Strategies for calibrating models of biology.

Computational and mathematical modelling has become a valuable tool for investigating biological systems. Modelling enables prediction of how biological components interact to deliver system-level properties and extrapolation of biological system performance to contexts and experimental conditions where this is unknown. A model's value hinges on knowing that it faithfully represents the biology under the contexts of use, or clearly ascertaining otherwise and thus motivating further model refinement. These qualities are evaluated through calibration, typically formulated as identifying model parameter values that align model and biological behaviours as measured through a metric applied to both. Calibration is critical to modelling but is often underappreciated. A failure to appropriately calibrate risks unrepresentative models that generate erroneous insights. Here, we review a suite of strategies to more rigorously challenge a model's representation of a biological system. All are motivated by features of biological systems, and illustrative examples are drawn from the modelling literature. We examine the calibration of a model against distributions of biological behaviours or outcomes, not only average values. We argue for calibration even where model parameter values are experimentally ascertained. We explore how single metrics can be non-distinguishing for complex systems, with multiple-component dynamic and interaction configurations giving rise to the same metric output. Under these conditions, calibration is insufficiently constraining and the model non-identifiable: multiple solutions to the calibration problem exist. We draw an analogy to curve fitting and argue that calibrating a biological model against a single experiment or context is akin to curve fitting against a single data point. Though useful for communicating model results, we explore how metrics that quantify heavily emergent properties may not be suitable for use in calibration. Lastly, we consider the role of sensitivity and uncertainty analysis in calibration and the interpretation of model results. Our goal in this manuscript is to encourage a deeper consideration of calibration, and how to increase its capacity to either deliver faithful models or demonstrate them otherwise.

Pharmacological Assessment of Sepiapterin Reductase Inhibition on Tactile Response in the Rat.

There is an unmet medical need for nonopioid pain therapies in human populations; several pathways are under investigation for possible therapeutic intervention. Tetrahydrobiopterin (BH4) has received attention recently as a mediator of neuropathic pain. Recent reports have implicated sepiapterin reductase (SPR) in this pain pathway as a regulator of BH4 production. To evaluate the role of SPR inhibition on BH4 reduction, we developed analytical methods to monitor the relationship between the plasma concentration of test article and endogenous pterins and applied these in the rat spinal nerve ligation pain model. Sepiapterin is an endogenous substrate, which accumulates upon inhibition of SPR. In response to a potent inhibitor of SPR, plasma concentrations of sepiapterin increased proportionally with exposure. An indirect-effect pharmacokinetic/pharmacodynamic model was developed to describe the relationship between the plasma pharmacokinetics of test article and plasma sepiapterin levels in the rat, which was used to determine an in vivo SPR IC50 value. SPR inhibition and mechanical allodynia were assessed coordinately with pterin biomarkers in plasma and at the site of neuronal injury (i.e., dorsal root ganglion). Upon daily oral administration for 3 consecutive days, unbound plasma concentrations of test article exceeded the unbound in vivo rat SPR IC90 throughout the dose intervals, leading to a 60% reduction in BH4 in the dorsal root ganglion. Despite evidence for pharmacological modulation of the BH4 pathway, there was no significant effect on the tactile paw withdrawal threshold relative to vehicle-treated controls.

Utilising a simulation platform to understand the effect of domain model assumptions.

Computational and mathematical modelling approaches are increasingly being adopted in attempts to further our understanding of complex biological systems. This approach can be subjected to strong criticism as substantial aspects of the biological system being captured are not currently known, meaning assumptions need to be made that could have a critical impact on simulation response. We have utilised the CoSMoS process in the development of an agent-based simulation of the formation of Peyer's patches (PP), gut-associated lymphoid organs that have a key role in the initiation of adaptive immune responses to infection. Although the use of genetic tools, imaging technologies and ex vivo culture systems has provided significant insight into the cellular components and associated pathways involved in PP development, interesting questions remain that cannot be addressed using these approaches, and as such well justified assumptions have been introduced into our model to counter this. Here we focus not on the development of the model itself, but instead demonstrate how the resultant simulation can be used to assess how these assumptions impact the simulation response. For example, we consider the impact of our assumption that the migration rate of lymphoid tissue cells into the gut remains constant throughout PP development. We demonstrate that an analysis of the assumptions made in the construction of the domain model may either increase confidence in the model as a representation of the biological system it captures, or may suggest areas where further biological experimentation is required.

