 This week, we are going to discuss about protein dynamics as probed by NMR spectroscopy. So, you know the dynamics is very very important thing because everything that happens in this world is all about time and motion. So, we will be looking how NMR contribute towards understanding the dynamics in in a profound manner. So, life actually is marked by change over time, right. So, if you look at any event that is happening to of the figure I am showing you like a nerve self-firing what is happening? Something changes over time or even anything development happens that we can see in the C. elegane which is a small organism, something continuously changes. You can probe that by putting some dye on some protein or gene and you see how it is changing. The question is that how it is changing with time and why it is changing? If we understand this how and why that is happening in life, we understand how life evolves, how life moves, how life develops and that is the importance of the dynamics which is encoded in time and motion. So, to understand these changes that happens in the in life or in organism or at cellular level or at molecular level, we need to probe the dynamics happening over time and the main factors that probe dynamics or which changes are the protein. So, protein in the last lectures we have seen that how we can get the structure of a protein, but you remember protein are not static entity. They are quite dynamic. They have a dynamic personality. So, they have a various sorts of motion that we are going to discuss this week. They have various sorts of motion and those motions are needed for their function. Now, they move to do catalysis. They move to communicate with each other or signal transduction or attacking to other organism in pathogenesis. So, everything is dictated by the protein dynamics and proteins are the main actor of all the cellular process that happens in the life. So, you can consider proteins as a soft matter and that has a multi-dimensional energy landscape where it is here it is shown. So, here what I draw is a entropy axis and here is the energy axis. So, you see the entropy of the protein changes with the like with the energy. So, on the top of this funnel this is typically called folding funnel or energy landscape. So, at the top of the funnel you see the energy is high and entropy is high. That means, protein is quite dynamic. It is sampling various states and as we come down it gets constricted, it dynamics reduces and energy also reduces. That means, it gets stabilized and this is typically called native structure of a protein that the structure that we saw that how we can solve using NMR. But other than that we can sample the other states which are populated at different location in the energy landscape view or the folding funnel. These are of higher energy states with more entropy. So, if you can probe what is the relative probability of these states which are not at the ground state, slightly excited state, then we can understand the dynamics sorry thermodynamics happening between the two states. What is the probability that it exists at the bottom? What is the probability that it is slightly up? That is given by the thermodynamics. And what are the energy barriers like if you draw a energy curve this is one state another state. So, what is this energy barrier between these two states, how it crosses from one state to another state is dictated by the kinetics. So, by understanding the protein dynamics, how it samples various states in the folding funnel or energy landscape, one can understand the thermodynamics that is happening in the protein as well as the kinetics parameter that happens in protein that samples various states. So, all those you can see the any cell is decorated by various proteins they are typically shown the bigger protein which is called monoclonal antibody this is smaller protein. So, all these proteins at all the time samples various state that means, they are dynamic. Now, the question is how we can understand this the fourth dimension of the protein. So, three dimension is a structure right x, y, g dimension. The fourth dimension is the time dimension and this fourth dimension is extremely important to decipher the protein function. As I am saying it protein is not an aesthetic entity it is dynamic it samples various time scale and that is what actually gives the gives the total function of protein. So, what is the importance of the dynamics I will show you here in a cartoonistic representation. If you take this bead the say necklace made up of pearl this is a beautiful necklace right. Here each of these beads are amino acid when you join together and fold in decorate in a certain manner that is a three dimensional structure of a protein or three dimensional structure of a necklace. But necklace in itself is not beautiful it becomes more beautiful when it decorates somebody's neck right. So, that is what actually protein dynamics does it decipher a function to a protein, it decipher a functional state of a protein. Therefore, the fourth dimension in protein structure is very much needed and that fourth dimension is a time dimension which tells about the functional aspects of a protein the different kind of motion that is present in the protein. So, together the structure and dynamics along with the folding determines the function of a protein this is called a revived structure function paradigm. So, a structure not only tells about the function a structure is not sufficient to tell about the function you require the dynamics information and also how the protein folds what kind of folds it has. So, folding and dynamics together with this structure tells about the function of a protein right. So, that is the energy landscape that we are talking about this is three dimensional energy landscape where in one dimension you are talking about the entropy or conformational excursion. Here is a native state energy stabilized states of a protein and there are some intermediate states where some of the parts are open that is a high in energy and that is what basically NMR can tell you that how the conformation from this state to this state this state to this state may change during the during the folding or during the dynamics. So, how protein is doing and conformational excursion. So, to give you more emphasis on why it is important you know