Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.     

Tumor necrosis factor alpha suppresses the induction of connective tissue growth factor by transforming growth factor-beta in normal and scleroderma fibroblasts

Connective tissue growth factor (CTGF) is overexpressed in a variety of fibrotic disorders, presumably secondary to the activation and production of transforming growth factor-beta (TGF-beta), a key inducer of fibroblast proliferation and matrix synthesis. The CTGF gene promoter has a TGF-beta response element that regulates its expression in fibroblasts but not epithelial cells or lymphocytes. Recent studies have shown that the macrophage-produced cytokine tumor necrosis factor alpha (TNFalpha) is necessary to promote inflammation and to induce genes, such as matrix metalloproteinases, involved with the early stages of wound healing. In this study, we examined the ability of TNFalpha to modulate CTGF gene expression. TNFalpha was found to suppress the TGF-beta-induced expression of CTGF protein in cultured normal fibroblasts. The activity of TNFalpha was blocked by NF-kappaB inhibitors. We showed that sequences between -244 and -166 of the CTGF promoter were necessary for both TGF-beta and TNFalpha to modulate CTGF expression. There was a constitutive expression of CTGF by scleroderma fibroblasts that was increased by TGF-beta treatment. Although TNFalpha was able to repress TGF-beta-induced CTGF and collagen synthesis both in normal and scleroderma skin fibroblasts, fibroblasts cultured from scleroderma patients were more resistant to TNFalpha as TNFalpha was unable to suppress the basal level of CTGF expression in scleroderma fibroblasts. Thus, we suspect that the high level of constitutive CTGF expression in scleroderma fibroblasts and its inability to respond to negative regulatory cytokines may contribute to the excessive scarring of skin and internal organs in patients with scleroderma.     

Increased expression of integrin alpha(v)beta3 contributes to the establishment of autocrine TGF-beta signaling in scleroderma fibroblasts

The constitutive secretion of latent TGF-beta by many cell types in culture suggests that extracellular mechanisms to control the activity of this potent cytokine are important in the pathogenesis of the diseases in which this cytokine may be involved, including fibrotic disorders. In this study, we focused on the alpha(v)beta3 integrin, which is recently demonstrated to function as an active receptor for latent TGF-beta1 through its interaction with latency-associated peptide-beta1, and investigated the involvement of this integrin in the pathogenesis of scleroderma. Scleroderma fibroblasts exhibited increased alpha(v)beta3 expression compared with normal fibroblasts in vivo and in vitro. In scleroderma fibroblasts, ERK pathway was constitutively activated and such abnormality induced the up-regulation of alpha(v)beta3. Transient overexpression of alpha(v)beta3 in normal fibroblasts induced the increase in the promoter activity of human alpha2(I) collagen gene and the decrease in that of human MMP-1 gene. These effects of alpha(v)beta3 were almost completely abolished by the treatment with anti-TGF-beta Ab or TGF-beta1 antisense oligonucleotide. Furthermore, the addition of anti-alpha(v)beta3) Ab reversed the expression of type I procollagen protein and MMP-1 protein, the promoter activity of human alpha2(I) collagen gene, and the myofibroblastic phenotype in scleroderma fibroblasts. These results suggest that the up-regulated expression of alpha(v)beta3 contributes to the establishment of autocrine TGF-beta loop in scleroderma fibroblasts, and this integrin is a potent target for the treatment of scleroderma.     

Propagation of extrinsic perturbation in a negatively auto-regulated pathway

The apparent precision of the output in multi-step biochemical pathways in the face of external and intrinsic perturbations is non-obvious and conceptually difficult. Using a simple three-step negatively auto-regulated model pathway, we show that the effect of perturbation at different steps of the pathway and its transmission through the network is dependent on the context (i.e., the position) of the particular reaction step in relation to the topology of the regulatory network, stoichiometry of reactions, type of nonlinearity involved in the reactions and also on the intrinsic dynamical state of the pathway variables. We delineate the qualitative and quantitative changes in the pathway dynamics for constant ('bias') and random external perturbations acting on the pathway steps locally or globally to all steps. We show that constant perturbation induces qualitative change in dynamics, whereas random fluctuations cause significant quantitative variations in the concentrations of the different variables. Thus, the dynamic response of multi-step biochemical pathways to external perturbation depends on their biochemical, topological and dynamical features.     

PathMiner: predicting metabolic pathways by heuristic search

MOTIVATION: Automated methods for biochemical pathway inference are becoming increasingly important for understanding biological processes in living and synthetic systems. With the availability of data on complete genomes and increasing information about enzyme-catalyzed biochemistry it is becoming feasible to approach this problem computationally. In this paper we present PathMiner, a system for automatic metabolic pathway inference. PathMiner predicts metabolic routes by reasoning over transformations using chemical and biological information. RESULTS: We build a biochemical state-space using data from known enzyme-catalyzed transformations in Ligand, including, 2917 unique transformations between 3890 different compounds. To predict metabolic pathways we explore this state-space by developing an informed search algorithm. For this purpose we develop a chemically motivated heuristic to guide the search. Since the algorithm does not depend on predefined pathways, it can efficiently identify plausible routes using known biochemical transformations.     

