Exploring Substrate Diffusion in Channels Using Biased Molecular Dynamics Simulations

Protocol
First Online:
Part of the Methods in Molecular Biology book series (MIMB, volume 914)

Abstract

Substrate transport and diffusion through membrane-bound channels are processes that can span a range of time scales, with only the fastest ones being amenable to most atomic-scale equilibrium molecular dynamics (MD) simulations. However, the application of forces within a simulation can greatly accelerate diffusion processes, revealing important structural and energetic features of the channel. Here, we demonstrate the use of two methods for applying biases to a substrate in a simulation, using the ammonia/ammonium transporter AmtB as an example. The first method, steered MD, applies a constant force or velocity constraint to the substrate, permitting the exploration of potential substrate pathways and the barriers encountered, although typically far outside of equilibrium. On the other hand, the second method, adaptive biasing forces, is quasi-equilibrium, permitting the derivation of a potential of mean force, which characterizes the free energy of the substrate during transport.

Key words

Steered molecular dynamics Adaptive biasing forces Potential of mean force AmtB Ammonia/ammonium transport 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

This work was supported by the National Institutes of Health (P41-RR005969). Simulations were run at the National Center for Supercomputing Applications (MCA93S028).

References

  1. 1.
    Khalili-Araghi F et al (2009) Molecular dynamics simulations of membrane channels and transporters. Curr Opin Struct Biol 19:128–137PubMedCrossRefGoogle Scholar
  2. 2.
    Izrailev S et al (1997) Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys J 72:1568–1581PubMedCrossRefGoogle Scholar
  3. 3.
    Sotomayor M, Schulten K (2007) Single-molecule experiments in vitro and in silico. Science 316:1144–1148PubMedCrossRefGoogle Scholar
  4. 4.
    Hummer G, Szabo A (2001) Free energy reconstruction from nonequilibrium single-molecule pulling experiments. Proc Natl Acad Sci U S A 98:3658–3661PubMedCrossRefGoogle Scholar
  5. 5.
    Jarzynski C (1997) Equilibrium free-energy differences from nonequilibrium measurements: a master equation approach. Phys Rev E 56:5018–5035CrossRefGoogle Scholar
  6. 6.
    Jarzynski C (1997) Nonequilibrium equality for free energy differences. Phys Rev Lett 78:2690–2693CrossRefGoogle Scholar
  7. 7.
    Park S et al (2003) Free energy calculation from steered molecular dynamics simulations using Jarzynski’s equality. J Chem Phys 119:3559–3566CrossRefGoogle Scholar
  8. 8.
    Park S, Schulten K (2004) Calculating potentials of mean force from steered molecular dynamics simulations. J Chem Phys 120:5946–5961PubMedCrossRefGoogle Scholar
  9. 9.
    Darve E, Pohorille A (2001) Calculating free energies using average force. J Chem Phys 115:9169–9183CrossRefGoogle Scholar
  10. 10.
    Darve E, Rodríguez-Gómez D, Pohorille A (2008) Adaptive biasing force method for scalar and vector free energy calculations. J Chem Phys 128:144120PubMedCrossRefGoogle Scholar
  11. 11.
    Hénin J, Chipot C (2004) Overcoming free energy barriers using unconstrained molecular dynamics simulations. J Chem Phys 121:2904–2914PubMedCrossRefGoogle Scholar
  12. 12.
    Hénin J et al (2010) Exploring multidimensional free energy landscapes using time-dependent biases on collective variables. J Chem Theor Comp 6:35–47CrossRefGoogle Scholar
  13. 13.
    Chen H et al (2007) Charge delocalization in proton channels. I. The aquaporin channels and proton blockage. Biophys J 92:46–60PubMedCrossRefGoogle Scholar
  14. 14.
    Ilan B et al (2004) The mechanism of proton exclusion in aquaporin channels. Proteins 55:223–228PubMedCrossRefGoogle Scholar
  15. 15.
    Jensen MØ et al (2002) Energetics of glycerol conduction through aquaglyceroporin. GlpF. Proc Natl Acad Sci U S A 99:6731–6736PubMedCrossRefGoogle Scholar
  16. 16.
