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

Abstract

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.

Keywords: QSP modeling; bioinformatics; computational biology; data science; drug development; systems biology; systems pharmacology.

Figure 1

Review of PubMed citations by year for the search query (“systems pharmacology model”) OR (“quantitative systems pharmacology”) OR (“QSP model”).

Figure 2

(A) Network visualization of how entities (nodes) relate to each other (edges) based on relations expressed in natural language. The frequency of a relation among entities can be represented with a varying thickness. Red nodes are central nervous system-related entities, green ones represent gut/brain-related annotations, while orange nodes have been classified into the peripheral nervous system. (B) The linguistic relations from the graph can be organized into a flow diagram, allowing the exploration of the directed effects between biological domains. This example makes visible how families of cells are interacting onto cytokines (leftmost to middle layers) and then how and what cytokines related back to the host cells (middle to rightmost layers).

Figure 3

Top left: Example of a metabolic network known as reverse cholesterol transport in humans, described in reference McQuade et al. (2017). Top right: Graph of flux correlations. The nodes correspond to edges from the network. The relationships between fluxes in a cholesterol metabolism model at equilibrium. Nodes in the graph are fluxes. Red nodes to the left indicate independent fluxes and blue nodes are dependent fluxes. An edge between a red node and another node indicates that the expression for the dependent flux contains the independent flux. Dependent fluxes have edges between them when they share a dependent flux. Middle: The matrix S is the linear-in-flux-expression (LIFE) version of the stoichiometric matrix corresponding to the top left network. x₁ corresponds to v₁, etc. Bottom: The span of the positive null space is shown. Note that the nullity of S is 4. However, the positive basis requires six positively independent elements. The positive basis permits choosing a_i ≥0 results in flux vectors that lie in the null space of S and the positive orthant.