Rule-based multi-level modeling of cell biological systems

bnglViz: online visualization of rule-based models

MOTIVATION

Rule-based modeling is a powerful method to describe and simulate interactions among multi-site molecules and multi-molecular species, accounting for the internal connectivity of molecules in chemical species. This modeling technique is implemented in BioNetGen software that is used by various tools and software frameworks, such as BioNetGen stand-alone software, NFSim simulation engine, Virtual Cell simulation and modeling framework, SmolDyn and PySB software tools. These tools exchange models using BioNetGen scripting language (BNGL). Until now, there was no online visualization of such rule-based models. Modelers and researchers reading the manuscripts describing rule-based models had to learn BNGL scripting or master one of these tools to understand the models.

RESULTS

Here, we introduce bnglViz, an online platform for visualizing BNGL files as graphical cartoons, empowering researchers to grasp the nuances of rule-based models swiftly and efficiently, and making the exploration of complex biological systems more accessible than ever before. The produced visualizations can be used as supplemental figures in publications or as a way to annotate BNGL models on web repositories.

AVAILABILITY AND IMPLEMENTATION

Available at https://bnglviz.github.io/.

Rule-based modelling of biological systems using regulated rewriting

In systems biology, models play a crucial role in understanding studied systems. There are many modelling approaches, among which rewriting systems provide a framework for describing systems on a mechanistic level. Describing biochemical processes often requires incorporating knowledge on an abstract level to simplify the system description or substitute the missing details. For this purpose, we present regulation mechanisms, an extension of this formalism with additional controls on the rewriting process. We introduce several regulation mechanisms and apply them to a rule-based language, a notation suitable for modelling biological phenomena. Finally, we demonstrate the usage of such regulations on several case studies from the biochemical domain.

Methodology for development of single cell dendritic spine (SCDS) synaptic tagging and capture model using Virtual Cell (VCell)

Single cell dendritic spine modelling methodology has been adopted to explain structural plasticity and respective change in the neuronal volume previously. However, the single cell dendrite methodology has not been employed previously to explain one of the important aspects of memory allocation i.e., Synaptic tagging and Capture (STC) hypothesis. It is difficult to relate the physical properties of STC pathways to structural changes and synaptic strength. We create a mathematical model based on earlier reported synaptic tagging networks. We built the model using Virtual Cell (VCell) software and used it to interpret experimental data and investigate the behavior and characteristics of known Synaptic tagging candidates.•We investigate processes associated with synaptic tagging candidates and compare them to the assumptions based on the STC hypothesis.•We assess the behavior of several reported synaptic tagging candidates against the requirements outlined in the synaptic tagging hypothesis.

BioSANS: A software package for symbolic and numeric biological simulation

Modeling biochemical systems can provide insights into behaviors that are difficult to observe or understand. It requires software, programming, and understanding of the system to build a model and study it. Softwares exist for systems biology modeling, but most support only certain types of modeling tasks. Desirable features including ease in preparing input, symbolic or analytical computation, parameter estimation, graphical user interface, and systems biology markup language (SBML) support are not seen concurrently in one software package. In this study, we developed a python-based software that supports these features, with both deterministic and stochastic propagations. The software can be used by graphical user interface, command line, or as a python import. We also developed a semi-programmable and intuitively easy topology input method for the biochemical reactions. We tested the software with semantic and stochastic SBML test cases. Tests on symbolic solution and parameter estimation were also included. The software we developed is reliable, well performing, convenient to use, and compliant with most of the SBML tests. So far it is the only systems biology software that supports symbolic, deterministic, and stochastic modeling in one package that also features parameter estimation and SBML support. This work offers a comprehensive set of tools and allows for better availability and accessibility for studying kinetics and dynamics in biochemical systems.

Hybrid modelling of biological systems: current progress and future prospects

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.

Receptor/Raft Ratio Is a Determinant for LRP6 Phosphorylation and WNT/β-Catenin Signaling

Microdomains or lipid rafts greatly affect the distribution of proteins and peptides in the membrane and play a vital role in the formation and activation of receptor/protein complexes. A prominent example for the decisive impact of lipid rafts on signaling is LRP6, whose localization to the same lipid rafts domain as the kinase CK1γ is crucial for its successful phosphorylation and the subsequent activation of the signalosome, hence WNT/β-catenin signaling. However, according to various experimental measurements, approximately 25 to 35 % of the cell plasma membrane is covered by nanoscopic raft domains with diameters ranging between 10 to 200 nm. Extrapolating/Translating these values to the membrane of a “normal sized” cell yields a raft abundance, that, by far, outnumbers the membrane-associated pathway components of most individual signaling pathway, such as receptor and kinases. To analyze whether and how the quantitative ratio between receptor and rafts affects LRP6 phosphorylation and WNT/β-catenin pathway activation, we present a computational modeling study, that for the first time employs realistic raft numbers in a compartment-based pathway model. Our simulation experiments indicate, that for receptor/raft ratios smaller than 1, i.e., when the number of raft compartments clearly exceeds the number of pathway specific membrane proteins, we observe significant decrease in LRP6 phosphorylation and downstream pathway activity. Our results suggest that pathway specific targeting and sorting mechanism are required to significantly narrow down the receptor/raft ratio and to enable the formation of the LRP6 signalosome, hence signaling.

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Multi-level gene regulatory network models to understand complex mechanisms underlying plant development

Patterning in plant development is the emergent outcome of the feedback-based interplay between tissue-coupled intracellular regulatory networks and physicochemical fields. This interplay gives rise to dynamics that evolve on a wide spectrum of spatiotemporal scales. This imposes important challenges for computational approaches to model the dynamics of plant development. These challenges are being tackled in recent times by computational and mathematical advances that have made progress in the modelling of regulatory networks, as well as in approaches to couple the latter to physicochemical fields. Efforts in this direction are fundamental to identify the dynamical constraints that emerge from non-cellular autonomous activity in cell-fate decisions and patterning, and requires an understanding of how multi-level and multi-scale processes are coupled. Here, we discuss the use of multi-level modeling and simulation tools for the study of multicellular systems, with emphasis on plants. As illustrative examples, we discuss recent works elucidating the mechanisms that underlie patterning in the root meristem of Arabidopsis thaliana, and in plant responses to environmental conditions.

