Water-Transporting Proteins

Abstract

Transport through lipids and aquaporins is osmotic and entirely driven by the difference in osmotic pressure. Water transport in cotransporters and uniporters is different: Water can be cotransported, energized by coupling to the substrate flux by a mechanism closely associated with protein. In the K⁺/Cl⁻ and the Na⁺/K⁺/2Cl⁻ cotransporters, water is entirely cotransported, while water transport in glucose uniporters and Na⁺-coupled transporters of nutrients and neurotransmitters takes place by both osmosis and cotransport. The molecular mechanism behind cotransport of water is not clear. It is associated with the substrate movements in aqueous pathways within the protein; a conventional unstirred layer mechanism can be ruled out, due to high rates of diffusion in the cytoplasm. The physiological roles of the various modes of water transport are reviewed in relation to epithelial transport. Epithelial water transport is energized by the movements of ions, but how the coupling takes place is uncertain. All epithelia can transport water uphill against an osmotic gradient, which is hard to explain by simple osmosis. Furthermore, genetic removal of aquaporins has not given support to osmosis as the exclusive mode of transport. Water cotransport can explain the coupling between ion and water transport, a major fraction of transepithelial water transport and uphill water transport. Aquaporins enhance water transport by utilizing osmotic gradients and cause the osmolarity of the transportate to approach isotonicity.

Appendix

Thermodynamics of Water Cotransport

The rate of water cotransport across a membrane can be described by

$$ {\text{J}}_{{{\text{H}}_{ 2} {\text{O}}}} = {\text{B}}\left( {\mu_{\text{i}} - \mu_{\text{o}} } \right) $$

(1)

For the KCC, μ equals R·T· (ln [K] + ln [Cl] + n · ln [C_w]) taken on the inside (i) and the outside (o) of the membrane; [K], [Cl] and [C_w] are the concentrations of K⁺, Cl⁻. The number of water molecules coupled to the transport of one K⁺ and one Cl⁻ ion (n) equals 500 for the KCC; in Table 1 this parameter is called “CR.” R is the gas constant, T the absolute temperature and B a constant that can be determined experimentally. At equilibrium, the rate of water cotransport is zero and the Gibbs criterion for equilibrium of water, μ_i = μ_o, can be written

$$ \left[ {{\text{K}}_{\text{i}} } \right]\left[ {{\text{Cl}}_{\text{i}} } \right]\left[ {{\text{C}}_{{{\text{w}},{\text{i}}}} } \right]^{\text{n}} = \left[ {{\text{K}}_{\text{o}} } \right]\left[ {{\text{Cl}}_{\text{o}} } \right]\left[ {{\text{C}}_{{{\text{w}},{\text{o}}}} } \right]^{\text{n}} $$

(2)

Since [C_w] is proportional to exp (−osm_i/n_w), where osm is the osmolarity and n_w is the molarity of water, 55 M, Eq. 2 can be written as

$$ \left[ {{\text{K}}_{\text{i}} } \right]\left[ {{\text{Cl}}_{\text{i}} } \right]{ \exp }\left( { - {\text{n\,osm}}_{\text{i}} /{\text{n}}_{\text{w}} } \right) = \left[ {{\text{K}}_{\text{o}} } \right]\left[ {{\text{Cl}}_{\text{o}} } \right]{ \exp }\left( { - {\text{n osm}}_{\text{o}} /{\text{n}}_{\text{w}} } \right) $$

(3)

This equation can be used to predict how high adverse osmotic gradients are required to stop transport under physiological conditions. For amphibians, [K_i] and [Cl_i] are typically 100 and 40 mM and [K_o] and [Cl_o] are 2 and 120. For n = 500, an osmotic difference, osm_i − osm_o, of 310 mOsm is required. For mammals, where [K_o] and [Cl_o] are 5 and 120 mM, an osmotic difference of 200 mOsm would be required to stop transport. These values are in good agreement with experiments in epithelia (see text).

