The advent of membrane protein crystallography first, and the shattering irruption of single particle cryogenic electron microscopy later, has allowed us to understand with an unprecedented level of detail the structural determinants of gating, permeation, and inactivation of K-channels, subjects that are covered in other reviews of this series. In this section, we briefly discuss the use of sucrose as an osmotic and viscosity agent in order to explore the functional architecture of voltage-gated K-channels during gating and K-permeation. We also discuss how these functional data complement the structural ones.

The exquisite selectivity of the K-channels for K⁺ over Na⁺ attracted the attention of membrane biophysicists from the start. Considering a difference of ∼0.4Å in their Pauling radius, they exhibited a remarkable permeability ratio of P_Na+/P_K+<0.01. The permeability ratios for alkali cation values obtained in the K-conductance of the myelinated nerve from frog (P_Tl+>P_K+>P_Rb+>P_NH+>>P_Li+∼P_Na+∼P_Cs+) were then explained in terms of the binding equilibrium contributed by steric, solvation, and electrostatic influences (Eisenman, 1962; Hille, 1973). Later on, in the giant squid axon, the high selectivity was explained in terms of size selection by a rigid structure, possibly lined by carbonyl groups, that could precisely accommodate dehydrated or partially dehydrated K⁺ ions but not Na⁺ ions (Bezanilla and Armstrong, 1972). Blockade experiments, best known for the foot in the door effect, of intracellular organic cations, crafted an overall shape where the permeation pathway begins in a wide intracellular entrance, followed by the rigid selectivity filter (Bezanilla and Armstrong, 1972; Coronado and Miller, 1982; Latorre and Miller, 1983). Those architectural anticipations of the permeation system turned out to be accurate when the Mackinnon group served at the table the atomic coordinates of KcsA, a prokaryotic potassium channel from the soil bacterium Streptomyces lividans at 3.2 Å (Doyle et al., 1998). The channel structure, in a closed or near-closed state, showed a ∼18 Å-long pore with an intracellular bundle crossing and locking a presumably aqueous wider inner cavity. Such cavity possibly decreases the energetic penalties of placing a charged particle at the membrane center (Parsegian, 1975; Roux and MacKinnon, 1999). Although the resolution of that structure prevented direct assignment of the carbonyl’s oxygen atoms, the authors placed them facing the passing ions. (Heginbotham et al., 1994). Shortly after, the same group showed the carbonyl atoms acting as water surrogates, allowing them to strip away the K⁺ from their hydration cage with minor energy costs (Morais-Cabral et al., 2001; Zhou et al., 2001). The multi-ion nature of the pore, first anticipated by Hodgkin and Keynes (1955), was also confirmed in these structures. The electron density showed five equally populated binding sites: four in the selectivity filter and one in the inner cavity. The selectivity filter would be occupied in two energetically equivalent single-file configurations with 2W:2K stoichiometry, interchanging in a concerted fashion. In both configurations, two K⁺ ions alternate with two water molecules (see below (Alcayaga et al., 1989; Morais-Cabral et al., 2001; Zhou et al., 2001)).

Despite having identical selectivity filters, unitary conductance in small and large conductance K-channels can differ by 10-100-fold (Eisenman et al., 1986; Heginbotham and MacKinnon, 1993; Naranjo et al., 2016). The above question hovered in the field for a long time. Only after the structure of the Kv1.2, a small conductance channel (10 pS) was determined in 2005 (Long et al., 2005), the bacterial MthK, and the Aplysia Slo1.2 large conductance channels (250-300 pS) came to light, was there the possibility to look into the physical support for the conductance differences (Jiang et al., 2002; Tao et al., 2017). Sugars played a significant role in the development of a satisfactory conduction model that accounted for the functional differences. But first, a little bit of history.

