 Hello, so welcome to today's lecture. Today we are going to discuss shape and size of a molecule, macromolecule and how NMR can be used for getting some information about shape and size of a molecule. So the experiment that is called DOJI, diffusion ordered spectroscopy. So what we are going to measure is diffusion. Diffusion by NMR spectroscopy and that is why it is called diffusion ordered spectroscopy. So diffusion is a natural process that happens for all the molecules that are in solution and that diffusion can be measured by NMR spectroscopy and there are some dedicated pulse sequence for measuring the diffusion and then we can like there are some problem associated with DOJI if the sequence overlap happens that but that can be edited and taken care of that. So what DOJI does essentially is correlate the diffusion in one dimension. So this is diffusivity D and chemical shift information in another dimension. So directly you are now detecting the chemical shift information and indirectly you are detecting the diffusion of a particular molecule. Therefore from each peak you can find it out how this molecule is diffusing if it is a mixture of the molecules. That is what actually DOJI does. That is why it is called diffusion ordered spectroscopy or NMR can be used to measure the diffusion of a molecule. So essentially suppose we have a mixture of molecules with a different molecular weight therefore we can get a different chemical shift like here you can see and in this dimension like indirect dimension F1 dimension is indirect dimension you have the parameter D. Now here if you look at the molecule like di-oleoglisal or another glycerol molecule or semi-thylate-olate molecule have different diffusion depending upon their shape and size and that can be very well correlated with the chemical shift of each of these moiety like here can be correlated with this. So now we know that these peaks belongs to semi-thylate-olate and their diffusion coefficient is somewhere around minus 9. So we can differentiate on the basis of their diffusion rate and chemical shift to find that what these molecules are and what all in a mixture of molecules in solution it has. And those molecules have a different diffusion than a solvent diffusion like benzene or toluene has. So let us see what actually diffusion is. So as we discussed diffusion is a natural process. So if say something is flowing through a box so say is going through B of a box of say 1 centimeter by 1 centimeter so and the flowing rate you define as a flux J. So the number of molecule that is transported per second is dn by dt. So the J will be dn by dt per area square. So 1 centimeter by 1 centimeter how many molecules per second passing that is called diffusion. So A is sampling area of the reference plane like this and the rate with which they are passing that will be called flux. So diffusion is basically this event of diffusing through particular area with some flux and the unit of diffusion is meter square per second or centimeter square per second. How many molecule are diffusing per like meter square per second. So in this area how many molecules are diffusion that is a diffusion. So and diffusion can be of different type. So the concentration gradient is driven by diffusion. So suppose here in the same box here you have a concentrated molecule and with certain time t if you leave it then it will diffuse through whole volume. So diffusion of these molecules generally follows the fixed law which is like here the flux diffusivity d and change in the concentration of the molecule dn by dt is this terminology. So that result into net flux flow of the molecule from the concentrated to the diluted and this is generally driven by say thermal energy. If you say it is just simple example if you take a pinch of salt put in the water it diffuses through the water that is what is diffusion. So there are different kind of diffusion translational diffusion like just diffused by itself in linear dimension then there are rotational diffusion how the molecules rotate and then diffuse. So the most common one is translational diffusion and that is typically measured using NMR. So this diffusion basically can be measured translational diffusion we can measure and the molecules are randomly translating in the solution and that can be measured by something called like a gradient. So this diffusion to happen you do not need any gradient but to measure it in NMR you need gradient of the magnetic field that I am going to come how we are going to use it and basically this random fluctuation happens by the thermal energy of the molecule how they are getting dispersed in the solution. So how we measure diffusion by NMR spectroscopy that is I am going to discuss now. So if you look at other than NMR spectroscopy typically for shape and size of a molecule there are various technique that people use like say fluorescence correlation spectroscopy. This is also a technique where diffusion of the molecule is measured so fluorescence correlation spectroscopy in a small focal volume how the molecule diffuses at that small focal volume and it autocorrelates. So you plot a autocorrelation signal or function of a molecule that diffuses through the focal volume and that gives an idea about the shape and size of a molecule. The