Incorporating expression data in metabolic modeling: A case study of lactate dehydrogenase

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Abstract

Integrating biological information from different sources to understand cellular processes is an important problem in systems biology. We use data from mRNA expression arrays and chemical kinetics to formulate a metabolic model relevant to K562 erythroleukemia cells. MAP kinase pathway activation alters the expression of metabolic enzymes in K562 cells. Our array data show changes in expression of lactate dehydrogenase (LDH) isoforms after treatment with phorbol 12-myristate 13-acetate (PMA), which activates MAP kinase signaling. We model the change in lactate production which occurs when the MAP kinase pathway is activated, using a non-equilibrium, chemical-kinetic model of homolactic fermentation. In particular, we examine the role of LDH isoforms, which catalyse the conversion of pyruvate to lactate. Changes in the isoform ratio are not the primary determinant of the production of lactate. Rather, the total concentration of LDH controls the lactate concentration.

Introduction

Modeling of cellular metabolism has a long history of important contributions to biology. Approaches include kinetic modeling, metabolic control analysis, flux balance analysis, and metabolic network analysis (Stephanopoulos et al., 1998). A new era of research in metabolism is now possible, because large-scale expression studies can determine levels of many metabolites (Goodacre et al., 2004, Fan et al., 2004) and metabolic enzymes (Ferea et al., 1999, Kal et al., 1999). In this paper we use metabolic enzyme expression data to guide metabolic modeling, with a focus on small but significant changes in mRNA abundance. Our goal is to understand how biologically realistic changes in mRNA abundance of metabolic enzymes affect cellular metabolism. Previous work integrating expression data with metabolic modeling has been done in yeast (Akesson et al., 2004), but not, to our knowledge, in mammalian systems.

We focus on glycolysis, an essential ATP-producing metabolic pathway. The initial reactions of glycolysis break down glucose into pyruvate. Pyruvate can feed into either the citric acid cycle (aerobic metabolism) or homolactic fermentation (anaerobic metabolism) (Voet and Voet, 2004). The reactions involving pyruvate therefore control this important metabolic branch point. Homolactic fermentation is catalysed by lactate dehydrogenase (LDH) in a compulsory order, ternary reaction (Borgmann et al., 1975). LDH reversibly converts pyruvate and NADH into lactate and NAD+. The isozymes of LDH are tetramers formed from two types of monomers (a third isoform is usually germ-line specific, but can be expressed in cancers (Koslowski et al., 2002)). The two isoforms are labeled H (heart) and M (muscle), and their ratio varies between cell types. The LDH isoform ratio has been proposed to indicate the metabolic state of cells: it is believed that the M isoform favors lactate production while the H isoform favors pyruvate production (Boyer et al., 1963, Stambaugh and Post, 1966, Boyer, 1975, Voet and Voet, 2004). In this framework, the LDH isoform ratio can serve as an indicator of the relative flux through aerobic/anaerobic gycolytic pathways.

Here we use a mathematical model of homolactic fermentation to study the connections between growth-factor signaling and metabolism. It has been known since the work of Warburg that carcinogenesis is accompanied by changes in cellular metabolism (Stubbs et al., 2003, Griffiths et al., 2002, Dang and Semenza, 1999). In particular, tumors typically favor anaerobic metabolism, resulting in higher lactate production relative to non-cancerous cells (Walenta et al., 2004, Newell et al., 1993, Warburg, 1956). Although inhibition of glycolysis can kill tumor cells (Munoz-Pinedo et al., 2003), the connections between carcinogenesis and metabolic alterations are not fully understood (Fan et al., 2004). However, intriguing connections between metabolic enzymes and cancer have been demonstrated (Kondoh et al., 2005, Kim et al., 2004, Mazurek and Eigenbrodt, 2003). In particular, LDH expression is altered in many tumors (Walenta et al., 2004, Unwin et al., 2003, Maekawa et al., 2003) and cancer cell models (Li et al., 2004, Karan et al., 2002, Lewis et al., 2000). High tumor LDH levels have been shown to correlate with poor prognosis in lung cancer patients (Koukourakis et al., 2003).

In this study, we focus on changes in LDH expression induced by the mitogen-activated protein (MAP) kinase pathway. The MAP kinase cascade is important in cell growth, differentiation, and survival, and alterations of MAP kinase signaling have been found in many cancers (Lewis et al., 1998). The signal is transduced by a series of phosphorylation reactions: MAP kinase proteins phosphorylate and thereby activate their downstream targets. The pathway includes the MAP kinase proteins ERK 1 and 2 and their upstream activators, the MAP kinase kinases MKK 1 and 2. Recent work has found connections between MAP kinase signaling and metabolism. For example, increased expression of LDH-H in human tumors may occur in part because the transcription factor MYC, a downstream target of the MAP kinase pathway, transcriptionally up-regulates the LDH-H gene (Jungmann et al., 1998, Shim et al., 1997). Other genes involved in glycolysis are also affected by MYC (Osthus et al., 2000). Activation of the MAP kinase pathway has been shown to increase LDH activity, glucose uptake, and lactate production (Riera et al., 2003, Papas et al., 1999).

