Summary and conclusions

In this chapter, we presented a detailed study of the influence of the radius and the polarity of narrow hydrophilic pores on the water permeation. The structural and dynamical information obtained complements and expands the knowledge of the structure-activity relationship in water channels. Such knowledge is valuable to understand the permeation mechanism of naturally occurring channels and to design channels of desired properties. The presented results are useful to predict the response in the channel flux to changes in the concentration gradient between the solutions at each end of the channel, or which radius and polarity would allow a fast flux of water molecules while preserving the single-file regime.

Since single-file channels are generally a requirement for the selectivity towards different solutes, we therefore paid special attention to this permeation regime.

The analysis of the pore water density revealed characteristic oscillations in channels of radii smaller than three times the radius of a water molecule. Prior to the establishment of an uninterrupted flow of water molecules, on average at a radius of ∼0.17 nm, the density fluctuations can be well described by a liquid-vapor equilibrium [32]. A perfectly packed single-file configuration presents a local maximum in the pore water density as a function of the pore radius, followed by a local minimum indicating the transition to a double-file regime. The polarity of the channel scales the water pore density: an increase in hydrophilicity of the pore leads to a corresponding increase of the pore water density, and modulates at which radius the transitions between different regimes takes place. At large pore radii, all water pore densities converge to the bulk density, and therefore the pore occupancy directly scales with the area and length of the pore.

The permeability coefficients, both osmotic and diffusive, were characterized as function of the pore radius and the averaged occupancy. In the single-file regime, the osmotic permeability always increases with the pore radius, scaling linearly with the pore occupancy until the densest single-file configuration is achieved.

5.6. Summary and conclusions

On the contrary, the diffusive permeability experiences a local maximum at radii where the density fluctuations average to half the bulk water density, and falls to a local minimum at the densest single-file configuration. Along with the transition from single-file to double-file, the permeability coefficients increase with the radius. Both coefficients show a gradual increase in the slope depending on the radius, converging to the macroscopic radial dependence for large radii.

The ratio of osmotic and diffusive permeability coefficients was found to equal the averaged pore occupancy (plus one) for all pore polarities and radii that guarantee a no-pass condition. Beyond this single-file arrangement, the value of (p_f/p_d−1) remains almost constant, equal to the occupancy corresponding to the densely packed single-file configuration. This implies that the confinement of the water molecules preserves the collective motions of water chains, effectively acting like single-files in parallel. As the channel becomes much wider, the ratios converge towards their expected macroscopic radial dependence.

For the design of new water channels, we have seen that the radius and polar-ity play a major role in determining the flow of water molecules, in contrast to the results presented in the previous chapter, where we showed that the length has almost no impact on the osmotic permeability. In general, if the selectivity of the pore is not an issue, large apolar channels are the most effective in con-ducting the water flux. If we are constrained to the narrow single-file regime, less hydrophilic channels allow the single-file to persist at a larger radius than highly polar channels, and with faster rates.

5. Influence of the pore radius and polarity on the water permeability 5. Influence of the pore radius and polarity on the water permeability

6. Not only enthalpy: entropy dominates ion permeation

barriers in single-file channels

Summary

In previous chapters, we focused our study on the determinants of water perme-ability in narrow pores. Since the peptidic water channels presented before also function as cation channels, we will now concentrate on one of the multiple factors that influences ion permeability through single-file pores, and compare this with the determinants underlying water permeation. Here, we focused on the effect of channel length on the barrier for potassium ion permeation through single-file channels. Using series of peptidic gramicidin-like and simplified ring-structured channels, both embedded in model membranes, we obtained two distinct types of behavior: saturation of the central free energy barriers for peptidic channels and a linear increase in simplified ring structured channels with increasing chan-nel length. The saturation of the central free energy barrier for the peptidic channels occurs at relatively short lengths, and it is correlated with the desol-vation from the bulk water. Remarkably, decomposition of free energy barriers into enthalpic and entropic terms reveals an entropic cost for ion permeation.

Furthermore, this entropic cost dominates the ion permeation free energy bar-rier, since the corresponding free energy contribution is higher than the enthalpic barrier. We conclude that the length dependence of the free energy is enthalpy dominated, but the entropy is the major contribution to the permeation barrier.

The decrease in rotational water motion and the reduction of channel mobility are putative origins for the overall entropic penalty. The different length depen-dence of water and ion permeation opens up novel ways to steer the selectivity