Journal of Biomolecular Structure and Dynamics
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Kinetic simulation of malate-aspartate and citratepyruvate shuttles in association with Krebs cycle Kalyani Korla, Lakshmipathi Vadlakonda & Chanchal K. Mitra To cite this article: Kalyani Korla, Lakshmipathi Vadlakonda & Chanchal K. Mitra (2015) Kinetic simulation of malate-aspartate and citrate-pyruvate shuttles in association with Krebs cycle, Journal of Biomolecular Structure and Dynamics, 33:11, 2390-2403, DOI: 10.1080/07391102.2014.1003603 To link to this article: http://dx.doi.org/10.1080/07391102.2014.1003603
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Date: 06 November 2015, At: 04:50
Journal of Biomolecular Structure and Dynamics, 2015 Vol. 33, No. 11, 2390–2403, http://dx.doi.org/10.1080/07391102.2014.1003603
Kinetic simulation of malate-aspartate and citrate-pyruvate shuttles in association with Krebs cycle Kalyani Korlaa, Lakshmipathi Vadlakondab and Chanchal K. Mitraa* a
Department of Biochemistry, University of Hyderabad, Hyderabad, India; bKakatiya University, Warangal, India
Communicated by Ramaswamy H. Sarma
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(Received 12 October 2014; accepted 29 December 2014) In the present work, we have kinetically simulated two mitochondrial shuttles, malate–aspartate shuttle (used for transferring reducing equivalents) and citrate–pyruvate shuttle (used for transferring carbon skeletons). However, the functions of these shuttles are not limited to the points mentioned above, and they can be used in different arrangements to meet different cellular requirements. Both the shuttles are intricately associated with Krebs cycle through the metabolites involved. The study of this system of shuttles and Krebs cycle explores the response of the system in different metabolic environments. Here, we have simulated these subsets individually and then combined them to study the interactions among them and to bring out the dynamics of these pathways in focus. Four antiports and a pyruvate pump were modelled along with the metabolic reactions on both sides of the inner mitochondrial membrane. Michaelis–Menten approach was extended for deriving rate equations of every component of the system. Kinetic simulation was carried out using ordinary differential equation solver in GNU Octave. It was observed that all the components attained steady state, sooner or later, depending on the system conditions. Progress curves and phase plots were plotted to understand the steady state behaviour of the metabolites involved. A comparative analysis between experimental and simulated data show fair agreement thus validating the usefulness and applicability of the model. Keywords: energy machinery; redox equivalent; shuttles; TCA cycle; GNU Octave
Introduction Mitochondria are powerhouses of the cell where NADH and FADH2 are oxidised to build up electrochemical potential gradient (Δψ + ΔpH) across the inner mitochondrial membrane. This electrochemical potential gradient is used by ATP synthase to produce ATP from ADP and Pi. NADH and FADH2 required for this purpose are mainly supplied by Krebs cycle located close to the inner mitochondrial membrane inside the mitochondrial matrix. However, a substantial amount of NADH is also produced in the cytoplasm. NADH produced in cytoplasm has to be recycled back to NAD+ to maintain glycolytic flux and other metabolic reactions in cytosol. Therefore, NADH has to be transported to the mitochondrial matrix for its oxidation (Dawson, 1979). Mitochondrial inner membrane is, however, impermeable to both NAD+ and NADH (Purvis & Lowenstein, 1961). To bypass this limitation, cell has established shuttle systems that are used to transport electrons across the mitochondrial membrane via reducing equivalents instead of NADH itself (Williamson, Safer, LaNoue, Smith, & Walajtys, 1973). Two of the most widely studied shuttles used for transport across mitochondrial membrane are malate–aspartate and citrate–pyruvate shuttles. In the *Corresponding author. Email: [email protected] © 2015 Taylor & Francis
present study, we have modelled these two shuttles individually and then combined them with Krebs cycle, to study the interactions between them. The metabolic pathways have been extensively studied by biologists, and it has resulted in a static picture of the reactions involved in these pathways; however, the living system is inherently dynamic. This emphasises the need for a dynamic model which can predict the behavioural pattern of various components at any given point in time. Mitochondrial functions have been reported to be deregulated in insulin resistance, cancer and several other mitochondrial diseases. Mitochondrion shifts its function from ATP production to biosynthetic activity (anaplerosis) to support overall anabolic programs in cell. Chin et al. have shown that α-ketoglutarate inhibits ATP synthase and extends the lifespan of Caenorhabditis elegans (Chin et al., 2014). Kinetic modelling of Krebs cycle alone is insufficient to provide useful information because it is essentially a closed system (Korla & Mitra, 2014a). However, when considered in conjunction with the shuttles, Krebs cycle can supply reducing equivalents to outside of mitochondria. It can also provide carbon skeletons for other metabolic pathways such as citrate
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Kinetic simulation of mitochondrial shuttles for fatty acid biosynthesis and amino acids for protein synthesis. Here, we present a basic skeleton which can be expanded to address a broad range of biological questions. Computer modelling of mitochondrial metabolism has been previously reported. Wu et al. have reported a model based on detailed kinetic and thermodynamically balanced reaction mechanisms with a strict accounting of rapidly equilibrating biochemical species (Wu, Yang, Vinnakota, & Beard, 2007). Yugi and Tomita have reported a model that integrates the dynamics of the respiratory chain, Krebs cycle, the fatty acid β-oxidation and the inner membrane metabolite transport system to enable metabolic pathway simulation in a complete mitochondrial scale (Yugi & Tomita, 2004). Berndt et al. have reported the impact of reduced α-ketoglutarate dehydrogenase activity on ATP production using a kinetic model (Berndt, Bulik, & Holzhütter, 2012). Lu et al. (2008) have reported the role of malate–aspartate shuttle on the metabolic response to myocardial ischaemia. However, the above reports are restricted to specific conditions, whereas our approach is more general and easily extensible. Further, we have included membrane transport facilitated by well-established shuttle system. Also, a comparative analysis has been presented at the end. The experimental data as reported by Bennett et al. (2009) and the simulated data (comprising reactions of Krebs cycle, oxidative phosphorylation and the two shuttles) were tallied, and inferences were drawn. In the present work, we have not intended to address a particular biological problem but have attempted to formulate a generalised framework that can be easily extended for particular cases as the need arises. Malate–aspartate shuttle consists of two transporters, (glutamate–aspartate antiport transporter and malate–αketoglutarate antiport transporter) which transport four components, (aspartate, glutamate, α-ketoglutarate and malate) across the inner mitochondrial membrane (Figure 1). These two transporters are coupled by biochemical reactions between the metabolites on both sides (Nelson, Cox, and Freeman, 2004). The transporters, as seen in Figure 1, are antiports and facilitate transfer of equal molar equivalents of metabolites across the membrane in opposite direction. In other words, transfer of one mole of glutamate from the intermembrane space (IM) to the mitochondrial matrix (M) facilitates transfer of one mole of aspartate in the opposite direction. Direction of transport is determined by the concentration gradient of the two metabolites. Metabolite with a higher concentration gradient will flow from the higher concentration to the lower concentration side, and consequently, the other metabolite will flow in the opposite direction irrespective of its concentration gradient. Reactions involved are given in Table 2.
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Figure 1. Pictorial representation of malate–aspartate shuttle. The shuttle consists of two transporters, (aspartate–glutamate antiport transporter and malate–α-ketoglutarate antiport transporter) used for transferring reducing equivalents between two sides of the inner mitochondrial membrane. The diagram contains two circles, (i) moving clockwise and the other (ii) moving anti-clockwise, and these two circles are connected at two points by aspartate aminotransferase. The reaction scheme is completely symmetric on both sides as drawn. However, oxaloacetate, α-ketoglutarate and malate can be taken into Krebs cycle and control the kinetics of Krebs cycle.
Malate–aspartate shuttle moving in directions as shown in Figure 1 is used to transfer reducing equivalents from cytoplasm to the mitochondrial matrix. Conversion of oxaloacetate to malate in cytosolic side oxidises NADH to NAD+. Malate thus formed is transported to the mitochondrial matrix in exchange of α-ketoglutarate and is used to regenerate NADH from NAD+ in the matrix and produces oxaloacetate in the reaction. This oxaloacetate now combines with glutamate to generate αketoglutarate (which is transported in exchange of malate influx), and aspartate. Aspartate is transported to the cytosolic side in exchange for glutamate, which is further required for the reaction with oxaloacetate (Brand & Chappell, 1974). In cytosol, aspartate reacts with α-ketoglutarate (transported in exchange of malate) to give glutamate and oxaloacetate, which continues the cycle. In this process, all the components are internally used to ultimately transfer electrons from NADH in cytosolic side to generate NADH in the matrix side (Williamson et al., 1973). The enzymes involved in this shuttle work reversibly, and the shuttle can function in principle in the reverse direction. Malate–aspartate shuttle is considered as a major mechanism involved in transporting reducing equivalents from the IM space to the matrix and vice versa (Barron, Gu, & Parrillo, 1998). Although the diagram appears symmetric (Figure 1), malate, oxaloacetate and α-ketoglutarate also take part in Krebs cycle (not shown in Figure 1) in the mitochondrial matrix.
