On the computational modeling of the innate immune system

Embracing complexity in sepsis

Sepsis involves the dynamic interplay between a pathogen, the host response, the failure of organ systems, medical interventions and a myriad of other factors. This together results in a complex, dynamic and dysregulated state that has remained ungovernable thus far. While it is generally accepted that sepsis is very complex indeed, the concepts, approaches and methods that are necessary to understand this complexity remain underappreciated. In this perspective we view sepsis through the lens of complexity theory. We describe the concepts that support viewing sepsis as a state of a highly complex, non-linear and spatio-dynamic system. We argue that methods from the field of complex systems are pivotal for a fuller understanding of sepsis, and we highlight the progress that has been made over the last decades in this respect. Still, despite these considerable advancements, methods like computational modelling and network-based analyses continue to fly under the general scientific radar. We discuss what barriers contribute to this disconnect, and what we can do to embrace complexity with regards to measurements, research approaches and clinical applications. Specifically, we advocate a focus on longitudinal, more continuous biological data collection in sepsis. Understanding the complexity of sepsis will require a huge multidisciplinary effort, in which computational approaches derived from complex systems science must be supported by, and integrated with, biological data. Such integration could finetune computational models, guide validation experiments, and identify key pathways that could be targeted to modulate the system to the benefit of the host. We offer an example for immunological predictive modelling, which may inform agile trials that could be adjusted throughout the trajectory of disease. Overall, we argue that we should expand our current mental frameworks of sepsis, and embrace nonlinear, system-based thinking in order to move the field forward.

Coupled simultaneous analysis of vaccine and self-awareness strategies on evolutionary dilemma aspect with various immunity

On evolutionary game theory (EGT), two intervention policies: vaccination and self-awareness, are considered to account for how human attitude impacts disease spreading. Although these interventions can impose, their implementation may depend on the various immunity systems such as shield immunity, innate immunity, waning immunity, natural immunity, and artificial immunity. This framework provides an epidemic SEIRVA (susceptible-exposed-infected-removed-vaccinated-aware) model and two EGT dynamics to analyze the interplay between the immunity system and social learning interventions. The prospect of exploring the individual's strategy and social dilemma for removing a disease could assist design an effective vaccine program and self-awareness policy. Also, we evaluated the indicator of social efficiency deficit (SED) for a social dual-dilemma to measure the presence of a dilemma situation. Extensive theoretical analysis displays that stability includes the reproduction number, conditions for positivity and uniqueness, and the strength number analyzed in the equilibria, including fundamental properties validated by numerical simulation of the discretization method that appraises a variety of graphs at adjusting parameters. We present extensive numerical studies investigating the affect of controlling parameters, individual vulnerability, optimal policies, and individual costs. It turns out that, even with the affordable vaccine, individuals may have very different behaviors; self-awareness strategy plays a vital role in controlling diseases.

Infectious disease model generalization based on diffuse perturbations under conditions of body's temperature reaction

The infectious disease mathematical model is generalized based on the influence of diffuse perturbations on the development of the disease under conditions of the body's temperature reaction. The singularly perturbed model problem was reduced with delay to a sequence of problems without delay, for which the corresponding asymptotic expansions of solutions are obtained. The presented results of computer modeling in various situational states illustrate the expected decrease in the growth rate of the number of viral particles as a result of the action of the body's protective temperature reaction. The results of numerical experiments demonstrate the influence of the diffuse effect of "scattering" of forcing factors on the dynamics of a viral disease under conditions of the body's temperature reaction are presented too. It is noted that the decrease of the model amount of antigens in the epicenter of infection to a non-critical level caused by diffuse "scattering" over a relatively short time period makes them further destroyed by immune agents presented in the body, or requires the introduction of an injection solution with a smaller amount of donor antibodies.

