Global sensitivity analysis of a mathematical model of acute inflammation identifies nonlinear dependence of cumulative tissue damage on host interleukin-6 responses

Age-dependent ventilator-induced lung injury: Mathematical modeling, experimental data, and statistical analysis

A variety of pulmonary insults can prompt the need for life-saving mechanical ventilation; however, misuse, prolonged use, or an excessive inflammatory response, can result in ventilator-induced lung injury. Past research has observed an increased instance of respiratory distress in older patients and differences in the inflammatory response. To address this, we performed high pressure ventilation on young (2-3 months) and old (20-25 months) mice for 2 hours and collected data for macrophage phenotypes and lung tissue integrity. Large differences in macrophage activation at baseline and airspace enlargement after ventilation were observed in the old mice. The experimental data was used to determine plausible trajectories for a mathematical model of the inflammatory response to lung injury which includes variables for the innate inflammatory cells and mediators, epithelial cells in varying states, and repair mediators. Classification methods were used to identify influential parameters separating the parameter sets associated with the young or old data and separating the response to ventilation, which was measured by changes in the epithelial state variables. Classification methods ranked parameters involved in repair and damage to the epithelial cells and those associated with classically activated macrophages to be influential. Sensitivity results were used to determine candidate in-silico interventions and these interventions were most impact for transients associated with the old data, specifically those with poorer lung health prior to ventilation. Model results identified dynamics involved in M1 macrophages as a focus for further research, potentially driving the age-dependent differences in all macrophage phenotypes. The model also supported the pro-inflammatory response as a potential indicator of age-dependent differences in response to ventilation. This mathematical model can serve as a baseline model for incorporating other pulmonary injuries.

Deciphering signal transduction networks in the liver by mechanistic mathematical modelling

In health and disease, liver cells are continuously exposed to cytokines and growth factors. While individual signal transduction pathways induced by these factors were studied in great detail, the cellular responses induced by repeated or combined stimulations are complex and less understood. Growth factor receptors on the cell surface of hepatocytes were shown to be regulated by receptor interactions, receptor trafficking and feedback regulation. Here, we exemplify how mechanistic mathematical modelling based on quantitative data can be employed to disentangle these interactions at the molecular level. Crucial is the analysis at a mechanistic level based on quantitative longitudinal data within a mathematical framework. In such multi-layered information, step-wise mathematical modelling using submodules is of advantage, which is fostered by sharing of standardized experimental data and mathematical models. Integration of signal transduction with metabolic regulation in the liver and mechanistic links to translational approaches promise to provide predictive tools for biology and personalized medicine.

The underlying mechanism of intersite discrepancies in ejection time measurements from arterial waveforms and its validation in the Framingham Heart Study

Radial applanation tonometry is a well-established method for clinical hemodynamic assessment and is also becoming popular in wrist-worn fitness trackers. The time difference between the foot and the dicrotic notch of the arterial pressure waveform is a well-accepted approximation for the left ventricular ejection time (ET). However, several clinical studies have shown that ET measured from the radial pressure waveform deviates from that measured centrally. In this work, we consider the systolic wave and the dicrotic wave as two independent traveling waves and hypothesize that their wave speed difference leads to the intersite differences of measured ET (ΔET). Accordingly, we derived a mathematical dicrotic wave decomposition model and identified the most influential factors on ΔET via global sensitivity analysis. In our clinical validation on a heterogeneous cohort (N = 5,742) from the Framingham Heart Study (FHS), the local sensitivity analysis results resembled the sensitivity variation patterns of ΔET from model simulations. A regression analysis on FHS data, using morphological features of radial pressure waveforms to estimate the carotid ET, produced a root mean square error of 3.76 ms and R² of 0.91. The proposed dicrotic wave decomposition model can explain the intersite ET measurement discrepancies observed in the clinical data of FHS and can facilitate the precise identification of ET with radial pressure waveforms. Therefore, the proposed model will improve various physics-based pulse wave analysis methods as well as prospective artificial intelligence methods for tackling the subsequent big data produced from widespread wearable radial pressure monitoring.NEW & NOTEWORTHY Based on a new understanding of pressure wave propagation, we propose a novel dicrotic wave decomposition model considering the dicrotic wave as an independent traveling component. The proposed model can explain the mechanism underlying the intersite discrepancies in ejection time measurement from arterial waveforms and then, in principle, enhance the accuracy of both classical physics-based as well as more contemporary artificial intelligence-based pulse wave analysis methods in clinical and wearable radial blood pressure monitoring applications.

