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 Computational Electrophysiology |
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Studying Ion Channel Permeation and Selectivity with "Computational Electrophysiology"
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Carsten Kutzner,
Helmut Grubmüller,
Bert de Groot, and
Ulrich Zachariae
Ion channels play an essential role in cellular control and signalling processes. Ion selectivity and permeation rates are key quantities measured in experiments. We show that these quantities can be directly measured in molecular dynamics (MD) simulations by establishing a preserved ion gradient across the membrane, which leads to sustained ion flux through the channel. To preserve a chosen ionic gradient, we exchange ion/water pairs between both sides of the membrane.
We demonstrate this method using the bacterial channel PorB from pathogenic Neisseria meningitidis. During Neisserial infection, PorB inserts into the mitochondrial membrane of target cells, where it leads to apoptosis by dissipating the membrane potential. Our approach accurately predicts PorB ion conductance and selectivity and elucidates conduction mechanisms in atomistic detail.
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Fig. 1: Simulation setup
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(A) Using periodic boundaries, a double membrane partitions the system into two compartments α and β.
(B) Simulation system of PorB in a lipid membrane at 200 mM NaCl concentration.
(C) Time average of the electrostatic potential U along the z-axis for wild type PorB at 1 M NaCl, resulting from charge imbalances ∆q of up to 12 elementary charges.
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Control of ionic concentrations
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Every 0.2 ps, the number of anions and cations is determined in the compartments α and β (Fig. 1) and, if needed, the chosen reference numbers of ions are restored by exchanging ion/water pairs, thus providing a fixed charge imbalance ∆q between α and β. Since - apart from the exchanges - ions can only diffuse between α and β through a channel, the number of exchanged ions (Fig. 2) is also the number of ions having passed a channel, yielding the ionic current I.
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Fig. 2: Ion flux through PorB
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Ion flux through the PorB channels as recorded in the 1 M NaCl PorB simulation.
Calculation of ion selectivity and conductance
The transmembrane potential difference ∆U(z) is calculated by integrating the charge distribution twice (Fig. 1C). The conductance is Λ = I/∆U, the selectivity Ianion/Ication.
To obtain an error estimate, and since potential and flux are slightly time-dependent, multiple ∆U(t) and I(t) are determined from 20 ns time windows (10 ns overlap). For each window, ∆U(t) is determined as shown in Fig. 1C, while I(t) is derived by fitting a straight line to the ion flux in that time window. This way, each data point from Fig. 3A results in a cluster of data points in Fig. 3B. Combining the results from the three different ∆q values and then fitting linear functions to those data gives the straight lines shown in Fig. 3B. The selectivity ratio (Cl−/Na+) is provided by the slope ratios.
The conductance of wild type PorB was calculated to be 0.8 ± 0.1 nS, with an anion selectivity of 3.0 ± 0.6 (experiment [2]: 1.0 nS, selectivity 2.8, both in 1 M NaCl) – an improvement over potential of mean force calculations (Fig. 4B).
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Fig. 3: Computing the ionic current
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The ionic current can be computed using the slopes of the flux curves (Fig. 2).
(A) Net ion flux at the end of the simulation.
(B) Ionic current as a function of ∆U for multiple 20-ns-long slices of trajectories shown in Fig. 2.
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PorB ion conduction pathway
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The ion transfer mechanism inside PorB has been suggested to be unusual. Individual, hardly interacting pathways for the diffusion of anions and cations were postulated based on its crystal structure [3]. As shown by Fig. 4A, we find that there is indeed virtually no overlap of the pathway that cations and anions take along the pore. Anions pass along a cluster of basic residues on one side of the eyelet, while cations move along acidic residues lining the opposite wall.
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Fig. 4: PorB ion pathway
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(A) Overlay of ion positions from 500 snapshots of a 100 ns simulation at ∆q=4 e.
(B) Potential of mean force for Cl- and Na+ ions for wild type PorB.
(C) as A, but for PorB mutant G103K, which shows a disrupted cation pathway.
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Summary
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Computational electrophysiology allows a direct estimation of ion channel conductance and selectivity. Simultaneously, it provides mechanistic insight into channel function. As the method is applicable to channels of small and large conductance and size, we expect it to be useful to study the molecular mechanism of ion passage, e.g. for the improvement of drugs to overcome resistance mutations in bacterial porins, and to design drugs for a range of ion channel targets.
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References
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Kutzner C, Grubmüller H, de Groot BL, Zachariae U.
Computational Electrophysiology: The Molecular Dynamics of Ion Channel Permeation and Selectivity in Atomistic Detail.
Biophys J. 101: 809-817 (2011)
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Olesky M, Zhao S, Rosenberg R, Nicholas R.
Porin-mediated antibiotic resistance in Neisseria gonorrhoeae: Ion, solute, and antibiotic permeation through PIB proteins with penB mutations.
J. Bacteriol. 188: 2300-2308 (2006)
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Tanabe M, Nimigeau C, Iverson T.
Structural basis for solute transport, nucleotide regulation, and immunological recognition of Neisseria meningitidis PorB.
Proc. Natl. Acad. Sci. USA. 107: 6811-6816 (2010)
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