other one is by analytical ultracentrifugation it is commonly used in many labs or many companies to find it out the shape and size of a molecule. Suppose a molecule is aggregating 1 percent so you can find it out by analytical centrifugation that what is the fraction of those one what is the fraction of those aggregated sample. Then there is another technique called dynamic light scattering that is also commonly used for finding it out the size of the molecule. But those are different techniques many of them are the light based technique or the mass based like ultracentrifugation is the centrifugal force based technique. Here we are just going to exploit the concepts of NMR and then we can measure how the translational diffusion happens. So what we can measure is essentially translational diffusion and if we measure this translational diffusion we can measure like hydrodynamic radii of a molecule. So suppose this molecule is diffusing in solution and then we can measure what is the hydrodynamic R H hydrodynamic radii of this molecule. Smaller molecule can diffuse fast like you can simply say a small ball can float or can move in crowded environment fast and the bigger ball can move slow that is what actually it is. So if the diffusion coefficient is very well correlated with the hydrodynamic radii and in a moment we are going to look it how this is D and R H are correlated hydrodynamic radii and diffusivity. So using this diffusion based NMR technique one can measure the translational diffusion or diffusivity D and by measuring this D one can measure the hydrodynamic radii R H. So this technique in NMR called DOJI and actually it is useful for separation of signal of different component. Different component as we given the example of second slide. If say I have five small molecules that are mixed together I can do the diffusion experiment and we can find it out the signal coming from all these five molecules and how they are differently diffusing in solution. So signal can be separated based on their translational diffusion and also that can be correlated with the chemical shift of each of these individual components and that is how one can use it. So DOJI basically determines the mobility of the compound how fast or how slow they diffuse or they actually they have a translational diffusion in solution. But this diffusion rate of these molecules varies on basis of shape. So suppose a molecule is elongated. So its hydrodynamic radii is different and that is how that diffusion is different. So shape determines size determines smaller molecule can diffuse faster bigger molecule can diffuse slower. The another important temperature like as you said that translational diffusion depends upon the thermal energy. So if you increase temperature diffusion rate can change. Also viscosity in a like if the it is very viscous solvent then you have a viscosity is high then molecule can diffuse slowly if the viscosity is low it is a thinner solvent molecule can diffuse fast. So viscosity also plays an important role temperature plays an important role shape size of course plays an important role for diffusion. So D varies on all of these components but if suppose I keep temperature and viscosity is same then one can get an idea about shape and size of the molecule. So using this diffusivity or using doji experiment one can identify the component in a mixture based on this diffusion coefficient D. And of course if we can measure how they are diffusion and this can be diffusivity can be also used for binding of a small molecule to protein. In the last class we have looked at the line shape changes right and we have also looked the STD concepts we also looked at the T2 relaxation time changes and that is for line shape changes. Similarly diffusion can also change. So suppose a molecule is diffusing very fast diffusion is very fast translational diffusion. When it binds to macro molecule now its effective size increases and there its diffusion rate can change and then it is like it can diffuse very slowly compared to whatever it was doing. So actually it can also be used for binding of small molecule to a protein and suppose like you have a mixture of 4, 5 compound one of them which are more likely to bind to a macro molecule you can find it out by recording simple doji experiment that which is binder and which is non binder. Similar like concept that we had discussed in the last class. So diffusion actually takes account of Stoke and Stein relation and as we discussed it has a correlation with a diffusion constant D with hydrodynamic radii R. So RH which is hydrodynamic radius that will be K is Boltzmann constant KET is temperature and 6 pi eta is the viscosity and D is the diffusivity. So one can see this D and R are inversely correlated. So if the hydrodynamic radii is more that means diffusion value so RH is inversely proportional to D. If D is high that means R is low and if D is small R is more. So if we know this R and D so we can calculate the D from doji and therefore we can calculate the R H. Now by doing this one can study the solvation of a particular compound. So compound is getting solvated or not if it is solvated it is hydrodynamic radii can change it can become effectively become bigger molecule. You can study the hydrogen bonding. Suppose