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At least 217 records · Page 12Linked to original sources
arXiv2010

Toolbox model of evolution of metabolic pathways on networks of arbitrary topology

In prokaryotic genomes the number of transcriptional regulators is known to quadratically scale with the total number of protein-coding genes. Toolbox model was recently proposed to explain this scaling for metabolic enzymes and their regulators. According to its rules the metabolic network of an organism evolves by horizontal transfer of pathways from other species. These pathways are part of a larger "universal" network formed by the union of all species-specific networks. It remained to be understood, however, how the topological properties of this universal network influence the scaling law of functional content of genomes. In this study we answer this question by first analyzing the scaling properties of the toolbox model on arbitrary tree-like universal networks. We mathematically prove that the critical branching topology, in which the average number of upstream neighbors of a node is equal to one, is both necessary and sufficient for the quadratic scaling. Conversely, the toolbox model on trees with exponentially expanding, supercritical topology is characterized by the linear scaling with logarithmic corrections. We further generalize our model to include reactions with multiple substrates/products as well as branched or cyclic metabolic pathways. Unlike the original model the new version employs evolutionary optimized pathways with the smallest number of reactions necessary to achieve their metabolic tasks. Numerical simulations of this most realistic model on the universal network from the KEGG database again produced approximately quadratic scaling. Our results demonstrate why, in spite of their "small-world" topology, real-life metabolic networks are characterized by a broad distribution of pathway lengths and sizes of metabolic regulons in regulatory networks.

q-bio.MN↗
arXiv2010

Analysis of a Mathematical Model of Apoptosis: Individual Differences and Malfunction in Programmed Cell Death

Apoptosis is an important area of research because of its role in keeping a mature multicellular organism's number of cells constant hence, ensuring that the organism does not have cell accumulation that may transform into cancer with additional hallmarks. Firstly, we have carried out sensitivity analysis on an existing mitochondria-dependent mathematical apoptosis model to find out which parameters have a role in causing monostable cell survival i.e., malfunction in apoptosis. We have then generated three healthy cell models by changing these sensitive parameters while preserving bistability i.e., healthy functioning. For each healthy cell, we varied the proapoptotic production rates, which were found to be among the most sensitive parameters, to yield cells that have malfunctioning apoptosis. We simulated caspase-3 activation, by numerically integrating the governing ordinary differential equations of a mitochondria-dependent apoptosis model, in a hypothetical malfunctioning cell which is treated by four potential treatments, namely: (i) proteasome inhibitor treatment, (ii) Bcl-2 inhibitor treatment, (iii) IAP inhibitor treatment, (iv) Bid-like synthetic peptides treatment. The simulations of the present model suggest that proteasome inhibitor treatment is the most effective treatment though it may have severe side effects. For this treatment, we observed that the amount of proteasome inhibitor needed for caspase-3 activation may be different for cells in individuals with a different proapoptotic protein deficiency. We also observed that caspase-3 can be activated by Bcl-2 inhibitor treatment only in those hypothetical malfunctioning cells with Bax deficiency but not in others. These support the view that molecular heterogeneity in individuals may be an important factor in determining the individuals' positive or negative responses to treatments.

q-bio.MN↗
arXiv2010

Noise-induced oscillatory shuttling of NF-κB in a two compartment IKK-NF-κB-IκB-A20 signaling model

NF-κB is a pleiotropic protein whose nucleo-cytoplasmic trafficking is tightly regulated by multiple negative feedback loops embedded in the NF-κB signaling network and contributes to diverse gene expression profiles important in immune cell differentiation, cell apoptosis, and innate immunity. The intracellular signaling processes and their control mechanisms, however, are susceptible to both extrinsic and intrinsic noise. In this article, we present numerical evidence for a universal dynamic behavior of NF-κB, namely oscillatory nucleo-cytoplasmic shuttling, due to the fundamentally stochastic nature of the NF-κB signaling network. We simulated the effect of extrinsic noise with a deterministic ODE model, using a statistical ensemble approach, generating many copies of the signaling network with different kinetic rates sampled from a biologically feasible parameter space. We modeled the effect of intrinsic noise by simulating the same networks stochastically using the Gillespie algorithm. The results demonstrate that extrinsic noise diversifies the shuttling patterns of NF-κB response, whereas intrinsic noise induces oscillatory behavior in many of the otherwise non-oscillatory patterns. We identify two key model parameters which significantly affect the NF-κB dynamic response and deduce a two-dimensional phase-diagram of the NF-κB response as a function of these parameters. We conclude that if single-cell experiments are performed, a rich variety of NF-κB response will be observed, even if population-level experiments, which average response over large numbers of cells, do not evidence oscillatory behavior.

q-bio.MN↗
arXiv2010

Genotype networks, innovation, and robustness in sulfur metabolism

Metabolic networks are complex systems that comprise hundreds of chemical reactions which synthesize biomass molecules from chemicals in an organism's environment. The metabolic network of any one organism is encoded by a metabolic genotype, defined by a set of enzyme-coding genes whose products catalyze the network's reactions. Each metabolic genotype has a metabolic phenotype, such as the ability to synthesize biomass on a spectrum of different sources of chemical elements and energy. We here focus on sulfur metabolism, which is attractive to study the evolution of metabolic networks, because it involves many fewer reactions than carbon metabolism. Specifically, we study properties of the space of all possible metabolic genotypes, and analyze properties of random metabolic genotypes that are viable on different numbers of sulfur sources. We show that metabolic genotypes with the same phenotype form large connected genotype networks that extend far through metabolic genotype space. How far they reach through this space is a linear function of the number of super-essential reactions in such networks, the number of reactions that occur in all networks with the same phenotype. We show that different neighborhoods of any genotype network harbor very different novel phenotypes, metabolic innovations that can sustain life on novel sulfur sources. We also analyze the ability of evolving populations of metabolic networks to explore novel metabolic phenotypes. This ability is facilitated by the existence of genotype networks, because different neighborhoods of these networks contain very different novel phenotypes. In contrast to macromolecules, where phenotypic robustness may facilitate phenotypic innovation, we show that here the ability to access novel phenotypes does not monotonically increase with robustness.

q-bio.MN↗
arXiv2010

Saturation Probabilities of Continuous-Time Sigmoidal Networks

From genetic regulatory networks to nervous systems, the interactions between elements in biological networks often take a sigmoidal or S-shaped form. This paper develops a probabilistic characterization of the parameter space of continuous-time sigmoidal networks (CTSNs), a simple but dynamically-universal model of such interactions. We describe an efficient and accurate method for calculating the probability of observing effectively M-dimensional dynamics in an N-element CTSN, as well as a closed-form but approximate method. We then study the dependence of this probability on N, M, and the parameter ranges over which sampling occurs. This analysis provides insight into the overall structure of CTSN parameter space.

q-bio.NC↗
arXiv2010

Linear noise approximation of noise-induced oscillation in NF-κB signaling network

NF-κB, one of key regulators of inflammation, apoptosis, and differentiation, was found to have noisy oscillatory shuttling between the nucleus and the cytoplasm in single cells when cells are stimulated by cytokine TNFα. We present the analytical analysis which uncovers the underlying physical mechanisms of this spectacular noise-induced transition in biological networks. Starting with the master equation describing both signaling and transcription events in NF-κB signaling network, we derived the macroscopic and the Fokker-Planck equations by using van Kampen's sysem size expansion. Using the noise-induced oscillatory signatures present in the power spectrum, we constructed the two-dimensional phase diagram where the noise-induced oscillation emerges in the dynamically stable parameter space.

q-bio.MN↗
arXiv2010

Intercellular spiral waves of calcium in a two dimensional network of cells

It is shown, by means of numerical simulations, that intercellular spiral waves of calcium can be initiated in a network of coupled cells as a result of a de-synchronization between Ca2+ oscillations in two domains. No artificial heterogeneities need to be imposed to the system for spontaneous formation of spiral waves. The de-synchronization occurs near the interface of the stimulated region (which acts as a pacemaker) and propagates over the entire network. We also find the outcome of the collision of two spiral waves.

q-bio.MN↗
arXiv2010

Protein Interaction Networks are Fragile against Random Attacks and Robust against Malicious Attacks

The capacity to resist attacks from the environment is crucial to the survival of all organisms. We quantitatively analyze the susceptibility of protein interaction networks of numerous organisms to random and malicious attacks. We find for all organisms studied that random rewiring improves protein network robustness, so that actual networks are more fragile than rewired surrogates. This unexpected fragility contrasts with the behavior of networks such as the Internet, whose robustness decreases with random rewiring. We trace this surprising effect to the modular structure of protein networks.

physics.comp-ph↗
arXiv2010

How the Dimension of Space Affects the Products of Pre-Biotic Evolution: The Spatial Population Dynamics of Structural Complexity and The Emergence of Membranes

We show that autocatalytic networks of epsilon-machines and their population dynamics differ substantially between spatial (geographically distributed) and nonspatial (panmixia) populations. Generally, regions of spacetime-invariant autocatalytic networks---or domains---emerge in geographically distributed populations. These are separated by functional membranes of complementary epsilon-machines that actively translate between the domains and are responsible for their growth and stability. We analyze both spatial and nonspatial populations, determining the algebraic properties of the autocatalytic networks that allow for space to affect the dynamics and so generate autocatalytic domains and membranes. In addition, we analyze populations of intermediate spatial architecture, delineating the thresholds at which spatial memory (information storage) begins to determine the character of the emergent auto-catalytic organization.

q-bio.PE↗
arXiv2010

Characterization of differentially expressed genes using high-dimensional co-expression networks

We present a technique to characterize differentially expressed genes in terms of their position in a high-dimensional co-expression network. The set-up of Gaussian graphical models is used to construct representations of the co-expression network in such a way that redundancy and the propagation of spurious information along the network are avoided. The proposed inference procedure is based on the minimization of the Bayesian Information Criterion (BIC) in the class of decomposable graphical models. This class of models can be used to represent complex relationships and has suitable properties that allow to make effective inference in problems with high degree of complexity (e.g. several thousands of genes) and small number of observations (e.g. 10-100) as typically occurs in high throughput gene expression studies. Taking advantage of the internal structure of decomposable graphical models, we construct a compact representation of the co-expression network that allows to identify the regions with high concentration of differentially expressed genes. It is argued that differentially expressed genes located in highly interconnected regions of the co-expression network are less informative than differentially expressed genes located in less interconnected regions. Based on that idea, a measure of uncertainty that resembles the notion of relative entropy is proposed. Our methods are illustrated with three publically available data sets on microarray experiments (the larger involving more than 50,000 genes and 64 patients) and a short simulation study.

stat.AP↗
arXiv2010

Boolean Threshold Networks: Virtues and Limitations for Biological Modeling

Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of \textit{S. cerevisiae} and \textit{S. pombe}. Threshold networks assume that gene regulation processes are additive. This, however, contrasts with the mechanism proposed by S. Kauffman in which each of the logic functions must be carefully constructed to accurately take into account the combinatorial nature of gene regulation. While Kauffman Boolean networks have been extensively studied and proved to have the necessary properties required for modeling the fundamental characteristics of genetic regulatory networks, not much is known about the essential properties of threshold networks. Here we study the dynamical properties of these networks with different connectivities, activator-repressor proportions, activator-repressor strengths and different thresholds. Special attention is paid to the way in which the threshold value affects the dynamical regime in which the network operates and the structure of the attractor landscape. We find that only for a very restricted set of parameters, these networks show dynamical properties consistent with what is observed in biological systems. The virtues of these properties and the possible problems related with the restrictions are discussed and related to earlier work that uses these kind of models.

nlin.CD↗
arXiv2010

Quantification and Minimization of Crosstalk Sensitivity in Networks

Crosstalk is defined as the set of unwanted interactions among the different entities of a network. Crosstalk is present in various degrees in every system where information is transmitted through a means that is accessible by all the individual units of the network. Using concepts from graph theory, we introduce a quantifiable measure for sensitivity to crosstalk, and analytically derive the structure of the networks in which it is minimized. It is shown that networks with an inhomogeneous degree distribution are more robust to crosstalk than corresponding homogeneous networks. We provide a method to construct the graph with the minimum possible sensitivity to crosstalk, given its order and size. Finally, for networks with a fixed degree sequence, we present an algorithm to find the optimal interconnection structure among their vertices.

q-bio.MN↗
arXiv2010

Flows in complex biochemical networks: Role of low degree nodes

Metabolic networks have two properties that are generally regarded as unrelated: One, they have metabolic reactions whose single knockout is lethal for the organism, and two, they have correlated sets of reactions forming functional modules. In this review we argue that both essentiality and modularity seem to arise as a consequence of the same structural property: the existence of low degree metabolites. This observation allows a prediction of (a) essential metabolic reactions which are potential drug targets in pathogenic microorganisms and (b) regulatory modules within biological networks, from purely structural information about the metabolic network.

q-bio.MN↗
arXiv2010

Role-based similarity in directed networks

The widespread relevance of increasingly complex networks requires methods to extract meaningful coarse-grained representations of such systems. For undirected graphs, standard community detection methods use criteria largely based on density of connections to provide such representations. We propose a method for grouping nodes in directed networks based on the role of the nodes in the network, understood in terms of patterns of incoming and outgoing flows. The role groupings are obtained through the clustering of a similarity matrix, formed by the distances between feature vectors that contain the number of in and out paths of all lengths for each node. Hence nodes operating in a similar flow environment are grouped together although they may not themselves be densely connected. Our method, which includes a scale factor that reveals robust groupings based on increasingly global structure, provides an alternative criterion to uncover structure in networks where there is an implicit flow transfer in the system. We illustrate its application to a variety of data from ecology, world trade and cellular metabolism.

physics.soc-ph↗
arXiv2010

Exploring dimethylsulfate for in vivo proteome footprinting

Protein footprinting is a new methodology that is based on probing, typically with the use of mass spectrometry, of reactivity of different aminoacid residues to a modifying reagent. Data thus obtained allow one to make inferences about protein conformations and their intermolecular interactions. Most of the protein footprinting studies so far have been performed on individual proteins in vitro. We explore whether a similar approach is possible with the proteins inside of living cells, employing dimethylsulfate (DMS), a reagent widely used for the in vivo footprinting of nucleic acids. DMS can induce methylation of the lysine, histidine and glutamate residues on proteins. Using models of the histone H2B/H2AZ heterodimer assembled in vitro and from chromatin treated in vivo, we show that the methylation by deuterated DMS allows one to distinguish the accessibility of a particular residue in and out of the protein's environmental/structural context. The detection of changes in protein conformations or their interactions in vivo can provide a new approach to the identification of proteins involved in various intracellular pathways and help in the search for perspective drug targets and biomarkers of diseases.

q-bio.MN↗
arXiv2011

Pathways of Distinction Analysis: a new technique for multi-SNP analysis of GWAS data

Genome-wide association studies have become increasingly common due to advances in technology and have permitted the identification of differences in single nucleotide polymorphism (SNP) alleles that are associated with diseases. However, while typical GWAS analysis techniques treat markers individually, complex diseases are unlikely to have a single causative gene. There is thus a pressing need for multi-SNP analysis methods that can reveal system-level differences in cases and controls. Here, we present a novel multi-SNP GWAS analysis method called Pathways of Distinction Analysis (PoDA). The method uses GWAS data and known pathway-gene and gene-SNP associations to identify pathways that permit, ideally, the distinction of cases from controls. The technique is based upon the hypothesis that if a pathway is related to disease risk, cases will appear more similar to other cases than to controls for the SNPs associated with that pathway. By systematically applying the method to all pathways of potential interest, we can identify those for which the hypothesis holds true, i.e., pathways containing SNPs for which the samples exhibit greater within-class similarity than across classes. Importantly, PoDA improves on existing single-SNP and SNP-set enrichment analyses in that it does not require the SNPs in a pathway to exhibit independent main effects. This permits PoDA to reveal pathways in which epistatic interactions drives risk. In this paper, we detail the PoDA method and apply it to two GWA studies: one of breast cancer, and the other of liver cancer. The results obtained strongly suggest that there exist pathway-wide genomic differences that contribute to disease susceptibility. PoDA thus provides an analytical tool that is complementary to existing techniques and has the power to enrich our understanding of disease genomics at the systems-level.

q-bio.QM↗
arXiv2011

A proof of the Global Attractor Conjecture in the single linkage class case

This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems. Specifically, this paper provides a proof of the Global Attractor Conjecture in the setting where the underlying reaction diagram consists of a single linkage class, or connected component. The conjecture dates back to the early 1970s and is the most well known and important open problem in the field of chemical reaction network theory. The resolution of the conjecture has important biological and mathematical implications in both the deterministic and stochastic settings. One of our main analytical tools, which is introduced here, will be a method for partitioning the relevant monomials of the dynamical system along sequences of trajectory points into classes with comparable growths. We will use this method to conclude that if a trajectory converges to the boundary, then a whole family of Lyapunov functions decrease along the trajectory. This will allow us to overcome the fact that the usual Lyapunov functions of chemical reaction network theory are bounded on the boundary of the positive orthant, which has been the technical sticking point to a proof of the Global Attractor Conjecture in the past.

math.DS↗