Macrophage phenotype transitions in a stochastic gene-regulatory network model.

Polarization is the process by which a macrophage cell commits to a phenotype based on external signal stimulation. To know how this process is affected by random fluctuations and events within a cell is of utmost importance to better understand the underlying dynamics and predict possible phenotype transitions. For this purpose, we develop a stochastic modeling approach for the macrophage polarization process. We classify phenotype states using the Robust Perron Cluster Analysis and quantify transition pathways and probabilities by applying Transition Path Theory. Depending on the model parameters, we identify four bistable and one tristable phenotype configuration. We find that bistable transitions are fast but their states less robust. In contrast, phenotype transitions in the tristable situation have a comparatively long time duration, which reflects the robustness of the states. The results indicate parallels in the overall transition behavior of macrophage cells with other heterogeneous and plastic cell types, such as cancer cells. Our approach allows for a probabilistic interpretation of macrophage phenotype transitions and biological inference on phenotype robustness. In general, the methodology can easily be adapted to other systems where random state switches are known to occur.

A physiological model of the inflammatory-thermal-pain-cardiovascular interactions during an endotoxin challenge.

KEY POINTS: Inflammation in response to bacterial endotoxin challenge impacts physiological functions, including cardiovascular, thermal and pain dynamics, although the mechanisms are poorly understood. We develop an innovative mathematical model incorporating interaction pathways between inflammation and physiological processes observed in response to an endotoxin challenge. We calibrate the model to individual data from 20 subjects in an experimental study of the human inflammatory and physiological responses to endotoxin, and we validate the model against human data from an independent study. Using the model to simulate patient responses to different treatment modalities reveals that a multimodal treatment combining several therapeutic strategies gives the best recovery outcome. ABSTRACT: Uncontrolled, excessive production of pro-inflammatory mediators from immune cells and traumatized tissues can cause systemic inflammatory conditions such as sepsis, one of the ten leading causes of death in the USA, and one of the three leading causes of death in the intensive care unit. Understanding how inflammation affects physiological processes, including cardiovascular, thermal and pain dynamics, can improve a patient's chance of recovery after an inflammatory event caused by surgery or a severe infection. Although the effects of the autonomic response on the inflammatory system are well-known, knowledge about the reverse interaction is lacking. The present study develops a mathematical model analyzing the inflammatory system's interactions with thermal, pain and cardiovascular dynamics in response to a bacterial endotoxin challenge. We calibrate the model with individual data from an experimental study of the inflammatory and physiological responses to a one-time administration of endotoxin in 20 healthy young men and validate it against data from an independent endotoxin study. We use simulation to explore how various treatments help patients exposed to a sustained pathological input. The treatments explored include bacterial endotoxin adsorption, antipyretics and vasopressors, as well as combinations of these. Our findings suggest that the most favourable recovery outcome is achieved by a multimodal strategy, combining all three interventions to simultaneously remove endotoxin from the body and alleviate symptoms caused by the immune system as it fights the infection.

Bifurcation and sensitivity analysis reveal key drivers of multistability in a model of macrophage polarization.

In this paper, we present and analyze a mathematical model for polarization of a single macrophage which, despite its simplicity, exhibits complex dynamics in terms of multistability. In particular, we demonstrate that an asymmetry in the regulatory mechanisms and parameter values is important for observing multiple phenotypes. Bifurcation and sensitivity analyses show that external signaling cues are necessary for macrophage commitment and emergence to a phenotype, but that the intrinsic macrophage pathways are equally important. Based on our numerical results, we formulate hypotheses that could be further investigated by laboratory experiments to deepen our understanding of macrophage polarization.

Methods for determining key components in a mathematical model for tumor-immune dynamics in multiple myeloma.

In this work, we analyze a mathematical model we introduced previously for the dynamics of multiple myeloma and the immune system. We focus on four main aspects: (1) obtaining and justifying ranges and values for all parameters in the model; (2) determining a subset of parameters to which the model is most sensitive; (3) determining which parameters in this subset can be uniquely estimated given certain types of data; and (4) exploring the model numerically. Using global sensitivity analysis techniques, we found that the model is most sensitive to certain growth, loss, and efficacy parameters. This analysis provides the foundation for a future application of the model: prediction of optimal combination regimens in patients with multiple myeloma.

Insights into pathological mechanisms and interventions revealed by analyzing a mathematical model for cone metabolism.

This work analyzes a mathematical model for the metabolic dynamics of a cone photoreceptor, which is the first model to account for energy generation from fatty acids oxidation of shed photoreceptor outer segments (POS). Multiple parameter bifurcation analysis shows that joint variations in external glucose, the efficiency of glucose transporter 1 (GLUT1), lipid utilization for POS renewal, and oxidation of fatty acids affect the cone's metabolic vitality and its capability to adapt under glucose-deficient conditions. The analysis further reveals that when glucose is scarce, cone viability cannot be sustained by only fueling energy production in the mitochondria, but it also requires supporting anabolic processes to create lipids necessary for cell maintenance and repair. In silico experiments are used to investigate how the duration of glucose deprivation impacts the cell without and with a potential GLUT1 or oxidation of fatty acids intervention as well as a dual intervention. The results show that for prolonged duration of glucose deprivation, the cone metabolic system does not recover with higher oxidation of fatty acids and requires greater effectiveness of GLUT1 to recover. Finally, time-varying global sensitivity analysis (GSA) is applied to assess the sensitivity of the model outputs of interest to changes and uncertainty in the parameters at specific times. The results reveal a critical temporal window where there would be more flexibility for interventions to rescue a cone cell from the detrimental consequences of glucose shortage.

A tutorial review of mathematical techniques for quantifying tumor heterogeneity.

Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.

Transport of a 1D viscoelastic actin-myosin strip of gel as a model of a crawling cell.

Cell crawling is an important biological phenomenon because it underlies coordinated cell movement in morphogenesis, cancer and wound healing. This phenomenon is based on protrusion at the cell's leading edge, retraction at the rear, contraction and graded adhesion powered by the dynamics of actin and myosin protein networks. A few one-dimensional models successfully explain an anteroposterior organization of the motile cell, but don't sufficiently explore the viscoelastic nature of the actin-myosin gel. We develop and numerically solve a model of a treadmilling strip of viscoelastic actin-myosin gel. The results show that the strip translocates steadily as a traveling pulse, without changing length, and that protein densities, velocities and stresses become stationary. The simulations closely match the observed forces, movements and protein distributions in the living cell.