Exploring the conformational heterogeneity of biomolecules: theory and experiments

The atomic constituents of matter move continuously. Irrespective of the physical state, their kinetic energy is of the order of kT, which amounts to about 3 kJ mol⁻¹ at room temperature. Besides local motions, which always occur, biomolecules in solution can sample many different conformations, which can even be largely different from one another, provided these conformations have comparable energies and the energetic barriers among them for the interconversion are not much higher than kT. Intrinsically disordered proteins (IDPs) are the most striking example. For IDPs the very term “structure” is meaningless. Multidomain proteins may be constituted by well-structured domains but, if the domains are connected by flexible linkers, their reciprocal spatial arrangement may be as undetermined as the spatial arrangement of the individual residues in IDPs. Even single-domain, globular proteins can undergo large movements of secondary structure elements, leading to two or more conformers whose structures may differ significantly. Obviously, this dynamic behavior may greatly affect the function in vivo. Nucleic acids, both DNA and RNA, behave similarly, and it is still largely unknown how their conformational heterogeneity may vitally affect transcription and translation processes.

The structural determination of biomolecules in a crystalline form, almost by definition, provides a picture of only one or very few, usually similar, of the possible conformations. It is true that there are more and more examples of different structures of the same biomolecule, obtained under different crystallization conditions, which trap different conformers and thus reveal the presence of possible conformational heterogeneity. However, there is no direct link between the conformational heterogeneity suggested by a few different X-ray structures and the conformational space which is actually sampled by the same molecule in solution.

Solution techniques, mainly NMR but also SAXS, EPR and FRET, contain information on the conformational space sampled by the biomolecule, but the information is always a time-averaged or a space-averaged one. Therefore, no matter how many experimental datasets can be collected for a single system, there will never be enough information to describe analytically all the individual conformations that the system can assume. In mathematical terms, such a situation is known as an ill-posed inverse problem. In practice, from a given conformation one can predict the experimental data related to it; likewise, for a given ensemble of conformations one can predict the experimental data related to each of them, and therefore also their average (direct problem). However, from average data one cannot unequivocally reconstruct the ensemble of conformations that produced it (inverse problem), as there are an infinite number of different ensembles that are equally able to produce the same average data, and therefore the inverse problem is ill-posed.

Does this mean that one cannot hope to obtain any kind of information on systems that undergo conformational averaging? We can make a loose analogy with the uncertainty principle, which tells us that deterministic information on the motions and trajectories of electrons in atoms cannot be obtained. Yet, we also know that we can obtain electronic energy levels, probabilities of finding electrons in different regions of space, and the shapes of these regions, without violating the uncertainty principle. Also, in our case meaningful information on conformational space can be looked for and can be obtained, provided the intrinsic limitations in the achievable information content are clearly appreciated by the authors and correctly transmitted to the readers.

Extracting information from conformationally disordered systems is the central theme of this themed collection. The introductory contribution by Ravera, Sgheri, Parigi and myself is an attempt at “classifying” the various approaches into two main classes, called “Largest Weight” and “Maximum Entropy” [DOI: 10.1039/C5CP04077A]. In the first approach one aims at finding the minimum number of conformations that is sufficient to explain all the experimental data, according to the Occam's razor principle; in the second, one looks for solutions where all accessible conformations are given some weight, according to the Maximum Entropy principle. Broadly speaking, contributions by

DOI: 10.1039/C5CP07196H – Chen et al.

DOI: 10.1039/C5CP04556H – Liu et al.

DOI: 10.1039/C5CP04601G – Castañeda et al.

DOI: 10.1039/C5CP03781F – Schilder et al.

DOI: 10.1039/C5CP04540A – Panjkovich et al.

DOI: 10.1039/C5CP03993B – Andrałojć et al.

belong to the first group, while the contribution by

DOI: 10.1039/C5CP04886A – Antonov et al.

belongs to the second. Somewhat off-path but very relevant to the theme are contributions by

DOI: 10.1039/C5CP04549E – Rossetti et al.

DOI: 10.1039/C6CP00057F – Dolenc et al.

DOI: 10.1039/C5CP06197K – Gill et al.

DOI: 10.1039/C5CP05417F – Feng et al.

DOI: 10.1039/C5CP04753F – Stevens et al.

DOI: 10.1039/C5CP04670J – Fenwick et al.

DOI: 10.1039/C5CP04542H – Lee et al.

DOI: 10.1039/C5CP04858C – Kurzbach et al.

DOI: 10.1039/C5CP03044G – Sekhar et al..

Several contributions, such as

DOI: 10.1039/C5CP06197K – Gill et al.

DOI: 10.1039/C5CP04556H – Liu et al.

DOI: 10.1039/C5CP05417F – Feng et al.

DOI: 10.1039/C5CP04601G – Castañeda et al.

DOI: 10.1039/C5CP07196H – Chen et al.,

are “system oriented”, while others

DOI: 10.1039/C5CP03044G – Sekhar et al.

DOI: 10.1039/C5CP03781F – Schilder et al.

DOI: 10.1039/C5CP04858C – Kurzbach et al.

DOI: 10.1039/C5CP04542H – Lee et al.

DOI: 10.1039/C5CP04670J – Fenwick et al.

DOI: 10.1039/C5CP04753F – Stevens et al.

DOI: 10.1039/C5CP04886A – Antonov et al.

DOI: 10.1039/C5CP04540A – Panjkovich et al.

are more “method-oriented” and propose novel experimental approaches that can yield better insight into conformational heterogeneity. Some deal with the extreme case of IDPs

DOI: 10.1039/C5CP04549E – Rossetti et al.

DOI: 10.1039/C5CP06197K – Gill et al.

DOI: 10.1039/C5CP04886A – Antonov et al.

DOI: 10.1039/C5CP04858C – Kurzbach et al.,

one with the mobile parts of protein fibrils

DOI: 10.1039/C6CP00057F – Dolenc et al.,

and two with nucleic acids

DOI: 10.1039/C5CP04540A – Panjkovich et al.

DOI: 10.1039/C5CP03993B – Andrałojć et al.

Although certainly not exhaustive, the present issue contains a very valuable collection of timely papers that hopefully will contribute to the clarification of some misunderstandings about what can and cannot be obtained on disordered systems, will provide some interesting new examples of systems of this type, and will stimulate further research in this challenging and important field.

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