Conceived and designed the experiments: VAS TVV. Performed the experiments: TVV VNP JZ. Analyzed the data: VAS TS MT JR MC. Contributed reagents/materials/analysis tools: VAS. Wrote the paper: VAS TVV.
The authors have declared that no competing interests exist.
Reactive oxygen species (ROS) produced in the mitochondrial respiratory chain (RC) are primary signals that modulate cellular adaptation to environment, and are also destructive factors that damage cells under the conditions of hypoxia/reoxygenation relevant for various systemic diseases or transplantation. The important role of ROS in cell survival requires detailed investigation of mechanism and determinants of ROS production. To perform such an investigation we extended our rule-based model of complex III in order to account for electron transport in the whole RC coupled to proton translocation, transmembrane electrochemical potential generation, TCA cycle reactions, and substrate transport to mitochondria. It fits respiratory electron fluxes measured in rat brain mitochondria fueled by succinate or pyruvate and malate, and the dynamics of NAD+ reduction by reverse electron transport from succinate through complex I. The fitting of measured characteristics gave an insight into the mechanism of underlying processes governing the formation of free radicals that can transfer an unpaired electron to oxygen-producing superoxide and thus can initiate the generation of ROS. Our analysis revealed an association of ROS production with levels of specific radicals of individual electron transporters and their combinations in species of complexes I and III. It was found that the phenomenon of bistability, revealed previously as a property of complex III, remains valid for the whole RC. The conditions for switching to a state with a high content of free radicals in complex III were predicted based on theoretical analysis and were confirmed experimentally. These findings provide a new insight into the mechanisms of ROS production in RC.
Respiration at the level of mitochondria is considered as delivery of electrons and protons from NADH or succinate to oxygen through a set of transporters constituting the respiratory chain (RC). Mitochondrial respiration, dealing with transfer of unpaired electrons, may produce reactive oxygen species (ROS) such as O2− and subsequently H2O2 as side products. ROS are chemically very active and can cause oxidative damage to cellular components. The production of ROS, normally low, can increase under stress to the levels incompatible with cell survival; thus, understanding the ways of ROS production in the RC represents a vital task in research. We used mathematical modeling to analyze experiments with isolated brain mitochondria aimed to study relations between electron transport and ROS production. Elsewhere we reported that mitochondrial complex III can operate in two distinct steady states at the same microenvironmental conditions, producing either low or high levels of ROS. Here, this property of bistability was confirmed for the whole RC. The associations between measured ROS production and computed individual free radical levels in complexes I and III were established. The discovered phenomenon of bistability is important as a basis for new strategies in organ transplantation and therapy.
Reactive oxygen species (ROS) are side products of electron transport in the mitochondrial respiratory chain, the principal component of energy transformation in mitochondria. ROS generation starts with the formation of a superoxide radical (O2−) as a result of interaction between molecular oxygen and free radicals, e.g. semiquinone (Q−): O2+Q−→O2−+Q
Although electron transport and coupled ROS production have been the focus of intensive research, important details are still not understood. There is currently debate regarding the relative contribution of various sites of the respiratory chain to overall ROS production
The solution to such problems requires not only improvements in experimental techniques and new experiments, but also modification of methods for theoretical analysis. Specifically, kinetic modeling, which is an efficient method for investigating complex systems, still needs to be adopted for the mitochondrial respiratory chain. In fact, kinetic modeling in its classical form has been used for analysis of mitochondrial respiration. However, even the most detailed models
The prediction of bistability for the mitochondrial respiratory chain was based on analysis of the Q-cycle mechanism for complex III. The contribution of other parts of the respiratory chain and linked processes that provide substrates must affect the properties of the respiratory chain. To study mitochondrial respiration as a whole, we extended the model of complex III
Two reactions lead from pyruvate to succinate and further transformation to oxaloacetate reduce NAD+ to NADH. The latter is used by complex I to generate a transmembrane electrochemical proton potential (ΔμH+) and reduce ubiquinone (Q) to ubiquinol (QH2), oxidation of which by complex III also contributes to ΔμH+. Complex III reduces cytochrome
As described in the
The rates of respiration in the presence of ADP (state 3) or an uncoupler characterize the maximal capacity of the respiratory chain. In the absence of ADP (state 4), the respiration rate is characterized by proton leaks, which must be compensated by respiration. According to our measurements, the respiration rate is 480±40 and 170±30 ng atom O/min/mg protein in the uncoupled and in state 4 in succinate-fueled mitochondria, and 410±30 and 80±20 ng atom O/min/mg protein in mitochondria fueled by pyruvate and malate, respectively.
