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Department of Bioengineering, University of California San Diego, La Jolla, California 92093 - 0412
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Mitochondrial metabolism is a critical component in the functioning and maintenance of cellular organs. The stoichiometry of biochemical reaction networks imposes constraints on mitochondrial function. A modeling framework, flux-balance analysis (FBA), was used to characterize the optimal flux distributions for maximal ATP production in the mitochondrion. The model predicted the expected ATP yields for glucose, lactate, and palmitate. Genetic defects that affect mitochondrial functions have been implicated in several human diseases. FBA can characterize the metabolic behavior due to genetic deletions at the metabolic level, and the effect of mutations in the tricarboxylic acid (TCA) cycle on mitochondrial ATP production was simulated. The mitochondrial ATP production is severely affected by TCA-cycle mutations. In addition, the model predicts the secretion of TCA-cycle intermediates, which is observed in clinical studies of mitochondriopathies such as those associated with fumarase deficiency. The model provides a systemic perspective to characterize the effect of stoichiometric constraints and specific metabolic fluxes on mitochondrial function.
mitochondria; flux analysis; adenosine 5'-phosphate production; mitochondrial disease
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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CELLULAR RESPIRATION and, consequently, mitochondrial metabolism has a significant role in the functions of aerobic organs. In systems such as the heart, this process supports myofilament contraction, transmembrane ion, and intracellular calcium cycling. Normal well-perfused myocardium generates >90% of its ATP by oxidative metabolism and <10% by anaerobic glycolysis (11). Mitochondrial metabolism also plays a critical role in the function of other organs, such as the liver and the brain, where the impaired functioning of mitochondria has been implicated in several neurological disorders (16).
The link between the genetics and physiology of mitochondrial diseases is an area of intensive study. The genetic basis of mitochondrial disease is considered to arise from defects of nuclear DNA, including defects of protein import, defects of mitochondrial DNA (mtDNA), such as point mutations, deletions, and duplications, and defects of communication between nuclear and mitochondrial genomes (multiple deletions and mtDNA deletion) (5). The physiological manifestations of these genetic defects affect the normal functioning of substrate transport, substrate use, the tricarboxylic (TCA) cycle, the respiratory chain, and oxidation/phosphorylation coupling. mtDNA has no introns and has its own independent replication, transcription, and translation systems. Mutations in mtDNA accumulate 10-20 times faster than in comparable nuclear genes (17). The accumulation of mtDNA mutations is believed to be a key factor in aging and the progression of mitochondrial diseases (15).
Mitochondrial metabolism results from the concerted action of several biochemical reactions that are coordinately regulated. Genotypic and physiological factors interactively contribute to adversely affect mitochondrial metabolism (23). Mutations in the genetic content can lead to changes in enzyme expression and/or activity and thus alter mitochondrial function by changing fluxes of important metabolic reactions and consequently affecting the normal physiological behavior of cells, tissues, and organs. A genetic mutation that changes a flux or fluxes consequently forces the metabolic system to a new state and affects the attainment of its physiological objective. Therefore, an understanding of the systemic constraints on metabolism can provide significant insight into physiological function. The framework of flux-balance analysis (FBA) (2, 6, 20, 22) is a powerful methodology for the analysis of metabolic systems. This approach has been successfully applied to the analysis of adipocyte metabolism (6), hybidoma metabolism (1, 14), and bacterial growth (21), in which the constraints imposed by biochemical reaction stoichiometry are systemically modeled.
The application of systemic metabolic simulation approaches can significantly aid in understanding the metabolic basis of mitochondrial-linked disease. The biochemical reactions involved in mitochondrial energy metabolism function as a coordinated network subject to stoichiometric and regulatory constraints. The objective of this study was to first develop a model for mitochondrial function, using the methods of systems theory that can predict the effect of genotype changes on certain aspects of mitochondrial function. The model was to comprise of the metabolic pathways that constitute a functioning mitochondrion, including the reactions in the mitochondrial matrix, contributing reactions in the cytosol, and key shuttles. The analysis considers the constraints imposed by the stoichiometry of these biochemical reaction networks on the achievement of specific metabolic objectives. The model will be used to characterize energy metabolism on the standard substrates of mitochondrial metabolism.
