Quantitative Biology

In this letter, we analyze a genetic toggle switch recently studied in the literature where the expression of two repressor proteins can be tuned by controlling two different inputs, namely the concentration of two inducer molecules in the growth medium of the cells. Specifically, we investigate the dynamics of this system when subject to pulse-width modulated (PWM) input. We provide an analytical model that captures qualitatively the experimental observations reported in the literature and approximates its asymptotic behavior. We also discuss the effect that the system parameters have on the prediction accuracy of the model. Moreover, we propose a possible external control strategy to regulate the mean value of the fluorescence of the reporter proteins when the cells are subject to such periodic forcing.

Background: Networks in different domains are characterized by similar global characteristics while differing in local structures. To further extend this concept, we investigated network regularities on a fine scale in order to examine the functional impact of recurring motifs in signed oriented biological networks. In this work we generalize to signaling net works some considerations made on feedback and feed forward loops and extend them by adding a close scrutiny of Linear Triplets, which have not yet been investigate in detail. Results: We studied the role of triplets, either open or closed (Loops or linear events) by enumerating them in different biological signaling networks and by comparing their significance profiles. We compared different data sources and investigated the fine topology of protein networks representing causal relationships based on transcriptional control, phosphorylation, ubiquitination and binding. Not only were we able to generalize findings that have already been reported but we also highlighted a connection between relative motif abundance and node function. Furthermore, by analyzing for the first time Linear Triplets, we highlighted the relative importance of nodes sitting in specific positions in closed signaling triplets. Finally, we tried to apply machine learning to show that a combination of motifs features can be used to derive node function. Availability: The triplets counter used for this work is available as a Cytoscape App and as a standalone command line Java application. this http URL Keywords: Graph theory, graph analysis, graph topology, machine learning, cytoscape

Tumor metastasis is one of the main factors responsible for the high fatality rate of cancer. Metastasis can occur after malignant cells transition from the epithelial phenotype to the mesenchymal phenotype. This transformation allows cells to migrate via the circulatory system and subsequently settle in distant organs after undergoing the reverse transition from the mesenchymal to the epithelial phenotypes. The core gene regulatory network controlling these transitions consists of a system made up of coupled SNAIL/miRNA-34 and ZEB1/miRNA-200 subsystems. In this work, we formulate a mathematical model of the core regulatory motif and analyze its long-term behavior. We start by developing a detailed reaction network with 24 state variables. Assuming fast promoter and mRNA kinetics, we then show how to reduce our model to a monotone four-dimensional system. For the reduced system, monotone dynamical systems theory can be used to prove generic convergence to the set of equilibria for all bounded trajectories. The theory does not apply to the full model, which is not monotone, but we briefly discuss results for singularly-perturbed monotone systems that provide a tool to extend convergence results from reduced to full systems, under appropriate time separation assumptions.

This work analyses the transcriptional effects of some biochemical mechanisms proposed in previous literature which attempts to explain the differential spatial expression of Hedgehog target genes involved in Drosophila development. Specifically, the expression of decapentaplegic and patched, genes whose transcription is believed to be controlled by the activator and repressor forms of the transcription factor Cubitus interruptus (Ci). This study is based on a thermodynamic approach which provides binding equilibrium weighted average rate expressions for genes controlled by transcription factors competing and (possibly) cooperating for common binding sites, in the same way that Ci's activator and repressor forms might do. These expressions are refined to produce simpler equivalent formulae allowing their mathematical analysis. Thanks to this, we can evaluate the correlation between several molecular processes and biological features observed at tissular level. In particular, we will focus on how high/low/differential affinity and null/total/partial cooperation modify the activation/repression regions of the target genes or provoke signal modulation.

Clusters of circulating tumor cells (CTCs), although rare, may account for more than 95% of metastases. Inflammatory breast cancer (IBC) is a highly aggressive subtype that chiefly metastasizes via CTC clusters. Theory suggests that physical systems with hierarchical organization tend to be more adaptable due to their ability to efficiently span the set of available states. We used the cophenetic correlation coefficient (CCC) to quantify the hierarchical organization in the expression of collective dissemination associated and IBC associated genes, and found that the CCC of both gene sets was higher in (a) epithelial cell lines as compared to mesenchymal cell lines and (b) IBC tumor samples as compared to non-IBC breast cancer samples. A higher CCC of both networks was also correlated with a higher rate of metastatic relapse in breast cancer patients. Gene set enrichment analysis could not provide similar insights, indicating that the CCC provides additional information regarding the organizational complexity of gene expression. These results suggest that retention of epithelial traits in disseminating tumor cells as IBC progresses promotes successful metastasis and the CCC may be a prognostic factor for IBC.

