Toward a comprehensive language for biological systems

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.

A practical guide to mechanistic systems modeling in biology using a logic-based approach

Mechanistic computational models enable the study of regulatory mechanisms implicated in various biological processes. These models provide a means to analyze the dynamics of the systems they describe, and to study and interrogate their properties, and provide insights about the emerging behavior of the system in the presence of single or combined perturbations. Aimed at those who are new to computational modeling, we present here a practical hands-on protocol breaking down the process of mechanistic modeling of biological systems in a succession of precise steps. The protocol provides a framework that includes defining the model scope, choosing validation criteria, selecting the appropriate modeling approach, constructing a model and simulating the model. To ensure broad accessibility of the protocol, we use a logical modeling framework, which presents a lower mathematical barrier of entry, and two easy-to-use and popular modeling software tools: Cell Collective and GINsim. The complete modeling workflow is applied to a well-studied and familiar biological process-the lac operon regulatory system. The protocol can be completed by users with little to no prior computational modeling experience approximately within 3 h.

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.

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.

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.

Graphical Modeling Meets Systems Pharmacology

A main source of failures in systems projects (including systems pharmacology) is poor communication level and different expectations among the stakeholders. A common and not ambiguous language that is naturally comprehensible by all the involved players is a boost to success. We present bStyle, a modeling tool that adopts a graphical language close enough to cartoons to be a common media to exchange ideas and data and that it is at the same time formal enough to enable modeling, analysis, and dynamic simulations of a system. Data analysis and simulation integrated in the same application are fundamental to understand the mechanisms of actions of drugs: a core aspect of systems pharmacology.

Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective

In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.

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.

Transmembrane signaling in Saccharomyces cerevisiae as a model for signaling in metazoans: state of the art after 25 years

In the very first article that appeared in Cellular Signalling, published in its inaugural issue in October 1989, we reviewed signal transduction pathways in Saccharomyces cerevisiae. Although this yeast was already a powerful model organism for the study of cellular processes, it was not yet a valuable instrument for the investigation of signaling cascades. In 1989, therefore, we discussed only two pathways, the Ras/cAMP and the mating (Fus3) signaling cascades. The pivotal findings concerning those pathways undoubtedly contributed to the realization that yeast is a relevant model for understanding signal transduction in higher eukaryotes. Consequently, the last 25 years have witnessed the discovery of many signal transduction pathways in S. cerevisiae, including the high osmotic glycerol (Hog1), Stl2/Mpk1 and Smk1 mitogen-activated protein (MAP) kinase pathways, the TOR, AMPK/Snf1, SPS, PLC1 and Pkr/Gcn2 cascades, and systems that sense and respond to various types of stress. For many cascades, orthologous pathways were identified in mammals following their discovery in yeast. Here we review advances in the understanding of signaling in S. cerevisiae over the last 25 years. When all pathways are analyzed together, some prominent themes emerge. First, wiring of signaling cascades may not be identical in all S. cerevisiae strains, but is probably specific to each genetic background. This situation complicates attempts to decipher and generalize these webs of reactions. Secondly, the Ras/cAMP and the TOR cascades are pivotal pathways that affect all processes of the life of the yeast cell, whereas the yeast MAP kinase pathways are not essential. Yeast cells deficient in all MAP kinases proliferate normally. Another theme is the existence of central molecular hubs, either as single proteins (e.g., Msn2/4, Flo11) or as multisubunit complexes (e.g., TORC1/2), which are controlled by numerous pathways and in turn determine the fate of the cell. It is also apparent that lipid signaling is less developed in yeast than in higher eukaryotes. Finally, feedback regulatory mechanisms seem to be at least as important and powerful as the pathways themselves. In the final chapter of this essay we dare to imagine the essence of our next review on signaling in yeast, to be published on the 50th anniversary of Cellular Signalling in 2039.

From proteomes to complexomes in the era of systems biology

Protein complexes carry out almost the entire signaling and functional processes in the cell. The protein complex complement of a cell, and its network of complex-complex interactions, is referred to here as the complexome. Computational methods to predict protein complexes from proteomics data, resulting in network representations of complexomes, have recently being developed. In addition, key advances have been made toward understanding the network and structural organization of complexomes. We review these bioinformatics advances, and their discovery-potential, as well as the merits of integrating proteomics data with emerging methods in systems biology to study protein complex signaling. It is envisioned that improved integration of proteomics and systems biology, incorporating the dynamics of protein complexes in space and time, may lead to more predictive models of cell signaling networks for effective modulation.

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.