As part of the model development, the genes(s) involved in the metabolic reactions considered will be detailed. This provides a framework for studying the effect of genetic changes on metabolism. The model will be used to characterize the effect of genetic mutations on mitochondrial metabolism. These simulations will be compared with literature that describes the physiology of mitochondrial disease.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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FBA.
FBA is a modeling framework developed to characterize the capabilities
and properties of a metabolic network. The network comprises the
metabolites and the reactions they are involved in, including their
formation and degradation, transport, and cellular utilization. For
every metabolite (Xi), a material balance is
derived as follows
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(1) |
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i and
i, represent known constraints on the maximum or minimum
values that the fluxes assume. When the maximization of ATP
production is considered, the net flux of ATP hydrolysis
(vATP_PR) is maximized.
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i) and the reduced cost. The i are
associated with each metabolite and are defined as
i = dZ/dbi. For the
objective of maximization of ATP production, if the i of
NADH is 3.00, it means that an additional molecule of NADH can generate
three more molecules of ATP. The i, therefore,
represents the increase in the value of the objective with the addition
of the associated intermediate. The reduced costs are associated with
each flux (vi) and signify the amount by which
the objective function is decreased if vi is
brought into the basis solution. For instance, if the input flux of
lactate shows a reduced cost of 17.5, it means that increasing that
flux by one unit will increase ATP production by 17.5 units. Reduced
costs and shadow prices are terms commonly used in translating LP
solutions to real-life situations and carrying out an analysis of
alternate solutions from the original solution. We introduce these
quantities to analyze the physiological task of energy metabolism to
gain insight into the solutions as well as provide a
"microeconomic" perspective to the ATP-generation problem.
The mitochondrial model. The flux balance model for mitochondria presented here comprises the glycolytic pathways, TCA cycle, and the electron transport system (ETS). The pentose phosphate pathway has not been included, because its activity is believed to be quite low for mitochondria-related functions (19). The oxidative metabolism of substrates takes place in the mitochondria; thus the substrates, metabolites, and cofactors must cross the selectively permeable membrane that separates the mitochondrial space from the cytosolic space. The reactions comprising the TCA cycle occur in the mitochondrion and produce the reduced coenzymes NADH and FADH2 that transfer electrons to oxygen in a regulated manner. Shuttles play an important role in transporting reducing equivalents generated in the cytosol into the mitochondrion.
The reactions, which make up the model, are divided into three sets, based on whether they occur in the cytosol or in the mitochondria or in transporting an intermediate across the mitochondrial membrane. The enzymes considered in the FBA model and their E.C numbers are listed in Table 1. The glycolytic reactions take place in the cytosol. The reactions in the TCA cycle and the ETS take place in the mitochondrial matrix. This compartmentalization of reactions in an organelle leads to the need for special reaction sequences, or shuttles, to transport reducing equivalents generated in the cytosol into the mitochondria. There are two such shuttles that have been found to be active in mitochondria.
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-ketoglutarate with aspartate and glutamate by respective antiporters is a key feature of the shuttle (19, 24). The malate dehydrogenase reaction functions in opposite directions in the
cytosol and in the matrix. The cytosolic reaction forms malate from
oxaloacetate and involves the oxidation of NADH. Malate is then
transported into the matrix and through the matrix with concomitant
efflux of -ketoglutarate. Malate is used to form oxaloacetate in the matrix, and NADH is formed in this reaction. The
cycle is completed by the transamination reactions involving oxaloacetate, -ketoglutarate, glutamate, and aspartate. The
normal functioning of this shuttle is outlined in Fig.
1.
