Journal of Biomolecular NMR

, Volume 58, Issue 3, pp 209–225 | Cite as

Enhancing the quality of protein conformation ensembles with relative populations

  • Vijay Vammi
  • Tu-Liang Lin
  • Guang Song


The function and dynamics of many proteins are best understood not from a single structure but from an ensemble. A high quality ensemble is necessary for accurately delineating protein dynamics. However, conformations in an ensemble are generally given equal weights. Few attempts were made to assign relative populations to the conformations, mainly due to the lack of right experimental data. Here we propose a method for assigning relative populations to ensembles using experimental residue dipolar couplings (RDC) as constraints, and show that relative populations can significantly enhance an ensemble’s ability in representing the native states and dynamics. The method works by identifying conformation states within an ensemble and assigning appropriate relative populations to them. Each of these conformation states is represented by a sub-ensemble consisting of a subset of the conformations. Application to the ubiquitin X-ray ensemble clearly identifies two key conformation states, with relative populations in excellent agreement with previous work. We then apply the method to a reprotonated ERNST ensemble that is enhanced with a switched conformation, and show that as a result of population reweighting, not only the reproduction of RDCs is significantly improved, but common conformational features (particularly the dihedral angle distributions of ϕ 53 and ψ 52) also emerge for both the X-ray ensemble and the reprotonated ERNST ensemble.


Residual dipolar couplings Ubiquitin Relative populations Boltzmann weights Weighted ensemble Ensemble quality 



Funding from National Science Foundation (CAREER award, CCF-0953517) is gratefully acknowledged. The authors would also like to thank the two anonymous reviewers for their insightful comments.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Computer Science, Bioinformatics and Computational Biology ProgramIowa State UniversityAmesUSA
  2. 2.Department of Management Information SystemsNational Chiayi UniversityChiayi CityTaiwan
  3. 3.Baker Center for Bioinformatics and Biological StatisticsIowa State UniversityAmesUSA

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