Executable biochemical space for specification and analysis of biochemical systems

Computational systems biology provides multiple formalisms for modelling of biochemical processes among which the rule-based approach is one of the most suitable. Its main advantage is a compact and precise mechanistic description of complex processes. However, state-of-the-art rule-based languages still suffer several shortcomings that limit their use in practice. In particular, the elementary (low-level) syntax and semantics of rule-based languages complicate model construction and maintenance for users outside computer science. On the other hand, mathematical models based on differential equations (ODEs) still make the most typical used modelling framework. In consequence, robust re-interpretation and integration of models are difficult, thus making the systems biology paradigm technically challenging. Though several high-level languages have been developed at the top of rule-based principles, none of them provides a satisfactory and complete solution for semi-automated description and annotation of heterogeneous biophysical processes integrated at the cellular level. We present the second generation of a rule-based language called Biochemical Space Language (BCSL) that combines the advantages of different approaches and thus makes an effort to overcome several problems of existing solutions. BCSL relies on the formal basis of the rule-based methodology while preserving user-friendly syntax of plain chemical equations. BCSL combines the following aspects: the level of abstraction that hides structural and quantitative details but yet gives a precise mechanistic view of systems dynamics; executable semantics allowing formal analysis and consistency checking at the level of the language; universality allowing the integration of different biochemical mechanisms; scalability and compactness of the specification; hierarchical specification and composability of chemical entities; and support for genome-scale annotation.

Exploring the mechanistic and temporal regulation of LRP6 endocytosis in canonical WNT signaling

Endocytosis plays a pivotal regulatory role in canonical WNT signaling. Internalization of the low-density lipoprotein receptor-related protein 6 (LRP6) receptor complex can either promote or attenuate canonical WNT signaling, depending on the employed internalization pathway. Detailed analysis of the mechanism of LRP6 internalization and its temporal regulation is crucial for understanding the different cellular responses to WNT stimulation under varying conditions and in various cell types. Here, we elucidate the mechanisms involved in the internalization of LRP6 and re-evaluate existing, partly contradicting, theories on the regulation of LRP6 receptor internalization. We utilize a computational approach that aims at finding a set of mechanisms that accounts for the temporal dynamics of LRP6 receptor internalization upon WNT stimulation. Starting with a simple simulation model, we successively extend and probe the model's behavior based on quantitative measurements. The final model confirms that LRP6 internalization is clathrin independent in vertebrates, is not restricted to microdomains, and that signalosome formation delays LRP6 internalization within the microdomains. These findings partly revise the current understanding of LRP6 internalization in vertebrates.

ROS Dependent Wnt/β-Catenin Pathway and Its Regulation on Defined Micro-Pillars-A Combined In Vitro and In Silico Study

The physico-chemical surface design of implants influences the surrounding cells. Osteoblasts on sharp-edged micro-topographies revealed an impaired cell phenotype, function and Ca2+ mobilization. The influence of edges and ridges on the Wnt/β-catenin pathway in combination with the cells' stress response has not been clear. Therefore, MG-63 osteoblasts were studied on defined titanium-coated micro-pillars (5 × 5 × 5 µm) in vitro and in silico. MG-63s on micro-pillars indicated an activated state of the Wnt/β-catenin pathway. The β-catenin protein accumulated in the cytosol and translocated into the nucleus. Gene profiling indicated an antagonism mechanism of the transcriptional activity of β-catenin due to an increased expression of inhibitors like ICAT (inhibitor of β-catenin and transcription factor-4). Cells on pillars produced a significant reactive oxygen species (ROS) amount after 1 and 24 h. In silico analyses provided a detailed view on how transcriptional activity of Wnt signaling is coordinated in response to the oxidative stress induced by the micro-topography. Based on a coordinated expression of regulatory elements of the Wnt/β-catenin pathway, MG-63s are able to cope with an increased accumulation of β-catenin on micro-pillars and suppress an unintended target gene expression. Further, β-catenin may be diverted into other signaling pathways to support defense mechanisms against ROS.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

The Beacon Calculus: A formal method for the flexible and concise modelling of biological systems

Biological systems are made up of components that change their actions (and interactions) over time and coordinate with other components nearby. Together with a large state space, the complexity of this behaviour can make it difficult to create concise mathematical models that can be easily extended or modified. This paper introduces the Beacon Calculus, a process algebra designed to simplify the task of modelling interacting biological components. Its breadth is demonstrated by creating models of DNA replication dynamics, the gene expression dynamics in response to DNA methylation damage, and a multisite phosphorylation switch. The flexibility of these models is shown by adapting the DNA replication model to further include two topics of interest from the literature: cooperative origin firing and replication fork barriers. The Beacon Calculus is supported with the open-source simulator bcs (https://github.com/MBoemo/bcs.git) to allow users to develop and simulate their own models.

Simulating a model of a biological system can suggest ideas for future experiments and help ensure that conclusions about a mechanism are consistent with data. The Beacon Calculus is a new language that makes modelling simple by allowing users to simulate a biological system in only a few lines of code. This simplicity is critical as it allows users the freedom to come up with new ideas and rapidly test them. Models written in the Beacon Calculus are also easy to modify and extend, allowing users to add new features to the model or incorporate it into a larger biological system. We demonstrate the breadth of applications in this paper by applying the Beacon Calculus to DNA replication and DNA damage repair, both of which have implications for genome stability and cancer. We also apply it to multisite phosphorylation, which is important for cellular signalling. To enable users to create their own models, we created the open-source Beacon Calculus simulator bcs (https://github.com/MBoemo/bcs.git) which is easy to install and is well-supported by documentation and examples.

Potential based, spatial simulation of dynamically nested particles

BACKGROUND

To study cell biological phenomena which depend on diffusion, active transport processes, or the locations of species, modeling and simulation studies need to take space into account. To describe the system as a collection of discrete objects moving and interacting in continuous space, various particle-based reaction diffusion simulators for cell-biological system have been developed. So far the focus has been on particles as solid spheres or points. However, spatial dynamics might happen at different organizational levels, such as proteins, vesicles or cells with interrelated dynamics which requires spatial approaches that take this multi-levelness of cell biological systems into account.

