Attractor analysis of asynchronous Boolean models of signal transduction networks

Prior work on the dynamics of Boolean networks, including analysis of the state space attractors and the basin of attraction of each attractor, has mainly focused on synchronous update of the nodes’ states. Although the simplicity of synchronous updating makes it very attractive, it fails to take into account the variety of time scales associated with different types of biological processes. Several different asynchronous update methods have been proposed to overcome this limitation, but there have not been any systematic comparisons of the dynamic behaviors displayed by the same system under different update methods. Here we fill this gap by combining theoretical analysis such as solution of scalar equations and Markov chain techniques, as well as numerical simulations to carry out a thorough comparative study on the dynamic behavior of a previously proposed Boolean model of a signal transduction network in plants. Prior evidence suggests that this network admits oscillations, but it is not known whether these oscillations are sustained. We perform an attractor analysis of this system using synchronous and three different asynchronous updating schemes both in the case of the unperturbed (wild-type) and perturbed (node-disrupted) systems. This analysis reveals that while the wild-type system possesses an update-independent fixed point, any oscillations eventually disappear unless strict constraints regarding the timing of certain processes and the initial state of the system are satisfied. Interestingly, in the case of disruption of a particular node all models lead to an extended attractor. Overall, our work provides a roadmap on how Boolean network modeling can be used as a predictive tool to uncover the dynamic patterns of a biological system under various internal and environmental perturbations.     

New computational approaches for analysis of cis-regulatory networks

The investigation and modeling of gene regulatory networks requires computational tools specific to the task. We present several locally developed software tools that have been used in support of our ongoing research into the embryogenesis of the sea urchin. These tools are especially well suited to iterative refinement of models through experimental and computational investigation. They include: BioArray, a macroarray spot processing program; SUGAR, a system to display and correlate large-BAC sequence analyses; SeqComp and FamilyRelations, programs for comparative sequence analysis; and NetBuilder, an environment for creating and analyzing models of gene networks. We also present an overview of the process used to build our model of the Strongylocentrotus purpuratus endomesoderm gene network. Several of the tools discussed in this paper are still in active development and some are available as open source.     

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.     

Dynamical analysis of cellular networks based on the Green's function matrix

The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential equations (ODEs) have commonly been used to simulate dynamical behavior of cellular networks, to which a quantitative model analysis can be applied in order to gain biological insights. In this paper, we introduce a dynamical analysis based on the use of Green's function matrix (GFM) as sensitivity coefficients with respect to initial concentrations. In contrast to the classical (parametric) sensitivity analysis, the GFM analysis gives a dynamical, molecule-by-molecule insight on how system behavior is accomplished and complementarily how (impulse) signal propagates through the network. The knowledge gained will have application from model reduction and validation to drug discovery research in identifying potential drug targets, studying drug efficacy and specificity, and optimizing drug dosing and timing. The efficacy of the method is demonstrated through applications to common network motifs and a Fas-induced programmed cell death model in Jurkat T cell line.     

Model-based process analysis of partial nitrification efficiency under dynamic nitrogen loading

In this study, the ammonia removal efficiency for high ammonia-containing wastewaters was evaluated via partial nitrification. A nitrifier biocommunity was first enriched in a fill-and-draw batch reactor with a specific ammonium oxidation rate of 0.1 mg NH₄ ⁻-N/mg VSS.h. Partial nitrification was established in a chemostat at a hydraulic retention time (HRT) of 1.15 days, which was equal to the sludge retention time (SRT). The results showed that the critical HRT (SRT) was 1.0 day for the system. A maximum specific ammonium oxidation rate was achieved as 0.280 mg NH₄ ⁻-N/mg VSS.h, which is 2.8-fold higher than that obtained in the fill-and-draw reactor, indicating that more adaptive and highly active ammonium oxidizers were enriched in the chemostat. Dynamic modeling of partial nitrification showed that the maximum growth rate for ammonium oxidizers was found to be 1.22 day⁻¹. Modeling studies also validated the recovery period as 10 days.     

Metabolomics assisted metabolic network modeling and network wide analysis of metabolites in microbiology

Metabolomics is the science of qualitatively and quantitatively analyzing low molecular weight metabolites occur in a given biological system. It provides valuable information to elucidate the functional roles and relations of different metabolites in a metabolic pathway. In recent years, a large amount of research on microbial metabolomics has been conducted. It has become a useful tool for achieving highly efficient synthesis of target metabolites. At the same time, many studies have been conducted over the years in order to integrate metabolomics data into metabolic network modeling, which has yielded many exciting results. Additionally, metabolomics also shows great advantages in analyzing the relationship of metabolites network wide. Integrating metabolomics data into metabolic network construction and applying it in network wide analysis of cell metabolism would further improve our ability to control cellular metabolism and optimize the design of cell factories for the overproduction of valuable biochemicals. This review will examine recent progress in the application of metabolomics approaches in metabolic network modeling and network wide analysis of microbial cell metabolism.     

Economic analysis of royalactin production under uncertainty: Evaluating the effect of parameter optimization

Royalactin is a protein with several different potential uses in humans. Research, in insects and in mammalian cells, has shown that it can accelerate cell division and prevent apoptosis. The method of action is through the use of the epidermal growth factor receptor, which is present in humans. Potential use in humans could be to lower cholesterolemic levels in blood, and to elicit similar effects to those seen in bees, e.g., increased lifespan. Mass production of Royalactin has not been accomplished, though a recent article presented a Pichia pastoris fermentation and recovery by aqueous two‐phase systems at laboratory scale as a possible basis for production. Economic modelling is a useful tool with which compare possible outcomes for the production of such a molecule and in particular, to locate areas where additional research is needed and optimization may be required. This study uses the BioSolve software to perform an economic analysis on the scale‐up of the putative process for Royalactin. The key parameters affecting the cost of production were located via a sensitivity analysis and then evaluated by Monte Carlo analysis. Results show that if titer is not optimized the strategy to maintain a low cost of goods is process oriented. After optimization of this parameter the strategy changes to a product‐oriented and the target output becomes the critical parameter determining the cost of goods. This study serves to provide a framework for the evaluation of strategies for future production of Royalactin, by analyzing the factors that influence its cost of manufacture. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:744–749, 2015     

复杂疾病驱使的融合SDA-SVM集成基因挖掘方法

提出了一种新颖的复杂疾病驱使的融合SDA-SVM(Stepwise Discriminant Analysis-Support Vector Machine,SDA-SVM)技术的集成基因挖掘方法。该集成方法融合逐步判别分析和支持向量机的优点,能够有效地进行复杂疾病相关基因的深度挖掘,使得挖掘出的基因能够较好地识别疾病类型和亚型。通过将该方法应用于一套弥散性大B细胞淋巴瘤DNA表达谱数据,并与其它基因挖掘方法对比,结果表明该方法挖掘出的基因具有较高的疾病相关性和较强的疾病类型识别能力。     

Statistical uncertainty and its propagation in the analysis of quantitative polymerase chain reaction data: Comparison of methods

Most methods for analyzing real-time quantitative polymerase chain reaction (qPCR) data for single experiments estimate the hypothetical cycle 0 signal y₀ by first estimating the quantification cycle (C_q) and amplification efficiency (E) from least-squares fits of fluorescence intensity data for cycles near the onset of the growth phase. The resulting y₀ values are statistically equivalent to the corresponding C_q if and only if E is taken to be error free. But uncertainty in E usually dominates the total uncertainty in y₀, making the latter much degraded in precision compared with C_q. Bias in E can be an even greater source of error in y₀. So-called mechanistic models achieve higher precision in estimating y₀ by tacitly assuming E = 2 in the baseline region and so are subject to this bias error. When used in calibration, the mechanistic y₀ is statistically comparable to C_q from the other methods. When a signal threshold y_q is used to define C_q, best estimation precision is obtained by setting y_q near the maximum signal in the range of fitted cycles, in conflict with common practice in the y₀ estimation algorithms.     

Moisture Stability of Maltodextrin-Based Delivery Systems

The water sorption isotherms are exploited here for maltodextrin-based perfume-delivery systems with the aim of predicting water vapor stability of the samples at a given temperature. A combination of Couchman (glass-transition temperature) and Guggenheim-Anderson-deBoer (GAB) (fraction of water condensed) models is shown demonstrating important information hidden in a simple sorption experiment (rate of loss of perfume by diffusion and capacity to retain volatiles under humid air conditions). Pure maltodextrin and maltodextrin loaded with apolar and polar perfume components are treated using the same developed methodology. It is shown that apolar molecule release from classical carbohydrate spray dry particles follows a zero-order kinetic. This poster was presented at the 2nd International Symposium on Delivery of Functionality in Complex Food Systems, University of Massachusetts, Amherst, USA. October 8th to 10th, 2007.     

基于约束的建模方法在代谢网络中的应用研究

代谢网络在各种细胞功能和生命过程中发挥着至关重要的作用。随着细胞网络重建工程的迅速发展,可用的基因组水平代谢网络越来越多,因而计算方法在这些网络的结构功能分析中越来越重要。基于约束的建模方法不像图论方法那样仅考虑代谢模型的纯拓扑结构,也不像各种动力学建模方法那样需求详尽的热力学参数,因而极具优势。采用基于约束的建模方法对一个含619个基因,655个代谢物和743个代谢反应的金黄色葡萄球菌(Staphylococcusaureus)代谢网络进行了分析,主要研究了该模型的网络结构特征,以及其最优生长率、动态生长情况和基因删除学习等。本研究提供了一个对金黄色葡萄球菌代谢网络进行约束建模分析的初步框架。     

Combinatorial complexity of pathway analysis in metabolic networks

Elementary flux mode analysis is a promising approach for a pathway-oriented perspective of metabolic networks. However, in larger networks it is hampered by the combinatorial explosion of possible routes. In this work we give some estimations on the combinatorial complexity including theoretical upper bounds for the number of elementary flux modes in a network of a given size. In a case study, we computed the elementary modes in the central metabolism of Escherichia coli while utilizing four different substrates. Interestingly, although the number of modes occurring in this complex network can exceed half a million, it is still far below the upper bound. Hence, to a certain extent, pathway analysis of central catabolism is feasible to assess network properties such as flexibility and functionality.     

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective, communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires the know-how of all the methodological steps of the pipeline that manipulate the input brain signals and extract the functional network properties. On the other hand, knowledge of the neural phenomenon under study is required to perform physiologically relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes.     

Elementary network reconstruction: A framework for the analysis of regulatory networks in biological systems

Complexity of regulatory networks arises from the high degree of interaction between network components such as DNA, RNA, proteins, and metabolites. We have developed a modeling tool, elementary network reconstruction (ENR), to characterize these networks. ENR is a knowledge-driven, steady state, deterministic, quantitative modeling approach based on linear perturbation theory. In ENR we demonstrate a novel means of expressing control mechanisms by way of dimensionless steady state gains relating input and output variables, which are purely in terms of species abundances (extensive variables). As a result of systematic enumeration of network species in n×n matrix, the two properties of linear perturbation are manifested in graphical representations: transitive property is evident in a special L-shape structure, and additive property is evident in multiple L-shape structures arriving at the same matrix cell. Upon imposing mechanistic (lowest-level) gains, network self-assembly through transitive and additive properties results in elucidation of inherent topology and explicit cataloging of higher level gains, which in turn can be used to predict perturbation results. Application of ENR to the regulatory network behind carbon catabolite repression in Escherichia coli is presented. Through incorporation of known molecular mechanisms governing transient and permanent repressions, the ENR model correctly predicts several key features of this regulatory network, including a 50% downshift in intracellular cAMP level upon exposure to glucose. Since functional genomics studies are mainly concerned with redistribution of species abundances in perturbed systems, ENR could be exploited in the system-level analysis of biological systems.     

