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Particle-based modelling of isotope exchange at equilibrium in hyperpolarized [1-¹³C]pyruvate MR

Dylan Archer Dingwell^1,2 and Charles H Cunningham^1,2
¹Medical Biophysics, University of Toronto, Toronto, ON, Canada, ²Physical Sciences, Sunnybrook Research Institute, Toronto, ON, Canada

Synopsis

Keywords: Biology, Models, Methods, Modelling

Motivation: Isotope exchange at equilibrium complicates interpretation hyperpolarized [1-¹³C]pyruvate MR. Modelling this phenomenon could help to quantify the effect of exchange on HP MR signal.

Goal(s): Investigate how isotope exchange (compensatory backward conversion of unlabeled lactate concurrent with labeled lactate production) occurs and affects hyperpolarized [1-¹³C]pyruvate MR.

Approach: Develop a realistic computational model of pyruvate-lactate interconversion and apply it to characterize how different levels of endogenous lactate influence metabolic reaction kinetics and exchange.

Results: Elevation of unlabeled lactate increases isotope exchange at equilibrium. Net production of lactate occurs unless total lactate exceeds its equilibrium ratio with total pyruvate.

Impact: This in silico model of isotope exchange in hyperpolarized [1-13C]pyruvate MR realistically replicates spectroscopic measurements, with particle-level data for a range of conditions providing insight into metabolic dynamics relevant to complex cellular architectures with different local equilibria.

Introduction

It is well known that the pyruvate and lactate within the cytosol can exchange between one another through the two-way reaction catalyzed by the LDH enzyme family. This can confound interpretation of ¹³C-metabolite signals due to the phenomenon of “isotope exchange at equilibrium”.¹ In this scenario, [1-¹³C]lactate production occurs alongside compensatory reactions involving the unlabeled metabolite pools, resulting in zero net flux from pyruvate to lactate, as depicted in Figure 1. Homeostatic equilibrium generally favors a high ratio of lactate to pyruvate,^2–4, but hyperpolarized ¹³C MR (HP ¹³C MR) perturbs this state through injection of 250 mM [1-¹³C]pyruvate, supplying potentially supraphysiological levels of exogenous pyruvate to cells.^5,6 Since HP ¹³C MR signals only reflect labeled metabolites, the degree to which metabolic flux occurs is unclear; forward conversion reactions of [1-¹³C]pyruvate may be counterbalanced by exchange with the endogenous metabolite pool. In this study, we tested whether a particle-based in silico model of pyruvate-lactate interconversion would reproduce isotope exchange at equilibrium, making it useful for understanding the effect of this exchange phenomenon in more complex cell architectures involving cellular compartments with different equilibria, such as the human brain.

Methods

Simulations were conducted using the particle-based biochemical simulator Smoldyn⁷ with the MR module described previously.⁸ The core model was a 10 micron cubic volume containing ¹²C and ¹³C metabolites and LDH complexes bound with NADH or NAD⁺. Diffusion coefficients reference values were: 1120 μm²/s pyruvate,⁹ 1000 μm²/s lactate,^9,10 and 49.9 μm²/s LDH.¹¹ Both ¹²C and ¹³C metabolites could react with enzyme-coenzyme complexes (LDH-NADH, LDH-NAD⁺), with an initial NADH:NAD⁺ ratio of 10. Reaction rate constants were fixed for a time-to-equilibrium under 60 s. Initial particle populations were 100 ¹²C-pyruvate, 1,000 ¹³C-pyruvate, and ¹²C-lactate from 100 to 10,000, and no ¹³C-lactate. Particle populations were tracked over 60 s simulation time and counts of reacting metabolites were recorded at the start (0-1 s) and end (55-60 s).
MR spectroscopic results from an in vitro isotope exchange experiment¹² were replicated using this model. In the reference experiment, hyperpolarized ¹³C-pyruvate was injected over 10 s into a syringe containing 40 mM ¹²C-lactate, 20 mM NAD⁺, 10 mM NADH, and LDH-5. In silico, a zeroth-order reaction was added to instantiate pyruvate particles over 10 s, followed by another 80 s simulation time. Spectroscopic acquisitions of the phantom volume were taken over 90 s using a 2.5° flip angle pulse with 5000 Hz bandwidth, and a matching sequence was used to obtain simulated spectroscopic data.

