Bringing metabolic networks to life: convenience rate law and thermodynamic constraints

BACKGROUND: Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes. RESULTS: We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme. CONCLUSION: Convenience kinetics can be used to translate a biochemical network – manually or automatically - into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases

Chaperone-assisted translocation of a polymer through a nanopore

Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy $\epsilon$ between the chaperone and the chain and the chaperone concentration $N_c$ can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time $\tau$ has a transition from long-tailed distribution to Gaussian distribution with increasing $\epsilon$. $\tau$ rapidly decreases and then almost saturates with increasing binding energy for short chain, however, it has a minimum for longer chains at lower chaperone concentration. We also show that $\tau$ has a minimum as a function of the chaperone concentration. For different $\epsilon$, a nonuniversal dependence of $\tau$ on the chain length $N$ is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either crowding effect from high chaperone concentration or the intersegmental binding for the high binding energy.Comment: 10 pages, to appear in J. Am. Chem. So

Factor analysis for gene regulatory networks and transcription factor activity profiles

BACKGROUND: Most existing algorithms for the inference of the structure of gene regulatory networks from gene expression data assume that the activity levels of transcription factors (TFs) are proportional to their mRNA levels. This assumption is invalid for most biological systems. However, one might be able to reconstruct unobserved activity profiles of TFs from the expression profiles of target genes. A simple model is a two-layer network with unobserved TF variables in the first layer and observed gene expression variables in the second layer. TFs are connected to regulated genes by weighted edges. The weights, known as factor loadings, indicate the strength and direction of regulation. Of particular interest are methods that produce sparse networks, networks with few edges, since it is known that most genes are regulated by only a small number of TFs, and most TFs regulate only a small number of genes. RESULTS: In this paper, we explore the performance of five factor analysis algorithms, Bayesian as well as classical, on problems with biological context using both simulated and real data. Factor analysis (FA) models are used in order to describe a larger number of observed variables by a smaller number of unobserved variables, the factors, whereby all correlation between observed variables is explained by common factors. Bayesian FA methods allow one to infer sparse networks by enforcing sparsity through priors. In contrast, in the classical FA, matrix rotation methods are used to enforce sparsity and thus to increase the interpretability of the inferred factor loadings matrix. However, we also show that Bayesian FA models that do not impose sparsity through the priors can still be used for the reconstruction of a gene regulatory network if applied in conjunction with matrix rotation methods. Finally, we show the added advantage of merging the information derived from all algorithms in order to obtain a combined result. CONCLUSION: Most of the algorithms tested are successful in reconstructing the connectivity structure as well as the TF profiles. Moreover, we demonstrate that if the underlying network is sparse it is still possible to reconstruct hidden activity profiles of TFs to some degree without prior connectivity information

The Escherichia coli transcriptome mostly consists of independently regulated modules

Underlying cellular responses is a transcriptional regulatory network (TRN) that modulates gene expression. A useful description of the TRN would decompose the transcriptome into targeted effects of individual transcriptional regulators. Here, we apply unsupervised machine learning to a diverse compendium of over 250 high-quality Escherichia coli RNA-seq datasets to identify 92 statistically independent signals that modulate the expression of specific gene sets. We show that 61 of these transcriptomic signals represent the effects of currently characterized transcriptional regulators. Condition-specific activation of signals is validated by exposure of E. coli to new environmental conditions. The resulting decomposition of the transcriptome provides: a mechanistic, systems-level, network-based explanation of responses to environmental and genetic perturbations; a guide to gene and regulator function discovery; and a basis for characterizing transcriptomic differences in multiple strains. Taken together, our results show that signal summation describes the composition of a model prokaryotic transcriptome

Exploring matrix factorization techniques for significant genes identification of Alzheimer’s disease microarray gene expression data

