Abstract
Mitochondrial metabolism is of central importance to diverse aspects of cell and developmental biology. Defects in mitochondria are associated with many diseases, including cancer, neuropathology, and infertility. Our understanding of mitochondrial metabolism in situ and dysfunction in diseases are limited by the lack of techniques to measure mitochondrial metabolic fluxes with sufficient spatiotemporal resolution. Herein, we develop a new method to infer mitochondrial metabolic fluxes in living cells with subcellular resolution from fluorescence lifetime imaging of NADH. This result is based on the use of a coarse-grained model of mitochondrial metabolism. We test the model in mouse oocytes subject to a wide variety of perturbations by comparing predicted fluxes through the electron transport chain to direct measurements of oxygen consumption rate. Using this method, we discover a subcellular spatial gradient of mitochondrial metabolic flux in mouse oocytes. This label-free technique will help provide new insights into the spatiotemporal regulation of metabolic fluxes in developing organisms and in diseases.
Introduction
Decades of extensive work have produced a remarkable body of detailed information about the biochemistry of mitochondrial energy metabolism (Salway, 2017). In brief, metabolites, such as pyruvate, are transported into mitochondria, where they are broken down and their products enter the tricarboxylic acid cycle (TCA). The TCA is composed of a number of chemical reactions, which ultimately reduces NAD+ to NADH. NADH and oxygen are then utilized by the electron transport chain (ETC) to pump hydrogen ions across the mitochondrial membrane. ATP synthase uses this proton gradient to power the synthesis of ATP from ADP (Mitchell, 1961). The activities of mitochondrial energy metabolism are characterized by the fluxes through these pathways: i.e. the mitochondrial metabolic fluxes. However, despite the wealth of knowledge concerning mitochondrial biochemistry, it is still unclear what processes set mitochondrial metabolic fluxes in cells (Dumollard et al., 2007; Blerkom, 2011; Yellen 2018) or precisely how these fluxes are misregulated in diseases (Brand and Nicholls, 2011; Lin and Flint Beal, 2006; Wallace, 2012; Bratic and Larsson, 2013; Lowell and Shulman, 2005; Mick et al., 2020). The limitations of current techniques for measuring mitochondrial metabolic fluxes presents a major challenge. In particular, there is a lack of techniques to measure mitochondrial metabolic fluxes with subcellular spatial resolution. Bulk biochemical techniques, such as measures of oxygen consumption and nutrient uptake rates (Ferrick et al., 2008; Houghton et al., 1996; Lopes et al., 2005), and isotope tracing by mass spectrometry (Wiechert, 2001), require averaging over large populations of cells. Such techniques cannot resolve cellular, or subcellular, metabolic heterogeneity (Takhaveev and Heinemann, 2018; Aryaman et al., 2019). Biochemical approaches for measuring mitochondrial metabolic fluxes are also often destructive (Wiechert, 2001; Saks, et al 1998), and thus cannot be used to observe continual changes in fluxes over time. Fluorescence microscopy provides a powerful means to measure cellular and subcellular metabolic heterogeneity continuously and non-destructively, with high spatiotemporal resolution. However, while fluorescent probes can be used to measure mitochondrial membrane potential (Perry et al., 2011) and the concentration of key metabolites (Imamura et al., 2009; Berg et al., 2009; Díaz-García et al., 2017; Martin et al., 2014), it is not clear how to relate those observables to mitochondrial metabolic fluxes.
Endogenous NADH has long been used to non-invasively probe cellular metabolism because NADH is autofluorescent, while NAD+ is not (Heikal, 2010). Fluorescence lifetime imaging microscopy (FLIM) of NADH autofluorescence allows quantitative measurements of the concentration of NADH, the fluorescence lifetimes of NADH, and the fraction of NADH molecules bound to enzymes (Becker, 2012; Becker, 2019; Bird et al., 2005; Skala et al., 2007; Heikal, 2010; Sharick et al., 2018; Sanchez et al., 2018; Sanchez et al., 2019; Ma et al., 2019). It has been observed that the fraction of enzyme-bound NADH and NADH fluorescence lifetimes are correlated with the activity of oxidative phosphorylation, indicating that there is a connection between NADH enzyme-binding and mitochondrial metabolic fluxes (Bird et al., 2005; Skala et al., 2007). The mechanistic basis of this empirical correlation has been unclear. Here we show, that if properly interpreted, FLIM of NADH can be used to quantitatively measure flux through the mitochondrial electron transport chain, and thus provides a means to measure mitochondrial metabolic fluxes. Our results are based on a general, coarse-grained NADH redox model. We validate this model in mouse oocytes subject to a range of perturbations by comparing predicted fluxes from FLIM to direct measurements of the rate of oxygen consumption, and by selfconsistency criterion. Using this method, we discovered a subcellular spatial gradient of mitochondrial metabolic fluxes in mouse oocytes. Thus, FLIM of NADH can be used to non-invasively and continuously measure mitochondrial metabolic fluxes with subcellular resolution.
We used meiosis II arrested mouse oocytes as a model system to study mitochondrial metabolism with FLIM of NADH. ATP synthesis in mouse oocytes occurs primarily through oxidative phosphorylation using pyruvate, without an appreciable contribution from glycolysis (Houghton et al., 1996). Mouse oocyte can be cultured in vitro using chemically well-defined media (Biggers and Racowsky, 2002). They can directly take up pyruvate supplied to them or derive it from lactate through the activity of lactate dehydrogenase (LDH) (Lane and Gardner, 2000), and they can remain in a steady state for hours with constant metabolic fluxes. While NADH and NADPH are difficult to distinguish with fluorescence measurements, the concentration of NADH in mouse oocytes is 40 times greater than the concentration of NADPH (Bustamante et al., 2017), so the autofluorescence signal from these cells can be safely assumed to result from NADH.
