Predicting and characterizing selective multiple drug treatments for metabolic diseases and cancer

Background In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. Results The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the other cellular processes. Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human cell. The results we obtain are consistent with some of the available therapeutic indications and predict new multiple drug treatments. A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion The in silico prediction of drug synergisms can represent an important tool for the repurposing of drugs in a realistic perspective which considers also the selectivity of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, we have shown that also experimental drugs which have a different mechanism of action can be reconsider as potential ingredients of new multicompound therapeutic indications. Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.

Essentiality and synthetic lethality [7]: Through an algorithm which is similar to Optknock, this work identifies pairs, triple and some high-order gene deletions which are lethal in the Escherichia coli metabolism. Also in this method, the optimization is based on the biomass and does not consider any alternative objective reaction.
OPMET [6]: the aim is to search the gene knockout (of any cardinality) which stops a given objective reaction while inducing the minimum damage on the network (estimated as number of stopped reactions and unavailable metabolites). The approach used to model the network is similar to FBA but with a weaker assumption on the steady state: for instance, accumulation of metabolites is allowed. The search on the space of the combinations is performed dynamically through a branch-and-bound algorithm, refined with two filtering strategies. Properties of Linear Programming, like duality theory, which are useful for the efficiency of the algorithm have not been exploited.
Epistasis in human metabolism [3]: the investigation of gene epistasis has been here investigated through FBA formalism; no limitation on the cardinality of the gene deletions is imposed. However, since the search is based on an approximate determination of the elementary modes (called "pathway fragment generation"), solutions are suboptimal. An exact calculation of the elementary modes would have been computationally much more expensive and almost prohibitive for a large network such as the human. Moreover, no information on the side effect on the whole network is included.
Epistasis in yeast metabolism [5]: epistatic interactions are here studied performing an exhaustive search of all pairs of gene knockouts on the S.cerevisiae network modeled according to FBA; the effect is characterized through an epistasis indicator which quantifies the change of the biomass production of the multiple perturbation with respect to the two single perturbations. No objective reaction other than growth rate has been considered.
Drug targets in cancer [2]: also in this case only an exhaustive evaluation of all pairs of knockouts has been carried out; moreover, the side effect of the potential antitumoral treatments on the normal human cell is estimated in terms of ATP production, a central process in the metabolism. However, according to this evaluation criterion, all the antitumoral solutions we have found show the same impact on the human network, meaning that this definition of side effect is not able to discriminate among these different drug treatments, while our definition does. Indeed, instead of considering a single reaction, our approach estimates the impact as a global loss of the cellular functions, which in our opinion is fairly reasonable since no tissue-specific network of the human metabolism is available at the moment.

Algorithm for competitive organisms
The following version of the algorithm allows us to study the selectivity problem, in a multi-organism context, in which we would like to stop an objective reaction belonging to a first organism while having a minimal effect on a second metabolic network (whose fluxes are denoted here by w). We assume that the two organisms live in the same environment and hence are subject to the same drugs.

Minimize
As can be seen, flux constraints (Sw = 0, thermodynamical bounds w h ≤Ũ h and common drugs inequalities w h ≤Ũ h d k ) and side effect on the second network (calculated as σ(D) = min w w − w * ) are located only in the outer problem; therefore the fact that the side effect is now evaluated on w instead of on v does not interfer with the inner problem, i.e., with the application of the duality theorem for the first network. This separation guarantees the constraint max(v obj ) = 0 and the optimality of the solution.   Table S1: List of drugs selected from DrugBank database for human and cancer metabolic networks. Selection criteria are explained in the main text. Legend : "M": number of metabolic targets; "NM": number of non-metabolic targets; "R": number of inhibited reactions of the human metabolic network; "S.E.": side effect;"X": the drug acts also on the cancer network; (*): Simvastatin and Atorvastatin are also present in this group (they induce the same metabolic inhibitions as Pravastatin but they have one and two non-metabolic targets respectively).  Table S2: List of the inhibitions on human metabolism obtained by multiple drug solutions.
The reactions are sorted according to the pathway they belong. The solutions are classified as New inhibition, More selective and Less selective from a comparison with a possible single drug treatment; this information is reported in the third column. Last columns reports the class of the synergistic combination which cause the inhibition of the objective reaction (see Figure 2 on the paper).  Figure S1: Side effects comparison. The histogram analysis of the size effect induced by single and multiple drug solutions shows that both types of solution have more or less the same order of magnitude. Figure S2: Results on cancer metabolic network alone. Like for the human network (see Figure 3), the plot reports the new inhibitions that synergisms make possible and the inhibitions with different selectivity with respect to a single drug treatment. Notice how the number of new inhibitions is significantly higher than in the human metabolism, meaning that the cancer pathways are less robust (and redundant) than their counterparts in the human network.