Biotechnol. hog. 1993, 9, 374-384
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A Computer Model for Intracellular pH Regulation in Chinese Hamster Ovary Cells P.W U , ~N. G. Ray,$ and M. L. Shuler’vt School of Chemical Engineering, Cornell University, Ithaca, New York 14853, and VERAX Corporation, Etna Road, HC-61, Box 6, Lebanon, New Hampshire 03766
A single-cell model for Chinese hamster ovary (CHO) cells has been extended to study the regulation of intracellular pH. This model provides for the first time a direct mechanistic linkage between intracellular p H control and cellular metabolism. Among the known mechanisms that regulate and disturb pHi, the Na/H antiport, effect of lactate and ammonia, proton leakage, and external p H have been included in the model. The ability of the model t o predict both steady-state and transient pHi has been tested against experimental studies. The “regular model” that has been used t o predict cell growth in suspension and batch cultures can predict the steady-state pHi and the transient response of pHi to an alkaline load well, but it had to be modified in terms of the maximum activity of the Na/H antiport in order to simulate the transient response of pHi to an acid load. The modification indicates the possibility that a cell could activate the Na/H antiport under acute acid load but return to its basal level of Na/H antiport activity under steady-state conditions, even when the cell interior is under low-pH conditions (6.7-7.0).
Introduction Many biological processes are sensitive to the changes of intracellular pH @Hi). In mammalian cell culture, a strong correlation exists between pHj and cell proliferation (Gilies, 1981),and pHi has been implicated in the control of vital cellular functions (Nuccitelli and Deamer, 1982). The pHi of mammalian cells is easily disturbed under normal tissue culture conditions. Weak acids and bases from cell metabolism can accumulate significantly in the culture media of long-term and high cell density cell cultures, altering PHi. Although significant progress has been achieved in identifying and characterizing individual mechanisms that affect pHi, there has not been an integrated view of pHi regulation of cells growing in normal tissue culture medium. The purpose of this work is to combine all of the known mechanisms that affect PHi, especiallycellular metabolism, into an integrated framework, since the regulation of pHi in mammalian cells involves many aspects of the cellular activities, i.e., membrane transport, cell metabolism, and the medium alterations by cellular metabolism. To model such a broad network of effects on pHi, a whole-cell model is necessary. For example, Batt and Kompala (1987) have developed a model describing the growth of hybridoma cells. But their model does not contain sufficient mechanistic details to allow meaningful incorporation of pHicontrolling mechanisms with cellular metabolism. This study is a direct extension of the previous report by Wu et al. (1922) on the development of a single-cell model of Chinese hamster ovary (CHO) cells. The model makes predictions on growth characteristics and cellular metabolism. By incorporating the pHi-regulating mechanisms, an intracellular hydrogen ion balance, and the interconnecting pHi with cell metabolism, the single-cell model should be capable of predicting the pHi response t Cornel1 University.
VERAX Corp. 8756-7938/93/3009-0374$04.00/0
to alterations in extemal medium compositionand changes in cell metabolism. Previous attempts to model the pHi include work by Boron and De Weer (1976) and Keifer and Roos (1980), who identified the mathematical expressions for intracellular hydrogen ion balance and determined how weak acids and bases would influence this balance. Lee and Palsson (1991) presented a model of human red blood cells that includes the pHi effects on various cellular processes. The pHi prediction in their model is accomplished by assuming Donnan equilibrium, which is valid for nondividing red blood cells but not for most cultured mammalian cells. MQueen and Bailey (1990a) modeled in detail the effect of ammonia on pHi and correlated such results with the growth rate of hybridoma cells. The model described in this article differs from the previous work our model, on the whole-cell level, combines pHi with cell metabolism. The inhibition of protein synthesis, glycolysis, and nutrient uptake by low pH has been included in our model. For example, when glutamine is metabolized, ammonia is produced and the rate of production and the transport of ammonia affect PHi. The previous models are only capable of predicting pHi in response to added extracellular ammonia and not to endogenously generated ammonia. This modeling work is beneficial to high cell density, large-scale, and long-term tissue culture technology. The design of an optimal operating strategy which guarantees nutrient supply and waste product removal is especially important. Cells in long-term cultures could experience pH changes caused by lactate accumulation which exceeds the buffering capacity of the external medium (Feder, 1985). The accumulation of ammonia can also disturb the optimal pHi for growth and product formation (McQueen and Bailey, 199Ob). By studying the control of pHi in cells with a detailed mathematical model, we can understand better how one important parameter for cell growth and product formation is affected by the external
0 1993 American Chemical Society and American Institute of Chemical Engineers
Bbtechnoi. hog., 1993, Vol. 9, No. 4
environment and how to control pHi. In this article, we describe and experimentally test a model that is capable of predicting cellular response to perturbations in the external levels of glucose, amino acids, lactate, ammonia, external pH, and medium buffering capacity.
Materials and Methods To carry out the simulation, all differential equations in the model are numerically integrated using the LSODA solver routine (Livermore solver for ordinary differential equations, with automatic method switching for stiff and nonstiff problems) on a VAX station to predict the chemical composition of each component. The CHO cell line used in our experiment is a wild-type Chinese hamster ovary cell (CHO-K1) that requiires proline for growth. The cell line was a gift from Professor E. Pfefferkorn (Dartmouth Medical School). The cells were routinely maintained in a medium consisting of Dulbecco's Modified Eagle's Medium (DMEM) and Ham's F-12 Medium (a 75:25 mix). The medium was supplemented with 1%fetal boving serum (FBS). The intracellular pH values in CHO cells were measured by using the pHi-sensitive fluorescent probe 2,7-bis(carboxyethyl)d(and6)-carboxyfluorescein(BCECF) technique. The lipophilic acetoxymethyl ester form of BCECF, BCECF-AM, crosses the plasma membrane and is hydrolyzed by cytoplasmic esterases to yield the highly fluorescent, but impermeant, form BCECF (Rink et al., 1982). The fluorescent intensity depends on the intracellular pH. This technique has been widely used (Mooleanaar et al., 1984;Goldfarb and Nord, 1987;Brierley et al., 1989) and was adapted to the CHO cell line for our work. Before the intracellular pH was measured, CHO cells were harvested with 10% trypsin (v/v PUCK-A) and centrifuged at 170g for 10 min at 4 "C. After the cells were suspended in DMEM with 1% FBS to stop the trypsin action, they were resuspended to 1 X lo7 cells/mL in HCOa--free buffer solution with 10 pM BCECF-AM dye (Calbiochem Corp., La Jolla, CA) and incubated for 30 min at 37 OC. The cell suspension was constantly mixed to prevent cell clustering. The cells were then washed and resuspended in pH 7.4 buffer at a cell density of 1 X 107 cells/mL. For the measurement of the steady-state pHi, 200 pL of cells (1X lo7cells/mL) with loaded BCECF-AM dye were added to 1.8 mL of buffers with different pH values, and the fluorescent intensities were measured in a Hitachi (Hitachi Ltd., Tokyo, Japan) F-2000 fluorescence spectrophotometer with sample stir base and sample temperature control option. The excitation and emission wavelengths were set at 500 and 530 nm, respectively. The ammonia-induced alkaline load was accomplished by adding 20 ctL of NH&1 stock (1.25 M) to a 2-mL cell suspension (1X lo6cells/mL, already being measured for pHi in the fluorescence spectrophotometer) in which the cells had been loaded with BCECF-AM dye. Calibration of intracellular BCECF concentration as a function of pH was obtained from H+ equilibration methods using the K+/H+ionophore, nigericin. A total of 20011L of cells (1X lo7cells/mL) with loaded BCECF-AM dye was added to 1.8 mL of buffers with different pH (6.0, 6.5,7.0,7.5,8.0) values and 10 pM nigericin (Calbiochem Corp.) and allowed to equilibrate for 10min a t 30 OC before the fluorescence intensity measurements. The range of error with the above method is about 0.10.2 pH unit. To monitor the accurate change in pHi over a wide range of external pH and other medium conditions, a monolayer of cells can be grown on a coverslip and
375
inserted in a cuvette where the medium can be changed constantly without disturbing the cells.
