CALCULATION OF INTRACELLULAR pH FROM THE DISTRIBUTION OF 5,5-DIMETHYL-2,4-OXAZOLIDINEDIONE (DMO). APPLICATION TO SKELETAL MUSCLE OF THE DOG William J. Waddell, Thomas C. Butler J Clin Invest. 1959;38(5):720-729. https://doi.org/10.1172/JCI103852. Research Article Find the latest version: https://jci.me/103852/pdf CALCULATION OF INTRACELLULAR PH FROM THE DISTRIBUTION OF 5,5-DIMETHYL-2,A-OXAZOLIDINEDIONE (DMO). APPLICA- TION TO SKELETAL MUSCLE OF THE DOG* By WILLIAM J. WADDELL AND THOMAS C. BUTLER (From the Department of Pharmacology, University of North Carolina School of Medicine, Chapel Hill, N. C.) (Submitted for publication October 6, 1958; accepted January 2, 1959) Estimations of hydrogen ion activities in the that the undissociated form of an acid or base is in interior of cells have been attempted through a equal concentration on the two sides of the cellu- number of different experimental approaches. lar membrane permits the calculation of intracel- The methods that have been employed are of sev- lular pH from measurements of extracellular pH eral general types: measurements on preparations and the extracellular and intracellular concentra- of broken cells, measurements on fluid with- tions of the acid or base. In most of the work that drawn from cells, observations with visible in- has hitherto been done based on this principle, dicators, measurements with micro-electrodes carbon dioxide has been the compound used as the introduced into cells, measurements of the intra- indicator. It is assumed that the cellular mem- cellular and extracellular concentrations of weak brane is permeable to carbon dioxide and that the organic acids and bases, and calculation of the tension of carbon dioxide inside the cell is equal balance of ionic charges. The last named method to that measured in an external phase in equilib- has been proposed by Conway (1). The other rium with the cell. The total carbon dioxide re- methods are discussed in the review of Caldwell leased from the cells after addition of acid is de- (2), which contains a tabulation of the results of termined and is assumed to come from dissolved measurements on various types of cells with differ- carbon dioxide, carbonic acid and bicarbonate ion. ent experimental methods. Some of the methods These data are sufficient for calculation of the in- that have been used are of quite limited applica- tracellular concentration of bicarbonate ion and of bility, and most of the values arrived at by any of the intracellular pH. The pK1' of carbonic acid the methods are subject to question. is such that its ionization should furnish a sensi- Potentially, the method utilizing the distribu- tive measure of intracellular pH. However, the tion of weak organic acids and bases has a wider validity of pH measurements made with the car- range of applicability than the other methods, and bon dioxide method has been questioned. Conway it is not subject to some of the theoretical objec- and Fearon (3) concluded from their experiments tions that can be raised to other methods. There that a large part of the carbon dioxide released is a great deal of evidence that membranes of ani- from muscle cells by acid is derived from acid-la- mal and plant cells in general are characterized by bile material other than bicarbonate. If this should free permeability to the undissociated forms of be so, the pH values calculated from the assump- weak organic acids and bases and by impermea- tion that all acid-labile carbon dioxide comes bility or apparent impermeability to the ionic from bicarbonate would be seriously in error. forms. If the pH of the interior of a cell differs In the course of a study of the tissue distribution from that of the external medium in contact with of 5,5-dimethyl-2,4-oxazolidinedione ("DM0"), it, there will be a corresponding difference in the the product of metabolic N-demethylation of the concentration of an organic ion. The assumption antiepileptic agent, trimethadione (Tridione®) (4), we have found that the attributes desirable in * This investigation was supported in part by a re- a to be used for the measurement of search grant (B-384) from the National Institute of compound Neurological Diseases and Blindness, National Insti- intracellular pH are combined to an almost ideal tutes of Health, Public Health Service. degree in DMO. These properties will be dis- 720 INTRACELLULAR pH 721 cussed in detail below. The advantages of DMO material to the theory through what mechanism the pH over carbon dioxide are in the facility of analytical gradient is brought about or whether the membrane is determination and in the absence of any question considered to be truly impermeable to the ionic form of as to the