RESULTS

Based on the perception of particles forming hollow spheres, ML-Force contributes to the family of particle-based simulation approaches: in addition to excluded volumes and forces, it also supports compartmental dynamics and relating dynamics between different organizational levels explicitly. Thereby, compartmental dynamics, e.g., particles entering and leaving other particles, and bimolecular reactions are modeled using pair-wise potentials (forces) and the Langevin equation. In addition, forces that act independently of other particles can be applied to direct the movement of particles. Attributes and the possibility to define arbitrary functions on particles, their attributes and content, to determine the results and kinetics of reactions add to the expressiveness of ML-Force. Its implementation comprises a rudimentary rule-based embedded domain-specific modeling language for specifying models and a simulator for executing models continuously. Applications inspired by cell biological models from literature, such as vesicle transport or yeast growth, show the value of the realized features. They facilitate capturing more complex spatial dynamics, such as the fission of compartments or the directed movement of particles, and enable the integration of non-spatial intra-compartmental dynamics as stochastic events.

CONCLUSIONS

By handling all dynamics based on potentials (forces) and the Langevin equation, compartmental dynamics, such as dynamic nesting, fusion and fission of compartmental structures are handled continuously and are seamlessly integrated with traditional particle-based reaction-diffusion dynamics within the cell. Thereby, attributes and arbitrary functions allow to flexibly describe diverse spatial phenomena, and relate dynamics across organizational levels. Also they prove crucial in modeling intra-cellular or intra-compartmental dynamics in a non-spatial manner, and, thus, to abstract from spatial dynamics, on demand which increases the range of multi-compartmental processes that can be captured.

Myo-REG: A Portal for Signaling Interactions in Muscle Regeneration

Muscle regeneration is a complex process governed by the interplay between several muscle-resident mononuclear cell populations. Following acute or chronic damage these cell populations are activated, communicate via cell-cell interactions and/or paracrine signals, influencing fate decisions via the activation or repression of internal signaling cascades. These are highly dynamic processes, occurring with distinct temporal and spatial kinetics. The main challenge toward a system level description of the muscle regeneration process is the integration of this plethora of inter- and intra-cellular interactions. We integrated the information on muscle regeneration in a web portal. The scientific content annotated in this portal is organized into two information layers representing relationships between different cell types and intracellular signaling-interactions, respectively. The annotation of the pathways governing the response of each cell type to a variety of stimuli/perturbations occurring during muscle regeneration takes advantage of the information stored in the SIGNOR database. Additional curation efforts have been carried out to increase the coverage of molecular interactions underlying muscle regeneration and to annotate cell-cell interactions. To facilitate the access to information on cell and molecular interactions in the context of muscle regeneration, we have developed Myo-REG, a web portal that captures and integrates published information on skeletal muscle regeneration. The muscle-centered resource we provide is one of a kind in the myology field. A friendly interface allows users to explore, approximately 100 cell interactions or to analyze intracellular pathways related to muscle regeneration. Finally, we discuss how data can be extracted from this portal to support in silico modeling experiments.

Mechanistic Models of Cellular Signaling, Cytokine Crosstalk, and Cell-Cell Communication in Immunology

The cells of the immune system respond to a great variety of different signals that frequently reach them simultaneously. Computational models of signaling pathways and cellular behavior can help us explore the biochemical mechanisms at play during such responses, in particular when those models aim at incorporating molecular details of intracellular reaction networks. Such detailed models can encompass hypotheses about the interactions among molecular binding domains and how these interactions are modulated by, for instance, post-translational modifications, or steric constraints in multi-molecular complexes. In this way, the models become formal representations of mechanistic immunological hypotheses that can be tested through quantitative simulations. Due to the large number of parameters (molecular abundances, association-, dissociation-, and enzymatic transformation rates) the goal of simulating the models can, however, in many cases no longer be the fitting of particular parameter values. Rather, the simulations perform sweeps through parameter space to test whether a model can account for certain experimentally observed features when allowing the parameter values to vary within experimentally determined or physiologically reasonable ranges. We illustrate how this approach can be used to explore possible mechanisms of immunological pathway crosstalk. Probing the input-output behavior of mechanistic pathway models through systematic simulated variations of receptor stimuli will soon allow us to derive cell population behavior from single-cell models, thereby bridging a scale gap that currently still is frequently addressed through heuristic phenomenological multi-scale models.

Coloured Petri nets for multilevel, multiscale and multidimensional modelling of biological systems

Owing to the availability of data of one biological phenomenon at different levels/scales, modelling of biological systems is moving from single level/scale to multiple levels/scales, which introduces a number of challenges. Coloured Petri nets (ColPNs) have been successfully applied to multilevel, multiscale and multidimensional modelling of some biological systems, addressing many of these challenges. In this article, we first review the basics of ColPNs and some popular extensions, and then their applications for multilevel, multiscale and multidimensional modelling of biological systems. This understanding of how to use ColPNs for modelling biological systems will assist readers in selecting appropriate ColPN classes for specific modelling circumstances.

Mapping Tyrosine Kinase Receptor Dimerization to Receptor Expression and Ligand Affinities

Tyrosine kinase receptor (RTK) ligation and dimerization is a key mechanism for translating external cell stimuli into internal signaling events. This process is critical to several key cell and physiological processes, such as in angiogenesis and embryogenesis, among others. While modulating RTK activation is a promising therapeutic target, RTK signaling axes have been shown to involve complicated interactions between ligands and receptors both within and across different protein families. In angiogenesis, for example, several signaling protein families, including vascular endothelial growth factors and platelet-derived growth factors, exhibit significant cross-family interactions that can influence pathway activation. Computational approaches can provide key insight to detangle these signaling pathways but have been limited by the sparse knowledge of these cross-family interactions. Here, we present a framework for studying known and potential non-canonical interactions. We constructed generalized models of RTK ligation and dimerization for systems of two, three and four receptor types and different degrees of cross-family ligation. Across each model, we developed parameter-space maps that fully determine relative pathway activation for any set of ligand-receptor binding constants, ligand concentrations and receptor concentrations. Therefore, our generalized models serve as a powerful reference tool for predicting not only known ligand: Receptor axes but also how unknown interactions could alter signaling dimerization patterns. Accordingly, it will drive the exploration of cross-family interactions and help guide therapeutic developments across processes like cancer and cardiovascular diseases, which depend on RTK-mediated signaling.

Application of adaptive-network-based fuzzy inference systems to the parameter optimization of a biochemical rule-based model

In this study, the binding of allergens to antibody-receptor complexes was investigated. This process is important in understanding the allergic response. A BioNetGen model that simulates this process, combined with a novel method for encoding steric effects via the optimization of the cutoff distance and the rule binding rate, was previously developed. These parameters were optimized by fitting the model output to the output of a 3D simulation that explicitly represents molecular geometry. In this work, the parameters for the BioNetGen model were optimized using an adaptive-network-based fuzzy inference system in order to predict the rule rate and cutoff distance given a residual-sum-of-squares value or a probability distribution. The fuzzy systems were constructed using fuzzy c-means clustering with existing data from BioNetGen model parameter scans used as the training data. Fuzzy systems with various input data and number of clusters were created and tested. Their performance was analyzed with regard to the effective optimization of the rule-based model. The study found that the fuzzy system that uses a residual-sum-of-squares value as the input value performs acceptably well. However, the performance of the fuzzy systems that use probabilities as their input values performed inconsistently in the tests and need further development. This methodology could potentially be modified for use in fitting other biological models.

Multi-Level Modeling and Simulation of Cellular Systems: An Introduction to ML-Rules

ML-Rules is a rule-based language for multi-level modeling and simulation. ML-Rules supports dynamic nesting of entities and applying arbitrary functions on entity attributes and content, as well as for defining kinetics of reactions. This allows describing and simulating complex cellular dynamics operating at different organizational levels, e.g., to combine intra-, inter-, and cellular dynamics, like the proliferation of cells, or to include compartmental dynamics like merging and splitting of mitochondria or endocytosis. The expressiveness of the language is bought with additional efforts in executing ML-Rules models. Therefore, various simulators have been developed from which the user and automatic procedures can select. The experiment specification language SESSL facilitates design, execution, and reuse of simulation experiments. The chapter illuminates the specific features of ML-Rules as a rule-based modeling language, the implications for an efficient execution, and shows ML-Rules at work.

Rare-event sampling of epigenetic landscapes and phenotype transitions

Stochastic simulation has been a powerful tool for studying the dynamics of gene regulatory networks, particularly in terms of understanding how cell-phenotype stability and fate-transitions are impacted by noisy gene expression. However, gene networks often have dynamics characterized by multiple attractors. Stochastic simulation is often inefficient for such systems, because most of the simulation time is spent waiting for rare, barrier-crossing events to occur. We present a rare-event simulation-based method for computing epigenetic landscapes and phenotype-transitions in metastable gene networks. Our computational pipeline was inspired by studies of metastability and barrier-crossing in protein folding, and provides an automated means of computing and visualizing essential stationary and dynamic information that is generally inaccessible to conventional simulation. Applied to a network model of pluripotency in Embryonic Stem Cells, our simulations revealed rare phenotypes and approximately Markovian transitions among phenotype-states, occurring with a broad range of timescales. The relative probabilities of phenotypes and the transition paths linking pluripotency and differentiation are sensitive to global kinetic parameters governing transcription factor-DNA binding kinetics. Our approach significantly expands the capability of stochastic simulation to investigate gene regulatory network dynamics, which may help guide rational cell reprogramming strategies. Our approach is also generalizable to other types of molecular networks and stochastic dynamics frameworks.

Hemoglobin state-flux: A finite-state model representation of the hemoglobin signal for evaluation of the resting state and the influence of disease

SUMMARY

In this report we introduce a weak-model approach for examination of the intrinsic time-varying properties of the hemoglobin signal, with the aim of advancing the application of functional near infrared spectroscopy (fNIRS) for the detection of breast cancer, among other potential uses. The developed methodology integrates concepts from stochastic network theory with known modulatory features of the vascular bed, and in doing so provides access to a previously unrecognized dense feature space that is shown to have promising diagnostic potential. Notable features of the methodology include access to this information solely from measures acquired in the resting state, and analysis of these by treating the various components of the hemoglobin (Hb) signal as a co-varying interacting system.

APPROACH

The principal data-transform kernel projects Hb state-space trajectories onto a coordinate system that constitutes a finite-state representation of covariations among the principal elements of the Hb signal (i.e., its oxygenated (ΔoxyHb) and deoxygenated (ΔdeoxyHb) forms and the associated dependent quantities: total hemoglobin (ΔtotalHb = ΔoxyHb + ΔdeoxyHb), hemoglobin oxygen saturation (ΔHbO2Sat = 100Δ(oxyHb/totalHb)), and tissue-hemoglobin oxygen exchange (ΔHbO2Exc = ΔdeoxyHb-ΔoxyHb)). The resulting ten-state representation treats the evolution of this signal as a one-space, spatiotemporal network that undergoes transitions from one state to another. States of the network are defined by the algebraic signs of the amplitudes of the time-varying components of the Hb signal relative to their temporal mean values. This assignment produces several classes of coefficient arrays, most with a dimension of 10×10.

BIOLOGICAL MOTIVATION

Motivating our approach is the understanding that effector mechanisms that modulate blood delivery to tissue operate on macroscopic scales, in a spatially and temporally varying manner. Also recognized is that this behavior is sensitive to nonlinear actions of these effectors, which include the binding properties of hemoglobin. Accessible phenomenology includes measures of the kinetics and probabilities of network dynamics, which we treat as surrogates for the actions of feedback mechanisms that modulate tissue-vascular coupling.

