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

Quantification of the endogenous growth hormone and prolactin lowering effects of a somatostatin-dopamine chimera using population PK/PD modeling

A phase 1 clinical trial in healthy male volunteers was conducted with a somatostatin-dopamine chimera (BIM23B065), from which information could be obtained on the concentration-effect relationship of the inhibition of pulsatile endogenous growth hormone and prolactin secretion. Endogenous growth hormone profiles were analyzed using a two-step deconvolution-analysis-informed population pharmacodynamic modeling approach, which was developed for the analyses of pulsatile profiles. Prolactin concentrations were modelled using a population pool model with a circadian component on the prolactin release. During treatment with BIM23B065, growth hormone secretion was significantly reduced (maximal effect [E-MAX] = - 64.8%) with significant reductions in the pulse frequency in two out of three multiple ascending dose cohorts. A circadian component in prolactin secretion was identified, modelled using a combination of two cosine functions with 24 h and 12 h periods. Dosing of BIM23B065 strongly inhibited (E-MAX = - 91%) the prolactin release and demonstrated further reduction of prolactin secretion after multiple days of dosing. This study quantified the concentration-effect relationship of BIM23B065 on the release of two pituitary hormones, providing proof of pharmacology of the chimeric actions of BIM23B065

A two-step deconvolution-analysis-informed population pharmacodynamic modeling approach for drugs targeting pulsatile endogenous compounds

Pharmacodynamic modeling of pulsatile endogenous compounds (e.g. growth hormone [GH]) is currently limited to the identification of a low number of pulses. Commonly used pharmacodynamic models are not able to capture the complexity of pulsatile secretion and therefore non-compartmental analyses are performed to extract summary statistics (mean, AUC, Cmax). The aim of this study was to develop a new quantification method that deals with highly variable pulsatile data by using a deconvolution-analysis-informed population pharmacodynamic modeling approach. Pulse frequency and pulse times were obtained by deconvolution analysis of 24 h GH profiles. The estimated pulse times then informed a non-linear mixed effects population pharmacodynamic model in NONMEM V7.3. The population parameter estimates were used to perform simulations that show agonistic and antagonistic drug effects on the secretion of GH. Additionally, a clinical trial simulation shows the application of this method in the quantification of a hypothetical drug effect that inhibits GH secretion. The GH profiles were modeled using a turnover compartment in which the baseline secretion, kout, pulse secretion width, amount at time point 0 and pulse amplitude were estimated as population parameters. Population parameters were estimated with low relative standard errors (ranging from 2 to 5%). Total body water (%) was identified as a covariate for pulse amplitude, baseline secretion and the pulse secretion width following a power relationship. Simulations visualized multiple gradients of a hypothetical drug that influenced the endogenous secretion of GH. The established model was able to fit and quantify the highly variable individual 24 h GH profiles over time. This pharmacodynamic model can be used to quantify drug effects that target other endogenous pulsatile compounds.</p

Immunogenicity in Clinical Practice and Drug Development: When is it Significant?

Managing immunogenicity in clinical practice and during drug development was a recent topic at the ASCPT 2019 annual meeting. This commentary expands on the discussion to facilitate a broader engagement across the community. The intent is to provide a rationale for ongoing research into the current gaps in assessing and interpreting immunogenicity in drug development and managing clinical immunogenicity for an approved drug. The following are highlighted: (i) Immunogenicity Considerations in Clinical Practice, (ii) Immunogenicity Testing and Current Limitations, (iii) Immunogenicity Risk Assessment and Mitigation, and (iv) Quantitative Systems Pharmacology (QSP) models of Immunogenicity

Best practices to maximize the use and reuse of quantitative and systems pharmacology models: recommendations from the United Kingdom quantitative and systems pharmacology network

The lack of standardization in the way that quantitative and systems pharmacology (QSP) models are developed, tested, and documented hinders their reproducibility, reusability, and expansion or reduction to alternative contexts. This in turn undermines the potential impact of QSP in academic, industrial, and regulatory frameworks. This article presents a minimum set of recommendations from the UK Quantitative and Systems Pharmacology Network (UK QSP Network) to guide QSP practitioners seeking to maximize their impact, and stakeholders considering the use of QSP models in their environment

A Quantitative Systems Pharmacology perspective on the importance of parameter identifiability

There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this there is no "gold standard" for model development and assessment in QSP. Moreover, there can be confusion over terminology such as model and parameter identifiability; complex and simple models; virtual populations; and other concepts, which leads to potential miscommunication and misapplication of methodologies within modelling communities, both the QSP community and related disciplines. This perspective article highlights the pros and cons of using simple (often identifiable) vs. complex (more physiologically detailed but often non-identifiable) models, as well as aspects of parameter identifiability, sensitivity and inference methodologies for model development and analysis. The paper distills the central themes of the issue of identifiability and optimal model size and discusses open challenges

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