A Mathematical Model of the Dynamics of Cytokine Expression and Human Immune Cell Activation in Response to the Pathogen Staphylococcus aureus

Cell-based mathematical models have previously been developed to simulate the immune system in response to pathogens. Mathematical modeling papers which study the human immune response to pathogens have predicted concentrations of a variety of cells, including activated and resting macrophages, plasma cells, and antibodies. This study aims to create a comprehensive mathematical model that can predict cytokine levels in response to a gram-positive bacterium, S. aureus by coupling previous models. To accomplish this, the cytokines Tumor Necrosis Factor Alpha (TNF-α), Interleukin 6 (IL-6), Interleukin 8 (IL-8), and Interleukin 10 (IL-10) are included to quantify the relationship between cytokine release from macrophages and the concentration of the pathogen, S. aureus, ex vivo. Partial differential equations (PDEs) are used to model cellular response and ordinary differential equations (ODEs) are used to model cytokine response, and interactions between both components produce a more robust and more complete systems-level understanding of immune activation. In the coupled cellular and cytokine model outlined in this paper, a low concentration of S. aureus is used to stimulate the measured cellular response and cytokine expression. Results show that our cellular activation and cytokine expression model characterizing septic conditions can predict ex vivo mechanisms in response to gram-negative and gram-positive bacteria. Our simulations provide new insights into how the human immune system responds to infections from different pathogens. Novel applications of these insights help in the development of more powerful tools and protocols in infection biology.

A Validated Mathematical Model of the Cytokine Release Syndrome in Severe COVID-19

By June 2021, a new contagious disease, the Coronavirus disease 2019 (COVID-19), has infected more than 172 million people worldwide, causing more than 3.7 million deaths. Many aspects related to the interactions of the disease's causative agent, SAR2-CoV-2, and the immune response are not well understood: the multiscale interactions among the various components of the human immune system and the pathogen are very complex. Mathematical and computational tools can help researchers to answer these open questions about the disease. In this work, we present a system of fifteen ordinary differential equations that models the immune response to SARS-CoV-2. The model is used to investigate the hypothesis that the SARS-CoV-2 infects immune cells and, for this reason, induces high-level productions of inflammatory cytokines. Simulation results support this hypothesis and further explain why survivors have lower levels of cytokines levels than non-survivors.

Current and prospective computational approaches and challenges for developing COVID-19 vaccines

SARS-CoV-2, which causes COVID-19, was first identified in humans in late 2019 and is a coronavirus which is zoonotic in origin. As it spread around the world there has been an unprecedented effort in developing effective vaccines. Computational methods can be used to speed up the long and costly process of vaccine development. Antigen selection, epitope prediction, and toxicity and allergenicity prediction are areas in which computational tools have already been applied as part of reverse vaccinology for SARS-CoV-2 vaccine development. However, there is potential for computational methods to assist further. We review approaches which have been used and highlight additional bioinformatic approaches and PK modelling as in silico methods which may be useful for SARS-CoV-2 vaccine design but remain currently unexplored. As more novel viruses with pandemic potential are expected to arise in future, these techniques are not limited to application to SARS-CoV-2 but also useful to rapidly respond to novel emerging viruses.