Dynamic generation and qualitative analysis of metabolic pathways by a joint database/graph theoretical approach.

The dynamic generation and qualitative analysis of metabolic networks relying on continuously growing qualified metabolic data by a joint database/graph theoretical approach is described. The procedure is applied to analyze the connectivity of a metabolic network after enzyme removal and to subsequently perform shortest path analyses. The focus lies on the analysis of the connectivity of the metabolic network depending on model assumptions. Here we analyze the influence of the number of strongly connected components on the assignment of reversibility or irreversibility of the biochemical reactions.     

Systems analysis of metabolism in the pathogenic trypanosomatid Leishmania major

Systems analyses have facilitated the characterization of metabolic networks of several organisms. We have reconstructed the metabolic network of Leishmania major, a poorly characterized organism that causes cutaneous leishmaniasis in mammalian hosts. This network reconstruction accounts for 560 genes, 1112 reactions, 1101 metabolites and 8 unique subcellular localizations. Using a systems‐based approach, we hypothesized a comprehensive set of lethal single and double gene deletions, some of which were validated using published data with approximately 70% accuracy. Additionally, we generated hypothetical annotations to dozens of previously uncharacterized genes in the L. major genome and proposed a minimal medium for growth. We further demonstrated the utility of a network reconstruction with two proof‐of‐concept examples that yielded insight into robustness of the network in the presence of enzymatic inhibitors and delineation of promastigote/amastigote stage‐specific metabolism. This reconstruction and the associated network analyses of L. major is the first of its kind for a protozoan. It can serve as a tool for clarifying discrepancies between data sources, generating hypotheses that can be experimentally validated and identifying ideal therapeutic targets.     

Influence of weak hip abductor muscles on joint contact forces during normal walking: probabilistic modeling analysis

The weakness of hip abductor muscles is related to lower-limb joint osteoarthritis, and joint overloading may increase the risk for disease progression. The relationship between muscle strength, structural joint deterioration and joint loading makes the latter an important parameter in the study of onset and follow-up of the disease. Since the relationship between hip abductor weakness and joint loading still remains an open question, the purpose of this study was to adopt a probabilistic modeling approach to give insights into how the weakness of hip abductor muscles, in the extent to which normal gait could be unaltered, affects ipsilateral joint contact forces. A generic musculoskeletal model was scaled to each healthy subject included in the study, and the maximum force-generating capacity of each hip abductor muscle in the model was perturbed to evaluate how all physiologically possible configurations of hip abductor weakness affected the joint contact forces during walking. In general, the muscular system was able to compensate for abductor weakness. The reduced force-generating capacity of the abductor muscles affected joint contact forces to a mild extent, with 50th percentile mean differences up to 0.5 BW (maximum 1.7 BW). There were greater increases in the peak knee joint loads than in loads at the hip or ankle. Gluteus medius, particularly the anterior compartment, was the abductor muscle with the most influence on hip and knee loads. Further studies should assess if these increases in joint loading may affect initiation and progression of osteoarthritis.     

Integrated analysis of multiple data sources reveals modular structure of biological networks

It has been a challenging task to integrate high-throughput data into investigations of the systematic and dynamic organization of biological networks. Here, we presented a simple hierarchical clustering algorithm that goes a long way to achieve this aim. Our method effectively reveals the modular structure of the yeast protein-protein interaction network and distinguishes protein complexes from functional modules by integrating high-throughput protein-protein interaction data with the added subcellular localization and expression profile data. Furthermore, we take advantage of the detected modules to provide a reliably functional context for the uncharacterized components within modules. On the other hand, the integration of various protein-protein association information makes our method robust to false-positives, especially for derived protein complexes. More importantly, this simple method can be extended naturally to other types of data fusion and provides a framework for the study of more comprehensive properties of the biological network and other forms of complex networks.