Results

I.3.1 Sampling approach

With a number of different ways of computing free energy, the main complication lies in extracting accurate free energies from molecular simulations. The thorough exploration of free energy landscapes requires sampling large conformational changes and slow transitions. I, therefore, have chosen the accelerated weight histogram (AWH) method to calculate free energy along a reaction coordinate [145]. A technique that by using a probability weight histogram enables efficient free energy updates, AWH enhances sampling by adaptively biasing the simulation to promote exploration of the free energy landscape. A proper choice of reaction coordinate increases the scope of exploration of the configuration space and consequently resulting in a more accurate estimate of the free-energy profile along the chosen reaction coordinate. In the event of a poorly chosen reaction coordinate, detection is facilitated by the AWH method, as the weight histogram would in such cases deviate significantly from the target distribution.

I have calculated the energetics of the O to C1 deactivation landscape of the Shaker KV channel in its atomistic description inserted in both PUFA-free and PUFA-enriched lipid

Chapter I. Study IV 89 bilayers, using the AWH method. In selecting a suitable reaction coordinate to enable an enhanced sampling of the deactivation pathway, a natural choice is one associated with the deactivation pathway itself, namely, the vertical displacement of helix S4. In this framework, the reaction coordinate is determined by the spatial translation of the gating charge R4 located on S4 in transitioning from the O state to the C1 state of the channel, progressing down the deactivation pathway along a vector defined by helices S1 and S3 of the VSD (Figure IV.1). The free energies associated with the presence and absence of PUFAs on the Shaker KV channel  were  investigated  in  5  μs  long AWH samplings. However, as transitions along the deactivation pathway slowed down significantly and entire O - C1

transitions   barely   took   place   beyond   1   μs   into   the   simulations,  I decided to focus on this initial part of the sampling data.

I.3.2 PUFA affects the free-energy landscape of deactivation

Sampling  over  the  course  of  1  μs  allowed  the  calculation  of  free  energies  of  deactivation  for   the Shaker KV channel in membrane bilayers both free of and enriched with PUFAs. The resulting free-energy surface reveals striking differences in favorable states along the deactivation pathway (Figure IV.2). The average free energy, calculated across the four subunits of the channel, reveals a lower free energy in the open state of the KV channel in the PUFA enriched system with a difference of ~ 8 kcal/mol. In contrast, at the intermediary C1 state of the channel, with an energy level ~ 10 kcal/mol lower, the KV channel in the PUFA free membrane is at a more stable state. Noteworthy, is the comparison of the energy landscape before and after the transitioning across the hydrophobic barrier. Prior to the transition across this barrier, the PUFA enriched system maintains a much lower free energy, however, once the barrier has been crossed and the transition to the metastable C1

state is approaching the PUFA enriched system enters into a higher free-energy state.

Chapter I. Study IV 90

Figure IV.2 Free-energy profile of the O to C1 transition. Free-energy profiles along S4 backbone displacement for the Shaker KV channel in PUFA free (blue) and PUFA enriched (green) lipid bilayers. The error bars display the standard error of free energy across the four channel subunits. The shaded area depicts the energy barrier characterized by a hydrophobic zone along S2 and S4.

The large standard errors and the shape of the free energy profile lacking a barrier distinguishing the activated state from the intermediate C1 state by the absence of two stable minima suggests that a much more thorough sampling of the deactivation pathway may be required. This could increase the possibility that a finer description of the configurational space can potentially give rise to a smoother free-energy landscape with a visible barrier separating the two thermodynamically stable states. Deterred by overcoming the hydrophobic barrier within the scope of current sampling, I deduce that the obtained free-energy profile has not converged and requires further work.

I.3.3 PUFA stabilizes the open state configuration

The distortion of the channel during the transitions can be assessed by calculating the root mean-square deviation (RMSD) of the entire VSD and segments S1-S3. The tendency of the PUFA enriched system to stabilize the open state of the Shaker KV channel as observed by the free energy landscape, is also reflected in RMSD measurements of the VSD of the channel as illustrated in Figure IV.3. This is particularly evident in the RMSD of the initial O to C1 transition. With the S1-S3 domain of the KV channel in the PUFA enriched membrane bilayer deviating considerably less from the open state crystal structure, an RMSD between 1.5 – 2.0 Å is observed. In contrast, the S1-S3 domain of the PUFA free system displays higher perturbation and initially has an RMSD of roughly 2.0 – 2.5 Å. However, following

Chapter I. Study IV 91 the initial O to C1 transition in which S4 has translated down once, both the PUFA free and PUFA enriched systems converge to comparable RMSD values, fluctuating around an RMSD of ~ 2 Å. A similar pattern is observed in the RMSD for the entire VSD of the channel in both systems in which the same behavior is observed except for slightly higher RMSD values, which is due to the inclusion of S4 that contributes further by the pull-down motion along the deactivation pathway (Figure IV.3, inset).

Figure IV.3 Root-mean square deviation (RMSD) of the backbone atoms of segments S1-S3 during  1  μs  of  AWH  sampling.  S4  is  translated  in  a  downward  motion  driving  the  channel   from an open state to an intermediate C1 state in PUFA free (blue) versus PUFA enriched (green) systems. RMSD was calculated relative to the initial conformation after a least squares fitting of S1–S3, with error bars indicating the standard errors across the four subunits of the channel. (Inset) RMSD for the entire VSD compared in both systems.