Agent-based vs. equation-based multi-scale modeling for macrophage polarization

Macrophages show high plasticity and result in heterogenic subpopulations or polarized states identified by specific cellular markers. These immune cells are typically characterized as pro-inflammatory, or classically activated M1, and anti-inflammatory, or alternatively activated M2. However, a more precise definition places them along a spectrum of activation where they may exhibit a number of pro- or anti-inflammatory roles. To understand M1-M2 dynamics in the context of a localized response and explore the results of different mathematical modeling approaches based on the same biology, we utilized two different modeling techniques, ordinary differential equation (ODE) modeling and agent-based modeling (ABM), to simulate the spectrum of macrophage activation to general pro- and anti-inflammatory stimuli on an individual and multi-cell level. The ODE model includes two hallmark pro- and anti-inflammatory signaling pathways and the ABM incorporates similar M1-M2 dynamics but in a spatio-temporal platform. Both models link molecular signaling with cellular-level dynamics. We then performed simulations with various initial conditions to replicate different experimental setups. Similar results were observed in both models after tuning to a common calibrating experiment. Comparing the two models' results sheds light on the important features of each modeling approach. When more data is available these features can be considered when choosing techniques to best fit the needs of the modeler and application.

Computational models in inflammatory bowel disease

Inflammatory bowel disease (IBD) is a chronic and relapsing disease with multiple underlying influences and notable heterogeneity among its clinical and response-to-treatment phenotypes. There is no cure for IBD, and none of the currently available therapies have demonstrated clinical efficacies beyond 40%-60%. Data collected about its omics, pathogenesis, and treatment strategies have grown exponentially with time making IBD a prime candidate for artificial intelligence (AI) mediated discovery support. AI can be leveraged to further understand or identify IBD features to improve clinical outcomes. Various treatment candidates are currently under evaluation in clinical trials, offering further approaches and opportunities for increasing the efficacies of treatments. However, currently, therapeutic plans are largely determined using clinical features due to the lack of specific biomarkers, and it has become necessary to step into precision medicine to predict therapeutic responses to guarantee optimal treatment efficacy. This is accompanied by the application of AI and the development of multiscale hybrid models combining mechanistic approaches and machine learning. These models ultimately lead to the creation of digital twins of given patients delivering on the promise of precision dosing and tailored treatment. Interleukin-6 (IL-6) is a prominent cytokine in cell-to-cell communication in the inflammatory responses' regulation. Dysregulated IL-6-induced signaling leads to severe immunological or proliferative pathologies, such as IBD and colon cancer. This mini-review explores multiscale models with the aim of predicting the response to therapy in IBD. Modeling IL-6 biology and generating digital twins enhance the credibility of their prediction.

Regulation of STAT3 signaling in IFNγ and IL10 pathways and in their cross-talk

The pro-inflammatory IFNγ-STAT1 pathway and anti-inflammatory IL10-STAT3 pathway elicit cellular responses primarily utilizing their canonical STATs. However IL10 mediated STAT1 and IFNγ mediated STAT3 activation is also observed, suggesting crosstalk of these functionally opposing signaling pathways can potentially reshape the canonical dynamics both STATs and alter the expression of their target genes. Herein, we measured the dynamics of STATs in response to different doses of IL10 or IFNγ and in their co-stimulation and employed quantitative modeling to understand the regulatory mechanisms controlling signal responses in individual and co-simulation scenarios. Our experiments show, STAT3 in particular, exhibits a bell-shaped dose-response while treated with IFNγ or IL10 and our model quantiatively captured the dose-dependent dynamics of both the STATs in both pathways. The model next predicted and subsequent experiments validated that STAT3 dynamics would robustly remain IL10 specific when subjected to a co-stimulation of both IFNγ and IL10. Genes common to both pathways also exhibited IL10 specific expression during the co-stimulation. The findings thus uncover anovel feature of the IL10-STAT3 signaling axis during pathway crosstalk. Finally, parameter sampling coupled to information theory based analysis showed that bell-shaped signal-response of STAT3 in both pathways is primarily dependent on receptor concentration whereas robustness of IL10-STAT3 signaling axis in co-stimulation results from the negative regulation of the IFNγ pathway.

