From populations to networks: Relating diversity indices and frustration in signed graphs.

Diversity indices of quadratic type, such as fractionalization and Simpson index, are measures of heterogeneity in a population. Even though they are univariate, they have an intrinsic bivariate interpretation as encounters among the elements of the population. In the paper, it is shown that this leads naturally to associate populations to weakly balanced signed networks. In particular, the frustration of such signed networks is shown to be related to fractionalization by a closed-form expression. This expression allows to simplify drastically the calculation of frustration for weakly balanced signed graphs.

Quantifying leadership in climate negotiations: A social power game.

We consider complex multistage multiagent negotiation processes such as those occurring at climate conferences and ask ourselves how can an agent maximize its social power, intended as influence over the outcome of the negotiation. This question can be framed as a strategic game played over an opinion dynamics model, in which the action of an agent consists in stubbornly defending its own opinion. We show that for consensus-seeking opinion dynamics models in which the interaction weights are uniform, the optimal action obeys to an early mover advantage principle, i.e. the agents behaving stubbornly in the early phases of the negotiations achieve the highest social power. When looking at data collected from the climate change negotiations going on at the United Nations Framework Convention on Climate Change, we find evidence of the use of the early mover strategy. Furthermore, we show that the social powers computed through our model correlate very well with the perceived leadership roles assessed through independent survey data, especially when non-uniform weights incorporating economical and demographic factors are considered.

Proteomics reveal biomarkers for diagnosis, disease activity and long-term disability outcomes in multiple sclerosis.

Sensitive and reliable protein biomarkers are needed to predict disease trajectory and personalize treatment strategies for multiple sclerosis (MS). Here, we use the highly sensitive proximity-extension assay combined with next-generation sequencing (Olink Explore) to quantify 1463 proteins in cerebrospinal fluid (CSF) and plasma from 143 people with early-stage MS and 43 healthy controls. With longitudinally followed discovery and replication cohorts, we identify CSF proteins that consistently predicted both short- and long-term disease progression. Lower levels of neurofilament light chain (NfL) in CSF is superior in predicting the absence of disease activity two years after sampling (replication AUC = 0.77) compared to all other tested proteins. Importantly, we also identify a combination of 11 CSF proteins (CXCL13, LTA, FCN2, ICAM3, LY9, SLAMF7, TYMP, CHI3L1, FYB1, TNFRSF1B and NfL) that predict the severity of disability worsening according to the normalized age-related MS severity score (replication AUC = 0.90). The identification of these proteins may help elucidate pathogenetic processes and might aid decisions on treatment strategies for persons with MS.

Prominent epigenetic and transcriptomic changes in CD4+ and CD8+ T cells during and after pregnancy in women with multiple sclerosis and controls.

BACKGROUND: Multiple sclerosis (MS) is a neuroinflammatory disease in which pregnancy leads to a temporary amelioration in disease activity as indicated by the profound decrease in relapses rate during the 3rd trimester of pregnancy. CD4+ and CD8+ T cells are implicated in MS pathogenesis as being key regulators of inflammation and brain lesion formation. Although Tcells are prime candidates for the pregnancy-associated improvement of MS, the precise mechanisms are yet unclear, and in particular, a deep characterization of the epigenetic and transcriptomic events that occur in peripheral T cells during pregnancy in MS is lacking. METHODS: Women with MS and healthy controls were longitudinally sampled before, during (1st, 2nd and 3rd trimesters) and after pregnancy. DNA methylation array and RNA sequencing were performed on paired CD4+ and CD8+ T cells samples. Differential analysis and network-based approaches were used to analyze the global dynamics of epigenetic and transcriptomic changes. RESULTS: Both DNA methylation and RNA sequencing revealed a prominent regulation, mostly peaking in the 3rd trimester and reversing post-partum, thus mirroring the clinical course with improvement followed by a worsening in disease activity. This rebound pattern was found to represent a general adaptation of the maternal immune system, with only minor differences between MS and controls. By using a network-based approach, we highlighted several genes at the core of this pregnancy-induced regulation, which were found to be enriched for genes and pathways previously reported to be involved in MS. Moreover, these pathways were enriched for in vitro stimulated genes and pregnancy hormones targets. CONCLUSION: This study represents, to our knowledge, the first in-depth investigation of the methylation and expression changes in peripheral CD4+ and CD8+ T cells during pregnancy in MS. Our findings indicate that pregnancy induces profound changes in peripheral T cells, in both MS and healthy controls, which are associated with the modulation of inflammation and MS activity.

