nanoHUB-U Principles of Nanobiosensors/Lecture 3.1: Nanobiosensors Sensitivity and Types of Biosensors
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[Slide 1] Welcome back. I hope you are understanding and enjoying the course so far. We are now in the second part of this course where we'll be talking about the sensitivity of a biosensor. Now, relating the first part to the second part. In the first part, we essentially have talked about that when the molecule diffuse around, how long does it take for the molecules to land on the sensor's surface. And we have seen that that really depends on the geometry of the nanobiosensors and how the particles diffuse towards the sensor's surface. Now, once the molecules have come and landed on the sensor's surface, the question is how many molecules would you really need in order for the sensor to respond? Now, an analogy might be useful for this to interpret how the second part is related to the first part. Assume that you are looking for a bird in Amazon, let's say, and you have camped somewhere. Now, of course, the bird has to diffuse around or fly around and it has to come to you or come to where you are in order for it to be detected. However, it doesn't matter at that until that point the bird comes that whether how many megapixels of camera do you have. But once the bird comes, at that point, it matters a great deal of what type of camera you have in order to take its picture. So, we are talking about the quote end quote, "camera" in this section of this talk. There'll be nine lectures in this segment and we'll go through them one at a time. So, let me begin with some definitions and various types of nanobiosensors that one might expect to find in a typical laboratory.
[Slide 2] So, I'll begin with some background and interaction and I'll remind you about the importance of geometry of diffusion. That's the first thing. For nanobiosensors, being able to detect, ultra low concentration. And then, we'll be talking about three types of nanobiosensors and I remind you that there are many, many extraordinary nanobiosensors but the three that we'll be talking about are in some way label-free or tag-free that it depends on the intrinsic property of the sensor itself or intrinsic property of the biomolecule itself to get the transduction process. And then, we'll begin to discuss one of the three which is potentiometric sensor. And finally, I will say, I will begin to explain why a simple understanding of the potentiometric theory-- potentiometric sensor because after all, it has been around, as you'll see, for 100 years almost, why that really doesn't do it. And you need to understand the problem a little bit more deeply before you can understand the operation of a potentiometric sensors and then I will conclude.
[Slide 3] Now, a nanobiosensor as you're shown here is always helpful. Because as I told you that nanomolecules-- biomolecules are generally very small in size, like a segment of a DNA, a 100 base pair DNA would be only 3.4 nanometer long. And as you saw glucose molecules, protein molecules, it's very small. So, it always helps for a biomolecule to be comparable in size with the nanobiosensors because the sensitivity, as you might expect, would be somewhat larger once it lands on the sensor's surface. Now, of course, the opposite is also true, that if your sensor is very big, a classical sensor for example, in that case even if it had a mosquito bite and the elephant as a sensor in that sense, it probably wouldn't even notice. So the bottom line I want to point out that if a sensor doesn't notice the analyte or can detect-- cannot detect it, then as if the analyte doesn't exist and therefore, the sensor is actually useless. So, it's very important therefore that the sensor be in nano scale if we want to detect molecules which are small and few in number so that it can have a sensitive response.
[Slide 4] Now, just to remind you where we are in this broad scheme of things, in the first part, I discussed that how the sensitivity might go from millimolar all the way to femtomolar or attomolar simply by the geometry of diffusion. You may recall that these devices have different fractal dimension and therefore, it can capture particles. It captures the particles from the diffusion field by molecules from the diffusion field in a different way. So, these two do it in a different way. But once you have it in this region, let's say, a picomolar sensitivity, then this specific design can make it whether it is 0.1 picomolar or whether it is 10 picomolar. So, that range, that type of range would then be critically dependent on the design and the transduction mechanism and operating principle of the sensor themselves. In that case, it is no longer sensor agnostic. Now, let me remind you about how these various pieces are related.
[Slide 5] Assume that we are thinking about a nanobiosensor and the sensor is decorated with some capture probe. There's a segment of DNA. We'll talk about these details of these segments towards the end of the course. But for the time being, let's just assume that it is essentially a glue. And then that, in the presence of this capture probe, there'll be a current from source to drain and this will be the background current denoted by, let's say G naught, the conductors G naught. And then, once the molecule arrives, it will take a certain amount of time, once the molecule arrives, this extra charge will change the potential of this sensor and therefore change the conductivity. The red line essentially says the increasing conductivity, are decreasing freezing conductivity from source to drain because-- in response to the charges of the biomolecule. So, the response time, the first part of the course simply asks how long it takes before the molecule comes and the sensitivity simply says that once it comes, how big a change in the signal does it produce in order for the sensing, for the biomolecule to be detected. So, if you look at the same formula that we have derived before which was defined the limits of detection. One is this diffusion limit. That is the part one of the course which is the past 12 lectures. But the topic that we'll be talking about is how many molecules do you need-- really need in order for this sensor to respond. So, we are going to discuss the physics of Ns and the physics of Ns depends on specific sensor technology.