Model Formulation All equations and parameter values for the base model are given elsewhere (Wuet al., 1992). This section explains the derivations and significance of the supplementary equations required for pHi prediction and its relationship to cell metabolism. The biosynthetic and catabolic reactions of this cell model relate to intracellular pH primarily through a proton balance. Following the work by Boron and De Weer (1976) and Keifer and Roos (1980),the proton balance is written by taking the derivative of the definition of the buffering capacity (8 = dB/dpH): d[H+Ii 2.3[H+li V-=X dt P ((moles of H+ added per unit time) (moles of H+ taken out per unit time)} (1) where p is the intrinsic intracellular buffering power, B is the amount of strong base added to the cell per unit volume, and Vis the volume of the cell. The factor 2.3 is from the derivative of pH. The proton balance in the cytoplasmic space can be disturbed and regulated by the direct addition or release of protons, as in the case of Na/H antiport, or by the entrance and exit of a weak acid or base. Hydrogen ions can also leak into or out of the cells (Deamer, 1982). The intracellular protein provides the major buffering power (intrinsic buffering capacity) for the cell. Intracellular weak acids and bases can also provide additional buffering action (Roos and Boron, 1981). The proton balance is written about the cytoplasmic space. A weak acid can only disturb pHi if the acid molecule enters or leaves the cell or if it is produced as a metabolic byproduct. To understand pHi regulation a t the whole-cell level, the disturbance of both exogenous and endogenous weak acid and base is included in the model. The final hydrogen ion balance in the model has the form d[H+li 2.3[H+li V-=((H' flux in due to pHi-regulating dt P mechanism@))- (flux of H+ leaking out) + (net H+ flux in due to weak acid or weak base production) + (net H+ flux in due to weak acid or weak base transport)) (2) Equation 2 is an extended form of eq 1. It includes all of the pHi-altering mechanisms considered in this model. The followingsubsections will explain the four termswithin the brackets on the right-hand side of eq 2, the buffering capacity p, the effects of pHi on cell metabolism, and lysosomal pH response to changes in the cytoplasmic environment. Disturbanceof Intracellular pH by Weak Acid and Weak Base. In high-density, long-term cultivation of mammalian cells, lactate and ammonia can accumulate as the major metabolic byproducts of glucose and glutamine metabolism. Excess production of lactate is believed to exceed the buffering capacity of the medium, thereby lowering the culture pH and inhibiting cell growth (Feder, 1985; Boron and De Weer, 1976; Roos and Boron, 1981). Whether lactate itself is toxic to the cell growth is less clear. Ammonia can disturb the optimal cytoplasmic pH
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(Roos and Boron, 1981) by forming a "proton shuttle". Because of the high rate of glucose and glutamine metabolism in cell culture, lactate and ammonia are the only weak acid and weak base considered. Since both the production and the transport of weak acids and bases across cell membranes can disturb PHi, the model requires expressions for the production and the transport of lactate and ammonia. The Appendix summarizes the equations for the change of pHi due to weak acid and weak base. The modeling of lactate and ammonia production has been described in detail and experimentally verified (Wu et al., 1992). Only the transport of lactate and ammonia across the cell membrane will be described here. Two moles of lactate are produced from the glycolysis of one mole of glucose. Lactate can also be produced from glutamine metabolism in HeLa cells (Reitzer et al., 1979) and our CHO cell line. Under normal conditions (intracellular or extracellular pH of about 7.2-7.6) most lactate exists in the nonprotonated form (the pK, of lactate is 3.86), although it is the protonated form that is produced in glycolysis. By assuming that only the uncharged lactate can diffuse passively through the cell lipid bilayer membrane, the permeability coefficient for lactate transport is estimated to be about 2.8 X 103cm/s. This value is based on the requirement that lactate excretion equals production at steady state. This permeability value is even higher than that of free ammonia. Since the lactate molecule is much larger than the ammonia molecule, other mechanism(@ for lactate transport must exist. Carrier-mediated lactate transport in Ehrlich ascitestumor cells and in human erythrocytes has been studied by Spencer and Lehninger (1976) and Dubinsky and Racker (1978). According to their findings, lactate ion (L-) is cotransported with a proton. This symport does not require energy from the hydrolysis of ATP, because the downhill gradient of one ion can bring the other ion uphill against its concentration gradient. Since the intracellular pH is usually higher than the extracellular pH, the steady-state concentration of the lactate inside the cell is always higher than that of the lactate in the external medium, acting as if the carrier has a higher affinity for lactate in the external medium. Since a typical carrier is involved in lactate transport, a Michaelis-Menten-type equation is used to describe the lactate transport:
where J is the flux of lactate transport out across the cell membrane, v h c is the maximum rate of lactate transport by the lactate carrier, Lac is the cellular level of lactate (grams/cell), Vis the volume of the cell, K h Cis the affinity of the lactate carrier for lactate, C$, is the external concentration of lactate (grams/mL), and S is the surface area of the cell. Although the simple diffusion of lactate could be important at high lactate concentration, it is by far less significant than facilitated diffusion of the protonated form under physiological conditions. Ammonia can disturb the optimal cytoplasmic pH (Roos and Boron, 1981) by forming a proton shuttle, in which ammonia produced in the form of NH4+ exits the cell as NH3 (NH3exists only as a s m a l l fraction of the total amount of the ammonium ion under physiologicalconditions), and NH4+ enters the cell down its large electrical gradient due to the highly charged membrane. The passive transport of free ammonia (NH3) is very fast across the lipid bilayer of the plasma membrane, as studied by Ritchie and Gibson (1987). The permeability of NH3 is as high as 6 X 10-4
Figure 1. How lactate and ammonia disturb the intracellular pH in mammalian cells. Lactate and ammonia are produced inside the cell from glucose and glutamine. Unprotonatedlactate (L-) is transported along with a proton. Once outside the cell, the proton is released and the external pH is decreased. The intracellular pH is in turn disturbed. Free ammonia escapes the cell quickly, and the charged species NH,+ enters the cell down its electrochemical gradient. The NH$N&+ part of the diagram was essentially reproduced from a paper by Roos and Boron (1981).
