Virginia Bioinformatics Institute, Virginia Polytechnic and State University, Blacksburg, Virginia
Submitted 29 October 2004 ; accepted in final form 30 December 2004
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ABSTRACT |
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simulation; nucleotide phosphorylation; nucleoside transport; mitochondrial DNA
Mitochondrial DNA (mtDNA) replication occurs during all phases of the cell cycle, even in postmitotic cells in which nuclear DNA synthesis has ceased. The measured half-life of mtDNA in mammalian cells is 1030 days (25). Without this ongoing process of mtDNA replication and the nucleotide metabolism supporting replication, mtDNA depletion occurs rapidly, eventually disrupting the production of ATP and causing failure of the cell to function. Errors in the mitochondrial nucleotide metabolism also can be a cause of mtDNA mutations by changing the balance of the four deoxynucleotide triphosphate pools in the mitochondrion (72). Many genetic diseases characterized by mtDNA depletion or increased mtDNA mutation rates are caused by mutations in the nuclear genes for enzymes of nucleotide metabolism (48). To understand these diseases, we must first understand normal mitochondrial deoxynucleotide metabolism. In this paper, we describe a computational model of the deoxynucleotide metabolism within an individual mitochondrion, coupled to the deoxynucleotides and deoxynucleosides within the cytoplasm.
Transport and phosphorylation of mtDNA precursors. The mitochondrion is surrounded by a double membrane defining two separate compartments within the organelle: the intermembrane space between the outer and inner membranes and the matrix space within the inner membrane. The mtDNA molecules are located within the matrix space. The outer membrane is highly porous to all nucleosides and nucleotides; therefore, we consider the intermembrane space to be in equilibrium with the cell cytoplasm and do not consider it a separate compartment in the model. The mitochondrial inner membrane is highly impermeable to solutes, so specific transporters are located there to provide the precursors needed for mtDNA synthesis (Fig. 1). The inner membrane contains at least two proteins that transport DNA precursors into the mitochondrial matrix: the deoxynucleotide carrier (DNC) and an equilibrative nucleoside transporter (ENT). The DNC has been reported to transport deoxynucleotide diphosphates (dNDPs) into the mitochondrial matrix in exchange for ADP or ATP (13). The DNC also transports deoxynucleotide triphosphates (dNTPs), but less efficiently than dNDPs. In humans, hENT1 has been identified as a mitochondrial deoxynucleoside (dN) transporter (40). In addition to this general nucleoside transporter, a dN transporter specific for deoxyguanosine has been reconstituted from rat liver mitochondria (83). To summarize, mitochondrial deoxynucleotide metabolism is connected to cytoplasmic deoxynucleotide metabolism at both ends of the phosphorylation process: at the deoxynucleoside level and at the diphosphate and triphosphate levels.
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MtDNA replication.
With 210 mtDNA molecules per organelle and 1 h required for mtDNA synthesis in rapidly dividing cells (which must double their mtDNA content during the cell division period of
24 h), mtDNA replications most likely occur as individual events, with only one mtDNA molecule replicating at any one time within a single mitochondrion and often with no molecules replicating in the organelle. Slowly dividing or postmitotic cells are even less likely to have overlapping mtDNA replication events in a single mitochondrion. So, we may consider individual, nonoverlapping mtDNA replication events to be the normal situation.
The two strands of the mtDNA molecule are called the heavy and light strands because of a large imbalance in guanine between the two strands. Two distinct models have been proposed for mtDNA replication. In the classic Clayton-Vinograd model, mtDNA replication occurs through an asynchronous displacement mechanism using an origin of replication for the heavy strand of mtDNA (OH) and a separate origin of replication for the light strand (OL) (6). The OH is located in the displacement loop (D-loop) of mtDNA, a short stretch of 1,000 nucleotides that often contains single-stranded DNA adjacent to the duplex DNA. According to this asynchronous model of replication, a polymerase starts from OH and replicates two-thirds of the DNA molecule and then a separate polymerase begins DNA synthesis of the light strand in the reverse direction. Replication is coupled to mtDNA transcription because an RNA primer from transcription is used near OH for replication initiation.
A different model of synchronous mtDNA replication was recently suggested on the basis of observations of replication intermediates in two-dimensional gels (4). However, extensive verification of this model has yet to be performed, and the model is still controversial. In the simulation, we have used the asynchronous Clayton-Vinograd model.
MtDNA diseases.
A number of mitochondrial diseases are caused by errors in the mitochondrial nucleotide metabolism due to nuclear DNA mutations. These diseases include mitochondrial neurogastrointestinal encephalomyopathy (MNGIE), adult dominant and adult recessive progressive external ophthalmoplegia (adPEO and arPEO), Amish microcephaly, and mtDNA depletion syndrome (14, 48). MtDNA mutations and depletion can be caused either by a dysfunction of the mtDNA replicative machinery or by imbalances or deficiencies in the mitochondrial dNTP pools. MtDNA depletion diseases are an extreme form of mitochondrial disease in which the mtDNA in certain cell types is present in very low amounts. Mutations in TK2 and dGK have been shown to cause severe mtDNA depletion (14). Mutations in the mitochondrial adenine nucleotide translocase (ANT), a mtDNA helicase called twinkle, and polymerase- cause adPEO (48). Mutations in the cytoplasmic thymidine phosphorylase cause MNGIE, and mutations in the DNC cause Amish microcephaly (66).
Understanding the basic metabolism of deoxynucleotides within mitochondria is a necessary first step in understanding this significant group of mitochondrial diseases. For this reason, we have built a simulation model of this metabolism.
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METHODS |
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![]() | (1) |
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Phosphorylation model: Km dynamics with inhibitions.
For all but one (TK2 acting on dT) of the phosphorylation reactions, we calculated the reaction rates using the standard Km equation, including inhibition from all substrates that also interact with each enzyme. For the reversible reactions, this included the products as inhibitors (see Fig. 2 and Table 1). In general, the reaction rate Rs for a substrate with concentration [S] is calculated as follows:
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In experiments using the isolated TK2 enzyme, the nucleoside kinase reaction for dT has been shown to have negatively cooperative Hill kinetics (54). The mathematical model for this is as follows:
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MtDNA polymerase model.
The mtDNA polymerase requires a special model, which we have developed. The polymerase- adds dNTP molecules one at a time to the new strand of mtDNA. Each of the four deoxynucleotides may be added at different rates, denoted by rA, rC, rG, and rT, with each rate depending on the triphosphate concentration of that deoxynucleotide. We used Km dynamics to model these four rates, with a Vmax and Km value for each deoxynucleotide substrate determined on the basis of data reported in the literature (Table 2). Experiments show that polymerase-
has
50% the rate of polymerization on double-stranded DNA as it does on the short, overhanging DNA template with which the kinetic values were measured (34, 35, 43), and that adjustment is made to these Vmax values (Table 3).
Because the deoxynucleotides were added linearly to the growing mtDNA strand, we modeled the total time t to polymerize a segment of mtDNA strand of length L as a linear function as follows:
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This is the rate at which the polymerase- replicates a strand of mtDNA defined by the parameters fA, fC, fG, and fT. Replication of the mtDNA molecule is modeled as the asynchronous polymerization of the two strands (6). In this model, we used constant values of fA, fC, fG, and fT for each strand, although variation in these values by position along the strand also could be included. The rate of mtDNA synthesis was set at 0 until the replication start time, when we discontinuously set it to Rpoly to represent the replication of the heavy strand. The amount of new mtDNA polymerized on each strand was calculated, and replication of each strand was stopped, when the length of the newly polymerized mtDNA strand equaled the human mtDNA genome length of 16,568 bp.
Differential equations for the deoxynucleotide concentrations.