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Citrate–pyruvate shuttle consists of five enzymes (ATP-citrate lyase, malate dehydrogenase, malic enzyme, pyruvate carboxylase and citrate synthase, of which the first three are present in the intermembrane space and the last two in the mitochondrial matrix). There are two exchangers (citrate/malate exchanger and malate/phosphate exchanger) and a pyruvate pump, facilitating the transport of metabolites (Figure 2). Of the five enzymes, only malate dehydrogenase mediates reversible processes and the rest are essentially irreversible. Pyruvate pump functions as a symport transporting pyruvate and H+ ions (or OH− in the opposite direction) simultaneously to maintain the charge balance across the membrane (Halestrap, 1975). pH and membrane potential across the membrane are assumed to be constant. Rate of pyruvate pumping is regulated by pH gradient and concentration gradient. The pyruvate pump is modelled as a one-way transporter, regulated by its concentration gradient across the mitochondrial membrane. Non-zero potential difference across the membrane also affects the transport of pyruvate (in addition to the concentration gradient). The reactions are shown in Table 2. Citrate–pyruvate shuttle is used to transport pyruvate from the IM space to the mitochondrial matrix feeding Krebs cycle. Inner mitochondrial membrane is impermeable to acetyl-CoA and is, therefore, converted to citrate inside the matrix and transported to cytosol, where it undergoes ATP-dependent cleavage by ATP-citrate lyase to regenerate acetyl-CoA and oxaloacetate. Thus, an excess of acetyl-CoA inside the matrix is transported back to cytosol as citrate for fatty acid synthesis and other metabolic purposes (Guay, Madiraju, Aumais, Joly, & Prentki, 2007). The oxaloacetate is reduced to malate,
oxidising NADH to NAD+ in the reaction. This malate can be used for conversion of NADP to NADPH, forming pyruvate, or it can be transported to mitochondria by malate–α-ketoglutarate transporter, thus transporting electrons from NADH to the matrix. Pyruvate entering the matrix is channelled to Krebs cycle via acetyl-CoA or oxaloacetate forming citrate. Excess of citrate formed can be shuttled back to cytosol in exchange with malate. Shuttles and their regulation Shuttles help in maintaining metabolite concentrations at suitable level close to steady state in both sides of the inner mitochondrial membrane. They maintain optimal concentrations of metabolites and not necessarily equal concentrations. Such a shuttle system usually consists of several parts which are weakly coupled through the reactions on both sides of the membrane (Table 2). They are considered as weakly coupled because the metabolites connecting the transporters can enter other reactions on either side. The shuttles and Krebs cycle share components in the matrix side (common pool), and this results in close interdependence between these two sets of reactions. In fact, there are a couple of reactions in common between the two sets (LaNoue & Williamson, 1971).The presence of similar connections among different pathways suggests interrelated regulatory mechanism. Since Krebs cycle and shuttles share metabolites among themselves, they are expected to be located in the vicinity of each other. Further, as discussed earlier, Krebs cycle is expected to be located near the inner mitochondrial membrane by virtue of succinate dehydrogenase, which is also involved in ETC and is membrane-bound.
Figure 2. Pictorial representation of citrate–pyruvate shuttle. The figure shows five enzymes (ATP-citrate lyase, malate dehydrogenase, malic enzyme, pyruvate carboxylase and citrate synthase), two antiport transporters (citrate/malate and malate/phosphate) and pH-dependent pyruvate pump.
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Kinetic simulation of mitochondrial shuttles Malate is used in both malate–aspartate (Figure 1) and citrate–pyruvate (Figure 2) shuttles. Cells can use a combination of these processes to move a variety of carbon units or reducing equivalents from one side of the mitochondrial membrane to the other. Malate acquires electrons from NADH in the cytosol, and it can be exchanged with α-ketoglutarate (five-carbon compound), citrate (six-carbon compound) or simply, phosphate (no carbon). This presents an elegant mechanism by which cells can use several combinations of metabolites from different intracellular compartments to regulate metabolic processes. Besides, α-ketoglutarate, citrate, oxaloacetate and pyruvate are other metabolites which are involved in both Krebs cycle and shuttles. This indicates a close association among Krebs cycle and two shuttles in terms of function and regulation and urges us to model them together to have an overview of their metabolic interconnectivity. Figure 3 shows the diagrammatic representation of the complete set of reactions including those from the two shuttles and Krebs cycle. As already mentioned, transporters assist in the movement of carbon skeleton across the mitochondrial membrane, allowing molecules such as citrate, α-ketoglutarate and malate to cross the membrane. They also carry redox equivalents across the mitochondrial membrane. Some molecules, such as oxaloacetate and acetylCoA, cannot cross the mitochondrial membrane. As a result, separate, independently regulated pools of these components, which play important roles in the regulation of cellular metabolic processes and Krebs cycle in the matrix side, are maintained in a quasi-steady state. As mentioned earlier, mitochondria in addition to production of ATP also have considerable biosynthetic
Figure 3. Schematic diagram representing Krebs cycle (enclosed in grey rectangular box) and transporters involved with malate–aspartate and citrate–pyruvate shuttles. [Pyr = Pyruvate, Mal = malate, α-kg = α-ketoglutarate, Cit = citrate, Glu = glutamate, Asp = aspartate, Oaa = oxaloacetate, Pi = phosphate, Suc = succinate, Ac-CoA = acetyl-CoA ]. The numbers marked on the reaction lines indicate the reaction serial numbers from Table 2. 16 corresponds to pyruvate pump, 17–20 correspond to malate–phosphate, malate–citrate, malate–α-ketoglutarate and aspartate–glutamate transporters, respectively.
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activity. The partitioning of the two roles depends on the activity of the shuttle system and the ATP synthesis. The shuttle system transports reducing equivalents across the mitochondrial membrane. As NAD+/NADH are impermeable to the mitochondrial membrane, the shuttle system provides rather symmetric biochemical reactions on both sides of the membrane to perform this task. In the absence of the shuttle system, mitochondria would be forced to invest all the reducing equivalents generated in Krebs cycle into the production of ATP which may not be optimal (Mazat, Ransac, Heiske, Devin, & Rigoulet, 2013). Modelling these events, therefore, would help study the possible mode of partitioning of mitochondrial functions between energy generation and biosynthetic functions in the cell and would give biological explanation for the causes of metabolic pathologies such as NAFLD (non-alcoholic fatty liver disease) and carcinogenesis. Methods In the present study, we have individually simulated the kinetic aspects of two mitochondrial shuttles, viz., malate–aspartate and citrate–pyruvate shuttles and Krebs cycle. For simulation GNU Octave, a free software, has been used, particularly the ordinary differential equation (ode) solver (GNU Octave). A stochastic model that includes a large number of biochemical reactions, was considered slow and inefficient, has not been used. An ordinary differential equation (ode) in an equation of the general form f ðx; y0 ; y00 ; . . .; yn Þ ¼ 0 where y0 ¼ dy=dx and yn ¼ d n y=dxn n is called the order of the equation. The kinetic equations are first order but non-linear. First order means that only the first derivative is involved in any equation. In the present study, we have several variables for y, and therefore, we have a system of coupled equations. These values of y and y0 are treated as vectors. We have ignored diffusion in the present simulation. Diffusion in small systems is usually fast but can be slow if the concentration is low and the component needs to travel relatively long distance (e.g. hormone effects). A reaction diffusion system involves secondorder equation, and the solution strongly depends on the boundary conditions. A differential equation is called stiff if the conventional numerical methods of solution lead to unstable results. We have assumed that our systems of equations are not stiff. However, coupled chemical reaction kinetics in which concentration of different components varies widely can become stiff.
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In Octave, there are several methods available to solve ordinary differential equations. We have used lsode module. In this case, the linear first order differential equations are written in the form:
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y0 ðt Þ ¼ f ðt; yÞ where y and y0 are vectors usually supplied as a function. Lsode uses the most common method “Livermore Solver for Ordinary Differential Equations”, which is well documented in the literature (Hindmarsh, 1983). Rate equations were derived for each metabolite involved in the reactions. The rate equations were written based on Michaelis–Menten approach (also known as Henri–Michaelis–Menten equation or HMM equation (Deichmann, Schuster, Mazat, & Cornish‐Bowden, 2014). Few reasonable assumptions were made, and the approach was extended to fit the reaction mechanism. v¼
Vmax ½S v ½S =KM can be written as ¼ KM þ ½S Vmax 1 þ ½S =KM
Here, both v/Vmax and [S]/KM are dimensionless, and this equation is now suitable for numerical calculations. As a result of the scaling, the time also becomes a dimensionless quantity. The substrate concentrations, although reported in arbitrary units, are in reality in units of KM of the respective enzymes. In the present case, we use [S]/KM as the dimensionless quantity representing the concentration and explicit knowledge of KM is not needed. However, if we need the actual concentration for a given component we need to know the specific KM value. In reality, KM values for a particular enzyme reported by different authors vary widely and eliminating KM in this way appears to be an advantage. In the same way, v/Vmax is the dimensionless rate which can be easily correlated with experimental values when Vmax is known. Using dimensionless concentrations has an added advantage that all meaningful values lie close to unity. For multiple substrates, we have extended this formula to v ½S1 =KM 1 ½S2 =KM 2 ½S3 =KM 3 ¼ Vmax 1 þ ½S1 =KM 1 1 þ ½S2 =KM 2 1 þ ½S3 =KM 3 which is considered as an approximation here, at least to the first order. Similarly, the inhibitors were also taken into consideration and were incorporated in rate equations. The effects of other possible co-factors and several ionic components, were not explicitly investigated. Their effects were considered constant. Krebs cycle reactions were simulated using the scheme discussed in detail in our previous work (Korla & Mitra, 2014a). (One reviewer has raised some technical objections regarding our use of Michaelis–Menten kinetics and quasi-steady state approximation. The reviewer has
further suggested the use of full/complete reaction mechanisms avoiding the use of Michaelis–Menten formalism. In the present study, the methods used are approximate in nature but the broad philosophy remains sound. One of the difficulties in using an exact method is simply the lack of sufficient information. Often, the value of KM for a particular species is not available. Further, Vmax depends on the total concentration of the enzyme and its kinetic parameters that are also not available. In the present simulation, around 50 enzymes and metabolites are involved. We have simulated in the present work a large network and the agreement with the experimental results suggests that the method works.) Modelling the transporter In the present system, there are four antiporters, that is, glutamate–aspartate, malate–α-ketoglutarate, citrate– malate and malate–phosphate (Figure 3). The kinetics of antiport has been modelled using a modified version of Michaelis–Menten kinetics (Korla & Mitra, 2014b). The fluxes of various components specifically depend on the metabolite concentrations on both sides of the membrane. The transporters in the present study are all antiports, and thus, transport across the membrane will be facilitated only when the two metabolites occupy binding sites on the opposite sides of the membrane. All the four binding sites on transporters are considered independent and equivalent. It has been considered that there are four binding sites, two on each side of the membrane, and each one specific for the metabolite than can bind in any sequence. At a given point in time, the transporter can have one of the sixteen possible conformations, of which only two conformations can successfully facilitate metabolite transport across membranes. This forms the basis for modelling transport across the membrane. Four variables, alpha, beta, gamma and delta were introduced in the simulation script that correspond to the antiport pairs, glutamate/aspartate, malate/α-ketoglutarate, citrate/malate and malate/phosphate exchangers, respectively. These variables were appropriately added or subtracted from the relevant metabolite concentration depending on the flux directions (as shown in Figure 3). Further, the reactions involved in shuttles were simulated using a similar approach as for Krebs cycle. The two shuttles were first individually simulated and then combined with the reactions of Krebs cycle. Table 1 shows the list of components included in the kinetic simulation. Metabolites present on the two sides of the membrane have been considered as different entities and have been given separate symbols and have been marked with “-m” suffix for those present in the mitochondrial matrix and “-im” suffix for those present in the intermembrane space. The numbers allotted to each of the components remains the same throughout the
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Table 1. List of metabolites and numbers assigned to them for ease in simulation. Metabolites present on the two sides of the membrane have been considered as different entities and have been given separate symbols and have been marked here as “-m” for those present in the mitochondrial matrix and “-im” for those present in the intermembrane space. Metabolites followed by “(c)” were kept at a constant concentration within the script. Rate equations were derived for each component based on the reactions compiled from the literature.
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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
Oxaloacetate-m Acetyl-CoA-m Citrate-m Isocitrate-m α-ketoglutarate-m Succinyl-CoA-m Succinate-m Fumarate-m Malate-m CoA-SH-m NAD+-m (c) NADH-m (c) CO2-im (c)
14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.
script to maintain uniformity and avoid repetitions. Rate equations were derived for each component based on the reactions compiled from the literature. The reactions are listed in Table 2. Since these reactions form just a part of the mitochondrial metabolic network and the reactions are not self-sufficient; therefore, fifteen components were
GDP-m (c) GTP-m (c) FAD-m (c) FADH2-m (c) ATP-m (c) Aspartate-im Malate-im α-ketoglutarate-im Glutamate-im Glutamate-m Aspartate-m Citrate-im ATP-im (c)
27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.
CoA-SH-im (c) Acetyl-CoA-im (c) ADP-im (c) NADP-im (c) Pyruvate-im NADPH-im (c) Pyruvate-m Oxaloacetate-im NADH-im NAD+-im ADP-m (c) Phos-m Phos-im
designated as “sources and sinks” (denoted with “(c)” in Table 1). This approach assists the system in attaining self-sufficiency. While simulating pyruvate pump, which transports pyruvate from the IM space to the matrix and acts as the only source of pyruvate in the matrix, a new variable
Table 2. List of reactions included in the present study. The table includes reactions of Krebs cycle, malate–aspartate and citrate– pyruvate shuttle. Reactions in bold indicate reversible reactions. The suffixes -m and -im indicate the localisation (the matrix and the intermembrane space, respectively) of the respective components. The numbers indicate the assigned variable used in the script. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Acetyl-CoA-m + Oxaloacetate-m → Citrate-m + CoASH-m 2 + 1 → 3 + 10 Citrate-m → Isocitrate-m 3→4 Isocitrate-m + NAD+-m → α-ketoglutarate-m+ NADH-m + CO2-m 4 + 11 → 5 + 12 + 13 α-ketoglutarate-m + CoASH-m + NAD+-m → Succinyl CoA-m + NADH-m + CO2-m 5 + 10 + 11 → 6 + 12 + 13 Succinyl CoA-m + GDP-m + Phos-m → Succinate-m + GTP-m + CoASH-m 6 + 14 + 38 → 7 + 15 + 10 Succinate-m + FAD-m → Fumarate-m + FADH2-m 7 + 16 → 8 + 17 Fumarate-m + H2O → Malate-m 8→9 Malate-m + NAD+-m → Oxaloacetate-m + NADH-m 9 + 11 → 1 + 12 Citrate-im + ATP-im + CoA-SH-im → OAA-im + acetyl-CoA-im + ADP-im + Phos-im 25 + 26 + 27 → 34 + 28 + 29 + 39 OAA-im + NADH-im → Malate-im + NAD+-im 34 + 35 → 20 + 36 Malate-im + NADP-im → Pyruvate-im + NADPH-im + CO2-m 20 + 30 → 31 + 32 Pyruvate-m + ATP-m + CO2-m → Oxaloacetate-m + ADP-m + Phos-m 33 + 18 + 13 → 1 + 37 + 38 Aspartate-im + α-ketoglutarate-im → Oxaloacetate-im + Glutamate-im 19 + 21 → 34 + 22 Oxaloacetate-m + Glutamate-m → Aspartate-m + α-ketoglutarate-m 1 + 23 → 24 + 5 Pyruvate-m + NAD+-m + CoASH-m → Acetyl-CoA-m + CO2-m +NADH-m 33 + 11 + 10 → 2 + 13 + 12
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Table 3.
Script used for simulation of Krebs cycle along with malate–aspartate and citrate–pyruvate shuttles.
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“flux” was introduced in the script. “Flux” depends on the concentration gradient of pyruvate across the inner mitochondrial membrane was given as flux = .02*(pyruvate-im − pyruvate-m). The “Flux” was added to the matrix pyruvate and was subtracted from the IM pyruvate. Table 3 includes the complete script used for simulation. For comparative analysis, another script was written which included reactions from Krebs cycle, electron transport chain, ATP synthesis and malate–aspartate and citrate–pyruvate shuttle. The concentrations of the selected metabolites in the intermembrane space at 500 time point were taken. These concentrations were multiplied with their respective KM values to obtain absolute concentrations values. These concentrations were then compared with the concentrations obtained from the literature, and a histogram was plotted for illustration. GNUPLOT was used for graphical representations. Results and discussion The individual shuttles were first simulated using ordinary differential equation (ode) solver in Octave. The rate equations of the components of shuttles were combined with the rate equations of those from Krebs cycle. Since there are several components common among them, a unified notation suitable for use in the Octave script has been used (Table 1). In our earlier work, we have simulated Krebs cycle individually and then combined it with oxidative phosphorylation. We have suggested Krebs cycle as a giant catalyst, when it was taken as an individual independent entity (Korla & Mitra, 2014a). When Krebs cycle is combined with the shuttles, a number of metabolites are common to both, such that these
metabolites may be supplied or taken away from Krebs cycle. In such a case, Krebs cycle no more acts as a giant catalyst, and instead acts as a source of both NADH (and FADH2) for electron transport chain and also of various carbon compounds (e.g. citrate, malate, α-ketoglutarate and oxaloacetate) in the present study. The carbon compounds can be used elsewhere in the cell for other regulatory and functional purposes. A comparison of the two systems is shown by plotting the same components in different environments, (i) Krebs cycle and (ii) Krebs cycle with malate–aspartate and citrate– pyruvate shuttle (Figure 4). However, the concentration profiles of the selected metabolites show different values but are broadly comparable. The difference is seen as the metabolites are now involved in multiple reactions, and their concentration is now shared among different reactions. An interesting feature from the two graphs is that the metabolites tend to attain steady state in both the conditions, as expected, but the metabolites tend to attain, in general, steady state earlier in Figure 4(b), suggesting that the system when extrapolated to include more and more network connections among the metabolites becomes more robust. In general, large numbers of network connections among the metabolites create parallel paths and this increases the apparent (or overall) rate for product formation. Therefore, we suggest that the rate of attainment of the steady state is related qualitatively to the number of paths available for the reactants to reach the product. Intuitively, a larger number of possible alternate paths make the system more robust. This further suggests that metabolic pathways along with their normal range of concentrations for different metabolites are not at equilibrium but are at a steady state. This steady state is not perfectly defined but is
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Figure 4. Simulation curves for (a) Krebs cycle alone (b) Krebs cycle + malate–aspartate and citrate–pyruvate shuttles. [Oaa = oxaloacetate, AcCoA = acetyl-CoA, Cit = citrate, Isocit = isocitrate, Keglu = α-ketoglutarate, SucCoA = succinyl-coA].
more likely to be a region or area consistent with a range of concentrations for different metabolites. In the progress curve shown in Figure 5, we see that all concentrations (we have plotted only selected metabolites) within a reasonable time frame reach a steady state value. However to maintain the steady state in an isolated system as this, we must provide “source” and “sink” for several key metabolites. Although the reactions are not of the first order, we can still qualitatively assign a t1/2 value for comparison. The final equilibrium concentration can be estimated visually, and the time taken for the concentration to reach ½ of this value can be estimated for comparison. The t1/2 values are useful for comparing the rates of approach to the equilibrium or steady state.
Figure 5. Simulation curves for selected components of Krebs cycle–shuttle system. Isocit = Isocitrate, Keglu = α-ketoglutarate, Mal = malate, Glu = glutamate, Asp = aspartate, Pyr = pyruvate. Suffixes “-m” and “-im” indicate that the presence of component in the matrix and the intermembrane space respectively.