Relating balance and conditional independence in graphical models.

When data are available for all nodes of a Gaussian graphical model, then, it is possible to use sample correlations and partial correlations to test to what extent the conditional independencies that encode the structure of the model are indeed verified by the data. In this paper, we give a heuristic rule useful in such a validation process: When the correlation subgraph involved in a conditional independence is balanced (i.e., all its cycles have an even number of negative edges), then a partial correlation is usually a contraction of the corresponding correlation, which often leads to conditional independence. In particular, the contraction rule can be made rigorous if we look at concentration subgraphs rather than correlation subgraphs. The rule is applied to real data for elementary gene regulatory motifs.

RNA-sequencing and mass-spectrometry proteomic time-series analysis of T-cell differentiation identified multiple splice variants models that predicted validated protein biomarkers in inflammatory diseases.

Profiling of mRNA expression is an important method to identify biomarkers but complicated by limited correlations between mRNA expression and protein abundance. We hypothesised that these correlations could be improved by mathematical models based on measuring splice variants and time delay in protein translation. We characterised time-series of primary human naïve CD4+ T cells during early T helper type 1 differentiation with RNA-sequencing and mass-spectrometry proteomics. We performed computational time-series analysis in this system and in two other key human and murine immune cell types. Linear mathematical mixed time delayed splice variant models were used to predict protein abundances, and the models were validated using out-of-sample predictions. Lastly, we re-analysed RNA-seq datasets to evaluate biomarker discovery in five T-cell associated diseases, further validating the findings for multiple sclerosis (MS) and asthma. The new models significantly out-performing models not including the usage of multiple splice variants and time delays, as shown in cross-validation tests. Our mathematical models provided more differentially expressed proteins between patients and controls in all five diseases. Moreover, analysis of these proteins in asthma and MS supported their relevance. One marker, sCD27, was validated in MS using two independent cohorts for evaluating response to treatment and disease prognosis. In summary, our splice variant and time delay models substantially improved the prediction of protein abundance from mRNA expression in three different immune cell types. The models provided valuable biomarker candidates, which were further validated in MS and asthma.

Multi-omics protein-coding units as massively parallel Bayesian networks: Empirical validation of causality structure.

In this article we use high-throughput epigenomics, transcriptomics, and proteomics data to construct fine-graded models of the "protein-coding units" gathering all transcript isoforms and chromatin accessibility peaks associated with more than 4000 genes in humans. Each protein-coding unit has the structure of a directed acyclic graph (DAG) and can be represented as a Bayesian network. The factorization of the joint probability distribution induced by the DAGs imposes a number of conditional independence relationships among the variables forming a protein-coding unit, corresponding to the missing edges in the DAGs. We show that a large fraction of these conditional independencies are indeed verified by the data. Factors driving this verification appear to be the structural and functional annotation of the transcript isoforms, as well as a notion of structural balance (or frustration-free) of the corresponding sample correlation graph, which naturally leads to reduction of correlation (and hence to independence) upon conditioning.

Achieving consensus in multilateral international negotiations: The case study of the 2015 Paris Agreement on climate change.

The purpose of this paper is to propose a dynamical model describing the achievement of the 2015 Paris Agreement on climate change. To represent the complex, decade-long, multiparty negotiation process that led to the accord, we use a two time scale dynamical model. The short time scale corresponds to the discussion process occurring at each meeting and is represented as a Friedkin-Johnsen model, a dynamical multiparty model in which the parties show stubbornness, i.e., tend to defend their positions during the discussion. The long time scale behavior is determined by concatenating multiple Friedkin-Johnsen models (one for each meeting). The proposed model, tuned on real data extracted from the Paris Agreement meetings, achieves consensus on a time horizon similar to that of the real negotiations. Remarkably, the model is also able to identify a series of parties that exerted a key leadership role in the Paris Agreement negotiation process.