all the structure of a hemoglobin right hemoglobin that binds to oxygen. Now, you also know from your biochemistry knowledge that it has a cooperative binding to oxygen right. So, hemoglobin is a here is a hemoglobin here you can see in the motion oxygen is binding releasing binding releasing. So, if you look at it is doing conformational excursion or constantly it is moving and that is what actually dictates whether is in deoxy state or oxy state. So, to go from deoxy state to oxy state or vice versa it is doing lots of motion right quite a bit of motion. Motion happening at a local time scale here and motion happening at the global time scale like a whole protein is moving. So, these different kind of motion that we see in a protein which is quite relevant for their function right. So, this how to probe this right this came from very early idea of Kruth Uttarik when he was doing a basic like a he was working on a protein called BPTI doing a basic experiment. BPTI is a basic pancreatic trypsine inhibitor. So, what he was looking at the dynamics of an aromatic amino acid in the globular conformation of a BPTI just using simple proton 1D NMR. So, what he was looking basically there was a aromatic amino acid like phenyl anionine and how it is changing over time that is what he was looking and because of this change what was happening whether it is twisting or something you can see the distance between them change and NO e pyrton between them change. So, this was happening when he was just starting the protein and you can see there are lots of these aromatic amino acids encoded here. So, he was probing essentially aromatic amino acid and to probe the motion what he did he recorded the temperature dependence 1D NMR and looked at the chemical shift of these aromatic amino acids. So, essentially rotation because of temperature change rotation of this bulky aromatic amino acid within the hydrophobic core was probed. If you look at here the experiments were done all the way ranging from 4 degree centigrade to 81 degree centigrade and you can look at here we have a sharp line right at the lower temperature. As we go one thing you can notice that peak seems to be shifting and another thing you can notice some of the peaks the intensity is dropping that means, they are getting broader and broader. The stales that the hydrophobic core with temperature shows lots of motion lots of relevant motion because now peaks are getting disappeared. So, you can imagine that if disappearance happening some kind of motion is happening and that gives the information what kind of like a what kind of motion this molecule will play with will adopt with temperature. So, that was the first evidence that yes protein shows motion and you can probe just by recording 1D NMR looking at these aromatic amino acids and looking at their signature the chemical shifts peak pattern how it is appearing or disappearing you can learn about some motion. So, various time scale that are there in the motion I gave you example of like a hemoglobin oxy and deoxy. So, we saw that some kind of local motion is happening some kind of global motion happening. So, local motion we can define as local flexibility and bigger motion like a where domain large domain movement is happening we can call them as a collective motion. So, local motion we can define as kind of bond vibration a bond is vibrating the whole methyl is rotating the loop is moving like this or a side chain rotamers like in methyl moving something like this. So, that is a like a fan wings of a fan those are called local flexibility whereas, global flexibility whole large motion is doing motion like this. So, if you capture all these motion that may happen in a protein the time scale that can range from femtosecond to second time scale. The local motion will be at a faster time scale femtosecond picosecond nanosecond microsecond and larger domain motion can happen in microsecond millisecond and second time scale. Now, if you look at the different techniques in fact, can capture all these motions right. So, the one of the prominent that in this course we are discussing about the NMR technique. So, NMR relaxation can actually captures the motion that is coming from picosecond to second time scale. XA can also capture it reports you indirectly in terms of B factor it can captures again femtosecond to second time scale. The slower time scale motion using NMR can be captured using hydrogen deuterium exchange. So, if you couple hydrogen deuterium exchange with the NMR you can capture the slower time scale motion ranging from millisecond to time 2 to second time scale. We will be looking exclusively on these towards the end of this week where we are replacing proton with deuterium and looking at what is with what rate it goes off. Now, the another important technique fluorescence can also reports then UV visible can also capture Raman gives you about motion infrared or even MD simulation some of the faster motion you can capture from femtosecond to microsecond time scale. However, many of these techniques lack resolution like a fluorescence you need to have a tag and you are looking at the local motion of that tag or global motion of whole protein. UV visible in codes, but actually resolution lacks Raman lacks resolution infrared again is not that resolved. MD is high resolution, but it is a computational technique. So, you do not know right how they behave in solution you can mimic it, but essentially to prove that to prove that you have to do experiment. On the other hand, NMR is well tuned to give the motion at a various time scale in a residue specific manner or at an atomic resolution. So, that is what one can do it by probing some of like this NH probe in the protein and that will tell about local flexibility like a bound vibration methyl rotation, loop movement side chain rotamer or a collective motion if we understand how these like these two loops or two domains are showing correlative motion, a larger domain motion that will come in microsecond to second time scale. So, essentially NMR is tuned to provide you local flexibility as well as collective motion ranging from picrosecond to second time scale. So, basically various atomic resolution methods that we discussed in the last slide they are essentially can probe it. So, ideally structures of all subsets and their interconversion sheet