Introduction The gramicidin A (ga) channel forms by head-to-head association of two monomers at their amino termini, one from each bilayer leaflet. Th

Size: px

Start display at page:

Download "Introduction The gramicidin A (ga) channel forms by head-to-head association of two monomers at their amino termini, one from each bilayer leaflet. Th"

Thomasina Watson
5 years ago
Views:

1 Abstract When conductive, gramicidin monomers are linked by six hydrogen bonds. To understand the details of dissociation and how the channel transits from a state with 6H bonds to ones with 4H bonds or 2H bonds (both believed non-conductive), we generated two-dimensional topographic maps of the total non-bonded inter-monomer interaction energy as functions of the separation distance and rotation angle between monomers. Calculations for four distinct gramicidin structures (1MAG, 1JNO, 1JO3 & 1JO4 pdb files) led to complex, but qualitatively similar, energy maps with three wells (6H, 4H & 2H states), separated by high energy barriers. With rigid body monomer motion of 1MAG fully treated (including tilt and lateral displacement), two distinct dissociative pathways were observed in determinations of both energy and potential of mean force. Along both, initial motion is lateral, leading to a closed pore (nonconducting) structure. At a critical displacement on path 1 the monomers abruptly separate axially with simultaneous lateral relaxation and formation of an open, putatively conducting pore, stabilized by 4H bonds. Then dissociation occurs by further lateral motion, maintaining the 4H bond separation. On path 2 monomer movement is purely lateral, maintaining the 6H bond separation; no open pore forms.

2 Introduction The gramicidin A (ga) channel forms by head-to-head association of two monomers at their amino termini, one from each bilayer leaflet. The assembly is stabilized by six junctional hydrogen bonds; the dimer lifetimes are of the order of seconds [1]. Little is known about the kinetic mechanism for ga dissociation in membranes. Channel gating (closing and opening) is presumed due to the dissociation and association of the monomers with the closing transition triggered by breaking the dimer s stabilizing hydrogen bonds. As the monomers can rotate relative to each other, formation of a dimer with four or two hydrogen bonds is also possible. The channel is believed to be no longer conductive when the monomers separate by ~1.6 Å [2]. To study the detailed kinetics of ga dissociation we calculate the non-bonded interaction energy between the monomers allowing for free spatial and rotational motion. The intermonomer separation distance, the radial displacement and the effect of the tilt angle on the interaction energy are analyzed. The potential of mean force (PMF) along the minimum energy pathway for dimer dissociation is calculated using the free energy perturbation method.

3 Computational Model The non-bonded interaction energy between the ga monomers is calculated using our MCICP (Monte Carlo Ion Channel Proteins) code with the following simplifying assumptions [3]: 1) Bulk water regions are treated as continua with ε = 80. The monomers are immersed in a low dielectric (ε = 1) membrane slab, somewhat overestimating electrostatic effects. The reaction field is treated by the method of images; van der Waals and electrostatic interactions are computed with no cutoff. 2) We use partial charges and van der Waals parameters of the CHARMM22 allhydrogen force field. The crystallographic structure of the ga channel [1] (pdb entry 1MAG resolved using Solid State NMR) was used. The ga structure contains 552 explicit protein atoms including all hydrogens. The two ga monomers are held rigid. They are permitted free 3D relative rotation and translation. The Kinetic Monte Carlo Reaction Path Following (KMCRPF) technique [4] is used to determine the lowest energy pathways and the reaction coordinates for dissociating the dimer into monomers. Monomer B is held fixed and monomer A (Figure 1) allowed translational (three spatial degrees of freedom) and rotational (rotation and tilt angles) motion. To monitor the reaction coordinate only increases in the rotational angle φ are permitted [4].

