193 research outputs found
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
Replication Origins and Timing of Temporal Replication in Budding Yeast: How to Solve the Conundrum?
Similarly to metazoans, the budding yeast Saccharomyces cereviasiae replicates its genome with a defined timing. In this organism, well-defined, site-specific origins, are efficient and fire in almost every round of DNA replication. However, this strategy is neither conserved in the fission yeast Saccharomyces pombe, nor in Xenopus or Drosophila embryos, nor in higher eukaryotes, in which DNA replication initiates asynchronously throughout S phase at random sites. Temporal and spatial controls can contribute to the timing of replication such as Cdk activity, origin localization, epigenetic status or gene expression. However, a debate is going on to answer the question how individual origins are selected to fire in budding yeast. Two opposing theories were proposed: the “replicon paradigm” or “temporal program” vs. the “stochastic firing”. Recent data support the temporal regulation of origin activation, clustering origins into temporal blocks of early and late replication. Contrarily, strong evidences suggest that stochastic processes acting on origins can generate the observed kinetics of replication without requiring a temporal order. In mammalian cells, a spatiotemporal model that accounts for a partially deterministic and partially stochastic order of DNA replication has been proposed. Is this strategy the solution to reconcile the conundrum of having both organized replication timing and stochastic origin firing also for budding yeast? In this review we discuss this possibility in the light of our recent study on the origin activation, suggesting that there might be a stochastic component in the temporal activation of the replication origins, especially under perturbed conditions
A model for the spatiotemporal organization of DNA replication in Saccharomyces cerevisiae
DNA replication in eukaryotes is considered to proceed according to a precise program in which each chromosomal region is duplicated in a defined temporal order. However, recent studies reveal an intrinsic temporal disorder in the replication of yeast chromosome VI. Here we provide a model of the chromosomal duplication to study the temporal sequence of origin activation in budding yeast. The model comprises four parameters that influence the DNA replication system: the lengths of the chromosomes, the explicit chromosomal positions for all replication origins as well as their distinct initiation times and the replication fork migration rate. The designed model is able to reproduce the available experimental data in form of replication profiles. The dynamics of DNA replication was monitored during simulations of wild type and randomly perturbed replication conditions. Severe loss of origin function showed only little influence on the replication dynamics, so systematic deletions of origins (or loss of efficiency) were simulated to provide predictions to be tested experimentally. The simulations provide new insights into the complex system of DNA replication, showing that the system is robust to perturbation, and giving hints about the influence of a possible disordered firing
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
What Influences DNA Replication Rate in Budding Yeast?
BACKGROUND: DNA replication begins at specific locations called replication origins, where helicase and polymerase act in concert to unwind and process the single DNA filaments. The sites of active DNA synthesis are called replication forks. The density of initiation events is low when replication forks travel fast, and is high when forks travel slowly. Despite the potential involvement of epigenetic factors, transcriptional regulation and nucleotide availability, the causes of differences in replication times during DNA synthesis have not been established satisfactorily, yet. METHODOLOGY/PRINCIPAL FINDINGS: Here, we aimed at quantifying to which extent sequence properties contribute to the DNA replication time in budding yeast. We interpreted the movement of the replication machinery along the DNA template as a directed random walk, decomposing influences on DNA replication time into sequence-specific and sequence-independent components. We found that for a large part of the genome the elongation time can be well described by a global average replication rate, thus by a single parameter. However, we also showed that there are regions within the genomic landscape of budding yeast with highly specific replication rates, which cannot be explained by global properties of the replication machinery. CONCLUSION/SIGNIFICANCE: Computational models of DNA replication in budding yeast that can predict replication dynamics have rarely been developed yet. We show here that even beyond the level of initiation there are effects governing the replication time that can not be explained by the movement of the polymerase along the DNA template alone. This allows us to characterize genomic regions with significantly altered elongation characteristics, independent of initiation times or sequence composition
Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators
The linear noise approximation (LNA) offers a simple means by which one can
study intrinsic noise in monostable biochemical networks. Using simple physical
arguments, we have recently introduced the slow-scale LNA (ssLNA) which is a
reduced version of the LNA under conditions of timescale separation. In this
paper, we present the first rigorous derivation of the ssLNA using the
projection operator technique and show that the ssLNA follows uniquely from the
standard LNA under the same conditions of timescale separation as those
required for the deterministic quasi-steady state approximation. We also show
that the large molecule number limit of several common stochastic model
reduction techniques under timescale separation conditions constitutes a
special case of the ssLNA.Comment: 10 pages, 1 figure, submitted to Physical Review E; see also BMC
Systems Biology 6, 39 (2012
Controlling complex networks: How much energy is needed?
The outstanding problem of controlling complex networks is relevant to many
areas of science and engineering, and has the potential to generate
technological breakthroughs as well. We address the physically important issue
of the energy required for achieving control by deriving and validating scaling
laws for the lower and upper energy bounds. These bounds represent a reasonable
estimate of the energy cost associated with control, and provide a step forward
from the current research on controllability toward ultimate control of complex
networked dynamical systems.Comment: 4 pages paper + 5 pages supplement. accepted for publication in
Physical Review Letters;
http://link.aps.org/doi/10.1103/PhysRevLett.108.21870
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
Automated Ensemble Modeling with modelMaGe: Analyzing Feedback Mechanisms in the Sho1 Branch of the HOG Pathway
In systems biology uncertainty about biological processes translates into
alternative mathematical model candidates. Here, the goal is to generate, fit
and discriminate several candidate models that represent different hypotheses
for feedback mechanisms responsible for downregulating the response of the Sho1
branch of the yeast high osmolarity glycerol (HOG) signaling pathway after
initial stimulation. Implementing and testing these candidate models by hand is
a tedious and error-prone task. Therefore, we automatically generated a set of
candidate models of the Sho1 branch with the tool modelMaGe.
These candidate models are automatically documented, can readily be simulated
and fitted automatically to data. A ranking of the models with respect to
parsimonious data representation is provided, enabling discrimination between
candidate models and the biological hypotheses underlying them. We conclude that
a previously published model fitted spurious effects in the data. Moreover, the
discrimination analysis suggests that the reported data does not support the
conclusion that a desensitization mechanism leads to the rapid attenuation of
Hog1 signaling in the Sho1 branch of the HOG pathway. The data rather supports a
model where an integrator feedback shuts down the pathway. This conclusion is
also supported by dedicated experiments that can exclusively be predicted by
those models including an integrator feedback
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