Abstract
Currently, the description of chemical and biochemical phenomena is heavily based on the conception of a molecular “structure”, i. e. of a rigid arrangement of atoms in space, defining the conformation of a molecule. This view matches our limited means of representation and visualization with pen and pencil. Chemical reactions are conceived as instantaneous conversions of an initial into a final structure, occurring with a certain probability per unit time. Molecules are imagined to hop from one minimum to another on the potential-energy hypersurface.
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Discussion
Alfred Redfield - I have two questions. Your work cries out for comparison with perhaps among other things solid state NMR studies of frozen glasses or something like that which I guess is easier said than done. Do you think solid-state studies in frozen solutions could confirm your conclusions in any way? Would you like to express an opinion about such studies?
Richard Ernst - Yes. Being interested in peptide dynamics, I would be interested in investigating antamanide also in the solid state. Of course one has to expect an effect from the solid environment but still it would be very interesting to see what actually happens in the solid state. We started to do some experiments but they are by no means conclusive yet.
Redfield - What about going to low temperatures and just seeing if there are two species or would you not be able to see it?
Ernst - No, you can’t freeze these motions. You can’t get down enough in temperature. The processes are too fast. You can see some line broadening but you cannot really go below the coalescence point.
Redfield - The other question was that if I understand it correctly, which I may not, the relaxation studies you described have to do with the diagonal elements of the density matrix and I wondered if that understanding is correct.
Ernst - Yes.
Redfield - Have you considered off-diagonal elements i.e. T2 processes. Ernst - For cross relaxation, I obviously concentrated on the diagonal elements - on the Iz and IzSz term. But of course there is also some relaxation of the off-diagonal elements which we considered in some T2 and T1p relaxation measurements. The rf dependence of T1p proved to be particularly revealing. One could still do a more complete investigation.
There is still room for that.
Redfield - Thank you.
B. D. Nageswara Rao - Several people are using the so-called model free approach of Attila Szabo in deriving this internal motion information using order parameters and the like. On the basis of your detailed analysis using molecular dynamics and so on would you care to comment upon how your results would compare with a model free approach type of fitting the data.
Ernst - I think it’s certainly a valid approach to determine Lipari and Szabo parameters and then in a second step to interpret these parameters in terms of a model. This is essentially equally good. If you know which models you would like to compare, then you can do it directly. If you like to remain model free from the beginning then you better do it via Lipari Szabo parameters. That’s a little bit a matter of taste. If one interprets the data in terms of a particular model, then it doesn’t make much difference whether one does it in one step or two steps. The significance of comparison of two models is just given by the measurement errors which propagate through the two-step procedure as well. So both approaches are feasible.
Rao - Do you think you will reach the same conclusions?
Ernst - If you go down to specific models, yes. Of course you can’t just remain with the Lipari and Szabo parameters and say that’s what you want to publish and not say something about specific models, that’s up to you. But if you want to speak about specific models, then it’s equivalent.
Marc Adler - In terms of broad design, multiple conformations are often frowned upon because the theory is that there is only one conformation that binds to the enzyme. Therefore, the loss of entropy upon binding is not a disfavorable thing. Now, I was wondering with your molecule whether you might design methyl groups into it to freeze out the proline ring flipping and see if that was a more potent molecule.
Ernst - Yes, I think that’s exactly the type of information one would like to get if one does this type of dynamics studies in order to understand what is going on in a binding process, and how important dynamics of a flexible molecule is. If one understands this, one can start to tailor a molecule to a particular application. I think that’s the final philosophy behind it. Of course, we don’t go as far as that because we are biologically innocent.
Carol Post - About the prolines, there are two states for two prolines and one state for two of the other four prolines. What makes the two that are dynamic, different? Did you have any ideas about any coupling of that motion to conformational transitions?
Ernst - Yes. What we have done for example is to very slightly restrict the backbone angles in our peptide and then suddenly all the four prolines started to pucker. So it has to do with the conformation of the backbone and there is a slight asymmetry in the molecule. The molecule is almost symmetric but the asymmetry induces sufficient strain to hinder the puckering of two of the prolines. Of course, to understand this in simple terms is difficult. It’s just a complicated system. There is a lot of interactions but after all it has to do with the conformation of the backbone which restricts the possibility of motion of the sidechain.
