# Integrated Network Pharmacology Approach for Drug Combination Discovery: A Multi-Cancer Case Study

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Collection

#### 2.2. Gene Expression Analysis

^{t}

_{i}= abs(logFC

_{i}× −log(p value

^{t}

_{i}))

#### 2.3. Co-Expression Networks Inference

#### 2.4. Construction of the Multi-Layer Network

#### 2.5. Characterization of Drugs Properties

_{t}is the number of targets for each drug; M

_{R}is the median value of the rank indices of drug targets in the network, indicating the relevance of the drug targets within the cancer network in terms of centrality measures and SS.

#### 2.6. Final Drug Prioritization

- (1).
- MOA: the drugs in $x$ must have the most dissimilar mechanisms of action: ${\mathrm{max}}_{\mathrm{x}\subset \mathsf{\Sigma}}\mathrm{MOA}\left(\mathrm{x}\right)$, where $\mathrm{MOA}\left(\mathrm{x}\right)$ is the average HIM distance between each pair of drugs in $\mathrm{x}$: $\mathrm{MOA}\left(\mathrm{x}\right)=\frac{1}{\left|\mathrm{x}\right|}{{\displaystyle \sum}}_{\left.{\left\{\mathrm{d}\right.}_{\mathrm{I}},{\mathrm{d}}_{\mathrm{j}}\right\}\subset \mathrm{x}}^{}\mathrm{HIM}\left({\mathrm{d}}_{\mathrm{I}},{\mathrm{d}}_{\mathrm{j}}\right)$, where $\left|\mathrm{x}\right|$ is the number of drugs in $x$;
- (2).
- SMILES: the drugs in $\mathrm{x}$ must have the most different secondary structure: ${\mathrm{max}}_{\mathrm{x}\subset \mathsf{\Sigma}}\mathrm{SMILES}\left(\mathrm{x}\right)$, where $\mathrm{SMILES}\left(\mathrm{x}\right)$ is the average Levenshtein distance between each pair of drugs in $\mathrm{x}$: $\mathrm{SMILES}\left(\mathrm{x}\right)=\frac{1}{\left|\mathrm{x}\right|}{{\displaystyle \sum}}_{\left.{\left\{\mathrm{d}\right.}_{\mathrm{I}},{\mathrm{d}}_{\mathrm{j}}\right\}\subset \mathrm{x}}^{}\mathrm{L}\left({\mathrm{d}}_{\mathrm{I}},{\mathrm{d}}_{\mathrm{j}}\right)$;
- (3).
- TARGETS: the drugs in $x$ must target genes which are as far as possible between themselves in the cancer network: ${\mathrm{max}}_{\mathrm{x}\subset \mathsf{\Sigma}}\mathrm{TARGETS}\left(\mathrm{x}\right)$, where $\mathrm{TARGETS}\left(\mathrm{x}\right)$ is the average length of the shortest paths between the sets of targets of each pair of drugs in $\mathrm{x}$: $\mathrm{TARGETS}\left(\mathrm{x}\right)=\frac{1}{\left|\mathrm{x}\right|}{{\displaystyle \sum}}_{\left.{\left\{\mathrm{d}\right.}_{\mathrm{I}},{\mathrm{d}}_{\mathrm{j}}\right\}\subset \mathrm{x}}^{}\mathrm{SP}\left({\mathrm{d}}_{\mathrm{I}},{\mathrm{d}}_{\mathrm{j}}\right)$;
- (4).
- COVERAGE: the drugs in $\mathrm{x}$ must target as many genes as possible in the cancer network: ${\mathrm{max}}_{\mathrm{x}\subset \mathsf{\Sigma}}\mathrm{ES}\left(\mathrm{x}\right)$;
- (5).
- SIZE: we want the smallest subset of drugs ${\mathrm{min}}_{\mathrm{x}\subset \mathsf{\Sigma}}\left|\mathrm{x}\right|$.

## 3. Results and Discussion

#### 3.1. Implementation

#### 3.2. Case Study

#### 3.3. Robustness and Stability Evaluation

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Computational workflow for the detection of drug combinations strategy for drug repositioning.

**Figure 2.**Network representation of the drug combinations in the considered cancers. The color of the edges indicates the cancer type. The thickness of the edges indicates the number of occurrences of the combination in the solutions of the genetic algorithm.

**Figure 3.**Overview of drug combinations obtained for the cancers under consideration. (

**A**)—invasive breast cancer (BRCA); (

**B**)—prostate adenocarcinoma (PRAD); (

**C**)—colon adenocarcinoma (COAD); (

**D**)—lung squamous cell carcinoma (LUSC); (

**E**)—hepatocellular carcinoma best pairs (LIHC).

**Figure 4.**Trace plots showing the performance of the genetic algorithm in terms of stability of the obtained drug combinations. The color of the traces indicate the objective function that is optimized in the genetic algorithm.

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**MDPI and ACS Style**

Federico, A.; Fratello, M.; Scala, G.; Möbus, L.; Pavel, A.; del Giudice, G.; Ceccarelli, M.; Costa, V.; Ciccodicola, A.; Fortino, V.;
et al. Integrated Network Pharmacology Approach for Drug Combination Discovery: A Multi-Cancer Case Study. *Cancers* **2022**, *14*, 2043.
https://doi.org/10.3390/cancers14082043

**AMA Style**

Federico A, Fratello M, Scala G, Möbus L, Pavel A, del Giudice G, Ceccarelli M, Costa V, Ciccodicola A, Fortino V,
et al. Integrated Network Pharmacology Approach for Drug Combination Discovery: A Multi-Cancer Case Study. *Cancers*. 2022; 14(8):2043.
https://doi.org/10.3390/cancers14082043

**Chicago/Turabian Style**

Federico, Antonio, Michele Fratello, Giovanni Scala, Lena Möbus, Alisa Pavel, Giusy del Giudice, Michele Ceccarelli, Valerio Costa, Alfredo Ciccodicola, Vittorio Fortino,
and et al. 2022. "Integrated Network Pharmacology Approach for Drug Combination Discovery: A Multi-Cancer Case Study" *Cancers* 14, no. 8: 2043.
https://doi.org/10.3390/cancers14082043