A pipeline for testing drug mechanism of action and combination therapies: From microarray data to simulations via Linear-In-Flux-Expressions: Testing four-drug combinations for tuberculosis treatment.

Computational methods are becoming commonly used in many areas of medical research. Recently, the modeling of biological mechanisms associated with disease pathophysiology have benefited from approaches such as Quantitative Systems Pharmacology (briefly QSP) and Physiologically Based Pharmacokinetics (briefly PBPK). These methodologies show the potential to enhance, if not substitute animal models. The main reasons for this success are the high accuracy and low cost. Solid mathematical foundations of such methods, such as compartmental systems and flux balance analysis, provide a good base on which to build computational tools. However, there are many choices to be made in model design, that will have a large impact on how these methods perform as we scale up the network or perturb the system to uncover the mechanisms of action of new compounds or therapy combinations. A computational pipeline is presented here that starts with available-omic data and utilizes advanced mathematical simulations to inform the modeling of a biochemical system. Specific attention is devoted to creating a modular workflow, including the mathematical rigorous tools to represent complex chemical reactions, and modeling drug action in terms of its impact on multiple pathways. An application to optimizing combination therapy for tuberculosis shows the potential of the approach.

History and Future Perspectives on the Discipline of Quantitative Systems Pharmacology Modeling and Its Applications.

Mathematical biology and pharmacology models have a long and rich history in the fields of medicine and physiology, impacting our understanding of disease mechanisms and the development of novel therapeutics. With an increased focus on the pharmacology application of system models and the advances in data science spanning mechanistic and empirical approaches, there is a significant opportunity and promise to leverage these advancements to enhance the development and application of the systems pharmacology field. In this paper, we will review milestones in the evolution of mathematical biology and pharmacology models, highlight some of the gaps and challenges in developing and applying systems pharmacology models, and provide a vision for an integrated strategy that leverages advances in adjacent fields to overcome these challenges.

Experimental and Mathematical Analyses Relating Circadian Period and Phase of Entrainment in Neurospora crassa.

Circadian rhythms are observed in most organisms on earth and are known to play a major role in successful adaptation to the 24-h cycling environment. Circadian phenotypes are characterized by a free-running period that is observed in constant conditions and an entrained phase that is observed in cyclic conditions. Thus, the relationship between the free-running period and phase of entrainment is of interest. A popular simple rule has been that the entrained phase is the expression of the period in a cycling environment (i.e., that a short period causes an advanced phase and a long period causes a delayed phase). However, there are experimental data that are not explained by this simple relationship, and no systematic study has been done to explore all possible period-phase relationships. Here, we show the existence of stable period-phase relationships that are exceptions to this rule. First, we analyzed period-phase relationships using populations with different degrees of genome complexity. Second, we generated isogenic F1 populations by crossing 14 classical period mutants to the same female and analyzed 2 populations with a short period/delayed phase and a long period/advanced phase. Third, we generated a mathematical model to account for such variable relationships between period and phase. Our analyses support the view that the circadian period of an organism is not the only predictor of the entrained phase.

Single embryo-resolution quantitative analysis of reporters permits multiplex spatial cis-regulatory analysis.

Cis-regulatory modules (CRMs) control spatiotemporal gene expression patterns in embryos. While measurement of quantitative CRM activities has become efficient, measurement of spatial CRM activities still relies on slow, one-by-one methods. To overcome this bottleneck, we have developed a high-throughput method that can simultaneously measure quantitative and spatial CRM activities. The new method builds profiles of quantitative CRM activities measured at single-embryo resolution in many mosaic embryos and uses these profiles as a 'fingerprint' of spatial patterns. We show in sea urchin embryos that the new method, Multiplex and Mosaic Observation of Spatial Information encoded in Cis-regulatory modules (MMOSAIC), can efficiently predict spatial activities of new CRMs and can detect spatial responses of CRMs to gene perturbations. We anticipate that MMOSAIC will facilitate systems-wide functional analyses of CRMs in embryos.

Linear-In-Flux-Expressions Methodology: Toward a Robust Mathematical Framework for Quantitative Systems Pharmacology Simulators.

Quantitative Systems Pharmacology (QSP) modeling is increasingly used as a quantitative tool for advancing mechanistic hypotheses on the mechanism of action of a drug, and its pharmacological effect in relevant disease phenotypes, to enable linking the right drug to the right patient. Application of QSP models relies on creation of virtual populations for simulating scenarios of interest. Creation of virtual populations requires 2 important steps, namely, identification of a subset of model parameters that can be associated with a phenotype of disease and development of a sampling strategy from identified distributions of these parameters. We improve on existing sampling methodologies by providing a means of representing the structural relationship across model parameters and describing propagation of variability in the model. This gives a robust, systematic method for creating a virtual population. We have developed the Linear-In-Flux-Expressions (LIFE) method to simulate variability in patient pharmacokinetics and pharmacodynamics using relationships between parameters at baseline to create a virtual population. We demonstrate the importance of this methodology on a model of cholesterol metabolism. The LIFE methodology brings us a step closer toward improved QSP simulators through enhanced capture of the observed variability in drug and disease clinical data.