    Wang Y, Schulten K, Tajkhorshid E (2005) What makes an aquaporin a glycerol channel: a comparative study of AqpZ and GlpF. Structure 13:1107–1118PubMedCrossRefGoogle Scholar
  17. 17.
    Wang Y, Tajkhorshid E (2008) Electrostatic funneling of substrate in mitochondrial inner membrane carriers. Proc Natl Acad Sci U S A 105:9598–9603PubMedCrossRefGoogle Scholar
  18. 18.
    Celik L, Schiott B, Tajkhorshid E (2008) Substrate binding and formation of an occluded state in the leucine transporter. Biophys J 94:1600–1612PubMedCrossRefGoogle Scholar
  19. 19.
    Jensen MØ et al (2007) Sugar transport across lactose permease probed by steered molecular dynamics. Biophys J 93:92–102PubMedCrossRefGoogle Scholar
  20. 20.
    Yin Y et al (2006) Sugar binding and protein conformational changes in lactose permease. Biophys J 91:3972–3985PubMedCrossRefGoogle Scholar
  21. 21.
    Gumbart J, Wiener MC, Tajkhorshid E (2007) Mechanics of force propagation in TonB-dependent outer membrane transport. Biophys J 93:496–504PubMedCrossRefGoogle Scholar
  22. 22.
    Gumbart J, Schulten K (2006) Molecular dynamics studies of the archaeal translocon. Biophys J 90:2356–2367PubMedCrossRefGoogle Scholar
  23. 23.
    Gumbart J, Schulten K (2007) Structural determinants of lateral gate opening in the protein translocon. Biochemistry 46:11147–11157PubMedCrossRefGoogle Scholar
  24. 24.
    Gumbart J, Schulten K (2008) The roles of pore ring and plug in the SecY protein-conducting channel. J Gen Physiol 132:709–719PubMedCrossRefGoogle Scholar
  25. 25.
    Henin J et al (2008) Diffusion of glycerol through Escherichia coli aquaglyceroporin GlpF. Biophys J 94:832–839PubMedCrossRefGoogle Scholar
  26. 26.
    Dehez F, Pebay-Peyroula E, Chipot C (2008) Binding of ADP in the mitochondrial ADP/ATP carrier is driven by an electrostatic funnel. J Am Chem Soc 130:12725–12733PubMedCrossRefGoogle Scholar
  27. 27.
    Ivanov I et al (2007) Barriers to ion translocation in cationic and anionic receptors from the cys-loop family. J Am Chem Soc 129:8217–8224PubMedCrossRefGoogle Scholar
  28. 28.
    Bostick DL, Brooks CL III (2007) Deprotonation by dehydration: the origin of ammonium sensing in the AmtB channel. PLoS Comput Biol 3:e22PubMedCrossRefGoogle Scholar
  29. 29.
    Lamoureux G, Klein ML, Bernèche S (2007) A stable water chain in the hydrophobic pore of the AmtB ammonium transporter. Biophys J 92:L82–L84PubMedCrossRefGoogle Scholar
  30. 30.
    Lin Y, Cao Z, Mo Y (2006) Molecular dynamics simulations on the Escherichia coli ammonia channel protein AmtB: mechanism of ammonia/ammonium transport. J Am Chem Soc 128:10876–10884PubMedCrossRefGoogle Scholar
  31. 31.
    Luzhkov VB et al (2006) Computational study of the binding affinity and selectivity of the bacterial ammonium transporter AmtB. Biochemistry 45:10807–10814PubMedCrossRefGoogle Scholar
  32. 32.
    Nygaard TP et al (2006) Ammonium recruitment and ammonia transport by E. coli ammonia channel AmtB. Biophys J 91:4401–4412PubMedCrossRefGoogle Scholar
  33. 33.
    Yang H et al (2007) Detailed mechanism for AmtB conducting NH4+/NH3: molecular dynamics simulations. Biophys J 92:877–885PubMedCrossRefGoogle Scholar
  34. 34.
    Khademi S et al (2004) Mechanism of ammonia transport by Amt/MEP/Rh: structure of AmtB at 1.35 Å. Science 305:1587–1594PubMedCrossRefGoogle Scholar
  35. 35.
    Humphrey W, Dalke A, Schulten K (1996) VMD—visual molecular dynamics. J Mol Graph 14:33–38PubMedCrossRefGoogle Scholar
  36. 36.
    MacKerell AD Jr et al (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102:3586–3616CrossRefGoogle Scholar
  37. 37.
    MacKerell AD Jr, Feig M, Brooks CL III (2004) Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. J Comp Chem 25:1400–1415CrossRefGoogle Scholar
  38. 38.
    Phillips JC et al (2005) Scalable molecular dynamics with NAMD. J Comp Chem 26:1781–1802CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Biosciences DivisionArgonne National LaboratoryArgonneUSA

Personalised recommendations