Figure 5 indicates that all the metabolites do not reach the same “final” state concentrations. This is not expected as the steady state concentrations are related to their “distance” from the sources and sinks. This problem is not trivial because there are multiple sources, multiple sinks and multiple paths, and all paths are not equally traversed. Concentrations of several key metabolites have been plotted in Figure 5 as a function of time. The software needs initial (“guess”) values for simulation and these values are seen at time, t = 0. However, the initial values undergo large changes and settle close to the steady state values after a long time (t > 500). We are less interested in the initial parts of the graph (which are unrealistic) and are more interested in the values that are close to the steady state. The initial parts essentially show the instant response of the system towards any perturbation, when the system is forced to move out the steady state (due to intervention caused by the perturbation), and different components take divergent paths to ultimately fall in the steady state basin. This results in a stable system where all the components reach an adequate concentration to meet the cellular requirements. This amplifies the usefulness of the simulation and helps in understanding the behaviour of the system as a whole. In a system at the “resting” steady state concentration, where one of the metabolite’s concentration changes significantly beyond the “normal”, the system will attempt to return to the steady state. The path followed in this process can be seen more clearly in the next set of figures – the phase diagrams. The phase diagrams in Figures 6–8, show the return of the system to the stable steady state when one of the components is added or removed from the steady state values. These phase diagrams, rate of change of concentrations of the given metabolites vs. their concentrations, are similar to Michaelis–Menten curves and were plotted
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Figure 6. Phase diagram for selected important metabolites present in the mitochondrial matrix. [Pyr = Pyruvate, Mal = Malate, Keglu = α-ketoglutarate, Cit = Citrate, Glu = Glutamate, Asp = Aspartate]. Inset figure shows the magnified view of the selected region. The y-axis represents the rate of transformation of the corresponding substrate as indicated on the abscissa. The concentrations and time are expressed in arbitrary units.
for different metabolites. These curves show interesting features, particularly close to steady state. All the phase diagrams represent the change in concentration for the initial 900 time points, that is, 900 data points are plotted in each of the phase curves. It is interesting to note that a major distance between the first and the last concentration point is traversed by mere 20–30 data points, and more than 850 data points are clustered in a small region towards the end. This region is near the steady state condition where the changes are minimal. For clarity, the region close to steady state was expanded to show a closer perspective. It is seen that for several key metabolites, the return to steady state is not linear (or monotonic) and the behaviour is exemplified by the inset graphs. Inset figures show that the concen-
tration tends to localise in a small region and fluctuates with minimal changes as it approaches the steady state. In most of these images, a loop can be observed around the end points, which apparently indicates that steady state concentration is necessarily not a point but a region, which comprises several combinations of concentrations of various metabolites involved. Since the curves do not appear to be closed, the final steady state remains a point. The approximations made in the derivation do not allow us to explore this matter in detail. Figure 8 shows the phase curves for NADH and NAD+ in the IM space, and as expected, the two curves look complementary signifying their inconvertibility. Even as they approach the steady state the end regions also appear complementary.
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Kinetic simulation of mitochondrial shuttles
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Figure 7. Phase diagram for selected important metabolites present in the intermembrane space. [Pyr = Pyruvate, Mal = Malate, Keglu = α-ketoglutarate, Cit = Citrate, Glu = Glutamate, Asp = Aspartate]. Inset figure shows the magnified view of the selected region. The y-axis represents the rate of transformation of the corresponding substrate as indicated on the abscissa. The concentrations and time are expressed in arbitrary units.
Figure 8. Phase diagram for NADH-im and NAD + -im. The curves are complementary since they are interconvertible species. Inset figure shows the magnified view of the selected region. The y-axis represents the rate of transformation of the corresponding substrate as indicated on the abscissa. The concentrations and time are expressed in arbitrary units.
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Table 4. List of metabolites, enzymes, corresponding KM for the reactions and metabolite concentrations under the experimental and simulated conditions. Metabolite
Enzyme
Aspartate Citrate Glutamate α-Ketoglutarate Malate NAD+ NADH NADH/NAD+
Aspartate transaminase Citrate lyase Aspartate transaminase Aspartate transaminase Malate dehydrogenase Malate dehydrogenase Malate dehydrogenase –
Experimental concentration (Moles/L)
KM (Moles/L)
Simulated concentration
KM*Simulated concentration (Moles/L)
4.2e-03 2.0e-03 9.6e-02 4.4e-04 1.7e-03 2.6e-03 8.3e-05 8.3e-05/2.6e-03
2.22e-03 1.60e-04 1.50e-02 2.47e-04 2.60e-03 2.60e-04 6.10e-05
1.94e-01 2.56e-05 6.06e-01 3.78e-01 5.26e-03 2.9e-01 9.98e-03
.434e-03 4.096e-09 .909e-02 .934e-04 .0137e-03 .0754e-03 .0609e-05 .0609e-05/.0754e-03
Figure 9. Comparative analysis of experimental and simulated metabolite concentrations. The experimental data were taken from Bennett et al. (2009).
Mitochondrial functions have been implicated in several diseases. Mullen et al. have shown that oxidation of α-ketoglutarate is required for reductive carboxylation in cancer cells with mitochondrial defects (Mullen et al., 2014). They demonstrate that inhibiting α-ketoglutarate oxidation decreased reducing equivalent availability and suppressed reductive carboxylation. Their results demonstrate that reductive carboxylation requires bidirectional α-ketoglutarate metabolism along oxidative and reductive pathways. Lu et al. (2008) have suggested a direct relation between insulin resistance and the metabolism of branched chain amino acids (Lu et al., 2008). The branched chain amino acids via catabolism feed α-keto acids into Krebs cycle. It was reported that intake of branched chain amino acids was accompanied with increased energy expenditure and better insulin sensitivity (She et al., 2007). Our present model can be coupled with the catabolism of branched chain amino acids and Krebs cycle. Chin et al. have shown that α-ketoglutarate extends life span of adult C. elegans by inhibiting ATP synthase (Chin et al., 2014). Their results uncover new molecular link between
α-ketoglutarate, mitochondria and organismal lifespan. The effect of decrease in ATP synthesis increases the reducing environment inside the matrix and activates the shuttle services (Figure 1). In such a case, the shuttles move in reverse direction, actively transporting NADH via malate and α-ketoglutarate is transported to the matrix side. In an attempt to validate the simulation results with the experimental results, data from the experiments carried out by Bennett et al. (2009) were taken and compared with the simulation results obtained. The authors have presented absolute metabolite concentrations of several metabolites in Escherichia coli. The concentrations of selected metabolites were compared with their respective steady state concentrations as calculated using the present simulation scheme. It has been shown earlier that the concentration in the simulation scheme is reduced by a factor of their respective KM values; therefore, the concentrations obtained as simulation results were multiplied by their KM values to obtain absolute concentration. The list of metabolites, enzymes catalysing their reaction and the respective metabolite concentrations under experimental and simulated conditions are shown in Table 4. A histogram plotted to illustrate the comparative view of the experimental and simulated data-set is presented in Figure 9. The results presented in Figure 9 indicate applicability of the simulation scheme. Simulated concentrations of the selected metabolites are lower than the experimental values for all of them. However, it can be seen that the concentrations of all metabolites except citrate represent fair agreement between the experimental and simulated results. The major variation seen in citrate concentration could be due to the presence of other citrate sources and sinks in the cytoplasm, which are not included in our reaction scheme. It is known that the ratio of NADH and NAD+ is more relevant than the individual parameters, it can be clearly seen the difference in their ratio in the two sets is smaller than the differences between the individual components (NADH, NAD+).
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Kinetic simulation of mitochondrial shuttles It should be stressed here that the simulation presented here has taken no specific cellular or reaction (KM or Vmax) parameters into consideration, and the results were still quite close to the physiological values. This can be directly related to the robustness of the system. For systems with larger number of components, the present approach can become cumbersome and error-prone. Therefore, a modular approach is being considered for generic applications. The experimental data used here correspond to E. coli system that lacks mitochondria, and therefore, the cytosolic metabolite concentrations (assumed to be same as the metabolite concentrations in the IM space) are taken for comparison from the script. Also, this could explain the variations seen in the results, and it can still be considered quite a satisfactory agreement between the experimental and the simulated data.
Acknowledgements One of the authors (KK) acknowledges the receipt of Senior Research Fellowship from University Grants Commission (Govt. of India).
References Barron, J. T., Gu, L., & Parrillo, J. E. (1998). Malate–aspartate shuttle, cytoplasmic NADH redox potential, and energetics in vascular smooth muscle. Journal of Molecular and Cellular Cardiology, 30, 1571–1579. doi:10.1006/ jmcc.1998.0722 Bennett, B. D., Kimball, E. H., Gao, M., Osterhout, R., Van Dien, S. J., & Rabinowitz, J. D. (2009). Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli. Nature Chemical Biology, 5, 593–599. doi:10.1038/nchembio.186 Berndt, N., Bulik, S., & Holzhütter, H. G. (2012). Kinetic modeling of the mitochondrial energy metabolism of neuronal cells: The impact of reduced α-ketoglutarate dehydrogenase activities on ATP production and generation of reactive oxygen species. International Journal of Cell Biology, 2012, 11 pages, Article ID 757594. doi:10.1155/2012/ 757594 Brand, M. D., & Chappell, J. B. (1974). Glutamate and aspartate transport in rat brain mitochondria. Biochemical Journal, 140, 205–210. Chin, R. M., Fu, X., Pai, M. Y., Vergnes, L., Hwang, H., Deng, G., … Huang, J. (2014). The metabolite α-ketoglutarate extends lifespan by inhibiting ATP synthase and TOR. Nature, 510, 397–401. doi:10.1038/nature13264 Dawson, A. G. (1979). Oxidation of cytosolic NADH formed during aerobic metabolism in mammalian cells. Trends in Biochemical Sciences, 4, 171–176. doi:10.1016/0968-0004 (79)90417-1 Deichmann, U., Schuster, S., Mazat, J. P., & Cornish-Bowden, A. (2014). Commemorating the 1913 Michaelis–Menten paper Die Kinetik der Invertinwirkung: Three perspectives. FEBS Journal, 281, 435–463.
