A novel delta current method for transport stoichiometry estimation
 Xuesi M Shao^{2}Email author,
 Liyo Kao^{1} and
 Ira Kurtz^{1, 3}
DOI: 10.1186/s1362801400142
© Shao et al.; licensee BioMed Central Ltd 2014
Received: 19 August 2014
Accepted: 19 November 2014
Published: 11 December 2014
Abstract
Background
The ion transport stoichiometry (q) of electrogenic transporters is an important determinant of their function. q can be determined by the reversal potential (E_{rev}) if the transporter under study is the only electrogenic transport mechanism or a specific inhibitor is available. An alternative approach is to calculate delta reversal potential (ΔE_{rev}) by altering the concentrations of the transported substrates. This approach is based on the hypothesis that the contributions of other channels and transporters on the membrane to E_{rev} are additive. However, E_{rev} is a complicated function of the sum of different conductances rather than being additive.
Results
We propose a new delta current (ΔI) method based on a simplified model for electrogenic secondary active transport by Heinz (Electrical Potentials in Biological Membrane Transport, 1981). ΔI is the difference between two currents obtained from altering the external concentration of a transported substrate thereby eliminating other currents without the need for a specific inhibitor. q is determined by the ratio of ΔI at two different membrane voltages (V_{1} and V_{2}) where q = 2RT/(F(V_{2} –V_{1}))ln(ΔI_{2}/ΔI_{1}) + 1. We tested this ΔI methodology in HEK293 cells expressing the elctrogenic SLC4 sodium bicarbonate cotransporters NBCe2C and NBCe1A, the results were consistent with those obtained with the E_{rev} inhibitor method. Furthermore, using computational simulations, we compared the estimates of q with the ΔE_{rev} and ΔI methods. The results showed that the ΔE_{rev} method introduces significant error when other channels or electrogenic transporters are present on the membrane and that the ΔI equation accurately calculates the stoichiometric ratio.
Conclusions
We developed a ΔI method for estimating transport stoichiometry of electrogenic transporters based on the Heinz model. This model reduces to the conventional reversal potential method when the transporter under study is the only electrogenic transport process in the membrane. When there are other electrogenic transport pathways, ΔI method eliminates their contribution in estimating q. Computational simulations demonstrated that the ΔE_{rev} method introduces significant error when other channels or electrogenic transporters are present and that the ΔI equation accurately calculates the stoichiometric ratio. This new ΔI method can be readily extended to the analysis of other electrogenic transporters in other tissues.
Keywords
Electrogenic transporter Stoichiometry Membrane currentvoltage relationship Reversal potential HEK293 cells Patch clamp Computational simulationBackground
Based on their electrical properties, membrane protein transporters are classified as being either electrogenic (transport a net charge) or electroneutral [1][3]. Which of these categories a given transporter belongs to is dependent on its substrate (or ion) coupling ratio; its transport stoichiometry represented by the symbol q. Electrogenic transporters are sensitive to both the electrical and chemical gradients of the ions that are being transported across a membrane. Unlike electroneutral transporters, electrogenic transporters can utilize the membrane potential of a cell or organelle membrane to drive substrates or ions against their chemical gradients. For a given electrochemical gradient, the transport stoichiometry is therefore an important independent determinant of both the magnitude and direction of substrate or ion flux through a membrane transport protein. The simplest stoichiometry for an electrogenic transporter is 1:1 as in the case of the sodiumcoupled glucose transporter SGLT2 [4]. In many instances more complex stoichiometries have been reported [4],[5]. Furthermore, certain transporters have variable stoichiometry ratios [6][10].