Using high-throughput multi-omics data to investigate structural balance in elementary gene regulatory network motifs.

MOTIVATION: The simultaneous availability of ATAC-seq and RNA-seq experiments allows to obtain a more in-depth knowledge on the regulatory mechanisms occurring in gene regulatory networks. In this article, we highlight and analyze two novel aspects that leverage on the possibility of pairing RNA-seq and ATAC-seq data. Namely we investigate the causality of the relationships between transcription factors, chromatin and target genes and the internal consistency between the two omics, here measured in terms of structural balance in the sample correlations along elementary length-3 cycles. RESULTS: We propose a framework that uses the a priori knowledge on the data to infer elementary causal regulatory motifs (namely chains and forks) in the network. It is based on the notions of conditional independence and partial correlation, and can be applied to both longitudinal and non-longitudinal data. Our analysis highlights a strong connection between the causal regulatory motifs that are selected by the data and the structural balance of the underlying sample correlation graphs: strikingly, >97% of the selected regulatory motifs belong to a balanced subgraph. This result shows that internal consistency, as measured by structural balance, is close to a necessary condition for 3-node regulatory motifs to satisfy causality rules. AVAILABILITY AND IMPLEMENTATION: The analysis was carried out in MATLAB and the code can be found at https://github.com/albertozenere/Multi-omics-elementary-regulatory-motifs. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A signed network perspective on the government formation process in parliamentary democracies.

In parliamentary democracies, government negotiations talks following a general election can sometimes be a long and laborious process. In order to explain this phenomenon, in this paper we use structural balance theory to represent a multiparty parliament as a signed network, with edge signs representing alliances and rivalries among parties. We show that the notion of frustration, which quantifies the amount of "disorder" encoded in the signed graph, correlates very well with the duration of the government negotiation talks. For the 29 European countries considered in this study, the average correlation between frustration and government negotiation talks ranges between 0.42 and 0.69, depending on what information is included in the edges of the signed network. Dynamical models of collective decision-making over signed networks with varying frustration are proposed to explain this correlation.

Thermodynamic model of gene regulation for the Or59b olfactory receptor in Drosophila.

Complex eukaryotic promoters normally contain multiple cis-regulatory sequences for different transcription factors (TFs). The binding patterns of the TFs to these sites, as well as the way the TFs interact with each other and with the RNA polymerase (RNAp), lead to combinatorial problems rarely understood in detail, especially under varying epigenetic conditions. The aim of this paper is to build a model describing how the main regulatory cluster of the olfactory receptor Or59b drives transcription of this gene in Drosophila. The cluster-driven expression of this gene is represented as the equilibrium probability of RNAp being bound to the promoter region, using a statistical thermodynamic approach. The RNAp equilibrium probability is computed in terms of the occupancy probabilities of the single TFs of the cluster to the corresponding binding sites, and of the interaction rules among TFs and RNAp, using experimental data of Or59b expression to tune the model parameters. The model reproduces correctly the changes in RNAp binding probability induced by various mutation of specific sites and epigenetic modifications. Some of its predictions have also been validated in novel experiments.

Minimum energy control for complex networks.

The aim of this paper is to shed light on the problem of controlling a complex network with minimal control energy. We show first that the control energy depends on the time constant of the modes of the network, and that the closer the eigenvalues are to the imaginary axis of the complex plane, the less energy is required for complete controllability. In the limit case of networks having all purely imaginary eigenvalues (e.g. networks of coupled harmonic oscillators), several constructive algorithms for minimum control energy driver node selection are developed. A general heuristic principle valid for any directed network is also proposed: the overall cost of controlling a network is reduced when the controls are concentrated on the nodes with highest ratio of weighted outdegree vs indegree.

Qualitative and quantitative responses to press perturbations in ecological networks.

