A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins

Abstract

Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here, we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: (1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. (2) The highly different accessibilities in the membrane and water regions are addressed with a two-step, two-probe grid-labeling procedure. (3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe good agreement with the experimental results.

Figure 1

Grid point labeling scheme in the numerical SES surface definition. Here -4 stands for grid points in the bulk solvent; -2 stands for grid points within SAS spheres if not overwritten below; 2 stands for grid points within VDW spheres; 1 stands for grid points within bicones (shown as the fine dashed triangles) formed by overlapping SAS spheres if not overwritten below; -1 stands for grid points accessible to solvent probes placed on the solvent accessible arcs that are formed by overlapping SAS spheres. The Stern lay is omitted for clarity.

Figure 2

Sequence alignment of KcsA and hERG by ClustalX version 2.1. The identified S5 helix, S6 helix, amphipathic helix and pore helix are labeled above the sequence. Asterisks (*): conserved amino acid residues; colons (:): conserved substitutions; dots (.): semi-conserved substitutions.

Figure 3

Comparison of target and parent structures, showing the secondary structure elements in homology models of hEGH (red) and KcsA (blue). The plot shows three orientations of the aligned structure. Top: side view with the binding pocket on the top. Bottom left: view from the binding pocket/extracellular side. Bottom right: view from the intracellular side.

Figure 4

Solvent-solute interface determined with the new continuum membrane model. Left:mprob is set to be 1.4 Å, the default value of the solvent probe. Right: mprob is set to be 2.7 Å, the optimized value of the membrane probe. Three proteins are tested: 1K4C (top); 5CFB (middle); 5HCJ (bottom).

Figure 5

Same as the right panel with the optimized mprob in Figure 3, except without turning on the depth-first search in the pore region detection. Three proteins are tested: 1K4C (top); 5CFB (middle); 5HCJ (bottom).

Figure 6

Discrepancy between implicit and explicit water simulations. The protein surface of 1K4C (blue) is overlaid with a bond representation and sampled water positions (yellow). Left: a solvent region defined by the PBSA model but with no explicit water. Right: explicit water is detected in a region where no solvent is defined in the PBSA model.

Figure 7

MMPBSA binding affinities compared with experimental measurements. Binding affinities are in kcal/mol. Top: MMPBSA was computed with the classical nonpolar solvent model (INP=1);the correlation coefficient is 0.79. Bottom: MMPBSA was computed with the modern nonpolar solvent model (INP=2); the correlation coefficient is 0.73.