cm/s. Although the permeability of NH*+ is only about 1 X lo-' cm/s (Roos and Boron, 1981), its transport into the cell is significant because of the large electrical gradient of NH4+ pointing inward. This mechanism, proposed by Roos and Boron (1981),results in continuous pumping of H+ into the cytoplasm. Our model has both modes of ammonia transport:
JNH,+
(4b) where J is the flux of ammonia or ammonium ion transported out of the cells, P is the permeability coefficient, NH3 and NH4+ are the intracellular levels of free ammonia and ammonium ions, respectively, CkH, and Ch,+ are external concentrations of free ammonia and ammonium ions, respectively, V, is the membrane potential, V is the cell volume, F is the Faraday constant, R is the ideal gas law constant, and T is the temperature. See the Appendix for more details. The two mechanisms by which lactate and ammonia are transported and disturb intracellular pH and thereby inhibit cell growth are summarized in Figure 1. Intracellular pH-Regulating Mechanism. The c u rent model considers the Na/H antiport as the only pHregulating mechanism, it is the most important pHregulatory element in many mammalian cells,such as CHO cells (Moolenaar et al., 1983; Paris and Pouyssegur, 1983; Roos and Boron, 1981). However, this model is only a first approximation since other pHi-controlling mechanisms, such as the HCO$Cl exchange, also exist in CHO cells (L'Allemain et al., 1985). Consequently, the model is only capable of predicting the steady-state pHi under conditions where the dissolved C02 level does not change and the transient pHi response is for cells in bicarbonatefree medium. Dissolved C02 levels that change are uncommon in tissue culture since the partial pressure of C02 in the overhead gas space is usually controlled.
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Furthermore, the endogenousC02 is not believed to disturb pHi, while only the exogenously applied C02 has been shown to cause the intracellular acidification (Gillies, 1981). Thus, the absence of HC03-/C1- exchange in the model is a modest restriction on the model’s application to real culture conditions. In Chinese hamster lung fibroblast cells, the Na/H antiport has been characterized biochemically (Paris and Pouyssegur, 1983) as a reversible, amiloride-sensitive exchange system. Na+ and H+ have distinctive and mutually exclusive binding sites on both sides of the exchange. The antiport is electroneutral with a stoichiometry of 1:l. Na+ and H+ serve as competitive inhibitors to each other’s binding to the antiport. Since mammalian cells maintain a higher external Na+ concentration (145 mM) than internal Na+ concentration (12 mM) and the inward gradient of Na+ drives the acid extrusion mechanism of the Na/H antiport, the internal concentration of H+ is lower than the external concentration of H+. The interior of the cell is more alkaline under the action of the Na/H antiport, if there are not other disturbances. A simple mathematical formulation to describe the action of the Na/H antiport is as follows: JH+,Na/H
= vNa i
Nili
+ [Nali + K N a ( W c / 0 / K I N d )
-
The first term is the H+ entrance flux which is equal to the intracellular Na+ exit flux with internal H+ as the competitive inhibitor. The H+ release term is defined in a similar fashion. The v values are the maximum rates of Na+ transport for the antiport in both directions, and the K‘s are saturation constants or inhibition constants. The activity of the Na/H antiport is extremely sensitive to the change of intracellularpH. Pouyssegur et al. (1986) has measured the activity of the Na/H antiport by monitoring the uptake of 22Na+in response to intracellular pH and external pH. They concluded that the antiport was activated by intracellular H+ in an allosteric manner under acute acid load conditions and that the external H+ dependence of the antiport obeyed simple saturation kinetics. They suggested that there is an internal H+binding modifier site that activates the antiport when the interior of the cell is acidified. To mimic the finding about the extreme sensitivity of the antiport activity to intracellular H+ (Pouyssegur et al., 1986), the v’s are written as a sensitive function of the intracellular H+ concentration:
This mathematical form of the Na/H antiport in our model is a mechanistic expression of the Na/H antiport activity, not a simple discrete description of its activity at different pH values. The proton balance with the Na/H antiport term and the effects of lactate and ammonia is shown in dHc 2.3(Hc/V) -= dt B (JNH8&H4+ + JNH4+aNH,+ +
where Hc is the cytoplasmic level of H+ and a and a’ are conversion factors that convert the flux of weak acid and base into the flux of H+ addition resulting from the acid
and base fluxes:
KNH,+ (8) Since KNH,i= 10-9 M, + >> UNH,+ under physiological conditions. In other words, the release of one NH3 will basically add one H+ to the cell, while the addition of one NH4+ will add almost no H+to the cell. See the Appendix for details. Buffering Capacity. The review by Roos and Boron (1981) on intracellular pH regulation provides the basis for conclusionsand assumptions on buffering capacity used in this model. The buffering capacity (or buffering power) term B in eq 1is the total buffering capacity, PT, of the cytoplasm of the cell. Although its value has no effect on the prediction of the steady-state value of intracellular pH, the dynamic response of pHi to an acid or alkali load does depend on the buffering capacity. The total buffering capacity is the sum of the intrinsic buffering capacity, 01, which is provided by the large amount of cytoplasmic protein, and the buffering capacity provided by weak acid (BA) and base (OB)inside the cell. There have been direct measurements of the intrinsic buffering capacity in different cell lines, and the buffering capacity provided by weak acid and base can be calculated with knowledge of the total amount of the acidlbase and the intracellular pH. For example, on the basis of the assumption that NH3 inside the cell is in equilibrium with the medium NH3, the contribution of NH3/NH4+ to &, BNH~/NH,+,is given by (d[NH4+]i/dpHi)~~~, and it was calculated to be 2.3[NH4+1. Similarly, Pco2is 2.3[HCOs-I if the level of C02 in the medium is kept constant, the intracellular COz is in equilibrium with the medium C02, and the level of co32-is negligible compared to that of HCO3--. Proton Leakage. The net permeability coefficient of H+ (or its equivalent), Pnet, was calculated to be about 1V cm/s (Deamer, 19821,with the net permeability coefficient being defined by Nicholes and Deamer (1980) as Jnet
= pnet( W
I ,- [H’I
i)
(9)
Effect of Intracellular pH oncell Metabolism. The effects of pHi on cell metabolism feed back into the regulation of pHi. The pH sensitivities for many cellular processes have not all been determined. Only those processes which have been studied under different pH values have been included in the current model. Intracellular pH is an important secondary messenger in processes such as the activation of quiescent cells by growth factors, although pHi often is not the direct cause of the subsequent cellular activities after activation. This model is intended for predicting cell growth under normal cell culture conditions. Under such conditions, pHi affects the cellular activities mostly through its effect on enzymatic activities. Low pH inhibib glycolysis at the step of phosphofructokinase (Fidelman et al., 1982; Belt et al., 1979). If noncompetitive inhibition is assumed, then
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m r energy.