The individual Km, Hill, and polymerization equations were used in differential equations for the concentrations of the 16 metabolite pools in our model: dN, dNMP, dNDP, and dNTP for each A, C, T, and G. In this section, for clarity, we use only the generic forms of the differential equations. The specific equations for the four phosporylated forms of thymidine are provided as examples in the APPENDIX. The rates of change of the four dN pools are as follows:
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The rates at which the four dNMP pools change over time are calculated as follows:
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The rates of change of the four dNDP pools are calculated as follows:
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Finally, the rates of change of the four dNTP pools are calculated as follows:
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Numerical solution of the differential equations and metabolic control analysis. The simulations were written in Mathematica version 5 software using the numerical differential equation solver for a system of differential and algebraic equations. The Mathematica code and the deoxynucleotide model constants that we used are available online as supplemental material.1 The solver uses an adaptively selected step size and switches automatically between the Adams predictor-corrector method for nonstiff and backward difference formulas (Gear method) for stiff differential equations.
We used the Metabolic Control Analysis package, which is publicly available for the Mathematica system (46). We used flux response coefficients (36) to measure the extent of the control of the parameters of each enzyme in the system on the polymerization rate in the state with two polymerases active. In this paper, we present data only for the control of the 13 enzyme concentrations (Table 1) on the polymerization rate, because enzyme concentration is the parameter that is the most realistic to vary. We had to take into account the complication that each enzyme takes part in multiple pathways (Fig. 2), so an enzyme concentration had to be varied in the same way in each pathway in which it was involved. In the Km model, the Vmax parameters are proportional to the enzyme concentration. So, for the metabolic control analysis, we multiplied all the Vmax parameters of each enzyme by a normalized enzyme concentration ([enzyme]), set to 1, and measured the change in the polymerization rate due to variations in the 13 [enzyme] terms.
Simulating labeled and unlabeled mtDNA precursors.
We have extended the basic model to represent labeled and unlabeled deoxynucleotides, equivalent to radioactive or fluorescent labeling in the laboratory. Separate differential equations were set up for the labeled and unlabeled forms, with the reaction rates determined using the total concentration of labeled plus unlabeled deoxynucleotides. Each of the dN pool equations (Eqs. 69) was replaced by a pair of differential equations, with one representing the labeled form and one representing the unlabeled form. For example, for the deoxynucleoside pools (Eq. 6), we have the following two sets of equations. For the labeled deoxynucleosides, represented by a prime on the concentrations, we have
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This method also can be used to trace the flow of material through the mitochondrion. By starting the simulation with no deoxynucleotides or deoxynucleosides in the mitochondrion, with all of the cytoplasmic deoxynucleosides labeled and all of the cytoplasmic deoxynucleotides unlabeled, we measured the amount of dNTP incorporated into DNA from the cytoplasmic deoxynucleoside pools (through the nucleoside transporter route) and compared it with that originating in the cytoplasmic deoxynucleotide pools.
Defining simulated cell types. We defined three categories of normal cells: rapidly dividing cells, slowly dividing cells, and postmitotic cells. To this list we add a fourth abnormal cell type: cancer cells. Cancer cells are of interest in this model because the normal cytoplasmic nucleotide metabolism is altered in these cells and because cancer cells often show mtDNA mutations that might be caused by this altered metabolism. In principle, the enzyme concentrations in the model could be different in every cell type. However, the limited expression data available do not indicate that the enzyme levels of this metabolism vary greatly across cell types (18). For a simple model, we kept the enzyme levels constant across these four cell type categories (Table 4) and distinguished the cell categories by the cytoplasmic deoxynucleotide diphosphate and triphosphate concentrations (Table 5).
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Determining enzyme levels in the mitochondrion. For this simulation, the units of reaction rate and of the Vmax parameters are molecules per mitochondrion per minute. The standard units reported in the literature are micromoles per milligram of enzyme per minute, so we must use the number of enzyme molecules per mitochondrion and the enzyme molecular weight (Table 4) to convert data to the units needed in the simulation. Enzyme levels are measured by three basic methods; inhibitor binding, enzyme activity measures, and blotting experiments. Each method requires a different conversion.
