'll talk a little bit about the protein, very similar physics, and I hope you will understand them easily, and then we'll pull all these things together, surface charges, the DNA, the protein, and see how a MOSFET underneath actually views the whole system and is there any way to get rid of the surface charges so that you can see the biomolecules more clearly. Sort of, quote unquote, more clearly. We'll explain.
[Slide 3] Very brief reminder. You may remember that a biomolecule like DNA is a polymer, having many similar type of-- similar type of units, and these units are bases, for example. Are defined by bases called, A, T, C and G, four letters. And, what we-- what we found was that there was a central sugar ring, there was this base, which could be A, T, C, G, any of the four, but the charges I said was really coming from this PO4. And this PO4 came because this is a phosphoric acid. This is the phosphoric acid, lost its hydrogen and became positive in the process. Let me explain how that-- how that happens.
[Slide 4] You see, each one of the-- the residue associated with A, T, A, A, for example, and G, each one of them there is a phosphoric acid molecule associated with it. Now in water, remember, everything we are talking about in water, it may reduce one proton, it may sort of get rid of one proton, two proton, or three protons. So whatever number of original molecule you had in the dry, essentially will become charged when you put them in water. And this is the corresponding picture. This is neutral, you can see the four white -- three higher white hydrogen atoms hanging around. Here you see two, here you see one, and here you see nothing. So therefore charge three, two, one, and zero. How do I calculate the related proportion? Because remember overall that will determine what my charge of the biomolecule is. Once you know your pH of the solution, then everything becomes easy. This is how. So let's think about how it goes from a completely neutral to charge one. These dissociation rates are all known from experiment and in this case the value is 7.5 ten to the power minus three. That's the dissociation rate, and the dissociation rate going back and forth. What about going from charge one to charge two? Once again we are lucky. That value is experimentally known, and that value is essentially given by 6.2 ten to the power minus eight, relates the singly charged to doubly charged molecule. And the same is true for double to triply charged molecules. One thing you immediately see that in each case there is this concentration of hydrogen. Whatever number of hydrogen you have in the environment, defined by the pH, that will go in here and as soon as you know that value rest of those things becomes obvious because then you can calculate all the-- all the other values in a cascaded product. Let me explain how that works.
[Slide 5] Let's say you are very careful. You haven't put any orange juice, or you haven't brought any orange juice to your lab. Very careful. So you have pure water. And the pure water has pH of seven, as you know. And so therefore you put 10 to the power minus 7 molar and correspondingly you can relate singly charged-- neutral to singly charged, singly charged to double charge-- doubly charged, and from doubly charged to the triply charged molecules. The ratios are all given, obvious. And then one thing you immediately see that for every 100,000, approximately, 100,000 singly charged residues, singly charged DNA, DNA base, there is one which is not dissociated. So essentially what this is saying that at pH seven almost everybody will be at least be singly charged. And what we find here-- the statement here is that a fraction of them are also doubly charged. About .62. About half of them are also doubly charged. And triply charged in this condition, negligible. We can forget about it. And so therefore you can immediately solve for this equation singly plus doubly charged is equal to the original number, whatever number of dry molecules you put in. The ratio is known, you can solve for this singly and doubly charged, so if our base you'll have to multiply to one for singly charged, two with doubly charged, and on average what you find is you have 1.38q. So it's approximately 1.5q per base squared. Simple example, let's say you have a 100 base pair long DNA that has been diffusing around and eventually has just bound to the sensors surface. How much charge do you expect? Well, you say if the pH is 7 then I expect 100 multiplied by 1.38. 138 equivalent electronic charges. That is how much charge has landed and therefore if my sensor is sensitive enough it may be able to detect that binding.