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GNU Octave. 3.8.2 9. (2014). Retrieved from http://www.gnu. org/software/octave/ Guay, C., Madiraju, S. M., Aumais, A., Joly, E., & Prentki, M. (2007). A role for ATP-citrate lyase, malic enzyme, and pyruvate/citrate cycling in glucose-induced insulin secretion. Journal of Biological Chemistry, 282, 35657–35665. doi:10.1074/jbc.M707294200 Halestrap, A. P. (1975). The mitochondrial pyruvate carrier. Kinetics and specificity for substrates and inhibitors. Biochemical Journal, 148, 85–96. Hindmarsh, A. C. (1983). ODEPACK, a systematized collection of ODE solvers. In R. S. Stepleman (Ed.), Scientific computing (pp. 55–64). Amsterdam: North-Holland. Korla, K., & Mitra, C. K. (2014a). Kinetic modelling of coupled transport across biological membranes. Indian Journal of Biochemistry & Biophysics, 51, 93–99. Korla, K., & Mitra, C. K. (2014b). Modelling the Krebs cycle and oxidative phosphorylation. Journal of Biomolecular Structure & Dynamics, 32, 242–256. doi:10.1080/ 07391102.2012.762723 LaNoue, K. F., & Williamson, J. R. (1971). Interrelationships between malate–aspartate shuttle and citric acid cycle in rat heart mitochondria. Metabolism, 20, 119–140. doi:10.1016/ 0026-0495(71)90087-4 Lu, M., Zhou, L., Stanley, W. C., Cabrera, M. E., Saidel, G. M., & Yu, X. (2008). Role of the malate–aspartate shuttle on the metabolic response to myocardial ischemia. Journal of Theoretical Biology, 254, 466–475. doi:10.1016/ j.jtbi.2008.05.033 Mazat, J. P., Ransac, S., Heiske, M., Devin, A., & Rigoulet, M. (2013). Mitochondrial energetic metabolism – Some general principles. IUBMB Life, 65, 171–179. doi:10.1002/ iub.1138 Mullen, A. R., Hu, Z., Shi, X., Jiang, L., Boroughs, L. K., Kovacs, Z., … DeBerardinis, R. J. (2014). Oxidation of alpha-ketoglutarate is required for reductive carboxylation in cancer cells with mitochondrial defects. Cell Reports, 7, 1679–1690. doi:10.1016/j.celrep.2014.04.037 Nelson, D. L., & Cox, M. M. (2004). Lehninger principles of biochemistry (4th ed.). New York, NY: WH Freeman & Company. Purvis, J. L., & Lowenstein, J. M. (1961). The relation between intra- and extramitochondrial pyridine nucleotides. Journal of Biological Chemistry, 236, 2794–2803. She, P., Reid, T. M., Bronson, S. K., Vary, T. C., Hajnal, A., Lynch, C. J., & Hutson, S. M. (2007). Disruption of BCATm in mice leads to increased energy expenditure associated with the activation of a futile protein turnover cycle. Cell Metabolism, 6, 181–194. doi:10.1016/ j.cmet.2007.08.003 Williamson, J. R., Safer, B. R. I. A. N., LaNoue, K. F., Smith, C. M., & Walajtys, E. (1973). Mitochondrial-cytosolic interactions in cardiac tissue: Role of the malate–aspartate cycle in the removal of glycolytic NADH from the cytosol. Symposia of the Society for Experimental Biology, 27, 241–281. Wu, F., Yang, F., Vinnakota, K. C., & Beard, D. A. (2007). Computer modeling of mitochondrial tricarboxylic acid cycle, oxidative phosphorylation, metabolite transport, and electrophysiology. Journal of Biological Chemistry, 282, 24525–24537. doi:10.1074/jbc.M701024200 Yugi, K., & Tomita, M. (2004). A general computational model of mitochondrial metabolism in a whole organelle scale. Bioinformatics, 20, 1795–1796. doi:10.1093/bioinformatics/ bth125
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Kinetic simulation of malate-aspartate and citratepyruvate shuttles in association with Krebs cycle Kalyani Korla, Lakshmipathi Vadlakonda & Chanchal K. Mitra To cite this article: Kalyani Korla, Lakshmipathi Vadlakonda & Chanchal K. Mitra (2015) Kinetic simulation of malate-aspartate and citrate-pyruvate shuttles in association with Krebs cycle, Journal of Biomolecular Structure and Dynamics, 33:11, 2390-2403, DOI: 10.1080/07391102.2014.1003603 To link to this article: http://dx.doi.org/10.1080/07391102.2014.1003603
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Date: 06 November 2015, At: 04:50
Journal of Biomolecular Structure and Dynamics, 2015 Vol. 33, No. 11, 2390–2403, http://dx.doi.org/10.1080/07391102.2014.1003603
Kinetic simulation of malate-aspartate and citrate-pyruvate shuttles in association with Krebs cycle Kalyani Korlaa, Lakshmipathi Vadlakondab and Chanchal K. Mitraa* a
Department of Biochemistry, University of Hyderabad, Hyderabad, India; bKakatiya University, Warangal, India
Communicated by Ramaswamy H. Sarma
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(Received 12 October 2014; accepted 29 December 2014) In the present work, we have kinetically simulated two mitochondrial shuttles, malate–aspartate shuttle (used for transferring reducing equivalents) and citrate–pyruvate shuttle (used for transferring carbon skeletons). However, the functions of these shuttles are not limited to the points mentioned above, and they can be used in different arrangements to meet different cellular requirements. Both the shuttles are intricately associated with Krebs cycle through the metabolites involved. The study of this system of shuttles and Krebs cycle explores the response of the system in different metabolic environments. Here, we have simulated these subsets individually and then combined them to study the interactions among them and to bring out the dynamics of these pathways in focus. Four antiports and a pyruvate pump were modelled along with the metabolic reactions on both sides of the inner mitochondrial membrane. Michaelis–Menten approach was extended for deriving rate equations of every component of the system. Kinetic simulation was carried out using ordinary differential equation solver in GNU Octave. It was observed that all the components attained steady state, sooner or later, depending on the system conditions. Progress curves and phase plots were plotted to understand the steady state behaviour of the metabolites involved. A comparative analysis between experimental and simulated data show fair agreement thus validating the usefulness and applicability of the model. Keywords: energy machinery; redox equivalent; shuttles; TCA cycle; GNU Octave
Introduction Mitochondria are powerhouses of the cell where NADH and FADH2 are oxidised to build up electrochemical potential gradient (Δψ + ΔpH) across the inner mitochondrial membrane. This electrochemical potential gradient is used by ATP synthase to produce ATP from ADP and Pi. NADH and FADH2 required for this purpose are mainly supplied by Krebs cycle located close to the inner mitochondrial membrane inside the mitochondrial matrix. However, a substantial amount of NADH is also produced in the cytoplasm. NADH produced in cytoplasm has to be recycled back to NAD+ to maintain glycolytic flux and other metabolic reactions in cytosol. Therefore, NADH has to be transported to the mitochondrial matrix for its oxidation (Dawson, 1979). Mitochondrial inner membrane is, however, impermeable to both NAD+ and NADH (Purvis & Lowenstein, 1961). To bypass this limitation, cell has established shuttle systems that are used to transport electrons across the mitochondrial membrane via reducing equivalents instead of NADH itself (Williamson, Safer, LaNoue, Smith, & Walajtys, 1973). Two of the most widely studied shuttles used for transport across mitochondrial membrane are malate–aspartate and citrate–pyruvate shuttles. In the *Corresponding author. Email: [email protected] © 2015 Taylor & Francis
present study, we have modelled these two shuttles individually and then combined them with Krebs cycle, to study the interactions between them. The metabolic pathways have been extensively studied by biologists, and it has resulted in a static picture of the reactions involved in these pathways; however, the living system is inherently dynamic. This emphasises the need for a dynamic model which can predict the behavioural pattern of various components at any given point in time. Mitochondrial functions have been reported to be deregulated in insulin resistance, cancer and several other mitochondrial diseases. Mitochondrion shifts its function from ATP production to biosynthetic activity (anaplerosis) to support overall anabolic programs in cell. Chin et al. have shown that α-ketoglutarate inhibits ATP synthase and extends the lifespan of Caenorhabditis elegans (Chin et al., 2014). Kinetic modelling of Krebs cycle alone is insufficient to provide useful information because it is essentially a closed system (Korla & Mitra, 2014a). However, when considered in conjunction with the shuttles, Krebs cycle can supply reducing equivalents to outside of mitochondria. It can also provide carbon skeletons for other metabolic pathways such as citrate
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Kinetic simulation of mitochondrial shuttles for fatty acid biosynthesis and amino acids for protein synthesis. Here, we present a basic skeleton which can be expanded to address a broad range of biological questions. Computer modelling of mitochondrial metabolism has been previously reported. Wu et al. have reported a model based on detailed kinetic and thermodynamically balanced reaction mechanisms with a strict accounting of rapidly equilibrating biochemical species (Wu, Yang, Vinnakota, & Beard, 2007). Yugi and Tomita have reported a model that integrates the dynamics of the respiratory chain, Krebs cycle, the fatty acid β-oxidation and the inner membrane metabolite transport system to enable metabolic pathway simulation in a complete mitochondrial scale (Yugi & Tomita, 2004). Berndt et al. have reported the impact of reduced α-ketoglutarate dehydrogenase activity on ATP production using a kinetic model (Berndt, Bulik, & Holzhütter, 2012). Lu et al. (2008) have reported the role of malate–aspartate shuttle on the metabolic response to myocardial ischaemia. However, the above reports are restricted to specific conditions, whereas our approach is more general and easily extensible. Further, we have included membrane transport facilitated by well-established shuttle system. Also, a comparative analysis has been presented at the end. The experimental data as reported by Bennett et al. (2009) and the simulated data (comprising reactions of Krebs cycle, oxidative phosphorylation and the two shuttles) were tallied, and inferences were drawn. In the present work, we have not intended to address a particular biological problem but have attempted to formulate a generalised framework that can be easily extended for particular cases as the need arises. Malate–aspartate shuttle consists of two transporters, (glutamate–aspartate antiport transporter and malate–αketoglutarate antiport transporter) which transport four components, (aspartate, glutamate, α-ketoglutarate and malate) across the inner mitochondrial membrane (Figure 1). These two transporters are coupled by biochemical reactions between the metabolites on both sides (Nelson, Cox, and Freeman, 2004). The transporters, as seen in Figure 1, are antiports and facilitate transfer of equal molar equivalents of metabolites across the membrane in opposite direction. In other words, transfer of one mole of glutamate from the intermembrane space (IM) to the mitochondrial matrix (M) facilitates transfer of one mole of aspartate in the opposite direction. Direction of transport is determined by the concentration gradient of the two metabolites. Metabolite with a higher concentration gradient will flow from the higher concentration to the lower concentration side, and consequently, the other metabolite will flow in the opposite direction irrespective of its concentration gradient. Reactions involved are given in Table 2.