can be probed by various techniques high resolution technique like X-ray, but for X-ray you require in a homogeneous crystal and you can say that many times this homogeneous crystal could be trapped in one of the substrates. What I mean by if you draw the energy landscape here could be possible that your X-ray structure is trapped here or here or somewhere here or here. So, they can be trapped it gives the high resolution structure, but actually interconversion between these states may not be possible. You have to acquire the structure of this state acquire the structure of this state and then understand how it is possible, but that is again and chance where you can trap it. NMR gives you high resolution structure and dynamics, but its limitation that it is not suited for large molecule. Large molecule you lose resolution, you lose sense like a lines becomes quite merged. So, for large molecule this is not amenable. Chiroelectron microscopy on the other hand very well suited for bigger molecule its emerging technique. Now, one can even think of combining few of these techniques to work on a large molecule where you can look at the bigger picture using cryoelectron microscopy and on a like on a residue specific manner or localized motion using NMR. So, now a days is coming where you have to integrate multiple technique to understand the motion that is happening in protein. There is another technique called SACS small angle X-ray scattering. It is not atomic resolution, but this is also very well suited to understand where we cannot crystallize the protein or which we are we cannot do the cryoelectron microscopy. So, again you can club SACS and NMR where SACS will give you broader picture and NMR can give you local picture. The another technique which is slowly becoming popular is called free electron laser. The only problem is that it requires high power and it can destroy a sample. So, during the experiment sample will be burned out. Now, these are some of the high resolution technique that can be used to get structure as well as dynamics and nowadays one need to combine multiple techniques to get an correct picture of a biomolecule. So, coming back to NMR relaxation which proves the protein dynamics. As I mentioned it samples or it can prove the motion happening from say picosecond to second time scale. So, if this is a clock, what kind of experiment and what kind of motion that we have in a protein just let us look at and what are the events that one can capture. So, we can start from here. So, say if we want to understand the secondary structure formation. Secondary structure formation can happen very fast. Say it can happen between nanosecond to 2 millisecond time scale. You can basically combine the HD exchange and you can understand how the secondary structure formation happens in a protein. Now, if you go little slower motion like a loop closure or a hairpin closure that is little bit of slower time scale microsecond to 10 of millisecond. This can be proved by various NMR techniques that is called RDC this residual dipolar coupling or CPMG that probably we are going to look at or R1 row experiment. These can be used to understand the loop hairpin closure. Now, another important phenomena that happens in protein is called catalysis that happens in micro second to second time scale that can be also used that can be studied using probably CPMG and R1 row experiment. Now, the faster time scale motion that is backbone dynamics can be studied using classical R1 or T1, T2 NOE R1, R2 NOE which happens in picosecond to nanosecond time scale. So, how the side chain is moving, the side chain rotation picosecond time scale can be captured here. Now, even further slower like a protein folding, some protein folding happens in millisecond to hour time scale that again can be clubbed with a hydrogen deuterium exchange to study it. And the slowest time scale like a protein aggregation can be studied using diffusion NMR. How the protein is coming or self association protein happening slowly, slowly they are coming forming a nucleus and then nucleation growth happens and then forms a aggregate. That is a that can happen in from second to hour time scale can be studied using diffusion NMR. So, NMR has a various amines that can be tuned to understand a particular phenomena that protein can have a catalysis, a loop closure or hairpin movement or backbone dynamics or protein folding or aggregation. All of these have one or other experiment that can be used to understand. Now, NMR relaxation essentially looks at the nuclear spin relaxation and that provide the information. The first motion on time scale can be can we call it picosecond to nanosecond time scale. This can be done in laboratory from nuclear spin relaxation whereas, the slower time scale motion which comes in microsecond to millisecond time scale can be done in a rotating frame nuclear spin relaxation. And magnetization exchange spectroscopy that we will be looking at something called j-j exchange which is motion in time scale of millisecond to second time scale can be done by magnetization exchange spectroscopy. So, here first time scale like a typically we know that R 1, R 2 are first time scale it is a laboratory frame relaxation, R 1 row rotating frame relaxation can prove us microsecond to millisecond time scale and then something called magnetization exchange spectroscopy from millisecond to second time scale. So, these are typically experiment that one can do it. Now, typically we use heteronuclear spin because heteronuclear is very well suited to give you sharp lines and due to its excellent relaxation property proton is very abundant and it has a different relaxation property or faster relaxation property than heteronuclear. So, typically in protein NMR we do heteronuclear spin relaxation and that basically gives us an idea how to characterize the dynamics process in a protein. So, in this week we are going to look at what are the T 1, T 2 NOE phenomena how do we measure this and how they report about the dynamics in the protein. How we can derive the relaxation parameter from these experimental data that we record the T 1 experiment, T 2 experiment and heteronuclear NOE. What are the time scale that they capture and that we can measure by NMR and how these relaxation parameter presented to illustrate the motion that is happening in protein and essentially we are also going to look at how we can set up these experiment to measure the protein dynamics. So, let us talk little bit more about the motion and then that will help us in designing the experiment. So, as I was saying protein motion affects the NMR parameter. Various kind of motion this local motion it is a first time scale motion because second to ninth or second time scale. So, each bond is some making some motion either rotation or movement like a confirmation excursion all these are happening that will call that is called first time scale motion. Or the whole molecule if you look at this protein of two domain say beta domain and a helical domain and connected by loop the whole protein is tumbling which has a rotational correlation time that is a slow time scale motion. So, microsecond to millisecond time scale. So, if I want to probe this local motion as well as the collective motion I need different kind of experiment. In one case it should only probe here in another case it should probe whole motion and that is what we are saying for a local motion we just can exploit the NH bond the excursion that NH bond is doing the relaxation property of NH bond. And that can be proved by the bond vibration or a methyl rotation or loop movement loop movement. The collective motion which is essentially a larger domain motion like from here to here this can also be done right. So, another orthogonal technique like a fluorophore sense you can add a fluorophore here you add a fluorophore here and do time result freight you know how they are coming closer they are going far and you can plot it essentially that is by fluorescence, but then you are looking at how the how the two probes are coming together and going together. Essentially in NMR you do not need to add anything stringy you can look at this collective motion or cross correlated motion by understanding collective large domain motion. So, if you now draw this energy landscape here you can see the motion that is happening the local motion happening at picosecond time scale or nanosecond time scale happening essentially in this local minima of the protein local minima in the protein energy landscape whereas, the microsecond to millisecond time scale motion this is happening like when there is a another state which it has to cross this barrier to go the state. So, protein existing in state A and protein existing as a state B. So, local motion are these and whole domain motion you can see there is a structural change happening when protein goes from state A to state B and do these two states are having some energy difference which is of few k B T or few kilo calorie more. So, protein is constantly going from k A sorry from A to B with rate k A B and coming back B A. Now, this is motion this kind of motion is slower time scale motion or large amplitude collective motion and that basically samples fewer state may be 1 or may be maximum 2. However, the local motion since the energy barrier is very low it can with a thermal fluctuation it can samples many of those states because here energy barrier is very low it can easily cross over or here also it can cross over with a thermal fluctuation. So, local motion quite a bit of possible however whole domain motion it requires certain energy that is a that energy is given here which should be few kilo calorie per mole ok. So, slower time scale motion like something like here which is important in allosteric or structural rearrangement like a cis trans isomerization that may happen or here the whole domain is opening and closing up these are slower time scale motion. Cis trans isomerization during catalysis you see some kind of here the protein is changing from cis to trans it is a slower time scale it requires completely bound orientation or even in signal transduction or protein-protein interaction essentially happens at a slower time scale motion. Now, to sum up what we discussed till now what we discussed is NMR is a versatile tool for understanding the atomic structure and various time scale of transition. There are various time scale all the way ranging from picosecond to second time scale motion. The frequency if we want to understand it is a terahertz time a hertz frequency and those are basically can be done with various NMR experiment like a faster time scale motion in laboratory frame can be done using T1, T2, NOE relaxation in rotating frame can be done T1 rho, T2 rho or ROE and then we can understand with a line shape analysis or it is dual dipolar coupling these can capture various time scale motion. Typically in solution state we do all these experiments here and solid state it is a relatively slower time scale like a protein folding or aggregation or say tumbling of whole protein in the membrane that comes in second time scale which can be captured using solid state NMR. So, next like we are just focusing on the liquid state solid state I will be discussing in the last week of this course ok. So, to sum up relaxation is a process by which the spins spin return to their equilibrium population distribution and it is governed by the fluctuation that can happen because of local field and spin orient like what happens is here is a B magnetic field B0 right main magnetic field and here are my tiny spins. So, they are doing all random fluctuations and they are experiencing the local field and that is influenced by this main magnetic field ok. So, this reorientation of these spins cause variation in their interactions which are which we can define as a CSA chemical septanisotropy or dipolar coupling and as I mentioned that the heteronuclei are very well suited for relaxation mechanism proton has a complex relaxation. So, mostly liquid state experiments are done exploiting the heteronuclei and the relaxation parameter that contributes CSA and DD. So, we are going to now look at little more detail in the next class how the CSA DD contributes to us the relaxation phenomena and how we can exploit this heteronuclei like a 13 CE or N15 for understanding the relaxation mechanism. So, in this class I just give you the idea about why relaxation and why NMR is suited for relaxation what information the relaxation brings or the motion brings for understanding the protein function in a holistic manner. With this I am closing here for today. Thank you very much. See you in the next class. Thank you.