Results
Quantifying mitochondrial metabolism as a function of oxygen level using FLIM of NADH
To investigate the impact of quantitatively perturbing mitochondria, we continually varied the concentration of oxygen in the media, from 50±2 μM to 0.26±0.04 μM, while imaging NADH autofluorescence of oocytes with FLIM (Figure 1a, top, black curve; Video 1). We used a machinelearning based algorithm to segment mitochondria in the obtained images (Berg et al., 2019) (Figure 1b and Figure 1-figure supplement 1), allowing us to specifically study the response of NADH in mitochondria. The intensity of NADH in mitochondria, I, increased with decreasing oxygen concentration (Figure 1a, top, red), as is readily seen from the raw images (Figure 1a, middle). Restoring oxygen to its original level caused a recovery of NADH intensity, indicating that the observed changes are reversible (Figure 1a; Video 1). We next grouped all detected photons from mitochondria to form histograms of photon arrival times from NADH autofluorescence for each time point (Figure 1a. lower). We fit the histograms using a model in which the NADH fluorescence decay, F(τ), is described by the sum of two exponentials, , where τl and τs are long and short fluorescence lifetimes, corresponding to enzyme-bound NADH and freely-diffusing NADH, respectively, and f is the fraction of enzyme-bound NADH (Sanchez et al., 2018; Sanchez et al., 2019) (Methods).
We repeated the oxygen drop experiments for a total of 68 oocytes. We approximated the slow decrease in oxygen levels as quasistatic, and averaged data from all oocytes to determine how mitochondrial NADH intensity, I, lifetimes, τl and τs, and the fraction of enzyme-bound NADH, f, varied with oxygen level (Figure 1c). We next calibrated the measured intensity in oocytes by comparison with measures of known concentrations of NADH in vitro, and used the experimentally measured long and short lifetimes to correct for the difference in molecular brightness between free and bound NADH (Figure 1-figure supplement 2; Figure 1-figure supplement 3), to determine how the concentrations of free NADH, [NADHf], and enzyme-bound NADH, [NADHb], depend on oxygen level (Figure 1c, lower right). [NADHf] increased as oxygen fell below ~10 μM, while [NADHb] did not vary with oxygen level.
Video 1 | NADH intensity as a function of oxygen level in mouse oocyte. Left: Imaging of NADH from autofluorescence of mouse oocyte. Right: Real time measurement of oxygen level in the culturing media.
Developing coarse-grained NADH redox model to relate FLIM of NADH to activities of mitochondrial metabolic pathways
We next developed a mathematical model of NADH redox reactions to relate these quantitative FLIM measurements to activities of mitochondrial metabolic pathways. NADH is a central coenzyme that binds to enzymes and facilitates redox reactions by acting as an electron carrier. There are two categories of enzymes associated with NADH redox reactions, which together form a redox cycle: oxidases that oxidize NADH to NAD+ and reductases that reduce NAD+ to NADH. The major NADH oxidase in mitochondria is complex I of ETC for eukaryotic cells. There are many NADH reductases in mitochondria because NADH can be reduced through different pathways depending on the energy substrate. These pathways include the TCA cycle, fatty acid catabolism via beta oxidation, amino acid catabolism such as glutaminolysis and the malateaspartate shuttle (Salway 2017). To account for all possible NADH redox pathways, we start with a detailed NADH redox model with N oxidases and M reductases (Figure 2a). NADH and NAD+ can bind and unbind to each oxidase and reductase. Once bound, NADH can be oxidized reversibly to NAD+ by the oxidases, and NAD+ can be reduced reversibly to NADH by the reductases, forming a redox cycle. A complete model of NADH redox reactions would include all of the other metabolites and enzymes associated with these reactions (Salway 2017). In the model described here (Figure 2a), the impact of these metabolites, enzymes, and other factors (i.e. pH, membrane potential, etc.) enter indirectly by affecting the NADH binding and unbinding rates and reactions rates with the oxidases and reductases (Figure 2-figure supplement 1).
FLIM does not resolve the association of NADH with individual enzymes, but quantifies the global bound and free state of NADH. Therefore to relate the FLIM measurements to activities of mitochondrial metabolic pathways, we coarse-grain the detailed model to account for the global activities of the oxidation and reduction pathways in mitochondria. We achieve this by performing an analytically exact coarse-graining of all N oxidases into a single effective oxidase and of all M reductases into a single effective reductase, while preserving the global binding and unbinding fluxes and the global reaction fluxes through the oxidases and reductases (Appendix 2, Figure 2b). The preservation of global fluxes explicitly relates the effective binding and unbinding rates and the reaction rates of the coarse-grained model to those of the detailed model (Appendix 2, Figure 2-figure supplement 1). Thus, the coarse-grained model describes the global NADH redox cycle, without the loss of generality, in the following manner: NADH can be bound to the effective oxidase, NADH · ox, or to the effective reductase, NADH · re, or can be in a freely diffusing state, NADHf. Hence, the concentration of NADH bound to enzymes is, [NADHb] = [NADH · ox] + [NADH · re], and the total concentration of NADH is, [NADH] = [NADHb] + [NADHf]. The kinetics of the effective oxidase and reductase are represented by the forward, , and reverse, , oxidation rates, and the forward, , and reverse, , reduction rates. The model also includes eight binding and unbinding rates of NADH and NAD+ to the oxidase and reductase (Figure 2b). The coarse-grained reaction rates and binding and unbinding rates can be arbitrary functions of metabolite concentrations, enzyme concentrations, and other factors (i.e. pH, membrane potential, etc.). Hence this is a generic model of NADH redox reactions.
Accurately predicting mitochondrial metabolic flux from FLIM of NADH using the NADH redox model
Our key theoretical result, is that this coarse-grained NADH redox model predicts that the oxidative flux of NADH is a product of the turnover rate and the concentration of free NADH (Figure 2c; Appendix 3): where The turnover rate of free NADH, , is proportional to the difference between the NADH bound ratio, β = f/(1 – f), and the equilibrium NADH bound ratio, βeq (i.e. what the bound ratio would be if there was no net flux through the oxidase), with a constant of proportionality, α, that is independent of the reaction rates of the oxidase and reductase. α and βeq can be explicitly related to the binding and unbinding rates of the model (Appendix 3, equation S29 and S31). If detailed biophysical models of the NADH oxidases are available, then parameters of these models can be explicitly mapped to the coarse-grained parameters of the NADH redox model. Appendix 4 and Table 1 contain mappings between the coarse-grained model and a number of previously proposed detailed biophysical models of NADH oxidation in the ETC (Beard, 2005; Korzeniewski and Zoladz, 2001; Hill, 1977; Jin and Bethke 2002; Chang et al., 2011). The central assumption required for the validity of Equation 1 is that the redox reactions, and binding and unbinding processes, can be approximated as being at steady-state (i.e. undergoing only quasistatic changes over perturbations or development).
In mitochondria, the major NADH oxidation pathway is the ETC. Thus, Equation 1 shows that there is a direct connection between quantities that can be measured by FLIM of NADH in mitochondria (i.e. β and [NADHf]) and the flux through the ETC (i.e. Jox). Equation 1 suggests a procedure for using FLIM to infer flux through the ETC: if a condition can be found under which there is no net flux through the ETC, then βeq can be measured with FLIM. Once βeq is known, then subsequent FLIM measurements of β under other conditions allows , and hence Jox, to be inferred (up to a constant of proportionality) (Appendix 5). We applied this procedure to analyze our oxygen drop experiments (Figure 1) by assuming that there was no net flux through the ETC at the lowest oxygen level achieved for each oocyte (implying that the measured value of β at that oxygen concentration corresponds to βeq for that oocyte). This allowed us to obtain a prediction for Jox as a function of oxygen concentration for the oocytes (Figure 3a). To test these predictions, we directly determined Jox as a function of oxygen concentration by measuring the oxygen consumption rate (OCR) of the oocytes using a nanorespirometer (Lopes et al., 2005) (Methods). The direct measurements of Jox from OCR quantitatively agrees with the predictions of Jox from FLIM for all oxygen concentrations (Figure 3a), strongly arguing for the validity of the model and the inference procedure.
We next explored the impact of other perturbations. We first exposed oocytes to sodium oxamate, an inhibitor of lactate dehydrogenase (LDH), which resulted in large changes in the autoflourescence of NADH in mitochondria, including a 29% ± 2% decrease in intensity and a 10% ± 3% increase in bound ratio (Figure 3b). We dropped oxygen levels to determine βeq, and applied Equation 1 to infer the impact of sodium oxamate on Jox at 50 μM oxygen (i.e. control levels of oxygen). Surprisingly, this procedure revealed that while the addition of sodium oxamate greatly impacts FLIM parameters, it is predicted to not affect Jox (p = 0.94), which was confirmed by direct measurements of oocytes’ OCR (Figure 3b; p = 0.90). We next exposed oocytes to FCCP, an uncoupler of oxidative phosphorylation, and repeated the procedure to use FLIM measurements to infer Jox. This resulted in a predicted 32% ± 7% increase in Jox from the addition of FCCP, a result which is statistically indistinguishable from the 37% ± 11% increase measured by OCR (Figure 3c; p = 0.78). The quantitative agreement between predictions from FLIM and direct measurements from OCR under a variety of conditions (i.e. varying oxygen tension, sodium oxamate, and FCCP), demonstrates that Equation 1 can be successfully used to infer flux through the ETC.
The work described above used the relation to predict the flux through the ETC. We next show that the model also predicts a relationship between and the fluorescence lifetime of enzyme-bound NADH, τl, in mitochondria. This provides a second means to use the model to infer , and hence Jox, from FLIM of NADH. Specifically, we assume that NADH bound to the oxidase have a different average lifetime, τox, than NADH bound to the reductase, τre, which is reasonable because NADH bound to different enzymes do exhibit different fluorescence lifetimes (Sharick et al., 2018). This assumption implies that the experimentally measured long lifetime of NADH in mitochondria, τt, is a weighted sum of these two lifetimes, . This, in turn, leads to a non-trivial prediction of the NADH redox model: that τl is linearly related to 1/β (Appendix 5, equation (S47)). Such a linear relationship is indeed observed in individual oocytes subject to oxygen drops (Figure 3d). Experimentally measuring the slope and offset between τl and 1/β, which vary under different conditions (Figure 3d), provides a second means to infer from FLIM measurements (Figure 3-figure supplement 2). We next used the lifetime (τl) method and the bound ratio (β) method to separately infer , and hence Jox, in oocytes subject to a wide variety of conditions (varying oxygen levels, varying pyruvate levels, with sodium oxamate, FCCP, rotenone, and oligomycin). The two methods quantitatively agree under all conditions (Figure 3e, p = 0.98), which is a strong self-consistency check that further supports the use of the model to infer ETC flux from FLIM measurements of NADH (Figure 3-figure supplement 1).
As described above, FLIM of NADH can be used to infer the turnover rate of free NADH because , but the constant of proportionality cannot be determined by FLIM alone. Therefore, the redox model allows FLIM measurements to be used to quantitatively measure relative changes in flux through the ETC. If a separate measurement of flux through the ETC can be obtained at one condition, then the inferred relative changes from FLIM can be converted to absolute measurements. We used oocytes cultured in AKSOM media at 50±2 μM oxygen as a reference state, which, from our OCR measurements yielded Jox = 56.6 ± 2.0μM·s-1 and hence a constant of proportionality between and (β – βeq) of α = 5.4 ± 0.2s-1 (Equation (S45)). Using this value of α, we converted our measurements of relative changes in under different conditions (Figure 3e) to absolute values of (Figure 4-figure supplement 1) and absolute values of Jox (Figure 4). Note that Jox is a flux density with units of concentration per second. Multiplying Jox by the volume of mitochondria in an oocyte gives the total ETC flux in that oocyte. The resulting inferred changes in Jox from FLIM are consistent with expectations (Figure 4b-e). Jox is reduced upon decreasing oxygen level (oxygen is required to run the ETC), upon adding rotenone (which inhibits complex I of the ETC), and upon adding oligomycin (which inhibits ATP synthase and thereby hyperpolarizes mitochondria). Jox increases when FCCP is added (which depolarizes mitochondria). Jox is independent of pyruvate concentrations.
Revealing a subcellular spatial gradient of mitochondrial metabolic flux in mouse oocytes
Our results presented so far comparing the predicted mitochondrial metabolic flux from FLIM with the directly measured mitochondrial metabolic flux from OCR were performed by averaging together FLIM measurements from all mitochondria within an oocyte (Figures 3 and 4). However, FLIM data is acquired with optical resolution, enabling detailed subcellular measurements. To see if there are spatial variations in FLIM measurements within individual oocytes, we computed the mean decay time of NADH for each mitochondrial pixel. The NADH decay times display a clear spatial gradient, with higher values closer to the oocyte center (Figure 5a).