[Slide 6] Now, there are two different ways of detecting it. I want to specify that before. Assume that you have a sensor and that arrow-shaped region, that's really the receptor probe and the biomolecule comes and attaches to this. We can have charged mass, electron affinity, as a tag or as a marker for the biomolecule. Now, if it is an electrical-based sensor then we can simply look on the change in the current associated with the biomolecule or for the-- optical-based sensor. Then we can simply ask the question that how the refractive-- reflectivity of the surface changes once the biomolecule has been attached to the sensor's surface. So, we can essentially interrogate one of these properties by using one of these transduction mechanisms. That's the general principle of any sensor.
[Slide 7] Now, I have already mentioned that there are three types that we'll be talking about. One is called as potentiometric sensors where the charge of a biomolecule is reflected in the source to drain current. I will explain that a little bit later. There are other techniques called amperometric techniques and then there'll be cantilever base sensors which essentially measures the mass to the translators changing the frequency. Today, I wish to focus on the potentiometric sensor. This is one of the most beautiful, at least from a physics perspective, one of the most beautiful illustrations of a sensor technology that has wide technological relevance. I'll just remind you what these things are in the broader context of other sensor technology.
[Slide 8] You might remember in the first lecture, I mentioned that there is a corresponding history of biotechnology and there's a corresponding history of a nanotechnology evolving, electronics evolving. And one of the first sensors that was ever developed was pH a base sensors. This was used to measure the acidity of orange juices and this made, as I mentioned, Beckman a billionaire. So, that was almost 100 years ago, 7,500 years ago. But sensor, this potentiometric sensors is continues to be very important even as late as this year. So, there's a wide variety of application and in particular, for genome sequencing. I'll start from here and then, I will go back in history, talk about the pH sensor a little bit and then come back again at the very end. So that applications that we'll be looking into essentially spans almost a history of 100 years, compressed within an hour or so.
[Slide 9] Now, before I get into these potentiometric sensors, there are many different types of potentiometric sensors but we'll be talking about one which can be miniaturized, which can be used integrated with other things based on nanotechnology. And one of the most important ones are, of course, transistor based-- transistors-based potentiometric sensors. Here is how it works. This is a transistor physics in a single slide. You know, if you take a resistor and try to see-- put a voltage across it then there'll be a current flow. That's Ohm's Law, right? And the current depends on the electronic charge, the number of electrons or number of charge carriers you have, the velocity through which they're moving and the cross-sectional area. So that many particles are moving at a certain speed that gives you the current and that gives you this I equals gv, the conductants multiplied by the voltage, v because the velocity is directly proportional to the voltage you have applied. Now, a MOSFET is this likely generalized version of this resistor. The idea is this that you still have sort of a resistor, this is called the source, this is the drain and there is an insulator which separates a gate region from the quote end quote "channel region". And the purpose of this blue gate is to modulate the value of n. Now, if the transistor is said to be operating in accumulation, if you had whatever number or type of charge carrier you originally had. Let's say, you had electrons. If you have more of it in response to this gate charge or gate potential, then you have accumulated more and therefore it's called transistors operating in accumulation. There are two other methods by which you can operate the transistor. One is that you can by applying a voltage, you can essentially deplete these regions of mobile charges. In that case, the total current after the charge comes will be lower. Regardless from the delta I, you should still be able to detect the presence of the biomolecules shown here in blue. And that approach because your charges are being pushed away is called depletion mode operation. And finally, there's something called an inversion mode operation. Let's say you had n-type of bulk charge carriers in the beginning before the biomolecules came. Once the biomolecules came, biomolecule-- let's say, you have positive charges induced because these are negative charges. So there are the cat charged carriers are now are opposite type. Their type has been inverted and therefore it's called an inversion. Now, in all these three cases where the transistor operates, we are really focusing on modulating the number n through the biomolecules. You see, for this technology, we don't really worry about the v per se because we apply a small amount of voltage and therefore voltage is directly proportional to the electric field and given by the drain voltage and the length of the channel and the-- multiplied by the mobility. Bottom line is that unlike a transistors, semiconductor transistor which is often very complicated because of the complication of v in some sense, will not be a factor here. We'll just be focusing on n and how the biomolecules change n. So, let's begin.
[Slide 10] Assume that you have this set number of analytes which are coming to the biosensor surface. And current, before the biomolecule landed on the sensor's surface, or if you remember, the Amazon bird came to view of your lens, so to speak. Before that, I will call the current ID, coming from source to drain. And after the molecules have landed, here for example I show 4 molecules, there'll be corresponding charges. Because just like a capacitor is separated by a dielectric, 4 positive charges will be compensated by 4 negative charges, let's say. And therefore, this extra charge will change the current. And therefore, the definition of sensitivity is this relative change before and after normalized the original current. And essentially, we'll be calculating this for various cases, because if you knew how many molecules do you need in order to have a certain change in delta I, that is really what we are after. That should be a simple calculation, you see.
[Slide 11] This is simple in the following way. Assume that in this picture, I have taken the original transistor which was lying vertical, the oxide was lying vertical and I have turned it sidewise. And so now, my source is here and my drain is here and the biomolecules are on the left and the extra charges, these green charges are on the sensor's surface. Let's assume accumulation mode operation. Electron is going from-- the current is going from bottom to the top through the source and drain. Now, of course, if you have a certain amount of positive charge from the biomolecule, the channel would correspond and you will have a negative charge to compensate for it. This is capacitor, basic capacitor. And therefore, what would be your current? This change in the current will be whatever the extra charge, the most charged is because it's called metal-oxide semiconductor. Oxide is this oxide Ox and semiconductor is the channel. Generally, original technology has a metal gate and that has been removed and so therefore this is called a MOS, QMOS means charge on the MOSFET which is the green charge. And it will be equal to the charge on the biomolecule because these two have to be equal across the capacitor, to the blue and the green. And that, you could also write if you wanted to as the capacitance multiplied by the extra potential. That's good. Biomolecules have landed, we just have been charged. Remember, it could be DNA or it could be protein which has a certain amount of charge. The charge is reflected on the channel. Your current changes, you have detected the biomolecules. You may think that you can go home but not really and I'll explain why. Just to remind you one quick thing that this type
[Slide 12] of calculation we have done before, very quickly you may remember the analysis that I just showed was a general analysis. But for the particular case of a nanobiosensor, for this geometry of electrostatic in that discussion, we also did the same thing. We looked at the current before. This is the total number of carriers, cross-section area, multiplied by the velocity through-- of the-- charged carriers through this nanobiosensor. Once the molecule, red molecule landed on the sensor's surface, it depleted the charge carriers that was the white region with a new effective radius, Ra for conduction. Before it was Rb, now it's Ra. So, you do the current before and after and you may remember, just a quick reminder, that sensitivity could be calculated as a difference between before and after divided by before and we calculated this. So, this is nothing-- not be surprising, this calculation of sensitivity. In some way, we have already done but in that case, we found that that was relatively a small effect. But now, we want to explore that small effect because that's really important in terms of design of the biosensor itself.
[Slide 13] Now, let's continue. Let's say, I have already told you about how many biomolecule that-- once you have a certain number of blue biomolecules on the sensor's surface, you have a certain number of green inversion or accumulation charge and you can detect the corresponding presence of the biomolecule. Now, let's remind ourselves that these biomolecules came from this capture and release equation. You remember that the first part is capture and the second part is release. And if you ride long enough, then in that case, the equilibrium concentration of biomolecules will be equal to-- can be obtained by setting this equal to 0. Now, the bottom line I want to point out is the number of biomolecules in that context is directly proportional to the density of analyte you have in the solution. So, it's a fair measure of how many molecules you have in the solution. Now, therefore you could immediately say that your current should be proportional to the mole charge in the biomolecule. But that's-- biomolecule is proportional to the analyte density. So therefore, if you measure the current at 1 nanomolar versus 1 micromolar, then the current should increase by 3 orders of magnitude because the analyte density has increased by 3 orders of magnitude. And if you did an optical experiment where instead of interrogating the current cell going from the bottom source to the top drain, if you just put the optical tag, just counted how many molecules are coming in, optically detected how many have landed and how many have conjugated. If you do that, then you would see that indeed this is the case. If it's a linear dependence, take a log on both sides on a log-log plot, essentially a linear dependence at an extra high concentration of course, the surface is saturated, you don't get any additional enhancement. But the theory appears to be correct. Now, this word appears, is the key one because you see, there's the optical response. I haven't yet shown you what the electrical current does.
