Meredys, a multi-compartment reaction-diffusion simulator using multistate realistic molecular complexes

<p>Abstract</p> <p>Background</p> <p>Most cellular signal transduction mechanisms depend on a few molecular partners whose roles depend on their position and movement in relation to the input signal. This movement can follow various rules and take place in different compartments. Additionally, the molecules can form transient complexes. Complexation and signal transduction depend on the specific states partners and complexes adopt. Several spatial simulator have been developed to date, but none are able to model reaction-diffusion of realistic multi-state transient complexes.</p> <p>Results</p> <p><it>Meredys </it>allows for the simulation of multi-component, multi-feature state molecular species in two and three dimensions. Several compartments can be defined with different diffusion and boundary properties. The software employs a Brownian dynamics engine to simulate reaction-diffusion systems at the reactive particle level, based on compartment properties, complex structure, and hydro-dynamic radii. Zeroth-, first-, and second order reactions are supported. The molecular complexes have realistic geometries. Reactive species can contain user-defined feature states which can modify reaction rates and outcome. Models are defined in a versatile NeuroML input file. The simulation volume can be split in subvolumes to speed up run-time.</p> <p>Conclusions</p> <p><it>Meredys </it>provides a powerful and versatile way to run accurate simulations of molecular and sub-cellular systems, that complement existing multi-agent simulation systems. <it>Meredys </it>is a Free Software and the source code is available at <url>http://meredys.sourceforge.net/</url>.</p

STSE: Spatio-Temporal Simulation Environment Dedicated to Biology

<p>Abstract</p> <p>Background</p> <p>Recently, the availability of high-resolution microscopy together with the advancements in the development of biomarkers as reporters of biomolecular interactions increased the importance of imaging methods in molecular cell biology. These techniques enable the investigation of cellular characteristics like volume, size and geometry as well as volume and geometry of intracellular compartments, and the amount of existing proteins in a spatially resolved manner. Such detailed investigations opened up many new areas of research in the study of spatial, complex and dynamic cellular systems. One of the crucial challenges for the study of such systems is the design of a well stuctured and optimized workflow to provide a systematic and efficient hypothesis verification. Computer Science can efficiently address this task by providing software that facilitates handling, analysis, and evaluation of biological data to the benefit of experimenters and modelers.</p> <p>Results</p> <p>The Spatio-Temporal Simulation Environment (STSE) is a set of <it>open-source </it>tools provided to conduct spatio-temporal simulations in discrete structures based on microscopy images. The framework contains modules to <it>digitize, represent, analyze</it>, and <it>mathematically model </it>spatial distributions of biochemical species. Graphical user interface (GUI) tools provided with the software enable meshing of the simulation space based on the Voronoi concept. In addition, it supports to automatically acquire spatial information to the mesh from the images based on pixel luminosity (e.g. corresponding to molecular levels from microscopy images). STSE is freely available either as a stand-alone version or included in the linux live distribution Systems Biology Operational Software (SB.OS) and can be downloaded from <url>http://www.stse-software.org/</url>. The Python source code as well as a comprehensive user manual and video tutorials are also offered to the research community. We discuss main concepts of the STSE design and workflow. We demonstrate it's usefulness using the example of a signaling cascade leading to formation of a morphological gradient of Fus3 within the cytoplasm of the mating yeast cell <it>Saccharomyces cerevisiae</it>.</p> <p>Conclusions</p> <p>STSE is an efficient and powerful novel platform, designed for computational handling and evaluation of microscopic images. It allows for an uninterrupted workflow including digitization, representation, analysis, and mathematical modeling. By providing the means to relate the simulation to the image data it allows for systematic, image driven model validation or rejection. STSE can be scripted and extended using the Python language. STSE should be considered rather as an API together with workflow guidelines and a collection of GUI tools than a stand alone application. The priority of the project is to provide an easy and intuitive way of extending and customizing software using the Python language.</p

Hierarchical graphs for rule-based modeling of biochemical systems

<p>Abstract</p> <p>Background</p> <p>In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system.</p> <p>Results</p> <p>For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm.</p> <p>Conclusions</p> <p>Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language (BNGL). Thus, the proposed use of hierarchical graphs should promote clarity and better understanding of rule-based models.</p

