Equation-based models of dynamic biological systems

A statistical approach for systematic identification of transition cells from scRNA-seq data

Decoding cellular state transitions is crucial for understanding complex biological processes in development and disease. While recent advancements in single-cell RNA sequencing (scRNA-seq) offer insights into cellular trajectories, existing tools primarily study expressional rather than regulatory state shifts. We present CellTran, a statistical approach utilizing paired-gene expression correlations to detect transition cells from scRNA-seq data without explicitly resolving gene regulatory networks. Applying our approach to various contexts, including tissue regeneration, embryonic development, preinvasive lesions, and humoral responses post-vaccination, reveals transition cells and their distinct gene expression profiles. Our study sheds light on the underlying molecular mechanisms driving cellular state transitions, enhancing our ability to identify therapeutic targets for disease interventions.

Systems-level computational modeling in ischemic stroke: from cells to patients

Ischemic stroke, a significant threat to human life and health, refers to a class of conditions where brain tissue damage is induced following decreased cerebral blood flow. The incidence of ischemic stroke has been steadily increasing globally, and its disease mechanisms are highly complex and involve a multitude of biological mechanisms at various scales from genes all the way to the human body system that can affect the stroke onset, progression, treatment, and prognosis. To complement conventional experimental research methods, computational systems biology modeling can integrate and describe the pathogenic mechanisms of ischemic stroke across multiple biological scales and help identify emergent modulatory principles that drive disease progression and recovery. In addition, by running virtual experiments and trials in computers, these models can efficiently predict and evaluate outcomes of different treatment methods and thereby assist clinical decision-making. In this review, we summarize the current research and application of systems-level computational modeling in the field of ischemic stroke from the multiscale mechanism-based, physics-based and omics-based perspectives and discuss how modeling-driven research frameworks can deliver insights for future stroke research and drug development.

Individualized survival predictions using state space model with longitudinal and survival data

Monitoring disease progression often involves tracking biomarker measurements over time. Joint models (JMs) for longitudinal and survival data provide a framework to explore the relationship between time-varying biomarkers and patients' event outcomes, offering the potential for personalized survival predictions. In this article, we introduce the linear state space dynamic survival model for handling longitudinal and survival data. This model enhances the traditional linear Gaussian state space model by including survival data. It differs from the conventional JMs by offering an alternative interpretation via differential or difference equations, eliminating the need for creating a design matrix. To showcase the model's effectiveness, we conduct a simulation case study, emphasizing its performance under conditions of limited observed measurements. We also apply the proposed model to a dataset of pulmonary arterial hypertension patients, demonstrating its potential for enhanced survival predictions when compared with conventional risk scores.

Agent-based modeling to estimate the impact of lockdown scenarios and events on a pandemic exemplified on SARS-CoV-2

In actual pandemic situations like COVID-19, it is important to understand the influence of single mitigation measures as well as combinations to create most dynamic impact for lockdown scenarios. Therefore we created an agent-based model (ABM) to simulate the spread of SARS-CoV-2 in an abstract city model with several types of places and agents. In comparison to infection numbers in Germany our ABM could be shown to behave similarly during the first wave. In our model, we implemented the possibility to test the effectiveness of mitigation measures and lockdown scenarios on the course of the pandemic. In this context, we focused on parameters of local events as possible mitigation measures and ran simulations, including varying size, duration, frequency and the proportion of events. The majority of changes to single event parameters, with the exception of frequency, showed only a small influence on the overall course of the pandemic. By applying different lockdown scenarios in our simulations, we could observe drastic changes in the number of infections per day. Depending on the lockdown strategy, we even observed a delayed peak in infection numbers of the second wave. As an advantage of the developed ABM, it is possible to analyze the individual risk of single agents during the pandemic. In contrast to standard or adjusted ODEs, we observed a 21% (with masks) / 48% (without masks) increased risk for single reappearing participants on local events, with a linearly increasing risk based on the length of the events.

High-content high-throughput imaging reveals distinct connections between mitochondrial morphology and functionality for OXPHOS complex I, III, and V inhibitors

Cells can adjust their mitochondrial morphology by altering the balance between mitochondrial fission and fusion to adapt to stressful conditions. The connection between a chemical perturbation, changes in mitochondrial function, and altered mitochondrial morphology is not well understood. Here, we made use of high-throughput high-content confocal microscopy to assess the effects of distinct classes of oxidative phosphorylation (OXPHOS) complex inhibitors on mitochondrial parameters in a concentration and time resolved manner. Mitochondrial morphology phenotypes were clustered based on machine learning algorithms and mitochondrial integrity patterns were mapped. In parallel, changes in mitochondrial membrane potential (MMP), mitochondrial and cellular ATP levels, and viability were microscopically assessed. We found that inhibition of MMP, mitochondrial ATP production, and oxygen consumption rate (OCR) using sublethal concentrations of complex I and III inhibitors did not trigger mitochondrial fragmentation. Instead, complex V inhibitors that suppressed ATP and OCR but increased MMP provoked a more fragmented mitochondrial morphology. In agreement, complex V but not complex I or III inhibitors triggered proteolytic cleavage of the mitochondrial fusion protein, OPA1. The relation between increased MMP and fragmentation did not extend beyond OXPHOS complex inhibitors: increasing MMP by blocking the mPTP pore did not lead to OPA1 cleavage or mitochondrial fragmentation and the OXPHOS uncoupler FCCP was associated with OPA1 cleavage and MMP reduction. Altogether, our findings connect vital mitochondrial functions and phenotypes in a high-throughput high-content confocal microscopy approach that help understanding of chemical-induced toxicity caused by OXPHOS complex perturbing chemicals.

Hybrid modelling of biological systems: current progress and future prospects

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.

Using models to advance medicine: mathematical modeling of post-myocardial infarction left ventricular remodeling

The heart is an organ with limited capacity for regeneration and repair. The irreversible cell death and corresponding diminished ability of the heart to repair after myocardial infarction (MI), is a leading cause of morbidity and mortality worldwide. In this paper, a new mathematical model is presented to study the left ventricular (LV) remodeling and associated events after MI. The model accurately describes and predicts the interactions among heart cells and the immune system post-MI in the absence of medical interventions. The resulting system of nonlinear ordinary differential equations is studied both analytically and numerically in order to demonstrate the functionality and performance of the new model. To the best of our knowledge, this model is the only one of its kind to consider and correctly apply all of the known factors in diseased heart LV modeling. This model has the potential to provide researchers with a predictive computational tool to better understand the MI pathology and develop various cell-based treatment options, with benefits of lowering the cost and reducing the development time.

Under-sampling in epilepsy: Limitations of conventional EEG

The cyclical structure of epilepsy was recently (re)-discovered through years-long intracranial electroencephalography (EEG) obtained with implanted devices. In this review, we discuss how new revelations from chronic EEG relate to the practice and interpretation of conventional EEG. We argue for an electrographic definition of seizures and highlight the caveats of counting epileptiform discharges in EEG recordings of short duration. Limitations of conventional EEG have practical implications with regard to titrating anti-seizure medications and allowing patients to drive, and we propose that chronic monitoring of brain activity could greatly improve epilepsy care. An impending paradigm shift in epilepsy will involve using next-generation devices for chronic EEG to leverage known biomarkers of disease state.

Attractor Ranked Radial Basis Function Network: A Nonparametric Forecasting Approach for Chaotic Dynamic Systems

The curse of dimensionality has long been a hurdle in the analysis of complex data in areas such as computational biology, ecology and econometrics. In this work, we present a forecasting algorithm that exploits the dimensionality of data in a nonparametric autoregressive framework. The main idea is that the dynamics of a chaotic dynamical system consisting of multiple time-series can be reconstructed using a combination of different variables. This nonlinear autoregressive algorithm uses multivariate attractors reconstructed as the inputs of a neural network to predict the future. We show that our approach, attractor ranked radial basis function network (AR-RBFN) provides a better forecast than that obtained using other model-free approaches as well as univariate and multivariate autoregressive models using radial basis function networks. We demonstrate this for simulated ecosystem models and a mesocosm experiment. By taking advantage of dimensionality, we show that AR-RBFN overcomes the shortcomings of noisy and short time-series data.

A mathematical model of neuroinflammation in severe clinical traumatic brain injury

Background

Understanding the interdependencies among inflammatory mediators of tissue damage following traumatic brain injury (TBI) is essential in providing effective, patient-specific care. Activated microglia and elevated concentrations of inflammatory signaling molecules reflect the complex cascades associated with acute neuroinflammation and are predictive of recovery after TBI. However, clinical TBI studies to date have not focused on modeling the dynamic temporal patterns of simultaneously evolving inflammatory mediators, which has potential in guiding the design of future immunomodulation intervention studies.

Methods

We derived a mathematical model consisting of ordinary differential equations (ODE) to represent interactions between pro- and anti-inflammatory cytokines, M1- and M2-like microglia, and central nervous system (CNS) tissue damage. We incorporated variables for several cytokines, interleukin (IL)-1β, IL-4, IL-10, and IL-12, known to have roles in microglial activation and phenotype differentiation. The model was fit to cerebrospinal fluid (CSF) cytokine data, collected during the first 5 days post-injury in n = 89 adults with severe TBI. Ensembles of model fits were produced for three patient subgroups: (1) a favorable outcome group (GOS = 4,5) and (2) an unfavorable outcome group (GOS = 1,2,3) both with lower pro-inflammatory load, and (3) an unfavorable outcome group (GOS = 1,2,3) with higher pro-inflammatory load. Differences in parameter distributions between subgroups were ranked using Bhattacharyya metrics to identify mechanistic differences underlying the neuroinflammatory patterns of patient groups with different TBI outcomes.

Results

Optimal model fits to data showed different microglial and damage responses by patient subgroup. Upon comparison of model parameter distributions, unfavorable outcome groups were characterized by either a prolonged, pathophysiological or a transient, sub-physiological course of neuroinflammation.

Conclusion

By developing a mathematical characterization of inflammatory processes informed by clinical data, we have created a system for exploring links between acute neuroinflammatory components and patient outcome in severe TBI.

Electronic supplementary material

The online version of this article (10.1186/s12974-018-1384-1) contains supplementary material, which is available to authorized users.

Principal components derived from CSF inflammatory profiles predict outcome in survivors after severe traumatic brain injury

Studies have characterized absolute levels of multiple inflammatory markers as significant risk factors for poor outcomes after traumatic brain injury (TBI). However, inflammatory marker concentrations are highly inter-related, and production of one may result in the production or regulation of another. Therefore, a more comprehensive characterization of the inflammatory response post-TBI should consider relative levels of markers in the inflammatory pathway. We used principal component analysis (PCA) as a dimension-reduction technique to characterize the sets of markers that contribute independently to variability in cerebrospinal (CSF) inflammatory profiles after TBI. Using PCA results, we defined groups (or clusters) of individuals (n=111) with similar patterns of acute CSF inflammation that were then evaluated in the context of outcome and other relevant CSF and serum biomarkers collected days 0-3 and 4-5 post-injury. We identified four significant principal components (PC1-PC4) for CSF inflammation from days 0-3, and PC1 accounted for the greatest (31%) percentage of variance. PC1 was characterized by relatively higher CSF sICAM-1, sFAS, IL-10, IL-6, sVCAM-1, IL-5, and IL-8 levels. Cluster analysis then defined two distinct clusters, such that individuals in cluster 1 had highly positive PC1 scores and relatively higher levels of CSF cortisol, progesterone, estradiol, testosterone, brain derived neurotrophic factor (BDNF), and S100b; this group also had higher serum cortisol and lower serum BDNF. Multinomial logistic regression analyses showed that individuals in cluster 1 had a 10.9 times increased likelihood of GOS scores of 2/3 vs. 4/5 at 6 months compared to cluster 2, after controlling for covariates. Cluster group did not discriminate between mortality compared to GOS scores of 4/5 after controlling for age and other covariates. Cluster groupings also did not discriminate mortality or 12 month outcomes in multivariate models. PCA and cluster analysis establish that a subset of CSF inflammatory markers measured in days 0-3 post-TBI may distinguish individuals with poor 6-month outcome, and future studies should prospectively validate these findings. PCA of inflammatory mediators after TBI could aid in prognostication and in identifying patient subgroups for therapeutic interventions.

The inverse problem in mathematical biology

Biological systems present particular challengers to model for the purposes of formulating predictions of generating biological insight. These systems are typically multi-scale, complex, and empirical observations are often sparse and subject to variability and uncertainty. This manuscript will review some of these specific challenges and introduce current methods used by modelers to construct meaningful solutions, in the context of preserving biological relevance. Opportunities to expand these methods are also discussed.

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

The precise inflammatory role of the cytokine interleukin (IL)-6 and its utility as a biomarker or therapeutic target have been the source of much debate, presumably due to the complex pro- and anti-inflammatory effects of this cytokine. We previously developed a nonlinear ordinary differential equation (ODE) model to explain the dynamics of endotoxin (lipopolysaccharide; LPS)-induced acute inflammation and associated whole-animal damage/dysfunction (a proxy for the health of the organism), along with the inflammatory mediators tumor necrosis factor (TNF)-α, IL-6, IL-10, and nitric oxide (NO). The model was partially calibrated using data from endotoxemic C57Bl/6 mice. Herein, we investigated the sensitivity of the area under the damage curve (AUCD) to the 51 rate parameters of the ODE model for different levels of simulated LPS challenges using a global sensitivity approach called Random Sampling High Dimensional Model Representation (RS-HDMR). We explored sufficient parametric Monte Carlo samples to generate the variance-based Sobol' global sensitivity indices, and found that inflammatory damage was highly sensitive to the parameters affecting the activity of IL-6 during the different stages of acute inflammation. The AUCIL6 showed a bimodal distribution, with the lower peak representing healthy response and the higher peak representing sustained inflammation. Damage was minimal at low AUCIL6, giving rise to a healthy response. In contrast, intermediate levels of AUCIL6 resulted in high damage, and this was due to the insufficiency of damage recovery driven by anti-inflammatory responses from IL-10 and the activation of positive feedback sustained by IL-6. At high AUCIL6, damage recovery was interestingly restored in some population of simulated animals due to the NO-mediated anti-inflammatory responses. These observations suggest that the host's health status during acute inflammation depends in a nonlinear fashion on the magnitude of the inflammatory stimulus, on the host's propensity to produce IL-6, and on NO-mediated downstream responses.

Conceptualizing a model: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-2

The appropriate development of a model begins with understanding the problem that is being represented. The aim of this article is to provide a series of consensus-based best practices regarding the process of model conceptualization. For the purpose of this series of papers, the authors consider the development of models whose purpose is to inform medical decisions and health-related resource allocation questions. They specifically divide the conceptualization process into two distinct components: the conceptualization of the problem, which converts knowledge of the health care process or decision into a representation of the problem, followed by the conceptualization of the model itself, which matches the attributes and characteristics of a particular modeling type to the needs of the problem being represented. Recommendations are made regarding the structure of the modeling team, agreement on the statement of the problem, the structure, perspective and target population of the model, and the interventions and outcomes represented. Best practices relating to the specific characteristics of model structure, and which characteristics of the problem might be most easily represented in a specific modeling method, are presented. Each section contains a number of recommendations that were iterated among the authors, as well as the wider modeling taskforce, jointly set up by the International Society for Pharmacoeconomics and Outcomes Research and the Society for Medical Decision Making.

A three-dimensional mathematical and computational model of necrotizing enterocolitis

Necrotizing enterocolitis (NEC) is a severe disease that affects the gastrointestinal (GI) tract of premature infants. Different areas of NEC research have often been isolated from one another and progress on the role of the inflammatory response in NEC, on the dynamics of epithelial layer healing, and on the positive effects of breast feeding have not been synthesized to produce a more integrated understanding of the pathogenesis of NEC. We seek to synthesize these areas of research by creating a mathematical model that incorporates the current knowledge on these aspects. Unlike previous models that are based on ordinary differential equations, our mathematical model takes into account not only transient effects but also spatial effects. A system of nonlinear transient partial differential equations is solved numerically using cell-centered finite differences and an explicit Euler method. The model is used to track the evolution of a prescribed initial injured area in the intestinal wall. It is able to produce pathophysiologically realistic results; decreasing the initial severity of the injury in the system and introducing breast feeding to the system both lead to healthier overall simulations, and only a small fraction of epithelial injuries lead to full-blown NEC. In addition, in the model, changing the initial shape of the injured area can significantly alter the overall outcome of a simulation. This finding suggests that taking into account spatial effects may be important in assessing the outcome for a given NEC patient. This model can provide a platform with which to test competing hypotheses regarding pathological mechanisms of inflammation in NEC, suggest experimental approaches by which to clarify pathogenic drivers of NEC, and may be used to derive potential intervention strategies.

Conceptualizing a model: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force--2

The appropriate development of a model begins with understanding the problem that is being represented. The aim of this article was to provide a series of consensus-based best practices regarding the process of model conceptualization. For the purpose of this series of articles, we consider the development of models whose purpose is to inform medical decisions and health-related resource allocation questions. We specifically divide the conceptualization process into two distinct components: the conceptualization of the problem, which converts knowledge of the health care process or decision into a representation of the problem, followed by the conceptualization of the model itself, which matches the attributes and characteristics of a particular modeling type with the needs of the problem being represented. Recommendations are made regarding the structure of the modeling team, agreement on the statement of the problem, the structure, perspective, and target population of the model, and the interventions and outcomes represented. Best practices relating to the specific characteristics of model structure and which characteristics of the problem might be most easily represented in a specific modeling method are presented. Each section contains a number of recommendations that were iterated among the authors, as well as among the wider modeling taskforce, jointly set up by the International Society for Pharmacoeconomics and Outcomes Research and the Society for Medical Decision Making.

Use of models in identification and prediction of physiology in critically ill surgical patients

BACKGROUND

With higher-throughput data acquisition and processing, increasing computational power, and advancing computer and mathematical techniques, modelling of clinical and biological data is advancing rapidly. Although exciting, the goal of recreating or surpassing in silico the clinical insight of the experienced clinician remains difficult. Advances toward this goal and a brief overview of various modelling and statistical techniques constitute the purpose of this review.

METHODS

A review of the literature and experience with models and physiological state representation and prediction after injury was undertaken.

RESULTS

A brief overview of models and the thinking behind their use for surgeons new to the field is presented, including an introduction to visualization and modelling work in surgical care, discussion of state identification and prediction, discussion of causal inference statistical approaches, and a brief introduction to new vital signs and waveform analysis.

CONCLUSION

Modelling in surgical critical care can provide a useful adjunct to traditional reductionist biological and clinical analysis. Ultimately the goal is to model computationally the clinical acumen of the experienced clinician.

At the biological modeling and simulation frontier

We provide a rationale for and describe examples of synthetic modeling and simulation (M&S) of biological systems. We explain how synthetic methods are distinct from familiar inductive methods. Synthetic M&S is a means to better understand the mechanisms that generate normal and disease-related phenomena observed in research, and how compounds of interest interact with them to alter phenomena. An objective is to build better, working hypotheses of plausible mechanisms. A synthetic model is an extant hypothesis: execution produces an observable mechanism and phenomena. Mobile objects representing compounds carry information enabling components to distinguish between them and react accordingly when different compounds are studied simultaneously. We argue that the familiar inductive approaches contribute to the general inefficiencies being experienced by pharmaceutical R&D, and that use of synthetic approaches accelerates and improves R&D decision-making and thus the drug development process. A reason is that synthetic models encourage and facilitate abductive scientific reasoning, a primary means of knowledge creation and creative cognition. When synthetic models are executed, we observe different aspects of knowledge in action from different perspectives. These models can be tuned to reflect differences in experimental conditions and individuals, making translational research more concrete while moving us closer to personalized medicine.