Spartan: a comprehensive tool for understanding uncertainty in simulations of biological systems.

Integrating computer simulation with conventional wet-lab research has proven to have much potential in furthering the understanding of biological systems. Success requires the relationship between simulation and the real-world system to be established: substantial aspects of the biological system are typically unknown, and the abstract nature of simulation can complicate interpretation of in silico results in terms of the biology. Here we present spartan (Simulation Parameter Analysis RToolkit ApplicatioN), a package of statistical techniques specifically designed to help researchers understand this relationship and provide novel biological insight. The tools comprising spartan help identify which simulation results can be attributed to the dynamics of the modelled biological system, rather than artefacts of biological uncertainty or parametrisation, or simulation stochasticity. Statistical analyses reveal the influence that pathways and components have on simulation behaviour, offering valuable biological insight into aspects of the system under study. We demonstrate the power of spartan in providing critical insight into aspects of lymphoid tissue development in the small intestine through simulation. Spartan is released under a GPLv2 license, implemented within the open source R statistical environment, and freely available from both the Comprehensive R Archive Network (CRAN) and http://www.cs.york.ac.uk/spartan. The techniques within the package can be applied to traditional ordinary or partial differential equation simulations as well as agent-based implementations. Manuals, comprehensive tutorials, and example simulation data upon which spartan can be applied are available from the website.

In silico investigation into dendritic cell regulation of CD8Treg mediated killing of Th1 cells in murine experimental autoimmune encephalomyelitis.

BACKGROUND: Experimental autoimmune encephalomyelitis has been used extensively as an animal model of T cell mediated autoimmunity. A down-regulatory pathway through which encephalitogenic CD4Th1 cells are killed by CD8 regulatory T cells (Treg) has recently been proposed. With the CD8Treg cells being primed by dendritic cells, regulation of recovery may be occuring around these antigen presenting cells. CD4Treg cells provide critical help within this process, by licensing dendritic cells to prime CD8Treg cells, however the spatial and temporal aspects of this help in the CTL response is currently unclear. RESULTS: We have previously developed a simulator of experimental autoimmune encephalomyelitis (ARTIMMUS). We use ARTIMMUS to perform novel in silico experimentation regarding the priming of CD8Treg cells by dendritic cells, and the resulting CD8Treg mediated killing of encephalitogenic CD4Th1 cells. Simulations using dendritic cells that present antigenic peptides in a mutually exclusive manner (either MBP or TCR-derived, but not both) suggest that there is no significant reliance on dendritic cells that can prime both encephalitogenic CD4Th1 and Treg cells. Further, in silico experimentation suggests that dynamics of CD8Treg priming are significantly influenced through their spatial competition with CD4Treg cells and through the timing of Qa-1 expression by dendritic cells. CONCLUSION: There is no requirement for the encephalitogenic CD4Th1 cells and cytotoxic CD8Treg cells to be primed by the same dendritic cells. We conjecture that no significant portion of CD4Th1 regulation by Qa-1 restricted CD8Treg cells occurs around individual dendritic cells, and as such, that CD8Treg mediated killing of CD4Th1 cells occurring around dendritic cells is not critical for recovery from the murine autoimmune disease. Furthermore, the timing of the CD4Treg licensing of dendritic cells and the spatial competition between CD4Treg and CD8Treg cells around the dendritic cell is critical for the size of the cytotoxic T lymphocyte response, because dendritic cells have a limited lifespan. If treatments can be found to either speed up the licensing process, or increase the spatial competitiveness of CD8Treg cells, the magnitude of the cytotoxic T lymphocyte response can be increased.