[Slide 6] Now, this time it turns out that the math I just showed you in few lines of algebra you can essentially write a very simple formula for it and this is derived in the appendix. So I'll go very quickly. x naught in the original number of this phosphoric acid. x is the one that is still neutral after going through all this dissociation association process. y1 singly charged, doubly charged and triply charged. You can solve from the previous-- previous equation to see that-- that the value of m, it is just by definition can be obtained if you want-- if you know the pK value associated with-- dissociation constant with y1, y2, and y3. For example, if it is m2 that you are looking for, you want to know how many y2's you have in the solution, all you have to do is to add pK1 and pK2. Just these two terms. Not all three. And then i will be 2. 2 multiplied by the pH value of the solution, once you put it in you'll get 2. And you can see how you do 3, how would you do 1. And once you have this, you can plug this very beautiful curve. It says that as a function of pH related formation, relative to PO4, in the beginning you had almost 100 percent H3PO4. Nothing dissociated at that condition. And then you had singly charged, then you have doubly charged, and finally you have this residue. This residue where almost all the hydrogen protons have left. Very highly charged, here. Remember the calculation we just did in the previous slide? What was the answer? The answer was at pH equals 7 the charge is approximately 1.38, and you can calculate the ratio between the blue and the red at this point the pH is 7, is indeed close to .62, and that's what the calculation we did. We did for one particular value, but of course, if you wanted to do it any other pH, any other pH for example 6, then you'll say everything is singly charged. If you did it at 8 you'll say everything is doubly charged. So you can see the same length of biomolecule can go from, let's say 100 length, go-- the charge can go from 100 to 200 simply depending on your pH concentration.
[Slide 7] All right. That's about DNA's. DNA binding is necessary for genome sequencing as we said. Let's think about the protein quickly and see what type of pH dependence this protein has. Again, pH dependence would be something that will-- part of the charges associated with the protein.
[Slide 8] Recall that protein is also a polymer, very similar to the DNA, but the difference is this. That if you made a sort of a, well, to dream, or no... A-- a thread, then in that case there would be four elements for the DNA with this four different colors. For protein there are twenty of them. And each of one of them can, in principal, donate or accept electrons. So these individual units are called amino acid. And these amino acids are distinguished by this complex molecule R. Of course it has the NH2 group on one end and COOH group, carboxyl group on the other end, but this is the same for everyone, more or less. The R is different. There are twenty different version of R. And so therefore you can think about this chain having twenty different colored beads for this DNA. And what do you want to know? That if you have a sequence then what is the charge? Because once the molecule comes, that is what we'd like to detect through a potentiometric sensor. How do you calculate it? Let's-- let's take a specific
[inaudible]. And remember this is the biomarker that shows up when somebody is early indicator of prostate cancer. So if we can detect it in blood that will be very good, and we want to detect it by potentiometric sensor, so therefore we need to calculate the charge associated with it. Remember there will be twenty different colors in this biomolecule which will give this charge.
[Slide 9] Now, very quickly you can look it up in-- in Wikipedia or any other...reference material that these residues, the residue R is actually-- there are quite a different variety. They have very different property. But the important point is some of them will be positively charged, some of them will be negatively charged, some of them will be uncharged all together. So as far as potentiometric sensors are concerned, we'll just focus on the charges, focus on the amino acids that are charged. So, let's see how to calculate it.
[Slide 10] So for example here I have written out all the amino acids that are charged. Three positively charged. And four negatively charged, so the blue ones are negatively charged. So these negatively charged each has a pK value, that means dissociates and associates in water at a certain rate defined by this potential of K value. And then for each one of them there is a separate value and this value is important because this can be singly charged or uncharged, and therefore you remember that we have a simple formula to know what fraction of them with respect to the original content is charged, is simply given by m divided by m plus 1 and that depends on pH. Again, this will be in the appendix so don't worry about it. Yes, this formula, a simple formula, will do. And similarly for positive charges there's three positive charges, pK values are known, and so correspondingly you can find how many of them has actually accepted a proton and thereby have become positive. And so therefore a combination of positive and negative things overall will tell you, depending on the relative fraction of them, will tell you whether the biomolecule as a whole is positive, or negative, or at some it can even become charged neutral at point of 0 charge in the isoelectric point.