where intracellular concentrations of Na^{+} ([Na^{+}]_{i}) and HCO_{3} ^{−} ([HCO_{3} ^{−}]_{i}) as well as extracellular concentrations of Na^{+} ([Na^{+}]_{o}) and HCO_{3} ^{−} ([HCO_{3} ^{−}]_{o}) are known and E_{NBC} is the reversal potential of the transporter. F, R and T are Faraday’s constant, gas constant and absolute temperature respectively. RT/F = 25.69 at 25°C [13].
If the electrogenic transporter under consideration is the only transport mechanism in the membrane, q estimated by solving Eq. 1 is accurate. In most cells or expression systems, there are other channels or electrogenic transporters in the membrane, reversal potential method requires the use of a specific inhibitor to differentiate the transport process of interest from other transport pathways. Subtracting the IV curve in the presence of the inhibitor from the IV curve without inhibitor, one obtains the E_{rev} of the transportermediated current. Therefore, the relationship of Eq. 1 still holds.
There are some variations of the ΔE_{rev} approach such as estimating q by determining the slope of V_{I=0} vs. ion or substrate concentrations [2]. In this report, we show that ΔE_{rev} approach is correct only when the transport current under study is the only current in the membrane or in other words, currents mediated by other channels, electrogenic transporters, and leak current are negligible. When the currents mediated by other channels/transporters are not negligible, the implicit assumption underlying the ΔE_{rev} approach and its variations is that the reversal potentials due to other channels and transporters are additive to the E_{rev} of the transporter under study, therefore they can be eliminated by subtraction. However, the assumption that E_{rev} is additive is not valid since the effect of multiple channels/electrogenic transporters on ΔE_{rev} is a complicated function of the concentrations of ions and substrates involved, as well as the conductance and transport rate of those pathways [17],[18].
To address these issues, we have developed a new approach named the “delta current (ΔI) method”. The utility of the ΔI approach is demonstrated using the electrogenic sodium bicarbonate cotransporters NBCe2C and NBCe1A [14],[19][21] expressed in HEK293 cells. In vivo, NBCe2C is expressed in choroid plexus epithelial cells and other tissues. NBCe1A is expressed in the mammalian kidney proximal tubule and the eye. This method has several advantages: 1) The equation does not suffer from the aforementioned errors in the ΔE_{rev} method due to other channels and functional electrogenic transporters; 2) Like the ΔE_{rev} method, the measurement protocol does not require a specific inhibitor. In addition, by computational simulations, we show the advantage of the ΔI method in calculating the stoichiometry ratio of an electrogenic transporter, and demonstrate that the ΔE_{rev} method can introduce significant errors in estimating q.
Methods
Expression of NBCe2C and NBCe1A in HEK293 cells
The SLC4 human NBCe2C and NBCe1A proteins were expressed in HEK293 cells as follows. Fulllength human cDNA for each transporter was cloned into a pMSCVIRESEGFP (Clontech, Mountain View, CA) which expresses the transporters under a CMV promoter and also expresses EGFP as a separate protein under an internal ribosome entry site. The cDNA sequence of each of the constructs was verified by DNA sequencing. Use of human material and cell line are approved by UCLA Institutional Biosafety Committee (IBC#111.13.0r).
Electrophysiological recordings
Solutions
Components  Pipette  Bath  

