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NMR line shapes and multi-state binding equilibria

Journal of Biomolecular NMR volume 53, pages 257–270 (2012)Cite this article

Abstract

Biological function of proteins relies on conformational transitions and binding of specific ligands. Protein–ligand interactions are thermodynamically and kinetically coupled to conformational changes in protein structures as conceptualized by the models of pre-existing equilibria and induced fit. NMR spectroscopy is particularly sensitive to complex ligand-binding modes—NMR line-shape analysis can provide for thermodynamic and kinetic constants of ligand-binding equilibria with the site-specific resolution. However, broad use of line shape analysis is hampered by complexity of NMR line shapes in multi-state systems. To facilitate interpretation of such spectral patterns, I computationally explored systems where isomerization or dimerization of a protein (receptor) molecule is coupled to binding of a ligand. Through an extensive analysis of multiple exchange regimes for a family of three-state models, I identified signature features to guide an NMR experimentalist in recognizing specific interaction mechanisms. Results show that distinct multi-state models may produce very similar spectral patterns. I also discussed aggregation of a receptor as a possible source of spurious three-state line shapes and provided specific suggestions for complementary experiments that can ensure reliable mechanistic insight.

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Notes

  1. Briefly, an exchanging system is in the fast-exchange regime when the exchange rate constant (k ex) is much larger than a difference between the resonance frequencies of exchanging species (sites): \( {\text{k}}_{\text{ex}} \gg \Updelta \omega \). In fast exchange, a single resonance is observed at a frequency equal to the population-weighted average of frequencies of individual species (Kaplan and Fraenkel 1980). The condition of \( {\text{k}}_{\text{ex}} \ll \Updelta \omega \) corresponds to a slow-exchange regime, manifested by appearance of separate resonances for individual species with peak areas (volumes) proportional to their equilibrium populations. Intermediate exchange is when \( {\text{k}}_{\text{ex}} \approx \Updelta \omega \) and results in very significant broadening of the resonances and non-Lorentzian line shapes. For convenience, we also refer to the “fast-intermediate” (or “slow-intermediate”) exchange regime to specify situations when k ex is larger (smaller) than Δω but not to such extent that purely fast or slow behavior holds.

  2. To facilitate comparative analysis, the frequency of the “intermediate” species in the three-state mechanisms is always placed in between the frequencies of the “end” species in all simulations for Fig. 5 (i.e. the frequency of R is in between of R* and RL, etc.). Additional simulations established that alternative relative placement of frequencies for the three species does not produce qualitatively new results.

  3. For U-R, the ratio of R to R* is constant throughout the titration because the unimolecular isomerization is independent of the receptor concentration.

Abbreviations

R:

A receptor

L:

A ligand

CR, CL :

Total concentrations of R and L, mol/L

CL/CR :

A molar ratio of L and R in the sample serving as a marker of the titration progress

[X]:

An equilibrium concentration of species X, mol/L

Ka :

An equilibrium association constant for ligand binding

Kiso :

An equilibrium constant for intramolecular isomerization of the receptor (R ⇔ R*)

Kdim :

An equilibrium dimerization constant of the receptor (R ⇔ R2)

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Acknowledgments

The author is deeply indebted to Dr. James Kempf for innumerable corrections, suggestions and comments, and Dr. Marius Clore for critical reading of the manuscript. The author acknowledges Dr. Mark Foster, Dr. Linda Nicholson, Dr. Brian Volkman, Casey O’Connor and Ian Kleckner for helpful discussions and practical comments. The author acknowledges Snehal Patil for creating the web interface for the LineShapeKin Simulation software and the Marquette University Committee on Research for financial support of web design (2012 Regular Research Grant).

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  1. Department of Chemistry, Marquette University, PO Box 1881, Milwaukee, WI, 53201, USA

    Evgenii L. Kovrigin

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Correspondence to Evgenii L. Kovrigin.

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Kovrigin, E.L. NMR line shapes and multi-state binding equilibria. J Biomol NMR 53, 257–270 (2012). https://doi.org/10.1007/s10858-012-9636-3

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