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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 community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

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.g., as a system of differential equations using ODEINT, or be run by another program. The input language implements an extended version of the Cellerator arrow notation, including mass action, Hill functions, S-Systems, MWC, and reactions with user-defined kinetic laws. Simple flux balance analysis is also implemented. We will demonstrate the implementation and analysis of progressively more complex models, starting from simple mass action through indexed cascades. Pycellerator can be used as a library that is integrated into other programs, run as a command line program, or in iPython notebooks. It is implemented in Python 2.7 and available under an open source GPL license.

MotivationWe 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.ResultsCellerator reaction arrows are now input in text files. The arrows are parsed by Pycellerator and translated into differential equations in Python, and Python code is automatically generated to solve the system. Time courses are produced by executing the auto-generated Python code. Users have full freedom to modify the solver and utilize the complete set of standard Python tools. The new libraries are completely independent of the old Cellerator software and do not require Mathematica.Availability and implementationAll software is available (GPL) from the github repository at https://github.com/biomathman/pycellerator/releases. Details, including installation instructions and a glossary of acronyms and terms, are given in the Supplementary information.

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.

The fast-developing field of RNA nanotechnology requires the adoption and development of novel and faster computational approaches to modeling and characterization of RNA-based nano-objects. We report the first application of Elastic Network Modeling (ENM), a structure-based dynamics model, to RNA nanotechnology. With the use of an Anisotropic Network Model (ANM), a type of ENM, we characterize the dynamic behavior of non-compact, multi-stranded RNA-based nanocubes that can be used as nano-scale scaffolds carrying different functionalities. Modeling the nanocubes with our tool NanoTiler and exploring the dynamic characteristics of the models with ANM suggested relatively minor but important structural modifications that enhanced the assembly properties and thermodynamic stabilities. In silico and in vitro, we compared nanocubes having different numbers of base pairs per side, showing with both methods that the 10 bp-long helix design leads to more efficient assembly, as predicted computationally. We also explored the impact of different numbers of single-stranded nucleotide stretches at each of the cube corners and showed that cube flexibility simulations help explain the differences in the experimental assembly yields, as well as the measured nanomolecule sizes and melting temperatures. This original work paves the way for detailed computational analysis of the dynamic behavior of artificially designed multi-stranded RNA nanoparticles.