We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Cellular life depends on a complex web of functional associations between biomolecules. Among these associations, protein-protein interactions are particularly important due to their versatility, specificity and adaptability. The STRING database aims to integrate all known and predicted associations between proteins, including both physical interactions as well as functional associations. To achieve this, STRING collects and scores evidence from a number of sources: (i) automated text mining of the scientific literature, (ii) databases of interaction experiments and annotated complexes/pathways, (iii) computational interaction predictions from co-expression and from conserved genomic context and (iv) systematic transfers of interaction evidence from one organism to another. STRING aims for wide coverage; the upcoming version 11.5 of the resource will contain more than 14 000 organisms. In this update paper, we describe changes to the text-mining system, a new scoring-mode for physical interactions, as well as extensive user interface features for customizing, extending and sharing protein networks. In addition, we describe how to query STRING with genome-wide, experimental data, including the automated detection of enriched functionalities and potential biases in the user's query data. The STRING resource is available online, at https://string-db.org/.

/pdf/the-string-database-in-2021-customizable-protein-protein-2b9inm207c.pdf

The STRING database in 2021: customizable protein-protein networks, and functional characterization of user-uploaded gene/measurement sets.

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Survey paper: Set invariance in control

Introduction to linear and nonlinear programming

DEFINITIONS. Definitions and Conditions of Positivity. Influence Graphs. Irreducibility, Excitability and Transparency. PROPERTIES. Stability. Spectral Characterization of Irreducible Systems. Positivity of Equilibria. Reachability and Observability. Realization. Minimum Phase. Interconnected Systems. APPLICATIONS. Input-Output Analysis. Age-Structured Population Models. Markov Chains. Compartmental Systems. Queueing Systems. Conclusions. Annotated Bibliography. Bibliography. Appendices. Index.

Positive Linear Systems: Theory and Applications

This paper is a tutorial on the positive realization problem, that is the problem of finding a positive state-space representation of a given transfer function and characterizing existence and minimality of such representation. This problem goes back to the 1950s and was first related to the identifiability problem for hidden Markov models, then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory. Within this framework, developing some ideas sprang in the 1960s, during the 1980s, the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem. In this paper, the reader is carried through the key ideas which have proved to be useful in order to tackle this problem. In order to illustrate the main results, contributions and open problems, several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided.

A tutorial on the positive realization problem

We developed a genome-wide transcriptomic atlas of grapevine (Vitis vinifera) based on 54 samples representing green and woody tissues and organs at different developmental stages as well as specialized tissues such as pollen and senescent leaves. Together, these samples expressed ∼91% of the predicted grapevine genes. Pollen and senescent leaves had unique transcriptomes reflecting their specialized functions and physiological status. However, microarray and RNA-seq analysis grouped all the other samples into two major classes based on maturity rather than organ identity, namely, the vegetative/green and mature/woody categories. This division represents a fundamental transcriptomic reprogramming during the maturation process and was highlighted by three statistical approaches identifying the transcriptional relationships among samples (correlation analysis), putative biomarkers (O2PLS-DA approach), and sets of strongly and consistently expressed genes that define groups (topics) of similar samples (biclustering analysis). Gene coexpression analysis indicated that the mature/woody developmental program results from the reiterative coactivation of pathways that are largely inactive in vegetative/green tissues, often involving the coregulation of clusters of neighboring genes and global regulation based on codon preference. This global transcriptomic reprogramming during maturation has not been observed in herbaceous annual species and may be a defining characteristic of perennial woody plants.

/pdf/the-grapevine-expression-atlas-reveals-a-deep-transcriptome-127whtulxe.pdf

The Grapevine Expression Atlas Reveals a Deep Transcriptome Shift Driving the Entire Plant into a Maturation Program

Non-coding RNAs (ncRNAs) are emerging as key regulators of many cellular processes in both physiological and pathological states. Moreover, the constant discovery of new non-coding RNA species suggests that the study of their complex functions is still in its very early stages. This variegated class of RNA species encompasses the well-known microRNAs (miRNAs) and the most recently acknowledged long non-coding RNAs (lncRNAs). Interestingly, in the last couple of years, a few studies have shown that some lncRNAs can act as miRNA sponges, i.e. as competing endogenous RNAs (ceRNAs), able to reduce the amount of miRNAs available to target messenger RNAs (mRNAs). We propose a computational approach to explore the ability of lncRNAs to act as ceRNAs by protecting mRNAs from miRNA repression. A seed match analysis was performed to validate the underlying regression model. We built normal and cancer networks of miRNA-mediated sponge interactions (MMI-networks) using breast cancer expression data provided by The Cancer Genome Atlas. Our study highlights a marked rewiring in the ceRNA program between normal and pathological breast tissue, documented by its “on/off” switch from normal to cancer, and vice-versa. This mutually exclusive activation confers an interesting character to ceRNAs as potential oncosuppressive, or oncogenic, protagonists in cancer. At the heart of this phenomenon is the lncRNA PVT1, as illustrated by both the width of its antagonist mRNAs in normal-MMI-network, and the relevance of the latter in breast cancer. Interestingly, PVT1 revealed a net binding preference towards the mir-200 family as the bone of contention with its rival mRNAs.

/pdf/computational-analysis-identifies-a-sponge-interaction-106a938yoe.pdf

Computational analysis identifies a sponge interaction network between long non-coding RNAs and messenger RNAs in human breast cancer

It is becoming increasingly clear that short and long noncoding RNAs critically participate in the regulation of cell growth, differentiation, and (mis)function. However, while the functional characterization of short non-coding RNAs has been reaching maturity, there is still a paucity of well characterized long noncoding RNAs, even though large studies in recent years are rapidly increasing the number of annotated ones. The long noncoding RNA PVT1 is encoded by a gene that has been long known since it resides in the well-known cancer risk region 8q24. However, a couple of accidental concurrent conditions have slowed down the study of this gene, that is, a preconception on the primacy of the protein-coding over noncoding RNAs and the prevalent interest in its neighbor MYC oncogene. Recent studies have brought PVT1 under the spotlight suggesting interesting models of functioning, such as competing endogenous RNA activity and regulation of protein stability of important oncogenes, primarily of the MYC oncogene. Despite some advancements in modelling the PVT1 role in cancer, there are many questions that remain unanswered concerning the precise molecular mechanisms underlying its functioning.

/pdf/pvt1-a-rising-star-among-oncogenic-long-noncoding-rnas-3sngsojdda.pdf

Lorenzo Farina

Papers

Positive Linear Systems: Theory and Applications

A tutorial on the positive realization problem

The Grapevine Expression Atlas Reveals a Deep Transcriptome Shift Driving the Entire Plant into a Maturation Program

Computational analysis identifies a sponge interaction network between long non-coding RNAs and messenger RNAs in human breast cancer

PVT1: a rising star among oncogenic long noncoding RNAs.