Modeling energy depletion in rat livers using Nash equilibrium metabolic pathway analysis

Abstract

The current gold standard of Static Cold Storage (SCS), which is static cold storage on ice (about + 4 °C) in a specialized media such as the University of Wisconsin solution (UW), limits storage to few hours for vascular and metabolically active tissues such as the liver and the heart. The liver is arguably the pinnacle of metabolism in human body and therefore metabolic pathway analysis immediately becomes very relevant. In this article, a Nash Equilibrium (NE) approach, which is a first principles approach, is used to model and simulate the static cold storage and warm ischemia of a proposed model of liver cells. Simulations of energy depletion in the liver in static cold storage measured by ATP content and energy charge are presented along with comparisons to experimental data. In addition, conversion of Nash Equilibrium iterations to time are described along with an uncertainty analysis for the parameters in the model. Results in this work show that the Nash Equilibrium approach provides a good match to experimental data for energy depletion and that the uncertainty in model parameters is very small with percent variances less than 0.1%.

Figure 1

Overview of rat liver procurement, hypothermic preservation, and machine perfusion. (A) Temperature profile of static cold storage (SCS), Sub-Normothermic Machine Perfusion (SNMP), (B) Perfusion system 1. peristaltic pump, 2. media, 3. bubble trap, 4. membrane oxygenator, 5. pressure transducer, 6. pressure monitor, 7. organ basin; Steps in liver recovery, storage and perfusion starting with (C) liver in situ pre-flush, (D) procured and on ice post-flush, (E) at 24 h cold storage in UW solution, (F) Post lactated ringers flush, (G) starting SNMP, (H) end SNMP 3 h.

Figure 2

Superstructure representation of liver energy metabolism for study of preservation.

Figure 3

Nash equilibrium predictions of ATP, ADP, and AMP content (mM), and energy charge for static cold storage (SCS) as a Function of Storage Time: (a) ATP content (mM): NE simulation iterations, least-squares fit of NE iterations, Berendsen et al., Bruinsma et al., (b) ADP content (mM), (c) AMP content (mM), (d) Energy charge.

Figure 4

Time profile of select metabolites and pH during cold storage: (a) Lactate concentration, (b) Cumulative ammonia generation, (c) Cumulative urea synthesis, (d) pH. NE simulation iterations, least-squares fit of NE simulation iterations.

Figure 5

Snapshots of key transport fluxes as a function of time at days 1, 3 and 6 in static cold storage. Flux colors: green = TCA cycle, light blue = urea cycle, gold = fatty acid synthesis, red = glutaminolysis, purple = citrate shuttle, dark red = malonyl CoA. Higher fluxes are indicated by thicker lines.

Figure 6

Parameter Uncertainty Probability Density Functions for 100 Static Cold Storage Simulations. (a) ATP content (mM), (b) ADP content (mM), (c) AMP content (mM), (d) Energy charge.

Figure 7

Nash equilibrium predictions of ATP, ADP, and AMP content (m), and energy charge for warm ischemia (WI) as a Function of Time: (a) ATP content (mM): NE simulation iterations, least-squares fit of NE iterations, Kamiike et al. (rat liver), Bore et al. (rat kidney), Harrison et al. (rat heart), (b) ADP content (mM), (c) AMP content (mM), (d) Energy charge.