If mitochondria fueled by succinate do not expend the energy of the transmembrane electrochemical potential on ATP synthesis (state 4), succinate oxidation results in fast reduction of intramitochondrial NAD+. In the presence of rotenone, an inhibitor of electron transport in complex I, NAD+ reduction is characterized by NAD+-dependent reactions of the TCA cycle and in particular the forward respiratory flux resulting from succinate oxidation. In the absence of rotenone, reverse electron transport
(A) NADH reduction in state 4 in the absence (st4) and presence of rotenone (+rot). Points are experimental data (−e) measured in brain mitochondria fueled by 1 mM succinate, lines are calculated (−t). (B) Reversible electron flow through complex I computed in the simulations shown in (A). (C) Respiration (net forward flux to oxygen) and (D) ΔΨ under different substrate conditions (suc, 1 mM succinate; or pyr, 1 mM malate and 1.5 mM pyruvate ). State 4 respiration (st4) was simulated using the parameters described in
While succinate fuels complex III through succinate dehydrogenase, the oxidation of malate and pyruvate in the TCA cycle fuels complex I by reducing NAD+ to NADH. Respiration under such conditions defines the characteristics of complex I.
To evaluate the model parameters, we used a procedure that simulates all the different types of data listed above for the same set of parameters. The ratio of forward and reverse constants defined by a known midpoint potential or dissociation constant was kept fixed, and the conditions of substrate supply or membrane permeability for protons were changed in accordance with experimental conditions. The procedure fitted all the data by changing the free parameters within the order of magnitude indicated in
The best fit reproduces well the dynamics of NAD+ reduction measured in brain mitochondria in the presence and absence of rotenone using the same set of parameters (
Rotenone essentially changes the dynamics of NADH measured before succinate addition. It is slightly oxidized by the RC in the absence of rotenone, but slowly reduced in its presence. This reduction is a result of oxidation of internal substrates while electron flow through the RC is blocked. We found that the metabolites of TCA cycle cannot be substrates that provide NADH reduction, because oxidation of TCA cycle metabolites results in much faster initial reduction of NADH. If the parameters of TCA reactions are changed to slow down and reproduce the initial dynamics of NADH, maximal respiration rate with pyruvate becomes inconsistent with experimental data (not shown). Rather, slow oxidation of other metabolites, probably aminoacids or lipids, contributes to NADH reduction. The simulation of such slow oxidation did not prevent NADH oxidation in the absence of rotenone, and reproduced NADH reduction in its presence.
While, in the absence of rotenone, succinate induced much faster NADH reduction due to reverse electron transport, the steady state levels are lower than in the presence of rotenone. The steady state levels are defined by NADH production and consumption in respiration. Rotenone blocks the consumption, therefore NADH levels further increase when rotenone is added after succinate. The model parameters were adjusted without considering subsequent NADH increase and the reproduction of this phenomenon validates the model.
