1 Introduction
The application of theoretical and mathematical analyses has significantly improved our understanding of the biological systems (Mackey and Maini, 2015). Notable instances include the use of Ehrlich's receptor theory; the Michaelis–Menten description of enzyme kinetics; Hodgkin and Huxley's work on the dynamics of neuronal axon potentials; and Fisher, Haldane, and Wright's unification of Mendelian genetics, dynamics of infectious diseases, Darwinian evolution, and of course physiology. Thus, the field of “Mathematical Biology/Physiology,” as it is often described, has a long and successful history, and details can be found in many established textbooks (Antoniouk Alexandra and Melnik Roderick, 2012; Deutsch et al., 2007; Keener and Sneyd, 2009). One could likely argue that the advances in the description of physiological events, at either small or higher scales, have significantly outpaced the mathematical developments of the description of cellular and molecular events. This apparent “void” was slowly filled by the emergence of the field of “Systems Biology” (Alberhina and Westerhoff, 2005; Cassman et al., 2007; Covert, 2015; Ingalls, 2013; Palsson, 2011; Rigoutsos and Stephanopoulos, 2007).
The developments in the field of systems biology have been phenomenal, particularly the focus shift toward the “unexplored” territories defined by the cell, the intracellular mechanisms, and their emergent dynamic properties. Systems biology formalized the deployment of a systems engineering perspective to gain insights into the underlying design principles of biological networks. Important features shared between the dynamics of biological and engineered systems include, among others, robustness, optimality, and flexibility (Androulakis, 2015; Csete and Doyle, 2002). Biological systems generally function within a tightly constrained operational regime whereby deviations from this optimal regime have pathological implications. Furthermore, the robustness inherent to the dynamics of biological signaling networks is apparent to both biologists and systems engineers alike. While the definition of the term robustness in a biological context is slightly ambiguous, we take the robustness of biological systems to imply both stability to external perturbations as well as a robust flexibility either in response to or in anticipation of the changing external conditions (Kitano, 2004). Thus, the great successes of the 20th century biology can generally be defined by a strong emphasis on the characterization of the biological significance of individual signaling entities. Only with the recent advent of high-throughput quantitative molecular biology techniques, amid the completion of the Human Genome Project, has the construction of networks between individual signaling entities even become possible, enabling the application of mathematical formalisms to complex biological systems. While the enumeration of individual system components continues to progress at a rapid pace through the discovery of new biological entities, there is now a growing focus, based on systems biology, on understanding the underlying operating principles that describe how individual system components interact to yield robust emergent phenomena across multiple physiological scales (Gunawardena, 2013). Given that biological signaling pathways have arisen from evolutionary adjustments via natural selection, the apparent design solutions in biology have remarkably much in common with the design principles of complex engineered systems. Nonetheless, the concept of analyzing biological signaling pathways in the form of networks has naturally lent itself to comparison with engineered systems. This similarity has led to the discovery that biological signaling pathways have many of the essential features of the network structure found in well-designed complex engineered systems; these include modularity, feedback regulation, and redundancy (Androulakis, 2014, 2016).
In the following sections, we propose how these challenges would be addressed within the context of quantitative systems pharmacology (QSP). We elaborate on the multifaceted aspects encompassed by QSP models, namely (a) the integration of pharmacokinetic (PK) modeling with pharmacodynamics (PD) to explain drug exposure–response relationships in the context of a network of multiple interacting targets; (b) identification of the relevant network structure from high-dimensional -omics data; and (c) the challenge of accounting for these interactions within the context of a host that responds to a continually variable external environment. The progression of PK to PD and the link between -omics analysis and PD are presented in parallel, where the incorporation of these elements constitutes the QSP framework.
2 The emergence of QSP modeling
QSP explores integrative and model-based approaches leveraging our vast understanding and knowledge of computational tools across systems biology, PKs/PDs, and pharmacology (Berger and Iyengar, 2011). Classical pharmacology models generally consist of simple(r) transduction pathways attempting to link drug administration and drug response without accounting for internal system interactions (Danhof, 2016). Modeling in pharmacology dates back to Gerhard Levy’s pioneering work on the dynamics of pharmacologic effects (Levy, 1964, 1966). On the other hand, QSP has been defined as using both -omics-based experimental methods as well as in silico approaches to provide a data-driven, mechanistic basis for the interactions between the drug and its targets within the context of a homeostatic regulatory network (Zhao and Iyengar, 2012). As such, QSP provided a strong impetus for identifying the complex interactions that exist between the genotype (genetic makeup) and the disease phenotype (observable characteristic) that may otherwise remain unexplored (Yang et al., 2010). A key outcome of such focus is the ability to probe the link between genetic variability and environmental factors, inherently improving the ability to map the spectrum of patient responses to interindividual differences across physiological scales (Stern et al., 2016). In this context, integrated analysis of complex QSP models rationalizes drug action for the prediction of an individual's response to treatment, for the assessment of efficacy and safety, and for the rational design and explanation of clinical trial results. QSP models of this kind are most likely developed during the later preclinical stages and are expected to provide critical insight during clinical development (Ermakov et al., 2014; Kimko and Duffull, 2003; Kimko et al., 2011).
Over the years, mathematical and computational models substantially increased in complexity due to advances in biology, pharmacology, and physiology as well as due to our ability to accumulate high-quality and high-dimensional data. However, a biological model is only as good as the data from which it is built. In the past decades, the tremendous breakthroughs made in sequencing technology revolutionized our access to information about the human genome, transcriptome, proteome, and metabolome (Stephens et al., 2015). Fittingly, the capabilities of data storage and sharing drastically improved at the same time. Cloud computing today allows for faster and better dissemination of data, thus increasing the awareness of available information for researchers seeking to develop computer models (Murdoch and Detsky, 2013). In the meantime, pharmacologists also adopted advanced computational approaches. The synchronous combination of these two advancements has enabled QSP to become an invaluable tool for pharmaceutical development (Lee et al., 2011). Nevertheless, QSP should not be reduced to developing complex computational models. We argue that QSP instead provides a framework by which drugs are placed in an appropriate and broader context (Androulakis, 2016). Numerous reports discussed the opportunities, progress, and successes of QSP (Bai, 2013; Leil and Bertz, 2014; Sorger et al., 2011).
2.1 Multiscale modeling: Be...