Development of a homogeneous AlphaLISA ubiquitination assay using ubiquitin binding matrices as universal components for the detection of ubiquitinated proteins.

The Ubiquitin Proteasome Pathway (UPP) has become a target rich pathway for therapeutic intervention as its role in pathogenic disease is better understood. In particular many E3 ligases within this pathway have been implicated in cancer, inflammation and metabolic diseases. It has been of great interest to develop biochemical assays to identify inhibitors of catalytic E3 ubiquitination activity as a means of abrogating the disease mechanism. Here we describe a homogeneous biochemical assay that utilizes native ubiquitin and Tandem-repeated Ubiquitin-Binding Entities (TUBEs) as a detection technology for ubiquitination activity. We developed a TUBEs based proximity AlphaLisa® assay for Mdm2, which is an E3 ligase that negatively regulates p53 tumor suppressor protein. We further demonstrate that this assay strategy or design can also be applied to the development of assays to detect autoubiquitination of other E3 ligases that are also of interest for therapeutic intervention. This article is part of a Special Issue entitled: Ubiquitin Drug Discovery and Diagnostics.

Ubiquitin ligase substrate identification through quantitative proteomics at both the protein and peptide levels.

Protein ubiquitination is a key regulatory process essential to life at a cellular level; significant efforts have been made to identify ubiquitinated proteins through proteomics studies, but the level of success has not reached that of heavily studied post-translational modifications, such as phosphorylation. HRD1, an E3 ubiquitin ligase, has been implicated in rheumatoid arthritis, but no disease-relevant substrates have been identified. To identify these substrates, we have taken both peptide and protein level approaches to enrich for ubiquitinated proteins in the presence and absence of HRD1. At the protein level, a two-step strategy was taken using cells expressing His(6)-tagged ubiquitin, enriching proteins first based on their ubiquitination and second based on the His tag with protein identification by LC-MS/MS. Application of this method resulted in identification and quantification of more than 400 ubiquitinated proteins, a fraction of which were found to be sensitive to HRD1 and were therefore deemed candidate substrates. In a second approach, ubiquitinated peptides were enriched after tryptic digestion by peptide immunoprecipitation using an antibody specific for the diglycine-labeled internal lysine residue indicative of protein ubiquitination, with peptides and ubiquitination sites identified by LC-MS/MS. Peptide immunoprecipitation resulted in identification of over 1800 ubiquitinated peptides on over 900 proteins in each study, with several proteins emerging as sensitive to HRD1 levels. Notably, significant overlap exists between the HRD1 substrates identified by the protein-based and the peptide-based strategies, with clear cross-validation apparent both qualitatively and quantitatively, demonstrating the effectiveness of both strategies and furthering our understanding of HRD1 biology.

Discovery and optimization of potent and selective imidazopyridine and imidazopyridazine mTOR inhibitors.

mTOR is a critical regulator of cellular signaling downstream of multiple growth factors. The mTOR/PI3K/AKT pathway is frequently mutated in human cancers and is thus an important oncology target. Herein we report the evolution of our program to discover ATP-competitive mTOR inhibitors that demonstrate improved pharmacokinetic properties and selectivity compared to our previous leads. Through targeted SAR and structure-guided design, new imidazopyridine and imidazopyridazine scaffolds were identified that demonstrated superior inhibition of mTOR in cellular assays, selectivity over the closely related PIKK family and improved in vivo clearance over our previously reported benzimidazole series.

Drosophila Morgue is an F box/ubiquitin conjugase domain protein important for grim-reaper mediated apoptosis.