Dynamic analysis of the role of innate immunity in SEIS epidemic model

Consideration of every important aspect while modeling a disease makes the model more precise and the disease eradication strategy more powerful. In the present paper, we analyze the importance of innate immunity on SEIS modeling. We propose an SEIS model with Holling type II and type III functions representing innate immunity. We find the existence and stability conditions for the equilibria. When innate immunity is in the form of Holling type II function, the disease-free equilibrium exists for reproduction number less than unity and is locally asymptotically stable, and supercritical transcritical (forward) as well as subcritical transcritical (backward) bifurcation may occur where the contact rate β = β ∗ acts as the bifurcation parameter. Hence, disease-free equilibrium need not be globally stable. For reproduction number greater than unity unique endemic equilibrium exists which is locally asymptotically stable. The global stability conditions for the same are deduced with the help of Lozinski i ˘ measure. When innate immunity is considered a Holling type III function, the disease-free equilibrium point exists for reproduction number less than unity and is locally as well as globally stable. The existence of either unique or multiple endemic equilibria is found when reproduction number is greater than unity, and there exists at least one locally asymptotically stable equilibrium point and bistability can also be encountered. The conditions for the existence of Andronov-Hopf bifurcation are deduced for both cases. Moreover, we observe that ignoring innate immunity annihilates the possibility of Andronov-Hopf bifurcation. Numerical simulation is performed to validate the mathematical findings. Comparing the obtained results to the case when innate immunity is ignored, it is deduced that ignoring it ends the possibility of backward bifurcation, Andronov-Hopf bifurcation as well as the existence of multiple equilibria, and it also leads to the prediction of higher infection than the actual which may deflect the accuracy of the model to a high extent. This would further lead to false predictions and inefficient disease control strategies which in turn would make disease eradication a difficult and more expensive task.

Dynamical analysis of SEIS model with nonlinear innate immunity and saturated treatment

In this paper, we develop an SEIS model with Holling type II function representing the innate immunity as well as the saturated treatment. We obtain the existence and stability criteria for the equilibrium points. We observe that when the reproduction number is less than unity, the disease-free equilibrium always exists and is locally asymptotically stable. The multiple endemic equilibrium points can exist independent of the basic reproduction number, and the system may experience bistability. We find that the system can encounter backward or forward bifurcation at R 0 = 1 , where the contact rate β = β 0 is the bifurcation parameter. Therefore, the disease-free equilibrium may not be globally stable. We deduce the criteria for the presence of Hopf bifurcation where the parameter γ = γ ∗ acts as the bifurcation parameter and the system is a neutrally stable center. We also observe with the aid of a numerical example that a slight perturbation disrupts the neutral stability and the trajectories become either converging or diverging from the equilibrium point. Numerical simulation is performed with the help of MATLAB to justify the findings. We study the effect of nonlinearity of immunity function and the treatment rate on the dynamics of the disease spread. We find that when both are linear, the reproduction number is the same, but the system has a unique endemic equilibrium point that exists for reproduction number greater than unity. We find that there is neither backward bifurcation nor Hopf bifurcation. We also observe that the saturation in treatment enlarges the domain of backward bifurcation making disease eradication an extremely difficult task. The endemic equilibria in the case of saturated treatment may exist far more to the left of the bifurcation parameter β = β 0 . Hence, the nonlinearity of immunity function and treatment function affects the dynamics of an SEIS model highly; therefore, one must be precautious to choose an appropriate function for both while modeling.

Global well-posedness and pattern formations of the immune system induced by chemotaxis

This paper studies a reaction-diffusion-advection system describing a directed movement of immune cells toward chemokines during the immune process. We investigate the global solvability of the model based on the bootstrap argument for minimal chemotaxis models. We also examine the stability of nonconstant steady states and the existence of periodic orbits from theoretical aspects of bifurcation analysis. Through numerical simulations, we observe the occurrence of steady or time-periodic pattern formations.

Complex Stability and an Irrevertible Transition Reverted by Peptide and Fibroblasts in a Dynamic Model of Innate Immunity

We here apply a control analysis and various types of stability analysis to an in silico model of innate immunity that addresses the management of inflammation by a therapeutic peptide. Motivation is the observation, both in silico and in experiments, that this therapy is not robust. Our modeling results demonstrate how (1) the biological phenomena of acute and chronic modes of inflammation may reflect an inherently complex bistability with an irrevertible flip between the two modes, (2) the chronic mode of the model has stable, sometimes unique, steady states, while its acute-mode steady states are stable but not unique, (3) as witnessed by TNF levels, acute inflammation is controlled by multiple processes, whereas its chronic-mode inflammation is only controlled by TNF synthesis and washout, (4) only when the antigen load is close to the acute mode's flipping point, many processes impact very strongly on cells and cytokines, (5) there is no antigen exposure level below which reduction of the antigen load alone initiates a flip back to the acute mode, and (6) adding healthy fibroblasts makes the transition from acute to chronic inflammation revertible, although (7) there is a window of antigen load where such a therapy cannot be effective. This suggests that triple therapies may be essential to overcome chronic inflammation. These may comprise (1) anti-immunoglobulin light chain peptides, (2) a temporarily reduced antigen load, and (3a) fibroblast repopulation or (3b) stem cell strategies.