FINDINGS

Qualitative and quantitative features of this space, and their potential to serve as markers of disease, have been explored by examining continuous-wave fNIRS 3D tomographic time series obtained from the breasts of women who do and do not have breast cancer. Inspection of the coefficient arrays reveals that they are governed predominantly by first-order rate processes, and that each array class exhibits preferred structure that is mainly independent of the others. Discussed are strategies that may serve to extend evaluation of the accessible feature space and how the character of this information holds potential for development of novel clinical and preclinical uses.

High-Performance Agent-Based Modeling Applied to Vocal Fold Inflammation and Repair

Fast and accurate computational biology models offer the prospect of accelerating the development of personalized medicine. A tool capable of estimating treatment success can help prevent unnecessary and costly treatments and potential harmful side effects. A novel high-performance Agent-Based Model (ABM) was adopted to simulate and visualize multi-scale complex biological processes arising in vocal fold inflammation and repair. The computational scheme was designed to organize the 3D ABM sub-tasks to fully utilize the resources available on current heterogeneous platforms consisting of multi-core CPUs and many-core GPUs. Subtasks are further parallelized and convolution-based diffusion is used to enhance the performance of the ABM simulation. The scheme was implemented using a client-server protocol allowing the results of each iteration to be analyzed and visualized on the server (i.e., in-situ) while the simulation is running on the same server. The resulting simulation and visualization software enables users to interact with and steer the course of the simulation in real-time as needed. This high-resolution 3D ABM framework was used for a case study of surgical vocal fold injury and repair. The new framework is capable of completing the simulation, visualization and remote result delivery in under 7 s per iteration, where each iteration of the simulation represents 30 min in the real world. The case study model was simulated at the physiological scale of a human vocal fold. This simulation tracks 17 million biological cells as well as a total of 1.7 billion signaling chemical and structural protein data points. The visualization component processes and renders all simulated biological cells and 154 million signaling chemical data points. The proposed high-performance 3D ABM was verified through comparisons with empirical vocal fold data. Representative trends of biomarker predictions in surgically injured vocal folds were observed.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

Modelling and simulating decision processes of linked lives: An approach based on concurrent processes and stochastic race

Individuals' decision processes play a central role in understanding modern migration phenomena and other demographic processes. Their integration into agent-based computational demography depends largely on suitable support by a modelling language. We are developing the Modelling Language for Linked Lives (ML3) to describe the diverse decision processes of linked lives succinctly in continuous time. The context of individuals is modelled by networks the individual is part of, such as family ties and other social networks. Central concepts, such as behaviour conditional on agent attributes, age-dependent behaviour, and stochastic waiting times, are tightly integrated in the language. Thereby, alternative decisions are modelled by concurrent processes that compete by stochastic race. Using a migration model, we demonstrate how this allows for compact description of complex decisions, here based on the Theory of Planned Behaviour. We describe the challenges for the simulation algorithm posed by stochastic race between multiple concurrent complex decisions.

Multi-level and hybrid modelling approaches for systems biology

During the last decades, high-throughput techniques allowed for the extraction of a huge amount of data from biological systems, unveiling more of their underling complexity. Biological systems encompass a wide range of space and time scales, functioning according to flexible hierarchies of mechanisms making an intertwined and dynamic interplay of regulations. This becomes particularly evident in processes such as ontogenesis, where regulative assets change according to process context and timing, making structural phenotype and architectural complexities emerge from a single cell, through local interactions. The information collected from biological systems are naturally organized according to the functional levels composing the system itself. In systems biology, biological information often comes from overlapping but different scientific domains, each one having its own way of representing phenomena under study. That is, the different parts of the system to be modelled may be described with different formalisms. For a model to have improved accuracy and capability for making a good knowledge base, it is good to comprise different system levels, suitably handling the relative formalisms. Models which are both multi-level and hybrid satisfy both these requirements, making a very useful tool in computational systems biology. This paper reviews some of the main contributions in this field.

Quantitative computational models of molecular self-assembly in systems biology

Molecular self-assembly is the dominant form of chemical reaction in living systems, yet efforts at systems biology modeling are only beginning to appreciate the need for and challenges to accurate quantitative modeling of self-assembly. Self-assembly reactions are essential to nearly every important process in cell and molecular biology and handling them is thus a necessary step in building comprehensive models of complex cellular systems. They present exceptional challenges, however, to standard methods for simulating complex systems. While the general systems biology world is just beginning to deal with these challenges, there is an extensive literature dealing with them for more specialized self-assembly modeling. This review will examine the challenges of self-assembly modeling, nascent efforts to deal with these challenges in the systems modeling community, and some of the solutions offered in prior work on self-assembly specifically. The review concludes with some consideration of the likely role of self-assembly in the future of complex biological system models more generally.

Extending rule-based methods to model molecular geometry and 3D model resolution

BACKGROUND

Computational modeling is an important tool for the study of complex biochemical processes associated with cell signaling networks. However, it is challenging to simulate processes that involve hundreds of large molecules due to the high computational cost of such simulations. Rule-based modeling is a method that can be used to simulate these processes with reasonably low computational cost, but traditional rule-based modeling approaches do not include details of molecular geometry. The incorporation of geometry into biochemical models can more accurately capture details of these processes, and may lead to insights into how geometry affects the products that form. Furthermore, geometric rule-based modeling can be used to complement other computational methods that explicitly represent molecular geometry in order to quantify binding site accessibility and steric effects.

RESULTS

We propose a novel implementation of rule-based modeling that encodes details of molecular geometry into the rules and binding rates. We demonstrate how rules are constructed according to the molecular curvature. We then perform a study of antigen-antibody aggregation using our proposed method. We simulate the binding of antibody complexes to binding regions of the shrimp allergen Pen a 1 using a previously developed 3D rigid-body Monte Carlo simulation, and we analyze the aggregate sizes. Then, using our novel approach, we optimize a rule-based model according to the geometry of the Pen a 1 molecule and the data from the Monte Carlo simulation. We use the distances between the binding regions of Pen a 1 to optimize the rules and binding rates. We perform this procedure for multiple conformations of Pen a 1 and analyze the impact of conformation and resolution on the optimal rule-based model.

CONCLUSIONS

We find that the optimized rule-based models provide information about the average steric hindrance between binding regions and the probability that antibodies will bind to these regions. These optimized models quantify the variation in aggregate size that results from differences in molecular geometry and from model resolution.

Rule-based modeling with Virtual Cell

Rule-based modeling is invaluable when the number of possible species and reactions in a model become too large to allow convenient manual specification. The popular rule-based software tools BioNetGen and NFSim provide powerful modeling and simulation capabilities at the cost of learning a complex scripting language which is used to specify these models. Here, we introduce a modeling tool that combines new graphical rule-based model specification with existing simulation engines in a seamless way within the familiar Virtual Cell (VCell) modeling environment. A mathematical model can be built integrating explicit reaction networks with reaction rules. In addition to offering a large choice of ODE and stochastic solvers, a model can be simulated using a network free approach through the NFSim simulation engine.

AVAILABILITY AND IMPLEMENTATION

Available as VCell (versions 6.0 and later) at the Virtual Cell web site (http://vcell.org/). The application installs and runs on all major platforms and does not require registration for use on the user's computer. Tutorials are available at the Virtual Cell website and Help is provided within the software. Source code is available at Sourceforge.

CONTACT

vcell_support@uchc.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Influence of model resolution on geometric simulations of antibody aggregation

It is estimated that allergies afflict up to 40% of the world's population. A primary mediator for allergies is the aggregation of antigens and IgE antibodies bound to cell-surface receptors, FcεRI. Antibody/antigen aggregate formation causes stimulation of mast cells and basophils, initiating cellular degranulation and releasing immune mediators which produce an allergic or anaphylactic response. Understanding the shape and structure of these aggregates can provide critical insights into the allergic response. We have previously developed methods to geometrically model, simulate and analyze antibody aggregation inspired by rigid body robotic motion simulations. Our technique handles the large size and number of molecules involved in aggregation, providing an advantage over traditional simulations such as molecular dynamics (MD) and coarse-grained energetic models. In this paper, we study the impact of model resolution on simulations of geometric structures using both our previously developed Monte Carlo simulation and a novel application of rule-based modeling. These methods complement each other, the former providing explicit geometric detail and the latter providing a generic representation where multiple resolutions can be captured. Our exploration is focused on two antigens, a man-made antigen with three binding sites, DF3, and a common shrimp allergen (antigen), Pen a 1. We find that impact of resolution is minimal for DF3, a small globular antigen, but has a larger impact on Pen a 1, a rod-shaped molecule. The volume reduction caused by the loss in resolution allows more binding site accessibility, which can be quantified using a rule-based model with implicit geometric input. Clustering analysis of our simulation shows good correlation when compared with available experimental results. Moreover, collisions in all-atom reconstructions are negligible, at around 0.2% at 90% reduction.

Multi-class and multi-scale models of complex biological phenomena

Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.

Autophagy Regulatory Network - a systems-level bioinformatics resource for studying the mechanism and regulation of autophagy

Autophagy is a complex cellular process having multiple roles, depending on tissue, physiological, or pathological conditions. Major post-translational regulators of autophagy are well known, however, they have not yet been collected comprehensively. The precise and context-dependent regulation of autophagy necessitates additional regulators, including transcriptional and post-transcriptional components that are listed in various datasets. Prompted by the lack of systems-level autophagy-related information, we manually collected the literature and integrated external resources to gain a high coverage autophagy database. We developed an online resource, Autophagy Regulatory Network (ARN; http://autophagy-regulation.org), to provide an integrated and systems-level database for autophagy research. ARN contains manually curated, imported, and predicted interactions of autophagy components (1,485 proteins with 4,013 interactions) in humans. We listed 413 transcription factors and 386 miRNAs that could regulate autophagy components or their protein regulators. We also connected the above-mentioned autophagy components and regulators with signaling pathways from the SignaLink 2 resource. The user-friendly website of ARN allows researchers without computational background to search, browse, and download the database. The database can be downloaded in SQL, CSV, BioPAX, SBML, PSI-MI, and in a Cytoscape CYS file formats. ARN has the potential to facilitate the experimental validation of novel autophagy components and regulators. In addition, ARN helps the investigation of transcription factors, miRNAs and signaling pathways implicated in the control of the autophagic pathway. The list of such known and predicted regulators could be important in pharmacological attempts against cancer and neurodegenerative diseases.

Modeling for (physical) biologists: an introduction to the rule-based approach

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Spatio-temporal model of endogenous ROS and raft-dependent WNT/beta-catenin signaling driving cell fate commitment in human neural progenitor cells

Canonical WNT/β-catenin signaling is a central pathway in embryonic development, but it is also connected to a number of cancers and developmental disorders. Here we apply a combined in-vitro and in-silico approach to investigate the spatio-temporal regulation of WNT/β-catenin signaling during the early neural differentiation process of human neural progenitors cells (hNPCs), which form a new prospect for replacement therapies in the context of neurodegenerative diseases. Experimental measurements indicate a second signal mechanism, in addition to canonical WNT signaling, being involved in the regulation of nuclear β-catenin levels during the cell fate commitment phase of neural differentiation. We find that the biphasic activation of β-catenin signaling observed experimentally can only be explained through a model that combines Reactive Oxygen Species (ROS) and raft dependent WNT/β-catenin signaling. Accordingly after initiation of differentiation endogenous ROS activates DVL in a redox-dependent manner leading to a transient activation of down-stream β-catenin signaling, followed by continuous auto/paracrine WNT signaling, which crucially depends on lipid rafts. Our simulation studies further illustrate the elaborate spatio-temporal regulation of DVL, which, depending on its concentration and localization, may either act as direct inducer of the transient ROS/β-catenin signal or as amplifier during continuous auto-/parcrine WNT/β-catenin signaling. In addition we provide the first stochastic computational model of WNT/β-catenin signaling that combines membrane-related and intracellular processes, including lipid rafts/receptor dynamics as well as WNT- and ROS-dependent β-catenin activation. The model’s predictive ability is demonstrated under a wide range of varying conditions for in-vitro and in-silico reference data sets. Our in-silico approach is realized in a multi-level rule-based language, that facilitates the extension and modification of the model. Thus, our results provide both new insights and means to further our understanding of canonical WNT/β-catenin signaling and the role of ROS as intracellular signaling mediator.