<p>Abstract</p> <p>Background</p> <p>The wide use of high-throughput DNA microarray technology provide an increasingly detailed view of human transcriptome from hundreds to thousands of genes. Although biomedical researchers typically design microarray experiments to explore specific biological contexts, the relationships between genes are hard to identified because they are complex and noisy high-dimensional data and are often hindered by low statistical power. The main challenge now is to extract valuable biological information from the colossal amount of data to gain insight into biological processes and the mechanisms of human disease. To overcome the challenge requires mathematical and computational methods that are versatile enough to capture the underlying biological features and simple enough to be applied efficiently to large datasets.</p> <p>Methods</p> <p>Unsupervised machine learning approaches provide new and efficient analysis of gene expression profiles. In our study, two unsupervised knowledge-based matrix factorization methods, independent component analysis (ICA) and nonnegative matrix factorization (NMF) are integrated to identify significant genes and related pathways in microarray gene expression dataset of Alzheimer’s disease. The advantage of these two approaches is they can be performed as a biclustering method by which genes and conditions can be clustered simultaneously. Furthermore, they can group genes into different categories for identifying related diagnostic pathways and regulatory networks. The difference between these two method lies in ICA assume statistical independence of the expression modes, while NMF need positivity constrains to generate localized gene expression profiles.</p> <p>Results</p> <p>In our work, we performed FastICA and non-smooth NMF methods on DNA microarray gene expression data of Alzheimer’s disease respectively. The simulation results shows that both of the methods can clearly classify severe AD samples from control samples, and the biological analysis of the identified significant genes and their related pathways demonstrated that these genes play a prominent role in AD and relate the activation patterns to AD phenotypes. It is validated that the combination of these two methods is efficient.</p> <p>Conclusions</p> <p>Unsupervised matrix factorization methods provide efficient tools to analyze high-throughput microarray dataset. According to the facts that different unsupervised approaches explore correlations in the high-dimensional data space and identify relevant subspace base on different hypotheses, integrating these methods to explore the underlying biological information from microarray dataset is an efficient approach. By combining the significant genes identified by both ICA and NMF, the biological analysis shows great efficient for elucidating the molecular taxonomy of Alzheimer’s disease and enable better experimental design to further identify potential pathways and therapeutic targets of AD.</p

外汇风险溢酬理论述评

外汇风险溢酬是从资产定价角度研究汇率变化的核心内容,但还未获得一致结论。目前,对外汇风险溢酬的时间序列建模并不理想,隐含变量模型和仿射模型都不能刻画外汇风险溢酬的时间序列特征;对外汇风险溢酬风险因子的研究缺乏一个统一框架,消费、微观市场因子和货币政策都只能部分解释外汇风险溢酬的变化。基于随机贴现因子的模型目前相对零散,但这一框架是后续研究的重点。一个亟待研究的课题是既把汇率作为投资性资产的价格,又考虑汇率作为两国货币的相对比价,研究外汇风险溢酬与两国经济波动、两国经济相关性的内在联系,从理论上厘清影响外汇风险溢酬的因素

Ranked retrieval of Computational Biology models

<p>Abstract</p> <p>Background</p> <p>The study of biological systems demands computational support. If targeting a biological problem, the reuse of existing computational models can save time and effort. Deciding for potentially suitable models, however, becomes more challenging with the increasing number of computational models available, and even more when considering the models' growing complexity. Firstly, among a set of potential model candidates it is difficult to decide for the model that best suits ones needs. Secondly, it is hard to grasp the nature of an unknown model listed in a search result set, and to judge how well it fits for the particular problem one has in mind.</p> <p>Results</p> <p>Here we present an improved search approach for computational models of biological processes. It is based on existing retrieval and ranking methods from Information Retrieval. The approach incorporates annotations suggested by MIRIAM, and additional meta-information. It is now part of the search engine of BioModels Database, a standard repository for computational models.</p> <p>Conclusions</p> <p>The introduced concept and implementation are, to our knowledge, the first application of Information Retrieval techniques on model search in Computational Systems Biology. Using the example of BioModels Database, it was shown that the approach is feasible and extends the current possibilities to search for relevant models. The advantages of our system over existing solutions are that we incorporate a rich set of meta-information, and that we provide the user with a relevance ranking of the models found for a query. Better search capabilities in model databases are expected to have a positive effect on the reuse of existing models.</p