The model reproduces measured maximal and state 4 respiratory electron flows for succinate-fueled mitochondria, as well as for mitochondria fueled by pyruvate/malate (
max | min | bestfit | |
kqp_FS | 267000 | 117000 | 200000 |
kFS_c1 | 1585000 | 305000 | 527000 |
kqp_bl | 121000 | 25000 | 37000 |
kbl_bh | 114000 | 17000 | 27000 |
Kbh-qn1 | 214000 | 32000 | 47000 |
kbh_qn2 | 1118000 | 225000 | 254000 |
kqHbnd | 4000 | 1700 | 2800 |
kqnbnd | 23000 | 5000 | 7200 |
kqpdis | 9500 | 1700 | 2300 |
kqhnds | 9500 | 3300 | 4100 |
kc1c | 290 | 240 | 260 |
kfI0 | 724000 | 460000 | 640000 |
kfI1 | 525000 | 138000 | 140000 |
kfI2 | 816000 | 255000 | 770000 |
kfI3 | 34500 | 15000 | 23000 |
kfI6 | 360000 | 138000 | 164000 |
kfI8 | 721000 | 143000 | 205000 |
kfI7 | 340000 | 148000 | 187000 |
ktca | 1600 | 650 | 710 |
kMDH | 1100 | 270 | 460 |
kspe | 340 | 140 | 270 |
kme | 0.000382 | 0.000064 | 0.000280 |
kpyrIn | 1200 | 500 | 600 |
ksfe | 8.5 | 2.11 | 6.48 |
kcs | 1300 | 500 | 1290 |
st4-suc | 0.23318 | 0.07607 | 0.16491 |
+rot | 0.23310 | 0.07602 | 0.16482 |
st4-pyr | 0.01808 | 0.01615 | 0.01756 |
st4-suc | 0.12456 | 0.11350 | 0.06705 |
+rot | 0.07607 | 0.06562 | 0.07120 |
st4-pyr | 0.01293 | 0.00556 | 0.00835 |
st4-suc | 0.00486 | 0.00407 | 0.02525 |
+rot | 0.04094 | 0.02176 | 0.03152 |
st4-pyr | 0.00702 | 0.00284 | 0.00439 |
st4-suc | 0.135 | 0.12507 | 0.07098 |
+rot | 0.07407 | 0.06320 | 0.06914 |
st4-pyr | 0.00723 | 0.00327 | 0.00482 |
These intervals were calculated for each parameter separately among the sets of parameters that give χ2 below than a fixed threshold
These simulations of measured data provide an insight into important hidden characteristics, such as the capacity of ROS production. ROS are produced by the respiratory chain as a consequence of one-electron transfer directly to oxygen from free radicals of electron transporters such as the semiquinone radical (SQ) at the Qo site in complex III
The model describes various states of respiratory complexes formed in the process of electron transport, including those containing free radicals. Such radicals could be responsible for passing unpaired electrons to oxygen thus forming superoxide radicals and other forms of ROS. The contributions of various radicals to ROS production remain unknown; to clarify it we compared measured ROS production and the levels of various free radicals predicted by the model for the same conditions. A similar change in radical content and measured ROS production indicates qualitative accordance between the model and the described process and thus validates the model.
It is generally known that inhibition of reverse electron transport by rotenone decreases ROS production in succinate-fueled brain mitochondria
(A) ROS production measured. (B–D) Model prediction of the content of various free radicals. The dynamics of (B) SQ bound to Qo sites of complex III, (C) SQ at Qn sites of complex I and (D) FMNH were taken from the same simulations of state 4 respiration in succinate-fueled mitochondria for rotenone addition (+rot), either initially or in the course of measurements, as in
The model predicts that rotenone essentially decreases initial levels of SQ bound on site Qn (
The fact that the species of complex I can contain more than one radical makes it more difficult to understand the contribution of each site. In particular, the species 1101001 (the positions of digits correspond to Qp-Qp-Qn-Qn-N2-FMN-FMN), which contain SQ and FMNH radicals, slowly accumulate after inhibition by rotenone. This accumulation defines the dynamics of SQ and FMNH, whereas 1101100 defines the fast component in levels of Qn-bound SQ and reduced N2 (inset in
Overall, according to the model predictions, rotenone hardly affects SQ levels in complex III, but initially it significantly decreases the levels of free radicals produced in complex I; this is the reason for the decrease in ROS production induced by rotenone in succinate-fueled mitochondria. The model also explains the subsequent increase in ROS production as a result of the formation of malate in rotenone-inhibited mitochondria.
Rotenone induces a large increase in ROS production in pyruvate/malate-fueled mitochondria (
(A) ROS production measured in state 4 respiration and the change on addition of rotenone. (B) Model prediction of free radical levels in a simulation of the conditions for (A). The model parameters are the same as for the simulation shown in
Stimulation of electron transport by addition of ADP or an uncoupler such as FCCP to succinate-fueled mitochondria results in a decrease in ROS production (
(A) ROS production measured in state 4 and the change on addition of 1 mM ADP. (B) Model prediction of free radical content. The dynamics of free radical levels in a simulation of the conditions for (A). The model parameters are the same as for the simulation shown in
Mitochondria fueled by pyruvate/malate also produce less ROS when electron transport is stimulated by an uncoupler (
(A) ROS production measured in state 4 and in the presence of uncoupler FCCP. (B) Model prediction of free radical content on addition of FCCP. The model parameters are the same as for the simulation shown in
At high succinate concentrations, brain mitochondria produce much more ROS than those fueled by pyruvate (
(A) ROS production measured in brain mitochondria. (B) Predicted levels of free radicals in complexes I and III. Succinate (blue curves) or pyruvate (orange) was used as substrate. Semiquinone levels in complexes I (c1) and III (c3) are presented as indicators of ROS production.