Identification of a time-varying intracellular signalling model through data clustering and parameter selection: application to NF-[inline-formula removed]B signalling pathway induced by LPS in the presence of BFA

Developing a model for a signalling pathway requires several iterations of experimentation and model refinement to obtain an accurate model. However, the implementation of such an approach to model a signalling pathway induced by a poorly-known stimulus can become labour intensive because only limited information on the pathway is available beforehand to formulate an initial model. Therefore, a large number of iterations are required since the initial model is likely to be erroneous. In this work, a numerical scheme is proposed to construct a time-varying model for a signalling pathway induced by a poorly-known stimulus when its nominal model is available in the literature. Here, the nominal model refers to one that describes the signalling dynamics under a well-characterised stimulus. First, global sensitivity analysis is implemented on the nominal model to identify the most important parameters, which are assumed to be piecewise constants. Second, measurement data are clustered to determine temporal subdomains where the parameters take different values. Finally, a least-squares problem is solved to estimate the parameter values in each temporal subdomain. The effectiveness of this approach is illustrated by developing a time-varying model for NF-[inline-formula removed]B signalling dynamics induced by lipopolysaccharide in the presence of brefeldin A.

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines.

TGF-β and IL-6 family signalling crosstalk: an integrated model

Mathematical models for TGF-β and IL-6 signalling have been linked, providing a platform for analyzing the crosstalk between the systems. An integrated IL-6:TGF-β model was developed via a reduced set of reaction equations which incorporate both feedback loops and appropriate time-delays for transcription and translation processes. The model simulates stable, robust and realistic responses to both ligands. Pulsatile (multiple pulses) inputs for both TGF-β and IL-6 have been simulated to investigate the effects of each ligand on the sensitivity, equilibrium and dynamic responses of the integrated signalling system. In our simulations the crosstalk between constant IL-6 and TGF-β signalling via SMAD7 does not appear to be sufficient to render the cells resistant to TGF-β inhibition. However, the simulations predict that pulsatile IL-6 stimulation would increase SMAD7 levels substantially and consequentially, lead to resistance to TGF-β. The model also allows the prediction of the integrated signalling pathway responses to the mutation of key components, e.g. Gp130 ^F/F.

Regularization Techniques to Overcome Overparameterization of Complex Biochemical Reaction Networks

Models of biochemical reaction networks commonly contain a large number of parameters while at the same time there is only a limited amount of (noisy) data available for their estimation. As such, the values of many parameters are not well known as nominal parameter values have to be determined from the open scientific literature and a significant number of the values may have been derived in different cell types or organisms than that which is modeled. There clearly is a need to estimate at least some of the parameter values from experimental data, however, the small amount of available data and the large number of parameters commonly found in these types of models, require the use of regularization techniques to avoid over fitting. A tutorial of regularization techniques, including parameter set selection, precedes a case study of estimating parameters in a signal transduction network. Cross validation rather than fitting results are presented to further emphasize the need for models that generalize well to new data instead of simply fitting the current data.

Computational modeling of cytokine signaling in microglia

Neuroinflammation due to glial activation has been linked to many CNS diseases. We developed a computational model of a microglial cytokine interaction network to study the regulatory mechanisms of microglia-mediated neuroinflammation. We established a literature-based cytokine network, including TNFα, TGFβ, and IL-10, and fitted a mathematical model to published data from LPS-treated microglia. The addition of a previously unreported TGFβ autoregulation loop to our model was required to account for experimental data. Global sensitivity analysis revealed that TGFβ- and IL-10-mediated inhibition of TNFα was critical for regulating network behavior. We assessed the sensitivity of the LPS-induced TNFα response profile to the initial TGFβ and IL-10 levels. The analysis showed two relatively shifted TNFα response profiles within separate domains of initial condition space. Further analysis revealed that TNFα exhibited adaptation to sustained LPS stimulation. We simulated the effects of functionally inhibiting TGFβ and IL-10 on TNFα adaptation. Our analysis showed that TGFβ and IL-10 knockouts (TGFβ KO and IL-10 KO) exert divergent effects on adaptation. TFGβ KO attenuated TNFα adaptation whereas IL-10 KO enhanced TNFα adaptation. We experimentally tested the hypothesis that IL-10 KO enhances TNFα adaptation in murine macrophages and found supporting evidence. These opposing effects could be explained by differential kinetics of negative feedback. Inhibition of IL-10 reduced early negative feedback that results in enhanced TNFα-mediated TGFβ expression. We propose that differential kinetics in parallel negative feedback loops constitute a novel mechanism underlying the complex and non-intuitive pro- versus anti-inflammatory effects of individual cytokine perturbations.