Knowledge-based matrix factorization temporally resolves the cellular responses to IL-6 stimulation

<p>Abstract</p> <p>Background</p> <p>External stimulations of cells by hormones, cytokines or growth factors activate signal transduction pathways that subsequently induce a re-arrangement of cellular gene expression. The analysis of such changes is complicated, as they consist of multi-layered temporal responses. While classical analyses based on clustering or gene set enrichment only partly reveal this information, matrix factorization techniques are well suited for a detailed temporal analysis. In signal processing, factorization techniques incorporating data properties like spatial and temporal correlation structure have shown to be robust and computationally efficient. However, such correlation-based methods have so far not be applied in bioinformatics, because large scale biological data rarely imply a natural order that allows the definition of a delayed correlation function.</p> <p>Results</p> <p>We therefore develop the concept of graph-decorrelation. We encode prior knowledge like transcriptional regulation, protein interactions or metabolic pathways in a weighted directed graph. By linking features along this underlying graph, we introduce a partial ordering of the features (e.g. genes) and are thus able to define a graph-delayed correlation function. Using this framework as constraint to the matrix factorization task allows us to set up the fast and robust graph-decorrelation algorithm (GraDe). To analyze alterations in the gene response in <it>IL-6 </it>stimulated primary mouse hepatocytes, we performed a time-course microarray experiment and applied GraDe. In contrast to standard techniques, the extracted time-resolved gene expression profiles showed that <it>IL-6 </it>activates genes involved in cell cycle progression and cell division. Genes linked to metabolic and apoptotic processes are down-regulated indicating that <it>IL-6 </it>mediated priming renders hepatocytes more responsive towards cell proliferation and reduces expenditures for the energy metabolism.</p> <p>Conclusions</p> <p>GraDe provides a novel framework for the decomposition of large-scale 'omics' data. We were able to show that including prior knowledge into the separation task leads to a much more structured and detailed separation of the time-dependent responses upon <it>IL-6 </it>stimulation compared to standard methods. A Matlab implementation of the GraDe algorithm is freely available at <url>http://cmb.helmholtz-muenchen.de/grade</url>.</p

Hydrophobicity and Charge Shape Cellular Metabolite Concentrations

What governs the concentrations of metabolites within living cells? Beyond specific metabolic and enzymatic considerations, are there global trends that affect their values? We hypothesize that the physico-chemical properties of metabolites considerably affect their in-vivo concentrations. The recently achieved experimental capability to measure the concentrations of many metabolites simultaneously has made the testing of this hypothesis possible. Here, we analyze such recently available data sets of metabolite concentrations within E. coli, S. cerevisiae, B. subtilis and human. Overall, these data sets encompass more than twenty conditions, each containing dozens (28-108) of simultaneously measured metabolites. We test for correlations with various physico-chemical properties and find that the number of charged atoms, non-polar surface area, lipophilicity and solubility consistently correlate with concentration. In most data sets, a change in one of these properties elicits a ∼100 fold increase in metabolite concentrations. We find that the non-polar surface area and number of charged atoms account for almost half of the variation in concentrations in the most reliable and comprehensive data set. Analyzing specific groups of metabolites, such as amino-acids or phosphorylated nucleotides, reveals even a higher dependence of concentration on hydrophobicity. We suggest that these findings can be explained by evolutionary constraints imposed on metabolite concentrations and discuss possible selective pressures that can account for them. These include the reduction of solute leakage through the lipid membrane, avoidance of deleterious aggregates and reduction of non-specific hydrophobic binding. By highlighting the global constraints imposed on metabolic pathways, future research could shed light onto aspects of biochemical evolution and the chemical constraints that bound metabolic engineering efforts