Mathematical modeling of ventilator-induced lung inflammation

Despite the benefits of mechanical ventilators, prolonged or misuse of ventilators may lead to ventilation-associated/ventilation-induced lung injury (VILI). Lung insults, such as respiratory infections and lung injuries, can damage the pulmonary epithelium, with the most severe cases needing mechanical ventilation for effective breathing and survival. Damaged epithelial cells within the alveoli trigger a local immune response. A key immune cell is the macrophage, which can differentiate into a spectrum of phenotypes ranging from pro- to anti-inflammatory. To gain a greater understanding of the mechanisms of the immune response to VILI and post-ventilation outcomes, we developed a mathematical model of interactions between the immune system and site of damage while accounting for macrophage phenotype. Through Latin hypercube sampling we generated a collection of parameter sets that are associated with a numerical steady state. We then simulated ventilation-induced damage using these steady state values as the initial conditions in order to evaluate how baseline immune state and lung health affect outcomes. We used a variety of methods to analyze the resulting parameter sets, transients, and outcomes, including a random forest decision tree algorithm and parameter sensitivity with eFAST. Analysis shows that parameters and properties of transients related to epithelial repair and M1 activation are important factors. Using the results of this analysis, we hypothesized interventions and used these treatment strategies to modulate the response to ventilation for particular parameters sets.

Neuro-Inflammation in Pediatric Traumatic Brain Injury-from Mechanisms to Inflammatory Networks

Compared to traumatic brain injury (TBI) in the adult population, pediatric TBI has received less research attention, despite its potential long-term impact on the lives of many children around the world. After numerous clinical trials and preclinical research studies examining various secondary mechanisms of injury, no definitive treatment has been found for pediatric TBIs of any severity. With the advent of high-throughput and high-resolution molecular biology and imaging techniques, inflammation has become an appealing target, due to its mixed effects on outcome, depending on the time point examined. In this review, we outline key mechanisms of inflammation, the contribution and interactions of the peripheral and CNS-based immune cells, and highlight knowledge gaps pertaining to inflammation in pediatric TBI. We also introduce the application of network analysis to leverage growing multivariate and non-linear inflammation data sets with the goal to gain a more comprehensive view of inflammation and develop prognostic and treatment tools in pediatric TBI.

Toward a model-free feedback control synthesis for treating acute inflammation

An effective and patient-specific feedback control synthesis for inflammation resolution is still an ongoing research area. A strategy consisting of manipulating a pro and anti-inflammatory mediator is considered here as used in some promising model-based control studies. These earlier studies, unfortunately, suffer from the difficultly of calibration due to the heterogeneity of individual patient responses even under similar initial conditions. We exploit a new model-free control approach and its corresponding "intelligent" controllers for this biomedical problem. A crucial feature of the proposed control problem is as follows: the two most important outputs which must be driven to their respective desired states are sensorless. This difficulty is overcome by assigning suitable reference trajectories to the other two outputs that do have sensors. A mathematical model, via a system of ordinary differential equations, is nevertheless employed as a "virtual" patient for in silico testing. We display several simulation results with respect to the most varied situations, which highlight the effectiveness of our viewpoint.

Modeling Cell-to-Cell Communication Networks Using Response-Time Distributions

Cell-to-cell communication networks have critical roles in coordinating diverse organismal processes, such as tissue development or immune cell response. However, compared with intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Major complications include: cells are themselves regulated by complex intracellular signaling networks; individual cells are heterogeneous; and output of any one cell can recursively become an additional input signal to other cells. Here, we make use of a framework that treats intracellular signal transduction networks as "black boxes" with characterized input-to-output response relationships. We study simple cell-to-cell communication circuit motifs and find conditions that generate bimodal responses in time, as well as mechanisms for independently controlling synchronization and delay of cell-population responses. We apply our modeling approach to explain otherwise puzzling data on cytokine secretion onset times in T cells. Our approach can be used to predict communication network structure using experimentally accessible input-to-output measurements and without detailed knowledge of intermediate steps.

Computational analysis identifies putative prognostic biomarkers of pathological scarring in skin wounds

Background

Pathological scarring in wounds is a prevalent clinical outcome with limited prognostic options. The objective of this study was to investigate whether cellular signaling proteins could be used as prognostic biomarkers of pathological scarring in traumatic skin wounds.

Methods

We used our previously developed and validated computational model of injury-initiated wound healing to simulate the time courses for platelets, 6 cell types, and 21 proteins involved in the inflammatory and proliferative phases of wound healing. Next, we analysed thousands of simulated wound-healing scenarios to identify those that resulted in pathological (i.e., excessive) scarring. Then, we identified candidate proteins that were elevated (or decreased) at the early stages of wound healing in those simulations and could therefore serve as predictive biomarkers of pathological scarring outcomes. Finally, we performed logistic regression analysis and calculated the area under the receiver operating characteristic curve to quantitatively assess the predictive accuracy of the model-identified putative biomarkers.

Results

We identified three proteins (interleukin-10, tissue inhibitor of matrix metalloproteinase-1, and fibronectin) whose levels were elevated in pathological scars as early as 2 weeks post-wounding and could predict a pathological scarring outcome occurring 40 days after wounding with 80% accuracy.

Conclusion

Our method for predicting putative prognostic wound-outcome biomarkers may serve as an effective means to guide the identification of proteins predictive of pathological scarring.

Electronic supplementary material

The online version of this article (10.1186/s12967-018-1406-x) contains supplementary material, which is available to authorized users.

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.

Computational identification and analysis of signaling subnetworks with distinct functional roles in the regulation of TNF production

Inflammation is a complex process driven by the coordinated action of a vast number of pro- and anti-inflammatory molecular mediators. While experimental studies have provided an abundance of information about the properties and mechanisms of action of individual mediators, essential system-level regulatory patterns that determine the time-course of inflammation are not sufficiently understood. In particular, it is not known how the contributions from distinct signaling pathways involved in cytokine regulation combine to shape the overall inflammatory response over different time scales. We investigated the kinetics of the intra- and extracellular signaling network controlling the production of the essential pro-inflammatory cytokine, tumor necrosis factor (TNF), and its anti-inflammatory counterpart, interleukin 10 (IL-10), in a macrophage culture. To tackle the intrinsic complexity of the network, we employed a computational modeling approach using the available literature data about specific molecular interactions. Our computational model successfully captured experimentally observed short- and long-term kinetics of key inflammatory mediators. Subsequent model analysis showed that distinct subnetworks regulate IL-10 production by impacting different temporal phases of the cAMP response element-binding protein (CREB) phosphorylation. Moreover, the model revealed that functionally similar inhibitory control circuits regulate the early and late activation phases of nuclear factor κB and CREB. Finally, we identified and investigated distinct signaling subnetworks that independently control the peak height and tail height of the TNF temporal trajectories. The knowledge of such subnetwork-specific regulatory effects may facilitate therapeutic interventions aimed at precise modulation of the inflammatory response.

Automated parameter estimation for biological models using Bayesian statistical model checking

Background

Probabilistic models have gained widespread acceptance in the systems biology community as a useful way to represent complex biological systems. Such models are developed using existing knowledge of the structure and dynamics of the system, experimental observations, and inferences drawn from statistical analysis of empirical data. A key bottleneck in building such models is that some system variables cannot be measured experimentally. These variables are incorporated into the model as numerical parameters. Determining values of these parameters that justify existing experiments and provide reliable predictions when model simulations are performed is a key research problem.

Domain experts usually estimate the values of these parameters by fitting the model to experimental data. Model fitting is usually expressed as an optimization problem that requires minimizing a cost-function which measures some notion of distance between the model and the data. This optimization problem is often solved by combining local and global search methods that tend to perform well for the specific application domain. When some prior information about parameters is available, methods such as Bayesian inference are commonly used for parameter learning. Choosing the appropriate parameter search technique requires detailed domain knowledge and insight into the underlying system.

Results

Using an agent-based model of the dynamics of acute inflammation, we demonstrate a novel parameter estimation algorithm by discovering the amount and schedule of doses of bacterial lipopolysaccharide that guarantee a set of observed clinical outcomes with high probability. We synthesized values of twenty-eight unknown parameters such that the parameterized model instantiated with these parameter values satisfies four specifications describing the dynamic behavior of the model.

Conclusions

We have developed a new algorithmic technique for discovering parameters in complex stochastic models of biological systems given behavioral specifications written in a formal mathematical logic. Our algorithm uses Bayesian model checking, sequential hypothesis testing, and stochastic optimization to automatically synthesize parameters of probabilistic biological models.

Computational Identification of Mechanistic Factors That Determine the Timing and Intensity of the Inflammatory Response

Timely resolution of inflammation is critical for the restoration of homeostasis in injured or infected tissue. Chronic inflammation is often characterized by a persistent increase in the concentrations of inflammatory cells and molecular mediators, whose distinct amount and timing characteristics offer an opportunity to identify effective therapeutic regulatory targets. Here, we used our recently developed computational model of local inflammation to identify potential targets for molecular interventions and to investigate the effects of individual and combined inhibition of such targets. This was accomplished via the development and application of computational strategies involving the simulation and analysis of thousands of inflammatory scenarios. We found that modulation of macrophage influx and efflux is an effective potential strategy to regulate the amount of inflammatory cells and molecular mediators in both normal and chronic inflammatory scenarios. We identified three molecular mediators − tumor necrosis factor-α (TNF-α), transforming growth factor-β (TGF-β), and the chemokine CXCL8 − as potential molecular targets whose individual or combined inhibition may robustly regulate both the amount and timing properties of the kinetic trajectories for neutrophils and macrophages in chronic inflammation. Modulation of macrophage flux, as well as of the abundance of TNF-α, TGF-β, and CXCL8, may improve the resolution of chronic inflammation.

A recent approach to quantitatively characterize the timing and intensity of the inflammatory response relies on the use of four quantities termed inflammation indices. The values of the inflammation indices may reflect the differences between normal and pathological inflammation, and may be used to gauge the effects of therapeutic interventions aimed to control inflammation. Yet, the specific inflammatory mechanisms that can be targeted to selectively control these indices remain unknown. Here, we developed and applied a computational strategy to identify potential target mechanisms to regulate such indices. We used our recently developed model of local inflammation to simulate thousands of inflammatory scenarios. We then subjected the corresponding inflammation index values to sensitivity and correlation analysis. We found that the inflammation indices may be significantly influenced by the macrophage influx and efflux rates, as well as by the degradation rates of three specific molecular mediators. These results suggested that the indices can be effectively regulated by individual or combined inhibition of those molecular mediators, which we confirmed by computational experiments. Taken together, our results highlight possible targets of therapeutic intervention that can be used to control both the timing and the intensity of the inflammatory response.

Conditional robustness analysis for fragility discovery and target identification in biochemical networks and in cancer systems biology

Background

The study of cancer therapy is a key issue in the field of oncology research and the development of target therapies is one of the main problems currently under investigation. This is particularly relevant in different types of tumor where traditional chemotherapy approaches often fail, such as lung cancer.

Results

We started from the general definition of robustness introduced by Kitano and applied it to the analysis of dynamical biochemical networks, proposing a new algorithm based on moment independent analysis of input/output uncertainty. The framework utilizes novel computational methods which enable evaluating the model fragility with respect to quantitative performance measures and parameters such as reaction rate constants and initial conditions. The algorithm generates a small subset of parameters that can be used to act on complex networks and to obtain the desired behaviors. We have applied the proposed framework to the EGFR-IGF1R signal transduction network, a crucial pathway in lung cancer, as an example of Cancer Systems Biology application in drug discovery. Furthermore, we have tested our framework on a pulse generator network as an example of Synthetic Biology application, thus proving the suitability of our methodology to the characterization of the input/output synthetic circuits.

Conclusions

The achieved results are of immediate practical application in computational biology, and while we demonstrate their use in two specific examples, they can in fact be used to study a wider class of biological systems.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0216-5) contains supplementary material, which is available to authorized users.

A Neutrophil Phenotype Model for Extracorporeal Treatment of Sepsis

Neutrophils play a central role in eliminating bacterial pathogens, but may also contribute to end-organ damage in sepsis. Interleukin-8 (IL-8), a key modulator of neutrophil function, signals through neutrophil specific surface receptors CXCR-1 and CXCR-2. In this study a mechanistic computational model was used to evaluate and deploy an extracorporeal sepsis treatment which modulates CXCR-1/2 levels. First, a simplified mechanistic computational model of IL-8 mediated activation of CXCR-1/2 receptors was developed, containing 16 ODEs and 43 parameters. Receptor level dynamics and systemic parameters were coupled with multiple neutrophil phenotypes to generate dynamic populations of activated neutrophils which reduce pathogen load, and/or primed neutrophils which cause adverse tissue damage when misdirected. The mathematical model was calibrated using experimental data from baboons administered a two-hour infusion of E coli and followed for a maximum of 28 days. Ensembles of parameters were generated using a Bayesian parallel tempering approach to produce model fits that could recreate experimental outcomes. Stepwise logistic regression identified seven model parameters as key determinants of mortality. Sensitivity analysis showed that parameters controlling the level of killer cell neutrophils affected the overall systemic damage of individuals. To evaluate rescue strategies and provide probabilistic predictions of their impact on mortality, time of onset, duration, and capture efficacy of an extracorporeal device that modulated neutrophil phenotype were explored. Our findings suggest that interventions aiming to modulate phenotypic composition are time sensitive. When introduced between 3–6 hours of infection for a 72 hour duration, the survivor population increased from 31% to 40–80%. Treatment efficacy quickly diminishes if not introduced within 15 hours of infection. Significant harm is possible with treatment durations ranging from 5–24 hours, which may reduce survival to 13%. In severe sepsis, an extracorporeal treatment which modulates CXCR-1/2 levels has therapeutic potential, but also potential for harm. Further development of the computational model will help guide optimal device development and determine which patient populations should be targeted by treatment.

Sepsis occurs when a patient develops a whole body immune response due to infection. In this condition, white blood cells called neutrophils circulate in an active state, seeking and eliminating invading bacteria. However, when neutrophils are activated, healthy tissue is inadvertently targeted, leading to organ damage and potentially death. Even though sepsis kills millions worldwide, there are still no specific treatments approved in the United States. This may be due to the complexity and diversity of the body’s immune response, which can be managed well using computational modeling. We have developed a computational model to predict how different levels of neutrophil activation impact survival in an overactive inflammatory conditions. The model was utilized to assess the effectiveness of a simulated experimental sepsis treatment which modulates neutrophil populations and activity. This evaluation determined that treatment timing plays a critical role in therapeutic effectiveness. When utilized properly the treatment drastically improves survival, but there is also risk of causing patient harm when introduced at the wrong time. We intend for this computational model to support and guide further development of sepsis treatments and help translate these preliminary results from bench to bedside.

Systems Modeling of Interactions between Mucosal Immunity and the Gut Microbiome during Clostridium difficile Infection

Clostridium difficile infections are associated with the use of broad-spectrum antibiotics and result in an exuberant inflammatory response, leading to nosocomial diarrhea, colitis and even death. To better understand the dynamics of mucosal immunity during C. difficile infection from initiation through expansion to resolution, we built a computational model of the mucosal immune response to the bacterium. The model was calibrated using data from a mouse model of C. difficile infection. The model demonstrates a crucial role of T helper 17 (Th17) effector responses in the colonic lamina propria and luminal commensal bacteria populations in the clearance of C. difficile and colonic pathology, whereas regulatory T (Treg) cells responses are associated with the recovery phase. In addition, the production of anti-microbial peptides by inflamed epithelial cells and activated neutrophils in response to C. difficile infection inhibit the re-growth of beneficial commensal bacterial species. Computational simulations suggest that the removal of neutrophil and epithelial cell derived anti-microbial inhibitions, separately and together, on commensal bacterial regrowth promote recovery and minimize colonic inflammatory pathology. Simulation results predict a decrease in colonic inflammatory markers, such as neutrophilic influx and Th17 cells in the colonic lamina propria, and length of infection with accelerated commensal bacteria re-growth through altered anti-microbial inhibition. Computational modeling provides novel insights on the therapeutic value of repopulating the colonic microbiome and inducing regulatory mucosal immune responses during C. difficile infection. Thus, modeling mucosal immunity-gut microbiota interactions has the potential to guide the development of targeted fecal transplantation therapies in the context of precision medicine interventions.

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.

Quantitative Analysis of Robustness of Dynamic Response and Signal Transfer in Insulin mediated PI3K/AKT Pathway

Robustness is a critical feature of signaling pathways ensuring signal propagation with high fidelity in the event of perturbations. Here we present a detailed quantitative analysis of robustness in insulin mediated PI3K/AKT pathway, a critical signaling pathway maintaining self-renewal in human embryonic stem cells. Using global sensitivity analysis, we identified robustness promoting mechanisms that ensure (1) maintenance of a first order or overshoot dynamics of self-renewal molecule, p-AKT and (2) robust transfer of signals from oscillatory insulin stimulus to p-AKT in the presence of noise. Our results indicate that negative feedback controls the robustness to most perturbations. Faithful transfer of signal from the stimulating ligand to p-AKT occurs even in the presence of noise, albeit with signal attenuation and high frequency cut-off. Negative feedback contributes to signal attenuation, while positive regulators upstream of PIP₃ contribute to signal amplification. These results establish precise mechanisms to modulate self-renewal molecules like p-AKT.