\\
-N Y +
H+
Figure 2. Schematic model of intracellular pH maintenance and intralysosomal pH maintenancein CHO cells with ammonia production inside the cell and exogenous ammonia. This model is essentially a combination of the intracellularpH maintenance model by Roos and Boron (1981) and the intralysosomal pH maintenance model by Pool and Ohkuma (1981). where KL is the maximum rate, KGLCLis the saturation constant, and KIGLCH is the inhibition constant of H+ on glycolysis (with a value of 6.3 X 10-lOmol/mLor a ~KIGLCK was estimated from the study by Belt et of 6.2) (KIGLCH al. (1979) on Ehrlich ascites cells). This inhibition term has also been incorporated into the rate equation for the complete oxidation of glucose. Studies in sea urchin eggs indicated that pH is the major signal for protein synthesis at fertilization (Grainger et al., 1979). Our model adopts the shape of the protein synthesis rate-pH dependence curve in the work by Grainger et al. (19791, which indicates a highly sensitive response. From our reevaluation of their data, the inhibition term has the form, K I M , N ~ / ( [ H+ + ]KIM,H~), ~ with 4.36 for the value of n. The inhibition of nutrient uptake by low pH is also included in the model for the uptake of glucose, glutamine, and the other amino acids. The extent of inhibition on nutrient uptake was determined from our T-flask experiments, in which one T-flask had a lower pH than the other T-flask and the uptake of glucose was inhibited in the first T-flask. The form of inhibition is the same as the one for protein synthesis, and the value of n is assumed to be 2.0. The same inhibition terms are then used for glutamine uptake and amino acid uptake. Lysosomal pH. Weak acid and base can enter the lysosomein their uncharged forms and be trapped in their charged forms once the weak acid and base are protonated inside the lysosome (de Duve et al., 1974). This accumulation alters lysosomal pH and function, resulting in serious disorders such as lysosomal storage diseases (Schneider, 1980). In cultured cells,lysosomal pH elevated by exogenously supplied amines can prevent the dissociation of internalized complexes,resulting in a progressive intracellular accumulation of occupied receptors (Dean, 1984). Ammonia accumulates in the acidic compartments of the cells due to the high permeability of NH3 and the relatively impermeable form, NH4+ (Pool and Ohkuma, 1981). The normal intracellular pH is about 7.4, while the normal intralysosomal pH is about 5.0. If the NH3 species inside and outside the lysosome are in equilibrium, the difference in NH4+ species across the lysosomalmembrane should be 140-fold. Such a dramatic concentration gradient could drive NH4+across the lysosomal membrane and form a proton shuttle along with the flux of NH3, disturbing the optimal intralysosomal pH. This concept is very similar to the one illustrated earlier in Figure 1;it was first proposed in a paper by de Duve (1974),and it was
extended by Pool and Ohkuma (1981) to include the lysosomal acidification mechanism. The lysosomal proton shuttle and the cytoplasmic membrane proton shuttle were combined our model (Figure 2). The acidification of the lysosomal interior is ATPdependent, and this proton pump has been characterized by Schneider (1980). The leakage of H+ out of the lysosome is also included in the model. The permeability coefficient was estimated from the fact that the intralysosomal pH is about 5 when the intracellular pH is about 7 under ammonia-free conditions. The ammonia and proton balances of the lysosome are given in eqs 11 and 12, and they were included in an previous publication (Wu et al. (1992) Table 111, eqs 28 and 29). dNH3 1 -=
dt
where the subscript 1 denotes lysosomal properties. V H , ~ is the maximum rate at which the ATP-driven pump acidifies the lysosome, and it is inhibited by the intralysosomal hydrogen ion concentration, with an inhibition constant of KBH,~.
Results and Discussion Proton Leakage Does Not Influence Intracellular pH Significantly. Under the conditions used in this work, the leakage of H+ estimated by the model does not affect the model predictions of pHi significantly, although the permeability coefficient for H+ is extremely high (10-4 cm/s) compared to those for some other ions (10-7-10-10 cm/s). Since the absolute concentration of H+ is extremely low under physiological conditions (lo-' M), the actual flux of the leakage is very small compared to the other mechanisms that control or disturb pHi. For example, the so-called proton shuttle which involves the diffusive flux of NH3 and NH4+ can pump in H+ at a much higher rate. Since biological membranes are capable of maintaining a transmembrane electrochemicalproton gradient, a biological membrane still offers a sufficient barrier to proton flux. Intracellular pH Supported by the Na/H Antiport. On the basis of the model formulation, the model predictions of pHi supported by the Na/H antiport should be the intracellular pH when both the external glutamine and ammonia concentrations are zero. In experimental studies, the PHi under Na/H antiport control is accomplished by suspending cells in saline solutions of different pH values without HCO3-. Figure 3 compares the model predictions of pHi when only the Na/H antiport affects the intracellular pH with the experimental measurements by L'Allemain et al. (1984) and the results of our own measurements. Note that only eq 5 is responsible for the model predictions in Figure 3. The form of eq 5 is based on the facts that the Na+gradient drives the Na/H antiport and that the H+ is extruded or taken in the opposite direction of the Na+ flux with a ratio of lNa+:lH+. H+ acts as an inhibitor of Na+ binding. The only other attempts to model the Na/H antiport has been by McQueen and Bailey (1990a). They divided
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t
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u65 A
h
6.5
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Figure 3. Intracellular pH as a function of extracellular pH when Na+/H+antiport is the only pHi-influencing mechanism. pHi was measured in HCOpfree buffer solutions. The model predictionsfor pHi under such conditionswere accomplished by setting extracellular levels of glutamine and ammonia to zero. Note that the model does not include the other possible pHiregulating mechanism, the HCOs-/Cl- exchange. The circles (0) are experimentalmeasurements of pHi by Paris and Pouyssegur (1983)in Chinese hamster lung fibroblasts,and the triangles (A) are our measurements on pHj of CHO cells. The solid line is the model prediction, and the dashed line is a reference line of pHi = pH,. the response of the antiport into three pHi regions, with a maximum response in the low-pH region, zero response in the high-pH region (if the pH is too high, another mechanism is assumed to take over), and a linear response to pHi in the intermediate-pHi region. Compared to this formulation by McQueen and Bailey (1990a), our model equation of the Na/H antiport is a more mechanistic and continuous description of the antiport activity. The values of KN*(2.5 mM) and K I N ~(1.6 H X 10-8 MI are direct results of the study by Paris and Pouyssegur (1983) (also summarized in Table IV of Wu et al. (1992)). The same study measured the H+release and uptake rates in response to the intra- and extracellular levels of Na+. Although the authors did not conclude specifically that the antiport was symmetrical, the maximum rates of H+ release and uptake are very similar in value. Our model adopted the value of the maximum H+ release rate (which is the essentially the term YN4-i in eq 5) from the study by Paris and Pouyssegur (1983)to be 5.2 mol/(h-cm2),while the H+ uptake rate (which is equivalent to VNa,i-) was adjusted to about 7.9 mol/(h*cm2)to better match the experimental observation. These values of the maximum rates of the Na/H antiport are about one-half of the values used by McQueen and Bailey (1990a) for a hybridoma cell. Under high extracellular pH conditions, the model is incapable of making predictions of PHi, as illustrated by Figure 3 above the pH,value 7.7. Other mechanisms could be active in cells under the alkaline conditions for which we have not accounted. Consequently, the model simulation of pHi is only good below pH 7.7. However, the limitation of the model in the high-pH region does not restrict the model's ability to simulate cell growth in tissue culture since the tissue culture medium seldom turns basic under most of the operating conditions. Model Predictions of the Steady-State Intracellular pH under Normal Tissue Culture Conditions. Most of the biochemical studies on the intracellular pH involved conditions that are not common in tissue culture bioreactors. For example, to study the mechanism of the Na/H antiport, cells were usually grown in an exponential culture first but then resuspended in buffer solutions during the experiments, where Na+ was replaced by other