In Drosophila melanogaster, apoptosis is controlled by the integrated actions of the Grim-Reaper (Grim-Rpr) and Drosophila Inhibitor of Apoptosis (DIAP) proteins (reviewed in refs 1 4). The anti-apoptotic DIAPs bind to caspases and inhibit their proteolytic activities. DIAPs also bind to Grim-Rpr proteins, an interaction that promotes caspase activity and the initiation of apoptosis. Using a genetic modifier screen, we identified four enhancers of grim-reaper-induced apoptosis that all regulate ubiquitination processes: uba-1, skpA, fat facets (faf), and morgue. Strikingly, morgue encodes a unique protein that contains both an F box and a ubiquitin E2 conjugase domain that lacks the active site Cys required for ubiquitin linkage. A reduction of morgue activity suppressed grim-reaper-induced cell death in Drosophila. In cultured cells, Morgue induced apoptosis that was suppressed by DIAP1. Targeted morgue expression downregulated DIAP1 levels in Drosophila tissue, and Morgue and Rpr together downregulated DIAP1 levels in cultured cells. Consistent with potential substrate binding functions in an SCF ubiquitin E3 ligase complex, Morgue exhibited F box-dependent association with SkpA and F box-independent association with DIAP1. Morgue may thus have a key function in apoptosis by targeting DIAP1 for ubiquitination and turnover.

Discovery of triazine-benzimidazoles as selective inhibitors of mTOR.

mTOR is part of the PI3K/AKT pathway and is a central regulator of cell growth and survival. Since many cancers display mutations linked to the mTOR signaling pathway, mTOR has emerged as an important target for oncology therapy. Herein, we report the discovery of triazine benzimidazole inhibitors that inhibit mTOR kinase activity with up to 200-fold selectivity over the structurally homologous kinase PI3Kα. When tested in a panel of cancer cell lines displaying various mutations, a selective inhibitor from this series inhibited cellular proliferation with a mean IC(50) of 0.41 µM. Lead compound 42 demonstrated up to 83% inhibition of mTOR substrate phosphorylation in a murine pharmacodynamic model.

Macrophage Transactivation for Chemokine Production Identified as a Negative Regulator of Granulomatous Inflammation Using Agent-Based Modeling.

Cellular activation in trans by interferons, cytokines, and chemokines is a commonly recognized mechanism to amplify immune effector function and limit pathogen spread. However, an optimal host response also requires that collateral damage associated with inflammation is limited. This may be particularly so in the case of granulomatous inflammation, where an excessive number and/or excessively florid granulomas can have significant pathological consequences. Here, we have combined transcriptomics, agent-based modeling, and in vivo experimental approaches to study constraints on hepatic granuloma formation in a murine model of experimental leishmaniasis. We demonstrate that chemokine production by non-infected Kupffer cells in the Leishmania donovani-infected liver promotes competition with infected KCs for available iNKT cells, ultimately inhibiting the extent of granulomatous inflammation. We propose trans-activation for chemokine production as a novel broadly applicable mechanism that may operate early in infection to limit excessive focal inflammation.

Extending and Applying Spartan to Perform Temporal Sensitivity Analyses for Predicting Changes in Influential Biological Pathways in Computational Models.

Through integrating real time imaging, computational modelling, and statistical analysis approaches, previous work has suggested that the induction of and response to cell adhesion factors is the key initiating pathway in early lymphoid tissue development, in contrast to the previously accepted view that the process is triggered by chemokine mediated cell recruitment. These model derived hypotheses were developed using spartan, an open-source sensitivity analysis toolkit designed to establish and understand the relationship between a computational model and the biological system that model captures. Here, we extend the functionality available in spartan to permit the production of statistical analyses that contrast the behavior exhibited by a computational model at various simulated time-points, enabling a temporal analysis that could suggest whether the influence of biological mechanisms changes over time. We exemplify this extended functionality by using the computational model of lymphoid tissue development as a time-lapse tool. By generating results at twelve- hour intervals, we show how the extensions to spartan have been used to suggest that lymphoid tissue development could be biphasic, and predict the time-point when a switch in the influence of biological mechanisms might occur.

Assays for RING family ubiquitin ligases.

Many eukaryotic proteins are regulated by the covalent attachment of ubiquitin or polyubiquitin chains. These include proteins involved in cell cycle control, tumor suppression, and many signaling pathways. Ubiquitination of proteins occurs through an enzymatic cascade of three discrete steps, which results in covalent attachment of ubiquitin to the substrate. The first two steps in this cascade involve the activating and conjugating enzymes, E1 and E2. The third and final step is performed by the E3 ubiquitin ligase. The ubiquitin ligase is responsible for two distinct activities: targeting specific substrates by bringing the substrate and activated ubiquitin together, as well as catalyzing the ligation of ubiquitin to the substrate. There are two main classes of E3 ligases, the HECT domain and the RING finger-containing ligases. RING finger-based ubiquitination utilizes RING-containing protein subunits, or proteins with intrinsic RING domains, to catalyze the formation of polyubiquitin chains. In this chapter we describe step by step protocols to assay for the activity of the RING finger-type of E3 ligase both in vitro and in vivo.

Using argument notation to engineer biological simulations with increased confidence.

The application of computational and mathematical modelling to explore the mechanics of biological systems is becoming prevalent. To significantly impact biological research, notably in developing novel therapeutics, it is critical that the model adequately represents the captured system. Confidence in adopting in silico approaches can be improved by applying a structured argumentation approach, alongside model development and results analysis. We propose an approach based on argumentation from safety-critical systems engineering, where a system is subjected to a stringent analysis of compliance against identified criteria. We show its use in examining the biological information upon which a model is based, identifying model strengths, highlighting areas requiring additional biological experimentation and providing documentation to support model publication. We demonstrate our use of structured argumentation in the development of a model of lymphoid tissue formation, specifically Peyer's Patches. The argumentation structure is captured using Artoo (www.york.ac.uk/ycil/software/artoo), our Web-based tool for constructing fitness-for-purpose arguments, using a notation based on the safety-critical goal structuring notation. We show how argumentation helps in making the design and structured analysis of a model transparent, capturing the reasoning behind the inclusion or exclusion of each biological feature and recording assumptions, as well as pointing to evidence supporting model-derived conclusions.

Modelling biological behaviours with the unified modelling language: an immunological case study and critique.

We present a framework to assist the diagrammatic modelling of complex biological systems using the unified modelling language (UML). The framework comprises three levels of modelling, ranging in scope from the dynamics of individual model entities to system-level emergent properties. By way of an immunological case study of the mouse disease experimental autoimmune encephalomyelitis, we show how the framework can be used to produce models that capture and communicate the biological system, detailing how biological entities, interactions and behaviours lead to higher-level emergent properties observed in the real world. We demonstrate how the UML can be successfully applied within our framework, and provide a critique of UML's ability to capture concepts fundamental to immunology and biology more generally. We show how specialized, well-explained diagrams with less formal semantics can be used where no suitable UML formalism exists. We highlight UML's lack of expressive ability concerning cyclic feedbacks in cellular networks, and the compounding concurrency arising from huge numbers of stochastic, interacting agents. To compensate for this, we propose several additional relationships for expressing these concepts in UML's activity diagram. We also demonstrate the ambiguous nature of class diagrams when applied to complex biology, and question their utility in modelling such dynamic systems. Models created through our framework are non-executable, and expressly free of simulation implementation concerns. They are a valuable complement and precursor to simulation specifications and implementations, focusing purely on thoroughly exploring the biology, recording hypotheses and assumptions, and serve as a communication medium detailing exactly how a simulation relates to the real biology.

Functional complexity of the Leishmania granuloma and the potential of in silico modeling.

In human and canine visceral leishmaniasis and in various experimental models of this disease, host resistance is strongly linked to efficient granuloma development. However, it is unknown exactly how the granuloma microenvironment executes an effective antileishmanial response. Recent studies, including using advanced imaging techniques, have improved our understanding of granuloma biology at the cellular level, highlighting heterogeneity in granuloma development and function, and hinting at complex cellular, temporal, and spatial dynamics. In this mini-review, we discuss the factors involved in the formation and function of Leishmania donovani-induced hepatic granulomas, as well as their importance in protecting against inflammation-associated tissue damage and the generation of immunity to rechallenge. Finally, we discuss the role that computational, agent-based models may play in answering outstanding questions within the field.