4 Dissociation Kinetics of the ga Dimer Figure 1 illustrates the molecular model. The lowest energy pathway was determined by rotating monomer A along the φ coordinate from the 6H state to the 4H state, then to the 2H state and finally to the 6H state. The reaction coordinates (separation distance and radial displacement between the monomers, tilt angle of monomer A) corresponding to the lowest energy path were determined simultaneously. Figure 2 presents an energy map as a function of the separation distance and rotation angle between the monomers (the d,φ-map). Radial displacement and tilting of monomer A is forbidden. The map is calculated by the grid method, with separation distance steps of 0.05 Å and angular steps of 0.5º. There are three clear energy wells corresponding to 6H(ydrogen bond), 4H and 2H states. Large energy barriers separate the wells. For the 1MAG structure used here, the energy, separation distance and rotation angle differences between the 6H, 4H and 2H states are tabulated. E [kt] E [kt] d [Å] d [Å] φ [deg] φ [deg] 6H-4H 4H-2H 6H-4H 4H-2H 6H-4H 4H-2H

5 Figure 3 shows the lowest energy contours on the d,φ-map as a function of φ. The results are presented for the four experimental ga structures available, each corresponding to a different conformation and structure. 1MAG and 1JNO are for gramicidin A. 1JO3 is gramicidin B. 1JO4 is gramicidin C. Nonetheless, all have similar lowest energy pathways for dissociation into monomers. The profile shape is conserved. Differences in energy maxima and minima most likely reflect different conformational states of the side chains. These profiles suggest that dissociation kinetics in gramicidin is basically independent of the structural details. Results are unaltered if CO and NH bond bending and stretching is included; the inter-monomer interaction energy does not change (calculations, not shown, were performed for the 1MAG structure). Figure 4 illustrates the effect of the membrane dielectric constant, ε, on the energy profile for axial displacement of monomer A along the Z-axis, starting from the 6H state; rotation is forbidden. Increasing ε greatly alters the 6H energy well depth, with saturation at ε ~10. The 6H energy well (~30 kt) is conserved when all partial charges on the protein atoms are turned off. The inter-monomer van der Waals interaction contributes significantly to the stabilization energy.

6 Figure 5 illustrates the lowest energy profiles corresponding to the reaction coordinate for dimer dissociation. The results of several Monte Carlo (MC) runs are illustrated. Monomer A is permitted radial displacement and tilt. The importance of these additional degrees of freedom is evident from the difference between the MC curves and the d,φ-curve (in black). The energy barriers decreased significantly. The barrier separating 6H and 4H wells is ~40 kt. The well depth difference is ~18 kt. Inter-monomer hydrogen bonds break much more easily if monomer A undergoes screw type motion with simultaneous lateral displacement rather than direct axial separation. At the peak of the barrier between the 6H and 4H states the reaction pathway bifurcates. Path 1 leads to formation of the 4H state. There is switching between hydrogen bonds at the inter-monomer junction (a rotational shift) with an abrupt discontinuity in the separation distance (~1.6 Å, see Figure 2). Two hydrogen bonds break in transiting from the 6H to the 4H state. Along path 2 the monomers dissociate directly from the native 6H state by coupled screw type and lateral motion with neither a separation distance discontinuity nor a rotational shift between hydrogen bonds. The probability for realizing these paths depends on the tilt permitted monomer A, the specific membrane, etc. For φ > 150º (escape from the 4H state) the energy fluctuates between 40 and 60 kt. The barriers between 4H and 2H wells and 2H and 6H wells disappear (compare the MC curves with the d,φ-curve).