a  b  c  d  A  B  C  D  E  
NaCl  110  110  55  15  
CsCl  10  10  10  
CaCl_{2}  1  1  1  1  1.5  1.5  1.5  1.5  1.5 
MgCl_{2}  1  1  1  1  1  
TEACl  10  10  10  10  
TMACl  55  120  105  
EGTA  10  10  10  10  
HEPES  10  50  50  50  10  10  10  10  10 
NaHCO_{3}  8  25  25  25  25  10  10  
CsGluconate  125  105  105  90  
CsHCO_{3}  17  
TMAHCO_{3}  15  15  
NaGluconate  10  15  25  
ATPMg  1  1  1  1  
ATPNa_{2}  1  1  
Glucose  15  15  15  15  15 
Data analysis
Signals from intracellular recordings were digitized at 2 KHz sampling frequency with the Digidata 1440A and software Clampex 10 (Molecular Devices Co., CA, USA). The signals were saved as data files for further analyses offline. Data are expressed as mean ± SE. Paired ttest was used for determining statistical significance. p ≤ 0.05 was taken as the criterion for significance.
Results
Estimation of NBCe2C transport stoichiometry with the conventional reversal potential method
To estimate the NBCe2C HCO_{3} ^{−} to Na^{+} transport stoichiometry q, the conventional method of measuring the reversal potential with the inhibitor DIDS was used initially. At known intracellular and extracellular concentrations of Na^{+} and HCO_{3} ^{−}, q could be estimated with Eq. 1.
A novel delta current method for estimation of transport stoichiometry
Where $\sum _{j}{I}_{j}$ is the sum of all other currents mediated by various channels and electrogenic transporters including leak current on the membrane. $\sum _{j}{I}_{j}$ can be a nonlinear function of V while a general assumption is that it is independent of NBC transport current.
$\sum _{j}{I}_{j}$ is completely eliminated. For simplicity, we take ν_{Na} = 1 and q = ν_{HCO3}/ν_{Na}.
Therefore, at V = 0, the delta current ΔI_{V1=0} is the pure NBC transport current at [Na^{+}]_{o2}.
In the following applications, to minimize the effects of possible K_{c} voltage dependence, we also take a V_{2} value close to 0 (e.g. ± 10 to 15 mV). Therefore the calculation involves only experimental measurements of currents close to equilibrium conditions.
Transport stoichiometry of NBCe2C estimated with the delta current method
Transport stoichiometry of NBCe1A estimated with the delta current method
Computational simulation: ΔI method estimates q accurately when there are additional conductances other than electrogenic NBC transport
In native tissue or expression systems such as oocytes or HEK293 cells, there are endogenous channels and electrogenic transporters other than the one under study. In these cases, the Δ current method is based on the assumption of additivity of membrane currents while the ΔE_{rev} method and its variations based on the assumption of additivity of reversal potentials [2],[15],[16]. Were the latter true, by altering the concentrations of the transported species, the contribution of other channels and electrogenic transporters could be subtracted and the relationship between delta E_{rev} and transported species concentrations and the transport stoichiometry easily obtained based on Eq. 1. This method, although widely used, is not consistent with GoldmanHodgkinKatz (GHK) theory [17],[18] where E_{rev} is a logarithmic function of sum of concentrations of ions inside and outside of the membrane; i.e. not additive.
Again, a simple expression for the relationship between stoichiometry and reversal potential is not obtained.
Computational simulation of ΔI and ΔE _{ rev } methods to estimate q in the absence or presence of a Cl ^{ − } channel
[HCO _{3} ^{−}] _{i} = [HCO _{3} ^{−}] _{o} = 25  V _{I=0}(mV)  ΔE _{rev}(mV)  q (ΔE _{rev})  ΔI _{2}/ ΔI _{0}(V _{2} = 12 mV)  q (ΔI)  

