# Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology

## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Networks

#### 1.3. Cancer Networks Taxonomy

## 2. Methodological Themes

#### 2.1. On Entropy

^{−1}$\sum}\mathrm{i$ p

_{i}log(p

_{i}), and MI is the normalized mutual information, or MI = log(N)

^{−1}∑

_{ij}p

_{ij}log p

_{ij}(p

_{ij}/p

_{i}p

_{j}). In general, a set of variables may be conceived to be subject (or not) to dependence in collective terms, i.e., all set members contribute to some extent to the prediction of one of them. This sort of pattern is useful for interpreting network constraints of functional relevance from a biological viewpoint. In genomics, this might be relevant for capturing nonlinear or high-order interactions underlying highly complex regulation signatures that simple gene lists cannot represent. This concept also implies that biological networks presenting modular architectures can maximize the set complexity. Modularity basically enforces the connectivity between nodes and represents a structural feature, one quantitatively reflected in the MI measure whose advantage is to detect significant functional dependence beyond simple correlation.

_{I}s

_{i}log s

_{i}

_{i}indicates the size of the basin i. Notably, bS is minimal when one basin has all the states and maximal when the states are distributed into different attractors.

#### 2.2. Metastasis and Its Stochastic Dynamics

_{i}and X

_{j}, assuming they are constant over time and depend only on the reference state. This way, the transition matrix would define a discrete-time Markov process explaining state evolution dynamics of the population of cells under consideration [37,38]. At a network scale, a dynamic rewiring occurs through the node interactions determining the network state trajectory. Under no change of state over time, an attractor may be observed (or an attractor landscape if all possible state trajectories are considered). Both genetic and epigenetic alterations can underlie such a network evolution process, and the genomic instability and/or loss of proteostasis may explain uncontrolled cell proliferation [39].

_{i}π

_{i}S

_{i}

_{i}computed locally (at each state). A change in entropy rate would imply that the effects of signaling are likely present in response to some type of perturbation.

#### 2.3. Therapy and Phase Transitions

_{i}= −[log(k)]

^{−1}∑

_{i}p

_{i}log p

_{i}

_{i}as the probability linking the reference node with other nodes. An important consequence is that cancer phenotypes can be assessed by their local entropies from degree computed node-wise. The related distribution allows to assess network heterogeneity, and how randomness characterizes metastatic versus non-metastatic networks.

#### 2.4. On Symmetry

- (1)
- Do symmetric patterns induce localized network dynamics, i.e., those represented by modules, clusters, motifs? If this is the case, how specific these structures are?
- (2)
- Are the possibly observed patterns robust or fragile with regard to symmetry breaking? The latter would imply the presence of fluctuations leading the system to a critical point, and thus a likely change of state that in cancer might be a signature of metastasis.

- (1)
- How the influences exerted by symmetry patterns depend on cancer heterogeneity?
- (2)
- Are such patterns controllable?

_{ij}= 1 (if node i and node j are adjacent) or 0 (otherwise), a symmetry is present when a permutation P is applied to A, leaving it unchanged, i.e., PA = A. This establishes a so-called automorphism, indicating that nodes are topologically equivalent if their permutation does not affect the network structure.

^{AP}= −∑

_{n}p

_{n}log p

_{n}

_{n}= |n

_{i}|/n

^{N}

^{n}S

^{AP}= S

^{AP}/log N

^{N}(Pd) = min ∑

_{i}p

_{i}log p

_{i}

#### 2.5. On Controllability

- (i)
- The presence of interactions involved in core cell-cycle and DNA-damage repair pathways that are significantly rewired in tumors, indicating a significant impact on key genome-stabilizing mechanisms;
- (ii)
- Several flipped genes that are serine/threonine kinases which act as biological switches, reflecting cellular switching mechanisms between stages;
- (iii)
- Different sets of genes flipped during the initial and final stages, indicating a progressive pattern.

^{P−1}B} = P

## 3. Results

#### 3.1. Use Case 1: Entropic Patterns in Metastatic Breast Cancer

#### 3.2. Use Case 2—Controllability in Metastatic Stomach Cancer

#### 3.3. Use Case 3—Symmetry and Synchronization in Melanoma State Transitions

## 4. Discussion

## Acknowledgments

## Conflicts of Interest

## Materials and Methods

## References

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**Figure 1.**Protein Interaction Networks (PIN) from 16 metastatic over-expressed genes in BC. Top panel: Left, whole network; Right, modular map of reduced sub-network. Bottom panel: left, whole TF-gene network; Right, modular map of reduced sub-network.

**Figure 2.**PIN from 31 metastatic under-expressed genes in BC. Top panel: Left, whole network; Right, modular map of reduced sub-network. Bottom panel: left, whole TF-gene network; Right, modular map of reduced sub-network.

**Figure 3.**PIN from 21 metastatic and 11 non-metastatic stomach adenocarcinoma genes. Top panel: whole (left) and reduced networks induced by mixed gene group; Bottom panel: over-expressed (left) and under-expressed hubs.

**Figure 4.**PIN from proliferative DEG signature in melanoma (left panel). Top: whole network. Bottom: reduced networks, with the top 150 over-expressed values (left) and the rest (right).

**Figure 5.**PIN from invasive DEG signature in melanoma (right panel). Top: whole network. Bottom: reduced networks, with top150 down-expressed values (left) and the rest (right).

**Figure 6.**PIN from TEAD knockdown experiments. Top-left under-expressed DEG values; Top-right: over-expressed DEG values. Bottom: TEAD target DEG values.

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Capobianco, E.
Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology. *J. Clin. Med.* **2019**, *8*, 664.
https://doi.org/10.3390/jcm8050664

**AMA Style**

Capobianco E.
Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology. *Journal of Clinical Medicine*. 2019; 8(5):664.
https://doi.org/10.3390/jcm8050664

**Chicago/Turabian Style**

Capobianco, Enrico.
2019. "Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology" *Journal of Clinical Medicine* 8, no. 5: 664.
https://doi.org/10.3390/jcm8050664