Renal tubular acidoses (RTAs) are forms of metabolic acidoses that are thought to arise from a lack of urine excretion of protons or loss of bicarbonate (HCO₃^-) due to a variety of tubular disorders. Characteristically, this causes a hyperchloraemic (non-anion gap) acidosis without impaired glomerular filtration. Molecular studies have identified genetic or acquired defects in transporters of protons and HCO₃^- in many forms of RTA. However, at the same time these transporters have been found also to be involved in transport of Cl^- and Na⁺. Furthermore, in a few cases RTA has been associated with primary defects in electrolyte transporters alone.

The core of Stewart theory is that transport of protons as such is unimportant to regulation of pH. In contrast, the theory states that acid–base homeostasis is directly regulated by electrolyte transport in the renal tubules. H⁺ is effectively a balancing requirement imposed by physical chemistry. Accounting for how this occurs will probably lead to an improved understanding of homeostasis.

We begin the review by describing the classical formulation of the renal regulation of acid–base homeostasis. We then describe the quantitative physical chemistry notion of acid–base as described by Stewart (henceforth called the 'physicochemical approach'). On this basis we analyze some of the mechanisms that are active in RTA. We show that the physicochemical approach may lead to new questions that can be pursued experimentally to supplement insights already gained with classical theory. Several authors have suggested that the physicochemical approach could be used to the benefit of our understanding of RTA 12.

According to traditional concepts 3, daily acid production is calculated as the combined excretion of sulphate anion (SO₄^2-) and organic anions in the urine, whereas renal elimination of acid equivalents is computed as the combined titrable acidity + ammonium - excreted HCO₃^-, called net acid excretion (NAE). Cohen and coworkers 4 reviewed evidence indicating that the traditional view may be inconsistent with observations in patients in renal failure and in a number of experimental studies. In one of the studies assessed, Halperin and coworkers 5 examined rats loaded with extra alkali on top of already basic ordinary rat chow. Amazingly, increasing unmeasured organic anions had a 10-fold greater effect on alkali disposal than did changes in NAE, as traditionally computed. Similar findings had already been reported by Knepper and coworkers 6 in 1989. That acid–base balance is always accounted for by standard measurements may therefore be disputed. Although fervently rejected 3, this has given rise to a proposal of a new classification system for NAE that includes the regulation of loss of organic anions or potential HCO₃^-7.

Difficulties in measuring titrable acidity and organic anions are one main source of disagreement with regard to acid–base homeostasis 4 both in normal persons and in those with renal impairment 8. A recent Danish study 9 reinforced the concept from studies of healthy humans exposed to acid loads that nonmetabolizable base excretion is important to renal regulation of acid–base homeostasis.

Central to renal acid–base physiology is excretion of ammonium. One view 10 is that ammonium is produced as NH₄⁺ in large quantities from hydrolysis of peptide bonds, and its excretion in urine has no bearing on acid–base chemistry except for the fact that for nitrogen balance it would otherwise have to be converted to urea – a process seen to consume bicarbonate. Exactly this argument was used again by Nagami 11 in an authoritative review of renal ammonia production and excretion. Most recently a study of normal individuals 12 showed that ureagenesis increased during experimental acidosis produced by CaCl₂. This contrasted with the authors' expectations because urea-genesis was supposed to cost alkali.

However, the traditional view is that NH₄⁺ excretion is one ofthe most important mechanisms for eliminating metabolic acid equivalents because the leftover from deamination of glutamine is effectively bicarbonate and the process comes to a halt if NH₄⁺ is not eliminated 13. As stated in recent accounts, this view also accounts for the bicarbonate toll of ureagenesis 14 but the details of regulation and overall stoichiometry are still debated. However, it seems that the handling of NH₄⁺ in the kidney is of great importance because a complicated network of transport mechanisms have evolved 11. Most recently, a new group of putative NH₄⁺ (and NH₃?) transporters related to the rhesus group of proteins has been described 15. As far as we know, the result of missing one or more of these transporters on acid–base balance is not yet known, and because of redundancy it could be limited. Finally, apart from being a transported quantity that is of importance per se, NH₄⁺ hasalso been found to influence a number of other tubular processesthat are involved in acid–base regulation 1617.

Hence, although there can be no doubt that excretion of is important to acid–base homeostasis, it is not entirely NH₄⁺ clear why this is so. We suggest that the physicochemical approach to acid–base provides a more coherent picture of the role played by NH₄⁺.