7 Figure 6 illustrates the angular dependence of the separation distance between monomers. Zero separation corresponds to the crystal state. For the d,φ-path (no tilt allowed) monomers separate ~4 Å in transition from the 6H state to the 4H state. This arises because of a large electrostatic barrier since for φ ~60º COs and NHs from the individual monomers are in opposition. (HN)VAL 1 (A) abuts (HN)ALA 5 (B) (CO)VAL 1 (A) abuts (CO)ALA 3 (B) (HN)ALA 3 (A) abuts (HN)ALA 3 (B) (CO)ALA 3 (A) abuts (CO)VAL 1 (B) (HN)ALA 5 (A) abuts (HN)VAL 1 (B) The separation distance is very different when radial displacement and tilt are allowed (MC curves). The monomers do not separate for φ 75º and the separation distance fluctuates near zero. This results from strong inter-monomer interaction due to the six native (original) inter-monomer hydrogen bonds, which are not easily broken. Along path 1 the separation then abruptly increases by ~1.6 Å, corresponding to formation of the 4H state. Here there is a rotational shift between the hydrogen bonds at the intermonomer junction. Along path 2 the monomers do not separate; they are displaced radially. Dissociation occurs from the native 6H state with no rotational shift between hydrogen bonds. As the model treated here doesn t account for membrane elasticity, at large radial displacement (> 4 Å) the monomers slip by one another (a non-physical artifact) and the separation distance between them becomes negative.

8 Figure 7 illustrates the radial displacement between the monomers along the dissociative path. The inter-monomer junction is displaced radially by ~3.5 Å at the peak of the barrier separating the 6H and 4H wells; here φ ~75º and the dimer pore is fully occluded. For larger φ along path 1 the monomers radial displacement again approaches zero (forming the 4H state) and the pore reopens fully. Dissociation from the 4H state takes place radially. Beyond φ ~75º along path 2 separation occurs laterally without reforming an open pore. Figure 8 illustrates the tilt angle of monomer A. The tilt angle fluctuates by ~8º on both paths. Depending on the tilt restrictions either path 1 or 2 can be realized. If tilt is forbidden or near zero path 1 occurs frequently (nine out of ten MC runs). When tilt is freely variable direct dissociation from the 6H state (path 2) is most probable. The presence of the membrane greatly modifies monomer behavior [5]. Figure 9 illustrates the potential of mean force (PMF) along the reaction coordinate for dimer dissociation, calculated by free energy perturbation [6]. Unlike computational alchemy, which proceeds via non-physical intermediate states, the PMF is calculated for a physically achievable dissociation process. The reaction coordinate (rotation angle φ) was increased from 0 to 360º in 0.3º steps. In the main the PMF mimics the total energy profiles along both reaction pathways. In the 6H region there is no difference between the PMF and total energy profiles. The PMF barriers separating the 6H and 4H states are lower than the total energy barriers.

9 Conclusions and Observations To overcome a large electrostatic barrier separating the 6H and 4H states the monomers are displaced radially. Axial separation is energetically far more expensive than lateral motion. The two possible reaction pathways are observed for dissociation. On path 1 the 4H state forms (a fully open pore). Here the monomers undergo an abrupt displacement in the axial separation by ~1.6 Å. On path 2 the monomers dissociate laterally and their separation remains near zero. In transiting from the 6H state to the 4H state ionic conduction is interrupted as the monomers undergo a radial shift at the inter-monomer junction by 3 Å with no axial separation. Radial displacement fluctuations in the 6H state may provide a rationale for fast closure events (flickers) at sub-millisecond times [7]. Our results demonstrate that the transition state for channel dissociation (breaking some hydrogen bonds at the dimer junction) may occur by lateral displacement, without axially separating the monomers by 1.6 Å [2]. Introducing membrane elasticity into the model eliminates the non-physical artifact of the monomers slipping by one another at large radial displacements. Membrane elasticity also substantially stabilizes formation of 4H and even 2H states [5]. Along the reaction pathways the PMF mimics the total energy profile. However, the PMF barrier between 6H and 4H states is less than the total energy barrier.

10 Acknowledgements Work supported by a grant from the National Institutes of Health, GM References 1. T.C. Vogt et al., Biochemistry 31: (1992) 2. J.A. Lundbæk & O.S. Andersen, Biophys. J. 76: (1999) 3. P.C. Jordan & G.V. Miloshevsky, Biophys. J. 82:199a (2002) 4. G.V. Miloshevsky & P.C. Jordan, Biophys. J. 84: 412a (2003) 5. M.B. Partenskii et al., Biophys. J. 84: 2520a (2003) 6. A.R. Leach, Molecular modelling: principles and applications, Harlow, England: Longman, K.M. Armstrong & S. Cukierman, Biophys. J. 82: (2002)

Y ETA φ d X R θ Z Monomer B FOR Monomer A Figure 1. Two ga monomers (A & B) are illustrated as separate mobile structural elements. The helices are shown in blue and green.

