Deriving Structural Information from Experimentally Measured Data on Biomolecules

Abstract

During the past half century, the number and accuracy of experimental techniques that can deliver values of observables for biomolecular systems have been steadily increasing. The conversion of a measured value Q of an observable quantity Q into structural information is, however, a task beset with theoretical and practical problems: 1) insufficient or inaccurate values of Q , 2) inaccuracies in the function Q(r→) used to relate the quantity Q to structure r→ , 3) how to account for the averaging inherent in the measurement of Q , 4) how to handle the possible multiple-valuedness of the inverse r→(Q) of the function Q(r→) , to mention a few. These apply to a variety of observable quantities Q and measurement techniques such as X-ray and neutron diffraction, small-angle and wide-angle X-ray scattering, free-electron laser imaging, cryo-electron microscopy, nuclear magnetic resonance, electron paramagnetic resonance, infrared and Raman spectroscopy, circular dichroism, Förster resonance energy transfer, atomic force microscopy and ion-mobility mass spectrometry. The process of deriving structural information from measured data is reviewed with an eye to non-experts and newcomers in the field using examples from the literature of the effect of the various choices and approximations involved in the process. A list of choices to be avoided is provided.

Interpretation of Seemingly Contradictory Data: Low NMR S2 Order Parameters Observed in Helices and High NMR S2 Order Parameters in Disordered Loops of the Protein hGH at Low pH

“…[25] Such paradoxes can be resolved by applying MD simulation, possibly with restraining to as et of values of particular quantitiest hat are to be satisfied to allow for ar eliable interpretation of the simulated results. Such ap aradox mayb ed ue to approximations and simplifications employed when deriving molecular structure, an on-observable quantity,f rom measured values of observable quantities.…”

“…[25,36] This has been illustrated by the comparison of S 2 order parameters for NÀHb ond vectors obtained from observed NMR relaxation rates of hGH with S 2 values derived from chemical shift data using an empirical relationship.T he differences observed between the respective sets of S 2 values led to different structural interpretations, which constitutes aw arning for an overly simplistic interpretationo fe xperimental data. [25,36] This has been illustrated by the comparison of S 2 order parameters for NÀHb ond vectors obtained from observed NMR relaxation rates of hGH with S 2 values derived from chemical shift data using an empirical relationship.T he differences observed between the respective sets of S 2 values led to different structural interpretations, which constitutes aw arning for an overly simplistic interpretationo fe xperimental data.…”

Validation of Molecular Simulation: An Overview of Issues

“…Fore xample,i ft he pressure of the system, P(t), is calculated using the virial formula [Eq. (8)]. When coupling the system to at emperature bath and ap ressure bath, the coupling to the temperature bath should be tighter than to the pressure bath to avoid resonance of P(t)a nd E kin (t)i nduced by Equation (7).…”

“…[8] First, experimentally measured values Q exp are subject to uncertainty or error. Herein, the statistical-mechanical definition of ac onfiguration r N consisting of theC artesian coordinatesofthe system is used.T hisa ppliesf or example, to thesoluteand solventmolecules combined.Werefer to agroup of closelyrelated configurations of asolutemoleculethathave ap articulars et of geometricf eaturesa saconformation.F or example,all configurations ofasolutethathaveslightlyvarying bond lengths, bond angles and torsional angles within alimited range,f or example,1 5 8 8 from each other, may be considered as inglec onformation.T hisc an be done when thed ifferences betweent he configurations that belong to this conformation have no effect on thephenomenonthatisconsidered.…”

“…[45],quantities Q(r N )that can be calculated from configurations r N can be either observable quantities Q obs (r N )t hat are directly measurable experimentally,o rn on-observable quantities Q der (r N )t hat are derived from < Q obs > exp values by applying ag iven procedure, f [Eq. [8] Q der ¼ f ð<Q obs > exp Þ ð10Þ Angewandte Chemie Reviews 892 www.angewandte.org Peak location and intensity from X-ray diffraction or NMR spectroscopic experiments are examples of observable quantities Q obs .M olecular structure,t orsional angles,h ydrogen bonds,NMR order parameters or atom-atom radial distribution functions are examples of derived quantities Q der .T hey incorporate the assumptions and approximations associated with the procedure f used to convert < Q obs > exp values into Q der values.Depending on the validity of the assumptions and the reliability of the approximations involved, the Q der values obtained may in reality carry little experimental information. [8] Q der ¼ f ð<Q obs > exp Þ ð10Þ Angewandte Chemie Reviews 892 www.angewandte.org Peak location and intensity from X-ray diffraction or NMR spectroscopic experiments are examples of observable quantities Q obs .M olecular structure,t orsional angles,h ydrogen bonds,NMR order parameters or atom-atom radial distribution functions are examples of derived quantities Q der .T hey incorporate the assumptions and approximations associated with the procedure f used to convert < Q obs > exp values into Q der values.Depending on the validity of the assumptions and the reliability of the approximations involved, the Q der values obtained may in reality carry little experimental information.…”