 So, we will continue the discussion with protein folding and to introduce this protein folding phenomenon. So, I have here a particular example, we will deal with this particular protein called sumo. This is a small ubiquitin modifier protein is called sumo and what is shown here is the so called folding funnel or it is energy landscape of the protein of the protein in a sense. What are the things which are, it is very important to understand this picture. What are the things which are present here? This bottom portion represents here, this is the native protein which is very well folded and on this axis we have the energy of the system and what is on the surface here, this is the model which is called as the funnel model. What is here is the unfolded state of the protein and the unfolded state, you see the funnel is very broad on the top. What does it mean? What does it indicate? It indicates a different degree of freedom. This is the conformational heterogeneity is quite a lot. So that is all represented by the width of this funnel. So this is so wide here, there are trillions of conformations for any particular protein. See how many conformations are possible for a particular amino acid. Let us say I have a 100 amino acid residue protein, 100 amino acids and each amino acid 2 degrees of freedom the phi and psi, phi psi 2 torsion angles and each amino acid can take this any of these combinations of this. Therefore how many degrees of freedom will be there 2 to the power 100, each amino acid has 2 degrees, 2 degrees of freedom. So the 2 to the power 100 conformations are possible for this particular protein 100 amino acid residue protein and the proteins in general fold relatively faster if the system has to scan through all these conformational degrees of freedom, how long it will take, it will take the age of the universe. 2 to the power 100 conformations if it has to scan through the system has to scan through and then finally reach a particular folded state that is an enormous amount of time. But nonetheless we do see that the proteins fold in much smaller time scales, sometimes minutes, sometimes seconds, sometimes hours, so on and so forth. So this was actually called as the Leventhal's paradox, how does the protein fold, how does it scan through the conformational space and reach to the particular ground state or the lowest energy state, does it pass through the entire energy landscape, this is the landscape energy landscape of the protein. So here on the funnel on the top of the funnel you have this trillions of conformations which are possible, they are all interconverting very rapidly and if it has to fold the system has to fold it has to go down the funnel, losing the degrees of freedom slowly as it starts to fold, some degrees of freedom are satisfied and some degrees of freedom remain and eventually it has to reach here but the path it can take from this point to this point or this point to this point can be very different. So there can be multiple paths for the folding, multiple paths for folding because it has to eventually reach the same native state because the native state is supposed to be very, very narrow, it does not have too many do many conformations, it is one conformation. So we know that that is what is called as the folded protein and this is the one which is responsible for the varieties of functions of the protein and we try to understand that. Now as it is going down here, as the protein is going down it can have different paths. So if I want to plot here the energies of this, suppose I have an unfolded state with a certain energy here which is high energy and if it has to go to the folded state it has to come down to the folded state here, this is the folded state let us say, this is the folded state energy, this is unfolded, does it come directly here like this or does it come like this, like this and like this and these are the various barriers and at every step there can be, there can be kinetic process is operating which is the one which is going faster. If the barrier is very high then actually the protein may get stuck in any of these minimum here, there can be a local minimum here, a local minimum here then if it gets stuck here is not able to come out of this minimum then of course it will reach what is called as the misfolded state. So the system will have to come out because of such kind of situation that is what is schematically indicated here, there are various barriers indicated here and therefore there are local minima, there are many local minima present in this folding funnel. So depending upon that so the particular amino acid can fold go over this, this applies to every amino acid residue because of the folding has to happen for all the amino acid residues, the system has to, is there a cooperativity in this? If there is a amino acid residue which is folding does it induce the next amino acid to fold in a particular manner, so is there a cooperativity in that? What is the energy landscape? For every amino acid residue to go down the funnel, go down the funnel and come down here. So these are the various intermediate states that can happen, there can be an intermediate state, an intermediate state here eventually it will have to pass through different intermediate states and finally reach a particular folded state. If it is able to reach one particular folded state then we say it has the unique pathway and all the molecules are coming down to this but if a particular segment is such that it is not able to come down to this state, gets trapped somewhere here then you generate a so called misfolded state and this misfolded states can deal to all kinds of problems, they can aggregate and they can lead to different diseases and things like that. So to understand the folding process is quite an important thing to do. Now so how do we do this, we have to create certain situations like this, how do we understand what is the state of the protein at somewhere at the intermediate level here, ideally one can do it in a kinetic manner but the kinetic manner to do that is you do not have the tools for doing so appropriately at the residue level but we can actually do the equilibrium states. Equilibrium states because these also represent the confirmation, equilibrium confirmations are also sampled by this process and it is going down. What are the equilibrium states that are present at this, if it passes through here I create a situation that the protein gets trapped somewhere here in this some of these ones. The various equilibrium states I can create at different stages of the folding as it comes down from here to here I can trap the thing at different stages and these ones by doing artificially certain kind of denaturants. So this is what can be done by using the denaturants. By controlling the denaturant concentration you can create intermediate equilibrium states they may not necessarily be the kinetic intermediate states but they can be the equilibrium intermediate states the protein will possibly flow go through some of those states as well when it has to reach finally these states different segments because you notice here the different parts of the unfolded states can fold 2 different pathways here to reach the final folded state. How do we do this? This is what is indicated here this is a strategy you actually denature the protein first of all we have to create this unfolded state. So you denature the protein artificially by adding 8 molar urea. Notice here when you denature the protein the chemical shift dispersion on the amide proton these are HSQC spectra amide proton here and this is the N15 chemical shift here and you are plotting here the HSQC spectra at a different urea concentrations this is 8 molar urea, 7 molar urea, 6 molar urea, 5, 4, 3, 2, 1 and 0 this is the final folded state that corresponds to this state here and this corresponds to this state here and notice here the chemical shift dispersion is very, very small and that is indicated so 8.0 to 8.6 only 0.5 to 0.6 ppm is a dispersion here that is why these peaks are looking quite broad in this area you compare that with the situation here this is 7 ppm to 10 ppm this is 3 ppm whereas this is only 0.6 ppm 0.5 to 0.6 ppm. And therefore the peaks are looking quite bigger here and that is just the because of the scales. So 8 molar urea you have this very narrow chemical shift dispersion here the N15 dispersion is of course good but now you see we had these tools which we discussed last time with regard to handling unfolded proteins the IDPs intrinsically disorder proteins or unfolded proteins so there you can use this HNN, HNC and spectra to assign the individual peaks. Now you have to assign the individual peaks in every spectra because there can be differences here in the chemical shifts depending upon what the 8 molar urea is doing because the urea goes and interacts with the backbone of the protein therefore there can be differences in the chemical shifts you will have to identify individual residues in each condition. What is changing from here to here? What is changing from here to here the chemical shifts will change intensities will change the relaxation properties will change as you go from down the funnel like this as you go down as I said the number of degrees of freedom will start decreasing as you go down here you have the maximum degrees of freedom as you start folding some degrees some structures that are getting formed which will restrict the degrees of freedom therefore the number of degrees of freedom will start going down as you go down the funnel here. So, therefore if as you move down the funnel here so you have the peaks some structures are getting formed some areas are getting mobile and that can be seen by the relaxation properties of the individual nuclei I mean I said residues. So, let us see what is it we get in this how do we measure the structural changes that are happening as we are going down the funnel of the protein. Here is one particular parameter which is extremely useful that is known as the secondary chemical shifts. You know that in the particular protein the chemical shift indicates the environment around the particular nucleus if the protein is folded it has a particular kind of an environment if it is unfolded completely random coil it has a different environment and the random coil is more like an individual amino acid residue individual amino acid residue does not have any structure therefore the random coil confirmation can be taken as the individual amino acid residue. So, if there is a chemical shift which is different from the random coil chemical shift it indicates a certain degree of structure around this particular amino acid residue for any particular nucleus if you are monitoring it shows a certain amount of restriction or the confirmation preference around the particular residue. So, you define a what is called as the secondary chemical shift delta S which is delta observed minus the delta random coil. This random coil is basically an individual amino acid residue here of course the neighboring residues also will have an influence. So, typically one generates a table for it every particular amino acid residue keeping different neighbors and you get a certain kind of a near neighbor effect etc all of that put together you generate a random coil chemical shift for a particular amino acid residue you add corrections for all those neighboring effects. Now and what are the nuclei one can monitor you can monitor whatever are the nuclei possible for you can monitor the N15s and you can monitor the amide protons you can monitor the C alphas H alpha CO and I have shown here a few of those here typically these are the ones which are more sensitive to the secondary structures of the amino acid residues. So, here you have the C alpha and the H alpha and CO these are now because you have these chemical shifts one has to obtain I showed you earlier the N15 proton HSQC spectra but that alone is not enough that will only give you the N15 proton chemical shifts having obtained those N15 proton amide proton chemical shifts you will have to also carry out other experiments which we discussed earlier like the HNCA CB, HNCO, HNCA all of these experiments one has to carry out to obtain the C alpha H alpha and CO chemical shifts all of those. Now is there a trend in this for particular secondary structures yes there is a trend here now if you plot here if you look at the secondary shifts for an alpha helical structure if there is a propensity so in a denatured state there is no regular structure but there can be a propensity what does the propensity meaning it has a higher probability of obtaining a particular kind of a structure it will not be permanently there it forms and goes forms and goes forms and goes so that is what is called as the propensity is certain propensity for a helical structure. So, if we have that sort of a situation there what will be the secondary shifts the observed chemical shift minus the random coil shifts for the C alpha this secondary shift will be positive the carbonyl also it will be positive but the H alpha will be negative. So, if a particular amino acid residues has a propensity to be in a alpha helical conformation then you have this combination of chemical of secondary shifts whereas if the same amino acid residues has the propensity to be in the beta sheet structure or the extended beta structure is completely the opposite. You have the C alpha will be negative H alpha will be positive and carbonyl will be negative. So, this kind of chemical shift changes you will observe in your experimental spectrum for all of these. We will illustrate this for the sumo protein and what are the secondary shifts which are plotted here is in illustration we have done that for various with along with the other nuclei as well C alpha and CO what is shown here is for the H alpha H alpha these are the secondary shifts. So, now notice here the at 8 molar urea this is the structure of the folded protein shown on the top here this has a long tail and terminal which is unstructured you have a beta sheet a beta sheet the helix small beta sheets beta sheet helix and a beta sheet again this is the sort of a structure which is present in this. Now in 8 molar urea what sort of a preferences do you have these are all positive. So, most of these are positive here most of this H alpha H alpha secondary shift these are all positive and what does that indicate what does that indicate that indicates that you have a beta sheet propensity. So, most residues prefer to be in an extended conformation like in a beta sheet like in a beta sheet at 8 molar urea. So, this is indicated by this here these ones indicate this small rectangles here these are the areas you can see continuously a range of 4-5 residues if you find then you draw a kind of a bar here. So, that can be with all beta sheet structure. Now this is the beta sheet structure this is not present in the native protein here this is extended and here you have a beta sheet structure once more then you have the beta sheet structure this is present in the native protein beta sheet structure this is present in the native protein partly here and all over the place where there is a helix here you do not find any helical propensity there you have a beta a sheet propensity again very small region and other regions you have the beta sheet everywhere beta sheet where there is a helix you are not seeing the helical propensity there. Now you decrease the urea concentration go down to 8 molar sorry from 8 molar you go down to 7 molar. Now you see the changes that are happening here see these all these with the big positive slowly there is a decrease there is a decrease in the positive values and this remains everywhere there is a small decrease in the positive values of these secondary shifts. So now you go to 6 molar 6 molar here while the decrease in the positive value continues to happen you start seeing some little bit of a stretch of helix here a stretch of a helix here therefore indicate that as a helix here little bit of the helix is getting formed here but rest of it is still beta although the propensity has decreased is decreased there is a change happening there is a change happening in the structure but the propensity is still there because we said this is the probability this is the probability at every amino acid residue what is plotted is against the probability. So now you see there is a small helix getting formed here okay go to 5 molar urea now you see a small helix getting formed here to a small helix getting formed here to this continues and these numbers have decreased again compared to this these numbers have decreased again okay. Now you come from this to 4 molar urea this is the same this has decreased this is the same and this has vanished this was about 4 5 residue is long here and that is that is vanished this is gone is not so much there and you come down to 3 molar urea most of these helices are gone is all negative all small small small things there no structural preference it appears there is no structural preference at all here the propensities are not there what does it indicate the initially when we went from 8 molar down to 3 molar go slowly the initial extended structure propensity was there this started decreasing and some helices were getting formed so one helix here and then 3 helical propensity is not that this these helices are not permanently stable they are there they are propensity we are talking about the propensity that is it is being formed and getting broken formed and broken formed and broken that is the way it is happening and therefore we reach a stage when we come to 3 molar urea so all these structural propensities which are there these ones have gone okay what does it indicate this is shown in the next slide here so here you can see this is the very dynamic 8 molar urea state dynamic 8 molar urea state and we come down to 7 molar urea what is the color change here this color change is the change in the dynamicity in the protein there is a change in the relaxation properties why does it happen because some constraints some structures are getting formed because of that the dynamics in the protein is getting reduced okay it is not as flexible as it was in this case here so as you go down to the 6 molar you saw a formation of a helix here and the dynamics is reduced further and it is see it is going all the way until here also the dynamics is getting reduced because because some as you as you form some structures it reduces certain constraints for the protein to follow therefore that will reduce the dynamics in the protein this will get reflected in the relaxation properties especially the r2 values which we have not shown here here but this information comes from the relaxation measurements so you have this reduction in the dynamics as you go down in this here so from high frequency dynamics you come down to low frequency dynamics because it is constrained and the motions are getting constrained low so that is millisecond you come down to the microsecond to millisecond time scale r2 values go up okay now you go to 5 molar here as I shown you you got 3 helices formed 3 helices formed and the constraints are still there the motions are reduced as more and more structures are getting formed protein is getting more and more restricted with regard to the motions and that will be reflected in this other portions of the protein as well because it is continuously changing the protein is continuously changing you go to 4 molar see this helix has disappeared as I indicated there in the previous one this helix has disappeared and you have these 2 helices are still there and this one is still there but overall the motions are constrained that this there is a dynamic is getting changed and now you come to the 3 molar everything has vanished everything is vanished why is it so and this is very important why is it so because now if I look at these residues where there is a on the basis of the relaxation measurements it turns out that these are protein is undergoing a certain kind of a dynamics which will eventually lead it to the proper folded state what is the folded state that is here this is the folded state okay this are the original 0 molar and the 1 molar structure is here because it has to form so many beta sheets here it has to form so many beta sheets and then it has to form this helices at these 2 points but in none of these states these helices are there and none of these states you have these beta sheets permanently formed therefore the protein has to change from these states into this state so therefore what we call these as the non-native contacts these are the non-native contacts initially the protein when we went it went through a kinetic process of preferential structure adaptation and then it forms certain structures which are kinetically favorable therefore it formed some non-covalent non-native contacts non-native contacts and these non-native contacts will have to be removed so for that purpose the protein got prepared into a this state where this all these non-native contacts have been removed okay now it is all set it is all set to fold into a state where it is more like a native protein so when you go from 3 molar to 1 molar so you see start seeing some data sheet formed here some helices formed here and these are the native contacts and that you can see here as well in the in this spectra so in this spectra you see from from 3 molar already you saw when you come to the 2 molar the spectral dispersion is increased the spectral dispersion has already compared to this spectral dispersion is was only 0.4 ppm the spectral dispersion is increased quite a lot here you see these ones are small tiny dots and this is and even more increase better the peaks are becoming even more sharper and you are starting a greater dispersion along the amide proton chemical shifts okay and then you come to 0 molar therefore it is all clean beautiful spectrum every peak is separated and the spectral range has gone from 7 ppm to 10 ppm and that is what you can see as the structure is getting formed so here you see that sort of a thing happening at this point so the structure is getting formed at 1 molar beta sheets are formed and the beta sheets typically have a wider spectral dispersion compared to the alpha helices alpha helices are typically within the small range of 8.0 to 8.5 ppm whereas the beta sheet goes all the way to 9.5 to 10 ppm and that we saw in the in the HHSQC spectra as well and this is reflected in this changes in the dynamics in the protein and the secondary shifts and the helical propensities formed in the protein as we are going down the funnel from here to here and remember these are all average effects these are not one particular molecule but these are average effects we are talking about the propensities when you say propensities is the average effect so therefore on the average you have no structural propensities at this point and then you go to the 1 molar you have the propensity increase now they are stable structures getting formed when the stable structures are there you have clean chemical shift dispersion and you have a wide range of chemical shifts reflecting the beta structure formation and then of course when you go to 0 molar you have the proper helices formed the beta sheets formed and this is how the protein is getting formed therefore what is the message from here the message is the proteins when they fold they follow a kinetic pathway and they do not necessarily go through the native contacts it is not that these structures are getting formed straight away as the protein starts to fold protein these helices are not getting formed straight away as the protein starts to fold you provide these conditions for folding it does not necessarily go to these states these states it goes through whatever is feasible in the kinetic pathway so these ones are feasible in the kinetic pathway and therefore they form helices here but these are not the helices that have to be there but as you provide further and further folding conditions these conditions these are not the most stable states so therefore these are temporarily formed and as you are getting providing better folding conditions these eventually these non-native contacts will have to be removed and these ones are getting removed system is prepared and you see there is exchange rates appear there in this situation there are residues which come close and go close and go close and go like this when it is happening the ones regions which are coming close by they are making contacts you will see larger changes in the relaxation rates there the intermediate exchange will increase it is reflected in the R2 values and that indicating that those contacts are similar to what are present in this state therefore the the relaxation data there was indicating that these structures are getting formed because we saw changes in the properties relaxation properties of the molecule indicating that the such a structure is getting formed so once one this is formed then of course you go to the completely go to zero molar you have this sort of a structure which is formed so this is how you can study the protein folding phenomenon by following the equilibrium transitions there so these represent the changes that are happening down the funnel and it can it is an average effect every residue can follow different pathways but of course in every molecule every molecule you have this changes happening in different ways but what you see is the ensemble average on the ensemble average what you are seeing is what is reflected in this way so this is this is the great application of NMR for studying the folding protein folding phenomena in this in any particular protein this is a small example but of course one can do this for larger proteins as well now okay so I think this is we will go into the next class with NMR of large proteins and assemblies and this possibility of studying unfolded states allows us to study aggregation phenomena in proteins I think we will stop here we will take up this in the next class