We studied mRNA expression in K562 erythroleukemia cells, a cell line used as a model for leukemia. In our experiments, MAP kinase signaling was either (i) activated with phorbol 12-myristate 13-acetate (PMA) or (ii) simultaneously activated with PMA and inhibited with U0126, a specific MKK inhibitor. We found small but reproducible changes in the expression of LDH isoforms in response to MAP kinase pathway activation (Fig. 1), with no significant changes in other enzymes that catalyse reactions involving pyruvate. This result suggests that activating the MAP kinase pathway alters the relative flux through aerobic and anaerobic glycolysis in these cells. We chose to model the expected changes in cellular lactate production to better understand the connections between signaling and metabolism. We hypothesized that the LDH isoform ratio plays an important role in determining cellular lactate levels, as suggested previously (Riera et al., 2003, Dang and Semenza, 1999).

We formulated a chemical-kinetic model of homolactic fermentation based on in vitro biochemistry (Borgmann et al., 1975). Our goal was to determine how changes in the LDH isoform ratio alter the amount of lactate produced by K562 cells. We used the experimentally determined abundance changes as model inputs. The model describes the mass-action kinetics of homolactic fermentation. We included metabolic flux terms in the model to describe the connection between homolactic fermentation and the larger metabolic network of the cell. The metabolic flux is a constant rate of production/consumption of a metabolite through other reactions or transport. Several model inputs—the steady-state concentrations of pyruvate, NADH, and NAD+—have not been measured in K562 cells. Therefore we validated our results with a robustness analysis (von Dassow et al., 2000, Barkai and Leibler, 1997).

We present several unexpected findings. In a preliminary analysis, we examined the behavior of each isoform individually. Our results predict that LDH-H produces a larger steady-state lactate concentration than an equivalent amount of LDH-M under typical cellular conditions. This result is surprising because it disagrees with the statement, often found in the literature, that the M isoform favors lactate production while the H isoform favors pyruvate production (Boyer et al., 1963, Stambaugh and Post, 1966, Boyer, 1975, Voet and Voet, 2004). We discuss the reason for this difference and explain why our results are more applicable in vivo.

Second, we predict a decrease in the steady-state lactate concentration when the LDH isoform abundance shifts from control to PMA-treated levels. This result means that the H:M isoform ratio alone does not control the lactate concentration. After PMA treatment the ratio of LDH-H to LDH-M changes from 1.02 to 1.35 in our experiments. According to our single-isoform model, an increasing isoform ratio should lead to an increase in lactate concentration. This finding led us to consider separately how the isoform ratio and the total abundance of LDH control the lactate concentration. We demonstrate that while the isoform ratio does affect the production of lactate, the experimentally determined total LDH abundance change plays a larger role in determining the lactate concentration.

Section snippets

Cell extraction and microarray analysis

K562 erythroleukemia cells were grown in suspension in 10% FBS/RPMI and treated with 10 nM phorbol 12-myristate 13-acetate (PMA) and 20μM U0126 (Promega) as described previously (Sevinsky et al., 2004). Cells (7×105) were washed twice in ice cold phosphate buffered saline, 1 mM EDTA, 1 mM EGTA, and total RNA was isolated by TRIzol extraction (Invitrogen). First and second strand cDNA synthesis, in vitro transcription of biotin-labeled cRNA, and fragmentation were carried out following standard

Single-isoform results

We examined the steady-state production of lactate by a single LDH isoform. Under typical cellular conditions our model predicts that LDH-H produces more lactate than LDH-M. This result is surprising because many authors state that LDH-M produces lactate more efficiently than LDH-H (Boyer et al., 1963, Stambaugh and Post, 1966, Boyer, 1975, Voet and Voet, 2004). We explain the reason for this difference, which results from different model assumptions, and argue that our analysis is more

Discussion

Our mRNA expression data show that activating MAP kinase signaling changes the ratio of LDH isoforms in K562 cells. We used a mathematical model of lactate production by LDH to calculate the changes in steady-state lactate concentration which result from changes in LDH concentration. We assume that changes in gene expression predict changes in enzyme concentration. We predict that for the experimentally observed changes in LDH, the cellular lactate concentration undergoes a small but

Acknowledgements

This work was supported by NIGMS project number 1540281. MDB acknowledges support from the Alfred P. Sloan foundation.

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