6.0I/ 6.0
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8.0
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Figure 4. Model predictions of the steady-state values of pHi under different external pH and different external levels of glutamine and ammonia: line 1, zero glutamine and zero ammonia; line 2,0.14 mM glutamineand 1.0 mM ammonia; line 3, 1.4 mM glutamine, and 1.0 mM ammonia; line 4, 1.4 mM glutamine and 15 mM ammonia; line 5, 1.4 mM glutamine and 30 mM ammonia. ions (Paris and Pouyssegur, 1983;Moonlenaar et al., 1983). Although these experiments isolated the mechanisms of interest, few efforts have been made to measure the intracellular pH of cells in a normal tissue culture medium. One difficulty in our attempt to measure the pHi of CHO cells in anormal tissue culture medium with the fluorescent probe BCECF has been interference from the background fluorescence in the medium. On the basis of our model formulation, lactate only disturbs the steady-state pH in the external medium, while both endogenous and exogenousammonia can disturb pHi. Since ammonia is produced intracellularly from the metabolism of glutamine, amodel simulation with external glutamine can predict pHi with endogenous ammonia. The results are given in Figure 4, where the model predictions of intracellular pH are plotted as a function of extracellular pH, external level of glutamine, and ammonia. The dashed line is simply a line of pHi = pH,, so that any point below the dashed line indicates that the interior of the cell is more acidic than the external medium. Line 1 is the reproduction of the line in Figure 3, included in this figure as a reference to the pHi values supported only by the Na/H antiport. Line 2 illustrates a scenario where 0.14 mM glutamine and 1.0 mM ammonia are present in the external medium. The model predicts a change of about 0.1 pH unit at pHe 7.3. If instead of such low level of glutamine there is 1.4 mM glutamine in the medium and same level of ammonia, the model predicts a further decrease in pHi of about 0.3 pH unit at pH, 7.3, as shown by line 3. A further increase in the external ammonia concentration of 15 mM (line 4) resulted in a decrease in pHi of 0.1 pH unit. If the external glutamine level is still kept at 1.4 mM, an even higher level of ammonia of 30 mM gives a much acidified cell cytoplasm of 6.8 a t the external pH 7.3. The model clearly predicts a severe decrease in pHi in the presence of ammonia, both endogenous and exogenous. This prediction means that, under normal tissue culture medium pH, cells fail to maintain a constant pHi when the level of ammonia increases, even a t the moderate level of a few millimolar. McQueen and Bailey (1991) experimentally observed that pHi in hybridoma cells remained constant from pHe 7.6 to 6.8. Our model also predicted almost constant pHi from pHe 7.3 to 6.8 under fixed external conditions. The model suggests that cells maintain a constant pHi even when the medium pH becomes alkaline, at least when
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the ammonia level is low. This model prediction does not imply that cell cultures are less affected by higher pH values than lower. Alkaline pH inhibits cell growth. Under alkaline pH, nutrient molecules may have the wrong ionic charges for uptake, and cell surface proteins may take the wrong configurations for their proper functions. The model does not include the inhibitory effects of alkaline pH on cellular activities, in part because a high medium pH (above 7.7) is of little practical value to the study of tissue culture reactors. McQueen and Bailey (1991) also measured pHi in cells in a normal growth medium and observed a drop of 0.5pH unit in pHi when 30 mM ammonia was added to the external medium. This result is comparable with the model prediction, as illustrated by the drop in pHi from line 3 to line 5 in Figure 4 at pH, 7.3. There are several multiple-phase natures in Figure 4 that can be explained by the importance of the proton shuttle (Figure 1) relative to that of the Na/H antiport. One interesting feature in Figure 4 is that under the condition of an increased ammonia level, pHi decreases when pHe increases up to a certain point. For example, line 4 exhibits a decrease in pHi when pH, is above 6.8and below 7.4,a feature not seen in line 2. The difference in the shapes of lines 2 and 4 is due to the increased significance of the proton shuttle at higher levels of ammonia. As pH, increases, line 2 indicates a scenario where the proton shuttle is slowed down due to the redistribution of the NH3/NHr+species. More and more NH3 is present in the medium to decrease the flow of NH3 out of the cells. In the line 2 situation, the activity of the proton shuttle is not strong enough to alter the shape of the line, which is dictated by the Na/H antiport. It would be difficult to detect significantly a slight decrease in pHi (such as the one in line 4)with the current pHi measurement method. The measured pHi would appear to be constant over the range pHe 6.6-7.7. When pHe is highly alkaline, the direction of the proton shuttle is eventually reversed and pHi starts to increase. Lines 3-5 intersect at pH, 7.7-8.0. The higher the ammonia level a line represents, the more likely it will be to have a concave upward shape a t high pH,. The reversed proton shuttle brings hydrogen ions out of the cells, and pHi increases. Although umimportant to the performance of a cultured cell reactor, the reversal of the proton shuttle is an interesting feature of pHi regulation that has not been predicted or experimentally studied before. The model predicted a severe nutrient uptake limitation below pH, 6.6 and could not maintain sufficient intracellular levels of nutrients for any growth. No further predictions could be made beyond pHe 6.6. Effect of Lactate Accumulation on Medium pH. The extensive glycolysis in cultured mammalian cells results in the accumulationof lactate and the acidification of the external medium. In a typical experiment, 3.4 g/L glucose was converted to 1g/L lactate in a 2-day T-flask culture. The model prediction of the acidification of the medium (buffering capacity of 3 X 10-5 mM) compares well with that observed in the experiment (Figure 5). The acidification of the tissue culture medium results in the inhibition of nutrient uptake. According to the model predictions in Figure 4,the decrease in the medium pH can also lower PHi. In many tissue culture reactors the medium pH is controlled by adding base after the buffering capacity has been exceeded by lactate accumulation. If the added base solution has the same tonicity as the medium, dilution of the nutrient will occur. Again, the ability of the model to predict lactate accumulation makes it possible to predict
7.5
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48
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Figure 5. External pH decline in a T-flask experiment due to lactate accumulation. The model prediction is indicated by the solid line,and it is comparedwith the experimentalmeasurements (0). The initial glucose concentration was 3.3 g/L, and the final lactate accumulation after 2 days was 1.0 g/L.