Systems biology of IL-6, IL-12 family cytokines

Interleukin-6-type cytokines play important roles in the communication between cells of multicellular organisms. They are involved in the regulation of complex cellular processes such as proliferation and differentiation and act as key player during inflammation and immune response. A major challenge is to understand how these complex non-linear processes are connected and regulated. Systems biology approaches are used to tackle this challenge in an iterative process of quantitative experimental and mathematical analyses. Here we review quantitative experimental studies and systems biology approaches dealing with the function of Interleukin-6-type cytokines in physiological and pathophysiological conditions. These approaches cover the analyses of signal transduction on a cellular level up to pharmacokinetic and pharmacodynamic studies on a whole organism level.

A Kinetic-Model-Based Approach to Identify Malfunctioning Components in Signal Transduction Pathways from Artificial Clinical Data

Detection of malfunctioning reactions or molecules from clinical data is essential for disease treatments. In order to find an alternative to the existing oversimplistic mathematical models, a kinetic model is developed in this work to infer the malfunctioning reactions/molecules by quantifying the similarity between the clinical profile and the output profiles predicted from the model in which certain reactions/molecules malfunction. The new approach was tested in IL-6 and TNF-α/NF-κB signaling pathway, for four abnormal conditions including up/downregulation of single reaction rate constants and up/downregulation of single molecules. Since limited quantitative clinical data were available, the IL-6 ODE model was used to generate artificial clinical data for the abnormal steady-state value shown in two key molecules: nuclear STAT3 and SOCS3. Similarly, the TNF-α/NF-κB model was used to obtain the data in which abnormal oscillation dynamic was shown in the profile of NF-κB. The results show that the approach developed in this study was able to successfully identify the malfunctioning reactions and molecules from the clinical data. It was also found that this new approach was noise-robust and that it managed to reveal unique solution for the faulty components in a network.

A multiscale model of interleukin-6-mediated immune regulation in Crohn's disease and its application in drug discovery and development

In this study, we have developed a multiscale systems model of interleukin (IL)-6-mediated immune regulation in Crohn's disease, by integrating intracellular signaling with organ-level dynamics of pharmacological markers underlying the disease. This model was linked to a general pharmacokinetic model for therapeutic monoclonal antibodies and used to comparatively study various biotherapeutic strategies targeting IL-6-mediated signaling in Crohn's disease. Our work illustrates techniques to develop mechanistic models of disease biology to study drug-system interaction. Despite a sparse training data set, predictions of the model were qualitatively validated by clinical biomarker data from a pilot trial with tocilizumab. Model-based analysis suggests that strategies targeting IL-6, IL-6Rα, or the IL-6/sIL-6Rα complex are less effective at suppressing pharmacological markers of Crohn's than dual targeting the IL-6/sIL-6Rα complex in addition to IL-6 or IL-6Rα. The potential value of multiscale system pharmacology modeling in drug discovery and development is also discussed.CPT: Pharmacometrics & Systems Pharmacology (2014) 3, e89; doi:10.1038/psp.2013.64; advance online publication 8 January 2014.

Multi-scale modeling predicts a balance of tumor necrosis factor-α and interleukin-10 controls the granuloma environment during Mycobacterium tuberculosis infection

Interleukin-10 (IL-10) and tumor necrosis factor-α (TNF-α) are key anti- and pro-inflammatory mediators elicited during the host immune response to Mycobacterium tuberculosis (Mtb). Understanding the opposing effects of these mediators is difficult due to the complexity of processes acting across different spatial (molecular, cellular, and tissue) and temporal (seconds to years) scales. We take an in silico approach and use multi-scale agent based modeling of the immune response to Mtb, including molecular scale details for both TNF-α and IL-10. Our model predicts that IL-10 is necessary to modulate macrophage activation levels and to prevent host-induced tissue damage in a granuloma, an aggregate of cells that forms in response to Mtb. We show that TNF-α and IL-10 parameters related to synthesis, signaling, and spatial distribution processes control concentrations of TNF-α and IL-10 in a granuloma and determine infection outcome in the long-term. We devise an overall measure of granuloma function based on three metrics - total bacterial load, macrophage activation levels, and apoptosis of resting macrophages - and use this metric to demonstrate a balance of TNF-α and IL-10 concentrations is essential to Mtb infection control, within a single granuloma, with minimal host-induced tissue damage. Our findings suggest that a balance of TNF-α and IL-10 defines a granuloma environment that may be beneficial for both host and pathogen, but perturbing the balance could be used as a novel therapeutic strategy to modulate infection outcomes.