In silico investigation of novel biological pathways: the role of CD200 in regulation of T cell priming in experimental autoimmune encephalomyelitis.

The use of simulation to investigate biological domains will inevitably lead to the need to extend existing simulations as new areas of these domains become more fully understood. Such simulation extensions can entail the incorporation of additional cell types, molecules or molecular pathways, all of which can exert a profound influence on the simulation behaviour. Where the biological domain is not well characterised, a structured development methodology must be employed to ensure that the extended simulation is well aligned with its predecessor. We develop and discuss such a methodology, relying on iterative simulation development and sensitivity analysis. The utility of this methodology is demonstrated using a case study simulation of experimental autoimmune encephalomyelitis (EAE), a murine T cell-mediated autoimmune disease model of multiple sclerosis, where it is used to investigate the activity of an additional regulatory pathway. We discuss how application of this methodology guards against creating inappropriate simulation representations of the biology when investigating poorly characterised biological mechanisms.

Determining disease intervention strategies using spatially resolved simulations.

Predicting efficacy and optimal drug delivery strategies for small molecule and biological therapeutics is challenging due to the complex interactions between diverse cell types in different tissues that determine disease outcome. Here we present a new methodology to simulate inflammatory disease manifestation and test potential intervention strategies in silico using agent-based computational models. Simulations created using this methodology have explicit spatial and temporal representations, and capture the heterogeneous and stochastic cellular behaviours that lead to emergence of pathology or disease resolution. To demonstrate this methodology we have simulated the prototypic murine T cell-mediated autoimmune disease experimental autoimmune encephalomyelitis, a mouse model of multiple sclerosis. In the simulation immune cell dynamics, neuronal damage and tissue specific pathology emerge, closely resembling behaviour found in the murine model. Using the calibrated simulation we have analysed how changes in the timing and efficacy of T cell receptor signalling inhibition leads to either disease exacerbation or resolution. The technology described is a powerful new method to understand cellular behaviours in complex inflammatory disease, permits rational design of drug interventional strategies and has provided new insights into the role of TCR signalling in autoimmune disease progression.

Discovery of novel, induced-pocket binding oxazolidinones as potent, selective, and orally bioavailable tankyrase inhibitors.

Tankyrase (TNKS) is a poly-ADP-ribosylating protein (PARP) whose activity suppresses cellular axin protein levels and elevates ß-catenin concentrations, resulting in increased oncogene expression. The inhibition of tankyrase (TNKS1 and 2) may reduce the levels of ß-catenin-mediated transcription and inhibit tumorigenesis. Compound 1 is a previously described moderately potent tankyrase inhibitor that suffers from poor pharmacokinetic properties. Herein, we describe the utilization of structure-based design and molecular modeling toward novel, potent, and selective tankyrase inhibitors with improved pharmacokinetic properties (39, 40).

Development of novel dual binders as potent, selective, and orally bioavailable tankyrase inhibitors.

Tankyrases (TNKS1 and TNKS2) are proteins in the poly ADP-ribose polymerase (PARP) family. They have been shown to directly bind to axin proteins, which negatively regulate the Wnt pathway by promoting ß-catenin degradation. Inhibition of tankyrases may offer a novel approach to the treatment of APC-mutant colorectal cancer. Hit compound 8 was identified as an inhibitor of tankyrases through a combination of substructure searching of the Amgen compound collection based on a minimal binding pharmacophore hypothesis and high-throughput screening. Herein we report the structure- and property-based optimization of compound 8 leading to the identification of more potent and selective tankyrase inhibitors 22 and 49 with improved pharmacokinetic properties in rodents, which are well suited as tool compounds for further in vivo validation studies.