Results & Discussion

Net production of [1-¹³C]lactate and change in total lactate with variable initial populations of unlabeled lactate are plotted in Figure 2. As expected, higher levels of ¹²C-lactate increase production of [1-¹³C]lactate, with gradually diminishing effects from marginal increases in unlabeled lactate. Simultaneously, the net change in total lactate has a decreasing trend. Figure 3 provides further insight into this phenomenon. In the lower lactate case, with [1-¹³C]pyruvate as the most populated substrate, net lactate production occurs. In the higher lactate case, the number of reactions increases due to the increased overall particle population, so [1-¹³C]lactate production, exchange, and equilibration of the system are all faster; however, the high population of ¹²C-lactate also means that unlabeled metabolites now participate in a higher proportion of reactions relative to labeled metabolites. Under such conditions, the total lactate population goes down, since the balance of rate constants favors an equilibrium with a lower proportion of lactate than in the initial populations. Increased [1-¹³C]lactate is thus not straightforwardly correlated with overall metabolic production of lactate. Because the model implements isotope exchange as a stochastic particle simulation, it is capable of replicating non-linear dynamics which are difficult to describe with first-order kinetic rate equations alone, such as when kinetics are disrupted by depletion of the coenzyme pool. Accurate simulation of such a case from a phantom experiment is plotted in Figure 4: particle population counts (top right) reproduce the in vitro time course (top left) after the latter was corrected for loss of magnetization due to flip-down magnetization and T₁ decay of hyperpolarized substrates. Pyruvate and lactate peak amplitudes from MR spectroscopic measurements also align closely with simulated values using an equivalent pulse sequence (Figure 4, bottom row).

Conclusions

This model is a realistic and versatile in silico implementation of metabolic isotope exchange, a process which is critical to understanding the physiological relevance of HP ¹³C MR results. The model generated results consistent with an in vitro isotope exchange experiment that deviated from simple first-order kinetic rate equations, while providing additional information through particle-scale data.

Acknowledgements

No acknowledgement found.

References

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Figures

Figure 1 - Schematic of the isotope exchange process. LDH-mediated pyruvate-lactate interconversion depends on the coenzyme NADH/NAD⁺, with NADH being critical to fuel the forward reaction converting pyruvate to lactate. The need for replenishment of NADH after forward conversion of labeled pyruvate can transiently promote backward conversion of unlabelled lactate, since that reaction causes the reduction of NAD⁺ to NADH. Thus, [1-¹³C]lactate signal can emerge without net production of lactate.

Figure 2 - Change in ¹³C-labeled and total lactate with increasing ¹²C-lactate population. (A) ¹³C-labeled lactate produced in a 60 s simulation increases with increased unlabeled lactate. (B) Net change in total lactate decreases as additional unlabeled lactate is added to the model. Net production of pyruvate occurs once the lactate proportion surpasses the favored equilibrium ratio (K_eq = 10); this is less physiologically relevant, as endogenous lactate is likely to be closer to equilibrium.

Figure 3 - Results from the in silico model of isotope exchange for high and low unlabeled lactate conditions. (A) When the unlabeled lactate population is low (top), both total and labeled lactate increase over time, decreasing NADH (bottom). The number of reactions involving labeled and unlabeled metabolites is of a similar magnitude (middle). (B) With high unlabeled lactate, most reactions involve unlabeled metabolites (middle), and NADH population increases (bottom), indicating a net reduction in total lactate despite net production of labeled lactate.

Figure 4 - Replication of in vitro isotope exchange in a phantom. On the left, results from Leung (2011) show signal from [1-¹³C]pyruvate and [1-¹³C]lactate in a syringe phantom. Magnetization corrected for T₁ decay (top left) reflects metabolite populations; depletion of NADH arrests buildup of lactate signal around 20 s. Modelling the same reagent ratios reproduces in vitro results (top right). On the bottom, uncorrected plots show the raw MRS signal time courses (left), which are also replicated by MR outputs from the Smoldyn-integrated MR model (right).

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

4719

DOI: https://doi.org/10.58530/2024/4719