Abstract
In the current era of antiviral drug therapy, combining multiple drugs is a primary approach for improving antiviral effects, reducing the doses of individual drugs, relieving the side effects of strong antiviral drugs, and preventing the emergence of drug-resistant viruses. Although a variety of new drugs have been developed for HIV, HCV and influenza virus, the optimal combinations of multiple drugs are incompletely understood. To optimize the benefits of multi-drugs combinations, we must investigate the interactions between the combined drugs and their target viruses. Mathematical models of viral infection dynamics provide an ideal tool for this purpose. Additionally, whether drug combinations computed by these models are synergistic can be assessed by two prominent drug combination theories, Loewe additivity and Bliss independence. By combining the mathematical modeling of virus dynamics with drug combination theories, we could show the principles by which drug combinations yield a synergistic effect. Here, we describe the theoretical aspects of multi-drugs therapy and discuss their application to antiviral research.
Highlights
Several landmark mathematical modeling studies of anti-retroviral therapy were reported in 1995 [1,2,3,4]
Thereafter, mathematical modeling has provided quantitative insights into antiviral drugs targeting HIV [5,6,7,8,9,10,11,12,13], hepatitis C virus (HCV) [14,15,16,17,18], HBV [19,20] and influenza virus [21,22]. These studies have elucidated the key steps of viral replication cycles and viral infection dynamics, such as the half-life of viruses and how viruses replicate in cells
To understand the principle behind optimal drug combinations and doses, we focused on the essential features of HCV replication and the mechanisms of the antiviral drugs (Figure 1A)
Summary
Several landmark mathematical modeling studies of anti-retroviral therapy were reported in 1995 [1,2,3,4]. We discuss two primary concepts of drug combination theory: Loewe additivity and Bliss independence We apply these models to viral replication in a host cell, and discuss their utility for understanding two-drug interactions and viral dynamics. The effects of the drug combination at specific doses could be evaluated by the Loewe additivity In this way, we could estimate the synergistic dose point of a drug combination that enhances the anti-HCV effects (Figure 1B). Unlike the Loewe additivity, the Bliss independence can evaluate the effect of a drug combination without requiring dose–response curves of the single drugs. Applying drug combination theories to these studies, mathematical models of HCV dynamics could be used to optimize the anti-HCV drug dosage and combination, thereby enhancing the anti-viral effect and reducing the risk of drug-resistant viruses (Figure 3)
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