Prediction of enzyme kinetic parameters based on statistical learning

Values of enzyme kinetic parameters are a key requisite for the kinetic modelling of biochemical systems. For most kinetic parameters, however, not even an order of magnitude is known, so the estimation of model parameters from experimental data remains a major task in systems biology. We propose a statistical approach to infer values for kinetic parameters across species and enzymes making use of parameter values that have been measured under various conditions and that are nowadays stored in databases. We fit the data by a statistical regression model in which the substrate, the combination enzyme-substrate and the combination organism-substrate have a linear effect on the logarithmic parameter value. As a result, we obtain predictions and error ranges for unknown enzyme parameters. We apply our method to decadic logarithmic Michaelis-Menten constants from the BRENDA database and confirm the results with leave-one-out crossvalidation, in which we mask one value at a time and predict it from the remaining data. For a set of 8 metabolites we obtain a standard prediction error of 1.01 for the deviation of the predicted values from the true values, while the standard deviation of the experimental values is 1.16. The method is applicable to other types of kinetic parameters for which many experimental data are available

Biochemical networks with uncertain parameters

The modelling of biochemical networks becomes delicate if kinetic parameters are varying, uncertain or unknown. Facing this situation, we quantify uncertain knowledge or beliefs about parameters by probability distributions. We show how parameter distributions can be used to infer probabilistic statements about dynamic network properties, such as steady-state fluxes and concentrations, signal characteristics or control coefficients. The parameter distributions can also serve as priors in Bayesian statistical analysis. We propose a graphical scheme, the `dependence graph', to bring out known dependencies between parameters, for instance, due to the equilibrium constants. If a parameter distribution is narrow, the resulting distribution of the variables can be computed by expanding them around a set of mean parameter values. We compute the distributions of concentrations, fluxes and probabilities for qualitative variables such as flux directions. The probabilistic framework allows the study of metabolic correlations, and it provides simple measures of variability and stochastic sensitivity. It also shows clearly how the variability of biological systems is related to the metabolic response coefficients

J Comput Biol

Physiological concentrations of metabolites can partly be explained by their molecular structure. We hypothesize that substances containing certain chemical groups show increased or decreased concentration in cells. We consider here, as chemical groups, local atomic configurations, describing an atom, its bonds, and its direct neighbor atoms. To test our hypothesis, we fitted a linear statistical model that relates experimentally determined logarithmic concentrations to feature vectors containing count numbers of the chemical groups. In order to determine chemical groups that have a clear effect on the concentration, we use a regularized (lasso) regression. In a dataset on 41 substances of central metabolism in different organisms, we found that the physical concentrations are increased by the occurrence of amino and hydroxyl groups, while aldehydes, ketones, and phosphates show decreased concentrations. The model explains about 22% of the variance of the logarithmic mean concentrations

SBMLmerge, a System for Combining Biochemical Network Models

The Systems Biology Markup Language (SBML) is an XML-based format for representing mathematical models of biochemical reaction networks, and it is likely to become a main standard in the systems biology community. As published mathematical models in cell biology are growing in number and size, modular modelling approaches will gain additional importance. The main issue to be addressed in computer-assisted model combination is the specification and handling of model semantics. The software SBMLmerge assists the user in combining models of biological subsystems to larger biochemical networks. First, the program helps the user in annotating all model elements with unique identifiers pointing to databases such as KEGG or Gene Ontology. Second, during merging, SBMLmerge detects and resolves various syntactic and semantic problems. Typical problems are conflicting variable names, elements which appear in more than one input model, and mathematical problems arising from the combination of equations. If the input models make contradicting statements about a biochemical quantity, the user is asked to choose between them. In the end the merging process results in a new, valid SBML model

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

Retrieval, alignment, and clustering of computational models based on semantic annotations

As the number of computational systems biology models increases, new methods are needed to explore their content and build connections with experimental data. In this Perspective article, the authors propose a flexible semantic framework that can help achieve these aims

Quantitation of angiogenesis in vitro induced by VEGF-A and FGF-2 in two different human endothelial cultures : an all-in-one assay

Angiogenic therapy is considered to be a promising tool for treatment of ischemic diseases. Many in vivo and in vitro assays have been developed to identify potential proangiogenic drugs and to investigate their mode of action. However, until now no validated system exists that would allow quantitation of angiogenesis in vitro in only one assay. Here, a previously established all-in-one in vitro assay based on staging of the angiogenic cascade was validated by quantitation of the effects of the known proangiogenic factors VEGF-A and FGF-2. Both growth factors were applied separately or in combination to human endothelial cell cultures derived from the heart and the foreskin, and angiogenesis was quantitated over 30 days of culture. Additionally, gene expression of VEGFR-1, VEGFR-2 and FGFR-1 at 3, 10, 20 or 40 days of cultivation was quantitated by RT-qPCR. In both cultures, VEGF-A as well as FGF-2 induced a run through all defined stages of angiogenesis in vitro. Application of VEGF-A only led to formation of irregular globular endothelial structures, while FGF-2 resulted in development of regular capillary-like structures. Quantitation of the angiogenic effects of VEGF-A and transcripts of VEGFR-1 and VEGFR-2 showed that a high VEGFR-1/VEGFR-2 ratio evoked deceleration of angiogenesis

Knowledge-based gene expression classification via matrix factorization

Motivation: Modern machine learning methods based on matrix decomposition techniques, like independent component analysis (ICA) or non-negative matrix factorization (NMF), provide new and efficient analysis tools which are currently explored to analyze gene expression profiles. These exploratory feature extraction techniques yield expression modes (ICA) or metagenes (NMF). These extracted features are considered indicative of underlying regulatory processes. They can as well be applied to the classification of gene expression datasets by grouping samples into different categories for diagnostic purposes or group genes into functional categories for further investigation of related metabolic pathways and regulatory networks. Results: In this study we focus on unsupervised matrix factorization techniques and apply ICA and sparse NMF to microarray datasets. The latter monitor the gene expression levels of human peripheral blood cells during differentiation from monocytes to macrophages. We show that these tools are able to identify relevant signatures in the deduced component matrices and extract informative sets of marker genes from these gene expression profiles. The methods rely on the joint discriminative power of a set of marker genes rather than on single marker genes. With these sets of marker genes, corroborated by leave-one-out or random forest cross-validation, the datasets could easily be classified into related diagnostic categories. The latter correspond to either monocytes versus macrophages or healthy vs Niemann Pick C disease patients.Siemens AG, MunichDFG (Graduate College 638)DAAD (PPP Luso - Alem˜a and PPP Hispano - Alemanas

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