SBML Level 3: an extensible format for the exchange and reuse of biological models.

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose.

A Pycellerator Tutorial.

We present a tutorial on using Pycellerator for biomolecular simulations. Models are described in human readable (and editable) text files (UTF8 or ASCII) containing collections of reactions, assignments, initial conditions, function definitions, and rate constants. These models are then converted into a Python program that can optionally solve the system, e.

Pycellerator: an arrow-based reaction-like modelling language for biological simulations.

Motivation: We introduce Pycellerator, a Python library for reading Cellerator arrow notation from standard text files, conversion to differential equations, generating stand-alone Python solvers, and optionally running and plotting the solutions. All of the original Cellerator arrows, which represent reactions ranging from mass action, Michales-Menten-Henri (MMH) and Gene-Regulation (GRN) to Monod-Wyman-Changeaux (MWC), user defined reactions and enzymatic expansions (KMech), were previously represented with the Mathematica extended character set. These are now typed as reaction-like commands in ASCII text files that are read by Pycellerator, which includes a Python command line interface (CLI), a Python application programming interface (API) and an iPython notebook interface.

Analysis of cell division patterns in the Arabidopsis shoot apical meristem.

The stereotypic pattern of cell shapes in the Arabidopsis shoot apical meristem (SAM) suggests that strict rules govern the placement of new walls during cell division. When a cell in the SAM divides, a new wall is built that connects existing walls and divides the cytoplasm of the daughter cells. Because features that are determined by the placement of new walls such as cell size, shape, and number of neighbors are highly regular, rules must exist for maintaining such order.

Using cellzilla for plant growth simulations at the cellular level.

Cellzilla is a two-dimensional tissue simulation platform for plant modeling utilizing Cellerator arrows. Cellerator describes biochemical interactions with a simplified arrow-based notation; all interactions are input as reactions and are automatically translated to the appropriate differential equations using a computer algebra system. Cells are represented by a polygonal mesh of well-mixed compartments.

Application of a generalized MWC model for the mathematical simulation of metabolic pathways regulated by allosteric enzymes.

In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica.

Application of a generalized MWC model for the mathematical simulation of metabolic pathways regulated by allosteric enzymes.

In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica.

An auxin-driven polarized transport model for phyllotaxis.

Recent studies show that plant organ positioning may be mediated by localized concentrations of the plant hormone auxin. Auxin patterning in the shoot apical meristem is in turn brought about by the subcellular polar distribution of the putative auxin efflux mediator, PIN1. However, the question of what signals determine PIN1 polarization and how this gives rise to regular patterns of auxin concentration remains unknown.

Modeling the organization of the WUSCHEL expression domain in the shoot apical meristem.

Motivation: The above-ground tissues of higher plants are generated from a small region of cells situated at the plant apex called the shoot apical meristem. An important genetic control circuit modulating the size of the Arabidopsis thaliana meristem is a feed-back network between the CLAVATA3 and WUSCHEL genes. Although the expression patterns for these genes do not overlap, WUSCHEL activity is both necessary and sufficient (when expressed ectopically) for the induction of CLAVATA3 expression.

Reproducibility, fidelity, and discriminant validity of mRNA amplification for microarray analysis from primary hematopoietic cells.

Analysis of gene expression in clinical samples poses special challenges, including limited RNA availability and poor RNA quality. Quantitative information regarding reliability of RNA amplification methodologies applied to primary cells and representativeness of resulting gene expression profiles is limited. We evaluated four protocols for RNA amplification from peripheral blood mononuclear cells.

A mathematical model for the branched chain amino acid biosynthetic pathways of Escherichia coli K12.

As a first step toward the elucidation of the systems biology of the model organism Escherichia coli, it was our goal to mathematically model a metabolic system of intermediate complexity, namely the well studied end product-regulated pathways for the biosynthesis of the branched chain amino acids L-isoleucine, L-valine, and L-leucine. This has been accomplished with the use of kMech (Yang, C.-R.

An enzyme mechanism language for the mathematical modeling of metabolic pathways.

Motivation: As a first step toward the elucidation of the systems biology of complex biological systems, it was our goal to mathematically model common enzyme catalytic and regulatory mechanisms that repeatedly appear in biological processes such as signal transduction and metabolic pathways.

Results: We describe kMech, a Cellerator language extension that describes a suite of enzyme mechanisms. Each enzyme mechanism is parsed by kMech into a set of fundamental association-dissociation reactions that are translated by Cellerator into ordinary differential equations that are numerically solved by Mathematica.

MathSBML: a package for manipulating SBML-based biological models.

Unlabelled: MathSBML is a Mathematica package designed for manipulating Systems Biology Markup Language (SBML) models. It converts SBML models into Mathematica data structures and provides a platform for manipulating and evaluating these models. Once a model is read by MathSBML, it is fully compatible with standard Mathematica functions such as NDSolve (a differential-algebraic equations solver).

Cellerator: extending a computer algebra system to include biochemical arrows for signal transduction simulations.

Cellerator describes single and multi-cellular signal transduction networks (STN) with a compact, optionally palette-driven, arrow-based notation to represent biochemical reactions and transcriptional activation. Multi-compartment systems are represented as graphs with STNs embedded in each node. Interactions include mass-action, enzymatic, allosteric and connectionist models.