[Na ^{+}] _{i}=10 mM  [Na ^{+}] _{o} = 10  [Na ^{+}] _{o} = 25  
q = 2  0  −23.5  −23.5  2.0  1.263  2.0 
q = 3  0  −11.75  −11.75  3.0  1.595  3.0 
q = 2, + G_{Cl}  −5.1  −25.3  −20.2  2.17  1.263  2.0 
q = 3, + G_{Cl}  −12.8  −18.75  −5.95  4.96  1.595  3.0 
q = 2, + 2 x G_{Cl}  −9.2  −26.9  −17.7  2.33  1.263  2.0 
q = 3, +2 x G_{Cl}  −19.7  −23.5  −3.8  7.2  1.595  3.0 
Simulation of ΔI and ΔE _{ rev } methods to estimate q in conditions similar to rat proximal tubule in the absence or presence of a Na ^{ + } /Dglucose cotransporter
[HCO _{3} ^{−}] _{o} = 24, [HCO _{3} ^{−}] _{i} = 13.4  V _{I=0}(mV)  ΔE _{rev}(mV)  q (ΔE _{rev})  ΔI _{2}/ΔI _{1}V _{2}V _{1} = 10 mV  q (ΔI)  

[Na ^{+}] _{i} = 17 mM  [Na ^{+}] _{o} = 150  [Na ^{+}] _{o} = 100  
q = 2  −89.6  −78.75  10.85  2.0  1.205  2.0 
q = 3  −52.6  −47.2  5.4  3.0  1.45  3.0 
q = 2, + Glu  −73.6  −62.75  10.85  2.0  1.205  2.0 
q = 3, + Glu  3.2  10.2  7.0  2.55  1.45  3.0 
These results indicate that the ΔE_{rev} method can significantly bias the estimate depending on the magnitude and electrophysiological properties (e.g. the IV relationship) of other channels and electrogenic transporters if there are any, while the ΔI method gives a more accurate estimate of the transport stoichiometry q.
Discussion
In this study, we have demonstrated the development and utility of a new method for estimating the transport stoichiometry of electrogenic transport proteins. With this ΔI method, one subtracts the currents due to channels and transporters other than the one under study and thereby obtains the stoichiometry of the transporter without the need for a specific inhibitor. Using this method, we showed that the transport stoichiometry of the bicarbonate cotransporter NBCe2C expressed in HEK293 cells is 2 HCO_{3} ^{−}: 1 Na^{+} that is consistent with the results obtained using the conventional reversal potential method with the inhibitor DIDS. A transport stoichiometry ratio of 2 was also obtained for NBCe1A with the ΔI method that is consistent with the data obtained previously using the conventional reversal potential method with DIDS [25]. In addition, we demonstrated that, with computational simulation, the estimation of q obtained using the new ΔI method was equivalent to that obtained with the conventional ΔE_{rev} methods when an electrogenic NBC transporter was the only transport mechanism in the cell membrane. However, if a chloride channel or a glucose cotransporter SGLT2 was present in the membrane, our simulations showed that the ΔE_{rev} method significantly biased the estimate of the transport stoichiometry q, while the ΔI method gave accurate results.
The method proposed in this study is based on Eq. 2 from Heinz [23] that describes the functional relationship between flux of a transporter and the concentrations of transport ions/substrates and the membrane voltage [24]. Unlike the GHK formulation that assumes independence of ion movement across the membrane [13] and does not involve the concept of stoichiometry, Eq. 2 explicitly expresses coupling of Na^{+} and HCO_{3} ^{−} (both are voltage dependent) as a product and the stoichiometry as a power of the concentrations and voltage. Linearity of the current and voltage relation is not a presumption for Eq. 2 nor is it for the GHK equations [17],[18]. Nonlinearity of the IV curves results from: 1) the GHK equation is based on solubilitydiffusion theory. In GHK current equation, the current is an exponential function of the voltage. Similarly Eq. 2 shows that flux is an exponential function of voltage; 2) transport mechanisms of membrane channels or transporters represented by the permeability term Ps in GHK equations and K_{c} in Eq. 2 may be voltage dependent. With the conventional E_{rev} method, if the transporter under study is the only electrogenic pathway, this