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

Ion Transport across Biological Membranes by Carborane-Capped Gold Nanoparticles

Carborane-capped gold nanoparticles (Au/carborane NPs, 2-3 nm) can act as artificial ion transporters across biological membranes. The particles themselves are large hydrophobic anions that have the ability to disperse in aqueous media and to partition over both sides of a phospholipid bilayer membrane. Their presence therefore causes a membrane potential that is determined by the relative concentrations of particles on each side of the membrane according to the Nernst equation. The particles tend to adsorb to both sides of the membrane and can flip across if changes in membrane potential require their repartitioning. Such changes can be made either with a potentiostat in an electrochemical cell or by competition with another partitioning ion, for example, potassium in the presence of its specific transporter valinomycin. Carborane-capped gold nanoparticles have a ligand shell full of voids, which stem from the packing of near spherical ligands on a near spherical metal core. These voids are normally filled with sodium or potassium ions, and the charge is overcompensated by excess electrons in the metal core. The anionic particles are therefore able to take up and release a certain payload of cations and to adjust their net charge accordingly. It is demonstrated by potential-dependent fluorescence spectroscopy that polarized phospholipid membranes of vesicles can be depolarized by ion transport mediated by the particles. It is also shown that the particles act as alkali-ion-specific transporters across free-standing membranes under potentiostatic control. Magnesium ions are not transported

The logic of the floral transition: reverse-engineering the switch controlling the identity of lateral organs

Much laboratory work has been carried out to determine the gene regulatory network (GRN) that results in plant cells becoming flowers instead of leaves. However, this also involves the spatial distribution of different cell types, and poses the question of whether alternative networks could produce the same set of observed results. This issue has been addressed here through a survey of the published intercellular distribution of expressed regulatory genes and techniques both developed and applied to Boolean network models. This has uncovered a large number of models which are compatible with the currently available data. An exhaustive exploration had some success but proved to be unfeasible due to the massive number of alternative models, so genetic programming algorithms have also been employed. This approach allows exploration on the basis of both data-fitting criteria and parsimony of the regulatory processes, ruling out biologically unrealistic mechanisms. One of the conclusions is that, despite the multiplicity of acceptable models, an overall structure dominates, with differences mostly in alternative fine-grained regulatory interactions. The overall structure confirms the known interactions, including some that were not present in the training set, showing that current data are sufficient to determine the overall structure of the GRN. The model stresses the importance of relative spatial location, through explicit references to this aspect. This approach also provides a quantitative indication of how likely some regulatory interactions might be, and can be applied to the study of other developmental transitions

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

Mathematical modeling of intracellular signaling pathways

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems

A Software Tool to Model Genetic Regulatory Networks. Applications to the Modeling of Threshold Phenomena and of Spatial Patterning in Drosophila

We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by the Mathematica software package GeneticNetworks. This package accepts as input the interaction graphs of the transcriptional activators and repressors of a biological process and, as output, gives the mathematical model in the form of a system of ordinary differential equations. All the relevant biological parameters are chosen automatically by the software. Within this framework, we show that concentration dependent threshold effects in biology emerge from the catalytic properties of genes and its associated conservation laws. We apply this methodology to the segment patterning in Drosophila early development and we calibrate the genetic transcriptional network responsible for the patterning of the gap gene proteins Hunchback and Knirps, along the antero-posterior axis of the Drosophila embryo. In this approach, the zygotically produced proteins Hunchback and Knirps do not diffuse along the antero-posterior axis of the embryo of Drosophila, developing a spatial pattern due to concentration dependent thresholds. This shows that patterning at the gap genes stage can be explained by the concentration gradients along the embryo of the transcriptional regulators

Stochasticity in Protein Levels Drives Colinearity of Gene Order in Metabolic Operons of Escherichia coli

Gene order in some bacterial metabolic operons reflects ordering in the metabolic pathway. That this is true uniquely for operons expressed at low levels highlights the selective importance of fluctuations in protein levels

Construction and analysis of a modular model of caspase activation in apoptosis

<p>Abstract</p> <p>Background</p> <p>A key physiological mechanism employed by multicellular organisms is apoptosis, or programmed cell death. Apoptosis is triggered by the activation of caspases in response to both extracellular (extrinsic) and intracellular (intrinsic) signals. The extrinsic and intrinsic pathways are characterized by the formation of the death-inducing signaling complex (DISC) and the apoptosome, respectively; both the DISC and the apoptosome are oligomers with complex formation dynamics. Additionally, the extrinsic and intrinsic pathways are coupled through the mitochondrial apoptosis-induced channel via the Bcl-2 family of proteins.</p> <p>Results</p> <p>A model of caspase activation is constructed and analyzed. The apoptosis signaling network is simplified through modularization methodologies and equilibrium abstractions for three functional modules. The mathematical model is composed of a system of ordinary differential equations which is numerically solved. Multiple linear regression analysis investigates the role of each module and reduced models are constructed to identify key contributions of the extrinsic and intrinsic pathways in triggering apoptosis for different cell lines.</p> <p>Conclusion</p> <p>Through linear regression techniques, we identified the feedbacks, dissociation of complexes, and negative regulators as the key components in apoptosis. The analysis and reduced models for our model formulation reveal that the chosen cell lines predominately exhibit strong extrinsic caspase, typical of type I cell, behavior. Furthermore, under the simplified model framework, the selected cells lines exhibit different modes by which caspase activation may occur. Finally the proposed modularized model of apoptosis may generalize behavior for additional cells and tissues, specifically identifying and predicting components responsible for the transition from type I to type II cell behavior.</p

Continuous-time modeling of cell fate determination in Arabidopsis flowers

<p>Abstract</p> <p>Background</p> <p>The genetic control of floral organ specification is currently being investigated by various approaches, both experimentally and through modeling. Models and simulations have mostly involved boolean or related methods, and so far a quantitative, continuous-time approach has not been explored.</p> <p>Results</p> <p>We propose an ordinary differential equation (ODE) model that describes the gene expression dynamics of a gene regulatory network that controls floral organ formation in the model plant <it>Arabidopsis thaliana</it>. In this model, the dimerization of MADS-box transcription factors is incorporated explicitly. The unknown parameters are estimated from (known) experimental expression data. The model is validated by simulation studies of known mutant plants.</p> <p>Conclusions</p> <p>The proposed model gives realistic predictions with respect to independent mutation data. A simulation study is carried out to predict the effects of a new type of mutation that has so far not been made in <it>Arabidopsis</it>, but that could be used as a severe test of the validity of the model. According to our predictions, the role of dimers is surprisingly important. Moreover, the functional loss of any dimer leads to one or more phenotypic alterations.</p

The Critical Richardson Number and Limits of Applicability of Local Similarity Theory in the Stable Boundary Layer

Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both of the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a 'critical value' of about 0.20 - 0.25, the inertial subrange associated with the Richardson-Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson-Kolmogorov energy cascade weakens; therefore, the applicability of local Monin-Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ri_cr and Rf < Rf_cr. However, it is found that Rf_cr = 0.20 - 0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin-Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson-Kolmogorov cascade) have been filtered out.Comment: Boundary-Layer Meteorology (Manuscript submitted: 16 February 2012; Accepted: 10 September 2012