To quantify this gradient in more detail, we partitioned mouse oocytes with equal-spaced concentric rings (Figure 5b), and fitted photon decay curves from mitochondrial pixels within each ring to obtain FLIM parameters as a function of distance from the oocyte center. NADH intensity, bound ratio and long lifetime in mitochondria all display significant spatial gradient within oocytes (Figure 5c). To further explore spatial variations in mitochondria in mouse oocytes, we next used the membrane potential-sensitive dye TMRM, which preferentially accumulates in mitochondria with higher membrane potential (AL-Zubaidi et al., 2019). We observed a strong spatial gradient of the intensity of TMRM in mitochondria within oocytes, with dimmer mitochondria near the cell periphery (Figure 5d, e), indicating that mitochondria near the periphery of the oocyte have a lower membrane potential. This result is robust to locally normalizing TMRM intensity by mitochondrial mass using a membrane insensitive dye (Mitotracker Red FM), or using an alternative membrane potential-sensitive dye, JC-1 (Figure 5-figure supplement 1).
Next, using Equation 1 and βeq obtained at the lowest oxygen level, and confirming that βeq is uniform within the oocyte with complete inhibition of ETC using rotenone (Figure 5-figure supplement 2), we predicted the ETC flux, Jox, as a function of distance from the oocyte’s center. The mitochondrial flux displayed a strong spatial gradient within oocytes, with a higher flux closer to the cell periphery (Figure 5f). Plotting the predicted mitochondrial metabolic flux vs TMRM intensity shows a strong negative correlation between these two variables (Figure 5g), indicating that mitochondrial metabolic flux increases with decreasing mitochondrial membrane potential throughout oocytes. Interestingly, a similar trend is observed upon inhibiting ATP-synthase, which decreases flux (Figure 4e, oligomycin) and increases membrane potential (Brand and Nicholls, 2011), or enhancing proton leak, which increases flux (Figure 4e, FCCP) and decreases membrane potential (Brand and Nicholls, 2011). Thus, the subcellular spatial variation in mitochondrial metabolic flux that we discovered (Figure 5f) might be caused by spatially varying ATP-synthesis or proton leak in mitochondria in mouse oocytes.
Discussion
The NADH redox model is a general model to relate FLIM measurements of NADH to mitochondrial metabolic fluxes
Despite extensive studies and applications of FLIM in metabolic research (Bird et al., 2005; Skala et al., 2007; Heikal, 2010; Sharick et al., 2018; Sanchez et al., 2018; Liu et al., 2018; Sanchez et al., 2019; Ma et al., 2019), it remains a challenge to relate FLIM measurements to the activities of the underlying metabolic pathways in cells. We overcome this challenge by developing a coarsegrained NADH redox model to relate FLIM measurements to mitochondrial metabolic fluxes. The model is constructed by explicitly coarse-graining a detailed NADH redox model with an arbitrary number of oxidases and reductases that represent all the possible enzymes involved in NADH redox reactions. The coarse-graining reduces all oxidases to an effective oxidase and all reductases to an effective reductase. The kinetic rates of the coarse-grained model are related to those of the detailed model by preserving the global fluxes through the oxidases and the reductases. In mitochondria, the coarse-grained oxidase represents the ETC. We have shown that the coarsegrained model predicts that the flux through the ETC is a product of the turnover rate and the concentration of free NADH (Equation 1). The turnover rate is proportional to the difference between the nonequilibrium and the equilibrium NADH bound ratio measured by FLIM of NADH. This model hence provides a generic framework to relate FLIM measurements of NADH to the flux through the ETC in mitochondria.
The model prediction of the ETC flux in Equation (1) is valid even if all of the reaction rates, and binding and unbinding rates, are arbitrary functions of metabolite concentrations, enzyme concentrations, and other variables (such as membrane potential, oxygen concentration, and the presence of added drugs). Remarkably, all the kinetic rates enter Equation (1) through only two effective parameters: α and βeq. We determined the value of α from an OCR measurement (Appendix 5, equation (S45)), and we determined the value of βeq from FLIM of NADH at low oxygen levels (Appendix 5, Figure 3-figure supplement 1). In MII mouse oocyte, a does not significantly vary in response to drug and nutrient perturbations. This is demonstrated by the agreement between predicted ETC flux and measured OCR with a constant a of 5.4 ± 0.2s-1. In contrast, βeq does vary with these perturbations (Figure 3-figure supplement 1). Using these two parameters, we inferred the turnover rate of free NADH, , from FLIM measurements of NADH (Figure 4-figure supplement 1). By multiplying this turnover rate with the concentration of free NADH, [W4DH=], we obtained the ETC flux from Equation (1) (Figure 4). Thus, all the complex behaviors of the binding and unbinding and reaction rates are captured by the variations in FLIM parameters of NADH, and our coarse-grained model provides a generic way to interpret these variations.
Finally, for mouse oocyte, βeq is smaller than β, and α has a positive value. This does not have to be the case, since the model also admits solutions with βeq larger than β and a negative α (Appendix 3, equation (S29)). Hence if a perturbation is observed to decrease the NADH bound ratio β, it does not necessarily imply a decrease of the ETC flux. A similar argument holds for the long lifetime of NADH, where a decrease of NADH long lifetime is not always associated with an increase of the ETC flux (Appendix 5, equation (S47)). Rather, measurements of α and βeq are required to use Equation 1 to infer ETC flux from FLIM of NADH.
The underlying assumptions and limitations of the NADH redox model
In this section, we clarify the underlying assumptions and limitations of the model to facilitate accurate interpretation of FLIM of NADH in different biological contexts.
To use the coarse-grained NADH model, segmentation needs to be performed to separate mitochondrial NADH signal from cytoplasmic NADH signal, because they encode different metabolic fluxes. In mouse oocyte, the segmentation can be reliably performed based on NADH images due to the higher NADH intensity in mitochondria than cytoplasm. Mitochondrial movements are also slow in MII oocyte (Video 1), hence longer exposure times can be used to obtain high contrast NADH images. For cells where NADH contrast is low, such as in yeast cells (Papagiannakis et al., 2016; Shaw and Nunnari, 2002), mitotracker dye (Appendix 1, Figure 1-figure supplement 1) or mitochondrial associated fluorescent proteins (Westermann and Neupert, 2000) will likely be needed for reliable segmentation of mitochondria.
