Mathematical modelling of the influence of ACE I/D polymorphism on blood pressure and antihypertensive therapy

The angiotensin-converting enzyme (ACE) gene (ACE) insertion/deletion (I/D) polymorphism raises the possibility of personalising ACE inhibitor therapy to optimise its efficiency and reduce side effects in genetically distinct subgroups. However, the extent of its influence among these subgroups is unknown. Therefore, we extended our computational model of blood pressure regulation to investigate the effect of the ACE I/D polymorphism on haemodynamic parameters in humans undergoing antihypertensive therapy. The model showed that the dependence of blood pressure on serum ACE activity is a function of saturation and therefore, the lack of association between ACE I/D and blood pressure levels may be due to high ACE activity in specific populations. Additionally, in an extended model simulating the effects of different classes of antihypertensive drugs, we explored the relationship between ACE I/D and the efficacy of inhibitors of the renin-angiotensin-aldosterone system. The model predicted that the response of cardiovascular and renal parameters to treatment directly depends on ACE activity. However, significant differences in parameter changes were observed only between groups with high and low ACE levels, while different ACE I/D genotypes within the same group had similar changes in absolute values. We conclude that a single genetic variant is responsible for only a small fraction of heredity in treatment success and its predictive value is limited.

Mathematical modeling of antihypertensive therapy

Hypertension is a multifactorial disease arising from complex pathophysiological pathways. Individual characteristics of patients result in different responses to various classes of antihypertensive medications. Therefore, evaluating the efficacy of therapy based on in silico predictions is an important task. This study is a continuation of research on the modular agent-based model of the cardiovascular and renal systems (presented in the previously published article). In the current work, we included in the model equations simulating the response to antihypertensive therapies with different mechanisms of action. For this, we used the pharmacodynamic effects of the angiotensin II receptor blocker losartan, the calcium channel blocker amlodipine, the angiotensin-converting enzyme inhibitor enalapril, the direct renin inhibitor aliskiren, the thiazide diuretic hydrochlorothiazide, and the β-blocker bisoprolol. We fitted therapy parameters based on known clinical trials for all considered medications, and then tested the model's ability to show reasonable dynamics (expected by clinical observations) after treatment with individual drugs and their dual combinations in a group of virtual patients with hypertension. The extended model paves the way for the next step in personalized medicine that is adapting the model parameters to a real patient and predicting his response to antihypertensive therapy. The model is implemented in the BioUML software and is available at https://gitlab.sirius-web.org/virtual-patient/antihypertensive-treatment-modeling.

BioUML-towards a universal research platform

BioUML (https://www.biouml.org)—is a web-based integrated platform for systems biology and data analysis. It supports visual modelling and construction of hierarchical biological models that allow us to construct the most complex modular models of blood pressure regulation, skeletal muscle metabolism, COVID-19 epidemiology. BioUML has been integrated with git repositories where users can store their models and other data. We have also expanded the capabilities of BioUML for data analysis and visualization of biomedical data: (i) any programs and Jupyter kernels can be plugged into the BioUML platform using Docker technology; (ii) BioUML is integrated with the Galaxy and Galaxy Tool Shed; (iii) BioUML provides two-way integration with R and Python (Jupyter notebooks): scripts can be executed on the BioUML web pages, and BioUML functions can be called from scripts; (iv) using plug-in architecture, specialized viewers and editors can be added. For example, powerful genome browsers as well as viewers for molecular 3D structure are integrated in this way; (v) BioUML supports data analyses using workflows (own format, Galaxy, CWL, BPMN, nextFlow). Using these capabilities, we have initiated a new branch of the BioUML development—u-science—a universal scientific platform that can be configured for specific research requirements.

Thoroughly Calibrated Modular Agent-Based Model of the Human Cardiovascular and Renal Systems for Blood Pressure Regulation in Health and Disease

Here we present a modular agent-based mathematical model of the human cardiovascular and renal systems. It integrates the previous models primarily developed by A. C. Guyton, F. Karaaslan, K. M. Hallow, and Y. V. Solodyannikov. We performed the model calibration to find an equilibrium state within the normal vital sign ranges for a healthy adult. We verified the model's abilities to reproduce equilibrium states with abnormal physiological values related to different combinations of cardiovascular diseases (such as systemic hypertension, chronic heart failure, pulmonary hypertension, etc.). For the model creation and validation, we involved over 200 scientific studies covering known models of the human cardiovascular and renal functions, biosimulation platforms, and clinical measurements of physiological quantities in normal and pathological conditions. We compiled detailed documentation describing all equations, parameters and variables of the model with justification of all formulas and values. The model is implemented in BioUML and available in the web-version of the software.

BioUML: an integrated environment for systems biology and collaborative analysis of biomedical data

BioUML (homepage: http://www.biouml.org, main public server: https://ict.biouml.org) is a web-based integrated environment (platform) for systems biology and the analysis of biomedical data generated by omics technologies. The BioUML vision is to provide a computational platform to build virtual cell, virtual physiological human and virtual patient. BioUML spans a comprehensive range of capabilities, including access to biological databases, powerful tools for systems biology (visual modelling, simulation, parameters fitting and analyses), a genome browser, scripting (R, JavaScript) and a workflow engine. Due to integration with the Galaxy platform and R/Bioconductor, BioUML provides powerful possibilities for the analyses of omics data. The plug-in-based architecture allows the user to add new functionalities using plug-ins. To facilitate a user focus on a particular task or database, we have developed several predefined perspectives that display only those web interface elements that are needed for a specific task. To support collaborative work on scientific projects, there is a central authentication and authorization system (https://bio-store.org). The diagram editor enables several remote users to simultaneously edit diagrams.

Model composition through model reduction: a combined model of CD95 and NF-κB signaling pathways

Background

Many mathematical models characterizing mechanisms of cell fate decisions have been constructed recently. Their further study may be impossible without development of methods of model composition, which is complicated by the fact that several models describing the same processes could use different reaction chains or incomparable sets of parameters. Detailed models not supported by sufficient volume of experimental data suffer from non-unique choice of parameter values, non-reproducible results, and difficulty of analysis. Thus, it is necessary to reduce existing models to identify key elements determining their dynamics, and it is also required to design the methods allowing us to combine them.

Results

Here we propose a new approach to model composition, based on reducing several models to the same level of complexity and subsequent combining them together. Firstly, we suggest a set of model reduction tools that can be systematically applied to a given model. Secondly, we suggest a notion of a minimal complexity model. This model is the simplest one that can be obtained from the original model using these tools and still able to approximate experimental data. Thirdly, we propose a strategy for composing the reduced models together. Connection with the detailed model is preserved, which can be advantageous in some applications. A toolbox for model reduction and composition has been implemented as part of the BioUML software and tested on the example of integrating two previously published models of the CD95 (APO-1/Fas) signaling pathways. We show that the reduced models lead to the same dynamical behavior of observable species and the same predictions as in the precursor models. The composite model is able to recapitulate several experimental datasets which were used by the authors of the original models to calibrate them separately, but also has new dynamical properties.

Conclusion

Model complexity should be comparable to the complexity of the data used to train the model. Systematic application of model reduction methods allows implementing this modeling principle and finding models of minimal complexity compatible with the data. Combining such models is much easier than of precursor models and leads to new model properties and predictions.