this molecule in one solvent or in normal case it is not hydrogen bonded but in some case it forms hydrogen bond. So it is effective side changes and then one can study that whether it is hydrogen bonding or not. You can also study the chelation and of course molecular shape and size of a molecule how they are diffusing in a particular solution. So same example now one can see it that these different molecules are diffusing differently. So here like a solvent diffusion is is around say 8.7 and if you increase size here the diffusivity is going to increase. So this is negative value. So one can see like this molecule has a higher diffusion rate than this molecule and therefore the different size and shape can be valid. Now this also can be used to simply understand the water in the cell right and outside cell. So you know cell can have two kind of water one water is here one water is here. So this is say cell and this is your water molecule. Now the water here can diffuse fast and water is because this water is compartmentalized. So its diffusion property will be restricted compared to this water. So now you can get by just taking cell and doing diffusion experiment you can get two diffusion rates one coming from the free water one coming from the cellular water and you can find it out which is the free water which is the cellular water looking at the diffusion rate. So now how these experiments are done in NMR. So we have studied this sequence called spin echo. You know that we apply a 90 degree pulse then we wait for some time apply 180 degree pulse and then you wait for some time and you form an echo right. So suppose we do some experiment and here we introduce an gradient pulse. So this is kind of a defaging gradient and this is called defaging gradient. So here we start with something like this and then with this time it will defage and then if you do not do anything of all the molecular diffusion perfectly fine it can be defaced. So after some time all can come in a phase like here this is the vector resultant vector. So if there is no diffusion all molecule can come here at the same time just like in spin echo ok. So no diffusion everything is diffusing together you get it. But if you have suppose mixture of compartment now everything is not diffusing together there is some difference and that you can do create a different field experience by the molecule by creating this gradient. So what essentially we do so say this is our homogeneous magnetic field B0 and then we are applying a gradient across the magnetic field. So here if you look at so gradient is in z direction. So gradient say in our typical case is 50 Gauss per cm like we are changing 50 Gauss per cm in z direction. So that means the Larmor frequency experienced by the molecule here and Larmor frequency experienced by the molecule here are going to be different. So here it will be B0 minus g into z like so Larmor frequency will be gamma B0 g minus z this is the gradient strength and it will be plus here. This is our NMR tube we are putting in the magnet we are applying a gradient with some time. Now molecule that experience gradient here and gradient here are going to be different. So if you leave it for time delay they are diffusing differently and then we leave it for time delay then we apply a reverse gradient. So the first gradient defases it then we wait for some time and then we apply a reverse gradient. So if there is no diffusion everything will come together here just with a reverse phase it will come here. But suppose molecules are diffusing so by diffusing you can say before gradient we have here after gradient it is here and then with time delay after reverse gradient so because of diffusion molecules are not coming in the phase so they are diffused little bit out of the phase. So the diffusion for each of this vector is different and that is what actually is captured in those experiments. So that means if the molecule have a different diffusion rate they will not come at the same position they will come at the different position and this inhomogeneity in the magnetic field along the height of the tube we are creating by applying the gradients. So magnetic field gradients which actually changes the magnetic field here and here therefore local magnetic field experience at these two points are different and now this molecule are diffusing therefore they come at the different position and that is what actually you measure by change in the intensity. So what how the experiments are done essentially? So essentially now we take a mixture of molecules and then we apply some sequence like this where we apply a 90 degree pulse and then we apply a gradient of duration delta and strength G and then there is a time tau here and then we have a 180 degree pulse to change the direction and then we have a refocusing gradient in a point and then we acquire. So this is called Schrodinger-Tanner pulse sequence for the doji experiment. So now two things to be to understood here now we are we are applying a gradient. Now gradient has a duration and it has a strength and then there is a time. So time of the delta here so if I go here this is the delta time. So three things needs to be strength of the gradient then time and the delta. So big delta small delta and the strength G three