Discovery and Model-Informed Drug Development of a Controlled-Release Formulation of Nonracemic Amisulpride that Reduces Plasma Exposure but Achieves Pharmacodynamic Bioequivalence in the Brain.

Nonracemic amisulpride (SEP-4199) is an investigational 85:15 ratio of aramisulpride to esamisulpride and currently in clinical trials for the treatment of bipolar depression. During testing of SEP-4199, a pharmacokinetic/pharmacodynamic (PK/PD) disconnect was discovered that prompted the development of a controlled-release (CR) formulation with improved therapeutic index for QT prolongation. Observations that supported the development of a CR formulation included (i) plasma concentrations of amisulpride enantiomers were cleared within 24-hours, but brain dopamine D2 receptor (D2R) occupancies, although achieving stable levels during this time, required 5 days to return to baseline; (ii) nonracemic amisulpride administered to non-human primates produced significantly greater D2R occupancies during a gradual 6-hour administration compared with a single bolus; (iii) concentration-occupancy curves were left-shifted in humans when nonracemic amisulpride was gradually administered over 3 and 6 hours compared with immediate delivery; (iv) CR solid oral dose formulations of nonracemic amisulpride were able to slow drug dissolution in vitro and reduce peak plasma exposures in vivo in human subjects. By mathematically solving for a drug distribution step into an effect compartment, and for binding to target receptors, the discovery of a novel PK/PD model (termed here as Distribution Model) accounted for hysteresis between plasma and brain, a lack of receptor saturation, and an absence of accumulation of drug occupancy with daily doses. The PK/PD disconnect solved by the Distribution Model provided model-informed drug development to continue in Phase III using the non-bioequivalent CR formulation with diminished QT prolongation as dose-equivalent to the immediate release (IR) formulation utilized in Phase II.

Model reduction in mathematical pharmacology : Integration, reduction and linking of PBPK and systems biology models.

In this paper we present a framework for the reduction and linking of physiologically based pharmacokinetic (PBPK) models with models of systems biology to describe the effects of drug administration across multiple scales. To address the issue of model complexity, we propose the reduction of each type of model separately prior to being linked. We highlight the use of balanced truncation in reducing the linear components of PBPK models, whilst proper lumping is shown to be efficient in reducing typically nonlinear systems biology type models. The overall methodology is demonstrated via two example systems; a model of bacterial chemotactic signalling in Escherichia coli and a model of extracellular regulatory kinase activation mediated via the extracellular growth factor and nerve growth factor receptor pathways. Each system is tested under the simulated administration of three hypothetical compounds; a strong base, a weak base, and an acid, mirroring the parameterisation of pindolol, midazolam, and thiopental, respectively. Our method can produce up to an 80% decrease in simulation time, allowing substantial speed-up for computationally intensive applications including parameter fitting or agent based modelling. The approach provides a straightforward means to construct simplified Quantitative Systems Pharmacology models that still provide significant insight into the mechanisms of drug action. Such a framework can potentially bridge pre-clinical and clinical modelling - providing an intermediate level of model granularity between classical, empirical approaches and mechanistic systems describing the molecular scale.

Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends.

Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed.

A combined model reduction algorithm for controlled biochemical systems.

BACKGROUND: Systems Biology continues to produce increasingly large models of complex biochemical reaction networks. In applications requiring, for example, parameter estimation, the use of agent-based modelling approaches, or real-time simulation, this growing model complexity can present a significant hurdle. Often, however, not all portions of a model are of equal interest in a given setting. In such situations methods of model reduction offer one possible approach for addressing the issue of complexity by seeking to eliminate those portions of a pathway that can be shown to have the least effect upon the properties of interest. METHODS: In this paper a model reduction algorithm bringing together the complementary aspects of proper lumping and empirical balanced truncation is presented. Additional contributions include the development of a criterion for the selection of state-variable elimination via conservation analysis and use of an 'averaged' lumping inverse. This combined algorithm is highly automatable and of particular applicability in the context of 'controlled' biochemical networks. RESULTS: The algorithm is demonstrated here via application to two examples; an 11 dimensional model of bacterial chemotaxis in Escherichia coli and a 99 dimensional model of extracellular regulatory kinase activation (ERK) mediated via the epidermal growth factor (EGF) and nerve growth factor (NGF) receptor pathways. In the case of the chemotaxis model the algorithm was able to reduce the model to 2 state-variables producing a maximal relative error between the dynamics of the original and reduced models of only 2.8% whilst yielding a 26 fold speed up in simulation time. For the ERK activation model the algorithm was able to reduce the system to 7 state-variables, incurring a maximal relative error of 4.8%, and producing an approximately 10 fold speed up in the rate of simulation. Indices of controllability and observability are additionally developed and demonstrated throughout the paper. These provide insight into the relative importance of individual reactants in mediating a biochemical system's input-output response even for highly complex networks. CONCLUSIONS: Through application, this paper demonstrates that combined model reduction methods can produce a significant simplification of complex Systems Biology models whilst retaining a high degree of predictive accuracy. In particular, it is shown that by combining the methods of proper lumping and empirical balanced truncation it is often possible to produce more accurate reductions than can be obtained by the use of either method in isolation.