The water flux mediated by the KCC $\left( {{\text{J}}_{{{\text{H}}_{ 2} {\text{O}}}}^{\text{KCC}} } \right)$ given in Eq. 1 can be written as

$$ {\text{J}}_{{{\text{H}}_{ 2} {\text{O}}}}^{\text{KCC}} = {\text{B}}\cdot{\text{R}}\cdot{\text{T}}\cdot \left[ {{ \ln }\left( {{\text{K}}_{\text{i}} /{\text{K}}_{\text{o}} } \right) + { \ln }\left( {{\text{Cl}}_{\text{i}} /{\text{Cl}}_{\text{o}} } \right) + {\text{n}}/{\text{n}}_{\text{w}} \left( {{\text{osm}}_{\text{i}} - {\text{osm}}_{\text{o}} } \right)} \right] $$

(4)

The validity of this equation is supported by data from the choroid plexus epithelium from Necturus maculosus. Here, ${\text{J}}_{{{\text{H}}_{ 2} {\text{O}}}}^{\text{KCC}}$ was a linear function of the external osmolarity (osm_o) when this was increased from its normal value of 200 mOsm to values up to 400 mOsm by addition of mannitol (Zeuthen 1994); the proportionality factor B · R · T was 6 × 10⁻⁶ cm s⁻¹ in this range. Given this value, it can be estimated that the KCC in the exit membrane could be responsible for a major component of the transepithelial water transport. In amphibians under steady-state conditions, K⁺ and Cl⁻ concentrations are typically 80 and 40 mM intracellular and 2 and 110 mM extracellular, with intra- and extracellular osmolarities around 200 mOsm. With these values ${\text{J}}_{{{\text{H}}_{ 2} {\text{O}}}}^{\text{KCC}}$ calculates as 18 nl cm⁻² s⁻¹. ${\text{J}}_{{{\text{H}}_{ 2} {\text{O}}}}^{\text{KCC}}$ has previously been estimated by a less exact approach to 3.5 nl cm⁻² s⁻¹ (Zeuthen 1995); this is smaller than the estimate obtained from Eq. 1 but still a good approximation to the measured values (see text).

For the NKCC1, μ in Eq. 1 equals R · T · $\left( {{ \ln }\left[ {\text{Na}} \right] + { \ln }\left[ {\text{K}} \right] +2\cdot{ \ln }\left[ {\text{Cl}} \right] + {\text{n}} \cdot { \ln }\left[ {{\text{C}}_{\text{w}} } \right]} \right)$. At equilibrium, the Gibbs equation becomes

$$ \left[ {{\text{Na}}_{\text{i}} } \right]\left[ {{\text{K}}_{\text{i}} } \right]\left[ {{\text{Cl}}_{\text{i}} } \right]^{ 2} \left[ {{\text{C}}_{{{\text{w}},{\text{i}}}} } \right]^{\text{n}} = \left[ {{\text{Na}}_{\text{o}} } \right]\left[ {{\text{K}}_{\text{o}} } \right]\left[ {{\text{Cl}}_{\text{o}} } \right]^{ 2} \left[ {{\text{C}}_{{{\text{w}},{\text{o}}}} } \right]^{\text{n}} $$

(5)

With C_w proportional to exp (−n · osm/n_w):

$$ \left[ {{\text{Na}}_{\text{i}} } \right]\left[ {{\text{K}}_{\text{i}} } \right]\left[ {{\text{Cl}}_{\text{i}} } \right]^{ 2} { \exp }\left( { - {\text{n osm}}_{\text{i}} /{\text{n}}_{\text{w}} } \right) = \left[ {{\text{Na}}_{\text{o}} } \right]\left[ {{\text{K}}_{\text{o}} } \right]\left[ {{\text{Cl}}_{\text{o}} } \right]^{ 2} { \exp }\left( { - {\text{n osm}}_{\text{o}} /{\text{n}}_{\text{w}} } \right) $$

(6)

The coupling ratio (n) for the NKCC1 can be determined by comparing two different situations which give the same rate of water transport. In the pigmented epithelium of the ciliary body of the eye, hyperosmolar addition of NaCl to the outside solution did not alter the transport rate for water by the NKCC1 (Hamann et al. 2005); when 37.5 mM of NaCl was added to the outside solution, the osmotic effect of the extra NaCl, i.e., 75 mOsm, was exactly matched by the increased chemical driving force originating from the extra 37.5 mM of Na⁺ and 37.5 mM of Cl⁻. If the rates of water transport in the NKCC1 are the same in the two situations, the chemical potential given by the outside solution μ_o must also be the same. If these are called o,1 and o,2, it follows from Eq. 1 that μ_{o,1 =} μ_o,2, or

