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Contact-tracing apps help curb the pandemics, but their effectivity depends on the contact networks

An example of a path of infection: the second app-user has received an exposure notification and has isolated her/himself since s/he can be infectious!

Since the beginning of the COVID-19 pandemic, dozens of countries have deployed contact tracing via smartphone apps to employ quarantine for individuals who are at risk of infecting others. The idea behind digital contact tracing is to use smartphone applications to inform people who have been close to infectious people who also use the same application. Data from a handful of nations show mounting evidence that digital contact tracing is useful in keeping the spread of infectious diseases at bay.


Using the toolbox of network science, K. Rizi et al. have investigated the effectiveness of this low-cost intervention method on models that assume more realistic assumptions about human populations. Their model makes it possible to see when and how large an outbreak can happen if a fraction of people adopts the contact tracing apps given several different heterogeneities in the population structure. Importantly, their model includes homophily in the application adoption: the tendency of people who use the application to be more in touch with each other than people who do not use the application. Their results indicate that contact tracing with apps raises the epidemic threshold and reduces the size of the emerging outbreaks. Their results bring this issue to light that digital contact tracing can curb the pandemic even if it is not done perfectly, but its effects are highly nonlinear and strongly dependent on how the connections are structured among application users and others.

K. Rizi, Abbas, et al. “Epidemic spreading and digital contact tracing: Effects of heterogeneous mixing and quarantine failures.”

Balance Theory of Signed Genetic Interactions Reveals Differences in Cancerous and Healthy Cells

Time: Monday 13.01.2020 13.30 – 14.00
Place: Meeting room A142, T-building
Speaker: Abbas K. Rizi
Citation: Rizi AK, Zamani M, Shirazi A, Jafari GR and Kertész J (2021) Stability of Imbalanced Triangles in Gene Regulatory Networks of Cancerous and Normal Cells. Front. Physiol. 11:573732. doi: 10.3389/fphys.2020.573732

Received: 17 June 2020; Accepted: 16 December 2020;
Published: 20 January 2021.

Balance Theory of Signed Genetic Interactions Reveals Differences in Cancerous and Healthy Cells

Abstract:

Genes are not independently functioning in the cell and their expressions are strongly correlated with each other. They communicate with each other through different regulatory effects which lead to the emergence of complex structures in the cells. Such structures are expected to be different for healthy and cancerous cells. To study the differences in the case of breast cancer, we have investigated the Gene Regulatory Network (GRN) of cells as inferred from the RNA-sequencing data using the maximum entropy principle. The GRN is a signed weighted network corresponding to the inductive or inhibitory interactions.
In this presentation, I will focus on a particular set of motifs in the GRN, the triangles, which can be imbalanced if the number of negative interactions in them is odd or balanced otherwise. I will show that the network in cancerous cells has fewer imbalanced triangles than in the healthy case. Moreover, in the healthy cells, imbalanced triangles are isolated from the main part of the network, while such motifs are part of the giant component of the network in cancerous cells.


Fundamental Papers on Balance Theory:


Biological Network Inference – Using the Principle of Max. Entropy


Graphical Lasso


Data

The data of mRNA (expression level) of 20532 genes in the case of Breast Cancer (BRCA: Breast invasive carcinoma) has been downloaded from The Cancer Genome Atlas (TCGA) project. For each gene, there exists 114 normal and 764 cancerous samples and the measurement of the expression levels have done with the technique of RNA sequencing (RNA-Seq). We have used the RPKM (Reads Per Kilobase transcript per Million reads.) normalized data. RPKM puts together the ideas of normalizing by sample and by the gene. When we calculate RPKM, we are normalizing for both the library size (the sum of each column) and the gene length. We had to reduce the number of genes because it is a difficult task to handle a 20532 in 20532 matrix computationally. For each gene, we have calculated the variance of its expression level over its samples and finally, we have store the first 483 genes with the highest variance due to more different activity patterns these genes show among the others. Note that there are so-called housekeeping genes that typically get transcribed continually. These genes are required for the maintenance of basic cellular function and are expressed in all cells of an organism under normal and patho-physiological conditions. Some housekeeping genes are expressed at relatively constant rates in most non-pathological situations.

Slides

Balance-Theory-of-Signed-Genetic-Interactions1

Balance Theory: From Psychology to Cancer Dynamics

Social Balance Theory

Imagine Alice and Bob have just gotten married and have a mutual friend called Chris. In this scenario, they form a triangle of husband-wife-friend relationship, and every edge of this triangle represents a friendship link. Obviously, in this triplet of relationships, people like each other and can spend time together without any conflicts! So this triplet is said to be balanced because everything is fine there, and people enjoy their current state. But If something goes wrong between Alice and Bob and they decide to get divorced, then the link between the husband and wife in the triangle turns into enmity, and from now on, this change makes Chris rethink his relationship with this ex-couple because he cannot simultaneously be friend with these guys who are enemy of each other! Chris has to change his attitude towards Alice or Bob; at last, he must decide to be in a friendship status only with one of them. The triplet of the relationship is now imbalanced, and Chris finally decides to turn his relationship with Alice or Bob into enmity (turning a positive link into a negative one), which leads to another balanced state for this triangle of relationship after experiencing an imbalance. The dynamics of this change are mimicked in the picture below.

Evolution of a married couple plus friend triplet. After a divorce the triangle becomes imbalanced, but balance is restored after another relationship change. Full and dashed lines represent friendly (+) and unfriendly (-) relations respectively. REF: arXiv:physics/0605183

So as you may guess, in a triplet of relationships, if odd numbers of the links are positive (friendship), the triangle is said to be balanced, and otherwise, it is imbalanced. A balanced triangle, therefore, fulfills the adage that: (i) a friend of my friend is my friend, (ii) an enemy of my friend is my enemy, (iii) a friend of my enemy is my enemy, and (iv) an enemy of my enemy is my friend. This notion of balance in social systems was first introduced by Heider (1946), an Austrian psychologist whose work was related to the Gestalt school.

The Energy of Social Networks

The key concept in Heider’s Balance Theory is, “We adjust our relationship based on reducing the psychological stresses.” On the other hand, an imbalanced triangle is analogous to a frustrated plaquette in a random magnet. Physicists know how to assign energy to a system based on the interactions of its constituents. Therefore, inspired by a random magnet, we can assign energy to a triplet of relationships by multiplying each link’s strength in the triangle of relationships. So in the case of the husband-wife-friend triangle, the energy is:

$$E = -R_{hw}R_{wf}R_{fh}$$

which $R_{hw}$ is the strength of the relationship between husband and wife. For a friendly relationship, $R_{hw}$ is a positive number, and $R_{hw}$ is a negative number for an unfriendly relationship. The minus sign is to make the analogy between the concept of social balance and stability in physics. In physical terms, the imbalanced triangles must have higher energy because the dynamics are toward more stable states with lower energy levels. The same reason that an apple falls off a tree and goes from a higher energy level at a higher altitude to lower energy levels toward the ground.

Now with this mechanism, calculating the energy of triangles formed in a social network is handy; we can just simply find the energy of each triangle and, by aggregating them, come to the energy of that network! The higher energy of a network, the more tendency toward attitude change is expected in that network!

The Cancerous Cell Has Less Energy!

When we look at the social life of the genes in the cell, we see that genes make dialogue with each other. It means that genes form a social network in a cell and that the relationships between each pair of genes can be positive or negative, in the sense that genes can alter the state of other genes through the so-called regulatory effects. So, again if the strength of the relationship between each pair of genes is known, we can find the cell’s energy. For the case of Breast Cancer, K. Rizi et al. at Shahid Beheshti University in Tehran have inferred the strength of the relationship between each pair of genes and showed that the energy level of the normal cell is higher than the cancerous one, meaning the normal cell has more tendency to change its attitude. Therefore it can tackle more challenges it experiences through its life cycle.

This is how interdisciplinary research is done nowadays in complex systems. The point is to be open to ideas from different disciplines and creative enough to construct a pathway to solve real-world problems. From a psychological theory from 1946, we have come to a question in 21st-century systems biology with a resolution equipped with the physics toolbox!

To see the detailed study, click here: