A systematic evaluation of the influence of macrophage phenotype descriptions on inflammatory dynamics.

Macrophages play a wide range of roles in resolving the inflammatory damage that underlies many medical conditions, and have the ability to adopt different phenotypes in response to different environmental stimuli. Categorising macrophage phenotypes exactly is a difficult task, and there is disparity in the literature around the optimal nomenclature to describe these phenotypes; however, what is clear is that macrophages can exhibit both pro- and anti-inflammatory behaviours dependent upon their phenotype, rendering mathematical models of the inflammatory response potentially sensitive to their description of the macrophage populations that they incorporate. Many previous models of inflammation include a single macrophage population with both pro- and anti-inflammatory functions. Here, we build upon these existing models to include explicit descriptions of distinct macrophage phenotypes and examine the extent to which this influences the inflammatory dynamics that the models emit. We analyse our models via numerical simulation in Matlab and dynamical systems analysis in XPPAUT, and show that models that account for distinct macrophage phenotypes separately can offer more realistic steady state solutions than precursor models do (better capturing the anti-inflammatory activity of tissue resident macrophages), as well as oscillatory dynamics not previously observed. Finally, we reflect on the conclusions of our analysis in the context of the ongoing hunt for potential new therapies for inflammatory conditions, highlighting manipulation of macrophage polarisation states as a potential therapeutic target.

Mathematical models of coagulation-are we there yet?

BACKGROUND: Mathematical models of coagulation have been developed to mirror thrombin generation in plasma, with the aim of investigating how variation in coagulation factor levels regulates hemostasis. However, current models vary in the reactions they capture and the reaction rates used, and their validation is restricted by a lack of large coherent datasets, resulting in questioning of their utility. OBJECTIVES: To address this debate, we systematically assessed current models against a large dataset, using plasma coagulation factor levels from 348 individuals with normal hemostasis to identify the causes of these variations. METHODS: We compared model predictions with measured thrombin generation, quantifying and comparing the ability of each model to predict thrombin generation, the contributions of the individual reactions, and their dependence on reaction rates. RESULTS: We found that no current model predicted the hemostatic response across the whole cohort and all produced thrombin generation curves that did not resemble those obtained experimentally. Our analysis has identified the key reactions that lead to differential model predictions, where experimental uncertainty leads to variability in predictions, and we determined reactions that have a high influence on measured thrombin generation, such as the contribution of factor XI. CONCLUSION: This systematic assessment of models of coagulation, using large dataset inputs, points to ways in which these models can be improved. A model that accurately reflects the effects of the multiple subtle variations in an individual's hemostatic profile could be used for assessing antithrombotics or as a tool for precision medicine.

The rate of platelet activation determines thrombus size and structure at arterial shear.

BACKGROUND: The response of platelets to activating stimuli and pharmaceutical agents varies greatly within the normal population. Current platelet function tests are used to measure end-point levels of platelet activation without taking the speed at which platelets activate into account, potentially missing vital metrics to characterize platelet reactivity. OBJECTIVES: To identify variability, to agonists and among individuals, in platelet activation kinetics and assess the impact of this on thrombus formation. METHODS: We have developed a bespoke real-time flow cytometry assay and analysis package to measure the rate of platelet activation over time using 2 parameters of platelet activation, fibrinogen binding and P-selectin exposure. RESULTS: The rate of platelet activation varied considerably within the normal population but did not correlate with maximal platelet activation, demonstrating that platelet activation rate is a separate and novel metric to describe platelet reactivity. The relative rate of platelet response between agonists was strongly correlated, suggesting that a central control mechanism regulates the rate of platelet response to all agonists. CONCLUSION: For the first time, we have shown that platelet response rate corresponds to thrombus size and structure, wherein faster responders form larger, more densely packed thrombi at arterial, but crucially not venous, shear. We have demonstrated that the rate of platelet activation is an important metric in stratifying individual platelet responses and will provide a novel focus for the design and development of antiplatelet therapy, targeting high-shear thrombosis without exacerbating bleeding at low shear.

An agent-based approach for modelling and simulation of glycoprotein VI receptor diffusion, localisation and dimerisation in platelet lipid rafts.

Receptor diffusion plays an essential role in cellular signalling via the plasma membrane microenvironment and receptor interactions, but the regulation is not well understood. To aid in understanding of the key determinants of receptor diffusion and signalling, we developed agent-based models (ABMs) to explore the extent of dimerisation of the platelet- and megakaryocyte-specific receptor for collagen glycoprotein VI (GPVI). This approach assessed the importance of glycolipid enriched raft-like domains within the plasma membrane that lower receptor diffusivity. Our model simulations demonstrated that GPVI dimers preferentially concentrate in confined domains and, if diffusivity within domains is decreased relative to outside of domains, dimerisation rates are increased. While an increased amount of confined domains resulted in further dimerisation, merging of domains, which may occur upon membrane rearrangements, was without effect. Modelling of the proportion of the cell membrane which constitutes lipid rafts indicated that dimerisation levels could not be explained by these alone. Crowding of receptors by other membrane proteins was also an important determinant of GPVI dimerisation. Together, these results demonstrate the value of ABM approaches in exploring the interactions on a cell surface, guiding the experimentation for new therapeutic avenues.

Exploring the constituent mechanisms of hepatitis: a dynamical systems approach.

Hepatitis is the term used to describe inflammation in the liver. It is associated with a high rate of mortality, but the underlying disease mechanisms are not completely understood and treatment options are limited. We present a mathematical model of hepatitis that captures the complex interactions between hepatocytes (liver cells), hepatic stellate cells (cells in the liver that produce hepatitis-associated fibrosis) and the immune components that mediate inflammation. The model is in the form of a system of ordinary differential equations. We use numerical techniques and bifurcation analysis to characterize and elucidate the physiological mechanisms that dominate liver injury and its outcome to a healthy or unhealthy, chronic state. This study reveals the complex interactions between the multiple cell types and mediators involved in this complex disease and highlights potential problems in targeting inflammation in the liver therapeutically.

A System-Wide Investigation and Stratification of the Hemostatic Proteome in Premature Myocardial Infarction.

Introduction: Advancing understanding of key factors that determine the magnitude of the hemostatic response may facilitate the identification of individuals at risk of generating an occlusive thrombus as a result of an atherothrombotic event such as an acute Myocardial Infarction (MI). While fibrinogen levels are a recognized risk factor for MI, the association of thrombotic risk with other coagulation proteins is inconsistent. This is likely due to the complex balance of pro- and anticoagulant factors in any individual. Methods: We compared measured levels of pro- and anticoagulant proteins in plasma from 162 patients who suffered an MI at an early age (MI <50 y) and 186 age- and gender-matched healthy controls with no history of CAD. We then used the measurements from these individuals as inputs for an established mathematical model to investigate how small variations in hemostatic factors affect the overall amplitude of the hemostatic response and to identify differential key drivers of the hemostatic response in male and female patients and controls. Results: Plasma from the MI patients contained significantly higher levels of Tissue Factor (P = 0.007), the components of the tenase (FIX and FVIII; P < 0.0001 for both) and the prothrombinase complexes (FX; P = 0.003), and lower levels of Tissue Factor Pathway Inhibitor (TFPI; P = 0.033) than controls. The mathematical model, which generates time-dependent predictions describing the depletion, activation, and interaction of the main procoagulant factors and inhibitors, identified different patterns of hemostatic response between MI patients and controls, and additionally, between males and females. Whereas, in males, TF, FVIII, FIX, and the inhibitor TFPI contribute to the differences seen between case and controls, and in females, FII, FVIII, and FIX had the greatest influence on the generation of thrombin. We additionally show that further donor stratification may be possible according to the predicted donor response to anticoagulant therapy. Conclusions: We suggest that modeling could be of value in enhancing our prediction of risk of premature MI, recurrent risk, and therapeutic efficacy.

Ultra-high-throughput Ca2+ assay in platelets to distinguish ITAM-linked and G-protein-coupled receptor activation.

Antiplatelet drugs targeting G-protein-coupled receptors (GPCRs), used for the secondary prevention of arterial thrombosis, coincide with an increased bleeding risk. Targeting ITAM-linked receptors, such as the collagen receptor glycoprotein VI (GPVI), is expected to provide a better antithrombotic-hemostatic profile. Here, we developed and characterized an ultra-high-throughput (UHT) method based on intracellular [Ca2+]i increases to differentiate GPVI and GPCR effects on platelets. In 96-, 384-, or 1,536-well formats, Calcium-6-loaded human platelets displayed a slow-prolonged or fast-transient [Ca2+]i increase when stimulated with the GPVI agonist collagen-related peptide or with thrombin and other GPCR agonists, respectively. Semi-automated curve fitting revealed five parameters describing the Ca2+ responses. Verification of the UHT assay was done with a robustness compound library and clinically relevant platelet inhibitors. Taken together, these results present proof of principle of distinct receptor-type-dependent Ca2+ signaling curves in platelets, which allow identification of new inhibitors in a UHT way.

G protein-coupled receptor kinase 5 regulates thrombin signaling in platelets via PAR-1.

The interindividual variation in the functional response of platelets to activation by agonists is heritable. Genome-wide association studies (GWASs) of quantitative measures of platelet function have identified fewer than 20 distinctly associated variants, some with unknown mechanisms. Here, we report GWASs of pathway-specific functional responses to agonism by adenosine 5'-diphosphate, a glycoprotein VI-specific collagen mimetic, and thrombin receptor-agonist peptides, each specific to 1 of the G protein-coupled receptors PAR-1 and PAR-4, in subsets of 1562 individuals. We identified an association (P = 2.75 × 10-40) between a common intronic variant, rs10886430, in the G protein-coupled receptor kinase 5 gene (GRK5) and the sensitivity of platelets to activate through PAR-1. The variant resides in a megakaryocyte-specific enhancer that is bound by the transcription factors GATA1 and MEIS1. The minor allele (G) is associated with fewer GRK5 transcripts in platelets and the greater sensitivity of platelets to activate through PAR-1. We show that thrombin-mediated activation of human platelets causes binding of GRK5 to PAR-1 and that deletion of the mouse homolog Grk5 enhances thrombin-induced platelet activation sensitivity and increases platelet accumulation at the site of vascular injury. This corroborates evidence that the human G allele of rs10886430 is associated with a greater risk for cardiovascular disease. In summary, by combining the results of pathway-specific GWASs and expression quantitative trait locus studies in humans with the results from platelet function studies in Grk5-/- mice, we obtain evidence that GRK5 regulates the human platelet response to thrombin via the PAR-1 pathway.

Kinetx: A Combined Flow Cytometry Assay and Analysis Software Framework to Quantitatively Measure and Categorize Platelet Activation in Real-time.

Platelets react rapidly to vascular injury and undergo activation in response to a range of stimuli to limit blood loss. Many platelet function tests measure endpoint responses after a defined time period and not the rate of platelet activation. However, the rate at which platelets convert extracellular stimuli into a functional response is an essential factor in determining how efficiently they can respond to injury, bind to a forming thrombus, and signal to recruit other platelets. This paper describes a flow cytometry-based platelet function assay that enables simultaneous data acquisition and sample stimulation and utilizes newly developed bespoke open-source software (Kinetx) to enable quantitative kinetic measurements of platelet granule release, fibrinogen binding, and intracellular calcium flux. Kinetix was developed in R so that users can alter parameters such as degree of smoothing, identification of outlying data points, or time scales. To aid users unfamiliar with the R environment, Kinetix analysis of data can be performed by a single command. Together, this allows real-time platelet activation metrics, such as rate, acceleration, time to peak-rate, time to peak-calcium, and qualitative shape changes, to be accurately and reproducibly measured and categorized. Kinetic measurements of platelet activation give a unique insight into platelets' behavior during the first stages of activation and may provide a method of predicting the recruitment of platelets into a forming thrombus.

Multiparameter phenotyping of platelet reactivity for stratification of human cohorts.

Accurate and comprehensive assessment of platelet function across cohorts of donors may be key to understanding the risk of thrombotic events associated with cardiovascular disease, and, hence, to help personalize the application of antiplatelet drugs. However, platelet function tests can be difficult to perform and analyze; they also can be unreliable or uninformative and poorly standardized across studies. The Platelet Phenomic Analysis (PPAnalysis) assay and associated open-source software platform were developed in response to these challenges. PPAnalysis utilizes preprepared freeze-dried microtiter plates to provide a detailed characterization of platelet function. The automated analysis of the high-dimensional data enables the identification of subpopulations of donors with distinct platelet function phenotypes. Using this approach, we identified that the sensitivity of a donor's platelets to an agonist and their capacity to generate a functional response are distinct independent metrics of platelet reactivity. Hierarchical clustering of these metrics identified 6 subgroups with distinct platelet phenotypes within healthy cohorts, indicating that platelet reactivity does not fit into the traditional simple categories of "high" and "low" responders. These platelet phenotypes were found to exist in 2 independent cohorts of healthy donors and were stable on recall. PPAnalysis is a powerful tool for stratification of cohorts on the basis of platelet reactivity that will enable investigation of the causes and consequences of differences in platelet function and drive progress toward precision medicine.

Modeling Thrombus Shell: Linking Adhesion Receptor Properties and Macroscopic Dynamics.

Damage to arterial vessel walls leads to the formation of platelet aggregate, which acts as a physical obstacle for bleeding. An arterial thrombus is heterogeneous; it has a dense inner part (core) and an unstable outer part (shell). The thrombus shell is very dynamic, being composed of loosely connected discoid platelets. The mechanisms underlying the observed mobility of the shell and its (patho)physiological implications are unclear. To investigate arterial thrombus mechanics, we developed a novel, to our knowledge, two-dimensional particle-based computational model of microvessel thrombosis. The model considers two types of interplatelet interactions: primary reversible (glycoprotein Ib (GPIb)-mediated) and stronger integrin-mediated interaction, which intensifies with platelet activation. At high shear rates, the former interaction leads to adhesion, and the latter is primarily responsible for stable platelet aggregation. Using a stochastic model of GPIb-mediated interaction, we initially reproduced experimental curves that characterize individual platelet interactions with a von Willebrand factor-coated surface. The addition of the second stabilizing interaction results in thrombus formation. The comparison of thrombus dynamics with experimental data allowed us to estimate the magnitude of critical interplatelet forces in the thrombus shell and the characteristic time of platelet activation. The model predicts moderate dependence of maximal thrombus height on the injury size in the absence of thrombin activity. We demonstrate that the developed stochastic model reproduces the observed highly dynamic behavior of the thrombus shell. The presence of primary stochastic interaction between platelets leads to the properties of thrombus consistent with in vivo findings; it does not grow upstream of the injury site and covers the whole injury from the first seconds of the formation. А simplified model, in which GPIb-mediated interaction is deterministic, does not reproduce these features. Thus, the stochasticity of platelet interactions is critical for thrombus plasticity, suggesting that interaction via a small number of bonds drives the dynamics of arterial thrombus shell.

Spatial considerations in the resolution of inflammation: Elucidating leukocyte interactions via an experimentally-calibrated agent-based model.

Many common medical conditions (such as cancer, arthritis, chronic obstructive pulmonary disease (COPD), and others) are associated with inflammation, and even more so when combined with the effects of ageing and multimorbidity. While the inflammatory response varies in different tissue types, under disease and in response to therapeutic interventions, it has common interactions that occur between immune cells and inflammatory mediators. Understanding these underlying inflammatory mechanisms is key in progressing treatments and therapies for numerous inflammatory conditions. It is now considered that constituent mechanisms of the inflammatory response can be actively manipulated in order to drive resolution of inflammatory damage; particularly, those mechanisms related to the pro-inflammatory role of neutrophils and the anti-inflammatory role of macrophages. In this article, we describe the assembly of a hybrid mathematical model in which the spatial spread of inflammatory mediators is described through partial differential equations, and immune cells (neutrophils and macrophages) are described individually via an agent-based modelling approach. We pay close attention to how immune cells chemotax toward pro-inflammatory mediators, presenting a model for cell chemotaxis that is calibrated against experimentally observed cell trajectories in healthy and COPD-affected scenarios. We illustrate how variations in key model parameters can drive the switch from resolution of inflammation to chronic outcomes, and show that aberrant neutrophil chemotaxis can move an otherwise healthy outcome to one of chronicity. Finally, we reflect on our results in the context of the on-going hunt for new therapeutic interventions.

Control of Platelet CLEC-2-Mediated Activation by Receptor Clustering and Tyrosine Kinase Signaling.

Platelets are blood cells responsible for vascular integrity preservation. The activation of platelet receptor C-type lectin-like receptor II-type (CLEC-2) could partially mediate the latter function. Although this receptor is considered to be of importance for hemostasis, the rate-limiting steps of CLEC-2-induced platelet activation are not clear. Here, we aimed to investigate CLEC-2-induced platelet signal transduction using computational modeling in combination with experimental approaches. We developed a stochastic multicompartmental computational model of CLEC-2 signaling. The model described platelet activation beginning with CLEC-2 receptor clustering, followed by Syk and Src family kinase phosphorylation, determined by the cluster size. Active Syk mediated linker adaptor for T cell protein phosphorylation and membrane signalosome formation, which resulted in the activation of Bruton's tyrosine kinase, phospholipase and phosphoinositide-3-kinase, calcium, and phosphoinositide signaling. The model parameters were assessed from published experimental data. Flow cytometry, total internal reflection fluorescence and confocal microscopy, and western blotting quantification of the protein phosphorylation were used for the assessment of the experimental dynamics of CLEC-2-induced platelet activation. Analysis of the model revealed that the CLEC-2 receptor clustering leading to the membrane-based signalosome formation is a critical element required for the accurate description of the experimental data. Both receptor clustering and signalosome formation are among the rate-limiting steps of CLEC-2-mediated platelet activation. In agreement with these predictions, the CLEC-2-induced platelet activation, but not activation mediated by G-protein-coupled receptors, was strongly dependent on temperature conditions and cholesterol depletion. Besides, the model predicted that CLEC-2-induced platelet activation results in cytosolic calcium spiking, which was confirmed by single-platelet total internal reflection fluorescence microscopy imaging. Our results suggest a refined picture of the platelet signal transduction network associated with CLEC-2. We show that tyrosine kinase activation is not the only rate-limiting step in CLEC-2-induced activation of platelets. Translocation of receptor-agonist complexes to the signaling region and linker adaptor for T cell signalosome formation in this region are limiting CLEC-2-induced activation as well.

Interspecies differences in protein expression do not impact the spatiotemporal regulation of glycoprotein VI mediated activation.

BACKGROUND: Accurate protein quantification is a vital prerequisite for generating meaningful predictions when using systems biology approaches, a method that is increasingly being used to unravel the complexities of subcellular interactions and as part of the drug discovery process. Quantitative proteomics, flow cytometry, and western blotting have been extensively used to define human platelet protein copy numbers, yet for mouse platelets, a model widely used for platelet research, evidence is largely limited to a single proteomic dataset in which the total amount of proteins was generally comparatively higher than those found in human platelets. OBJECTIVES: To investigate the functional implications of discrepancies between levels of mouse and human proteins in the glycoprotein VI (GPVI) signalling pathway using a systems pharmacology model of GPVI. METHODS: The protein copy number of mouse platelet receptors was determined using flow cytometry. The Virtual Platelet, a mathematical model of GPVI signalling, was used to determine the consequences of protein copy number differences observed between human and mouse platelets. RESULTS AND CONCLUSION: Despite the small size of mouse platelets compared to human platelets they possessed a greater density of surface receptors alongside a higher concentration of intracellular signalling proteins. Surprisingly the predicted temporal profile of Syk activity was similar in both species with predictions supported experimentally. Super resolution microscopy demonstrates that the spatial distribution of Syk is similar between species, suggesting that the spatial distribution of receptors and signalling molecules in activated platelets, rather than their copy number, is important for signalling pathway regulation.

Predicting tyrosinaemia: a mathematical model of 4-hydroxyphenylpyruvate dioxygenase inhibition by nitisinone in rats.

Nitisinone or 2-(2-nitro-4-trifluoromethylbenzoyl)cyclohexane-1,3-dione is a reversible inhibitor of 4-hydroxyphenylpyruvate dioxygenase (HPPD), an enzyme important in tyrosine catabolism. Today, nitisinone is successfully used to treat Hereditary Tyrosinaemia type 1, although its original expected role was as a herbicide. In laboratory animals, treatment with nitisinone leads to the elevation of plasma tyrosine (tyrosinaemia). In rats and Beagle dogs, repeat low-dose exposure to nitisinone leads to corneal opacities whilst similar studies in the mouse and Rhesus monkey showed no comparable toxicities or other treatment related findings. The differences in toxicological sensitivities have been related to the upper limit of the concentration of tyrosine that accumulates in plasma, which is driven by the amount/activity of tyrosine aminotransferase. A physiologically based, pharmacodynamics ordinary differential equation model of HPPD inhibition to bolus exposure of nitisinone in vivo is presented. Going beyond traditional approaches, asymptotic analysis is used to separate the different timescales of events involved in HPPD inhibition and tyrosinaemia. This analysis elucidates, in terms of the model parameters, a critical inhibitor concentration (at which tyrosine concentration starts to rise) and highlights the contribution of in vitro measured parameters to events in an in vivo system. Furthermore, using parameter-fitting methods, a systematically derived reduced model is shown to fit well to rat data, making explicit how the parameters are informed by such data. This model in combination with in vitro descriptors has potential as a surrogate for animal experimentation to predict tyrosinaemia, and further development can extend its application to other related medical scenarios.

The macrophage and its role in inflammation and tissue repair: mathematical and systems biology approaches.

Macrophages are central to the inflammatory response and its ability to resolve effectively. They are complex cells that adopt a range of subtypes depending on the tissue type and stimulus that they find themselves under. This flexibility allows them to play multiple, sometimes opposing, roles in inflammation and tissue repair. Their central role in the inflammatory process is reflected in macrophage dysfunction being implicated in chronic inflammation and poorly healing wounds. In this study, we discuss recent attempts to model mathematically and computationally the macrophage and how it partakes in the complex processes of inflammation and tissue repair. There are increasing data describing the variety of macrophage phenotypes and their underlying transcriptional programs. Dynamic mathematical and computational models are an ideal way to test biological hypotheses against experimental data and could aid in understanding this multi-functional cell and its potential role as an attractive therapeutic target for inflammatory conditions and tissue repair.

Regulation of Early Steps of GPVI Signal Transduction by Phosphatases: A Systems Biology Approach.

We present a data-driven mathematical model of a key initiating step in platelet activation, a central process in the prevention of bleeding following Injury. In vascular disease, this process is activated inappropriately and causes thrombosis, heart attacks and stroke. The collagen receptor GPVI is the primary trigger for platelet activation at sites of injury. Understanding the complex molecular mechanisms initiated by this receptor is important for development of more effective antithrombotic medicines. In this work we developed a series of nonlinear ordinary differential equation models that are direct representations of biological hypotheses surrounding the initial steps in GPVI-stimulated signal transduction. At each stage model simulations were compared to our own quantitative, high-temporal experimental data that guides further experimental design, data collection and model refinement. Much is known about the linear forward reactions within platelet signalling pathways but knowledge of the roles of putative reverse reactions are poorly understood. An initial model, that includes a simple constitutively active phosphatase, was unable to explain experimental data. Model revisions, incorporating a complex pathway of interactions (and specifically the phosphatase TULA-2), provided a good description of the experimental data both based on observations of phosphorylation in samples from one donor and in those of a wider population. Our model was used to investigate the levels of proteins involved in regulating the pathway and the effect of low GPVI levels that have been associated with disease. Results indicate a clear separation in healthy and GPVI deficient states in respect of the signalling cascade dynamics associated with Syk tyrosine phosphorylation and activation. Our approach reveals the central importance of this negative feedback pathway that results in the temporal regulation of a specific class of protein tyrosine phosphatases in controlling the rate, and therefore extent, of GPVI-stimulated platelet activation.