quantitatively the extent of nutrient dilution and the effect of reduced nutrient concentration on cell growth. Since lactate is produced and transported as the protonated form, external lactate should not affect pHi under steady-state conditions. Ozturk et al. (1992) demonstrated experimentally that the addition of lactate to the external medium only affected the transient pHi but not the steady-state PHj. In the case of the addition of pure base (e.g., NaOH pellets) to the medium to control its pH, the osmolarity of the medium increases. In fact, the effect of added lactate on cell growth can be attributed to the increase of the medium osmolarity, and lactate itself only affects cellular activities when present a t a very high concentration (>40 mM) (Ozturk et al., 1992). The cells are less sensitive to changes in osmolarity than to changes in PHi. Since lactate does not disturb pHi as ammonia does, cell cultures can tolerate 40 mM lactate with external pH control, but they cannot tolerate a few millimoles of ammonia. The extent of osmolarity increase due to lactate increase could be predicted with a modified model; the current model does not include the effect of osmolarity on cell growth. TransientResponse of Intracellular pH. Since the proton balance is a transient mass balance and the model formulation is also based on the time derivatives of each component, the model is capableof predicting the transient changes in intracellular pH. The simulation of the transient response of pHi can reveal more information about pHiregulationand allow f i e tuning of the parameter values. For example, the value of the buffering capacity does not affect the model predictions of steady-state pHi (from eq 11, but it does affect the transient response of pHi. Since the literature values on the buffering capacity span 1order of magnitude in animal cells from about 9 to 70 mM/pH (Roos and Boron, 1981), it is possible to estimate the real value of buffering capacity when direct experimental measurements are not available. Figure 6 shows the results of the simulation of an alkali load experiment compared with experimental observations. As described by Boron and De Weer (19761,when cells in an ammonia-free medium are suddenly switched to an ammonia-containing medium, the NH3 in the medium will quickly enter the cells and be protonated; pHi will rise quickly. The pHi-regulating mechanism will eventually bring pHi backto alower steady-state pHivalue due to the presence of ammonia in the medium. Our experimental measurements indicated a sudden rise in pHi of 0.2 unit from 7.44to 7.6and a return a t steady state to 7.35(final value not shown in Figure 6)when CHO cells
381
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i >-
0
0.1
z
7.7
7.5
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Time (min)
Figure 6. Transient response of pHi to an alkalineload induced by 12.5 mM ammonia exposure using an intrinsic buffering capacity of 60 mM/pH: (-1 model predictions of pHi; (A) experimental measurements of pHi in CHO cells; (- -) model prediction of the accumulation of intracellular ammonia. were exposed to 12.5 mM NH4C1. The model simulation agrees well with the experimental results without parameter adjustment, providing independent confirmation of the plausibility of the model. The intrinsic buffering capacity used in the model is 60 mM/pH. If only this value is used in the simulation, the model will overpredict the initial rise in pHi, indicating that the cell does not provide sufficient buffering action against a pH disturbance. As expressed in the Model Formulation section, weak acid and base could provide additional buffering power to the cytoplasm of the cells. When the buffering power of the NH3/NH4+ couple was added to the model, the model correctly predicted the transient change in pHi, as in Figure 6. As the model predicted, the intracellular level of ammonia (totalamount including NH3 and NH4+) was close to 10 mM after the cells were exposed to 12.5 mM ammonia. This level of intracellular ammonia corresponds to about a 26 mM buffering capacity by the intracellular NH3/NH4+couple. Therefore, over 30% of the intracellular buffering capacity is provided by the ammonia species. Roos and Boron (1981) estimated that, when pHi is 7.1 and the partial pressure of COz is 37 mmHg, the C02/HC03-/COs”system in the cell could provide over 40% of the intracellular buffering power in mammalian muscle. The buffering capacity provided by intracellular weak acids and bases has often been overlooked in models of pHi regulations, and the simulation in Figure 6 demonstrates its importance. If the intrinsic buffering capacityis about 15mM (within the range of reported values 10-90 mM), the transient response of pHi is predicted to rise more rapidly than with a 60 mM buffering capacity and overshoots the experimental data (compare Figure 7 to Figure 6). Although the predictions with 60 mM follow the data more closely than those with 15 mM, the differences are not so great that low values of intrinsic buffering capacity can be firmly excluded. The return of pHi to its normal value after the alkaline load could be the result of two mechanisms. One is the action of the Na/H antiport, and the other is the slow entrance of the NH4+ species (a third possibility, the action of the HCO3-/Cl-exchange to recover cells from an alkaline load, is ruled out since the medium was HC03- free). Moolenaar et al. (1984) performed an experiment similar to that illustrated in Figure 6, by pulsing human fibroblasts with 15 mM NH4C1; they observed a similar response by pHi. They attributed the decline of pHi after its initial rise to the slow entrance of NH4+. The modeling effort simply rules out the possibility that the entrance of the
r
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I
I
IO
20
1
1-0.3 30
Time (min)
Figure 7. Transient response of pHi to an alkalineload induced by 12.5 mM ammonia exposure predicted by a model with a intrinsic buffering capacity of 15 mM/pH (this result should be compared to Figure 6 where the intrinsic buffering capacity was 60 mM/pH): (-) model predictions of pHi; (A)experimental measurements of pHi in CHO cells, (- -1 model prediction of the accumulation of intracellular ammonia.
-
NH4+ species is responsible for the gradual decline. In a simple model of proton shuttle by ammonia species in mammalian cells by Boron and De Weer (19761, it was concluded that the permeability coefficient of NH4+ had to be about l e 1 0 6 cm/s in order for that model to have the shape of the pHi decline after the initial pHi rise shown in Figure 6. This value for the NHI+ permeability (1Wlobcm/s) coefficient is about 100times higher than the typical value of le7cm (Roos and Boron, 1981). Furthermore, the model simulation shows that the Na/H antiport is capable of bringing the pHi back to its normal value (Figure 6). The model simulation of the transient response in pHi can provide improved estimations of some parameters, but it can also discern between possible mechanisms of pHi recovery after an alkaline load. Model Simulation of the Transient Response in Intracellular pH to an Acute Acid Load. If the situation in the alkaline load experiment is reversed, i.e., the cells are switched from an ammonia-containing medium to an ammonia-free medium, the acidification of the cell cytoplasm will occur. Again, the high permeability of free ammonia is responsible for the fast change in PHI. L’Allemain et al. (1984) monitored the transient pHi response in Chinese hamster lung fibroblast cells to an acid load induced by switching cells from an ammoniafree medium to a medium containing 20 mM ammonia. The initial pH decrease was about 0.3 unit from pHj 7.3, and the final PHi reached 7.5, which is also the pH1 of cells that were incubated in an ammonia-free medium under steady-state conditions. The total response time was about 20 min. When the model was used to simulate the experiment by L’Allemain et al. (1984), the initial simulation results, shown in Figure 8, were overly sluggish. Although the steady-state values predicted by the model were also lower than the experimental observations, a slight adjustment in the permeability coefficients of ammonia would bring the simulation results nearer to the experimental results. However, even using the lowest literature value for the intracellular buffering capacity, the model prediction of pHi response was still much longer than 20 min. Equation 6 indicates that theNa/H antiportunder acute acid load could dramatically increase ita activity. If the expression of eq 6 is added to the expression of the Na/H antiport in the model, the model could predict well the pHiresponse to the acid load induced by 20 mM ammonia, as shown in Figure 9. In the model for this simulation (Figure 8), the acid extrusion rate (yo) is 35 mol/(h*cm2),
Bbtechnol. Rog., 1993, Vol. 9, No. 4
982
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change after an acid load induced by 20 mM ammonia removal: (-) model predictions of PHI;(A)experimental measurements of pHi by L'Allemain et al. (1983)in Chinese hamster lung fibroblastcella that had been switchedfrom a medium containing 20 mM ammonia to an ammonia-free medium; ( 0 )experimental measurements of pHi by L'Allemain et al. (1983)in Chinese hamster lung fibroblast cella that had been incubated inammoniafree medium; (-.) line connecting 0;(- -) model predictions of the depletion of intracellular ammonia.
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Figure 9. Model simulationby the acid model of the pHi change
after an acid load induced by 20 mM ammonia removal (the acid model incorporates eq 6): (-) model predictions of pHi; (A) experimentalmeasurements of pHi by L'Allemain et al. (1983) in Chinese hamster lung fibroblast cella that had been switched from a medium containing20 mM ammonia to an ammonia-free medium; ( 0 )experimentalmeasurements of pHi by L'Allemain et al. (1983)in Chinese hamster lung fibroblast cells that had been incubated in ammonia-freemedium; (- -) model prediction of the depletion of intracellular ammonia.
-
which is 7 times higher than the value used for the model that predicted the steady-state pHi values; the value of n is 2.5, indicating a very sensitive response to PHi, and in eq 5). PKadivation is 7.3 ( u in eq 6 corresponds to These values were selected to fit the response in Figure 8. The agreement in Figure 9 between the model and the experimental results indicates that eq 6 can successfully describe the action of the N 4 H antiport under acute acid load. The parameter values are the results of the modeling and are not determined by fitting to the curve. One immediate question is whether the model that predicted the results in acid load experiments (referred to as the "acid model", and the previous model that had been used for all other simulations will be referred as the "regular model") could be used to predict the steady-state experimental observations. The answer is shown in Figure 10, which is the model prediction by the acid model of steadystate pHi under conditions identical to those used in Figure 4. Since the activity of the Na/H antiport in the acid model is higher than that of the original model, the regulation of pHi is predicted to be much tighter. All of
the features in Figure 4 are still present in Figure 10,except that they have been compressed. Several possible explanations can be offered. The differences in cell lines could certainly be responsible for Na/H antiports with much different activities. A more plausible explanation is that the Na/H antiport has a basal level of activity that regulates pHi under steady-state conditions. But when the cells are under an acute acid load, the Na/H is activated and remains activated until pHi returns to ita normal value and eventually relaxes to its basal activities. Such speculations are very difficult to prove experimentally, since any long-term monitoring of pHi is impossible. For the pHi measurement technique used in our experiment, the leakage of the fluorescent probe out of the cells causes the base line to drift away from the true steady-state value. More accurate measurements in steady-state pHi values could at least determine which predictions among those in Figures 4 and 10 are more correct. Figure 4 agreed well with a study of hybridoma cells (McQueen and Bailey, 19911,while the acid model that predicted the results in Figure 9 was based on Chinese hamster lung fibroblasts. Until such experimental results are available, the fiial form of the Na/H antiport equation cannot be determined. But we believe that a form which shows switching of the mechanism in response to an acid load is the most plausible candidate. Lysosomal pH. The sensitivity of the intralysosomal or intraendosomal pH to the cytoplasmic level of ammonia is predicted by the model and compared with experimental measurements in Figure 11. Only 6 mM cytoplasmic ammonia is enough to change the lysosomal pH from 5 to
Bbtechnol. Bog..,1993, Vol. 9, No. 4
6. Because the model is capable of predicting the cytoplasmic pH, the cytoplasmic concentration of ammonia, and the lysosomal pH under these cytoplasmic conditions,the model can now predict how lysosomal pH would change in response to ammonia in the extracellular medium. The ability of the model to predict lysosomal pH under tissue culture conditions can be extended to prediction of the pH of other acidic cytoplasmic compartments such as endosome8 and the Golgi apparatus. Anderson and Goochee (1992) have implied that ammonia affects glycosylation through disruption of the pH of trans-Golgi. If the pH-regulating mechanism of the trans-Golgi is known or is similar to that of lysosome, this model can be used to predict the trans-Golgi pH under a few millimolar medium ammonia as studied by Anderson and Goochee (1992). One possible extension of the current model to include the inhibitory effect of alkaline medium pH on cells is to include the disturbance of the cellular activities by the elevated lysosomal pH. Once more knowledge is available on how elevated lysosomal pH disturbs cell metabolism, this model can be modified to include those details.
where J is the flux of the uncharged species C into (cells/ unit area) the plasma membrane. The transport of a charged species across the plasma membrane is assumed to follow the constant field equation:
and
where the Pc’s are the permeability coefficients, V , is the membrane potential, F is the Faraday constant, and R is the ideal gas law constant. For a weak acid HA and its conjugate base A- (the total amount of this acid is ITA1 = [HA] + [A-I), the rate of change in the intracellular concentration of TA due to diffusion is
Conclusion We have extended a CHO single-cell model to include the mechanisms of intracellular pH regulation, which allows us to relate changes in tissue culture conditions to disturbancesoptimal intracellularpH. The model’sability to relate mechanisms of intracellularpH control to cellular metabolism is novel. The model predictions of both steady-state and transient intracellular pH compare well with experimental observations. The model predictions explained certain commonly observed tissue culture requirements,such as the low tolerance for ammonia in terms of altered intracellular pH. The structure of the model allows simple extension of the model to include features such as other intracellular pH-regulating mechanisms or intralysosomal pH effects on cellular activities.
Acknowledgment
where the subscripts i and o refer to inside and outside of the cell, respectively, and S and V are the cellular surface area and volume, respectively. If there was no TA (HA and A-) in the cell before the addition of dHA, the amount of H+ entering the cell due to the entry of HA would be d[HAl&/(Km + [Hli). This approach was used by Boron and De Weer (1976). Keifer and Roos (1980) refined this part of the derivation and recognized that the weak acid has a self-burning effect, i.e., the decrease in pHi resulting from a given addition of HA will be less if TA is already present in the solution. In mathematical terms, 2.3[Hli d[HIi = -X 6
We are grateful to Ms. Cheryl K. Grabe for the initial planning and testing of the intracellular pH-monitoring techniques and Mr. Bernard Beaulieu for the final measurements of intracellular pH. This work was supported, in part, by an SBIR grant from the NSF (ISI8700385).
645)
It follows that the entry of A- will affect the proton balance as
Appendix Summary of Equations Describing the Effect of Weak Acid and Base on Intracellular pH. The following equations describe how weak acid and base disturb intracellular pH. These equations have been derived by Boron and De Weer (1976) and modified by Keifer and Roos (1980). McQueen and Bailey (1990) rederived and utilized these equations for their modeling of the effect of ammonia on the intracellular pH of hybridoma cells. In this model, the inward flow is always positive and the membrane potential Vm has a positive value, so that -Vm is what is commonly called the ‘membrane potential”. The mammalian cell membrane is relatively positive on the outside and relatively negative on the inside. According to Boron and De Weer (1976),the transport of uncharged molecules follows Fick’s law:
Let
and
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frog skeletal muscle. Am. J.Physiol. 1982,242(Cell Physiol.
has the final form:
P,VJ
(K,/(K,
( - U T
ll), C87-C93.