The ENT levels were calculated from ligand binding experiments (5, 33, 58). An inhibitor of nucleoside transport was found to have 2,100 fmol/mg of mitochondrial protein binding sites. We used 3.3 x 1010 mitochondria/mg of mitochondrial protein, a value averaged from the values reported in the literature [ranging from 4.3 x 109 (22) to 5.3 x 1010 (56)] to convert this value to transporters per mitochondrion.
TK2, dGK, AK3, and dNT-2 enzyme levels were calculated from enzyme activity measurements (1, 17, 55, 63, 75). In these experiments, saturating substrate concentrations were administered to a known mass of mitochondria, so the number of molecules of enzyme present may be calculated using the known Vmax of the enzyme. For TK2 and dGK, an average value from several tissues was used.
DNC levels were approximated from Western blotting experiments (13) by comparison to a known quantity of recombinant DNC that was used as a standard. NDPK levels were roughly estimated from blotting experiments (39, 52, 53). These experiments showed that NDPK was highly expressed, so the number of enzymes per mitochondrion was set at 300, a relatively high value compared with the other levels shown in Table 4.
Unknowns in the model. In the mitochondrial matrix, adenylate kinase (AK3) phosphorylates dAMP (55, 74). It is hypothesized that a dCMP kinase phosphorylates dCMP and that a guanylate kinase phosphorylates dGMP in mammalian mitochondria, but such proteins have not yet been identified (10, 84). None of the kinetic values in the model were functionally determined (i.e., with values set to produce a particular behavior in the simulation). When values were not available, the values from the corresponding cytoplasmic enzymes were used.
It was reported previously that cells had only one type of dTMP kinase activity that is located in both the cytoplasm and the mitochondrion (42). However, this initial observation has yet to be confirmed. Mitochondria have been shown to possess a general nucleotidase that dephosphorylates nucleotide monophosphates (61). Whether the activity resides in the matrix space, however, remains controversial.
The relative forward and reverse reaction rates for mitochondrial nucleoside monophosphate kinases and NDPK are not known. However, the concentrations of mitochondrial dTMP, dTDP, and dTTP have been shown in experiments to be in the same proportions as concentrations of mitochondrial AMP, ADP, and ATP (60). In our model, mitochondrial AMP, ADP, and ATP concentrations are set at 8.0, 6.0, and 2.9 mM (76). We assume that the proportions of dTMP, dTDP, and dTTP are determined primarily by the rates of the forward and reverse phosphorylation reactions. We used these experimental results to set the maximum velocity of the reverse NDPK reaction to 75% (6.0/8.0) of the forward reaction, based on the ADP-to-ATP ratio. We also set the maximum velocities of the reverse NMPK reactions to 50% (
2.9/6.0) of the forward reactions using the AMP-to-ADP ratio.
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RESULTS |
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Different cell types have markedly different cytoplasmic deoxynucleotide levels. Because the cytoplasmic and mitochondrial deoxynucleotide pools are coupled, we would expect the cytoplasmic deoxynucleotide levels to have a strong effect on mtDNA replication time (Fig. 4). The minimum replication time in the simulation is 30 min and occurs when the mitochondrial dNTP concentrations are high enough to saturate the polymerase-
reaction rate. The replication time of
40 min in our simulated dividing cells is slightly faster than the time of
60 min found experimentally (6).
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On the basis of electron microscopic studies of mtDNA replication intermediates, Robberson et al. (65) hypothesized that the replication rate was nearly linear along the circular mtDNA molecule because all intermediates were observed in nearly equal amounts. For comparison with their observation, we calculated the polymerization rates of both the heavy and light strands in our simulation as a function of the position on the mtDNA molecule in different cell types (Fig. 5). High initial polymerization rates dropped quickly as the nucleotide levels dropped in the matrix. The rate of heavy-strand polymerization also decreased when light strand polymerization was initiated and both polymerases were operating simultaneously. Later, the light strand polymerization rate increased when the heavy strand synthesis completed. Despite these relatively minor changes, mtDNA polymerization rates in this simulation are fairly uniform across the mtDNA molecule.