Here we consider the approach to acid–base chemistry proposed by PA Stewart 1819. Biological fluids are dominated by a high concentration of water, approximately 55 mol/l. Physical chemistry determines the dissociation of water into protons and hydroxyl ions. If the determinants of that equilibrium are unchanged, then concentration of protons, and therefore pH, will be as well.

A number of important substances (e.g. many salts) dissociate completely to ions, when dissolved in water, whereas water itself dissociates to a very minor degree. Nonetheless, the dissociation of water into H⁺ and OH^- provides an inexhaustible source and sink of acid–base equivalents. The proton concentration, and hence pH, is determined by the requirement that positive and negative charges must balance and by the combined equations that govern dissociations of involved species. The approach is formally based on analysis of separate compartments and leads to the result that [H⁺] in a compartment of physiological fluid is determined by the concentrations of fully ionized substances (strong ion difference [SID]), partial CO₂ tension (PCO₂) and partly dissociated substances termed 'weak acids' in that compartment.

In a solution containing only fully dissociated salt (e.g. NaCl) the requirement for electrical neutrality leads to the following relation:

(Na⁺ + H⁺) - (Cl^- + OH^-) = 0     (1)

The water dissociation equilibrium must also be obeyed:

[H⁺] × [OH^-] = K_w × [H₂O] ≈ K_w'     (2)

The SID is defined as the difference between fully dissociated cations and anions, and in the NaCl solution it is calculated as follows:

SID = [Na⁺] - [CI^-]     (3)

Combining Eqns 1, 2 and 3 leads to the following relation:

[H⁺]² + SID × [H⁺] - K_w' = 0     (4)

The positive solution to this second-degree polynomial yields:

And from Eqn 2:

Hence, in a compartment/solution containing NaCl or similar salt solution, the proton concentration is simply determined by SID and the water ion product (K_w). Addition or removal of protons or hydroxyl ions may or may not be possible but will not change pH 20.

It is possible that the development of Stewart concepts to this extent will suffice for analysis of renal influences on acid–base homeostasis from a whole body or balance perspective. However, to present the theory of Stewart in a more complete form, we may also add weak acids and CO₂ to this framework. A full account of the Stewart approach with some later adaptations is available in a previous issue of this journal (see the report by Corey 21).

Adding a weak acid, specifically a substance that participates in proton exchanges and hence that has a charge that is dependent on pH, Stewart showed that Eqn 7 had to be satisfied.

[H⁺]³ + (KA + SID) × [H⁺]² + (KA × [SID - A_TOT] - Kw) × [H⁺] - KA × Kw' = 0     (7)

Where KA is the equilibrium constant and A_TOT is the total concentration of weak acids. To arrive at a satisfactory explanation for acid–base homeostasis from the whole body perspective, the pervasive effect of continuing production and transport and pulmonary excretion of CO₂ evidently must be taken into account. To do this, two more equations were needed:

[H⁺] × [HCO₃^-] = KC × PCO₂     (8)

[H⁺] × [CO₃^2-] = K3 × [HCO₃^-]     (9)

Solving these together, Stewart's model in its most integrative form is now given by Eqn 10:

[H⁺]⁴ + ([SID] + KA) × [H⁺]³ + (KA × [SID] - [A_TOT]] - KW - KC × PCO₂) × [H⁺]² - (KA × [KW + KC × PCO₂] - K3 × KC × PCO₂) × [H⁺] - KA × K3 × KC × PCO₂ = 0     (10)

These equations have explicit entries of constants and concentrations or tensions, but the practical use of the framework must be developed with detail sufficient to deal with the problem at hand. In plasma, other strong ions (e.g. Ca²⁺ and lactate) and weak acids are frequently found but they are treated on an equal footing.

A number of studies have shown that this algebra yields an accurate description or prediction of acid–base measurements. More importantly, however, the physicochemical approach may lead to a better understanding of mechanisms that are active in disease and treatment. An example of what may be accomplished is the successful application of the physicochemical approach to exercise physiology. Here, the ability of the independent variables to predict measured pH has been proven (correlation 0.985), but more importantly changes over time and between the different body compartments in these independent variables explain how a range of interventions influence acid–base as a part of muscle physiology 22.

CO₂ is transported in the body as a number of species and because the processes involved have variable latency (e.g. the Cl^-/HCO₃^- exchanger band3 in red blood cells 23), widely differing values of PCO₂ are found in the body 24. The physicochemical approach, focusing as it does on each compartment separately and having no special interest in the quantitatively lesser compartment of arterial blood, is at no disadvantage relative to conventional concepts in elucidating this difficult area. Although this is less of a problem when overall renal regulation of acid–base homeostasis is considered, notwithstanding that urine CO₂ may be of utility when diagnosing variants of RTA 25, it is a major problem with respect to understanding the underlying cellular transport processes. Further, recent results showing the complicated organization of transporters together in physically connected complexes indicate that much work will be needed if we are to understand the integrated molecular details of anion transport and metabolism in renal CO₂ tubules 26.

Whereas the physicochemical approach explains how pH is determined from independent variables, when applying this to urine the focus is not on regulation of urine pH but on the renal regulation of the independent variables that determine plasma and whole body acid–base balance. These independent variables are the SID, weak acids, and PCO₂. Hence, from the point of view of the physicochemical approach, assessing urine with the aim of understanding the renal contribution to acid–base balance amounts to deducing its effects on the independent variables for a specified body compartment. It has been reported that the concepts of SID and weak acids may be blurred. For example, pH may influence the behaviour of species as either strong ions (components of SID) or weak acids 27, and this applies, for instance, to phosphates and proteins. Furthermore, neither Na⁺ nor Ca²⁺ is invariably and totally dissociated, as implied by the common SID construct 28.

One important but thus far undeveloped aspect of the Stewart approach to whole body acid balance problems is that the independent variables for the extracellular compartment normally in focus may be only partly relevant to the much larger intracellular compartment. Excretion of large amounts of potassium, for example, may be minimally relevant to SID in the extracellular compartment but may, depending on the circumstances, be crucial to intracellular SID 29.

It is evident that there will be differences in the approach to accounting for acid–base balance in the classical compared with the physicochemical approach. In the classical setting we must perform difficult titrations 4 and measurements of NH₄⁺, PCO₂ and pH to compute a [HCO₃^-] after correction of pK for ionic strength. Every part of this is complicated, and the overall results with regard to our understanding of whole body balance are not universally accepted 4. In the physicochemical approach, renal involvement in acid–base balance is manifested in its influence on independent variables – nothing more and nothing less. For a first approximation, this is the urine excretion of SID components, principally Na⁺ and Cl^- when extracellular homeostasis alone is considered. It will be a practical matter to determine the extent to which the Stewart approach will be complicated by problems in computing both SID and weak acids in urine.

In the physicochemical approach, the urinary excretion of NH₄⁺ or organic anions will be important for acid–base balance only to the extent that it influences SID in a body compartment. Excretion of organic anions is from this perspective a way to excrete Na⁺ without Cl^- and thereby decrease SID in the body. This will result in increasing plasma H⁺, no matter what the nature of the organic anion is. This hypothesis can be tested experimentally. On a similar footing, NH₄⁺ excretion could be understood as means to excrete Cl^- without Na⁺ in order to increase SID in the body. However, apart from their influence on SID, the excretion of these substances may convey important information about underlying pathophysiological processes. Hence, Kellum 30 has proposed that, when analyzing the mechanism of hyperchloraemic acidosis, an initial distinction could be made between states in which the kidney reacted normally (i.e. increasing the excretion of Cl^- relative to Na⁺ and K⁺ by augmenting NH₄⁺ excretion and so causing urine SID to be more negative) and situations where, in spite of acidosis, the kidney continues to decrease whole body SID by excreting more Na⁺ and K⁺ than Cl^-. This will typically be the case in distal RTA (dRTA) without increased NH₄⁺ excretion during acidosis.

Several types of RTA may be discerned 31: proximal (type 2), distal (type 1), mixed (type 3), and a heterogeneous group of disorders characterized by hyperkalaemia and acidosis (type 4). RTA is a hyperchloraemic rather than an anion-gap-type metabolic acidosis. Typically, renal function (glomerular filtration rate) is unimpaired and the acidosis is not simply caused by absence of renal clearance. RTA must be separated from other forms of hyperchloraemic acidosis, some of which (e.g. the hyperchloraemic acidosis that occurs following saline infusion) are very important in the intensive care setting 3233.

Traditionally, dRTA is recognized by the inability to decrease urine pH below 5.5 in spite of metabolic acidosis. These patients are also characterized by an inability to augment NH₄⁺ excretion 60. A high urine PCO₂ after bicarbonate loading has traditionally been the criterion for declaring distal H⁺ secretion to be normal 61, and it was also recently found to identify patients with confirmed dRTA due to a proton pump problem 25.

Proximal RTA is characterized by high fractional excretion of bicarbonate (>15%) during loading, and an ability to achieve a urine pH below 5.5 during acidosis. Approaches are well described by Soriano 31 and Smulders and coworkers 62.

