A probabilistic approach to identify putative drug targets in biochemical networks

Abstract

Network-based drug design holds great promise in clinical research as a way to overcome the limitations of traditional approaches in the development of drugs with high efficacy and low toxicity. This novel strategy aims to study how a biochemical network as a whole, rather than its individual components, responds to specific perturbations in different physiological conditions. Proteins exerting little control over normal cells and larger control over altered cells may be considered as good candidates for drug targets. The application of network-based drug design would greatly benefit from using an explicit computational model describing the dynamics of the system under investigation. However, creating a fully characterized kinetic model is not an easy task, even for relatively small networks, as it is still significantly hampered by the lack of data about kinetic mechanisms and parameters values. Here, we propose a Monte Carlo approach to identify the differences between flux control profiles of a metabolic network in different physiological states, when information about the kinetics of the system is partially or totally missing. Based on experimentally accessible information on metabolic phenotypes, we develop a novel method to determine probabilistic differences in the flux control coefficients between the two observable phenotypes. Knowledge of how differences in flux control are distributed among the different enzymatic steps is exploited to identify points of fragility in one of the phenotypes. Using a prototypical cancerous phenotype as an example, we demonstrate how our approach can assist researchers in developing compounds with high efficacy and low toxicity.

Figure 1.

Workflow of our Monte Carlo approach. The Monte Carlo approach described in the text receives as input the two metabolic states under comparison (where each metabolic state is defined in terms of fluxes and metabolite concentrations at stationary condition). The computation of the control coefficients, following the sampling of the parameter values, is done assuming that the rate equations and the equilibrium constants are known. Where the detailed enzyme mechanism is unknown, heuristic approximate rate equations are used.

Figure 2.

Metabolic map of central carbon metabolism. The metabolic map was derived, in its main features, from Holzhütter's model of erythrocyte metabolism and subsequently enriched with a reaction representing the TCA cycle and a reaction representing the oxidative phosphorylation process. Glucose transporter (GLT), lactate transporter (LCT), phosphoribosylpyrophosphate synthetase (PRPPS) and the tricarboxylic acid (TCA) branch represent the exchange fluxes of the system. ALD, aldolase; TK, transketolase; TPI, triosephosphate isomerase.

Figure 3.

Calculated distributions of the control exerted by some enzymes over the glucose uptake flux in the normal phenotype. (a) Glucose transporter (GLT), (b) phosphofructokinase (PFK), (c) transketolase 1 (TK1), (d) phosphoglyceratekinase (PGK), (e) lactate dehydrogenase (LDH), (f) ATPase.

Figure 4.

Matrix of the flux control coefficient in the normal metabolic state. The matrix of the flux control coefficients in the normal metabolic phenotype is represented as a grey-scale matrix. The entry (j,i) is associated with the statistical control exerted by enzyme i (column index) upon flux j (row index). More in particular, the shade of the entry represents the percentage of calculated control coefficients that is positive. The ends of the colours scale represent the extreme situations in which the distribution lies entirely over positive (white) or negative (black) values. The numbers at the left and the bottom of the matrix refers to the different reaction steps in the system as depicted in figure 2.

Figure 5.

Calculated distributions of the selectivity coefficient. The distribution of the selectivity coefficients with respect to the uptake of glucose are shown for the same enzymes as in figure 3.

Figure 6.

The normalized selectivity (σ_i), safety (1/τ_i) and reliability (ρ_i), defined in equations (3.1)–(3.3), respectively, are plotted versus each other. Enzymes with negative values of (see text) are not represented in the graph. The grey plane in (a) represents the set of points in the three-dimensional space sharing the same score, as defined by equation (3.4). Different scores are represented by different planes, parallel to each other. (b–d) show the orthogonal projections of the three-dimensional scatter-plot shown in (a).

Figure 7.

Effects induced on the principal fluxes of the system by decreasing the activity of PGK. The plots show the effect of decreasing the activity of PGK from 12.9 to 6.5 mM h⁻¹ in the two phenotypes (normal, thin solid line; disease, thick solid line). Six main fluxes are considered: (a) glucose uptake, (b) PRPP, (c) lactate production, (d) flux entering the TCA cycle, (e) ATPase and (f) flux through the oxidative phosphorylation process.