[Slide 11] So, very quickly, an example would help. For example this is a 261 amino acid in the prostate specific cancer. I just highlighted D, of course, and then there are-- you can see other letters. You can see it almost looks like a code. Not surprising because English letter has twenty-six letters and we have twenty DNA. And so therefore using the English letter to represent them makes very good sense. Each one of them has a certain amount of charge, specific to the pH remember. With different pH it will be slightly different and you just put it in a calculator and calculate how many positive and negative charges you have. This is a representative typical calculation. What you see that below pH of 7-- 6 essentially, or slightly-- slightly more than 6, things are positive. On average each molecule is bringing in 10 to 15 unit charge. There's a point when the positive and negative balance each other, so the although the molecule is still there, it-- it is as if it disappears from the potentiometric sensor's perspective. Disappears from the radar of the potentiometric sensor in some sense, and if you increase the pH the charges will become negative. And that's something represented by this card.
[Slide 12] And in fact this type of calculation are pretty accurate, so the blue lines are for different types of sensors-- different types of proteins. You will be doing it as a homework. You'll go to-- go to the protein databank, download the structure, write a little code, and that code will also be provided and you'll be able essentially calculate this pH specific charge for each one of the biomolecule. And if you just go and compare with experiment, you'll find the experiment to be surprisingly close because these quantities have been calculated over a long period of time.
[Slide 13] All right. So, we know now surface charges depend on pH, biomolecule charges, DNA and protein depend on pH. And so, we again have salt and we have all these pieces, so now how do we put them together? Turns out to be relatively very simple. This is how.
[Slide 14] So, we are thinking about biomolecules here on the top. And the sensors surface, this is silicon dioxides where the metal has been replaced and we have, of course, on the surface itself also positive and negative charges. And remember this value depends on the pH itself. And so each one of them, as soon as you tell what the pH is, I can tell you everybody what the charges for all the biomolecules and what the surface charge is. Right? So now this is the formula and we will-- we'll not worry about the formula right now, this would be derived in the appendix, but I discussed it a little bit ago. And you can see the important point is that as soon as you know the pH value of the bio solution
[phonetic], these individual values are all known and tabulated. So you will know what the value of the DNA is. Surface charge correspondingly do you see the corresponding pH appearing in here and once you know that value all other constants are known. You know the surface charge. Taken care of. PH taken care of.
[Slide 15] Next this is how it works. So you start with a certain DNA charge. Let's say you got 50 DNA on the sensor's surface, so for individual DNA you will have QDNA, you multiplied with 50. That gives you the total charge. Then you look at what the surface charge is on the surface using this formula. Then you calculate, put all the charges together, all the biomolecule charges which is the DNA, if you had protein around you'd put it in there, and the surface charges, and use the relationship between the potential and the logarithmic of the charge. You see you'll see from previous-- two lectures before, that there is this relationship between potential and charge. And once you have gotten the potential, then you have to do a self-consistency, because this will change the surface pH, and once you know the surface pH you will go back-- you will go back and recalculate that. So you can go back and forth and eventually to calculate what the net charge is. Now, of course, if you have salt on top of it you will have to do the corresponding self-consistant solution, and you'll be doing it in homework in the biosensor lab available in NanoHUB. And once the charges have been calculated in a stable way you can immediately calculate the charge in the MOSFET, which is the outside capacitance multiplied by the self-consistent potential here and the corresponding charges, therefore, this directly reflects the charges of the biomolecule. This is good and it turns out that it can interpret experiments pretty consistently. I'll give you an example.
