Lorenzo Farina

Positive Linear Systems: Theory and Applications

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.

A tutorial on the positive realization problem

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.

The grapevine expression atlas reveals a deep transcriptome shift driving the entire plant into a maturation program.

The authors developed a comprehensive transcriptome atlas in grapevine by comparing the genes expressed in 54 diverse samples accounting for ∼91% of all known grapevine genes. Using a panel of different statistical techniques, they found that the whole plant undergoes transcriptomic reprogramming, driving it towards maturity. 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.

On the existence of a positive realization

The positive realization problem for linear systems is to find conditions, for a given transfer function with nonnegative impulse response, to have a realization such that the resulting system is a positive system. Recently, it has been shown that, under a mild assumption on the long-term behaviour of the impulse response, this problem is related to the maximum modulus poles only. In this paper necessary and sufficient conditions for positive realizability of discrete-time systems are given. They show that also nondominant poles play a role in the most general case. Positive realizability conditions for the continuous-time case are also given.

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

BackgroundNon-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).ResultsWe 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.ConclusionsOur 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.

The plasticity of the grapevine berry transcriptome

BackgroundPhenotypic plasticity refers to the range of phenotypes a single genotype can express as a function of its environment. These phenotypic variations are attributable to the effect of the environment on the expression and function of genes influencing plastic traits. We investigated phenotypic plasticity in grapevine by comparing the berry transcriptome in a single clone of the vegetatively-propagated common grapevine species Vitis vinifera cultivar Corvina through 3 consecutive growth years cultivated in 11 different vineyards in the Verona area of Italy.ResultsMost of the berry transcriptome clustered by year of growth rather than common environmental conditions or viticulture practices, and transcripts related to secondary metabolism showed high sensitivity towards different climates, as confirmed also by metabolomic data obtained from the same samples. When analyzed in 11 vineyards during 1 growth year, the environmentally-sensitive berry transcriptome comprised 5% of protein-coding genes and 18% of the transcripts modulated during berry development. Plastic genes were particularly enriched in ontology categories such as transcription factors, translation, transport, and secondary metabolism. Specific plastic transcripts were associated with groups of vineyards sharing common viticulture practices or environmental conditions, and plastic transcriptome reprogramming was more intense in the year characterized by extreme weather conditions. We also identified a set of genes that lacked plasticity, showing either constitutive expression or similar modulation in all berries.ConclusionsOur data reveal candidate genes potentially responsible for the phenotypic plasticity of grapevine and provide the first step towards the characterization of grapevine transcriptome plasticity under different agricultural systems.

Functional essentiality from topology features in metabolic networks: A case study in yeast

The relation between the position of mutations in Saccharomyces cerevisiae metabolic network and their lethality is the subject of this work. We represent the topology of the network by a directed graph: nodes are metabolites and arcs represent the reactions; a mutation corresponds to the removal of all the arcs referring to the deleted enzyme. Using publicly available knock‐out data, we show that lethality corresponds to the lack of alternative paths in the perturbed network linking the nodes affected by the enzyme deletion. Such feature is at the basis of the recently recognized importance of ‘marginal’ arcs of metabolic networks.

Positive and compartmental systems

When dealing with compartmental systems, an important question is: given an experiment, i.e., an input-output sequence, and supposing there is no error in the data, is the sequence compatible with the compartmental assumption? If the process under analysis is linear, then the previous question is obviously equivalent to asking whether a given transfer function is that of a compartmental system. In this note we provide an answer to the latter question giving necessary and sufficient conditions for a transfer function to be that of a compartmental system of some finite order (i.e., number of compartments). Another problem tackled in this note originates from the observation that in many cases one wants to determine the number of compartments involved in the process. In this note we report a step toward the solution of this fundamental problem by proving necessary and sufficient conditions for a given third order transfer function with real poles to be that of a compartmental system with three compartments.

PVT1: A Rising Star among Oncogenic Long Noncoding RNAs

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.

Positive realizations of linear systems

Abstract This paper deals with the realization problem of linear systems in which a sign pattern is imposed on the realization{ A b c T }. This problem arises in the context of positive linear systems, i.e. systems in which state variables and the output take nonnegative values whenever initial states and inputs are nonnegative. Using a unitary framework for continuous-time and discrete-time systems we derive necessary and sufficient conditions for positive realizability by means of convex analysis. Moreover, the complete solution in the case of a transfer function of McMillan degree n ⩽ 3 is obtained.