Selectivity in K+ channels is due to topological control of the permeant ion's coordinated state
- Department of Molecular Biology and Center for Theoretical Biological Physics, The Scripps Research Institute, 10550 North Torrey Pines Road, TPC 6, La Jolla, CA 92037
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Edited by Roderick MacKinnon, The Rockefeller University, New York, NY, and approved April 11, 2007 (received for review January 20, 2007)
Abstract
The selectivity filter of K+ channels provides specific coordinative interactions between dipolar carbonyl ligands, water, and the permeant cation, which allow for selective flow of K+ over (most importantly) Na+ across the cell membrane. Although a structural viewpoint attributes K+ selectivity to coordination geometry provided by the filter, recent molecular dynamics simulation studies attribute it to dynamic and unique chemical/electrostatic properties of the filter's carbonyl ligands. Here we provide a simple theoretical analysis of K+ and Na+ complexation with water in the context of simplified binding site models and bulk solution. Our analysis reveals that water molecules and carbonyl groups can both provide K+ selective environments if equivalent constraints are imposed on the coordination number of the complex. Absence of such constraints annihilates selectivity, demonstrating that whether a coordinating ligand is a water molecule or a carbonyl group, “external” or “topological” constraints/forces must be imposed on an ion-coordinated complex to elicit selective binding. These forces must inevitably originate from the channel protein, because in bulk water, which, by definition, presents a nonselective medium, the coordination number is allowed to relax to suit the ion. We show that the coordination geometry of K+ channel binding sites is replicated by 8-fold complexation of K+ in both water and simplified binding site models due to dominance of local interactions within a complex and is thus a requirement for topologically constraining the coordination number to a specific value.
Footnotes
- *To whom correspondence should be addressed. E-mail: brooks{at}scripps.edu
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Author contributions: D.L.B. and C.L.B. designed research; D.L.B. performed research; D.L.B. and C.L.B. analyzed data; and D.L.B. wrote the paper.
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The authors declare no conflict of interest.
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This article is a PNAS Direct Submission.
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This article contains supporting information online at www.pnas.org/cgi/content/full/0700554104/DC1.
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↵ † The notion of free energy in this work in the case of simplified binding site model systems and of bulk hydrated ion systems treats the coordination volume of an ion as a subsystem of the whole, where “coordinators” are allowed to exchange with a surrounding bath of either a gas (in the case of a toy model with no “wall”) or a liquid (in the case of liquid solvated ions). A formal treatment of “subsystems,” in the context of a “small system” grand canonical ensemble has been given in previous work (22, 23). The natural thermodynamic potential for the grand canonical treatment is the grand potential, which we denote throughout this work using the letter J. This thermodynamic potential (or “free energy”) is equal to the quantity, −pv, for the system enclosed within the volume v at internal pressure p, and is relatable to the Helmholtz free energy, A, by the Legendre transform, J = A − Nμ, where N is the number of coordinators and μ is the chemical potential of a coordinator (whether it is a carbonyl or water). At fixed N, the grand potential is equivalent to the Helmholtz potential (24). It is also useful to note that, in the context of a grand ensemble, the isothermal bulk modulus, κ, of a system (in our case, a coordination complex), is related to the fluctuation, σ2, in the particle (in our case, the coordination) number (25): κ = −v(∂p/∂v)T = 〈N〉2 RT/vσ2. Thus, as σ→0, κ→∞, and, thermodynamically speaking, the system under scrutiny becomes infinitely incompressible.
- Abbreviation:
- MD,
- molecular dynamics.
- © 2007 by The National Academy of Sciences of the USA