Elucidating the crosstalk mechanism between IFN-gamma and IL-6 via mathematical modelling

Background

Interferon-gamma (IFN-gamma) and interleukin-6 (IL-6) are multifunctional cytokines that regulate immune responses, cell proliferation, and tumour development and progression, which frequently have functionally opposing roles. The cellular responses to both cytokines are activated via the Janus kinase/signal transducer and activator of transcription (JAK/STAT) pathway. During the past 10 years, the crosstalk mechanism between the IFN-gamma and IL-6 pathways has been studied widely and several biological hypotheses have been proposed, but the kinetics and detailed crosstalk mechanism remain unclear.

Results

Using established mathematical models and new experimental observations of the crosstalk between the IFN-gamma and IL-6 pathways, we constructed a new crosstalk model that considers three possible crosstalk levels: (1) the competition between STAT1 and STAT3 for common receptor docking sites; (2) the mutual negative regulation between SOCS1 and SOCS3; and (3) the negative regulatory effects of the formation of STAT1/3 heterodimers. A number of simulations were tested to explore the consequences of cross-regulation between the two pathways. The simulation results agreed well with the experimental data, thereby demonstrating the effectiveness and correctness of the model.

Conclusion

In this study, we developed a crosstalk model of the IFN-gamma and IL-6 pathways to theoretically investigate their cross-regulation mechanism. The simulation experiments showed the importance of the three crosstalk levels between the two pathways. In particular, the unbalanced competition between STAT1 and STAT3 for IFNR and gp130 led to preferential activation of IFN-gamma and IL-6, while at the same time the formation of STAT1/3 heterodimers enhanced preferential signal transduction by sequestering a fraction of the activated STATs. The model provided a good explanation of the experimental observations and provided insights that may inform further research to facilitate a better understanding of the cross-regulation mechanism between the two pathways.

Role of transcription factors in peripheral nerve regeneration

Following axotomy, the activation of multiple intracellular signaling cascades causes the expression of a cocktail of regeneration-associated transcription factors which interact with each other to determine the fate of the injured neurons. The nerve injury response is channeled through manifold and parallel pathways, integrating diverse inputs, and controlling a complex transcriptional output. Transcription factors form a vital link in the chain of regeneration, converting injury-induced stress signals into downstream protein expression via gene regulation. They can regulate the intrinsic ability of axons to grow, by controlling expression of whole cassettes of gene targets. In this review, we have investigated the functional roles of a number of different transcription factors - c-Jun, activating transcription factor 3, cAMP response element binding protein, signal transducer, and activator of transcription-3, CCAAT/enhancer binding proteins β and δ, Oct-6, Sox11, p53, nuclear factor kappa-light-chain-enhancer of activated B cell, and ELK3 - in peripheral nerve regeneration. Studies involving use of conditional mutants, microarrays, promoter region mapping, and different injury paradigms, have enabled us to understand their distinct as well as overlapping roles in achieving anatomical and functional regeneration after peripheral nerve injury.

Systems biology of JAK-STAT signalling in human malignancies

Originally implicated in the regulation of survival, proliferation and differentiation of haematopoietic cells, the JAK-STAT pathway has also been linked to developmental processes, growth control and maintenance of homeostasis in a variety of other cells and tissues. Although it remains a complex system, its relative simplicity and the availability of molecular data makes it particularly attractive for modelling approaches. In this review, we will focus on JAK-STAT signalling in the context of cancer and present efforts to investigate signalling dynamics with the help of mathematical models. We describe the modelling workflow that realises a systems biology approach and give an example for interferon-γ signalling in pancreatic stellate cells.