Human neural progenitor cells offer the promising perspective of using in-vitro grown neural cell populations for replacement therapies in the context of neurodegenerative diseases, such as Parkinson’s or Huntington’s disease. However, to control hNPC differentiation within the scope of stem cell engineering, a thorough understanding of cell fate determination and its endogenous regulation is required. Here we investigate the spatio-temporal regulation of WNT/β-catenin signaling in the process of cell fate commitment in hNPCs, which has been reported to play a crucial role for the differentiation process of hNPCs. Based on a combined in-vitro and in-silico approach we demonstrate an elaborate interplay between endogenous ROS and lipid raft dependent WNT/beta-catenin signaling controlling the nuclear beta-catenin levels throughout the initial phase of neural differentiation. The stochastic multi-level computational model we derive from our experimental measurements adds to the family of existing WNT models, addressing major biochemical and spatial aspects of WNT/beta-catenin signaling that have not been considered in existing models so far. Cross validation studies manifest its predictive capability for other cells and cell lines rendering the model a suitable basis for further studies also in the context of embryonic development, developmental disorders and cancers.

Multi-state modeling of biomolecules

Multi-state modeling of biomolecules refers to a series of techniques used to represent and compute the behavior of biological molecules or complexes that can adopt a large number of possible functional states. Biological signaling systems often rely on complexes of biological macromolecules that can undergo several functionally significant modifications that are mutually compatible. Thus, they can exist in a very large number of functionally different states. Modeling such multi-state systems poses two problems: the problem of how to describe and specify a multi-state system (the “specification problem”) and the problem of how to use a computer to simulate the progress of the system over time (the “computation problem”). To address the specification problem, modelers have in recent years moved away from explicit specification of all possible states and towards rule-based formalisms that allow for implicit model specification, including the κ-calculus [1], BioNetGen [2]–[5], the Allosteric Network Compiler [6], and others [7], [8]. To tackle the computation problem, they have turned to particle-based methods that have in many cases proved more computationally efficient than population-based methods based on ordinary differential equations, partial differential equations, or the Gillespie stochastic simulation algorithm[9], [10]. Given current computing technology, particle-based methods are sometimes the only possible option. Particle-based simulators fall into two further categories: nonspatial simulators, such as StochSim [11], DYNSTOC [12], RuleMonkey [9], [13], and the Network-Free Stochastic Simulator (NFSim) [14], and spatial simulators, including Meredys [15], SRSim [16], [17], and MCell [18]–[20]. Modelers can thus choose from a variety of tools, the best choice depending on the particular problem. Development of faster and more powerful methods is ongoing, promising the ability to simulate ever more complex signaling processes in the future.

Multi-level kinetic model of mRNA delivery via transfection of lipoplexes

Recent work on the use of mRNA lipoplexes for gene delivery demonstrates the need for a mathematical model that simulates and predicts kinetics and transfection efficiency. The small copy numbers involved make it necessary to use stochastic models and include statistical analysis of the variation observed in the experimental data. The modeling requirements are further complicated by the multi-level nature of the problem, where mRNA molecules are contained in lipoplexes, which are in turn contained in endosomes, where each of these entities displays a behavior of its own. We have created a mathematical model that reproduces both the time courses and the statistical variance observed in recent experiments using single-cell tracking of GFP expression after transfection. By applying a few key simplifications and assumptions, we have limited the number of free parameters to five, which we optimize to match five experimental determinants by means of a simulated annealing algorithm. The models demonstrate the need for modeling of nested species in order to reproduce the shape of the dose-response and expression-level curves.

Membrane related dynamics and the formation of actin in cells growing on micro-topographies: a spatial computational model

Background

Intra-cellular processes of cells at the interface to an implant surface are influenced significantly by their extra-cellular surrounding. Specifically, when growing osteoblasts on titanium surfaces with regular micro-ranged geometry, filaments are shorter, less aligned and they concentrate at the top of the geometric structures. Changes to the cytoskeleton network, i. e., its localization, alignment, orientation, and lengths of the filaments, as well as the overall concentration and distribution of key-actors are induced. For example, integrin is distributed homogeneously, whereas integrin in activated state and vinculin, both components of focal adhesions, have been found clustered on the micro-ranged geometries. Also, the concentration of Rho, an intracellular signaling protein related to focal adhesion regulation, was significantly lower.

Results

To explore whether regulations associated with the focal adhesion complex can be responsible for the changed actin filament patterns, a spatial computational model has been developed using ML-Space, a rule-based model description language, and its associated Brownian-motion-based simulator. The focus has been on the deactivation of cofilin in the vicinity of the focal adhesion complex. The results underline the importance of sensing mechanisms to support a clustering of actin filament nucleations on the micro-ranged geometries, and of intracellular diffusion processes, which lead to spatially heterogeneous distributions of active (dephosphorylated) cofilin, which in turn influences the organization of the actin network. We find, for example, that the spatial heterogeneity of key molecular actors can explain the difference in filament lengths in cells on different micro-geometries partly, but to explain the full extent, further model assumptions need to be added and experimentally validated. In particular, our findings and hypothesis referring to the role, distribution, and amount of active cofilin have still to be verified in wet-lab experiments.

Conclusion

Letting cells grow on surface structures is a possibility to shed new light on the intricate mechanisms that relate membrane and actin related dynamics in the cell. Our results demonstrate the need for declarative expressive spatial modeling approaches that allow probing different hypotheses, and the central role of the focal adhesion complex not only for nucleating actin filaments, but also for regulating possible severing agents locally.

Composing problem solvers for simulation experimentation: a case study on steady state estimation

Simulation experiments involve various sub-tasks, e.g., parameter optimization, simulation execution, or output data analysis. Many algorithms can be applied to such tasks, but their performance depends on the given problem. Steady state estimation in systems biology is a typical example for this: several estimators have been proposed, each with its own (dis-)advantages. Experimenters, therefore, must choose from the available options, even though they may not be aware of the consequences. To support those users, we propose a general scheme to aggregate such algorithms to so-called synthetic problem solvers, which exploit algorithm differences to improve overall performance. Our approach subsumes various aggregation mechanisms, supports automatic configuration from training data (e.g., via ensemble learning or portfolio selection), and extends the plugin system of the open source modeling and simulation framework James II. We show the benefits of our approach by applying it to steady state estimation for cell-biological models.