parameters has to be taken care and we apply the gradient. So now experimentally what we need to do we have to vary the gradient in different experiments. So how this experiment run? It runs as a pseudo 2D. We are going to change the gradient strength in each experiment. Experiment number one has a like one gradient strength experiment number two will be different, three will be different, fourth will be different. So we are going to change it and by changing it here we are measuring the intensity decay that is happening and that actually intensity decay follows this equation which is called Thetger-Tanner relation. So here i is the intensity at any particular gradient strength, i0 without any gradient strength and d is diffusivity this is the gyromagnetic ratio. These are G and small delta and big delta are those time duration that we and this is the gradient strength that we discussed. So if you fit this equation it will give us diffusivity. Now for experimental point we need a nice point so that it is like at a very low gradient we have intensity almost 100% and as we increase the gradient strength intensity should go down. So we have to make sure that curve comes like this. So this is the ideal case for this if the curve does not come out then we have to play around with this duration of the gradient pulse and the time delay. So this is in this case you have to increase these two parameter big delta and small delta in this case you have to decrease it and this is the ideal case. So now go back to again to pulse sequence here are these delta G and delta. Now as we said we are doing a pseudo 2D. So this is your T1 dimension and this is acquisition is 2 dimension. So you have pseudo 2D in one case it is just the gradient strength we are varying and here T2 is our chemical shift. So as I discussed the gradient strength is going to change we are going to change it from say 5% to 95%. So if we have a very less gradient you have almost highest in intensity and as we keep increasing this gradient strength your intensity decreases. And then you essentially you fit this intensity to the equation that is given here. So if you fit it and you can simplify this equation that I am going to come in a moment. If you fit this equation I by I0 you get the value of D. Now this is your diffusivity. Now once you get the diffusivity you can calculate the hydrodynamic radii by Stoke and Stein relation. Great. So the parameter to be understood is the small delta the gradient strength G and the big delta that big time delay. And we have to monitor the decay in the intensity that comes up to 95%. And the pulse sequence that we are going to do is this we are 90 degree X pulse we are applying first. Then we are encoding here in 0 to D dimension then we are applying a gradient strength of duration say small delta and strength G then this we are going to vary then we are have a refocusing 180 degree pulse. And then here we are applying a refocusing gradient and acquiring it. This is the relation that we are fitting the intensity decay. So now let us see how experimental data comes. So here suppose I take a proton so a proton spectrum for a protein we know that this is amide proton this is the sidechain proton. We record two experiments just to see how much signal has decay. So if we start with a 5% gradient we have high intensity and if we apply again 95% gradient just two experiment I did one where intensity decay whatever is at 5% gradient one at 95%. You can see intensity has decreased drastically for the amide proton. So that means my parameter seems to be okay. If the intensity has not decreased it was something like this then I need to play around with each of them to make at the lower one. If I do that then essentially I should get an ideal curve for fitting this equation. So that means 95% should be more or less here and 5% should be more or less here. If we have this kind of a curve that is an ideal decay for measuring the diffusivity then one can fit it. So in these two case it is a non-ideal case. So even if you fit it you get a wrong value so essentially we need to get this kind of curve. This is correct this is wrong. So we need to play around with small delta and big delta value. So now we are playing around with big delta and small delta to get this nice fitting curve. Then we are measuring the intensity i observed intensity and i0 is a reference intensity where we have not done anything. So now if you fit it you get and diffusivity. As we discussed gamma is gyromagnetic ratio of the observed nuclei, g is the gradient strength, delta is the length of gradient and D is the diffusion time that we are giving. So here the time that we are giving here is D. That is the diffusion time. Now how much it is diffusing? So if you do that now you can fit this equation and this equation as I said this Seigl-Tanner equation can be simplified. So how you can simplify? Gamma is constant and g we are keeping it like 5% to 95%. So typical say gradient strength for a spectrometer is 50 Gauss per cm. So you can include that value and then your delta you are keeping diffusion time some constant like 120 millisecond or so. Then here also you can vary it out. So if you fit it you can essentially you need to fit this equation which can be easily fitted q is a constant term