Scheme of the kinetic model.

<p>The scheme, equations and parameter values correspond to the kinetic model published previously <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080018#pone.0080018-Puigjaner1" target="_blank">[25]</a>. Parameters for HK: <i>K_M</i> = 0.40 mM, <i>K_i</i> = 0.11 mM. Parameters for GPI: <i>V^f_GPI</i> = 12474 nmol mg prot⁻¹ min⁻¹, <i>V^b_GPI</i> = 18125 nmol mg prot⁻¹ min⁻¹, <i>K_MS</i> = 0.48 mM, <i>K_MP</i> = 0.27 mM. Parameters for PFK: <i>K_S</i> = 0.061 mM, <i>h</i> = 1.47. Parameters for ALD: <i>V_ALD</i> = 6000 nmol mg prot⁻¹ min⁻¹, <i>K_M</i> = 0.13 mM. Limiting rates for HK (<i>V_HK</i>) and PFK (<i>V_PFK</i>) decrease at increasing values for Hg²⁺ and Cd²⁺ following <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080018#pone.0080018.e001" target="_blank">equations (1)</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080018#pone.0080018.e002" target="_blank">(2)</a>, respectively for Hg²⁺ and Cd²⁺, with <i>V⁰_HK</i> = 63.0 nmol mg prot⁻¹ min⁻¹ and <i>V⁰_PFK</i> = 434 nmol mg prot⁻¹ min⁻¹.</p

Model predictions showing the dependence of G6P concentrations on HK and PFK limiting rates.

<p>The proportional dysregulation predicts the broken grey line. The shades in the panels report the predicted G6P concentrations when the limiting rates of HK and PFK do not change proportionally. Solid black lines correspond to the model predictions for different levels of pre-incubation with Cu²⁺ (A), Cd²⁺ (B) and Hg²⁺ (C): they indicate how the metals change the limiting rates of the two enzymes and the consequent changes in metabolite concentrations. The same plot is for F6P, as G6P and F6P are in rapid equilibrium through the reaction catalysed by GPI.</p

Schemes for mechanisms of enzyme irreversible inhibition.

<p>Mechanisms of irreversible inhibition of HK activity and PFK activity by Hg²⁺ (A) and Cd²⁺ (B). <i>E</i> represents HK or PFK, <i>S</i> the respective substrate, <i>ES_n</i> the enzyme-substrate complex (HK follows a Michaelis-Menten equation (n = 1), whilst PFK is an allosteric enzyme (n>1)). <i>P</i> represents the products of the respective reactions, <i>X</i> the metal ions (Cd²⁺ or Hg²⁺), whilst <i>n</i> is the number of substrate binding sites and <i>m</i>+1 is the number of metal ion (<i>X</i>) molecules that can be bound irreversibly to the enzyme. The best agreement to the experimental results was obtained with m = 1 for HK and m = 2 for PFK.</p

Position for most relevant candidates to irreversible inhibition.

<p>(A) Cys 581 and Cys 794 on intersubunit interface of HK, (B) Cys 233 near to ATP binding site on PFK.</p

HepatoDyn: A Dynamic Model of Hepatocyte Metabolism That Integrates ¹³C Isotopomer Data

<div><p>The liver performs many essential metabolic functions, which can be studied using computational models of hepatocytes. Here we present HepatoDyn, a highly detailed dynamic model of hepatocyte metabolism. HepatoDyn includes a large metabolic network, highly detailed kinetic laws, and is capable of dynamically simulating the redox and energy metabolism of hepatocytes. Furthermore, the model was coupled to the module for isotopic label propagation of the software package IsoDyn, allowing HepatoDyn to integrate data derived from ¹³C based experiments. As an example of dynamical simulations applied to hepatocytes, we studied the effects of high fructose concentrations on hepatocyte metabolism by integrating data from experiments in which rat hepatocytes were incubated with 20 mM glucose supplemented with either 3 mM or 20 mM fructose. These experiments showed that glycogen accumulation was significantly lower in hepatocytes incubated with medium supplemented with 20 mM fructose than in hepatocytes incubated with medium supplemented with 3 mM fructose. Through the integration of extracellular fluxes and ¹³C enrichment measurements, HepatoDyn predicted that this phenomenon can be attributed to a depletion of cytosolic ATP and phosphate induced by high fructose concentrations in the medium.</p></div

Summary of candidate Cys residues.

<p>Summary of Cys residues with more than 30% exposed side chain or related to functionally relevant sites. Most relevant candidates for irreversible inhibition are shown in bold.</p

Bar graphs representing the experimentally determined metabolite productions (3.A) and isotopologue fractions (3.B) in experimental conditions.