Exact hybrid particle/population simulation of rule-based models of biochemical systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

Rule-based modeling is a modeling paradigm that addresses the problem of combinatorial complexity in biochemical systems. The key idea is to specify only those components of a biological macromolecule that are directly involved in a biochemical transformation. Until recently, this “pattern-based” approach greatly simplified the process of model building but did nothing to improve the performance of model simulation. This changed with the introduction of “network-free” simulation methods, which operate directly on the compressed rule set of a rule-based model rather than on a fully-enumerated set of reactions and species. However, these methods represent every molecule in a system as a particle, limiting their use to systems containing less than a few million molecules. Here, we describe an extension to the network-free approach that treats rare, complex species as particles and plentiful, simple species as population variables, while retaining the exact dynamics of the model system. By making more efficient use of computational resources for species that do not require the level of detail of a particle representation, this hybrid particle/population approach can simulate systems much larger than is possible using network-free methods and is an important step towards realizing the practical simulation of detailed, mechanistic models of whole cells.

ModeLang: a new approach for experts-friendly viral infections modeling

Computational modeling is an important element of systems biology. One of its important applications is modeling complex, dynamical, and biological systems, including viral infections. This type of modeling usually requires close cooperation between biologists and mathematicians. However, such cooperation often faces communication problems because biologists do not have sufficient knowledge to understand mathematical description of the models, and mathematicians do not have sufficient knowledge to define and verify these models. In many areas of systems biology, this problem has already been solved; however, in some of these areas there are still certain problematic aspects. The goal of the presented research was to facilitate this cooperation by designing seminatural formal language for describing viral infection models that will be easy to understand for biologists and easy to use by mathematicians and computer scientists. The ModeLang language was designed in cooperation with biologists and its computer implementation was prepared. Tests proved that it can be successfully used to describe commonly used viral infection models and then to simulate and verify them. As a result, it can make cooperation between biologists and mathematicians modeling viral infections much easier, speeding up computational verification of formulated hypotheses.

A rule-based kinetic model of RNA polymerase II C-terminal domain phosphorylation

The complexity of many RNA processing pathways is such that a conventional systems modelling approach is inadequate to represent all the molecular species involved. We demonstrate that rule-based modelling permits a detailed model of a complex RNA signalling pathway to be defined. Phosphorylation of the RNA polymerase II (RNAPII) C-terminal domain (CTD; a flexible tail-like extension of the largest subunit) couples pre-messenger RNA capping, splicing and 3' end maturation to transcriptional elongation and termination, and plays a central role in integrating these processes. The phosphorylation states of the serine residues of many heptapeptide repeats of the CTD alter along the coding region of genes as a function of distance from the promoter. From a mechanistic perspective, both the changes in phosphorylation and the location at which they take place on the genes are a function of the time spent by RNAPII in elongation as this interval provides the opportunity for the kinases and phosphatases to interact with the CTD. On this basis, we synthesize the available data to create a kinetic model of the action of the known kinases and phosphatases to resolve the phosphorylation pathways and their kinetics.

Living is information processing: from molecules to global systems

We extend the concept that life is an informational phenomenon, at every level of organisation, from molecules to the global ecological system. According to this thesis: (a) living is information processing, in which memory is maintained by both molecular states and ecological states as well as the more obvious nucleic acid coding; (b) this information processing has one overall function-to perpetuate itself; and (c) the processing method is filtration (cognition) of, and synthesis of, information at lower levels to appear at higher levels in complex systems (emergence). We show how information patterns, are united by the creation of mutual context, generating persistent consequences, to result in 'functional information'. This constructive process forms arbitrarily large complexes of information, the combined effects of which include the functions of life. Molecules and simple organisms have already been measured in terms of functional information content; we show how quantification may be extended to each level of organisation up to the ecological. In terms of a computer analogy, life is both the data and the program and its biochemical structure is the way the information is embodied. This idea supports the seamless integration of life at all scales with the physical universe. The innovation reported here is essentially to integrate these ideas, basing information on the 'general definition' of information, rather than simply the statistics of information, thereby explaining how functional information operates throughout life.

Logic modeling and the ridiculome under the rug

Logic-derived modeling has been used to map biological networks and to study arbitrary functional interactions, and fine-grained kinetic modeling can accurately predict the detailed behavior of well-characterized molecular systems; at present, however, neither approach comes close to unraveling the full complexity of a cell. The current data revolution offers significant promises and challenges to both approaches - and could bring them together as it has spurred the development of new methods and tools that may help to bridge the many gaps between data, models, and mechanistic understanding.

Have you used logic modeling in your research? It would not be surprising if many biologists would answer no to this hypothetical question. And it would not be true. In high school biology we already became familiar with cartoon diagrams that illustrate basic mechanisms of the molecular machinery operating inside cells. These are nothing else but simple logic models. If receptor and ligand are present, then receptor-ligand complexes form; if a receptor-ligand complex exists, then an enzyme gets activated; if the enzyme is active, then a second messenger is being produced; and so on. Such chains of causality are the essence of logic models (Figure 1a). Arbitrary events and mechanisms are abstracted; relationships are simplified and usually involve just two possible conditions and three possible consequences. The presence or absence of one or more molecule, activity, or function, [some icons in the cartoon] will determine whether another one of them will be produced (created, up-regulated, stimulated) [a 'positive' link] or destroyed (degraded, down-regulated, inhibited) [a 'negative' link], or be unaffected [there is no link]. The icons and links often do not follow a standardized format, but when we look at such a cartoon diagram, we believe that we 'understand' how the system works. Because our brain is easily able to process these relationships, these diagrams allow us to answer two fundamental types of questions related to the system: why (are certain things happening)? What if (we make some changes)?