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Figure 1. Pictorial representation of malate–aspartate shuttle. The shuttle consists of two transporters, (aspartate–glutamate antiport transporter and malate–α-ketoglutarate antiport transporter) used for transferring reducing equivalents between two sides of the inner mitochondrial membrane. The diagram contains two circles, (i) moving clockwise and the other (ii) moving anti-clockwise, and these two circles are connected at two points by aspartate aminotransferase. The reaction scheme is completely symmetric on both sides as drawn. However, oxaloacetate, α-ketoglutarate and malate can be taken into Krebs cycle and control the kinetics of Krebs cycle.
Malate–aspartate shuttle moving in directions as shown in Figure 1 is used to transfer reducing equivalents from cytoplasm to the mitochondrial matrix. Conversion of oxaloacetate to malate in cytosolic side oxidises NADH to NAD+. Malate thus formed is transported to the mitochondrial matrix in exchange of α-ketoglutarate and is used to regenerate NADH from NAD+ in the matrix and produces oxaloacetate in the reaction. This oxaloacetate now combines with glutamate to generate αketoglutarate (which is transported in exchange of malate influx), and aspartate. Aspartate is transported to the cytosolic side in exchange for glutamate, which is further required for the reaction with oxaloacetate (Brand & Chappell, 1974). In cytosol, aspartate reacts with α-ketoglutarate (transported in exchange of malate) to give glutamate and oxaloacetate, which continues the cycle. In this process, all the components are internally used to ultimately transfer electrons from NADH in cytosolic side to generate NADH in the matrix side (Williamson et al., 1973). The enzymes involved in this shuttle work reversibly, and the shuttle can function in principle in the reverse direction. Malate–aspartate shuttle is considered as a major mechanism involved in transporting reducing equivalents from the IM space to the matrix and vice versa (Barron, Gu, & Parrillo, 1998). Although the diagram appears symmetric (Figure 1), malate, oxaloacetate and α-ketoglutarate also take part in Krebs cycle (not shown in Figure 1) in the mitochondrial matrix.
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Citrate–pyruvate shuttle consists of five enzymes (ATP-citrate lyase, malate dehydrogenase, malic enzyme, pyruvate carboxylase and citrate synthase, of which the first three are present in the intermembrane space and the last two in the mitochondrial matrix). There are two exchangers (citrate/malate exchanger and malate/phosphate exchanger) and a pyruvate pump, facilitating the transport of metabolites (Figure 2). Of the five enzymes, only malate dehydrogenase mediates reversible processes and the rest are essentially irreversible. Pyruvate pump functions as a symport transporting pyruvate and H+ ions (or OH− in the opposite direction) simultaneously to maintain the charge balance across the membrane (Halestrap, 1975). pH and membrane potential across the membrane are assumed to be constant. Rate of pyruvate pumping is regulated by pH gradient and concentration gradient. The pyruvate pump is modelled as a one-way transporter, regulated by its concentration gradient across the mitochondrial membrane. Non-zero potential difference across the membrane also affects the transport of pyruvate (in addition to the concentration gradient). The reactions are shown in Table 2. Citrate–pyruvate shuttle is used to transport pyruvate from the IM space to the mitochondrial matrix feeding Krebs cycle. Inner mitochondrial membrane is impermeable to acetyl-CoA and is, therefore, converted to citrate inside the matrix and transported to cytosol, where it undergoes ATP-dependent cleavage by ATP-citrate lyase to regenerate acetyl-CoA and oxaloacetate. Thus, an excess of acetyl-CoA inside the matrix is transported back to cytosol as citrate for fatty acid synthesis and other metabolic purposes (Guay, Madiraju, Aumais, Joly, & Prentki, 2007). The oxaloacetate is reduced to malate,
oxidising NADH to NAD+ in the reaction. This malate can be used for conversion of NADP to NADPH, forming pyruvate, or it can be transported to mitochondria by malate–α-ketoglutarate transporter, thus transporting electrons from NADH to the matrix. Pyruvate entering the matrix is channelled to Krebs cycle via acetyl-CoA or oxaloacetate forming citrate. Excess of citrate formed can be shuttled back to cytosol in exchange with malate. Shuttles and their regulation Shuttles help in maintaining metabolite concentrations at suitable level close to steady state in both sides of the inner mitochondrial membrane. They maintain optimal concentrations of metabolites and not necessarily equal concentrations. Such a shuttle system usually consists of several parts which are weakly coupled through the reactions on both sides of the membrane (Table 2). They are considered as weakly coupled because the metabolites connecting the transporters can enter other reactions on either side. The shuttles and Krebs cycle share components in the matrix side (common pool), and this results in close interdependence between these two sets of reactions. In fact, there are a couple of reactions in common between the two sets (LaNoue & Williamson, 1971).The presence of similar connections among different pathways suggests interrelated regulatory mechanism. Since Krebs cycle and shuttles share metabolites among themselves, they are expected to be located in the vicinity of each other. Further, as discussed earlier, Krebs cycle is expected to be located near the inner mitochondrial membrane by virtue of succinate dehydrogenase, which is also involved in ETC and is membrane-bound.
Figure 2. Pictorial representation of citrate–pyruvate shuttle. The figure shows five enzymes (ATP-citrate lyase, malate dehydrogenase, malic enzyme, pyruvate carboxylase and citrate synthase), two antiport transporters (citrate/malate and malate/phosphate) and pH-dependent pyruvate pump.
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Kinetic simulation of mitochondrial shuttles Malate is used in both malate–aspartate (Figure 1) and citrate–pyruvate (Figure 2) shuttles. Cells can use a combination of these processes to move a variety of carbon units or reducing equivalents from one side of the mitochondrial membrane to the other. Malate acquires electrons from NADH in the cytosol, and it can be exchanged with α-ketoglutarate (five-carbon compound), citrate (six-carbon compound) or simply, phosphate (no carbon). This presents an elegant mechanism by which cells can use several combinations of metabolites from different intracellular compartments to regulate metabolic processes. Besides, α-ketoglutarate, citrate, oxaloacetate and pyruvate are other metabolites which are involved in both Krebs cycle and shuttles. This indicates a close association among Krebs cycle and two shuttles in terms of function and regulation and urges us to model them together to have an overview of their metabolic interconnectivity. Figure 3 shows the diagrammatic representation of the complete set of reactions including those from the two shuttles and Krebs cycle. As already mentioned, transporters assist in the movement of carbon skeleton across the mitochondrial membrane, allowing molecules such as citrate, α-ketoglutarate and malate to cross the membrane. They also carry redox equivalents across the mitochondrial membrane. Some molecules, such as oxaloacetate and acetylCoA, cannot cross the mitochondrial membrane. As a result, separate, independently regulated pools of these components, which play important roles in the regulation of cellular metabolic processes and Krebs cycle in the matrix side, are maintained in a quasi-steady state. As mentioned earlier, mitochondria in addition to production of ATP also have considerable biosynthetic
Figure 3. Schematic diagram representing Krebs cycle (enclosed in grey rectangular box) and transporters involved with malate–aspartate and citrate–pyruvate shuttles. [Pyr = Pyruvate, Mal = malate, α-kg = α-ketoglutarate, Cit = citrate, Glu = glutamate, Asp = aspartate, Oaa = oxaloacetate, Pi = phosphate, Suc = succinate, Ac-CoA = acetyl-CoA ]. The numbers marked on the reaction lines indicate the reaction serial numbers from Table 2. 16 corresponds to pyruvate pump, 17–20 correspond to malate–phosphate, malate–citrate, malate–α-ketoglutarate and aspartate–glutamate transporters, respectively.
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activity. The partitioning of the two roles depends on the activity of the shuttle system and the ATP synthesis. The shuttle system transports reducing equivalents across the mitochondrial membrane. As NAD+/NADH are impermeable to the mitochondrial membrane, the shuttle system provides rather symmetric biochemical reactions on both sides of the membrane to perform this task. In the absence of the shuttle system, mitochondria would be forced to invest all the reducing equivalents generated in Krebs cycle into the production of ATP which may not be optimal (Mazat, Ransac, Heiske, Devin, & Rigoulet, 2013). Modelling these events, therefore, would help study the possible mode of partitioning of mitochondrial functions between energy generation and biosynthetic functions in the cell and would give biological explanation for the causes of metabolic pathologies such as NAFLD (non-alcoholic fatty liver disease) and carcinogenesis. Methods In the present study, we have individually simulated the kinetic aspects of two mitochondrial shuttles, viz., malate–aspartate and citrate–pyruvate shuttles and Krebs cycle. For simulation GNU Octave, a free software, has been used, particularly the ordinary differential equation (ode) solver (GNU Octave). A stochastic model that includes a large number of biochemical reactions, was considered slow and inefficient, has not been used. An ordinary differential equation (ode) in an equation of the general form f ðx; y0 ; y00 ; . . .; yn Þ ¼ 0 where y0 ¼ dy=dx and yn ¼ d n y=dxn n is called the order of the equation. The kinetic equations are first order but non-linear. First order means that only the first derivative is involved in any equation. In the present study, we have several variables for y, and therefore, we have a system of coupled equations. These values of y and y0 are treated as vectors. We have ignored diffusion in the present simulation. Diffusion in small systems is usually fast but can be slow if the concentration is low and the component needs to travel relatively long distance (e.g. hormone effects). A reaction diffusion system involves secondorder equation, and the solution strongly depends on the boundary conditions. A differential equation is called stiff if the conventional numerical methods of solution lead to unstable results. We have assumed that our systems of equations are not stiff. However, coupled chemical reaction kinetics in which concentration of different components varies widely can become stiff.
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In Octave, there are several methods available to solve ordinary differential equations. We have used lsode module. In this case, the linear first order differential equations are written in the form:
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y0 ðt Þ ¼ f ðt; yÞ where y and y0 are vectors usually supplied as a function. Lsode uses the most common method “Livermore Solver for Ordinary Differential Equations”, which is well documented in the literature (Hindmarsh, 1983). Rate equations were derived for each metabolite involved in the reactions. The rate equations were written based on Michaelis–Menten approach (also known as Henri–Michaelis–Menten equation or HMM equation (Deichmann, Schuster, Mazat, & Cornish‐Bowden, 2014). Few reasonable assumptions were made, and the approach was extended to fit the reaction mechanism. v¼
Vmax ½S v ½S =KM can be written as ¼ KM þ ½S Vmax 1 þ ½S =KM
Here, both v/Vmax and [S]/KM are dimensionless, and this equation is now suitable for numerical calculations. As a result of the scaling, the time also becomes a dimensionless quantity. The substrate concentrations, although reported in arbitrary units, are in reality in units of KM of the respective enzymes. In the present case, we use [S]/KM as the dimensionless quantity representing the concentration and explicit knowledge of KM is not needed. However, if we need the actual concentration for a given component we need to know the specific KM value. In reality, KM values for a particular enzyme reported by different authors vary widely and eliminating KM in this way appears to be an advantage. In the same way, v/Vmax is the dimensionless rate which can be easily correlated with experimental values when Vmax is known. Using dimensionless concentrations has an added advantage that all meaningful values lie close to unity. For multiple substrates, we have extended this formula to v ½S1 =KM 1 ½S2 =KM 2 ½S3 =KM 3 ¼ Vmax 1 þ ½S1 =KM 1 1 þ ½S2 =KM 2 1 þ ½S3 =KM 3 which is considered as an approximation here, at least to the first order. Similarly, the inhibitors were also taken into consideration and were incorporated in rate equations. The effects of other possible co-factors and several ionic components, were not explicitly investigated. Their effects were considered constant. Krebs cycle reactions were simulated using the scheme discussed in detail in our previous work (Korla & Mitra, 2014a). (One reviewer has raised some technical objections regarding our use of Michaelis–Menten kinetics and quasi-steady state approximation. The reviewer has
further suggested the use of full/complete reaction mechanisms avoiding the use of Michaelis–Menten formalism. In the present study, the methods used are approximate in nature but the broad philosophy remains sound. One of the difficulties in using an exact method is simply the lack of sufficient information. Often, the value of KM for a particular species is not available. Further, Vmax depends on the total concentration of the enzyme and its kinetic parameters that are also not available. In the present simulation, around 50 enzymes and metabolites are involved. We have simulated in the present work a large network and the agreement with the experimental results suggests that the method works.) Modelling the transporter In the present system, there are four antiporters, that is, glutamate–aspartate, malate–α-ketoglutarate, citrate– malate and malate–phosphate (Figure 3). The kinetics of antiport has been modelled using a modified version of Michaelis–Menten kinetics (Korla & Mitra, 2014b). The fluxes of various components specifically depend on the metabolite concentrations on both sides of the membrane. The transporters in the present study are all antiports, and thus, transport across the membrane will be facilitated only when the two metabolites occupy binding sites on the opposite sides of the membrane. All the four binding sites on transporters are considered independent and equivalent. It has been considered that there are four binding sites, two on each side of the membrane, and each one specific for the metabolite than can bind in any sequence. At a given point in time, the transporter can have one of the sixteen possible conformations, of which only two conformations can successfully facilitate metabolite transport across membranes. This forms the basis for modelling transport across the membrane. Four variables, alpha, beta, gamma and delta were introduced in the simulation script that correspond to the antiport pairs, glutamate/aspartate, malate/α-ketoglutarate, citrate/malate and malate/phosphate exchangers, respectively. These variables were appropriately added or subtracted from the relevant metabolite concentration depending on the flux directions (as shown in Figure 3). Further, the reactions involved in shuttles were simulated using a similar approach as for Krebs cycle. The two shuttles were first individually simulated and then combined with the reactions of Krebs cycle. Table 1 shows the list of components included in the kinetic simulation. Metabolites present on the two sides of the membrane have been considered as different entities and have been given separate symbols and have been marked with “-m” suffix for those present in the mitochondrial matrix and “-im” suffix for those present in the intermembrane space. The numbers allotted to each of the components remains the same throughout the
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Table 1. List of metabolites and numbers assigned to them for ease in simulation. Metabolites present on the two sides of the membrane have been considered as different entities and have been given separate symbols and have been marked here as “-m” for those present in the mitochondrial matrix and “-im” for those present in the intermembrane space. Metabolites followed by “(c)” were kept at a constant concentration within the script. Rate equations were derived for each component based on the reactions compiled from the literature.
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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
Oxaloacetate-m Acetyl-CoA-m Citrate-m Isocitrate-m α-ketoglutarate-m Succinyl-CoA-m Succinate-m Fumarate-m Malate-m CoA-SH-m NAD+-m (c) NADH-m (c) CO2-im (c)
14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.
script to maintain uniformity and avoid repetitions. Rate equations were derived for each component based on the reactions compiled from the literature. The reactions are listed in Table 2. Since these reactions form just a part of the mitochondrial metabolic network and the reactions are not self-sufficient; therefore, fifteen components were
GDP-m (c) GTP-m (c) FAD-m (c) FADH2-m (c) ATP-m (c) Aspartate-im Malate-im α-ketoglutarate-im Glutamate-im Glutamate-m Aspartate-m Citrate-im ATP-im (c)
27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.
CoA-SH-im (c) Acetyl-CoA-im (c) ADP-im (c) NADP-im (c) Pyruvate-im NADPH-im (c) Pyruvate-m Oxaloacetate-im NADH-im NAD+-im ADP-m (c) Phos-m Phos-im
designated as “sources and sinks” (denoted with “(c)” in Table 1). This approach assists the system in attaining self-sufficiency. While simulating pyruvate pump, which transports pyruvate from the IM space to the matrix and acts as the only source of pyruvate in the matrix, a new variable
Table 2. List of reactions included in the present study. The table includes reactions of Krebs cycle, malate–aspartate and citrate– pyruvate shuttle. Reactions in bold indicate reversible reactions. The suffixes -m and -im indicate the localisation (the matrix and the intermembrane space, respectively) of the respective components. The numbers indicate the assigned variable used in the script. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
Acetyl-CoA-m + Oxaloacetate-m → Citrate-m + CoASH-m 2 + 1 → 3 + 10 Citrate-m → Isocitrate-m 3→4 Isocitrate-m + NAD+-m → α-ketoglutarate-m+ NADH-m + CO2-m 4 + 11 → 5 + 12 + 13 α-ketoglutarate-m + CoASH-m + NAD+-m → Succinyl CoA-m + NADH-m + CO2-m 5 + 10 + 11 → 6 + 12 + 13 Succinyl CoA-m + GDP-m + Phos-m → Succinate-m + GTP-m + CoASH-m 6 + 14 + 38 → 7 + 15 + 10 Succinate-m + FAD-m → Fumarate-m + FADH2-m 7 + 16 → 8 + 17 Fumarate-m + H2O → Malate-m 8→9 Malate-m + NAD+-m → Oxaloacetate-m + NADH-m 9 + 11 → 1 + 12 Citrate-im + ATP-im + CoA-SH-im → OAA-im + acetyl-CoA-im + ADP-im + Phos-im 25 + 26 + 27 → 34 + 28 + 29 + 39 OAA-im + NADH-im → Malate-im + NAD+-im 34 + 35 → 20 + 36 Malate-im + NADP-im → Pyruvate-im + NADPH-im + CO2-m 20 + 30 → 31 + 32 Pyruvate-m + ATP-m + CO2-m → Oxaloacetate-m + ADP-m + Phos-m 33 + 18 + 13 → 1 + 37 + 38 Aspartate-im + α-ketoglutarate-im → Oxaloacetate-im + Glutamate-im 19 + 21 → 34 + 22 Oxaloacetate-m + Glutamate-m → Aspartate-m + α-ketoglutarate-m 1 + 23 → 24 + 5 Pyruvate-m + NAD+-m + CoASH-m → Acetyl-CoA-m + CO2-m +NADH-m 33 + 11 + 10 → 2 + 13 + 12
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Table 3.
Script used for simulation of Krebs cycle along with malate–aspartate and citrate–pyruvate shuttles.
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“flux” was introduced in the script. “Flux” depends on the concentration gradient of pyruvate across the inner mitochondrial membrane was given as flux = .02*(pyruvate-im − pyruvate-m). The “Flux” was added to the matrix pyruvate and was subtracted from the IM pyruvate. Table 3 includes the complete script used for simulation. For comparative analysis, another script was written which included reactions from Krebs cycle, electron transport chain, ATP synthesis and malate–aspartate and citrate–pyruvate shuttle. The concentrations of the selected metabolites in the intermembrane space at 500 time point were taken. These concentrations were multiplied with their respective KM values to obtain absolute concentrations values. These concentrations were then compared with the concentrations obtained from the literature, and a histogram was plotted for illustration. GNUPLOT was used for graphical representations. Results and discussion The individual shuttles were first simulated using ordinary differential equation (ode) solver in Octave. The rate equations of the components of shuttles were combined with the rate equations of those from Krebs cycle. Since there are several components common among them, a unified notation suitable for use in the Octave script has been used (Table 1). In our earlier work, we have simulated Krebs cycle individually and then combined it with oxidative phosphorylation. We have suggested Krebs cycle as a giant catalyst, when it was taken as an individual independent entity (Korla & Mitra, 2014a). When Krebs cycle is combined with the shuttles, a number of metabolites are common to both, such that these
metabolites may be supplied or taken away from Krebs cycle. In such a case, Krebs cycle no more acts as a giant catalyst, and instead acts as a source of both NADH (and FADH2) for electron transport chain and also of various carbon compounds (e.g. citrate, malate, α-ketoglutarate and oxaloacetate) in the present study. The carbon compounds can be used elsewhere in the cell for other regulatory and functional purposes. A comparison of the two systems is shown by plotting the same components in different environments, (i) Krebs cycle and (ii) Krebs cycle with malate–aspartate and citrate– pyruvate shuttle (Figure 4). However, the concentration profiles of the selected metabolites show different values but are broadly comparable. The difference is seen as the metabolites are now involved in multiple reactions, and their concentration is now shared among different reactions. An interesting feature from the two graphs is that the metabolites tend to attain steady state in both the conditions, as expected, but the metabolites tend to attain, in general, steady state earlier in Figure 4(b), suggesting that the system when extrapolated to include more and more network connections among the metabolites becomes more robust. In general, large numbers of network connections among the metabolites create parallel paths and this increases the apparent (or overall) rate for product formation. Therefore, we suggest that the rate of attainment of the steady state is related qualitatively to the number of paths available for the reactants to reach the product. Intuitively, a larger number of possible alternate paths make the system more robust. This further suggests that metabolic pathways along with their normal range of concentrations for different metabolites are not at equilibrium but are at a steady state. This steady state is not perfectly defined but is
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Figure 4. Simulation curves for (a) Krebs cycle alone (b) Krebs cycle + malate–aspartate and citrate–pyruvate shuttles. [Oaa = oxaloacetate, AcCoA = acetyl-CoA, Cit = citrate, Isocit = isocitrate, Keglu = α-ketoglutarate, SucCoA = succinyl-coA].
more likely to be a region or area consistent with a range of concentrations for different metabolites. In the progress curve shown in Figure 5, we see that all concentrations (we have plotted only selected metabolites) within a reasonable time frame reach a steady state value. However to maintain the steady state in an isolated system as this, we must provide “source” and “sink” for several key metabolites. Although the reactions are not of the first order, we can still qualitatively assign a t1/2 value for comparison. The final equilibrium concentration can be estimated visually, and the time taken for the concentration to reach ½ of this value can be estimated for comparison. The t1/2 values are useful for comparing the rates of approach to the equilibrium or steady state.
Figure 5. Simulation curves for selected components of Krebs cycle–shuttle system. Isocit = Isocitrate, Keglu = α-ketoglutarate, Mal = malate, Glu = glutamate, Asp = aspartate, Pyr = pyruvate. Suffixes “-m” and “-im” indicate that the presence of component in the matrix and the intermembrane space respectively.
Figure 5 indicates that all the metabolites do not reach the same “final” state concentrations. This is not expected as the steady state concentrations are related to their “distance” from the sources and sinks. This problem is not trivial because there are multiple sources, multiple sinks and multiple paths, and all paths are not equally traversed. Concentrations of several key metabolites have been plotted in Figure 5 as a function of time. The software needs initial (“guess”) values for simulation and these values are seen at time, t = 0. However, the initial values undergo large changes and settle close to the steady state values after a long time (t > 500). We are less interested in the initial parts of the graph (which are unrealistic) and are more interested in the values that are close to the steady state. The initial parts essentially show the instant response of the system towards any perturbation, when the system is forced to move out the steady state (due to intervention caused by the perturbation), and different components take divergent paths to ultimately fall in the steady state basin. This results in a stable system where all the components reach an adequate concentration to meet the cellular requirements. This amplifies the usefulness of the simulation and helps in understanding the behaviour of the system as a whole. In a system at the “resting” steady state concentration, where one of the metabolite’s concentration changes significantly beyond the “normal”, the system will attempt to return to the steady state. The path followed in this process can be seen more clearly in the next set of figures – the phase diagrams. The phase diagrams in Figures 6–8, show the return of the system to the stable steady state when one of the components is added or removed from the steady state values. These phase diagrams, rate of change of concentrations of the given metabolites vs. their concentrations, are similar to Michaelis–Menten curves and were plotted
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Figure 6. Phase diagram for selected important metabolites present in the mitochondrial matrix. [Pyr = Pyruvate, Mal = Malate, Keglu = α-ketoglutarate, Cit = Citrate, Glu = Glutamate, Asp = Aspartate]. Inset figure shows the magnified view of the selected region. The y-axis represents the rate of transformation of the corresponding substrate as indicated on the abscissa. The concentrations and time are expressed in arbitrary units.
for different metabolites. These curves show interesting features, particularly close to steady state. All the phase diagrams represent the change in concentration for the initial 900 time points, that is, 900 data points are plotted in each of the phase curves. It is interesting to note that a major distance between the first and the last concentration point is traversed by mere 20–30 data points, and more than 850 data points are clustered in a small region towards the end. This region is near the steady state condition where the changes are minimal. For clarity, the region close to steady state was expanded to show a closer perspective. It is seen that for several key metabolites, the return to steady state is not linear (or monotonic) and the behaviour is exemplified by the inset graphs. Inset figures show that the concen-
tration tends to localise in a small region and fluctuates with minimal changes as it approaches the steady state. In most of these images, a loop can be observed around the end points, which apparently indicates that steady state concentration is necessarily not a point but a region, which comprises several combinations of concentrations of various metabolites involved. Since the curves do not appear to be closed, the final steady state remains a point. The approximations made in the derivation do not allow us to explore this matter in detail. Figure 8 shows the phase curves for NADH and NAD+ in the IM space, and as expected, the two curves look complementary signifying their inconvertibility. Even as they approach the steady state the end regions also appear complementary.
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Figure 7. Phase diagram for selected important metabolites present in the intermembrane space. [Pyr = Pyruvate, Mal = Malate, Keglu = α-ketoglutarate, Cit = Citrate, Glu = Glutamate, Asp = Aspartate]. Inset figure shows the magnified view of the selected region. The y-axis represents the rate of transformation of the corresponding substrate as indicated on the abscissa. The concentrations and time are expressed in arbitrary units.
Figure 8. Phase diagram for NADH-im and NAD + -im. The curves are complementary since they are interconvertible species. Inset figure shows the magnified view of the selected region. The y-axis represents the rate of transformation of the corresponding substrate as indicated on the abscissa. The concentrations and time are expressed in arbitrary units.
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Table 4. List of metabolites, enzymes, corresponding KM for the reactions and metabolite concentrations under the experimental and simulated conditions. Metabolite
Enzyme
Aspartate Citrate Glutamate α-Ketoglutarate Malate NAD+ NADH NADH/NAD+
Aspartate transaminase Citrate lyase Aspartate transaminase Aspartate transaminase Malate dehydrogenase Malate dehydrogenase Malate dehydrogenase –
Experimental concentration (Moles/L)
KM (Moles/L)
Simulated concentration
KM*Simulated concentration (Moles/L)
4.2e-03 2.0e-03 9.6e-02 4.4e-04 1.7e-03 2.6e-03 8.3e-05 8.3e-05/2.6e-03
2.22e-03 1.60e-04 1.50e-02 2.47e-04 2.60e-03 2.60e-04 6.10e-05
1.94e-01 2.56e-05 6.06e-01 3.78e-01 5.26e-03 2.9e-01 9.98e-03
.434e-03 4.096e-09 .909e-02 .934e-04 .0137e-03 .0754e-03 .0609e-05 .0609e-05/.0754e-03
Figure 9. Comparative analysis of experimental and simulated metabolite concentrations. The experimental data were taken from Bennett et al. (2009).
Mitochondrial functions have been implicated in several diseases. Mullen et al. have shown that oxidation of α-ketoglutarate is required for reductive carboxylation in cancer cells with mitochondrial defects (Mullen et al., 2014). They demonstrate that inhibiting α-ketoglutarate oxidation decreased reducing equivalent availability and suppressed reductive carboxylation. Their results demonstrate that reductive carboxylation requires bidirectional α-ketoglutarate metabolism along oxidative and reductive pathways. Lu et al. (2008) have suggested a direct relation between insulin resistance and the metabolism of branched chain amino acids (Lu et al., 2008). The branched chain amino acids via catabolism feed α-keto acids into Krebs cycle. It was reported that intake of branched chain amino acids was accompanied with increased energy expenditure and better insulin sensitivity (She et al., 2007). Our present model can be coupled with the catabolism of branched chain amino acids and Krebs cycle. Chin et al. have shown that α-ketoglutarate extends life span of adult C. elegans by inhibiting ATP synthase (Chin et al., 2014). Their results uncover new molecular link between
α-ketoglutarate, mitochondria and organismal lifespan. The effect of decrease in ATP synthesis increases the reducing environment inside the matrix and activates the shuttle services (Figure 1). In such a case, the shuttles move in reverse direction, actively transporting NADH via malate and α-ketoglutarate is transported to the matrix side. In an attempt to validate the simulation results with the experimental results, data from the experiments carried out by Bennett et al. (2009) were taken and compared with the simulation results obtained. The authors have presented absolute metabolite concentrations of several metabolites in Escherichia coli. The concentrations of selected metabolites were compared with their respective steady state concentrations as calculated using the present simulation scheme. It has been shown earlier that the concentration in the simulation scheme is reduced by a factor of their respective KM values; therefore, the concentrations obtained as simulation results were multiplied by their KM values to obtain absolute concentration. The list of metabolites, enzymes catalysing their reaction and the respective metabolite concentrations under experimental and simulated conditions are shown in Table 4. A histogram plotted to illustrate the comparative view of the experimental and simulated data-set is presented in Figure 9. The results presented in Figure 9 indicate applicability of the simulation scheme. Simulated concentrations of the selected metabolites are lower than the experimental values for all of them. However, it can be seen that the concentrations of all metabolites except citrate represent fair agreement between the experimental and simulated results. The major variation seen in citrate concentration could be due to the presence of other citrate sources and sinks in the cytoplasm, which are not included in our reaction scheme. It is known that the ratio of NADH and NAD+ is more relevant than the individual parameters, it can be clearly seen the difference in their ratio in the two sets is smaller than the differences between the individual components (NADH, NAD+).
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Kinetic simulation of mitochondrial shuttles It should be stressed here that the simulation presented here has taken no specific cellular or reaction (KM or Vmax) parameters into consideration, and the results were still quite close to the physiological values. This can be directly related to the robustness of the system. For systems with larger number of components, the present approach can become cumbersome and error-prone. Therefore, a modular approach is being considered for generic applications. The experimental data used here correspond to E. coli system that lacks mitochondria, and therefore, the cytosolic metabolite concentrations (assumed to be same as the metabolite concentrations in the IM space) are taken for comparison from the script. Also, this could explain the variations seen in the results, and it can still be considered quite a satisfactory agreement between the experimental and the simulated data.
Acknowledgements One of the authors (KK) acknowledges the receipt of Senior Research Fellowship from University Grants Commission (Govt. of India).
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