JNK regulates autocrine expression of TGF-beta1

The c-Jun NH2-terminal kinase (JNK) has been implicated in the function of transforming growth factor beta (TGF-beta). To test the role of JNK, we examined the effect of compound disruption of the murine genes that encode the ubiquitously expressed isoforms of JNK (Jnk1 and Jnk2). We report that JNK-deficient fibroblasts isolated from Jnk1-/- Jnk2-/- mice constitutively express TGF-beta1. Complementation studies demonstrate that JNK is a repressor of Tgf-beta1 gene expression. This mechanism of regulation of TGF-beta1 expression by JNK represents an unexpected form of cross-talk between two important signaling pathways. Together, these data demonstrate that the JNK pathway may contribute to the regulation of autocrine TGF-beta1-mediated biological responses in vivo.     

Mass spectrometry-based high-throughput proteomics and its role in biomedical studies and systems biology

There are multiple reasons why the next generation of biological and medical studies require increasing numbers of samples. Biological systems are dynamic, and the effect of a perturbation depends on the genetic background and environment. As a consequence, many conditions need to be considered to reach generalizable conclusions. Moreover, human population and clinical studies only reach sufficient statistical power if conducted at scale and with precise measurement methods. Finally, many proteins remain without sufficient functional annotations, because they have not been systematically studied under a broad range of conditions. In this review, we discuss the latest technical developments in mass spectrometry (MS)-based proteomics that facilitate large-scale studies by fast and efficient chromatography, fast scanning mass spectrometers, data-independent acquisition (DIA), and new software. We further highlight recent studies which demonstrate how high-throughput (HT) proteomics can be applied to capture biological diversity, to annotate gene functions or to generate predictive and prognostic models for human diseases.     

Phosphatidylinositol 3-kinase is involved in alpha2(I) collagen gene expression in normal and scleroderma fibroblasts

TGF-beta is implicated in the pathogenesis of fibrotic disorders. It has been shown that Smad3 promotes the human alpha2(I) collagen (COL1A2) gene expression by TGF-beta1 in human dermal fibroblasts. Here, we investigated the role of phosphatidylinositol 3-kinase (PI3K) in the COL1A2 gene expression in normal and scleroderma fibroblasts. In normal fibroblasts, the PI3K inhibitor, LY294002, significantly decreased the basal and the TGF-beta1-induced increased stability of COL1A2 mRNA. The TGF-beta1-induced COL1A2 promoter activity, but not the basal activity, was significantly attenuated by LY294002 or the dominant negative mutant of p85 subunit of PI3K, while the constitutive active mutant of p110 subunit of PI3K did not affect the basal or the TGF-beta1-induced COL1A2 promoter activity. LY294002 significantly decreased the phosphorylation of Smad3 induced by TGF-beta1. Furthermore, the transient overexpression of 2xFYVE, which induces the mislocalization of FYVE domain proteins, decreased the TGF-beta1-induced Smad3 phosphorylation to a similar extent to LY294002. In scleroderma fibroblasts, the blockade of PI3K significantly decreased the mRNA stability and the promoter activity of the COL1A2 gene. Furthermore, LY294002 and the transient overexpression of 2xFYVE completely diminished the constitutive phosphorylation of Smad3. These results indicate that 1) the basal activity of PI3K is necessary for the COL1A2 mRNA stabilization in normal and scleroderma fibroblasts, 2) there is an unidentified FYVE domain protein specifically interacting with Smad3, and 3) the basal activity of PI3K and the FYVE domain protein are indispensable for the efficient TGF-beta/Smad3 signaling in normal fibroblasts and for the establishment of the constitutive activation of TGF-beta/Smad3 signaling in scleroderma fibroblasts.     

What Can Causal Networks Tell Us about Metabolic Pathways?

Graphical models describe the linear correlation structure of data and have been used to establish causal relationships among phenotypes in genetic mapping populations. Data are typically collected at a single point in time. Biological processes on the other hand are often non-linear and display time varying dynamics. The extent to which graphical models can recapitulate the architecture of an underlying biological processes is not well understood. We consider metabolic networks with known stoichiometry to address the fundamental question: “What can causal networks tell us about metabolic pathways?”. Using data from an Arabidopsis BaySha population and simulated data from dynamic models of pathway motifs, we assess our ability to reconstruct metabolic pathways using graphical models. Our results highlight the necessity of non-genetic residual biological variation for reliable inference. Recovery of the ordering within a pathway is possible, but should not be expected. Causal inference is sensitive to subtle patterns in the correlation structure that may be driven by a variety of factors, which may not emphasize the substrate-product relationship. We illustrate the effects of metabolic pathway architecture, epistasis and stochastic variation on correlation structure and graphical model-derived networks. We conclude that graphical models should be interpreted cautiously, especially if the implied causal relationships are to be used in the design of intervention strategies.     

A Network Characteristic That Correlates Environmental and Genetic Robustness

As scientific advances in perturbing biological systems and technological advances in data acquisition allow the large-scale quantitative analysis of biological function, the robustness of organisms to both transient environmental stresses and inter-generational genetic changes is a fundamental impediment to the identifiability of mathematical models of these functions. An approach to overcoming this impediment is to reduce the space of possible models to take into account both types of robustness. However, the relationship between the two is still controversial. This work uncovers a network characteristic, transient responsiveness, for a specific function that correlates environmental imperturbability and genetic robustness. We test this characteristic extensively for dynamic networks of ordinary differential equations ranging up to 30 interacting nodes and find that there is a power-law relating environmental imperturbability and genetic robustness that tends to linearity as the number of nodes increases. Using our methods, we refine the classification of known 3-node motifs in terms of their environmental and genetic robustness. We demonstrate our approach by applying it to the chemotaxis signaling network. In particular, we investigate plausible models for the role of CheV protein in biochemical adaptation via a phosphorylation pathway, testing modifications that could improve the robustness of the system to environmental and/or genetic perturbation.