[Slide 16] So for example this is the biomolecules like this which has come and landed on a sensor's surface. And for a specific value of pH, for every spare value of pH it can either be positive or negative. And so therefore the corresponding transistor which is sitting on the net can either be in the depletion or in the accumulation. This, by the way, only happens for protein, which can have positive and negative molecules-- charges. Not for DNA, which is always negative. If you don't remember what the accumulation was, just to remind you that accumulation is whatever charge you have here, for example you have negative charge. If you have more of it, if you have more of it, that's accumulation, that's this branch. On the other hand when the-- the pH changes and the biomolecule become-- protein becomes positive of course you cannot change the transistor itself, so in that case the type of-- the charge carriers will invert and that's what this depletion is all about. And if you look at experiments the experimental results will be pretty close, and that's what always surprises me, how very simple concepts like this can explain very complicated experiment with lots of things going on pretty nicely.
[Slide 17] One final concept, and then I'll be done. Remember this surface charge. Surface charge is great for pH sensors. PH monitors. And that's-- that's very good. But in this particular case I just want to see the blue molecules. I don't care about the surface charges. Because they're interfering. They're producing a parasitic current, given the-- given the impression that as if the molecules have landed. Which is not the case at all. So then, how do I get-- make this rate disappear? The surface charge disappear? Well, you know the answer. The answer is that for-- for that particular surface, like on silicon dioxide, there's a point of zero charge. For example, in this case, let's say the point of zero charge is four. So if you bring the pH to four, remember originally we are not planning to change the pH, because we said we'll be very careful, want to work with pure water. But it turns out that if you do change the pH then all of the sudden the surface charge will disappear. There were still positive and negative charges, they will balance each other out. And therefore this red line will disappear and the whole charge associated with the blue molecules will shine through, will essentially get reflected on the sensor's surface. Of course, save the part associated which has already been consumed by the salt itself, which is taken away by the salt. Now, this particular amount of charge will be very good, but remember, it's very important the-- the DNA is not too far away from the isoelectric point. It has all this positive and negative charges that allows it to fold in a particular way, and if you move things out too much, everything becomes very positive, then the shape may not remain the same. And therefore the antibody which is supposed to catch it may not recognize the shape. And so therefore you may not always want to go for maximum charge. A little bit below may sometimes still suppress the surface charge, but still be good for detection and capture. Let me end, then...
[Slide 18] So my conclusions are the following. The conclusions are that many biomolecules are in charge in solution. Not everybody. You saw that part of the amino acid, even if you put it in the solution they did not get charged. But DNA and a large fraction of seven molecules in the amino acid and protein actually got charged. And this charges are about one to two for DNA, negative one to two, by the way. And on the other hand protein charged couldn't go from positive to negative depending on the pH you have. And at the point at which the protein charge vanishes is called the isoelectric point. We have to be very careful to stay away from the isoelectric point, because at the isoelectric point the protein molecule disappears from the sensor-- sensor response because the charge essentially is zero, and potentiometric sensor only sees charge and nothing else. Now it turns out that if you do some charge calculation compare with experiment for DNA as you'll do in the homework, turns out that the results would be pretty good, and you'll be actually impressed how close it is to the experimental value. Finally, I want to caution you a little bit. You see, we said for a given pH, the solutions that will have the surface charge of biomolecules-- the receptors will have a certain amount of charge. Everything is nice and good. Now let's say with a pipet you put a little bit of analyte molecule in. If you are not careful, maybe the analyte molecule had some DNA, which is something you are trying to detect, but somehow if it disturbs the pH, remember pH is essentially just protons. The protons will diffuse very quickly to the sensor's surface. It will change the surface charge, it will change the receptors-- charges of the receptors giving an impression as if the biomolecule has come and landed on the surface, because the MOSFET doesn't know any better. And this false impression can give you-- and this can give you a false impression that the biomolecule has been captured. Looks like it's a very careful-- so you're very careful to do the experiment right, but it will turn out as I'll show you in Lecture 28 this parasitic effect is the basis of all modern genome sequences. Something that looks like an accidental thing, something that you didn't want, remember the pH disturbance sort of being a vanguard of the molecule that are coming later on? That turns out to be basis of the most modern technology we have. But you have to wait a little bit until we get to that point.