Computational protocol: Spatio-temporal Model of Endogenous ROS and Raft-Dependent WNT/Beta-Catenin Signaling Driving Cell Fate Commitment in Human Neural Progenitor Cells

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Protocol publication

[…] Our model is defined in ML-Rules, a multi-level, rule-based modeling language []. Rule-based modeling languages use the notations of chemical equations to describe cell biological systems. Thereby, the state of the model is represented by chemical solutions, i.e. mappings from species to concentrations or discrete numbers, while the transitions between different model states are defined in terms of reactions. For execution, a well defined semantic translates the model into its corresponding mathematical definition, e.g. ordinary differential equations (ODEs) or stochastic processes [, ].Rule-based approaches further benefit from the possibility of describing different molecule states (like phosphorylation states or binding sites) in terms of attributes. This allows to define rules with reaction patterns, where a single rule represents a set of multiple reactions, depending on the attribute values of the species [, , ]. Thereby the size of the model can be significantly reduced, because a reaction network can be defined in terms of schematic rules instead of enlisting all possible combinations of species and reactions. For a comprehensive review of rule-based modeling the interested reader is referred to [].The semantics of ML-Rules is based on continuous time Markov chains (CTMC). ML-Rules models are executed by stochastic, discrete event execution algorithms []. All entities are expressed in terms of concrete numbers, like molecules, compartments or cells, instead of concentrations. In our model stochastic events play a crucial role due to the comparatively low molecule number of the key player AXIN. In this setting, a deterministic ODE based execution might miss important dynamics as has been shown in []: in comparison to the ODE based execution, the stochastic execution revealed artifacts in simulating β-catenin signaling within hNPCs-cells if adopting the very low AXIN concentration as given by []. Therefore in [], a still comparatively low but ∼ 10 times higher number of AXIN molecules was determined as more realistic for hNPCs, a result which was later confirmed for various mammal cells by wet-lab studies []. The implemented WNT/β-catenin signaling model makes extensive use of rule-schemata provided by the ML-Rules syntax. This is necessary, since the model contains several hierarchical levels as well as protein specific binding and phosphorylation states, that are in particular necessary for the representation of the signalosome. Accordingly, in our model the central component of the signalosome, LRP6, is attributed with four different attributes: diffusion rate, raft affinity, phosphorylation state and binding state. Further individual LRP6 receptors continuously diffuse between membrane and raft regions according to its raft affinity value. Using a non-attributed modeling formalism, these states had to be represented as individual species and the respective reactions had to be considered separately, which would significantly increase the complexity of the model in terms of species/reactants and reactions. Further we’d like to emphasize that ML-Rules allows an easy and straight forward extension of the presented model. As discussed in the outlook, endocytosis and multi-vesicular body handling can be included in the model similar to lipid rafts, i.e. as dynamic, cytosolic compartments. A more detailed description of the model specification in ML-Rules and the corresponding specification of the simulation experiments is given as Supporting Information (). For a thorough introduction to the general ML-Rules modeling formalism, the interested reader is referred to []. [...] ML-Rules is implemented on top of the modeling and simulation framework JAMES II []. JAMES II is implemented in Java and provides various plug-ins to realize complex simulation experiments, e.g., for parameter optimization, sensitivity analysis, and output data storage []. In our experiments, we used the approximative τ-leaping simulator for ML-Rules [] to speed up the simulation. We set up most experiments with the domain-specific language SESSL []. SESSL is based on the Scala programming language [] and allows to concisely specify JAMES II experiments. For a description of two typical experiment setups (a parameter scan and an optimization experiment), that illustrate the specification of simulation experiments in SESSL, see Supporting Information (). To reproduce our experiment, please find a sandbox to simulate ML-Rules models and a setup to execute SESSL experiments at The sandbox also contains a user manual to the modeling formalism ML-Rules, describing its concrete syntax and illustrating how ML-Rules can be used for modeling various biochemical and multi-level systems. […]

Pipeline specifications

Software tools ML-Rules, SESSL
Application Mathematical modeling
Organisms Homo sapiens
Diseases Neoplasms, Neurodegenerative Diseases
Chemicals Oxygen