One of the most important assumptions that enables the coarse-grained model to be used to predict fluxes is that the NADH redox cycle can be well approximated as being at steady state, i.e. the rate of change of NADH concentrations is much slower than the kinetic rates, including the binding/unbinding rates and the reaction rates. This is true for mouse oocyte, where the NADH intensity does not significantly change over the course of hours. This assumption also holds for slow processes such as cell cycles (Papagiannakis et al., 2016), which occurs on the timescale of hours compared to timescales of seconds for the kinetic rates. The steady-state approximation could fail for rapid dynamics of NADH, such as the transient overshoot of NADH in neurons induced by acute external stimulus (Díaz-García et al., 2020).
Another assumption is that the dominant autofluorescence FLIM signal comes from NADH, while NADPH, which shares a similar spectrum as NADH, is negligible in mitochondria. This assumption is valid for mouse oocyte, where NADH concentration is 40 times greater than the concentration of NADPH (Bustamante et al., 2017). NADPH autofluorescence might be significant for other cells such as yeast (Park et al., 2016).
Finally, when relating NADH FLIM measurements to the ETC flux we did not explicitly consider the contribution to the flux through FADH2. This is a valid approximation when the FADH2 oxidative flux is much smaller than the NADH oxidative flux, as is often the case since pyruvate dehydrogenase plus the TCA cycle yields 4 NADH molecules but only one FADH2 molecule per cycle. Alternatively, if the FADH2 flux is proportional to the NADH flux then a rescaled value of α can be used in Equation 1 to effectively account for both fluxes. While a proportionality of FADH2 flux and NADH flux is expected under some circumstances, it will not generally hold since FADH2 and NADH can be independently reduced in mitochondria, for example, via the glycerol phosphate shuttle.
Given these underlying assumptions, the model needs to be tested before being applied to different biological systems. The present study provides an example for such tests in mouse oocytes by comparing the predicted ETC flux with directly measured oxygen consumption rate across a wide range of perturbations (Figure 3).
Towards spatiotemporal regulations of metabolic fluxes in cells and tissues
By employing the coarse-grained model described above, FLIM of NADH can be used to measure spatial variations in metabolic fluxes. We used this approach to discover subcellular spatial gradient of mitochondrial metabolic fluxes in mouse oocytes. Metabolic heterogeneities, between and within individual cells, are believed to be widespread, but remain poorly characterized (Takhaveev and Heinemann 2018; Aryaman et al., 2019). We hope that this combination of coarse-grained modeling and FLIM of NADH will also prove useful in studying metabolic heterogeneities in other systems.
Materials and methods
Culturing of mouse oocytes
Frozen MII mouse oocytes (Strain B6C3F1) were purchased from EmbryoTech. Oocytes were thawed and cultured in droplets of AKSOM media purchased from Millipore Sigma in plastic petri dish. Mineral oil from VitroLife was applied to cover the droplets to prevent evaporation of the media. Oocytes were then equilibrated in an incubator at 37°C, with 5% CO2 and air saturated oxygen before imaging. For imaging, oocytes were transferred to a 2μl media droplet in a 35mm glass bottom FluoroDish from WPI covered with 400-500μl of oil. The glass bottom dish was placed in an ibidi chamber with temperature and gas control during imaging. Temperature was maintained at 37°C via heated chamber and objective heater. CO2 was maintained at 5% using gas tanks.
FLIM measurements
Our FLIM system consists of a two-photon confocal microscope with a 40X 1.25NA water immersion Nikon objective, Becker and Hickle Time Correlated Single Photon Counting (TCSPC) acquisition system and a pulsed MaiTai DeepSee Ti:Sapphire laser from Spectra-Physics. NADH autofluorescence was obtained at 750nm excitation wavelength with a 460/50nm emission filter. Laser power at the objective was maintained at 3mW. The scanning area was 512 by 512 pixels with a pixel size of 420nm. Acquisition time was 30 seconds per frame. A histogram of NADH decay times was obtained at each pixel of the image.
Oxygen measurement
Oxygen level was measured in the Ibidi chamber with an electrode-based oxygen sensor (Gaslab). Since the oil layer covering the media droplet was very thin, the oxygen level in the droplet was assumed to be in instant equilibration with the chamber.
Image and FLIM data analysis
To separate mitochondrial NADH signal from cytoplasmic signal, we performed machine learning based segmentation algorithms on NADH intensity images. We used the freeware ilastik (Berg et al., 2019), which implements a supervised learning algorithm for pixel classification. The classifiers were trained to separate mitochondrial pixels from cytoplasmic pixels with a greater than 80% accuracy, as tested by MitoTracker Red FM (Appendix 1, Figure 1-figure supplement 1). We grouped photons from all mitochondrial pixels to obtain a histogram of NADH decay times for each oocyte. To extract the FLIM parameters of NADH bound fraction f, long lifetime τl and short lifetime τs, we fitted the histogram with G = IRF *(C1F + C2), where * indicates a convolution, and IRF is the instrument response function of the FLIM system, measured using a urea crystal. is the two-exponential model for the NADH fluorescence decay. C1 is the amplitude of the decay and C2 is the background noise. The fitting was performed with an custom MATLAB code using a Levenberg-Marquardt algorithm. To obtain the intensity, I, of mitochondrial NADH, we first measured the average number of photons per mitochondrial pixel, and divided it by the pixel area, 0.185μm2, and pixel scanning time 4.09μs. The flux of ETC is inferred using equation 1 for each oocyte. Heatmaps of mean NADH decay times were obtained by computing NADH decay time of each mitochondrial pixel and averaging over neighboring mitochondrial pixels weighted by a gaussian kernel with a standard deviation of 20 pixels. All FLIM measurements were taken from distinct individual oocytes and error bars in all figures of FLIM represent standard error of the mean across different individual oocytes. Number of oocytes is reported with n.