Post - And then a point of clarification about the same system. From NMR you measured the correlation time for the jump between the two states of 40 ps and you showed CHARMm gave something a little bit shorter, more dynamic and you also had a correlation time for the other two that were not dynamic.
Ernst - Of course, there is also fast motion going on, local motion within one energy minimum, this means fluctuations about the equilibrium position with correspondingly short correlation times. But this is not really conformational motion.
Post - Were those numbers obtained from some proton-proton vector in the computation?Ernst - There is a small-angle motion which is very rapid. The parameters are lumpedtogether in the same table. They don’t refer to the same process.You are correct. Oneshouldn’t do that.
Maurice Guéron - I might have misunderstood about the computations. You showed thatyou were getting effects which were fitted with a given correlation time for the wholemolecule and then a longer correlation time for rotation of the phenylalanine, I think it was’ζ 2 • In both cases these motions are affecting the dipolar interaction if I am not mistaken.Now if you have a fast ’ζ c with isotropic or nearly isotropic motion affecting the dipolarrelaxation, how can you detect anything which corresponds to slower modulation of thedipolar interaction?
Ernst - It depends on how much slower the intramolecular motion is. If it is within the same order of magnitude, within a factor of 10 smaller or larger, then it will still affect the relaxation. Even for anisotropic motion of the whole molecule the sensitivity to these processes might not be great. One has to do a lot of measurements. But there are weak influences.
Bernard Brooks - In the analysis of models of X l and X 2 distributions for the phenyl alanines, looking at the various models, did you try looking at the distributions of the states obtained from molecular dynamics and see if that has any improvement or does it give you any differences in the simpler model?
Ernst - Molecular dynamics simulations are very difficult to apply in this case since the motions are relatively slow, especially the X 2 motion where the correlation times are about 1000 ps or so. One has to perform enormously long computations to get any reliable results, and we didn’t do that. We were investigating the potential energy surface to see if it is compatible. But to obtain real sidechain dynamics from molecular dynamics is very difficult as one has to calculate way up into the nanoseconds, 100 ns or so to get reliable results. So that is the limitation at the moment. Yuan Xu - I have two questions. The first one is about the multiple conformations. For instance, in this molecule you have multiple conformations, so you see the several conformations. and put those that contribute together. In doing so, the experimental data can be better explained than a single conformation. So in this case how did you determine the contribution for eac~ individual conformation. For the proline, one contributes 40% and the other one contributes 50%, so could you explain how this was done?
Ernst - It’s very simple in principle. You just have a fit parameter which is the relative population of the two conformations and you vary this fit parameter till you find the best fit. The only question is that how sensitive are the results to this fit parameter. We found that for proline 3 and proline 8, when we added the second conformation in order to try to make the fit better, the second conformation contributed only about 5-10% which is hardly a significant contribution. So we just concluded that the residue is rigid and the second conformation can be ignored. But of course, there is a certain error in this population and we don’t want to say much more than either the equilibrium is much on one side or it is approximately in the middle.
Xu -What happens if you have more conformations to put together and more parameters to vary?
Ernst - From the fitting, one cannot decide whether there are even more conformations present. So we also performed some MD computer simulations. All the computations which we have done using different MD programs invariably gave us two rigid conformations, two well defined conformations which did not differ much between the different programs. Only the timescale of interconversion was a little different due to the different force fields.
Xu - My second question is when you investigate the multiple conformations using the molecular dynamics approach, is that as good as molecular dynamics if you use Monte Carlo simulations to investigate the multiple conformations?
Ernst - We did some Monte Carlo simulations as well. One obtains similar results.
Yuan Xu - So the two approaches are pretty much the same.
Ernst - Yes.
Xu - Thank you.
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Ernst, R.R. et al. (1996). Intramolecular Dynamics of Biomolecules, Possibilities and Limitations of NMR. In: Rao, B.D.N., Kemple, M.D. (eds) NMR as a Structural Tool for Macromolecules. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0387-9_2
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