[Slide 14] Unfortunately, it turns out that if you look at the corresponding electrical current, you'd find a completely different story. What would you find that in this case although both axes is a log, essentially a linear dependence. In here, if you look at the relative change in the current divided by the original current, remember the sensitivity, as a function of log of concentration, you would find that this axis is not a log. This is a linear axis. And in fact, there are many experiments which have shown this linear to log dependence. Do you understand what did just happen? You see here, if you increase the concentration by a factor of, let's say, 10, then from there-- let's say from 10 to 100, then in this case there would be almost a factor of 10 enhancement in the intensity. Because the intensity has simply-- goes linearly proportions, linearly proportional to the density. Here, however, what it means that you will have only a factor of two enhancement because for log of concentration, you have linear increase. Potentiometric sensors stands out to be far less sensitive than what you'd have expected seen from a classical simple theory. What has gone wrong? And that is the essence of the story that I'm going to tell you in next six lectures.
[Slide 15] You see, in order to understand it, I'll just tell you the basic thing that we missed. The MOSFET that we considered is really not exactly like a classical MOSFET. I cheated a little bit. I have to come clean and once I do from the next lecture onward, you will see how important there's additional pieces of information are. Now, this is the original MOSFET, with the metal gate, channel and the oxide, that's where the word MOS comes from. Now, when you made a biosensor, when you made your biosensors, we essentially pushed the metal electrode up in here as reference electrode and filled it with fluid, water for example. So, this region is now exposed. Now, when the biomolecules came, they came within the fluid. The gate was actually here and then they changed the conductivity or conductance of these biosensors and often we simply treated them as a homogenous charge, that's what we did. But you see one thing we forgot to mention and which is that this region, this fluid is not just pure water. You need salt in it. Now why would you need salt? That's where the real trick is that will explain the logarithm independence that we saw in the last case. The salt is the culprit.
[Slide 16] The reason we need salt, you may remember, that-- let's assume that this is the biosensor surface. This is their DNA, we're just trying to capture the diffusing target molecule. And once the target molecule comes, they are-- they essentially bind with each other, up to that point, no problem. But do you realize that this, I told you this before that this biomolecule is negatively charged. Another state of biomolecule, the DNA that just came in is also negatively charged. How is it possible that they are going to essentially not rip each other out? How is it possible that they will stay together? It turns out, the only way you can make them stay together is put them in salt. So that this repulsion, this is sodium chloride. The sodium atoms essentially come inside. They essentially prevent the mutual repulsion or reduce the mutual repulsion so that they can stay together. And this mutual repulsion, this role of salt, salt coming in essentially drains every-- a certain fraction of this charge so the MOSFET underneath doesn't really see it. You see, the salt is very important. Without the salt, the two DNA molecules, they say we have, you know, genome, you know, genome about 4 billion long, the chain, 4 billion base pair long DNA chain. The two DNAs in it would have repelled each other as if, if you held an apple in your hand, the force you have is a certain amount the force, trying to pull it down. The force of repulsion had the same magnitude. So, therefore, it would be impossible without salt. Essentially all our DNAs would self-explode, they will essentially repel each other very quickly. So by understanding these potentiometric sensors, we are sort of understanding a basic physics of why we exist and why we are stable to begin with.
[Slide 17] So, what I want to conclude with is that the classical, if you did a simple classical theory, it predicts the sensitivity should be proportional to the analyte density. There's no salt anywhere, no dependence of salt, no discussion about time, how long it takes for a certain sensitivity to be achieved. In practice once you do the theory correctly, you will see the dependence is really logarithmic on density. Logarithmic on salt concentration and the time comes as the log also. So therefore, the sensor actually, in potentiometric sense are just found far more weakly compared to what you will have expected from a naive perspective.
[Slide 18] So let me conclude here. I told you in the beginning, two things define sensor response. One is this geometry of defusion. How essentially particles come and land on the sensor surface. And second is the transduction mechanism that once it lands, how it can get the observable that we are looking into. Now geometry of diffusion defines the optimal limit while the geometry and the transduction together define the sensor-specific limit. You know the transduction mechanism defines the factor Ns, the number of molecules you need in order for the sensor to give a signal that can be detected. There are many types of sensors and we are discussing this potentiometric sensors based on transistor technology which can be integrated. And as I have told you that this is a very important technology to begin with. So therefore. understanding how this potentiometric sensors work is very important. But we'd add in to the trouble, right, we saw that if you just stick a normal transistor, put some charge in it. You expect a linear dependence with analyte density, very sensitive in that case. Turned out that it has only a logarithm independence and we suspect that salt has something to do with it. That discussion will be up next. And until next time, take care.