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Molecular transport through membranes: Accurate permeability coefficients from multidimensional potentials of mean force and local diffusion constants.

Authors
  • Sun, Rui1
  • Han, Yining1
  • Swanson, Jessica M J1
  • Tan, Jeffrey S2
  • Rose, John P2
  • Voth, Gregory A1
  • 1 Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, USA.
  • 2 Small Molecule Design and Development, Lilly Corporate Center, Eli Lilly and Company, Indianapolis, Indiana 46285, USA. , (India)
Type
Published Article
Journal
The Journal of Chemical Physics
Publisher
American Institute of Physics
Publication Date
Aug 21, 2018
Volume
149
Issue
7
Pages
72310–72310
Identifiers
DOI: 10.1063/1.5027004
PMID: 30134730
Source
Medline
Language
English
License
Unknown

Abstract

Estimating the permeability coefficient of small molecules through lipid bilayer membranes plays an important role in the development of effective drug candidates. In silico simulations can produce acceptable relative permeability coefficients for a series of small molecules; however, the absolute permeability coefficients from simulations are usually off by orders of magnitude. In addition to differences between the lipid bilayers used in vitro and in silico, the poor convergence of permeation free energy profiles and over-simplified diffusion models have contributed to these discrepancies. In this paper, we present a multidimensional inhomogeneous solubility-diffusion model to study the permeability of a small molecule drug (trimethoprim) passing through a POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid bilayer. Our approach improves the permeation model in three ways: First, the free energy profile (potential of mean force, PMF) is two-dimensional in two key coordinates rather than simply one-dimensional along the direction normal to the bilayer. Second, the 2-D PMF calculation has improved convergence due to application of the recently developed transition-tempered metadynamics with randomly initialized replicas, while third, the local diffusivity coefficient was calculated along the direction of the minimum free energy path on the two-dimensional PMF. The permeability is then calculated as a line integral along the minimum free energy path of the PMF. With this approach, we report a considerably more accurate permeability coefficient (only 2-5 times larger than the experimental value). We also compare our approach with the common practice of computing permeability coefficients based only on the translation of the center of mass of the drug molecule. Our paper concludes with a discussion of approaches for minimizing the computational cost for the purpose of more rapidly screening a large number of drug candidate molecules.

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