A personalized computational model of edema formation in myocarditis based on long-axis biventricular MRI images

Background

Myocarditis is defined as the inflammation of the myocardium, i.e. the cardiac muscle. Among the reasons that lead to this disease, we may include infections caused by a virus, bacteria, protozoa, fungus, and others. One of the signs of the inflammation is the formation of edema, which may be a consequence of the interaction between interstitial fluid dynamics and immune response. This complex physiological process was mathematically modeled using a nonlinear system of partial differential equations (PDE) based on porous media approach. By combing a model based on Biot’s poroelasticity theory with a model for the immune response we developed a new hydro-mechanical model for inflammatory edema. To verify this new computational model, T2 parametric mapping obtained by Magnetic Resonance (MR) imaging was used to identify the region of edema in a patient diagnosed with unspecific myocarditis.

Results

A patient-specific geometrical model was created using MRI images from the patient with myocarditis. With this model, edema formation was simulated using the proposed hydro-mechanical mathematical model in a two-dimensional domain. The computer simulations allowed us to correlate spatiotemporal dynamics of representative cells of the immune systems, such as leucocytes and the pathogen, with fluid accumulation and cardiac tissue deformation.

Conclusions

This study demonstrates that the proposed mathematical model is a very promising tool to better understand edema formation in myocarditis. Simulations obtained from a patient-specific model reproduced important aspects related to the formation of cardiac edema, its area, position, and shape, and how these features are related to immune response.

Game of neutrophils: modeling the balance between apoptosis and necrosis

Background

Neutrophils are one of the key players in the human innate immune system (HIIS). In the event of an insult where the body is exposed to inflammation triggering moieties (ITMs), neutrophils are mobilized towards the site of insult and antagonize the inflammation. If the inflammation is cleared, neutrophils go into a programmed death called apoptosis. However, if the insult is intense or persistent, neutrophils take on a violent death pathway called necrosis, which involves the rupture of their cytoplasmic content into the surrounding tissue that causes local tissue damage, thus further aggravating inflammation. This seemingly paradoxical phenomenon fuels the inflammatory process by triggering the recruitment of additional neutrophils to the site of inflammation, aimed to contribute to the complete neutralization of severe inflammation. This delicate balance between the cost and benefit of the neutrophils’ choice of death pathway has been optimized during the evolution of the innate immune system. The goal of our work is to understand how the tradeoff between the cost and benefit of the different death pathways of neutrophils, in response to various levels of insults, has been optimized over evolutionary time by using the concepts of evolutionary game theory.

Results

We show that by using evolutionary game theory, we are able to formulate a game that predicts the percentage of necrosis and apoptosis when exposed to various levels of insults.

Conclusion

By adopting an evolutionary perspective, we identify the driving mechanisms leading to the delicate balance between apoptosis and necrosis in neutrophils’ cell death in response to different insults. Using our simple model, we verify that indeed, the global cost of remaining ITMs is the driving mechanism that reproduces the percentage of necrosis and apoptosis observed in data and neutrophils need sufficient information of the overall inflammation to be able to pick a death pathway that presumably increases the survival of the organism.

Supplemented Alkaline Phosphatase Supports the Immune Response in Patients Undergoing Cardiac Surgery: Clinical and Computational Evidence

Alkaline phosphatase (AP) is an enzyme that exhibits anti-inflammatory effects by dephosphorylating inflammation triggering moieties (ITMs) like bacterial lipopolysaccharides and extracellular nucleotides. AP administration aims to prevent and treat peri- and post-surgical ischemia reperfusion injury in cardiothoracic surgery patients. Recent studies reported that intravenous bolus administration and continuous infusion of AP in patients undergoing coronary artery bypass grafting with cardiac valve surgery induce an increased release of liver-type “tissue non-specific alkaline phosphatase” (TNAP) into the bloodstream. The release of liver-type TNAP into circulation could be the body's way of strengthening its defense against a massive ischemic insult. However, the underlying mechanism behind the induction of TNAP is still unclear. To obtain a deeper insight into the role of AP during surgery, we developed a mathematical model of systemic inflammation that clarifies the relation between supplemented AP and TNAP and describes a plausible induction mechanism of TNAP in patients undergoing cardiothoracic surgery. The model was validated against clinical data from patients treated with bovine Intestinal AP (bIAP treatment) or without AP (placebo treatment), in addition to standard care procedures. We performed additional in-silico experiments adding a secondary source of ITMs after surgery, as observed in some patients with complications, and predicted the response to different AP treatment regimens. Our results show a strong protective effect of supplemented AP for patients with complications. The model provides evidence of the existence of an induction mechanism of liver-type tissue non-specific alkaline phosphatase, triggered by the supplementation of AP in patients undergoing cardiac surgery. To the best of our knowledge this is the first time that a quantitative and validated numerical model of systemic inflammation under clinical treatment conditions is presented.

A review of inflammatory mechanism in airway diseases

BACKGROUND

Inflammation in the lung is the body's natural response to injury. It acts to remove harmful stimuli such as pathogens, irritants, and damaged cells and initiate the healing process. Acute and chronic pulmonary inflammation are seen in different respiratory diseases such as; acute respiratory distress syndrome, chronic obstructive pulmonary disease (COPD), asthma, and cystic fibrosis (CF).

FINDINGS

In this review, we found that inflammatory response in COPD is determined by the activation of epithelial cells and macrophages in the respiratory tract. Epithelial cells and macrophages discharge transforming growth factor-β (TGF-β), which trigger fibroblast proliferation and tissue remodeling. Asthma leads to airway hyper-responsiveness, obstruction, mucus hyper-production, and airway-wall remodeling. Cytokines, allergens, chemokines, and infectious agents are the main stimuli that activate signaling pathways in epithelial cells in asthma. Mutation of the CF transmembrane conductance regulator (CFTR) gene results in CF. Mutations in CFTR influence the lung epithelial innate immune function that leads to exaggerated and ineffective airway inflammation that fails to abolish pulmonary pathogens. We present mechanistic computational models (based on ordinary differential equations, partial differential equations and agent-based models) that have been applied in studying the complex physiological and pathological mechanisms of chronic inflammation in different airway diseases.

CONCLUSION

The scope of the present review is to explore the inflammatory mechanism in airway diseases and highlight the influence of aging on airways' inflammation mechanism. The main goal of this review is to encourage research collaborations between experimentalist and modelers to promote our understanding of the physiological and pathological mechanisms that control inflammation in different airway diseases.

Development of a Computational Model of Abscess Formation

In some bacterial infections, the immune system cannot eliminate the invading pathogen. In these cases, the invading pathogen is successful in establishing a favorable environment to survive and persist in the host organism. For example, S. aureus bacteria survive in organ tissues employing a set of mechanisms that work in a coordinated and highly regulated way allowing: (1) efficient impairment of the immune response; and (2) protection from the immune cells and molecules. S. aureus secretes several proteins including coagulases and toxins that drive abscess formation and persistence. Unless staphylococcal abscesses are surgically drained and treated with antibiotics, disseminated infection and septicemia produce a lethal outcome. Within this context, this paper develops a simple mathematical model of abscess formation incorporating characteristics that we judge important for an abscess to be formed. Our aim is to build a mathematical model that reproduces some characteristics and behaviors that are observed in the process of abscess formation.

Mathematical modeling and its analysis for instability of the immune system induced by chemotaxis

In this paper, we study how chemotaxis affects the immune system by proposing a minimal mathematical model, a reaction-diffusion-advection system, describing a cross-talk between antigens and immune cells via chemokines. We analyze the stability and instability arising in our chemotaxis model and find their conditions for different chemotactic strengths by using energy estimates, spectral analysis, and bootstrap argument. Numerical simulations are also performed to the model, by using the finite volume method in order to deal with the chemotaxis term, and the fractional step methods are used to solve the whole system. From the analytical and numerical results for our model, we explain not only the effective attraction of immune cells toward the site of infection but also hypersensitivity when chemotactic strength is greater than some threshold.

Physiological Dynamics in Demyelinating Diseases: Unraveling Complex Relationships through Computer Modeling

Despite intense research, few treatments are available for most neurological disorders. Demyelinating diseases are no exception. This is perhaps not surprising considering the multifactorial nature of these diseases, which involve complex interactions between immune system cells, glia and neurons. In the case of multiple sclerosis, for example, there is no unanimity among researchers about the cause or even which system or cell type could be ground zero. This situation precludes the development and strategic application of mechanism-based therapies. We will discuss how computational modeling applied to questions at different biological levels can help link together disparate observations and decipher complex mechanisms whose solutions are not amenable to simple reductionism. By making testable predictions and revealing critical gaps in existing knowledge, such models can help direct research and will provide a rigorous framework in which to integrate new data as they are collected. Nowadays, there is no shortage of data; the challenge is to make sense of it all. In that respect, computational modeling is an invaluable tool that could, ultimately, transform how we understand, diagnose, and treat demyelinating diseases.

Computational Studies of the Intestinal Host-Microbiota Interactome

A large and growing body of research implicates aberrant immune response and compositional shifts of the intestinal microbiota in the pathogenesis of many intestinal disorders. The molecular and physical interaction between the host and the microbiota, known as the host-microbiota interactome, is one of the key drivers in the pathophysiology of many of these disorders. This host-microbiota interactome is a set of dynamic and complex processes, and needs to be treated as a distinct entity and subject for study. Disentangling this complex web of interactions will require novel approaches, using a combination of data-driven bioinformatics with knowledge-driven computational modeling. This review describes the computational approaches for investigating the host-microbiota interactome, with emphasis on the human intestinal tract and innate immunity, and highlights open challenges and existing gaps in the computation methodology for advancing our knowledge about this important facet of human health.

On the coupling of two models of the human immune response to an antigen

The development of mathematical models of the immune response allows a better understanding of the multifaceted mechanisms of the defense system. The main purpose of this work is to present a scheme for coupling distinct models of different scales and aspects of the immune system. As an example, we propose a new model where the local tissue inflammation processes are simulated with partial differential equations (PDEs) whereas a system of ordinary differential equations (ODEs) is used as a model for the systemic response. The simulation of distinct scenarios allows the analysis of the dynamics of various immune cells in the presence of an antigen. Preliminary results of this approach with a sensitivity analysis of the coupled model are shown but further validation is still required.

Computational modeling of microabscess formation

Bacterial infections can be of two types: acute or chronic. The chronic bacterial infections are characterized by being a large bacterial infection and/or an infection where the bacteria grows rapidly. In these cases, the immune response is not capable of completely eliminating the infection which may lead to the formation of a pattern known as microabscess (or abscess). The microabscess is characterized by an area comprising fluids, bacteria, immune cells (mainly neutrophils), and many types of dead cells. This distinct pattern of formation can only be numerically reproduced and studied by models that capture the spatiotemporal dynamics of the human immune system (HIS). In this context, our work aims to develop and implement an initial computational model to study the process of microabscess formation during a bacterial infection.