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems

Rule-based modeling was developed to address the limitations of traditional approaches for modeling chemical kinetics in cell signaling systems. These systems consist of multiple interacting biomolecules (e.g., proteins), which themselves consist of multiple parts (e.g., domains, linear motifs, and sites of phosphorylation). Consequently, biomolecules that mediate information processing generally have the potential to interact in multiple ways, with the number of possible complexes and posttranslational modification states tending to grow exponentially with the number of binary interactions considered. As a result, only large reaction networks capture all possible consequences of the molecular interactions that occur in a cell signaling system, which is problematic because traditional modeling approaches for chemical kinetics (e.g., ordinary differential equations) require explicit network specification. This problem is circumvented through representation of interactions in terms of local rules. With this approach, network specification is implicit and model specification is concise. Concise representation results in a coarse graining of chemical kinetics, which is introduced because all reactions implied by a rule inherit the rate law associated with that rule. Coarse graining can be appropriate if interactions are modular, and the coarseness of a model can be adjusted as needed. Rules can be specified using specialized model-specification languages, and recently developed tools designed for specification of rule-based models allow one to leverage powerful software engineering capabilities. A rule-based model comprises a set of rules, which can be processed by general-purpose simulation and analysis tools to achieve different objectives (e.g., to perform either a deterministic or stochastic simulation).

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.

In silico modeling: methods and applications to trauma and sepsis

OBJECTIVES

To familiarize clinicians with advances in computational disease modeling applied to trauma and sepsis.

DATA SOURCES

PubMed search and review of relevant medical literature.

SUMMARY

Definitions, key methods, and applications of computational modeling to trauma and sepsis are reviewed.

CONCLUSIONS

Computational modeling of inflammation and organ dysfunction at the cellular, organ, whole-organism, and population levels has suggested a positive feedback cycle of inflammation → damage → inflammation that manifests via organ-specific inflammatory switching networks. This structure may manifest as multicompartment "tipping points" that drive multiple organ dysfunction. This process may be amenable to rational inflammation reprogramming.

Spatial rule-based modeling: a method and its application to the human mitotic kinetochore

A common problem in the analysis of biological systems is the combinatorial explosion that emerges from the complexity of multi-protein assemblies. Conventional formalisms, like differential equations, Boolean networks and Bayesian networks, are unsuitable for dealing with the combinatorial explosion, because they are designed for a restricted state space with fixed dimensionality. To overcome this problem, the rule-based modeling language, BioNetGen, and the spatial extension, SRSim, have been developed. Here, we describe how to apply rule-based modeling to integrate experimental data from different sources into a single spatial simulation model and how to analyze the output of that model. The starting point for this approach can be a combination of molecular interaction data, reaction network data, proximities, binding and diffusion kinetics and molecular geometries at different levels of detail. We describe the technique and then use it to construct a model of the human mitotic inner and outer kinetochore, including the spindle assembly checkpoint signaling pathway. This allows us to demonstrate the utility of the procedure, show how a novel perspective for understanding such complex systems becomes accessible and elaborate on challenges that arise in the formulation, simulation and analysis of spatial rule-based models.

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.

Bio-logic builder: a non-technical tool for building dynamical, qualitative models

Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized “bio-logic” modules have been defined to provide users with the building blocks for many biological processes. To build/modify computational models, experimentalists provide purely qualitative information about a particular regulatory mechanisms as is generally found in the laboratory. The Bio-Logic Builder subsequently converts the provided information into a mathematical representation described with Boolean expressions/rules. We used this tool to build a number of dynamical models, including a 130-protein large-scale model of signal transduction with over 800 interactions, influenza A replication cycle with 127 species and 200+ interactions, and mammalian and budding yeast cell cycles. We also show that any and all qualitative regulatory mechanisms can be built using this tool.

The Cell Collective: toward an open and collaborative approach to systems biology

BACKGROUND

Despite decades of new discoveries in biomedical research, the overwhelming complexity of cells has been a significant barrier to a fundamental understanding of how cells work as a whole. As such, the holistic study of biochemical pathways requires computer modeling. Due to the complexity of cells, it is not feasible for one person or group to model the cell in its entirety.

RESULTS

The Cell Collective is a platform that allows the world-wide scientific community to create these models collectively. Its interface enables users to build and use models without specifying any mathematical equations or computer code - addressing one of the major hurdles with computational research. In addition, this platform allows scientists to simulate and analyze the models in real-time on the web, including the ability to simulate loss/gain of function and test what-if scenarios in real time.

CONCLUSIONS

The Cell Collective is a web-based platform that enables laboratory scientists from across the globe to collaboratively build large-scale models of various biological processes, and simulate/analyze them in real time. In this manuscript, we show examples of its application to a large-scale model of signal transduction.