A Survey of Best Monotone Degree Conditions for Graph Properties

We survey sufficient degree conditions, for a variety of graph properties, that are best possible in the same sense that Chvatal's well-known degree condition for hamiltonicity is best possible.Comment: 25 page

Characterization of small molecules inhibiting the pro-angiogenic activity of the zinc finger transcription factor Vezf1

Discovery of inhibitors for endothelial-related transcription factors can contribute to the development of anti-angiogenic therapies that treat various diseases, including cancer. The role of transcription factor Vezf1 in vascular development and regulation of angiogenesis has been defined by several earlier studies. Through construction of a computational model for Vezf1, work here has identified a novel small molecule drug capable of inhibiting Vezf1 from binding to its cognate DNA binding site. Using structure-based design and virtual screening of the NCI Diversity Compound Library, 12 shortlisted compounds were tested for their ability to interfere with the binding of Vezf1 to DNA using electrophoretic gel mobility shift assays. We identified one compound, T4, which has an IC50 of 20 μM. Using murine endothelial cells, MSS31, we tested the effect of T4 on endothelial cell viability and angiogenesis by using tube formation assay. Our data show that addition of T4 in cell culture medium does not affect cell viability at concentrations lower or equal to its IC 50 but strongly inhibits the network formation by MSS31 in the tube formation assays. Given its potential efficacy, this inhibitor has significant therapeutic potential in several human diseases

Analytical description of finite size effects for RNA secondary structures

The ensemble of RNA secondary structures of uniform sequences is studied analytically. We calculate the partition function for very long sequences and discuss how the cross-over length, beyond which asymptotic scaling laws apply, depends on thermodynamic parameters. For realistic choices of parameters this length can be much longer than natural RNA molecules. This has to be taken into account when applying asymptotic theory to interpret experiments or numerical results.Comment: 10 pages, 13 figures, published in Phys. Rev.

Computational analysis of a plant receptor interaction network

Trabajo fin de máster en Bioinformática y Biología ComputacionalIn all organisms, complex protein-protein interactions (PPI) networks control major biological functions yet studying their structural features presents a major analytical challenge. In plants, leucine-rich-repeat receptor kinases (LRR-RKs) are key in sensing and transmitting non-self as well as self-signals from the cell surface. As such, LRR-RKs have both developmental and immune functions that allow plants to make the most of their environments. In the model organism in plant molecular biology, Arabidopsis thaliana, most LRR-RKs are still represented by biochemically and genetically uncharacterized receptors. To fix this an LRR-based Cell Surface Interaction (CSI LRR ) network was obtained in 2018, a protein-protein interaction network of the extracellular domain of 170 LRR-RKs that contains 567 bidirectional interactions. Several network analyses have been performed with CSI LRR . However, these analyses have so far not considered the spatial and temporal expression of its proteins. Neither has it been characterized in detail the role of the extracellular domain (ECD) size in the network structure. Because of that, the objective of the present work is to continue with more in depth analyses with the CSI LRR network. This would provide important insights that will facilitate LRR-RKs function characterization. The first aim of this work is to test out the fit of the CSI LRR network to a scale-free topology. To accomplish that, the degree distribution of the CSI LRR network was compared with the degree distribution of the known network models of scale-free and random. Additionally, three network attack algorithms were implemented and applied to these two network models and the CSI LRR network to compare their behavior. However, since the CSI LRR interaction data comes from an in vitro screening, there is no direct evidence whether its protein-protein interactions occur inside the plant cells. To gain insight on how the network composition changes depending on the transcriptional regulation, the interaction data of the CSI LRR was integrated with 4 different RNA-Seq datasets related with the network biological functions. To automatize this task a Python script was written. Furthermore, it was evaluated the role of the LRR-RKs in the network structure depending on the size of their extracellular domain (large or small). For that, centrality parameters were measured, and size-targeted attacks performed. Finally, gene regulatory information was integrated into the CSI LRR to classify the different network proteins according to the function of the transcription factors that regulate its expression. The results were that CSI LRR fits a power law degree distribution and approximates a scale- free topology. Moreover, CSI LRR displays high resistance to random attacks and reduced resistance to hub/bottleneck-directed attacks, similarly to scale-free network model. Also, the integration of CSI LRR interaction data and RNA-Seq data suggests that the transcriptional regulation of the network is more relevant for developmental programs than for defense responses. Another result was that the LRR-RKs with a small ECD size have a major role in the maintenance of the CSI LRR integrity. Lastly, it was hypothesized that the integration of CSI LRR interaction data with predicted gene regulatory networks could shed light upon the functioning of growth-immunity signaling crosstalk

Vibrational Branching Ratios From The Dissociation Of The NeIBr Van Der Waals Molecule

The degree of vibrational excitation in the IBr fragment from the vibrational predissociation of NeIBr (A (3)PI(1)) has been measured using two-color pump-probe laser-induced fluorescence spectroscopy. We find that for the lowest initial vibrational states examined, DELTA-upsilon = -1 dissociation pathways dominate the dynamics, while this channel is closed for upsilon greater-than-or-equal-to 17. From this result, the A state binding energy (D0) of the complex is determined to be 67 +/- 4 cm-1, while that in the X electronic state is found to be 73 +/- 4 cm-1. The X state binding energy is identical to that for NeI2 and NeBr2, suggesting that the potential energy surface for NeIBr can be constructed from a summation of atom-atom pair potentials; we present such a model potential energy surface. The variations in the vibrational branching ratios, when combined with the trends in the predissociation rates, point to the importance of fragment rotational excitation in the dynamics of the dissociation

