Model free approach to kinetic analysis of real-time hyperpolarized 13C magnetic resonance spectroscopy data

Abstract

Real-time detection of the rates of metabolic flux, or exchange rates of endogenous enzymatic reactions, is now feasible in biological systems using Dynamic Nuclear Polarization Magnetic Resonance. Derivation of reaction rate kinetics from this technique typically requires multi-compartmental modeling of dynamic data, and results are therefore model-dependent and prone to misinterpretation. We present a model-free formulism based on the ratio of total areas under the curve (AUC) of the injected and product metabolite, for example pyruvate and lactate. A theoretical framework to support this novel analysis approach is described, and demonstrates that the AUC ratio is proportional to the forward rate constant k. We show that the model-free approach strongly correlates with k for whole cell in vitro experiments across a range of cancer cell lines, and detects response in cells treated with the pan-class I PI3K inhibitor GDC-0941 with comparable or greater sensitivity. The same result is seen in vivo with tumor xenograft-bearing mice, in control tumors and following drug treatment with dichloroacetate. An important finding is that the area under the curve is independent of both the input function and of any other metabolic pathways arising from the injected metabolite. This model-free approach provides a robust and clinically relevant alternative to kinetic model-based rate measurements in the clinical translation of hyperpolarized (13)C metabolic imaging in humans, where measurement of the input function can be problematic.

Figure 1. A representation of the fate of hyperpolarized [1-¹³C]pyruvate (P) that is injected into a system with input function P_in(t).

Observable ¹³C signals originating from [1-¹³C]pyruvate are indicated in red. The schematic shows the transport of pyruvate into a cell, facilitated by MCT1 transporters, and its conversion to other metabolites. Solid lines correspond to the cell membrane and dashed lines to the mitochondrial membrane. is the effective relaxation rate of the hyperpolarized signal for metabolite i. Conversion to metabolites [1-¹³C]lactate (L), [1-¹³C]alanine (A), and [1-¹³C]bicarbonate (B) occur with reaction rates (k), and enzymes that catalyze reactions are shown. k_EL and k_LE are the rates of lactate transport into and out of the cell, governed by the MCT4 transporters. Entry of pyruvate into the TCA cycle results in conversion of the 1-¹³C label to CO₂ and then to bicarbonate. Acetyl-CoA is not seen owing to the [1-¹³C] label of pyruvate being utilized in the formation of CO₂. The grey box indicates the terms that need to be considered for the AUC ratio analysis method when the reaction of interest is pyruvate-lactate conversion, whereas kinetic modeling requires fitting of all terms depicted here, except for acetyl-CoA.

Figure 2. The sum of 128 dynamic ¹³C spectra from representative in vitro (top) and in vivo (bottom) data acquired after injection of hyperpolarized [1-¹³C]pyruvate.

In vitro spectra were acquired at 11.7 T from an SW1222 colon carcinoma cell suspension. Peaks arising from pyruvate (171 ppm), lactate (183 ppm) and pyruvate hydrate (179 ppm), an unreactive molecule formed from hydration of pyruvate. A very small peak at 177 ppm, attributed to alanine, was only observable once spectra were summed. In vivo spectra were acquired at 7 T from a control HT29 colon carcinoma xenograft and shows peaks arising from pyruvate, lactate, pyruvate hydrate and alanine.

Figure 3. Representative dynamic spectra from a WM266.4 melanoma cell suspension.

Kinetic modeling was performed using a 2-site (left) and 3-site (right) model. Total (T), intracellular (I) and extracellular (E) [1-¹³C]lactate fits, derived from the 3-site kinetic model are shown. Residuals between the data and the model are shown (central row). The concentration curves (bottom) were generated by correcting data for hyperpolarized relaxation.

Figure 4. Representative dynamic ¹³C time-courses from an in vivo HT29 colon carcinoma xenograft at 7 T.

The model fits to pyruvate, lactate and alanine are shown with a solid line and residuals between the data and the plots are displayed.

Figure 5. In vitro AUC ratios plotted against forward rate constant (k_PL), derived from the 2-site model.

Data is normalized to initial pyruvate concentration and cell number. An excellent correlation is observed between AUC ratio and k_PL across a range of cell lines. Clustering between cell types can also be seen, and spread between data points of the same cell type tends to be in the direction of the best-fit line.

Figure 6. In vitro AUC ratios plotted against forward rate constant (k_PL), derived from the 3-site model.

Data is normalized to initial pyruvate concentration and cell number. A strong correlation is observed between AUC ratio and k_PL across a range of cell lines. Clustering between cell types can also be seen.

Figure 7. In vivo AUC ratios plotted against forward rate constant (k_PL), derived from kinetic modeling.

Data was acquired from tumor xenografts at 3 T (triangles) or 7 T (circles). A strong correlation is observed between AUC ratio and k_PL at 3 T and 7 T for both HT29 and SW1222 xenografts. Drug treatment with dichloroacetate (DCA) did not appear to affect the relationship between k_PL and AUC ratio.