Genetic Susceptibility Loci in Rheumatoid Arthritis Establish Transcriptional Regulatory Networks with Other Genes

Linkage studies have identified the human leukocyte antigen (HLA)-DRB1 as a putative rheumatoid arthritis (RA) susceptibility locus (SL). Nevertheless, it was estimated that its contribution was partial, suggesting that other non-HLA genes may play a role in RA susceptibility. To test this hypothesis, we conducted microarray transcription profiling of peripheral blood mononuclear cells in 15 RA patients and analyzed the data, using bioinformatics programs (significance analysis of microarrays method and GeneNetwork), which allowed us to determine the differentially expressed genes and to reconstruct transcriptional networks. The patients were grouped according to disease features or treatment with tumor necrosis factor blocker. Transcriptional networks that were reconstructed allowed us to identify the interactions occurring between RA SL and other genes, for example, HLA-DRB1 interacting with FNDC3A (fibronectin type III domain containing 3A). Given that fibronectin fragments can stimulate mediators of matrix and cartilage destruction in RA, this interaction is of special interest and may contribute to a clearer understanding of the functional role of HLA-DRB1 in RA pathogenesis.

Genes that code for T cell signaling proteins establish transcriptional regulatory networks during thymus ontogeny

Gene expression profiling by cDNA microarrays during murine thymus ontogeny has contributed to dissecting the large-scale molecular genetics of T cell maturation. Gene profiling, although useful for characterizing the thymus developmental phases and identifying the differentially expressed genes, does not permit the determination of possible interactions between genes. In order to reconstruct genetic interactions, on RNA level, within thymocyte differentiation, a pair of microarrays containing a total of 1,576 cDNA sequences derived from the IMAGE MTB library was applied on samples of developing thymuses (14-17 days of gestation). The data were analyzed using the GeneNetwork program. Genes that were previously identified as differentially expressed during thymus ontogeny showed their relationships with several other genes. The present method provided the detection of gene nodes coding for proteins implicated in the calcium signaling pathway, such as Prrg2 and Stxbp3, and in protein transport toward the cell membrane, such as Gosr2. The results demonstrate the feasibility of reconstructing networks based on cDNA microarray gene expression determinations, contributing to a clearer understanding of the complex interactions between genes involved in thymus/thymocyte development.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

A coupled boundary element/differential equation method formulation for plate-beam interaction analysis

In this work, a new boundary element formulation for the analysis of plate-beam interaction is presented. This formulation uses a three nodal value boundary elements and each beam element is replaced by its actions on the plate, i.e., a distributed load and end of element forces. From the solution of the differential equation of a beam with linearly distributed load the plate-beam interaction tractions can be written as a function of the nodal values of the beam. With this transformation a final system of equation in the nodal values of displacements of plate boundary and beam nodes is obtained and from it, all unknowns of the plate-beam system are obtained. Many examples are analyzed and the results show an excellent agreement with those from the analytical solution and other numerical methods. (C) 2009 Elsevier Ltd. All rights reserved.

Darcy`s law and the differential equation of motion

This note addresses the relation between the differential equation of motion and Darcy`s law. It is shown that, in different flow conditions, three versions of Darcy`s law can be rigorously derived from the equation of motion.

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

INDEX OF AN IMPLICIT DIFFERENTIAL EQUATION

In this paper we introduce the concept of the index of an implicit differential equation F(x,y,p) = 0, where F is a smooth function, p = dy/dx, F(p) = 0 and F(pp) = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in R(5).

A singular integro-differential equation model for dryout in LMFBR boiler tubes

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem Appropriate boundary conditions for the now are discussed The resulting non-lineal singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques) Predictions for the length to the dryout point from the entry of the annular regime are made The influence of both the traction tau provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter eta on the dryout length is investigated

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our system remains oscillatory. (C) 2009 Elsevier Inc. All rights reserved.

The impact of measurement errors in the identification of regulatory networks

Background: There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise. Results: This article investigates the effects of measurement error on the estimation of the parameters in regulatory networks. Simulation studies indicate that, in both time series (dependent) and non-time series (independent) data, the measurement error strongly affects the estimated parameters of the regulatory network models, biasing them as predicted by the theory. Moreover, when testing the parameters of the regulatory network models, p-values computed by ignoring the measurement error are not reliable, since the rate of false positives are not controlled under the null hypothesis. In order to overcome these problems, we present an improved version of the Ordinary Least Square estimator in independent (regression models) and dependent (autoregressive models) data when the variables are subject to noises. Moreover, measurement error estimation procedures for microarrays are also described. Simulation results also show that both corrected methods perform better than the standard ones (i.e., ignoring measurement error). The proposed methodologies are illustrated using microarray data from lung cancer patients and mouse liver time series data. Conclusions: Measurement error dangerously affects the identification of regulatory network models, thus, they must be reduced or taken into account in order to avoid erroneous conclusions. This could be one of the reasons for high biological false positive rates identified in actual regulatory network models.

Transcriptional regulation differs in affected facioscapulohumeral muscular dystrophy patients compared to asymptomatic related carriers

Facioscapulohumeral muscular dystrophy (FSHD) is a progressive muscle disorder that has been associated with a contraction of 3.3-kb repeats on chromosome 4q35. FSHD is characterized by a wide clinical inter- and intrafamilial variability, ranging from wheelchair-bound patients to asymptomatic carriers. Our study is unique in comparing the gene expression profiles from related affected, asymptomatic carrier, and control individuals. Our results suggest that the expression of genes on chromosome 4q is altered in affected and asymptomatic individuals. Remarkably, the changes seen in asymptomatic samples are largely in products of genes encoding several chemokines, whereas the changes seen in affected samples are largely in genes governing the synthesis of GPI-linked proteins and histone acetylation. Besides this, the affected patient and related asymptomatic carrier share the 4qA161 haplotype. Thus, these polymorphisms by themselves do not explain the pathogenicity of the contracted allele. Interestingly, our results also suggest that the miRNAs might mediate the regulatory network in FSHD. Together, our results support the previous evidence that FSHD may be caused by transcriptional dysregulation of multiple genes, in cis and in trans, and suggest some factors potentially important for FSHD pathogenesis. The study of the gene expression profiles from asymptomatic carriers and related affected patients is a unique approach to try to enhance our understanding of the missing link between the contraction in D4Z4 repeats and muscle disease, while minimizing the effects of differences resulting from genetic background.

Inferring Contagion in Regulatory Networks

Several gene regulatory network models containing concepts of directionality at the edges have been proposed. However, only a few reports have an interpretable definition of directionality. Here, differently from the standard causality concept defined by Pearl, we introduce the concept of contagion in order to infer directionality at the edges, i.e., asymmetries in gene expression dependences of regulatory networks. Moreover, we present a bootstrap algorithm in order to test the contagion concept. This technique was applied in simulated data and, also, in an actual large sample of biological data. Literature review has confirmed some genes identified by contagion as actually belonging to the TP53 pathway.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.