Thus, the study of associations between measured ROS production and predicted radical levels in RC revealed qualitative consistency of measurements with all types of radicals and therefore validated the model, or showed a way of discrimination between possible sites of ROS production, and even between possible ROS producing species. However, in the latter case, a special, quantitative study is needed, which currently is beyond of the scope of presented study.
It has been predicted that the Q-cycle mechanism of complex III can in principle induce bistable behavior
(A) Predicted dynamics of semiquinones bound to the Qo site of complex III when the system is initially in an oxidized or a reduced state. Substrate concentrations: succinate 0.1 mM, pyruvate 0.25 mM. (B) Steady-state levels of semiquinones bound at the Qo site of complex III and the Qn site of complex I as a function of succinate concentration. The pyruvate concentration for the blue curve is 0.1 mM.
With increase in succinate concentration at some point the system switches to the state with the highest levels of semiquinone radicals at Qo site of complex III. The difference here from the similar curve in
Thus, bistable behavior remains valid for the extended model of the RC with proton translocation and transmembrane potential (ΔΨ) generation, and with parameters defined by fitting the experimental data and validated by qualitatively similar predicted and measured ROS production. The model predicts also that a pulse of succinate is associated with decrease of ΔΨ. Such counterintuitive decrease of ΔΨ induced by increase of substrate for respiration is shown in
(A) Predicted dynamics of the transition induced by addition of 2 mM succinate to mitochondria initially in the oxidized state in the presence of 5 mM pyruvate, under the conditions of various proton leaks through the inner menbrane, slow leak, klk = 17000, and fast leak, klk = 80000 mL/(s·mg prot) (eq.H.1). (B) ΔΨ measured as safranine O fluorescence (lower values correspond to higher ΔΨ) at various succinate concentrations (as indicated). The initial levels of fluorescence (∼400 AFU) is slightly increased in the moment of addition of mitochondria and, then, energization and uptake of the dye results in decrease of fluorescence. The initial levels after the addition of mitochondria correspond to deenergized mitochondria and final corresponds to maximally energized mitochondria.
The succinate threshold for a switch to the reduced state depends on the parameters of pyruvate transport and TCA reactions; here we do not investigate the quantitative details with respect to bistability, but emphasize only the qualitative similarity of predicted and measured behavior. With regards to the considered in the previous sections normal “working” steady state, the predicted levels of free radicals are robust with respect to the model parameters, as the next section shows.
The sensitivity of simulations to variations in model parameters is shown in
Different sets in the global space of parameters that fit the experimental data could be identified using our stochastic algorithm for minimization of the objective function χ2 (sum of squares of deviations from measured data normalized by standard deviations). The algorithm identified confidence intervals for parameters based on fixed thresholds of χ2
To construct a detailed mathematical model that accounts for all redox states formed during electron and proton transport in complexes III and I, we used our rule-based methodology for automated construction of large systems of ODE
After fixing the ratios of forward and reverse rate constants for electron transport reactions, free parameters were defined by fitting of forward and reverse electron flows measured under various conditions. High variability of parameters with a good fit to experimental data precluded definition of their values. However, the levels of free radicals calculated in the model showed much less variability. Different sets of parameters with a good fit to experimental data define very similar patterns for free radicals formed in complexes I and III. Thus, the analysis gives a valid insight into the mechanism of respiration and ROS production, even without precise evaluation of the model parameters.
A substantial body of experimental data on mitochondrial ROS production cannot be satisfactorily explained within the current experimentally based paradigm. Some of these results were obscure, such as acceleration of succinate-driven ROS production after initial inhibition by rotenone (
A body of evidence indicate that either FMNH
The similarity between changes in the ROS production rate and in the levels of specific free radicals validates the model and also provides an insight into the mechanism of ROS production. Rotenone inhibition of ROS production in succinate-fueled mitochondria correlated with the free radicals formed in complex I, but not in complex III. Evidently, under the given conditions, reverse electron transport must contribute to free radical formation in complex I, although the net flux reducing NAD+ through complex I exists for only a very limited period of time.