When assessing urine to gauge whether the physicochemical approach or the classical theory is best able to explain the acidosis in RTA, it is possible that both will do so successfully. From the physicochemical approach, the lack of urine NH₄⁺ in distal RTA will force excretion of urine with a relatively high SID and this will explain the acidosis. An old study did in fact indicate that, in type 1 RTA, Na⁺ loss and to a lesser degree Cl^- handling was abnormal in spite of long-term correction of acidosis 63.

The classical theory also explains the acidosis by a lack of amplification of NH₄⁺ excretion. Likewise, for proximal RTA bicarbonate loss and high SID excretion will be equivalent. It was recently suggested that even though it may be difficult mechanistically to separate the implications of the theories, by using the physicochemical approach the focus is forced toward movements of Na⁺ and Cl^-, and this may lead to a new understanding 2. Indeed, analysis of WNK mutations confirms this expectation.

From the clinical viewpoint, the advantage of employing the physicochemical approach is that the renal contribution to acid–base homeostasis, even in complicated settings, can be ascertained in principle by simple chemical analysis of the urine. It is possible to explain RTA in general as a hyperchloraemic form of metabolic acidosis that can be described as a low SID acidosis, which has focused attention primarily on the net handling of SID constituents, namely Na⁺, K⁺, and Cl^-. This handling of SID constituents has not had a central position in our understanding of the various disease states, and in some cases only seems to be a consequence of anions necessarily being filled in by Cl^- as HCO₃^- goes down and reversely. However, in the future efforts will focus on which transport mechanism is active (e.g. is Cl^- moving with H⁺ or K⁺ or against it to shunt the potential generated by the vacuolar H-ATPase 44) and on which moiety is actually regulated by the tubular processes. A number of studies have recently focused on apical anion handling in the collecting duct via a newly characterized transporter, namely pendrin 64. This exchanger seems well poised to react to Cl^- balance 65 and could therefore also be sensitive to the independent variable in acid–base regulation (i.e. SID) 66.

One defining point in the physicochemical approach that has an impact on the interpretation of acid–base phenomena is the concept of [H⁺] as a dependent variable, which tends to imply that clinical or physiological phenomena might more fundamentally depend on the baseline independent variables (e.g. SID, weak acids and PCO₂). The necessity when analyzing renal phenomena to differentiate metabolic and respiratory acidosis may be an indicator that pH as such is not actually the sensed quantity.

In fact, how derangements in acid–base balance are sensed by the kidneys remains elusive, although there it is a general belief that such detection happens there. Quite recently, a protein, Pyk2, that was sensitive to pH and that regulated isoform 3 of the Na⁺/H⁺ exchanger in the proximal tubules was described 67. Furthermore, in experiments identifying this alleged pH sensor, SID was directly varied but PCO₂ did not change. Hence, it is not evident that pH was really sensed, and in an accompanying editorial Gluck 68 expressed reservations regarding this notion. As explained above in relation to proximal RTA, recent studies conducted by Boron and coworkers 43 indicate that that bicarbonate and PCO₂ are the regulated entities, rather than pH, which is in accordance with the physicochemical approach to acid–base physiology insofar as bicarbonate and SID are equivalent.

Finally, if whole body acid–base balance is to be untangled, then the intracellular domains, which are likely to vary, must also be understood. In exercise physiology 69 advances have been made using the Stewart approach in elucidating plasma acid–base balance as it is perturbed by transfer of putative independent influences, but modelling cells or whole organs themselves from this point of view has not been done. This will entail such difficulties as determining water structure in cells and small confines 70 and modelling the pH effects of the structural proteins and nucleic acids as they fold and integrate. Modelling potassium balance in order to draw inferences regarding intracellular SID will likewise be necessary and interesting.

A recent study of patients in acute renal failure 71, employing state of the art methods, found that almost 80% of total body water appeared to be extracellular. This indicates that a great deal of experimental work must be done before analytical solutions 72 to the whole body multicompartment system can be derived and applied in clinical practice. We suggest that the physicochemical approach will prove useful in formulating hypotheses for future work aimed at developing a coherent, unpretentious and practical understanding of mechanisms involved in renal acid–base regulation.

A_TOT = total concentration of weak acids; CA = carbonic anhydrase; CD = collecting duct; DCT = distal convoluted tubule; dRTA = distal renal tubular acidosis; kNBC = kidney Na⁺/HCO₃^-; cotransporter; NAE = net acid excretion; PCO₂ = partial CO₂ tension; PHA = pseudohypoaldostero-nism; ROMK = renal outer medullar K⁺ channel; RTA = renal tubular acidosis; SID = strong ion difference; SLC = solute carrier; TSC = thiazide-sensitive cotransporter.

The author(s) declare that they have no competing interests.