Bruce E. Shapiro

BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems

BioModels Database (), part of the international initiative BioModels.net, provides access to published, peer-reviewed, quantitative models of biochemical and cellular systems. Each model is carefully curated to verify that it corresponds to the reference publication and gives the proper numerical results. Curators also annotate the components of the models with terms from controlled vocabularies and links to other relevant data resources. This allows the users to search accurately for the models they need. The models can currently be retrieved in the SBML format, and import/export facilities are being developed to extend the spectrum of formats supported by the resource.

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. Here we address these questions by using mathematical modeling combined with confocal imaging. We propose a model that is based on the assumption that auxin influences the polarization of its own efflux within the meristem epidermis. We show that such a model is sufficient to create regular spatial patterns of auxin concentration on systems with static and dynamic cellular connectivities, the latter governed by a mechanical model. We also optimize parameter values for the PIN1 dynamics by using a detailed auxin transport model, for which parameter values are taken from experimental estimates, together with a template consisting of cell and wall compartments as well as PIN1 concentrations quantitatively extracted from confocal data. The model shows how polarized transport can drive the formation of regular patterns.

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. Reactions are translated into differential equations and can be solved numerically to generate predictive time courses or output as systems of equations that can be read by other programs. Cellerator simulations are fully extensible and portable to any operating system that supports Mathematica, and can be indefinitely nested within larger data structures to produce highly scaleable models.

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. However, upregulation of CLAVATA3 in conjunction with the receptor kinase CLAVATA1 results in the downregulation of WUSCHEL. Despite much work, experimental data for this network are incomplete and additional hypotheses are needed to explain the spatial locations and dynamics of these expression domains. Predictive mathematical models describing the system should provide a useful tool for investigating and discriminating among possible hypotheses, by determining which hypotheses best explain observed gene expression dynamics. RESULTS We are developing a method using in vivo live confocal microscopy to capture quantitative gene expression data and create templates for computational models. We present two models accounting for the organization of the WUSCHEL expression domain. Our preferred model uses a reaction-diffusion mechanism in which an activator induces WUSCHEL expression. This model is able to organize the WUSCHEL expression domain. In addition, the model predicts the dynamical reorganization seen in experiments where cells, including the WUSCHEL domain, are ablated, and it also predicts the spatial expansion of the WUSCHEL domain resulting from removal of the CLAVATA3 signal. AVAILABILITY An extended description of the model framework and image processing algorithms can be found at http://www.computableplant.org, together with additional results and simulation movies. SUPPLEMENTARY INFORMATION http://www.computableplant.org/ and alternatively for a direct link to the page, http://computableplant.ics.uci.edu/bti1036 can be accessed.

Osmotic Forces and Gap Junctions in Spreading Depression: A Computational Model

In a computational model of spreading depression (SD), ionic movement through a neuronal syncytium of cells connected by gap junctions is described electrodiffusively. Simulations predict that SD will not occur unless cells are allowed to expand in response to osmotic pressure gradients and K+ is allowed to move through gap junctions. SD waves of [K+]out ≈ 25 to ≈60 mM moving at ≈2 to ≈18 mm/min are predicted over the range of parametric values reported in gray matter, with extracellular space decreasing up to ≈50%. Predicted waveform shape is qualitatively similar to laboratory reports. The delayed-rectifier, NMDA, BK, and Na+ currents are predicted to facilitate SD, while SK and A-type K+ currents and glial activity impede SD. These predictions are consonant with recent findings that gap junction poisons block SD and support the theories that cytosolic diffusion via gap junctions and osmotic forces are important mechanisms underlying SD.

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). MathSBML also provides an application programming interface for viewing, manipulating, running numerical simulations; exporting SBML models; and converting SBML models in to other formats, such as XPP, HTML and FORTRAN. By accessing the full breadth of Mathematica functionality, MathSBML is fully extensible to SBML models of any size or complexity. AVAILABILITY Open Source (LGPL) at http://www.sbml.org and http://www.sf.net/projects/sbml

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. In addition, we present methods that use commonly available kinetic measurements to estimate rate constants required to solve these differential equations.

Signalling in multicellular models of plant development

The shoot apical meristem (SAM) is the source of the complete part of a plant above ground. Arabidopsis thaliana has become a model system for dicot plants (Meinke et al., 1998; The-Arabidopsis-Genome-Initiative, 2000), and it has a SAM of about 10^3 cells. It retains this size and its almost half-spherical shape throughout the post-embryonic life of the plant. The SAM can be divided into cytologically defined zones where the central zone is at the very apex, the peripheral zone is on the sides, and the rib meristem is in the central parts of the meristem (Steeves and Sussex, 1989; Meyerowitz, 1997).

Analysis of cell division patterns in the Arabidopsis shoot apical meristem

Significance Plant cells are incapable of sliding past each other, so generation of shape and structure in plant tissue is dependent on cells dividing and expanding in particular directions. Therefore, understanding how cells choose where to build new walls is critical in understanding how plant tissue is patterned. In the present study we expand on previous models of cell division to further understand what parameters of cell geometry and growth influence the position of new walls. 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. Here we present a quantitative model of these rules that incorporates different observed features of cell division. Each feature is incorporated into a “potential function” that contributes a single term to a total analog of potential energy. New cell walls are predicted to occur at locations where the potential function is minimized. Quantitative terms that represent the well-known historical rules of plant cell division, such as those given by Hofmeister, Errera, and Sachs are developed and evaluated against observed cell divisions in the epidermal layer (L1) of Arabidopsis thaliana SAM. The method is general enough to allow additional terms for nongeometric properties such as internal concentration gradients and mechanical tensile forces.

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. In this paper, we describe a more flexible model in Cellerator, which generalizes the Monod, Wyman, Changeux (MWC) model for enzyme allosteric regulation to allow for multiple substrate, activator and inhibitor binding sites. Furthermore, we have developed a model that describes the behavior of the bifunctional allosteric enzyme aspartate Kinase I-Homoserine Dehydrogenase I (AKI-HDHI). This model predicts the partition of enzyme activities in the steady state which paves a way for a more generalized prediction of the behavior of bifunctional enzymes.