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Metabolic control analysis. One of the most important uses of metabolic modeling is determining the enzymes that exert the most control over the system. To obtain this information, metabolic control analysis (MCA) may be performed on the steady states of the system. MCA also indicates the sensitivity of the system to changes in parameter values. The Clayton-Vinograd model of mtDNA replication has four steady states: no polymerization, polymerization of just the heavy strand of mtDNA, polymerization of both strands, and polymerization of just the light strand of mtDNA. In the example shown here, we chose to perform MCA at the steady state when both the heavy and light strands were replicating. Under this condition, dCTP has the lowest concentration of the four dNTPs and appears to have limited polymerization in all cell types examined (Fig. 3). In Fig. 10, we show the enzymes with a flux-response coefficient of the polymerization reaction of magnitude >0.1 in any of the four simulated cell types.
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DISCUSSION |
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Comparison to experiments with labeled thymidine. Many experiments have been performed administering labeled thymidine to cells in culture that either possessed or were lacking the cytosolic thymidine kinase TK1 (3, 60, 62). In TK1 cells, the only enzyme that phosphorylates thymidine is the mitochondrial enzyme TK2. Therefore, all labeled thymidine nucleotides in these cells had to be phosphorylated in the mitochondria. Thymidine administered to normal (i.e., TK1+) cells could first be phosphorylated in the cytoplasm and then enter the mitochondrion through the DNC. Measuring the specific activity, the amount of labeled dTTP compared with total dTTP, or the amount of labeling in mtDNA compared with the amount of total mtDNA in both cell types lets one determine the predominant route of transport in situ. Experiments using TK1 and TK1+ cultured mouse L cells demonstrated that 95% of thymidine in mtDNA was transported into mtDNA after it had first been phosphorylated in the cytoplasm (3). Experiments measuring cytoplasmic dTTP recently confirmed these observations (60). Therefore, the DNC is almost the sole provider of thymidine under these conditions. Our simulation showed that 98% of the thymidine in mtDNA (Fig. 9) in simulated dividing cells was transported through the DNC, a finding that is in excellent agreement with the value observed in experiments.
Efflux of mitochondrial nucleotides. Our model allows the efflux of nucleotides from the mitochondrion into the cytoplasm through the DNC (Fig. 9). In the early 1970s, Berk and Clayton (3) found almost exclusive labeling of mtDNA (but not nuclear DNA) by administering labeled thymidine to TK1 cells. The specific activity of nuclear DNA in their experiment was 3% of the mtDNA and <0.05% that of nuclear DNA in TK1+ cells. Therefore, for >25 years, it had been assumed that mitochondria used their nucleotides in mtDNA and did not export them to the cytoplasm. Others have also used TK1 cells and bromodeoxyuridine to exclusively label mtDNA as well (2, 45). However, recent experiments (62) refuted this conclusion by measuring a strong efflux of labeled dTTP from mitochondria into the cytoplasm. The disagreement between these experiments may be due to differing DNC properties in different cell types (31). The simulations followed the recent experimental data (62) more closely when mitochondrial deoxynucleotide efflux was allowed to occur in the model (i.e., our standard model) than when efflux through the DNC was completely blocked in the simulation (data not shown).
Model significance and suggestions for new studies. On the basis of our simulations of mitochondrial deoxynucleotide metabolism, we draw five main conclusions that could be used as testable hypotheses in future experiments.
1. The deoxynucleotide pools within each mitochondrion are not sufficient to support even a single mtDNA replication (see Fig. 3). Deoxynucleotides and/or deoxynucleosides must be imported into the organelle from the cytoplasm during mtDNA replication. The rate of this import and the concentration of dNTPs in the cytoplasm have a strong effect on the replication time for mtDNA.
2. The mtDNA replication time is quite long in simulations of postmitotic cells in which cytoplasmic deoxynucleotide levels are low (see Fig. 4). The slow reaction rate of dGK for dA is the primary cause of this finding in our model. We suggest that the kinetics of this reaction may be more rapid in vivo than those measured with the purified enzyme. This becomes important when cytoplasmic dADP and dATP concentrations fall below 0.1 µM. This simulation result emphasizes the importance of conducting experiments on postmitotic cells, not just on easily cultured dividing cells, because the behavior of the mtDNA can be significantly different in the two types of cells, and it is the postmitotic cells that are primarily of medical relevance.
3. The deoxynucleotide metabolism within the mitochondrion can be described by three states: phosphorylating, efficient, and dephosphorylating (see Fig. 6). In rapidly dividing cells, the mitochondria act as net sinks for deoxynucleotides and net sources for deoxynucleosides in the cytoplasm. In postmitotic cells, the reverse is true, with mitochondria exporting dNTPs and dNDPs into the cytoplasm.
4. The main controlling enzyme of this metabolism in rapidly dividing cells is the DNC (see Fig. 10). The control parameters are very different in simulated postmitotic cells, with control held mainly by NDPK (the final phosphorylation) and TK2 (the first phosphorylation).
5. Rapidly dividing cells derive almost all of their mtDNA precursors as dNDPs and dNTPs from the cytoplasm (see Fig. 9). Aside from the final phosphorylation of dNDP to dNTP, the nucleotide metabolism in the mitochondrion does little to support mtDNA replication in these cells.
Let us end with a discussion of two of the assumptions of this simulation. In this simple model, we have assumed equal enzyme levels in the four simulated cell types, based on the observation of equal expression levels for most of these enzymes in many tissues (1). It is possible that enzyme levels are varied across cell types by posttranslational modifications or degradation control to put the mitochondria into the efficient state of deoxynucleotide metabolism, or at least closer to it. There is evidence for variable enzyme levels with tissue types of TK2 and dNT-2. The enzyme dNT-2 is highly expressed in postmitotic tissues (heart, brain, and skeletal muscle) (63). Activity of TK-2 was observed to be 10 times lower in skeletal muscle than in liver, fibroblasts, and heart tissue (68). Both of these variations would extend the range of the efficient state of dT metabolism shown in Fig. 8.
Finally, we have assumed a volume of 2 x 1016 L for the mitochondrion (11, 22, 23). For the purposes of this model, this volume should represent the volume within the mitochondrial matrix from which a replicating mtDNA molecule can take dNTP molecules. The formation of large networks of mitochondria in some cell types could reduce the need to import mtDNA precursors from the cytoplasm during mtDNA replications if the inner membranes of the connected mitochondria also were fused to allow the free movement of dNTPs within the matrix of the network.
Model limitations.
The most important limitations of this model are the lack of kinetic data for the nucleoside monophosphate kinases, the possible existence of other deoxynucleotide transporters, the effect of membrane potential on DNC transport, and the unknown concentrations of cytoplasmic dNTPs in postmitotic tissues. We are also concerned with the ability of Km kinetics to model the system when the enzyme concentrations are nearly equal to the substrate concentrations. This concern holds for all models in which the metabolites are present in submicromolar quantities. Another limitation of the model is the ability of the polymerization equation to reflect polymerase kinetics in postmitotic cells. The kinetics of mitochondrial polymerase- were measured under saturating dNTP conditions (34). This is adequate for modeling rapidly dividing cells, but the kinetics may be more complex when the dNTP concentrations are low and not saturating the enzyme. A more detailed model may be necessary to describe polymerization kinetics in this case.
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APPENDIX |
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Vmax, Km, and Ki terms are shown in matrix format to specify the values in Table 2. Values for Ki terms not listed in matrix notation can be found by identifying the inhibitor in the middle column of Table 1.
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
1 Supplementary material for this article is available directly from the authors and also can be found at http://ajpcell.physiology.org/cgi/content/full/00530.2004/dc1.
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