<p>Measurements were taken after incubating hepatocytes for 2 hours with 20 mM glucose 50% enriched in [1,2-¹³C₂]-glucose and 3 mM fructose (condition A1), 20 mM glucose and 3 mM fructose 50% enriched in [U-¹³C₆]-fructose (condition A2) and 20 mM glucose 50% enriched in [1,2-¹³C₂]-glucose and 20 mM fructose (condition B). The red dot indicates the value fractions simulated by HepatoDyn using the best fit parameter set. Results of the isotopologue fractions are reported as m0, m1, m2, etc. where m0, m1, m2… indicate the number of ¹³C atoms in the isotopologue fractions of a given metabolite.</p

Schematic representation of the metabolic network used in the model.

<p>In this representation, reactions associated with the glycolytic and gluconeogenic pathways are coloured in blue, reactions associated with glycogen metabolism are coloured in purple, reactions associated with the pentose phosphate pathway are coloured in pink, reactions associated with the Krebs cycle are coloured in orange, reactions associated with fatty acid metabolism are coloured in red and other reactions associated with redox and energy metabolism are coloured in green. Specifically, the reactions id of each reaction represented are 1:glctr, 2: gka, 3 g6pasea, 4: gkb, 5: g6paseb, 6: gpia, 7: gpib, 8: pfkla1, 9: fbasea1, 10: pfklb1, 11: fbaseb1, 12: pfkla2, 13: fbasea2, 14: pfklb2, 15: fbaseb2, 16: aldo1, 17: aldo2, 18: aldo3, 19: tim, 20: trik, 21: fruhk, 22: frutr, 23: gapdh, 24: pgk, 25: pgm, 26: eno, 27: pepck, 28: pk, 29: ldh, 30: lactr, 31: pyrtr, 32: mpyrtr, 33: pc, 34: dic, 35: pglm, 36: ugt, 37: gs, 38: gp, 39: g6pdh, 40: pgndh, 41: rpi, 42: rul5pepi, 43: tk1, 44: tk2, 45: tk3, 46: ta, 47: pdh, 48: cs, 49: aco, 50: idh, 51: kdh, 52: scs, 53: sdh, 54: fh, 55: mmdh, 56: malic, 57: citmtr, 58: citly, 59: acoacar, 60: fasyn, 61: box, 62: aatc, 63: aspglumtrans, 64: aatm, 65: malkgmtrans, 66: cmdh, 67: transa, 68: glutr, 69: glyc3pcdh, 70: glyc3pmdh, 71: nadhdh, 72: coqhoxi, 73: atpase, 74: pimtr, 75: pitr, 76: ppase, 77: atpmtrans, 78: cndk1, 79: cndk2, 80: mndk and 81 adk. Invisible reactions are not shown for clarity. The full lists of metabolites and reactions can be found on <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004899#pcbi.1004899.s010" target="_blank">S1</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004899#pcbi.1004899.s011" target="_blank">S2</a> Tables respectively.</p

Example of how ODEs are automatically built for isotopomers and metabolites consumed or produced by the pyruvate dehydrogenase catalysed reaction (PDH).

<p>PDH irreversibly transforms mitochondrial pyruvate (mPyr), NAD (mNAD), and coenzyme A (mCoA) into mitochondrial acetyl-CoA (mACoA) and NADH (mNADH). The system of differential equations is solved taking into account all equations for total concentrations of metabolites and for concentrations of isotopomers. From the previous step in the simulation, the PDH flux (J_pdh) is computed, which is a function of the concentrations of the reactants and products (m) and the kinetic parameters of PDH (p). For the ODEs describing the concentration of metabolites the computed value is added (+ =) and subtracted (- =) for products and substrates, respectively. For the ODE describing a particular isotopomer, the flux value is scaled according to the relative abundance of the isotopomer for the substrate (mPyr_i) and the resulting scaled flux (J_PDHi) is added (+ =) and subtracted (- =) to d[mACoA_i]/dt and d[mPyr_i]/dt, respectively. Isotopomers are not simulated for CoA, NAD or NADH because it is assumed that ¹³C from labelled substrates does not propagate to such metabolites.</p

Plot of the simulated concentrations over time for extracellular fructose (eFru), fructose 1-phosphate (Fru1P), cytosolic phosphate (cPi) and cytosolic ATP (cATP).

<p>Specifically, the simulated concentrations in hepatocytes incubated with 20 mM glucose and 3 mM fructose (conditions A1 and A2, described in the main text) or 20 mM glucose and 20 mM fructose (condition B, described in the main text) are shown. The red plot indicates the values predicted with the best fit parameter set and the grey area indicates the estimated range of variations taking parameter sets within the 95% confidence intervals derived from the identifiability analysis.</p