the indicator compound. The apparent ionization con- chemical identity of the material deter- stant and the activity coefficient of the ion are assumed mined by the analytical procedure. The present to be equal in all the aqueous phases. Then, if the indi- report comprises a theoretical consideration of the cator compound is a weak organic acid with apparent estimation of intracellular pH from the distribu- ionization exponent, pK', the pH of the intracellular tion of acids and bases and an application of the water, pH,, can be expressed in terms of measurable quantities or values mathematically derived from meas- DMO method to the estimation of intracellular urable quantities: pH of skeletal muscle of the dog under various conditions. We have been particularly inter- pHi = pK' + log {[C (1 + V.) V ested in muscle because other methods of esti- mating intracellular pH have been applied more X [10(PH-pK I) + 1] i}.- 1) extensively to muscle than to other mamma- lian tissues, and because changes of pH in mus- If the indicator compound is a weak organic base with cle are of great importance in buffering on ac- apparent acid ionization exponent, pK.', count of the large bulk of the tissue. With muscle, V. unlike some other tissues, it is possible to take pHi = pKa' - log {[C( +V.) several successive samples from a single animal X [1O(PK& 'PHe) + 1 ] - 1}. 2) during the course of an experiment without dis- turbing the conditions. Furthermore, there is The partial derivative of the ratio (Ct/C.) with re- evidence that the chloride of muscle is largely ex- spect to pH, is an index of the precision with which pHt tracellular (5), and determination of the chlo- can be calculated from measured concentrations of the ride space affords a method of measuring extra- indicator compound. For an acid, cellular water that is convenient and probably =(Ct/C) = 1n 10(V V( lOp sufficiently accurate for this purpose. Extracel- a (pH)-O V + Ve/\1OP][e + l0pK1') 3) lular water of some other tissues cannot be esti- For a base, mated with as great ease or certainty. a(Ct/C) = -n 10 ( V i+ VJ)(10-PH+10PK ) 4) THEORETICAL CONSIDERATIONS These partial derivatives as functions of the ionization Mathematical formulations. We shall consider a tis- exponents of acids and bases are shown in Figures 1 and sue containing intracellular water of volume V1 and ex- 2, respectively. In these figures, pH. is assumed to be 7.4 tracellular water of volume V., the intracellular phase and pH, 7.0 (approximately the pH, of muscle as found being contained within membranes freely permeable to in this study). The functions are without maxima, in- the undissociated form of a weak organic acid or base creasing to approach asymptotic limits with decreasing (to be called the "indicator compound"). V. can be de- values of pK' for acids and increasing values of pK.' for rived from the distribution of a substance confined to ex- bases. If pH, is less than pH., as is assumed in these tracellular water, and V, from the difference between V. figures, the limiting value is greater for a base than for and total tissue water. Neither the intracellular nor the an acid. The stronger an acid or a base, the more sen- extracellular tissue phase is individually accessible for sitive an indicator it is of intracellular pH.' If intracel- analysis, but the concentration, Ct, of the indicator com- lular pH is less than plasma pH, a base of sufficient pound in the water of the entire tissue can be determined. strength can be a more sensitive indicator than any acid. By determinations in plasma with corrections for the Don- For an acid of the strength of DMO and for the values nan equilibria, the pH and the concentration of the indi- of pH,, pH., VI, and V. assumed in Figures 1 and 2, an cator compound in the extracellular tissue water (pH. error of 0.01 unit in the calculated value of pH, would and C., respectively) can be derived. It is assumed that be introduced by an error of 1.4 per cent in the ratio the aqueous phases are homogeneous and that the indi- (Ct/Ce) or by an error of 7.7 per cent in V.. If the cator compound is fully equilibrated, the concentration of ionic strength of intracellular water should differ from the undissociated form being equal in intracellular water, that of extracellular water by as much as 0.05, the pK' extracellular tissue water and plasma water. If this equality of concentration of the undissociated form is 1 This theory is not applicable to compounds that are maintained regardless of pH differences that may exist completely dissociated such as sulfonic acids and quater- between the two sides of the cellular membrane, it is im- nary nitrogen compounds. 722 WILLIAM J. WADDELL AND THOMAS C.