The Gramicidin A channel is a linear decapeptide with antibiotic capabilities that, in its dimeric form, induces discrete ion conduction events that saturate at high electrolyte concentrations (Hladky and Haydon, 1970; Veatch and Stryer, 1977). Interestingly, the ionic selectivity of the Gramicidin A channel mirrors the ion mobilities in solution, which, at first glance, suggests a water-filled hole (Myers and Haydon, 1972). But both the small diameter of the conduction pathway (4 Å) and streaming potential measurements are incompatible with that model, suggesting instead a single-file conduction mechanism (Rosenberg and Finkelstein, 1978b; Levitt et al., 1978). In this scenario, diffusionally limited access to the channel pore would strongly influence the association rate of the permeant ions. How to estimate the size of the pore entrance? Imagine a pore embedded in the plasma membrane bathed in a saline solution, where the ion flux through it is driven by the transmembrane potential (Figure 1A). If we can increase the transmembrane potential in an unlimited way, inevitably, at some point the ion flux will be limited by the arrival of the ions at the channel entrance, becoming voltage independent (Lauger, 1976; Figure 1A). Eq. 1 describes this diffusion-limited current, i _DL , as: i D L = 2 π z e o r C D c (1) where z is the valence of the permeant ion, e _o is the value of an elementary charge, r _C is the radius of capture, D is the diffusion coefficient, and c is the bulk concentration of the permeant ion expressed as ions/cm³. Assuming that the channel pore is a cylinder with neutral walls and the approaching ions are point charges, r _C is the pore size required to capture enough ions to account for i _DL . With known z, e _o , D, and c, i _DL provides a unique estimation of the pore-opening dimensions. To be sure that the currents saturation is of diffusional origin, its amplitude should be proportional to the concentration and diffusion coefficient of the permeant ion. Andersen experimentally decreased D in four different ways: by substitution of H₂O for D₂O, with temperature changes, and with the addition of sucrose or glycerol to increase the viscosity of the aqueous solution (because D is inversely proportional to η). However, r _C is an operational parameter because ions are not point charges and are not alone. Ions have a finite radius and usually travel with a gang of several hydration water molecules attached with different degrees of adherence. Then, the radius of capture does not, and should not, coincide with the physical dimensions of the pore. A better description of r _C is the difference between the physical pore radius and the hydrodynamic ion radius (Ferry, 1936; Andersen, 1983; Brelidze and Magleby, 2005). Then: r C = r p − r i o n (2) where r _P is the pore entrance radius and r _ion is the hydrodynamic radius of the ion in an aqueous solution. This equation states that the total number of effective collisions for a point, or spherical, charge is identical for equal radial deviations from the central trajectory.

The results obtained in 0.1M salt solution for Gramicidin A converged on capture radii of ∼0.2 Å for K⁺, Rb⁺ and Cs⁺, that having in mind structural estimations of r _P ∼2 Å (Urry et al., 1971; Koeppe et al., 1979), would make a reasonable use of Eq. 2 only if we consider the naked ionic radii for these ions (1.4-1.7 Å). But we all know that metal cations do not go around naked. With a hydrodynamic radius contributed by ∼6-8 water hydration layer, r _ion = 3.6-4.0 Å, the pore radius r _p would be ∼4 Å, doubling the structural estimation. The causes of such discord may be several, such as a lower effective sucrose concentration in the vicinity of the membrane or a binding reaction that departs from models that envision ion access to the pore as a simple collision with a spherical surface (Andersen, 1984). However, the important point is that the capture radius is perhaps the most realistic functional estimate of the behavior of an ion in the vicinity of the channel, and as we will see later, under certain conditions, it is also able to provide unique information about the pore architecture.