Metabolic perturbations
Oxygen drop experiments were performed by mixing nitrogen-balanced 5% O2 gas with 0% O2 gas at different ratios to create a continuous oxygen drop profile. CO2 was maintained at 5%. Oocytes were imaged for 10mins at 5% O2, 30mins during the continuous drop from 5% O2 to approximately 0% O2, and 20mins after quickly returning to 5% O2. Oxygen levels were simultaneously monitored with an electrode-based oxygen sensor in the ibidi chamber. 5% O2 corresponds to ~50μM of oxygen concentration in the culturing media. All the drug perturbations were performed by equilibrating oocytes in the AKSOM media containing the corresponding drug for 15-30mins before the oxygen drop experiments. 9mM sodium oxamate, 15-60μM rotenone, 5-50μM oligomycin and 1-50μM FCCP were used for the perturbations. Pyruvate perturbations were performed by making KSOM media following Cold Spring Harbor Laboratory protocols with varying concentrations of sodium pyruvate. For oligomycin, FCCP, rotenone and pyruvate perturbations, 9mM of sodium oxamate was also added to the media to suppress cytoplasmic NADH signal for better mitochondrial segmentation. The addition of the oxamate does not change the ETC flux of the mitochondria. All drugs were purchased from Sigma Aldrich. Temperature was maintained at 37°C. Oocytes were selected and assigned to different perturbation groups randomly. Data were also collected in random order for different oocytes.
Oxygen consumption rate (OCR) measurement
The oxygen consumption rate of the oocytes was measured using the nanorespirometer from Unisense (Lopes et al., 2005). A batch of 15 oocytes were placed at the bottom of a glass capillary with a diameter of 0.68mm and a height of 3mm. The capillary well is filled with AKSOM media. After an equilibration time of ~2 hours, a steady state linear oxygen gradient is established in the capillary well due to the balance of oocyte respiration and oxygen diffusion. An electrode-based oxygen sensor (Unisense) is used to measure the oxygen gradient. The oxygen consumption rate is calculated as the product of the oxygen gradient, diffusivity of oxygen in the media, taken to be 3.37 × 10-5cm2/s, and the cross sectional area of the capillary well, which was 0.36mm2. The entire system was enclosed in a custom built chamber with temperature and gas control. Temperature was maintained at 37°C. Oxygen level was continuously varied during oxygen drop experiments, and maintained at the air saturation level for drug and pyruvate perturbations. All OCR measurements were taken from distinct batches of oocytes in groups of 15. Error bars in all figures of OCR represent standard error of the mean across different groups of oocytes normalized by the number of oocytes in each group. Number of oocytes is reported with n. Number of batches is reported with N.
Mitochondrial membrane potential measurement
The spatial distribution of mitochondrial membrane potential within oocytes was measured with a potential-sensitive dye TMRM (Sigma Aldrich). Oocytes were cultured in AKSOM with 100nM TMRM for 30 minutes before imaging. Heatmaps of TMRM intensity were obtained by computing photon counts for each mitochondrial pixel and averaging over neighboring mitochondrial pixels weighted by a gaussian kernel with a standard deviation of 20 pixels. To normalize TMRM intensity by mitochondrial mass, we cultured oocytes in AKSOM with 100nM Mitotracker Red FM and 25nM TMRM for 30 minutes before imaging. We also cultured oocytes in AKSOM with 1μg/ml JC-1 dye for 3 hours before imaging.
Author contributions
X.Y. and D.J.N. conceptualized the work. X.Y. performed the experiments, modeling and data analysis. X.Y. and D.J.N. wrote the manuscript.
Acknowledgements
We thank Carlos Manlio Díaz-García, Gary Yellen, Peter Foster, Easun Arunachalam, Yu-Chen Chao, Bill Ireland and Denis Titov for suggestions, advice, and comments on the manuscript. This work is supported by the National Institute of Health (R01HD092550-01) and the National Science Foundation (PFI-TT-1827309, PHY-2013874, MCB-2052305). X.Y. and D.J.N. acknowledge discussions with participants of the “Cellenergy19” and the “Active20” KITP programs, supported in part by the National Science Foundation Grant No. NSF PHY-1748958, NIH Grant No. R25GM067110, and the Gordon and Betty Moore Foundation Grant No. 2919.02.
Appendix 1 Segmentation of mitochondria and calculation of NADH concentrations
Segmentation of mitochondria
We used Ilastik, a machine-learning-based software for image analysis, to classify pixels in the NADH images containing mitochondria (Berg et al., 2019). For each experiment, we generated a time lapse movie of NADH (Video 1). We used a few images in the movie as the training data set to train the software to classify mitochondrial pixels by manually selecting clustered high brightness pixels. Other pixels are classified as either cytoplasm or background. We then applied the trained pixel classifier to generate a mitochondrial probability map for each image in the entire movie, with each pixel assigned a probability between 0 to 1 to be mitochondrial pixel. Pixels with a probability higher than 0.7 were considered to be mitochondrial pixels.
To test the accuracy of this segmentation algorithm, we immersed the oocytes in media containing MitoTracker Red FM, a dye that specifically labels mitochondria. Pixels with intensity above 60 percentile in the MitoTracker image were considered to be mitochondrial pixels. We imaged NADH and MitoTracker for the same oocyte and compared the resulting distribution of mitochondria (Figure 1-figure supplement 1). The accuracy of the NADH-based segmentation of mitochondria is 80.6 ± 1.0% (SEM) as averaged over 7 oocytes.
Converting NADH intensity to NADH concentrations
Since the molecular brightness of NADH depends on the fluorescence lifetime of NADH, which changes drastically upon binding enzymes, the NADH concentration is not linearly proportional to NADH intensity. FLIM provides an accurate way of measuring NADH concentrations by simultaneously measuring fluorescence intensity and lifetime. We now derive the NADH intensity-concentration relation from the FLIM measurements. Assuming molecular brightness is proportional to the fluorescence lifetime, and therefore that free and bound NADH have different contributions to the measured intensity, we have where I is the intensity of NADH and cs is a calibration factor that depends on the laser power. From equation (S1), we obtained the concentrations of free and bound NADH: where f is the fraction of bound NADH.
To get the calibration factor cs, we titrated NADH in AKSOM solutions and fitted the calibration curve using: where τsol is the lifetime of NADH in solution. τso6 was directly measured by FLIM (Figure 1-figure supplement 2b), allowing us to obtain cs from the fit (Figure 1-figure supplement 2a). Using equations (S2)–(S3), we obtained the free and bound NADH concentrations in mouse oocytes for oxygen drop (Figure 1c) and drug perturbations (Figure 3-figure supplement 1e-f).