In accordance with our previous study that revealed bistability for complex III
Q-cycle mechanism of complex III operation assumes bifurcation of electron flow at Qo site: one electron goes to Rieske center and further to complex IV, and another one reduces cytochrome b. This bifurcation of electron flow underlies the bifurcation between the two steady states. If in some moment the rate of first electron transition to Rieske center is higher than that for the second electron (because cytochrome b is reduced), semiquinones at Qo accumulate, thus preventing Qo liberation, binding and oxidation new molecules of ubiquinol, and thus limiting electron flow. In the case, shown in
The decrease of ΔΨ, in the case shown in
The presented new insight into mitochondrial respiration was possible due to the application of novel methodology of modeling that allowed a detailed mathematical description of mitochondrial respiration. The phenomenon of bistability, predicted based on this methodology, has a potential to be a basis of new paradigm for the mechanism of ROS production, which will initiate new research with outcome on academic and practical levels.
The file executable in Linux, which runs the simulations, and the C++ code of the program could be downloaded free from
The model of complex III described elsewhere
kqp_FS | 200000 | ΔE | 50 | krqp_FS | 28000 |
kFS_c1 | 528000 | ΔE | 33 | krFS_c1 | 143000 |
kqp_bl | 90000 | ΔE | 80 | krqp_bl | 4000 |
kbl_bh | 80000 | ΔE | 119 | krbl_bh | 900 |
Kbh-qn1 | 100000 | ΔE | 29 | Krbh-qn1 | 33000 |
kbh_qn2 | 250000 | ΔE | 50 | krbh_qn2 | 25000 |
kc1c | 260 | ||||
kqHbnd | 3700 | krqHbnd | 2600 | ||
kqnbnd | 7000 | krqnbnd | 200 | ||
kqpdis | 3600 | krqpdis | 1000 | ||
kqhnds | 4000 | krqhnds | 2500 | ||
kros | 0.02652 |
Reverse rate constants marked (Kr) are calculated from the respective forward rate constants and midpoint potentials (ΔE) as described in
The overall process catalyzed by complex I is oxidation of NADH coupled with ubiquinone reduction and pumping 4 protons from negative to positive side of the membrane:
It is assumed that proton translocation is a result of Q reduction (with proton binding) at the negative side and its oxidation (and proton release) at the positive side. If several protons are translocated per one electron, then this electron must pass several cycles of Q reduction and oxidation. Such mechanism, similar to that accepted for complex III, called Q-cycle, was suggested for complex I (see e.g.
The initial step of such transport is the oxidation of NADH coupled with the reduction of FMN; further, electrons from FMN pass through a relay of eight different iron-sulfur (Fe-S) containing centers
The mechanism of interaction of N2 center with ubiquinone that results in the translocation of four protons from matrix to cytosol and one ubiquinol synthesized is not fully understood. Here we implemented in the model a proposed mechanism, which we consider as a working hypothesis that could be checked by the analysis of model behavior. In this way the model could serve as a tool for checking different possible mechanisms.
According to the EPR data
The proposed mechanism of N2-ubiquinone interactions, which we implemented in the model, is shown in
Numbers above or below a species indicate the redox state of the complex as a combination of electron transporters. The last two digits indicate the presence (1) or absence (0) of two valence electrons of FMN (not shown graphically). The third digit from the right denotes the state of the N2 center, the next two digits from the right indicate the presence or absence of two valence electrons of Q/Q−/QH2 at the n-site. The next two digits from the right indicate the valence electrons of Q/Q−/QH2 at the p-site. Numbers 0–8 above arrows denote individual reactions. 0, FMN reduction by NADH; 1, electron transition from FMN to the N2 center; 2, electron transition from reduced N2 to n-site ubiquinone. This interaction results in electron transfer from p-side ubiquinol to n-side semiquinone, which is coupled to binding of two protons taken from the matrix side and release of two protons to the intermembrane space. 3, ubiquinol thus produced is released and p-site semiquinone changes its position, releasing the p-site, which binds the released ubiquinol; 4, n-site semiquinone takes an electron from p-site ubiquinol and forms ubiquinol, taking two protons from the matrix, while the p-site semiquinone formed releases two protons to the p-side of the membrane. 6, ubiquinol formed at the n-site dissociates and semiquinone bound at the p-site changes its location, binding to the n-site. 7, the non-paired electron of N2 is captured by n-site semiquinone, which subsequently takes two protons from the matrix and is converted to ubiquinol. 8, release of n-site bound ubiquinol, and binding of ubiquinol at the p-site and ubiquinone at the n-site.
