Interaction of a polar molecule with an ion channel

V. Levadny, V. M. Aguilella, M. Aguilella-Arzo, and M. Belaya

Phys. Rev. E 70, 041912 – Published 29 October 2004

Abstract

The binding of a polar macromolecule to a large ion channel is studied theoretically, paying special attention to the influence of external conditions (applied voltage and ion strength of solution). The molecule behavior in bound state is considered as random thermal fluctuations within a limited fraction of its phase space. The mean duration of molecule binding (residence time $τ_{r}$ ) is represented as the mean first passage time to reach the boundary of that restricted domain. By invoking the adiabatic approximation we reduce the problem to one dimension with the angle between macromolecule dipole and channel axes being the key variable of the problem. The model accounts for experimental measurements of $τ_{r}$ for the antibiotic Ampicillin within the bacterial porin OmpF of Escherichia coli. By assuming that the electrical interaction between Ampicillin dipole and OmpF ionizable groups affects the fluctuations, we find that the biased residence time-voltage dependence observed in experiments is the result of the strong transversal electric field in OmpF constriction with a tilt $\sim 30 °$ aside the cis side.

Received 7 November 2003

DOI:https://doi.org/10.1103/PhysRevE.70.041912

Authors & Affiliations

V. Levadny^1,2, V. M. Aguilella^1,*, M. Aguilella-Arzo¹, and M. Belaya³

¹Departamento de Ciencias Experimentales, Universidad Jaume I, 12080 Castellón, Spain
²The Scientific Council for Cybernetics, Russian Academy of Sciences, Vavilov str. 34, 333117 Moscow, Russia
³Institute of Plant Physiology, Russian Academy of Sciences; Botanicheskaya 35, 127276 Moscow, Russia

^*Corresponding author. Electronic address: aguilell@exp.uji.es

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Vol. 70, Iss. 4 — October 2004

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Images

Figure 1
Contour plot of the electric potential in the vicinity of the channel constriction (longitudinal cross section of one monomer pore), together with a vector representation of the electric field, for electrolyte concentration $C_{K Cl} = 1 M$ and no applied voltage. Thin solid lines represent sections of equipotential planes. The arrow size is proportional to the field magnitude and the shaded region corresponds to the protein. The plane shown forms 50° with the $x$ axis used in the protein crystal structure [15]. Numerical calculations based on this structure used the UHBD code [31]. Computations reveal a strong transversal electric field about $0.2 V ∕ nm$ at the narrowest part of the channel, in contrast with $\sim 0.01 V ∕ nm$ outside this zone. An Ampicillin molecule is also shown. See main text for details.Reuse & Permissions
Figure 2
Sketch of the system considered. Channel blockage takes place while Ampicillin is in the channel constriction. $d_{AP}$ is the AP electric dipole moment, and $E_{om}$ is the electric field created by OmpF ionizable groups in constriction zone. The bulk of trans solution is taken as virtual ground when an external electrical field is applied. $θ_{om}$ represents the fixed orientation of the effective OmpF electric field in the constriction zone; AP orientation, represented by its dipole moment, oscillates and $θ$ is the instant angle with respect to the channel axis.Reuse & Permissions
Figure 3
Change of normalized residence time $τ_{r} ∕ τ_{r}^{\max}$ with applied voltage $V$ [here $τ_{r}^{\max} = τ_{r} (V_{p})$ ]. The curves show the calculations according to Eqs. (4, 5, 6) for $θ_{om} = 120 °$ , $E_{om} = 0.2 V ∕ nm$ , $L_{cz} = 1.2 nm$ , and $d_{AP} = 30 Debye$ , and for different values of $(a + b) ∕ 2$ : solid line corresponds to 97°, dashed line to 120°, and dotted line to 130°. Experimental data (triangles) are taken from [11].Reuse & Permissions
Figure 4
Sketch of the potential profile of the system (left panel) and orientation of AP within the interval $[a, b]$ (right panel) for different values of the applied voltage: (A) $V = 0$ (solid line), $V_{p} > V > 0$ (dashed line), (B) $V > V_{p} > 0$ , (C) $V < 0$ . The initial tilt of AP is $θ_{0} \approx θ_{eq}$ . Here $a$ and $b$ are the boundaries of AP bound state, and shaded region correspond to nonbound states. See main text for details.Reuse & Permissions
Figure 5
Normalized residence time $τ_{r} ∕ τ_{r}^{\max}$ as a function of KCl concentration for $V = - 0.1 V$ (here $τ_{r}^{\max} = τ_{r}$ for $C_{K Cl} = 0.01 M$ ). The curve shows the theoretical calculations according to Eqs. (4, 5, 6) by using the same parameter values as in Fig. 3. Experimental data (triangles) are taken from Ref. 11.Reuse & Permissions

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