FLIM can be used to accurately measure concentrations of bound and free NADH in vitro
To test if absolute concentrations of free and bound NADH can be accurately measured from FLIM of NADH, we prepared solutions with known total concentration of NADH, and titrated the concentration of lactate dehydrogenase (LDH), an enzyme to which NADH can bind. We prepared the solutions with 50 mM TRIS buffer, 150 mM NaCl at pH 7.6 and 37°C. We added a total concentration of 50μM NADH to the solution and titrated LDH concentrations at 0, 1.4μM and 3.5μM. We first performed single exponential fitting of the NADH decay curve at 0μM LDH, where all NADH are free, to obtain the NADH short lifetime (Figure 1-figure supplement 3d). From the NADH intensity (Figure 1-figure supplement 3a), we obtained the calibration factor cs using equation (S4) with [NADHsol] = 50μM. We then fixed the short lifetime and performed two-exponential fitting of the NADH decay curve at LDH concentrations of 1.4μM and 3.5μM to obtain the bound ratio (Figure 1-figure supplement 3b) and long lifetime (Figure 1-figure supplement 3c). As expected, NADH bound ratio increases with LDH concentrations, as there is more enzyme for NADH to bind. Finally, we calculated free NADH concentration [NADHf] and bound NADH concentration [NADHb] using equations (S2) and (S3) from the FLIM parameters. Remarkably, the free and bound concentrations of NADH both change with LDH concentrations but the total concentration remains at 50μM (Figure 1-figure supplement 3e). This result shows that equations (S2)–(S3) can be used to accurately measure the concentrations of free and bound NADH from FLIM measurements of NADH.
Appendix 2 Coarse-graining the detailed NADH redox model
We coarse-grain the detailed NADH redox model (Figure 2-figure supplement 1) by coarse-graining all oxidases into a single effective oxidase and all reductases into a single effective reductase (Figure 2b). We relate the kinetic rates of the coarse-grained model to those of the detailed model by preserving the global binding and unbinding fluxes and the global reaction fluxes through the oxidases and reductases.
We first coarse-grain the oxidases and reductases:
We require the global binding and unbinding fluxes of NADH to the effective oxidase and reductase to be equal to the sum of their binding and unbinding fluxes to all of the individual oxidases and reductases: which leads to
We require the global forward and reverse reaction flux through the effective oxidase and reductase to be equal to the sum of the reaction fluxes through all of the individual oxidases and reductases: which leads to
By applying the same procedure to NAD+, we can obtain the effective reduction rates and the effective binding and unbinding rates of . We omit the derivation here because these rates are not needed to infer ETC flux. We hence explicitly related the kinetic rates of the coarse-grained model (Figure 2b) to those of the detailed model (Figure 2-figure supplement 1).
Appendix 3 Predicting the ETC flux using the coarse-grained NADH redox model
The coarse-grained NADH redox model
We start with the equations characterizing the dynamics of the coarse-grained NADH redox model as described in Figure 2b: where [NADHf] and are the concentrations of free NADH and free NAD+; [NADH · re] and [NAD+ · re] are concentrations of reductase-bound NADH and NAD+; [NADH · ox] and [NAD+ · ox] are concentrations of oxidase-bound NADH and NAD+; k denotes binding (b) and unbinding (u) rates, with subscript r and o denoting reductase and oxidase, respectively; , and are the forward and reverse reaction rates of the reductase; and are the forward and reverse reaction rates of the oxidase. The reaction rates, and binding and unbinding rates, can be arbitrary functions of metabolite concentrations, enzyme concentrations, and other variables (such as membrane potential, oxygen concentration, and the presence of added drugs).
Predicting the ETC flux
The flux through the ETC is
At steady state (or in the quasistatic limit), all the time derivatives are zero. Setting d[NADH · ox]/dt (equation (S18)) to zero, we obtained the steady state flux through the ETC:
Setting d[NADHf]/dt (eqn. (S17)) to zero gives: and using: from which we solved for [NADH · ox]:
Substituting [NADH · ox] in equation (S23) with equation (S26), we obtained our central result:
From equation (S27) we see that the flux through ETC is a product of the turnover rate of free NADH, , and the concentration of free NADH, [NADHf], where and where we defined the NADH bound ratio and its equilibrium counterpart as:
Appendix 4 Connecting the NADH redox model to detailed biophysical models of mitochondrial metabolism
In this section, we show that the coarse-grained NADH redox model described above, and in Figure 2b of the main text, can be directly related to detailed biophysical models of mitochondrial metabolism, including previously published models (Beard, 2005; Korzeniewski and Zoladz, 2001; Hill, 1977; Jin and Bethke 2002; Chang et al., 2011).
In mitochondria, NADH oxidation is catalyzed by complex I of the electron transport chain, which has the overall reaction: where two electrons are transferred from NADH to ubiquinone Q, and 4 protons are pumped out of the mitochondrial matrix. To connect our model with detailed model of complex I, we rewrite the flux through the ETC:
Using where as where
The last equality in Equation (S43) is obtained by assuming that the total concentration of NADH plus NAD+ is constant:
Equation (S40) allows us to connect our coarse-grained model to previously published detailed models of complex I. By equating the flux through complex I, JC1, in previous models to the flux through the ETC in our NADH redox model, Jox, we can determine (and and ) in terms of variables defined in those more detailed models. In Table 1, we summarize the relationship between the NADH redox model and several previously published models of complex I.
Appendix 5 Flux inference procedures using the coarse-grained NADH redox model
Equation (S27), or equivalently equation 1 from the main text, can be used to infer the flux through the ETC, Jox, from FLIM measurements of NADH across a wide range of metabolic perturbations (Figure 3-figure supplement 1). To do so, we infer the turnover rate of free NADH, , and the concentration of free NADH, [NADHf]. The product of and [NADHf] gives Jox. [NADHf] can be obtained using equation (S2) (Figure 3-figure supplement 1e). In this section, we introduce two procedures to obtain : one from the measurement of NADH bound ratio, and the other from the measurement of NADH long fluorescence lifetime.
Inferring from NADH bound ratio β
From equation (S28), . We measure the NADH bound ratio, β, using β = f/(1 – f), where f is the NADH bound fraction obtained by fitting the fluorescence decay curve of NADH (See Methods). We obtain the equilibrium bound ratio, βeq, by dropping the oxygen level to the lowest achievable value with our setup, [O2] = 0.26 ± 0.04 μM in our experiments. Note that βeq changes with culture conditions, and therefore needs to be separately determined for every drug and nutrient perturbation (Figure 3-figure supplement 1h). We obtain α using direct measurement of Jox from oxygen consumption rate (OCR) measurements: where Vm = 9.5 × 104 μm3 is the average volume of mitochondria per oocyte approximated from the area fraction of mitochondria based on the segmentation, where the mitochondrial area fraction is estimated at 46% and oocyte volume at 2 × 105 μm3. Using OCR=2.68±0.06 fmol/s per oocyte in the AKSOM media at 50μM oxygen level, we get α = 5.4 ± 0.2s-1. α is approximated as a constant that does not vary with drug and nutrient perturbations.