+ [Hli))[TAli1- e - V a / R T
(A81 Witha similar approach, a weak base B and its conjugate acid HB+ would disturb the intracellular pH by 2-3[Hli s 1 --dt B V
Gillies, R. J. In Transformed Cell; Cameron, I. L., Pool, T. B., Eds.; Academic Press, Inc.: New York, 1981;p 347. Goldfarb, D.; Nord, E. P. Asymmetric affinity of Na+-H+ antiporter for Na+at the cytoplasmicversusexternal transport site. Am. J. Physiol. 1987,253,F959-F968. Grainger, J. L.; Winkler, M. M.; Shen, S. S.; Steinhardt, R. A. Intracellular pH controls protein synthesis rate in the sea urchin egg and early embryo. Deu. Biol. 1979,68,396-406. Keifer, D. W.; Roos, A. Membrane permeability to the molecular and ionic forms of DMO in barnacle muscle. Am. J.Physiol. 1980,240,C73479.
L’Allemain, G.; Paris, S.; Pouyssegur, J. Growth factor action and intracellular pH regulation in fibroblasts. J.Biol. Chem. 1984,259(9),5809-5815.
L’Allemain,G.; Paris, S.; Pouyssegur,J. Role of aNa+-dependent Cl-/HCOs- exchange in regulation of intracellular pH in fibroblasts. J. Biol. Chem. 1986,260(8), 4877-4883. Lee, I. D.; Palason,B. 0.Acomplete modelof human erythrocyte metabolism. Extension to include pH effects. Biomed. Biochem. Acta 1992,49(8-9),771-789.
where a and a’ have the same meaning except that KHA is now defined The term [TBI is now [Bl + [BH+l, and note that the first terms in eq A8 and A9 are the proton donor terms, Le., HA and BH+ will release aproton when they enter the cytoplasm. They enter either by a simple transport process or by intracellular synthesis.
Literature Cited Alberta, B.; Bray, D.; Louis, J.; Raff, M.; Roberta, K.; Watson, J. D. Molecular Biology of the Cell; Garland Publishing Inc.: New York, 1983. Anderson, D. C.; Goochee, C. F. Cell Culture Effects on the 0-Linked Glycosylation of Granulocyts Colony-Stimulating Factor Produced by CHO Cells. Presentation at the AIChE 1992 Annual Meeting, Miami Beach, FL, November, 1992. Batt, B. C.; Kompala, D. S. Presentation at the 17th Annual BiochemicalEngineeringSymposium,Ames,IA,April 25,1987. Belt,J.A.;Thomas, J. A.;Buchsbaum,R.N.;Racker,E.Inhibition of lactate transport and glycolysis in Ehrlich ascites tumor cells by bioflavonoids. Biochemistry 1979,18,3506-3511. Boron, W. F.; de Weer, P. Intracellular pH transients in squid giant axons caused by COz, NHa, and metabolic inhibitors. J. Gen. Physiol. 1976,67,91-112.
Brierley, G.; Davis, M. H.; Cragoe, E. J., Jr.; Jung, D. W. Kinetic properties of the Na+/H+ antiport of heart mitochondria. Biochemistry 1989,28,4347-4345.
Busa, W. B. The proton as an integrating effector in Metabolic activation. In Nu+-H+ Exchange, IntracellularpH, and Cell Function;Aronson,P. S.,Boron, W. F., Eds.; Academic Press: Orlando, 1986; pp 291-305. Deamer, D. W. Proton permeability in biological and model membranes. In Intracellular p H Its Measurement, Regulation, and Utilization in Cellular Functions; Nuccitelli, R., Deamer, D. W., Eds.; Alan R. Lias, Inc.: New York, 1982;pp 173-187.
Dean, R. T.; Jessup, W.; Roberta, C. R. Effects of exogenous amines on mammalian cells, with particular reference to membrane flow. Biochem. J. 1984,217,27-40. de Duve, C.; de Barsy, T.; Pool, B.; Trouet, A.; Tulkens, P.; Van Hoof, F. Lysosomotropicagents. Biochem. Pharmacol. 1974, 23, 2495-2531.
Feder, J. In Large Scale Mammalian Cell Culture; Feder, J., Tolbert, W. R., Eds.; Academic Press: Orlando, 1985. Fidel”, M. L.; Seeholzer, S. H.; Walah, K. B.; Moore, R. D. Intracellular pH mediates action of insulin on glycolysis in
McQueen, A,; Bailey,J. E. Mathematical modeling of the effects of ammonia ion on the intracellular pH of hybridoma cells. Biotechnol. Bioeng. 1990a,35,897-906.
McQueen,A.; Bailey,J. E. Effect of ammoniaion and extracellular pH on hybridoma cell metabolism and antibody production. Biotechnol. Bioeng. 1990b,35, 1067-1077.
McQueen, A.; Bailey,J. E. Growth inhibition of hybridoma cells by ammonium ion: correlation with effects on intracellular pH. Bioprocess Eng. 1991,6, 49-61. Mooleanaar, W. H.; Tsien, R. Y.; van der Saag, P. T.; de Laat, S. W. Na+/H+exchange and cytoplasmic pH in the action of growth factors in human fibroblasts. Nature 1983,304(la), 645-648.
Mooleanaar, W. H.; Tertoolen, L. G. J.; de Laat, S. W. The regulation of cytoplasmic pH in human fibroblasts. J. Biol. Chem. 1984,259(12),7563-7569.
Nord, E. P.; Brown, S. E. S.; Crandall, E. D. Cl-/HCOa-exchange modulates intracellular pH in rat type I1 alveolar epithelial cells. J. Biol. Chem. 1988,263(12),5599-5606. Nuccitelli, R., Deamer, D. W., Eds. Intracellular pH; Alan R. Liss, Inc.: New York, 1982. Ozturk, S. S.;Riley, M. R.; Palsson, B. 0. Effects of ammonia and lactate on hybridoma growth, metabolism, and antibody production. Biotechnol. Bioeng. 1992,39,418-431. Paris, S.;Pouyssegur, J. Biochemical characterization of the amiloride-sensitiveNa+/H+antiport in Chinese hamster lung fibroblasts. J. Biol. Chem. 1983,258(6),3503-3508. Pool, B.; Ohkuma, S. Effect of weak bases on the intralysosomal pH in mouse peritoneal macrophages. J. Cell Biol. 1981,90, 665-669.
Pouyssegur, J.; Franchi, A.; Kohno, M.; L’Allemain, G.; Paris, S. In Nu+-H+ Exchange, Intracellular pH,and Cell Function; Aronson,P. S., Boron, W. F., Eds.; Academic Press: Orlando, 1986;pp 201-220. Reitzer, L. J.; Wise, B. M.; Kennel, D. Evidence that glutamine, not sugar, is the major energy sourcefor cultured HeLa cells. J. Biol. Chem. 1979,254,2669-2676. Rink, T. J.; Tsien, R. Y.; Pozzan, T. Cytoplasmic pH and free Mg++in lymphocytes. J. Cell Biol. 1982,95,185-196. Roos, A.; Boron, W. F. Intracellular pH. Physiol. Rev. 1981,61 (2),296-434.
Schneider, D. L. ATP-dependent acidification on intact and disrupted lysosomes. J.Biol. Chem. 1981,256(a), 3858-3864. Wu,P.;Ray, N. G.; Shuler, M. L. A Single Cell Model for CHO cells. Ann. N . Y . Acad. Sci. (Biochem. Eng. V I 0 1992,152187.
Accepted February 25, 1993.