nonlinearity would not be a problem since the current is 0 and at this point, the voltage is the reversal potential under the conditions of the experimental substrate concentrations. However, if there are other channels or electrogenic transporters in the membrane and if a specific inhibitor is not available, V_{I=0} that can be measured is not the reversal potential for the transporter under study, but rather is the voltage at a point on the IV curve where the net result of the transporter current under study and currents mediated by other transporters and channels is 0. The alternative ΔE_{rev} method is problematic in that the assumption of reversal potential additivity is inconsistent with nonlinearity property of GHK equations and Eq. 2. This is solved by employing the ΔI method where the contribution of other channels or transporters can be eliminated without the assumption of E_{ver} additivity.
This is essentially Eq. 1 if we take ν_{Na} = 1 and q = ν_{HCO3}/ν_{Na}. Starting from here, the widely used delta reversal potential method to estimate stoichiometry [2],[15],[16] can be easily derived:
From the above operations, we can see that reversal potential method, the ΔE_{rev} method and the ΔI method to estimate transport stoichiometry all have the same theoretical foundation (such as Eq. 2 and same assumptions). Moreover, they are equivalent if the electrogenic transporter under investigation is the only conductive process in the membrane.
However, if there are endogenous channels and electrogenic transporters other than the one under study, the relationship of ion activities and transport stoichiometry and reversal potential becomes very complicated as we can see in Eq. 8, Eq. 9 and Eq. 10. Therefore, a method to eliminate the confounding effects of additional transporters and channels on reversal potentials by simple subtraction of V_{I=0} is not valid. Our simulation results also indicate that the commonly used ΔE_{rev} method in this instance would not be accurate. The error increases as the currents mediated by other transporters and channels increase (Table 2) relative to the transporter under investigation.
Transport parameters of an electrogenic secondary active transport like K_{c} are affected by many factors. How a given transport process responds theoretically to an electrochemical gradient depends on the type of the transport kinetic models utilized, e.g. “affinity model”, “velocity model” or “mixed model” as described by Heinz [24], and whether the loaded or the unloaded carrier bears an electrical charge. Heinz [23] originally introduced equation 2 and referred to K_{c} as a function of mobility and concentrations of the free and loaded carrier, respectively, and hence may vary with the degree of saturation. In our approach, we made two assumptions that are implicitly shared with the ΔE_{rev} method: 1) K_{c} is constant in certain voltage range and does not vary when the concentration of the substrate of choice in the study ([Na^{+}]_{o} in this study) changes; 2) the sum of currents $\sum _{j}{I}_{j}$ mediated by other channels and transporters in the membrane as a function of V does not change when the substrate concentration is altered [2],[15],[16]. Based on these two assumptions the two methods offer benefits such as experimentally straightforward as changing the concentrations of a substrate without the need for specific blockers and share similar limitations. The difference between ΔI and ΔE_{rev} method in terms of assumption 2 is that with the ΔI method, $\sum _{j}{I}_{j}$ can be completely eliminated (Eq. 4) if it does not change when the substrate ([Na^{+}]_{o} in this study) is altered. On the contrary, with the ΔE_{rev} method, as long as $\sum _{j}{I}_{j}$ is not negligible, the confounding effects of $\sum _{j}{I}_{j}$ on V_{I=0} can not be eliminated and biases the estimation of q as shown in Figure 6 and Table 2 and Table 3, even if it does not change when the substrate concentration varies.