Once α is calibrated for one condition using equation (S45), and βeq is determined from an oxygen drop experiment, then subsequent FLIM measurements of β and [NADHf] can be used with equation (S27) to determine the absolute value of (Figure 4-figure supplement 1) and Jox (Figure 4) for all conditions.
Inferring from NADH long fluorescence lifetime τl
In this section, we derive an alternative procedure for determining the turnover rate of free NADH , and hence Jox from equation (S27), using changes in the NADH long fluorescence lifetime. The NADH long fluorescence lifetime, τl, is associated with enzyme-bound NADH (Sharick et al., 2018). In the coarse-grained NADH redox model described above, and in Figure 2b, the enzyme-bound NADH consists of reductase-bound NADH ([NADH · re]) and oxidase-bound NADH ([NADH · ox]). We therefore assume that the experimentally measured NADH long lifetime, τl, is a linear combination of the lifetimes of [NADH · ox] and [NADH · re]: where τox and τre are the fluorescence lifetimes corresponding to the oxidase-bound NADH and reductase-bound NADH, respectively. Substituting [NADH · ox] and [NADH · re] in equation (S46) with β using equations (S25)–(S26) and equation (S30), we derive that the NADH long fluorescence lifetime τl is linearly related to the inverse of the NADH bound ratio 1/β: with
The predicted linear relationship between τl and 1/β is empirically observed during oxygen drop experiments, as shown in Figure 3d and Figure 3-figure supplement 2. This self-consistency check argues for the validity of the assumption in equation (S46).
At equilibrium, when there is no flux through the ETC (i.e. Jox = 0), equation (S47) gives: where τeq is the NADH long lifetime at equilibrium. Using equations (S47) and (S50) in combination with (S28), we obtain in terms of τl: where A and B are the slope and offset of the linear relation between τl and 1/β in equation (S47).
We experimentally measure A and B for each oocyte from the slope and offset of a linear fit between τl and 1/β during oxygen drop experiments across all perturbations (Figure 3d; Figure 3-figure supplement 2). We obtain the equilibrium long lifetime, τeq, by FLIM measurements at the lowest achievable oxygen level, [O2] = 0.26 ± 0.04 μM in our experiments. Once A, B, and τeq are measured, equation (S51) can be used to determine from FLIM measurements of τl. If α is not known, this procedure can only be used to obtain up to a constant of proportionality. If α is independently measured from equation (S45), then equation (S51) can be used to determine the absolute value of (Figure 4-figure supplement 1).
As described in the main text, inferred using equation (S51) produces the same results as inferred using equation (S28) (Figure 3e in the main text). The agreement between these two methods is a strong self-consistency check of the model.
Appendix 6 Spatial gradient of mitochondrial metabolism in mouse oocyte
Subcellular spatial gradient of mitochondrial membrane potential
As shown in the main text, we observed a strong spatial gradient of the intensity of TMRM in mitochondria in oocytes. TMRM is a potential-sensitive dye that preferentially accumulates in mitochondria with higher membrane potential (Figure 5 d-e in the main text). To test whether this spatial gradient is due to the subcellular variation of mitochondrial membrane potential or the variation in mitochondrial mass, we labelled mitochondria with a potential-insensitive dye Mitotracker Red FM to quantify mitochondrial mass, together with TMRM. We did not observe a strong gradient of mitotracker intensity (Figure 5-figure supplement 1b,f) as compared to TMRM intensity (Figure 5-figure supplement 1a,e) within the same oocyte, indicating the mitochondrial mass is uniformly distributed. We further normalized the TMRM intensity by the mitotracker intensity, and observed a strong spatial gradient of the ratio (Figure 5-figure supplement 1c,g). These results suggest that the spatial gradient of TMRM is due to the variation of mitochondrial membrane potential, rather than the variation of mitochondrial mass. Finally, to test the robustness of the result, we used an alternative potential-sensitive dye JC-1, and observed a similar spatial gradient of mitochondrial membrane potential (Figure 5-figure supplement 1d,h). Taken together, these results show that the subcellular spatial gradient of mitochondrial membrane potential is a robust observation that does not depend on the variation of mitochondrial mass or the type of dye used.
βeq is uniform within the oocyte
To obtain subcellular ETC flux as a function of distance to the oocyte’s center using Equation 1 in the main text, we need to know the spatial variation of βeq. While the NADH bound ratio at the lowest oxygen level gives a good approximation for the average βeq of the cell (Figure 3-figure supplement 1h), subpopulations of mitochondria closer to the cell membrane are exposed to slightly higher oxygen level than those away from the cell membrane, obscuring the determination of the spatial variation of βeq. Hence to obtain the spatial variation of βeq throughout the oocyte, we inhibited the ETC completely using 15μM of sodium rotenone, an inhibitor of complex I in the ETC, for an extended period of time until the NADH bound ratio reaches the lowest level. We then fit the NADH decay curves from mitochondrial pixels within equal-distanced concentric rings (Figure 5-figure supplement 2a) to obtain βeq as a function of distance from the oocyte’s center (Figure 5-figure supplement 2b). The resulting βeq is uniform throughout the oocyte and is equal to the average βeq obtained by fitting the decay curve from all mitochondrial pixels in the oocyte at the lowest oxygen level (Figure 3-figure supplement 1h). Therefore, we used the average βeq at the lowest oxygen level to compute the subcellular ETC flux (Figure 5f).
Footnotes
Section "Developing coarse-grained NADH redox model to relate FLIM of NADH to activities of mitochondrial metabolic pathways" and Figure 2 and Appendix 2 are updated to clarify the coarse-graining procedure of the NADH redox model. Discussion section is updated to clarify the assumptions and limitations of the NADH redox model. Appendix 1 is updated to clarify the validity of using FLIM of NADH to measure concentrations of bound and free NADH. Video 1 updated to show the response of NADH to oxygen drop.