Rule-based multi-level modeling of cell biological systems

<p>Abstract</p> <p>Background</p> <p>Proteins, individual cells, and cell populations denote different levels of an organizational hierarchy, each of which with its own dynamics. Multi-level modeling is concerned with describing a system at these different levels and relating their dynamics. Rule-based modeling has increasingly attracted attention due to enabling a concise and compact description of biochemical systems. In addition, it allows different methods for model analysis, since more than one semantics can be defined for the same syntax.</p> <p>Results</p> <p>Multi-level modeling implies the hierarchical nesting of model entities and explicit support for downward and upward causation between different levels. Concepts to support multi-level modeling in a rule-based language are identified. To those belong rule schemata, hierarchical nesting of species, assigning attributes and solutions to species at each level and preserving content of nested species while applying rules. Further necessities are the ability to apply rules and flexibly define reaction rate kinetics and constraints on nested species as well as species that are nested within others. An example model is presented that analyses the interplay of an intracellular control circuit with states at cell level, its relation to cell division, and connections to intercellular communication within a population of cells. The example is described in ML-Rules - a rule-based multi-level approach that has been realized within the plug-in-based modeling and simulation framework JAMES II.</p> <p>Conclusions</p> <p>Rule-based languages are a suitable starting point for developing a concise and compact language for multi-level modeling of cell biological systems. The combination of nesting species, assigning attributes, and constraining reactions according to these attributes is crucial in achieving the desired expressiveness. Rule schemata allow a concise and compact description of complex models. As a result, the presented approach facilitates developing and maintaining multi-level models that, for instance, interrelate intracellular and intercellular dynamics.</p

Spatial Stochastic Modeling of the ErbB Receptor Family

ErbB transmembrane receptors are a family of 4 receptor tyrosine kinases that interact with one another through homo and heterodimer interactions. When these dimers form, the kinase domains on the receptor tails interact with one another, transphosphorylating one another, initiating a signal cascade. The signaling pathways these receptors participate in are responsible for many different cell functions including apoptosis, growth, and proliferation. The overexpression of these receptors has been linked to various forms of cancer, emphasizing the importance of understanding how these receptors interact with one another to trigger these cascades. Single Particle Tracking experiments have provided more precise and detailed measures of dimer lifetimes and diffusion. A major observation from the experiments is the anomalous diffusion of the receptors. One suggested contributor to this anomalous diffusion is confinement zones on the membrane. In this work, we develop, validate, and implement a spatial stochastic model to study these receptors and uncover how their kinetics and dynamics as well as the membrane landscape come together to impact erbB activation. We start by focusing on erbB1. Single particle tracking experiments show that receptor pairs interact repeatedly over a period of time. One possible explanation for these repeated interactions is to facilitate phosphorylation. An asymmetric phosphorylation model is proposed, where one receptor in the dimer pair is responsible for activating the other receptor, the receiver, which then in turn phosphorylates the original activator. The model shows that the confinement zones on the membrane play a critical role in causing repeated receptor interactions and reveals that receptors dynamically switch between different activation states over time. Our work continues by delving deeper into the membrane landscape. Single particle tracking data is analyzed to investigate the characteristics of the observed anomalous diffusion. The analysis gives an estimate for the size range of the confinement zones and shows that they are a series of domains, not corrals. Taking the single particle tracking analysis one step further, we develop a Domain Reconstruction Algorithm that reconstructs confinement zone shapes and sizes from single particle tracking trajectories. In the final study, we move on to erbB2 and erbB3 interactions. ErbB3, which is traditionally believed to be kinase dead, has recently been shown to have weak kinase activity. Through kinase assay experiments, we show in the presence of erbB2 and heregulin, erbB3 has measurable kinase activity. Using the reconstructed domains from erbB2 and erbB3 data to create a simulation space, and experimental data from the kinase assay and single particle tracking, we extend the erbB1 spatial stochastic model for this study. We show that erbB2 and erbB3 have significantly different interactions with the cellular membrane confinement zones, erbB3 is dependent on erbB2 activation, and erbB3 homodimer stability inhibits erbB3 activation. Extension of the model to investigate mutation behaviors in erbB3 receptors reveals insights into how a gain of function mutation in the erbB3 kinase domain impacts erbB2 and erbB3 interactions. Finally, discovery of a gain of function mutation in the kinase domain of erbB3 is connected to an uptick in erbB3 kinase activity. As a path forward from this work, we suggest using the spatial stochastic model to investigate more possible mutations in erbB3 receptors to give better insight into which mutations would be promising to explore