Predicting the sign of press perturbation responses in ecological networks is challenging, due to the poor knowledge of the strength of the direct interactions among the species, and to the entangled coexistence of direct and indirect effects. We show in this paper that, for a class of networks that includes mutualistic and monotone networks, the sign of press perturbation responses can be qualitatively determined based only on the sign pattern of the community matrix, without any knowledge of parameter values. For other classes of networks, we show that a semi-qualitative approach yields sufficient conditions for community matrices with a given sign pattern to exhibit mutualistic responses to press perturbations; quantitative conditions can be provided as well for community matrices that are eventually nonnegative. We also present a computational test that can be applied to any class of networks so as to check whether the sign of the responses to press perturbations is constant in spite of parameter variations.

Controllability of complex networks with unilateral inputs.

In this paper, we study the problem of controlling complex networks with unilateral controls, i.e., controls which can assume only positive or negative values, not both. Given a complex network represented by the adjacency matrix A, an algorithm is developed that constructs an input matrix B such that the resulting system (A, B) is controllable with a near minimal number of unilateral control inputs. This is made possible by a reformulation of classical conditions for controllability that casts the minimal unilateral input selection problem into well known optimization problems. We identify network properties that make unilateral controllability relatively easy to achieve as compared to unrestricted controllability. The analysis of the network topology for instance allows us to establish theoretical bounds on the minimal number of controls required. For various categories of random networks as well as for a number of real-world networks these lower bounds are often achieved by our heuristics.

The Geometric Phase of Stock Trading.

Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.

Drug combinatorics and side effect estimation on the signed human drug-target network.

BACKGROUND: The mode of action of a drug on its targets can often be classified as being positive (activator, potentiator, agonist, etc.) or negative (inhibitor, blocker, antagonist, etc.). The signed edges of a drug-target network can be used to investigate the combined mechanisms of action of multiple drugs on the ensemble of common targets. RESULTS: In this paper it is shown that for the signed human drug-target network the majority of drug pairs tend to have synergistic effects on the common targets, i.e., drug pairs tend to have modes of action with the same sign on most of the shared targets, especially for the principal pharmacological targets of a drug. Methods are proposed to compute this synergism, as well as to estimate the influence of the drugs on the side effect of another drug. CONCLUSIONS: Enriching a drug-target network with information of functional nature like the sign of the interactions allows to explore in a systematic way a series of network properties of key importance in the context of computational drug combinatorics.

Metabolic Adaptation Processes That Converge to Optimal Biomass Flux Distributions.

In simple organisms like E.coli, the metabolic response to an external perturbation passes through a transient phase in which the activation of a number of latent pathways can guarantee survival at the expenses of growth. Growth is gradually recovered as the organism adapts to the new condition. This adaptation can be modeled as a process of repeated metabolic adjustments obtained through the resilencings of the non-essential metabolic reactions, using growth rate as selection probability for the phenotypes obtained. The resulting metabolic adaptation process tends naturally to steer the metabolic fluxes towards high growth phenotypes. Quite remarkably, when applied to the central carbon metabolism of E.coli, it follows that nearly all flux distributions converge to the flux vector representing optimal growth, i.e., the solution of the biomass optimization problem turns out to be the dominant attractor of the metabolic adaptation process.

The phototransduction machinery in the rod outer segment has a strong efficacy gradient.

Rod photoreceptors consist of an outer segment (OS) and an inner segment. Inside the OS a biochemical machinery transforms the rhodopsin photoisomerization into electrical signal. This machinery has been treated as and is thought to be homogenous with marginal inhomogeneities. To verify this assumption, we developed a methodology based on special tapered optical fibers (TOFs) to deliver highly localized light stimulations. By using these TOFs, specific regions of the rod OS could be stimulated with spots of light highly confined in space. As the TOF is moved from the OS base toward its tip, the amplitude of saturating and single photon responses decreases, demonstrating that the efficacy of the transduction machinery is not uniform and is 5-10 times higher at the base than at the tip. This gradient of efficacy of the transduction machinery is attributed to a progressive depletion of the phosphodiesterase along the rod OS. Moreover we demonstrate that, using restricted spots of light, the duration of the photoresponse along the OS does not increase linearly with the light intensity as with diffuse light.

Partial inhibition and bilevel optimization in flux balance analysis.

MOTIVATION: Within Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug. RESULTS: In this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling. CONCLUSIONS: The method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus.

Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10∶90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.