0. Reduction of oxidized FMN by NADH.
In traditional form this equation is expressed as
The ratio of rate constants from I.0.1 could be found from the known redox potentials. Equilibrium constant for this reaction as a function of midpoint electrochemical potentials could be found from the condition of equality of electrochemical potentials at equilibrium:
1. Reduction of the N2 center by FMN (step 1 in
2. Reduction of Qn by the reduced N2 center (first electron) and by QH2 bound at Qp center (second electron):
We grouped together these two reactions:
3. Dissociation of QH2n at n-site, transition of p-site SQp to the n-site and binding of dissociated QH2n at p-site.
In this step the three reactions are combined: dissociation of QH2 formed at n-site, change of position of p-site bound semiquinone, and binding QH2 at p-site. Overall in binary form:
4. Second electron (from radical FMN−, which by convention occupied the right position) passes to N2 converting 0 into 1 in the third position from the right:
The transition of second electron characterized by the same ΔEm as accepted in (I.1), but it is not related with proton binding or release, therefore the right hand side value of (I.1.3) equals to the ratio kf/kr.
5. Reduction of N2 by FMN in step 4 induces the interaction of n-site semiquinone with p-site quinol resulted in the production of n-site quinol and p-site semiquinone coupled with the translocation of two protons:
6. The reduction of n-site semiquinone by N2 coupled with the binding of two protons:
7. QH2 dissociates, Q binds at n-site and QH2 binds at p-site, overall:
kfI0 | 640000 | ΔE | −20 | krI0 | 880000 |
kfI1 | 157000 | ΔE | 93 | krI1 | 4200 |
kfI2 | 770000 | ΔE | 60 | krI2 | 80000 |
kfI2 | 23000 | krI2 | 150 | ||
kfI4 | 157000 | ΔE | 93 | krI4 | 4200 |
kfI5 | 190000 | ΔE | 107 | krI5 | 3000 |
kfI6 | 160000 | krI6 | 16000 | ||
kfI8 | 200000 | krI8 | 3000 |
The units are the same as described in
Although the mathematical description of complex I and complex III are similar, they differ in the strictness of rules for electron transport and proton translocation. For complex III the transition between two transporters allowed for any states of other transporters. This assumes participation of all 400 redox forms in electron transport. For complex I the rules accepted in the model allow participation in electron transport only several selected form. This illustrates the flexibility of methodology applied.
Proton binding to ubiquinone at the matrix side of the membrane and their dissociation from ubiquinol to the intermembrane space results in the translocation of protons and arising the transmembrane gradient of H+ concentration and electric potential. As described above for complex I, the reactions (I.2), (I.5) and (I.7) reduce ubiquinone each time taking two protons from the matrix. In complex III the reduction of ubiquinone at Qi site by reduced cytochrome bH is coupled with binding two protons taken from the matrix. The rate of this process (v35) is calculated as described in
The differential equation for electric potential difference (ψ) used the same terms as that for proton concentration, but multiplied by a coefficient, which transforms the flux of ions into the change of electric potential:
Substrates for respiration, i.e. NADH and succinate are produced in TCA cycle inside mitochondria and in the model the connection of this part of intracellular metabolism with respiration through these common metabolites is taken into account by the simulations of following reactions.
Since the emphasis of work described here is the operation of respiratory chain, the reactions of TCA cycle were simulated in simplified form, as linear function of each substrate. Such expressions assume that the substrate concentrations are far from saturation, which should be true for the most cases. In this case the usual hyperbolic dependence of enzymatic reactions on substrate concentrations is close to the linear dependence. On the other hand, this simplification allows to avoid such unfavorable situation, when choosing inappropriate Km makes reactions artificially insensitive to substrate changes. Therefore we used such assumption as a first approximation, which could be easily corrected with obtaining more information about the properties of system.