In practice, ways to circumvent the limitations due to the above assumptions include: 1) using a smaller concentration change of the substrate, as long as it induces a significant delta current; 2) changing the concentrations of a particular substrate with less possibility of involving other electrogenic transporters. For example, in the case of electrogenic Na^{+}coupled glucose or amino acid transporters, one would choose to change either glucose or amino acids respectively rather than Na^{+}.
In this study, we changed [Na^{+}]_{o} from 10 to 25 mM because: 1) HCO_{3} ^{−} partakes in a volatile buffer system that involves pCO_{2} to keep the pH constant. pH would be stable when [HCO_{3} ^{−}]_{o} is unaltered; 2) switching [Na^{+}]_{o} from 10 to 25 mM would induce a significant delta current [15] and 3) at these relatively low concentrations, the possibility of transport saturation would be small, therefore variation of K_{c} in Eq. 2 and Eq. 3 would be minimized. We assigned V_{1} = 0 in the above application, therefore in the conditions of ${\left[N{a}^{+}\right]}_{i}={\left[N{a}^{+}\right]}_{o}\mathit{and}\phantom{\rule{0.25em}{0ex}}{\left[HC{{O}_{3}}^{}\right]}_{i}={\left[HC{{O}_{3}}^{}\right]}_{o},{I}_{M}={\displaystyle \sum _{j}{I}_{j}}$ is well defined and it is not close to 0. In addition, we assigned a V_{2} that is not far from 0 (+12 mV in this study), thus possible variation of K_{c} under extreme voltages can be minimized.
More detailed kinetic descriptions of the transport rate in order to characterize the entire IV relationship rely on a detailed understanding of the molecular transport steps [28][30]. This is not necessary for the purposes of our formulation, because we implicitly analyze the portion of the IV relationship that is close to the E_{rev} i.e., V_{1} = 0 when [Na^{+}]_{i} = [Na^{+}]_{o} and [HCO_{3} ^{−}]_{i} = [HCO_{3} ^{−}]_{o}.
The accuracy of stoichiometry estimation using wholecell patchclamp recordings also depends on the accuracy of wholecell current measurement and the voltages applied to the cell membrane from the patchclamp amplifier. The drift of the junction potential between the patch pipette solution and the Ag/AgCl coated wire that connects to the headstage of the amplifier is a major source of unstable current recording especially when the Cl^{−} concentration in the pipette is low [22]. We used a microagar salt bridge of 2 M KCl in the patch pipette that minimized the junction potential drift and therefore stabilized the wholecell current measurements [22].
Conclusions
We developed a new delta current (ΔI) method for estimating transport stoichiometry of electrogenic transporters based on a simplified model for electrogenic secondary active transport by Heinz (1981). We showed that this model reduces to the conventional reversal potential method when the transporter under study is the only electrogenic transport on the membrane. When there are other electrogenic transport processes such as ion channels or transporters, the ΔI method eliminates their contribution in estimation of q. We tested this new ΔI methodology in HEK293 cells expressing the electrogenic SLC4 sodium bicarbonate cotransporters NBCe2C and NBCe1A, as well as using computational simulations. Our simulations demonstrated that the ΔE_{rev} method introduces significant error when other channels or electrogenic transporters are present on the membrane with a significant conductance relative to the transporter under study, and that the ΔI equation accurately calculates the stoichiometric ratio. Our new ΔI method can be readily extended to the analysis of other electrogenic transporters.
Abbreviations
 CMV:

Cytomegalovirus
 DIDS:

4,4′Diisothiocyanatostilbene2,2′disulfonic acid
 EGFP:

Enhanced Green Fluorescent Protein
 Eq:

Equation
 E_{rev} :

Reversal potential
 F:

Faraday’s constant
 GHK:

GoldmanHodgkinKatz
 HEPES:

4(2Hydroxyethyl)1piperazineethanesulfonic acid
 IV:

Currentvoltage
 NBC:

Sodium bicarbonate cotransporter
 R:

Gas constant
 SGLT2:

Sodiumcoupled glucose transporter 2
 T:

Absolute temperature
 ΔE_{rev} :

Delta reversal potential
 ΔI:

Delta current
Declarations
Acknowledgement
We thank Dr. Donald D. F. Loo, for helpful discussions and comments on the manuscript.
This work was supported in part by funds from the NIH (R01DK077162), the Allan Smidt Charitable Fund, the Factor Family Foundation, and the Arvey Foundation (to IK) and R43DA03157801 (to X. M. S).
Authors’ Affiliations
References
 Kurtz I, Petrasek D, Tatishchev S: Molecular mechanisms of electrogenic sodium bicarbonate cotransport: structural and equilibrium thermodynamic considerations. J Membr Biol. 2004, 197 (2): 7790. 10.1007/s002320030643x.View ArticleGoogle Scholar
 Dong H, Dunn J, Lytton J: Stoichiometry of the Cardiac Na ^{+}/Ca ^{2+}exchanger NCX1.1 measured in transfected HEK cells. Biophys J 2002, 82(4):1943–1952.,
 Bacconi A, Virkki LV, Biber J, Murer H, Forster IC: Renouncing electroneutrality is not free of charge: switching on electrogenicity in a Na ^{+}coupled phosphate cotransporter. Proc Natl Acad Sci U S A 2005, 102(35):12606–12611.,
 Wright EM, Turk E: The sodium/glucose cotransport family SLC5. Pflugers Arch. 2004, 447 (5): 510518. 10.1007/s0042400312020.View ArticleGoogle Scholar
 Chen NH, Reith ME, Quick MW: Synaptic uptake and beyond: the sodium and chloridedependent neurotransmitter transporter family SLC6. Pflugers Arch. 2004, 447 (5): 519531. 10.1007/s0042400310645.View ArticleGoogle Scholar
 Coady MJ, Chen XZ, Lapointe JY: rBAT is an amino acid exchanger with variable stoichiometry. J Membr Biol. 1996, 149 (1): 18. 10.1007/s002329900001.View ArticleGoogle Scholar
 Alonso GL, Gonzalez DA, Takara D, Ostuni MA, Sanchez GA: Kinetic analysis of a model of the sarcoplasmic reticulum CaATPase, with variable stoichiometry, which enhances the amount and the rate of Ca transport. J Theor Biol. 2001, 208 (3): 251260. 10.1006/jtbi.2000.2185.View ArticleGoogle Scholar
 Sacher A, Cohen A, Nelson N: Properties of the mammalian and yeast metalion transporters DCT1 and Smf1p expressed in Xenopus laevis oocytes. J Exp Biol. 2001, 204 (Pt 6): 10531061.Google Scholar
 Gross E, Kurtz I: Structural determinants and significance of regulation of electrogenic Na ^{+}HCO _{3} ^{−}cotransporter stoichiometry. Am J Physiol Renal Physiol 2002, 283(5):F876–F887.,
 Iwamoto H, Blakely RD, De Felice LJ: Na ^{+}, Cl ^{−}, and pH dependence of the human choline transporter (hCHT) in Xenopus oocytes: the proton inactivation hypothesis of hCHT in synaptic vesicles. J Neurosci 2006, 26(39):9851–9859.,
 Ravera S, Virkki LV, Murer H, Forster IC: Deciphering PiT transport kinetics and substrate specificity using electrophysiology and flux measurements. Am J Physiol. 2007, 293 (2): C606C620. 10.1152/ajpcell.00064.2007.View ArticleGoogle Scholar
 Coady MJ, Wallendorff B, Bourgeois F, Charron F, Lapointe JY: Establishing a definitive stoichiometry for the Na ^{+}/monocarboxylate cotransporter SMCT1. Biophys J 2007, 93(7):2325–2331.,
 Hille B: Ion Channels of Excitable Membranes. 2001, Sinauer Associates, Sunderland, MassachusettsGoogle Scholar
 Sassani P, Pushkin A, Gross E, Gomer A, Abuladze N, Dukkipati R, Carpenito G, Kurtz I: Functional characterization of NBC4: a new electrogenic sodiumbicarbonate cotransporter. Am J Physiol. 2002, 282 (2): C408C416. 10.1152/ajpcell.00409.2001.View ArticleGoogle Scholar