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The postulated objective for mitochondrial energy metabolism. The flux-balance model as explained earlier, requires an objective, which the cell or the organelle, as is the case here, is attempting to achieve. This objective is generally a postulated theoretical assumption that completes the model formulation and enables us to simulate metabolic behavior. For this analysis, maximizing the production of ATP is chosen as the objective function. Therefore, a single flux that hydrolyses the net ATP produced was considered, and the objective function was mathematically represented as vATP_USE, with a corresponding cost of unity. Cairns et al. (4) considered the functional basis for control of mitochondrial oxidative phosphorylation in different organs for rat mitochondria. ATP production in the brain and heart mitochondrial systems was found to use more oxygen but produce ATP at a faster rate than liver systems. They attribute these qualities to the thermodynamic degree of oxidative coupling. The general conclusion is that maximizing the rate of energy production, rather than maintaining thermodynamic efficiency, is the important characteristic of mitochondria in physiological systems. This conclusion supports the postulate that the objective of mitochondrial metabolism is the maximization of ATP production. This postulate requires several detailed studies to be experimentally validated. In this modeling study, its role is to provide a complete theoretical framework to draw insights into the constraints imposed by stoichiometry on energy metabolism.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Substrate preferences.
The flux distributions for optimal production of ATP, shown in Fig.
2,
A-C, were determined under conditions in which
the substrate uptake is restricted to 1 mol · unit
time
1 · unit mass dry wt1 or one
unit. The simulations were carried out for the three
substrates, glucose, lactate, and palmitic acid. Table
2 lists the constraints imposed on the
different fluxes. The complete utilization of 1 mol of glucose results
in the formation of 38 ATP with the concomitant utilization of 6 mol of
O2. The utilization of 1 mol of lactate forms 17.5 ATP with
the utilization of 3.0 mol of O2, and the utilization of
palmitic acid (a 14-C fatty acid) produces 129 ATP but requires 23 mol
of O2. Glucose is the preferred substrate compared with
lactate and 14-carbon fatty acid when the oxygen flux is restricted and
all three substrates are made available. Because glucose uptake
produces maximum ATP per mole of oxygen consumed, ATP synthesis from
glucose is the optimal strategy for energy metabolism.
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17.5 and 129.00, respectively, when glucose is the
energy source. Because this is the number of ATP that can be
synthesized from either substrate, these fluxes represent an alternate
option for ATP synthesis. Therefore, if the oxygen uptake flux
increases by 3 units and the glucose uptake flux remains constant, the
uptake of 1 unit of lactate will yield an additional 17.5 units of ATP.
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Alterations in enzyme activity.
The FBA model can be used to evaluate the systemic consequences of
reduced enzyme activity. Mathematically, this is equivalent to setting
a constraint on a specific flux (e.g., vAKGDH,
the flux through -ketoglutarate dehydrogenase) to be either 0 or some specific value, i.e., i = i
= 0 or a specific value. The effect of alterations in the
activity of different enzymes involved in the metabolism of ATP
production was investigated for the different substrates. Table 2
details the constraints imposed for the following scenarios.
Glucose as substrate.
When citrate synthase, aconitase, or isocitrate dehydrogenase are
inactive, the ATP yield drops significantly and the model predicts the
accumulation of oxaloacetate. The predicted flux distribution for these
cases is shown in Fig. 4A. The
glucose input flux was maintained at 1 unit to compare with a normally functioning network. The carbon flux is partially cycled through phosphoenolpyruvate carboxylase and PDH. Figure 4B
shows the dependence of ATP production on the activity of these
enzymes. This dependence is linear, and the qualitative metabolic map
is constant in this range of enzyme activities. That is, the active
fluxes involved in energy metabolism remain the same until the enzyme
activity is zero. An interesting feature that is predicted in this
situation is the secretion of oxaloacetate, resulting from the excess
carbon flux through glycolysis entering the TCA cycle.
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-ketoglutarate dehydrogenase to
fumarase is inactive, the TCA cycle is again not completely functional.
Excess carbon in this situation is secreted as -ketoglutarate. An
excess of -ketoglutarate has in fact been identified as a feature of
mitochondrial diseases involving mutations in the genes that code for
these enzymes (12). The ATP yield is again significantly lower than the optimal value. The flux distribution for this scenario is shown in Fig. 5A. The
dependence of ATP production on the activity of these enzymes is also
linear and is shown in Fig. 5B.
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-ketoglutarate. Interestingly, the effect of malate dehydrogenase is
limited until the metabolic flux activity is reduced to <50% of the
normal activity. The flux distributions predicted in this situation are
different depending on the activity. Figure
6A shows the flux distribution
when the malate dehydrogenase flux is 75% active. Here, the
glycerol-3-phosphate shuttle is active and picks up the slack in
malate-aspartate shuttle activity. Thus the reducing equivalents are
shuttled by the glycerol-3-phosphate shuttle that exchanges a cytosolic
NADH for a mitochondrial FADH2. This results in a lower
stoichiometric yield of ATP. Malate dehydrogenase is active in the
cytosol as well as the mitochondria (18), and a loss in
the activity of either or both isozymes leads to the same predicted
metabolic state. When the malate dehydrogenase activity is zero, the
flux distribution (Fig. 6B) shows that the malate-aspartate
shuttle functions in the reverse direction compared with the normal
case and the ATP yield is decreased. The dependence of ATP production
on enzyme activity is therefore biphasic (Fig. 6C), and the
slope of the linear dependence is steeper when malate dehydrogenase
activity is <50%.
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Palmitate and lactate as substrates. When palmitate or lactate is the substrate, there is no ATP generation when any of the enzymes are fully inactive. During ATP generation from glucose, the anaplerotic reactions that are part of the TCA cycle are able to reroute the metabolites and provide some reduced cofactors for the ETS. This is not possible when lactate or palmitate is the substrate, because these substrates are directly converted into TCA cycle intermediates.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Mitochondrial function is a critical component of cellular physiology, and its metabolic objectives are constrained by stoichiometry. In this contribution, we have 1) constructed a model for mitochondrial energy metabolism under the stoichiometric constraints inherent in the biochemical reaction network, 2) applied the model to characterize the ATP production from three common substrates, and 3) simulated the effect of genetic changes on mitochondrial energy metabolism.
The network of biochemical reactions and metabolites that constitute the critical elements of mitochondrial function were identified. The steady-state mass balances on each metabolite were mathematically represented as an underdetermined matrix equation, S × v = 0, where the vector v represents the set of all feasible fluxes satisfying the stoichiometric constraints. To find a unique solution, it was postulated that the role of mitochondrial metabolism is the maximization of ATP production. Mathematically, the model is then formulated as an LP problem with this objective and the stoichiometric constraints. By adding additional constraints to the problem, which specify input fluxes for the different substrates, the LP can be solved to identify a unique flux distribution.
The model was applied to predict the maximal yield of ATP from the three common substrates of mitochondrial metabolism, glucose, lactate, and palmitate. The model predicts the expected ATP yields for each. The activities of the shuttles are also predicted in accordance with their accepted roles. The malate-aspartate shuttle is the preferred shuttle to transfer reducing equivalents across the mitochondrial membrane. The glycerol-3-phosphate shuttle is a secondary option, and it is also a less optimal route to synthesize ATP.
The model predictions are in qualitative agreement with key features of
shuttle operation. Safer et al. (13) showed that amino-oxyacetate, which inhibits tranasaminase reactions, is less effective in inhibiting the transport of reducing equivalents into
mitochondria with glucose than with lactate as substrate in rat
myocardium. With the inhibition of the malate-aspartate shuttle, the
glycerol-3-phosphate shuttle was found to allow a nearly equivalent
rate of redox transfer across the mitochondria. Additionally, the flux
of -ketoglutarate to malate is equal to the rate of acetyl-CoA entry
into the TCA cycle, which is also predicted by FBA (Fig.
2A).
The mitochondrial model was used to simulate the effect of changes in
enzyme activities. Mutations in TCA cycle enzymes, particularly fumarase, -ketoglutarate dehydrogenase, and succinate dehydrogenase have been implicated in mitochondrial diseases (3, 12).
These diseases have been characterized by the accumulation of
intermediates of the TCA cycle, primarily the presence of
-ketoglutarate and lactate. The result of loss of activity was
investigated for all the TCA enzymes, and it was observed that when the
enzymes in the series of reactions leading up to -ketoglutarate were
inactive, the ATP yield was very low and excess oxaloacetate was
produced. When the enzymes in the second span of the TCA cycle, from
-ketoglutarate dehydrogenase to malate dehydrogenase, are inactive,
the model predicts a low yield of ATP and the excess production of
-ketoglutarate. This prediction is in qualitative agreement with the
data presented by Rustin et. al (12). They have observed
that anomalous urinary excretion of specific organic acids,
particularly -ketoglutarate, occurs in patients with enzyme defects
affecting the TCA cycle.
The pathogenesis of mitochondrial diseases can be very complex, owing to the variety of inheritance patterns and the diversity of metabolic states (23). Mutations can lead to different metabolic states and different mutations can produce similar metabolic states. Models can play a role in understanding and characterizing these complex relationships. The model presented here provides a platform on which more biochemical networks can be overlaid and other processes in which mitochondrial function plays a role can be studied.
The production of reactive oxygen species (ROS) as a result of defects in electron transport can lead to processes that activate the mitochondrial permeability transition pore and initiate a sequence of events that ultimately leads to cell apoptosis (7). The incorporation of the biochemical networks involved in this process in the formulation of an extended FBA model is being considered.
Wallace (23) states that the phenotypic expression of mtDNA diseases may involve two factors: the predisposing mutation and an age-related factor that causes a decline in mitochondrial function, which exacerbates the inherited defect. In terms of the biochemistry, this can be viewed as a change in the constraints of key fluxes over time, which can lead to qualitative and quantitative changes in the metabolic state. FBA has the necessary capabilities to address these issues. Flux analysis models themselves are not dynamic representations of metabolic functions. However, they provide the means to obtain several static snapshots of metabolism based on steady-state flux activity. Therefore, if a certain allosteric effect is known to effect an enzymatic reaction, the outcome of the severity of the effect on the metabolic function can be characterized. This can help complement a dynamic representation of the same effect that factors in substrates and product concentrations and their effect on the enzyme flux.
Perspectives
This paper presents a model based on a systems-analysis approach to characterize the integrated energy metabolism of mitochondria. The model is completed by postulating that the objective of mitochondrial energy metabolism is to maximize the rate of ATP production. Such a postulate requires several experimental studies to be verified. However, the predictions from the postulated model can be used to drive such experiments. The model can incorporate genomic information to predict the combined effect of genotype changes and environmental perturbations on the metabolic state. For a well-characterized genotype, under certain environmental conditions, it is possible to determine metabolic states that represent all possible physiological outcomes. This paper explored the metabolic states related to mitochondrial energy metabolism under certain conditions. The model accurately predicts different scenarios of mitochondrial growth on the standard substrates. The model also is in qualitative agreement with studies on the physiology of mitochondrial diseases, particularly in the accumulation of TCA cycle intermediates. Flux analysis of mitochondrial metabolism promises to be a useful methodology to understand and characterize the pathophysiology of mitochondrial diseases. Mitochondrial function is a critical part of the physiology of several organs. The genetic defects in several enzymes can contribute to physiological diseases that manifest at the organ level. Flux analysis can link genetics and physiology by representing individual fluxes that are related to the action of a gene or a set of genes in a model and characterizing the overall flux distribution that is representative of the physiological response. The work is currently being extended to study further disease-related questions, particularly those involved in ROS formation.| |
ACKNOWLEDGEMENTS |
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Support for R. Ramakrishna through a grant from Procter and Gamble is gratefully acknowledged.
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FOOTNOTES |
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Present addresses: R. Ramakrishna, Physiome Sciences, Inc., 307, College Road East, Princeton, NJ 08540; J. S. Edwards, Dept. of Chemical Engineering, University of Delaware, Newark, DE 19716.
Address for reprint requests and other correspondence: R. Ramakrishna, Physiome Sciences, Inc., 307 College Rd. East, Princeton, NJ 08536.
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.
Received 17 May 1999; accepted in final form 3 October 2000.
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TOP
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RESULTS
DISCUSSION
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