Pyruvate transport and transformation to acetil coenzyme A:
The reactions converting citrate into succinate were joined together, taking into account that NAD+ is used in these reactions:
Succinate not only could be produced in TCA cycle but also transported from outside of mitochondria in exchange to fumarate or malate (which are lumped in one pool in the present version of the model):
The reactions linked with electron transport and respective parameters are summarized in
klk | 1500 | ||
Vsyn | 0 | KmADP | 0.01 |
kpyrin | 630 | ||
kcs | 1300 | ||
ktca | 750 | ||
VSDH | 170 | ||
KmQ | 0.5 | Kmsuc | 0.1459 |
ksfe | 6.5 | ||
kspe | 270 | ||
kMDHf | 460 | 460 | |
kme | 0.0003 |
Maximal rates (Vmax) are expressed in (nmol/mg prot)/s, Km are expressed in nmol/mg prot, rate constants for bimolecular reactions are in s−1·(mg prot)−1, monomolecular reactions are in s−1.
As the presented equations show, although the expressions for reaction rates are simplified, the stoichiometry of succinate and NADH production and succinate transport is reflected precisely in the model and this was the most important for the presented step of study of the link between central metabolism and ROS production by electron transport chain and the role of reverse electron transport in this process.
The whole model contains (22−6)+(18−7)+11 = 51 parameter (22 for complex III, 18 for complex 1, and 11 for the rest of reactions simulated). The six parameters of complex III and seven parameters of complex I are defined by the known values of midpoint potential. The other parameters were validated by fitting experimental data. To fit the experimental data our modification of Simulating Annealing algorithm was implemented in the way similar to that in
The fitting algorithm made the following actions:
made the stochastic perturbation of given set of parameters (Vmax for the reactions of TCA cycle and substrate transport through the membrane)
performed coordinate descent, taking the parameters one by one and changing them in the direction, which decreased χ2
after reaching the local minimum of χ2 the program saved the respective set of parameters
returned back to step 1.
The cycles of perturbations and coordinate descent repeated thousands times and saved sets of parameters were analyzed: program read the saved sets with corresponding values of χ2, defined the best fit (absolute minimum of χ2), the set of parameters, corresponding to the best fit, and defined confidence intervals for the parameters using the criterion of Δχ2
All procedures involving animals were approved by Children's Hospital of Pittsburgh and were in compliance with “Principles of Laboratory Animal Care” and the current laws of the United States.
The scheme of reactions performed by complex III as it is generally accepted (considered in Selivanov et al, 2009). One of two electrons taken from ubiquinol (QH2), which releases its two protons into the intermembrane space, recycles through cytochromes bh and bl reducing another quinone. The other electron continues its way to oxygen through cytochromes c1 and c and complex IV. Complexes I and II provide QH2. The reactions 0–12 are described in detail in the text.
(0.04 MB TIF)
Simulation of time course of reduction of cytochromes bH (thick grey line) and c1 (thin black line), and ubiquinone (dashed line). This simulation was made using initial set of parameters. Ordinate represents the content of reduced forms in nmol/mg of protein, time units are arbitrary.
(0.02 MB TIF)
Simulation of time course of reduction of cytochromes bH performed with various values of dissociation constants for Q ans QH2 species. Curve 0 calculated with initial values of parameters taken in (Selivanov et al, 2009), curve 1 calculated with the tenfold decrease of Kd for QH2 and Q binding at Qo and Qi respectively, and the tenfold increase of Kd for Q and QH2 dissociation at Qo and Qi respectively. All the changes favor forward direction of Q-cycle. Curve 2 calculated favoring the reverse direction of Q-cycle by the tenfold decrease of initial value of Kd for QH2 dissociation, and all other parameters as for curve 1.
(0.03 MB TIF)
Simulation of time course of reduction of cytochromes bH performed with various combinations of ΔEm for the first an second electron transitions from bH to Q at Qi. In all presented cases Em( bHox/bHred) = 61 mV. Curve 0 is the same as in
(0.03 MB TIF)
Sensitivity of simulation of mitochondrial respiration with regards to the parameters. First column gives the list of parameters, next four columns give the relative change of respectively dynamics of NAD+ reduction in the absence and presence of rotenone, uncoupled respiration fueled by succinate, and pyruvate/malate. Next four columns give the relative change of SQ at Qo site of complex III, in the same four simulations as above, then, relative change of SQ at Qn site of complex I, then FMNH, and finally, reduced N2 centers. The highest changes marked black.
(0.03 MB XLS)
Analysis of triphasic dynamics of cytochrome bH reduction using the model of Complex III from our publication (PLoS Comput Biol 2009, 5(12): e1000619) for the validation of parameter.
(0.08 MB PDF)