Effect of Doublon-Holon Binding on Mott transition---Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models

To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length $\xi_{\rm dh}$ and the minimum D-D exclusion length $\xi_{\rm dd}$. Generally, a Mott transition occurs when $\xi_{\rm dh}$ becomes comparable to $\xi_{\rm dd}$. In the conductive (superfluid) state, domains of D-H pairs overlap with each other ($\xi_{\rm dh}>\xi_{\rm dd}$); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.Comment: 16 pages, 22 figures, submitted to J. Phys. Soc. Jp

Transcriptional memory emerges from cooperative histone modifications

Background
Transcriptional regulation in cells makes use of diverse mechanisms to ensure that functional states can be maintained and adapted to variable environments; among them are chromatin-related mechanisms. While mathematical models of transcription factor networks controlling development are well established, models of transcriptional regulation by chromatin states are rather rare despite they appear to be a powerful regulatory mechanism.
Results
We here introduce a mathematical model of transcriptional regulation governed by histone modifications. This model describes binding of protein complexes to chromatin which are capable of reading and writing histone marks. Molecular interactions between these complexes and DNA or histones create a regulatory switch of transcriptional activity possessing a regulatory memory. The regulatory states of the switch depend on the activity of histone (de-) methylases, the structure of the DNA-binding regions of the complexes, and the number of histones contributing to binding. 
We apply our model to transcriptional regulation by trithorax- and polycomb- complex binding. By analyzing data on pluripotent and lineage-committed cells we verify basic model assumptions and provide evidence for a positive effect of the length of the modified regions on the stability of the induced regulatory states and thus on the transcriptional memory.
Conclusions
Our results provide new insights into epigenetic modes of transcriptional regulation. Moreover, they implicate well-founded hypotheses on cooperative histone modifications, proliferation induced epigenetic changes and higher order folding of chromatin which await experimental validation. Our approach represents a basic step towards multi-scale models of transcriptional control during development and lineage specification. 
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Under-dominance constrains the evolution of negative autoregulation in diploids

Regulatory networks have evolved to allow gene expression to rapidly track changes in the environment as well as to buffer perturbations and maintain cellular homeostasis in the absence of change. Theoretical work and empirical investigation in Escherichia coli have shown that negative autoregulation confers both rapid response times and reduced intrinsic noise, which is reflected in the fact that almost half of Escherichia coli transcription factors are negatively autoregulated. However, negative autoregulation is exceedingly rare amongst the transcription factors of Saccharomyces cerevisiae. This difference is all the more surprising because E. coli and S. cerevisiae otherwise have remarkably similar profiles of network motifs. In this study we first show that regulatory interactions amongst the transcription factors of Drosophila melanogaster and humans have a similar dearth of negative autoregulation to that seen in S. cerevisiae. We then present a model demonstrating that this fundamental difference in the noise reduction strategies used amongst species can be explained by constraints on the evolution of negative autoregulation in diploids. We show that regulatory interactions between pairs of homologous genes within the same cell can lead to under-dominance - mutations which result in stronger autoregulation, and decrease noise in homozygotes, paradoxically can cause increased noise in heterozygotes. This severely limits a diploid's ability to evolve negative autoregulation as a noise reduction mechanism. Our work offers a simple and general explanation for a previously unexplained difference between the regulatory architectures of E. coli and yeast, Drosophila and humans. It also demonstrates that the effects of diploidy in gene networks can have counter-intuitive consequences that may profoundly influence the course of evolution

Network-based approaches to explore complex biological systems towards network medicine

Network medicine relies on different types of networks: from the molecular level of protein–protein interactions to gene regulatory network and correlation studies of gene expression. Among network approaches based on the analysis of the topological properties of protein–protein interaction (PPI) networks, we discuss the widespread DIAMOnD (disease module detection) algorithm. Starting from the assumption that PPI networks can be viewed as maps where diseases can be identified with localized perturbation within a specific neighborhood (i.e., disease modules), DIAMOnD performs a systematic analysis of the human PPI network to uncover new disease-associated genes by exploiting the connectivity significance instead of connection density. The past few years have witnessed the increasing interest in understanding the molecular mechanism of post-transcriptional regulation with a special emphasis on non-coding RNAs since they are emerging as key regulators of many cellular processes in both physiological and pathological states. Recent findings show that coding genes are not the only targets that microRNAs interact with. In fact, there is a pool of different RNAs—including long non-coding RNAs (lncRNAs) —competing with each other to attract microRNAs for interactions, thus acting as competing endogenous RNAs (ceRNAs). The framework of regulatory networks provides a powerful tool to gather new insights into ceRNA regulatory mechanisms. Here, we describe a data-driven model recently developed to explore the lncRNA-associated ceRNA activity in breast invasive carcinoma. On the other hand, a very promising example of the co-expression network is the one implemented by the software SWIM (switch miner), which combines topological properties of correlation networks with gene expression data in order to identify a small pool of genes—called switch genes—critically associated with drastic changes in cell phenotype. Here, we describe SWIM tool along with its applications to cancer research and compare its predictions with DIAMOnD disease genes