$$ \left[ {{\text{Na}}_{{{\text{o}}, 1}} } \right]\left[ {{\text{K}}_{{{\text{o}}, 1}} } \right]\left[ {{\text{Cl}}_{{{\text{o}}, 1}} } \right]^{ 2} { \exp }\left( { - {\text{n osm}}_{{{\text{o}}, 1}} /{\text{n}}_{\text{w}} } \right) = \left[ {{\text{Na}}_{{{\text{o}}, 2}} } \right]\left[ {{\text{K}}_{{{\text{o}}, 2}} } \right]\left[ {{\text{Cl}}_{{{\text{o}}, 2}} } \right]^{ 2} { \exp }\left( { - {\text{n osm}}_{{{\text{o}}, 2}} /{\text{n}}_{\text{w}} } \right)] $$

(7)

Given values of [Na_o,1], [K_o,1], [Cl_o,1], osm_o,l of 120, 2, 120 mM and 290 mOsm and values of [Na_o,2], [K_o,2], [Cl_o,2], osm_o,2 of 157.5, 2, 157.5 mM and 365 mOsm, n calculates as 590. Eq. 7 can now be used to predict how high adverse osmotic gradients are required to stop transport under physiological conditions. For mammals [Na_i], [K_i] and [Cl_i] are typically 10, 100 and 60 mM and [Na_o], [K_o] and [Cl_o] are 150, 5 and 120. For n = 590, an osmotic difference, osm_i − osm_o, of 100 mOsm is required.

For the SGLT1 the Gibbs equation takes the following forms (Meinild et al. 1998):

$$ \left[ {{\text{Na}}_{\text{i}} } \right]^{ 2} \left[ {{\text{G}}_{\text{i}} } \right]\left[ {{\text{C}}_{{{\text{w}},{\text{i}}}} } \right]^{\text{n}} { \exp }\left[ { 2 {\text{F}}\Uppsi_{\text{i}} /{\text{RT}}} \right] = \left[ {{\text{Na}}_{\text{o}} } \right]^{ 2} \left[ {{\text{G}}_{\text{o}} } \right]\left[ {{\text{C}}_{{{\text{w}},{\text{o}}}} } \right]^{\text{n}} { \exp }\left[ { 2 {\text{F}}\Uppsi_{\text{o}} /{\text{RT}}} \right] $$

(8)

$$ {\text{RTln}}\left[ {{\text{Na}}_{\text{o}} /{\text{Na}}_{\text{i}} } \right]^{ 2} + {\text{RTln }}\left[ {{\text{G}}_{\text{o}} /{\text{G}}_{\text{i}} } \right] + {\text{RTln }}\left[ {{\text{C}}_{{{\text{w}},{\text{o}}}} /{\text{C}}_{{{\text{w}},{\text{i}}}} } \right]^{\text{n}} = 2 {\text{F}}\left[ {\Uppsi_{\text{i}} -\Uppsi_{\text{o}} } \right] $$

(9)

Na is the Na⁺ concentration, G the glucose concentration and Ψ the electrical potential (other symbols as above). In a physiological situation, where the Na⁺ concentration is 10 times higher on the outside than on the inside, the glucose concentrations the same, and the membrane potential is –50 mV; it can be calculated that the inward flux of water would proceed in face of an adverse osmotic gradient of up to about 1,700 mOsm.

At constant Na⁺ and glucose concentrations, the relation between changes in external water concentration, proportional to exp(−osm/n_w), and the reversal potential (Ψ_i – Ψ_o) becomes

$$ \Updelta \left( {\Uppsi_{\text{i}} -\Uppsi_{\text{o}} } \right) = -{\text{n}}/{\text{n}}_{\text{w}} {\text{ RT}}/ 2 {\text{F }}\Updelta {\text{osm}}_{\text{o}} $$

(10)

This relation has been used for a determination of the coupling ratio (n) for the rabbit SGLT1 (Zeuthen and MacAulay 2002a). Here, a shift in the outside osmolarity of 100 mOsm resulted in a shift in the reversal potential of about 5 mV, equivalent to an n of 247. This compares well with estimates of n obtained under non-steady-state conditions (Table 1).