and by fitting it one can determine the D value which comes from this curve fitting. So nowadays actually many software does it but you can write and MATLAB code for fitting this equation. So if you do that here is a mixture of say three compound that we have now. Say one we have a caffeine, one we have a glycol and one have a D2O. We recorded 1D spectrum. So here is your water signal, water H2O D2O. This is your glycol signal and these three are coming from caffeine but a priori we do not know which is signal coming from which because this is a mixture of compound. Now we recorded a diffusion experiment and we found that caffeine is diffusion different than glycol and which is diffusion different than the D2O. So you can find it out the caffeine is here because we have a free signal and also its diffusion is higher than the glycol than the water. So here one can separate this compound not physically separate but spectroscopically we can separate the caffeine glycol and D2O by recording doji experiment. So now I will come to little bigger molecule. Suppose I have a protein what we can do. So I have I am showing you here three experiment. Alpha-synuclein is a natively unstructured protein of 140 amino acid. So natively unstructured means a long chain. Then we have a ubiquitin. This is 76 amino acid long glodular protein and we have alizohyne which is also a little bigger than the ubiquitin. So if you record similar kind of experiment here I am showing you for ubiquitin you can see here I am varying the gradient strength. So this parameter is varied from 5 percent to 95 percent and therefore say less than 5 goss per cm to almost 46 goss per cm and here is the normalized intensity. So here very less 5 percent gradient strength here 95 percent gradient strength you have a nice curve. Now I fitted that equation Tanner equation and one can find it out that the hydrodynamic radii of say ubiquitin is approximately 2 nanometer. Lysohyne is little big but if you look at the alpha-synuclein. Alpha-synuclein as I discuss it is intrinsically disorder protein of not too big size like it is certainly twice of size of this ubiquitin this is 76 this is 140. But since it is disorder its hydrodynamic radii is quite a bit like 3.5 or so nanometer because this is disorder. So hydrodynamic radii it is a it is a like little open chain it is not completely disorder but it is a intrinsically disorder. So it is hydrodynamic radii is more than ubiquitin and lysohyne just by recording dynamic hydrodynamic radii or diffusion experiment we now guess the shape and size of a molecule. This I was knowing to so just I have taken a known molecule to show you but you can take unknown molecule and guess about the shape and size of a biomolecule. So essentially these are the data we recorded at different pH of lysohyne and synuclein and one can find it out all of them fit nicely and you can then translate that to hydrodynamic radii of the molecule. So if you have a diffusion rate so you can use this Stokes Einstein relation and then one can find it out this R and that is what I represent here the hydrodynamic radii. So another example I am just taking a small molecule. A small molecule its diffusion is calculated by doji and you get an hydrodynamic radii by putting like all those parameters. So your diffusion rate comes 1.58 into 10 to the power minus 10 meter square per second square. So hydrodynamic radii translates to 1.7 high and if you convert to diameter by just measuring in pymol you get 3.2. So this is very well correlated with the diameter that is measured from the experiment. You see this molecule is solvated therefore some bigger hydrodynamic radii is coming because this molecule is not bare there are water molecules around it. So if you take a diameter that comes 3.5 and here we are getting very well correlation just by measuring from here to here is 3.02 nanometer. Great so that is what I give you a brief background how you can use diffusion based concept to measure the hydrodynamic radii of a molecule using this NMR technique. So it is little bit different we have to introduce the gradient here and one can measure in pseudo 2D manner where one dimension is your diffusion rate, another diffusivity another dimension is chemical shift. So one can measure it and I showed you few example of protein molecule similar thing can be done even for the chemical macromolecule one can measure it. So I hope you understood and you got the idea of shape and size of molecule measurement by NMR. So at the end I would like to thank you and all those things that we discussed are related to this big magnet and big technology of this beautiful technology called nuclear magnetic resonance. So as a curious student you have to stand in front of the magnet with the sample here and you can do a structure one can do dynamics you can get a shape and size you can do lots of bio-pharma study you can do chemical pharma study this will this technique is going to open a many a venue for you in future. So I hope this course was useful for you for depth we will try to float again new course where we discuss about protein and peptide NMR and let us see when we can do that. Thank you very much for being part of this course looking forward to see you and perform well in your exam. Thank you very much.