11 Y ETA φ d X R θ Z Monomer B FOR Monomer A Figure 1. Two ga monomers (A & B) are illustrated as separate mobile structural elements. The helices are shown in blue and green. Atoms of the FOR and ETA residues are displayed in their conventional colors. Arrows demonstrate the monomers separation distance, radial displacement, tilt angle, and rotation direction.

12 Figure 2. Contour map of the total (electrostatic + vdw) energy as a function of the separation distance d and rotation angle φ between ga monomers. The energy wells corresponding to the states with 6H, 4H and 2H hydrogen bonds are illustrated.

13 Energy difference, (kt) H 4H Angle ϕ, (deg) Figure 3. The energy profiles corresponding to the lowest energy path on the d,φ-map between 6H, 4H and 2H states as a function of the rotation angle φ between monomers. Profiles are shown for four experimental gramicidin structures. 2H 1MAG 1JNO 1JO3 1JO4

14 0 Energy difference, (kt) H ε = 1 ε = 4 no charges Separation Distance d, (Å) Figure 4. Energy profiles as a function of the axial monomer separation distance (movement along the Z-axis directly from the 6H state). Profiles are shown for ε = 1 and 4, and when all partial charges on the protein atoms are excluded (ε ).

15 Energy difference, (kt) 60 path H 4H path 1 (d,ϕ) path MC run 1 MC run 2 MC run 3 MC run 4 MC run 5 MC run Figure 5. Energy profiles corresponding to the lowest energy pathways for dimer dissociation. Two paths are indicated. Path 1 corresponds to formation of the 4H state. Along path 2 monomers dissociate directly from the 6H state by radial displacement. The black curve is the energy profile in d,φ-space (tilt and lateral motion excluded). 2H Angle ϕ, (deg)

16 Separation Distance d, (Å) H (d,ϕ) path MC run 1 MC run 2 MC run 3 path 2 4H path 1 MC run 4 MC run 5 MC run Figure 6. Separation distance between the ga monomers along the lowest energy pathways for paths 1 and 2 and for the d,φ-path. The separation distance discontinuity occurs at 75º on the path to the 4H state. 2H Angle ϕ, (deg)

17 Radial Displacement R, (Å) 10 MC run 4 MC run 5 MC run H path 1 path 2 4H MC run 1 MC run 2 MC run Angle ϕ, (deg) Figure 7. Radial displacement between monomers on the two paths is illustrated. When the 4H state forms (path 1) a conductive ga dimer reforms (R near zero). Along path 2 the monomers dissociate directly from the 6H state.

18 12 Tilt Angle θ, (deg) MC run 1 MC run 2 MC run Angle ϕ, (deg) Figure 8. Tilt angle of monomer A is illustrated. The tilt profiles are similar for paths 1 and 2. The tilt angle fluctuates around 8º.

19 Energy difference, (kt) H 4H Energy, path 1 PMF, path 1 Energy, path 2 PMF, path Angle ϕ, (deg) Figure 9. Total energy and potential of mean force (PMF) profiles along the reaction coordinate (rotation angle φ) for the dimer to monomer reaction. Profiles are illustrated for pathways 1 and 2.

Gating Gramicidin Channels in Lipid Bilayers: Reaction Coordinates and the Mechanism of Dissociation

92 Biophysical Journal Volume 86 January 2004 92 104 Gating Gramicidin Channels in Lipid Bilayers: Reaction Coordinates and the Mechanism of Dissociation Gennady V. Miloshevsky and Peter C. Jordan Department