 Yamaguchi S, Ishikawa T: Electrophysiological characterization of native Na ^{+}HCO _{3} ^{−}cotransporter current in bovine parotid acinar cells. J Physiol 2005, 568(Pt 1):181–197.,
 Owe SG, Marcaggi P, Attwell D: The ionic stoichiometry of the GLAST glutamate transporter in salamander retinal glia. J Physiol. 2006, 577 (Pt 2): 591599. 10.1113/jphysiol.2006.116830.View ArticleGoogle Scholar
 Goldman DE: Potential, Impedance, and Rectification in Membranes. J Gen Physiol. 1943, 27 (1): 3760. 10.1085/jgp.27.1.37.View ArticleGoogle Scholar
 Hodgkin AL, Katz B: The effect of sodium ions on the electrical activity of giant axon of the squid. J Physiol. 1949, 108 (1): 3777. 10.1113/jphysiol.1949.sp004310.View ArticleGoogle Scholar
 Kurtz I: SLC4 Sodiumdriven bicarbonate transporters. Seldin and Giebisch's The Kidney: Physiology and Pathophysiology. Edited by: Alpern RJ, Moe OW, Caplan M. 2013, Elsevier/Academic Press, Amsterdam, Boston, 18371860. 10.1016/B9780123814623.000537. 5View ArticleGoogle Scholar
 Kao L, Kurtz LM, Shao X, Papadopoulos MC, Liu L, Bok D, Nusinowitz S, Chen B, Stella SL, Andre M, Weinreb J, Luong SS, Piri N, Kwong JMK, Newman D, Kurtz I: Severe neurologic impairment in mice with targeted disruption of the electrogenic sodium bicarbonate cotransporter NBCe2 (Slc4a5 gene). J Biol Chem. 2011, 286 (37): 3256332574. 10.1074/jbc.M111.249961.View ArticleGoogle Scholar
 Millar ID, Brown PD: NBCe2 exhibits a 3 HCO _{3} ^{−}:1 Na + stoichiometry in mouse choroid plexus epithelial cells. Biochem Biophys Res Commun 2008, 373(4):550–554.,
 Shao XM, Feldman JL: Microagar salt bridge in patchclamp electrode holder stabilizes electrode potentials. J Neurosci Methods. 2007, 159 (1): 108115. 10.1016/j.jneumeth.2006.07.001.View ArticleGoogle Scholar
 Heinz E: Membrane Potential in Secondary Active Transport. Electrical Potentials in Biological Membrane Transport. 1981, SpringerVerlag, Berlin, 4650. 10.1007/9783642816758.View ArticleGoogle Scholar
 Geck P, Heinz E: Coupling in secondary transport. Effect of electrical potentials on the kinetics of ion linked cotransport. Biochim Biophys Acta. 1976, 443 (1): 4963. 10.1016/00052736(76)904909.View ArticleGoogle Scholar
 Zhu Q, Shao XM, Kao L, Azimov R, Weinstein AM, Newman D, Liu W, Kurtz I: Missense mutation T485S alters NBCe1A electrogenicity causing proximal renal tubular acidosis. Am J Physiol. 2013, 305 (4): C392C405. 10.1152/ajpcell.00044.2013.View ArticleGoogle Scholar
 Yoshitomi K, Burckhardt BC, Fromter E: Rheogenic sodiumbicarbonate cotransport in the peritubular cell membrane of rat renal proximal tubule. Pflugers Arch. 1985, 405 (4): 360366. 10.1007/BF00595689.View ArticleGoogle Scholar
 Hummel CS, Lu C, Loo DD, Hirayama BA, Voss AA, Wright EM: Glucose transport by human renal Na ^{+}/Dglucose cotransporters SGLT1 and SGLT2. Am J Physiol 2011, 300(1):C14–C21.,
 Sanders D: Generalized kinetic analysis of iondriven cotransport systems: II. Random ligand binding as a simple explanation for nonmichaelian kinetics. J Membr Biol. 1986, 90 (1): 6787. 10.1007/BF01869687.View ArticleGoogle Scholar
 Parent L, Supplisson S, Loo DD, Wright EM: Electrogenic properties of the cloned Na ^{+}/glucose cotransporter: II. A transport model under nonrapid equilibrium conditions. J Membr Biol 1992, 125(1):63–79.,
 Gross E, Hopfer U: Voltage and cosubstrate dependence of the NaHCO3 cotransporter kinetics in renal proximal tubule cells. Biophys J. 1998, 75 (2): 810824. 10.1016/S00063495(98)775708.View ArticleGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.