We analyze the Conradi-Kahle Algorithm for detecting binomiality. We present experiments using two implementations of the algorithm in Macaulay2 and Maple on biological models and assess the performance of the algorithm on these models. We compare the two implementations with each other and with Gröbner bases computations up to their performance on these biological models.

Single-cell stochastic gene expression, with gene state switching, transcription, translation, and negative feedback, can exhibit oscillatory kinetics that is statistically characterized in terms of a non-monotonic power spectrum. Using a solvable model, we illustrate the oscillation as a stochastic circulation along a hysteresis loop. A triphasic bifurcation upon the increasing strength of negative feedback is observed, which reveals how random bursts evolve into stochastic oscillations. Translational bursting is found to enhance the efficiency and the regime of stochastic oscillations. Time-lapse data of the p53 protein from MCF7 single cells validate our theory; the general conclusions are further supported by numerical computations for more realistic models. These results provide a resolution to R. Thomas' two conjectures for the single-cell stochastic gene expression kinetics.

The analysis of a protein-expression pattern from tissue microarray (TMA) data will not immediately give an answer on synergistic or antagonistic effects between the expression of the observed proteins. But contrary to apparent first impression, it is possible to reveal those cooperative phenomena from TMA data. We present here a largely assumption-free combinatorial analysis, related to correlation networks but with much less arbitrary constraints. A strong focus was put on the analysis of the basic data to analyze how the cooperative phenomena might be imprinted in the TMA data structure. The study design was based on two independent panels of 589 and 366 invasive breast cancer cases from different institutions, assembled on tissue microarrays. The combinatorial analysis generates an optimal rank ordering of protein-expression coherence. The outcome of the analysis corresponds to all the single observations scattered over several publications and integrates them in one context. This means all these scattered observations can also be deduced from one TMA experiment. A comprehensive statistical meta-analysis of the TMA data suggests the existence of a superposition of three basic coherence situations, and offers the opportunity to analyze these data properties with additional real-world data and synthetic data in more detail. The presented algorithm gives molecular pathologists a tool to extract dependency information from TMA data. Beyond this practical benefit, some light was shed on how dependency aspects might be imprinted into expression data. This will certainly foster the refinement of algorithms to reconstruct dependency networks. The implementation of the algorithm is at the moment not end-user suitable, but available on request.

G protein coupled receptors (GPCRs) produce pleiotropic effects by their capacity to engage numerous signaling pathways once activated. Functional selectivity (also called biased signaling), where specific compounds can bring GPCRs to adopt conformations that enable selective receptor coupling to distinct signaling pathways, continues to be significantly investigated. However, an important but often overlooked aspect of functional selectivity is the capability of ligands such as angiotensin II (AngII) to adopt specific conformations that may preferentially bind to selective GPCRs structures. Understanding both receptor and ligand conformation is of the utmost importance for the design of new drugs targeting GPCRs. In this study, we examined the properties of AngII cyclic analogs to impart biased agonism on the angiotensin type 1 receptor (AT1R). Positions 3 and 5 of AngII were substituted for cysteine and homocysteine residues ([Sar1Hcy3,5]AngII, [Sar1Cys3Hcy5]AngII and [Sar1Cys3,5]AngII) and the resulting analogs were evaluated for their capacity to activate the Gq/11, G12, Gi2, Gi3, Gz, ERK and \b{eta}-arrestin (\b{eta}arr) signaling pathways via AT1R. Interestingly, [Sar1Hcy3,5]AngII exhibited potency and full efficacy on all pathways tested with the exception of the Gq pathway. Molecular dynamic simulations showed that the energy barrier associated with the insertion of residue Phe8 of AngII within the hydrophobic core of AT1R, associated with Gq/11 activation, is increased with [Sar1Hcy3,5]AngII. These results suggest that constraining the movements of molecular determinants within a given ligand by introducing cyclic structures may lead to the generation of novel ligands providing more efficient biased agonism.

The chapter reviews the syntax to store machine-readable annotations and describes the mapping between rule-based modelling entities (e.g., agents and rules) and these annotations. In particular, we review an annotation framework and the associated guidelines for annotating rule-based models of molecular interactions, encoded in the commonly used Kappa and BioNetGen languages, and present prototypes that can be used to extract and query the annotations. An ontology is used to annotate models and facilitate their description.