As mentioned above, the pore in the KscA structure crystallized in KCl clearly showed ∼5 fully occupied electronic densities in single file formation, four in the selectivity filter and one in the cavity (Doyle et al., 1998; Zhou et al., 2001). Because the densities located in the selectivity filter could represent occupation by either K⁺ or H₂O, based on, let´s say, common sense, K⁺ ions in the selectivity filter were assigned to be, ∼7Å apart, separated by one water molecule ∼3.5Å away. Closer proximity of two naked K⁺ would be energetically forbidden. Considering streaming-potentials measurements on BK-channels and energetic calculations on KcsA, a 1:1 K⁺/H₂O (K/W) transport stoichiometry was suggested (Alcayaga et al., 1989; Morais-Cabral et al., 2001). Thus, the four binding sites occupancy should alternate between two energetically equivalent, and concertedly inter-exchanging, sequence configurations: WKWK or KWKW (Morais-Cabral et al., 2001). Such a model predicted the basic aspects of ion conduction, such as high K⁺ transport rates, K⁺ dependency and selectivity (Morais-Cabral et al., 2001). This permeation mechanism reigned for about a decade, until Molecular Dynamic simulations with applied transmembrane potential to produce permeation events challenged this vision, suggesting that such a permeation mechanism is not unique in KcsA and nor generalized to the different K-channels. Defying common sense, permeation events could be induced by direct K⁺-K⁺ interaction without intervening water; worse, three or four K⁺ could normally occupy the selectivity filter sites, totally excluding water, and with not equally distributed binding probabilities (Furini and Domene, 2009; Jensen et al., 2010; Jensen et al., 2013; Kopec et al., 2018; Domene et al., 2021). Thus, conduction in K-channels seemed to be fairly anarchic and distinct across K-channels, where the transport K:W stoichiometry is larger than 1:1 and often with no water being co-transported. In addition, analysis of experimental 2D IR spectra of synthetic KcsA supports mechanisms of ion permeation with and without co-permeating water (Kopec et al., 2018).

Clearly, new experimental data are necessary to assess the K:W transport stoichiometry on different K-channels. Beside Alcayaga et al. (1989), to our knowledge, no other electrophysiological attempt has been made to determine the number of water molecules escorting K⁺ ions across the K-channels pore. Here we superficially review how to calculate the K:W transport stoichiometry from streaming potential measurements. For more detail, see Rosenberg and Finkelstein (1978a).

Consider a membrane with cation-selective channels that separates two compartments containing a diluted monovalent salt (let´s say 50 mM, much less than the sugar concentration). The ion channel pore is long enough to host a number of water molecules and one ion in single file (Figure 1B). When challenged with a unilateral addition of 1 M sugar to impose an osmotic gradient, water moves from the hypotonic side, dragging the ions dwelling in the pore. This extra charge-flow creates an additional electrical transmembrane potential. Equilibrium is reached when the new transmembrane potential (the streaming potential, v _s ) completely counterbalances the water differential potential energy (Rosenberg and Finkelstein, 1978a). A pore lacking ions would only move water, and one lacking water would be undisturbed by the osmotic gradient. In these two cases, no streaming potential would result. As a result, a non-zero v _s necessitates the coexistence of water and ions in a single file within the pore. The streaming potential at low ionic concentration for a channel hosting one ion would be: v s ≈ N R T F φ s n s n w (3) where N is the number of H₂O per ion, R,T and F have their usual meanings, n _s and n _w are the molar concentration of sucrose (∼1M) and water, respectively. φ _s is the molal osmotic coefficient. In a voltage clamp experiment, v _s could be, in principle, measured directly as the K-channel reversal potential (V _C ) Figure 1B). However, it is necessary to introduce a correction for the effect of sugar on the activity of the ionic species. This correction is usually carried out by adding to both sides of the membrane an excess of valinomycin, a dehydrated-K⁺ selective ionophore, and measuring the ionophore-induced new reversal potential (V _V ) (Rosenberg and Finkelstein, 1978a; Alcayaga et al., 1989). Thus, as Figure 1B shows: v s = V C − V V (4) When, φ _s n _s ≈ 1 (sucrose around 1M) and room T^o, Eq. 3 reduces to v _s ≈ Nx0.46 mV. For gramicidin A channel in 10 and 100 mM NaCl, KCl or CsCl solutions, v _s ≈ 3 mV/Osm per kg, pointing to a W:ion stoichiometry of 6-7:1, value in agreement with recent MD simulations (Rosenberg and Finkelstein, 1978a; Paulino et al., 2020). The hemocyanin and the sarcoplasmic reticulum K⁺ channels in sugar or urea gradient showed v _s ≈ 1.2 and 1.1 mV/Osm per kg, respectively, pointing to two to three coupled water molecules (Cecchi et al., 1982; Miller, 1982). In the probably most relevant finding for the discussion here, the skeletal muscle BK-single channel recordings in artificial lipid bilayer exposed to 2M unilateral sucrose exposure gave v _s ≈ 0.85 mV/Osm per kg, pointing to a 1-2:1 W:K stoichiometry in physiological solutions (Alcayaga et al., 1989). Considering that BK-channels are multi-ion channels, these results are in good agreement with, and possibly inspired, the classic 2W:2K permeation mechanism (Morais Cabral et al., 1998; Morais-Cabral et al., 2001; Zhou et al., 2001).

It is worth noting that with a gradient of 2 Osm/kg, Alcayaga et al. (1989) obtained v _s =1.86 ± 0.3 mV. This small number is reliable thanks to the exceptional signal-to-noise ratio offered by the BK-channel. Two additional criteria strengthen this type of determination: First, the streaming potential should be proportional to the osmotic gradients (Cecchi et al., 1982; Miller, 1982). Second, in the Alcayaga et al. (1989) measurements, v _s decreased significantly as the K⁺ concentration was symmetrically raised from 20 to 500 mM, a concentration range in which BK single channel conductance grows ∼4 fold (Eisenman et al., 1986). These two determinations reported strong functionally congruent changes in the K⁺ occupancy in the BK-channel, providing a critical support for water being co-transported in the BK channel. To replicate these experiments in small/intermediate conductance Kv-channels, where, according to molecular simulations, water is severely excluded, would be exceedingly difficult to perform. Increasing the osmolyte by two or fourfold to circumvent this difficulty, could enable the identification of conduction modes that exclude water or have a low W:K stoichiometry. Because of their high conductance, the interesting cases of KcsA and MthK channels, among others, could still offer a manageable signal-to-noise ratio to perform osmotic measurements that could contribute to clarifying the W:K stoichiometric discord in K-channel permeation (Naranjo et al., 2016).

Voltage-gated activation is the most distinctive conformational change in voltage-gated K-channels (Kv). This structural change allows the channel to open, conducting K⁺-ions. Kv channels have a dedicated Voltage-Sensor-Domain, VSD, which undergoes a large conformational change in response to changes in the transmembrane electric field. Over the past 25 years, the nature and extent of these conformational changes have been intensively debated. This section will exclusively discuss the structure-function lessons we learned using sucrose as an osmotic agent.

Consider a protein having two conformations. The addition of an osmotic agent to the protein surroundings will shift the equilibrium in favor of the conformation that exposes less hydrated surfaces that are not in contact with the osmolyte (Figure 1C). Thus, the impact of the osmolyte on the free energy of the conformation change makes it possible to estimate its extension if it involves fluctuations in the protein’s level of hydration. This estimation is reported as a change in volume exposed to the solvent but buried from the osmolyte (Figure 1C). This technique was initially used to infer the pore aqueous volume variations on the opening of the reconstituted mitochondrial voltage-gated porin (VDAC) during activation (Zimmerberg and Parsegian, 1986).

Examining activation-induced conformational changes in TTX-poisoned squid giant axons was the first application of this technique to voltage-gated potassium channels. Sucrose osmotic effects revealed a voltage independent increment of sucrose inaccessible aqueous volume of 1500ų (Zimmerberg et al., 1990). With the development of molecular cloning and heterologous expression of channels, experiments could be carried out under circumstances where the targeted protein is responsible for most of the signal. As a result, Shaker K-channels subjected to a moderate unilateral increase in external osmotic pressure showed only a slight effect on their ability to activate, indicating, either, little external physical changes to the water-filled volume or that modifications with similar glucose accessibility occurred. Therefore, rather than the voltage-sensing conformational change, the pore opening may have been primarily responsible for the volume variation. Similar outcomes were obtained from tests employing Kv1.4 expressed in Xenopus oocytes, but with an unusual twist. The estimated change in cytosolic volume during activation was around three times bigger than the estimate for giant squid axon K-channels and comparable to that of slow-type inactivation (Jiang et al., 2003). These findings showed that, similar to Shaker and Kv1.2, the activation gate and, at least, one of the slow inactivation gates had a large structural overlap, as indicated by the internal TEA interference with both gates (Gonzalez-Perez et al., 2008; Suarez-Delgado et al., 2020). Other slow inactivation gate (C-type) that appears to be toward the external pore opening (Choi et al., 1991; Oliva et al., 2005), seems to be sensitive to the external osmolarity. Ostemeyer et al. (2013) conducted extensive molecular simulations of KcsA channels, finding that, in the slow inactivated state, the selectivity filter is stabilized by three water molecules situated behind the pore-lining residues. Removal of these waters helps the filter to assume a conductive state. Accordingly, electrophysiological experiments revealed an accelerated recovery from inactivation in 2M external sucrose, suggesting that the conductive conformation of the selectivity filter is favored when sucrose grabs nasty inactivation waters from the channel (Ostmeyer et al., 2013). Thus, water may play a critical role in the channel’s conformational equilibrium.

Conceptually speaking, the isolation of the VSD from the rest of the protein yields a simpler system and more straightforward data interpretation of volumetric changes. However, only when it became evident that the VSD activation implied an 8–15 Å displacement of the voltage sensing charges did it become necessary to explore the volumetric extent of the VSD conformational change (Vargas et al., 2012). But, as mentioned above, such conformational change was, if not undetectable, at least obscured by the one occurring at the pore gate (Zimmerberg et al., 1990; Starkus et al., 1995; Jiang et al., 2003).

The use of sucrose is far from being limited to the study of ion conduction and the gating of Kv channels. It has been used in the study of hemoglobin, allowing us to observe that their tense and relaxed conformations in their deoxy and oxygenated states, respectively, have significant changes on their solvent exposed surfaces, suggesting a role for hydration in the protein conformational dynamics (Shaanan, 1983). After assessing the effect of several organic osmolytes on the O₂ binding curves, Colombo et al. concluded 50 to 70 water molecules are gained during the deoxy to oxy transition of the Hb tetramer (Colombo et al., 1992) in agreement with previous determinations obtained with the method of modulation of entropy by alcohols (Bulone et al., 1991). De Cristofaro et al. performed osmotic stress experiments using sucrose to address the role of water in the thrombin-thrombomodulin complex formation, concluding that ∼35 water molecules are released into the bulk solution during the process (De Cristofaro et al., 1995). Sucrose has also contributed to understanding the underlying mechanism of the unparalleled temperature dependence of thermoTRP channels. Diaz-Franulic el at. (2020), showed that the carboxy terminal coiled coil of the TRPM8 channel was not only required for making the channel cold sensitive but also that it experienced a significant increase in its solvent-inaccessible aqueous volume of ∼1500ų upon cold exposure (Diaz-Franulic et al., 2020), which was compatible with the channel structure determined by Cryo-EM (Yin et al., 2018). Considering these findings, it seems plausible that the steep temperature dependence of channel gating arises from a folding/unfolding reaction at the carboxy terminus domain, which increases its molar heat capacity in the unfolded state (Clapham and Miller, 2011; Diaz-Franulic et al., 2020; Diaz-Franulic et al., 2021). Overall, the above studies highlight the importance of considering hydration not only as a major player in protein folding but also as an agent capable of shaping the conformational landscape governing their biological activity.