AFD: an application for bi-molecular interaction using axial frequency distribution

  • Saad Raza
  • Syed Sikander Azam
Original Paper


Conformational flexibility and generalized structural features are responsible for specific phenomena existing in biological pathways. With advancements in computational chemistry, novel approaches and new methods are required to compare the dynamic nature of biomolecules, which are crucial not only to address dynamic functional relationships but also to gain detailed insights into the disturbance and positional fluctuation responsible for functional shifts. Keeping this in mind, axial frequency distribution (AFD) has been developed, designed, and implemented. AFD can profoundly represent distribution and density of ligand atom around a particular atom or set of atoms. It enabled us to obtain an explanation of local movements and rotations, which are not significantly highlighted by any other structural and dynamical parameters. AFD can be implemented on biological models representing ligand and protein interactions. It shows a comprehensive view of the binding pattern of ligand by exploring the distribution of atoms relative to the x-y plane of the system. By taking a relative centroid on protein or ligand, molecular interactions like hydrogen bonds, van der Waals, polar or ionic interaction can be analyzed to cater the ligand movement, stabilization or flexibility with respect to the protein. The AFD graph resulted in the residual depiction of bi-molecular interaction in gradient form which can yield specific information depending upon the system of interest.


Molecular dynamics simulation Conformational analysis Software Axial frequency distribution Radial distribution function Binding pattern 



The authors would like to acknowledge the valuable insight and testing done by Klaus R. Liedl and Julian E. Fuch at Theoretical Chemistry, Faculty of Chemistry and Pharmacy, Center for Molecular Biosciences, Leopold-Franzens-University Innsbruck. The authors would also like to acknowledge Higher Education Commission, Pakistan, International Foundation for Science and Ernst Mach follow-up grant for financial assistance.

Author contributions

SSA designed, conceived and drafted the manuscript. SR programmed and debugged the software and also drafted the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

Supplementary material

894_2018_3601_MOESM1_ESM.docx (14 kb)
ESM 1 (DOCX 13 kb)


  1. 1.
    Boehr DD, Nussinov R, Wright PE (2009) The role of dynamic conformational ensembles in biomolecular recognition. Nat Chem Biol 5:789–796CrossRefGoogle Scholar
  2. 2.
    Grossman M, Born B, Heyden M et al (2011) Correlated structural kinetics and retarded solvent dynamics at the metalloprotease active site. Nat Struct Mol Biol 18:1102–1108CrossRefGoogle Scholar
  3. 3.
    Buch I, Giorgino T, De Fabritiis G (2011) Complete reconstruction of an enzyme-inhibitor binding process by molecular dynamics simulations. Proc Natl Acad Sci 108:10184–10189CrossRefGoogle Scholar
  4. 4.
    Clore GM, Schwieters CD (2004) Amplitudes of protein backbone dynamics and correlated motions in a small α/β protein: correspondence of dipolar coupling and heteronuclear relaxation measurements. Biochemistry 43:10678–10691CrossRefGoogle Scholar
  5. 5.
    Salmon L, Yang S, Al-Hashimi HM (2014) Advances in the determination of nucleic acid conformational ensembles. Annu Rev Phys Chem 65:293CrossRefGoogle Scholar
  6. 6.
    Henzler-Wildman K, Kern D (2007) Dynamic personalities of proteins. Nature 450:964–972CrossRefGoogle Scholar
  7. 7.
    Lindorff-Larsen K, Best RB, DePristo MA et al (2005) Simultaneous determination of protein structure and dynamics. Nature 433:128–132CrossRefGoogle Scholar
  8. 8.
    Karplus M, McCammon JA (2002) Molecular dynamics simulations of biomolecules. Nat Struct Mol Biol 9:646–652CrossRefGoogle Scholar
  9. 9.
    Donohue J (1954) Radial distribution functions of some structures of the polypeptide chain. Proc Natl Acad Sci U S A 40:377CrossRefGoogle Scholar
  10. 10.
    Azam SS, Abro A, Raza S (2015) Binding pattern analysis and structural insight into the inhibition mechanism of sterol 24-C methyltransferase by docking and molecular dynamics approach. J Biomol Struct Dyn 33:2563–2577CrossRefGoogle Scholar
  11. 11.
    Abbasi S, Raza S, Azam SS et al (2016) Interaction mechanisms of a melatonergic inhibitor in the melatonin synthesis pathway. J Mol Liq 221:507–517CrossRefGoogle Scholar
  12. 12.
    Ul Haq F, Abro A, Raza S et al (2017) Molecular dynamics simulation studies of novel β-lactamase inhibitor. J Mol Graph Model 74:143–152CrossRefGoogle Scholar
  13. 13.
    Ahmad S, Raza S, Uddin R, Azam SS (2017) Binding mode analysis, dynamic simulation and binding free energy calculations of the MurF ligase from Acinetobacter baumannii. J Mol Graph Model 77:72-85Google Scholar
  14. 14.
    Azam SS, Abro A, Raza S, Saroosh A (2014) Structure and dynamics studies of sterol 24-C-methyltransferase with mechanism based inactivators for the disruption of ergosterol biosynthesis. Mol Biol Rep 41:4279–4293CrossRefGoogle Scholar
  15. 15.
    Jeffrey GA (1997) An introduction to hydrogen bonding. J Am Chem Soc 120:5604–5604Google Scholar
  16. 16.
    Wallace AC, Laskowski RA, Thornton JM (1995) LIGPLOT: a program to generate schematic diagrams of protein-ligand interactions. Protein Eng 8:127–134CrossRefGoogle Scholar
  17. 17.
    Accelrys Inc (2012) Visualizer DS release 3.5. Accelrys Inc, San DiegoGoogle Scholar
  18. 18.
    Humphrey W, Dalke A, Schulten K (1996) VMD: visual molecular dynamics. J Mol Graph 14:33–38CrossRefGoogle Scholar
  19. 19.
    Pettersen EF, Goddard TD, Huang CC et al (2004) UCSF chimera—a visualization system for exploratory research and analysis. J Comput Chem 25:1605–1612CrossRefGoogle Scholar
  20. 20.
    Case DA, Darden T, Iii TEC et al (2014) Amber 14. University of California, San Francisco.
  21. 21.
    MathWorks I (2012) MATLAB and statistics toolbox. Scholar
  22. 22.
    Unistat L (2010) Unistat Version 6.5. Unistat, LondonGoogle Scholar
  23. 23.
    Eaton JW et al (2015) GNU Octave, version 4.0. Scholar
  24. 24.
    Debye P (1913) Interferenz von röntgenstrahlen und wärmebewegung. Ann Phys 348:49–92CrossRefGoogle Scholar
  25. 25.
    Zwanzig RW (1954) High-temperature equation of state by a perturbation method. I. Nonpolar gases. J Chem Phys 22:1420–1426CrossRefGoogle Scholar
  26. 26.
    Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78:2690CrossRefGoogle Scholar
  27. 27.
    Kirkwood JG (1935) Statistical mechanics of fluid mixtures. J Chem Phys 3:300–313CrossRefGoogle Scholar
  28. 28.
    Calabro G, Woods CJ, Powlesland F et al (2016) Elucidation of non-additive effects in protein-ligand binding energies: thrombin as a case study. J Phys Chem B 120:5340–5350Google Scholar
  29. 29.
    Kamenik AS, Kahler U, Fuchs JE, Liedl KR (2016) Localization of millisecond dynamics: dihedral entropy from accelerated MD. J Chem Theory Comput 12:3449–3455CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computational Biology Lab, National Center for BioinformaticsQuaid-i-Azam UniversityIslamabadPakistan

Personalised recommendations