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

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

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

SBMLsqueezer: A CellDesigner plug-in to generate kinetic rate equations for biochemical networks

<p>Abstract</p> <p>Background</p> <p>The development of complex biochemical models has been facilitated through the standardization of machine-readable representations like SBML (Systems Biology Markup Language). This effort is accompanied by the ongoing development of the human-readable diagrammatic representation SBGN (Systems Biology Graphical Notation). The graphical SBML editor CellDesigner allows direct translation of SBGN into SBML, and vice versa. For the assignment of kinetic rate laws, however, this process is not straightforward, as it often requires manual assembly and specific knowledge of kinetic equations.</p> <p>Results</p> <p>SBMLsqueezer facilitates exactly this modeling step via automated equation generation, overcoming the highly error-prone and cumbersome process of manually assigning kinetic equations. For each reaction the kinetic equation is derived from the stoichiometry, the participating species (e.g., proteins, mRNA or simple molecules) as well as the regulatory relations (activation, inhibition or other modulations) of the SBGN diagram. Such information allows distinctions between, for example, translation, phosphorylation or state transitions. The types of kinetics considered are numerous, for instance generalized mass-action, Hill, convenience and several Michaelis-Menten-based kinetics, each including activation and inhibition. These kinetics allow SBMLsqueezer to cover metabolic, gene regulatory, signal transduction and mixed networks. Whenever multiple kinetics are applicable to one reaction, parameter settings allow for user-defined specifications. After invoking SBMLsqueezer, the kinetic formulas are generated and assigned to the model, which can then be simulated in CellDesigner or with external ODE solvers. Furthermore, the equations can be exported to SBML, LaTeX or plain text format.</p> <p>Conclusion</p> <p>SBMLsqueezer considers the annotation of all participating reactants, products and regulators when generating rate laws for reactions. Thus, for each reaction, only applicable kinetic formulas are considered. This modeling scheme creates kinetics in accordance with the diagrammatic representation. In contrast most previously published tools have relied on the stoichiometry and generic modulators of a reaction, thus ignoring and potentially conflicting with the information expressed through the process diagram. Additional material and the source code can be found at the project homepage (URL found in the Availability and requirements section).</p

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

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

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

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks