mathematical pharmacology  (MP) Session 2

Abstract: When a drug enters the blood stream, on its way to a pharmaceutical target, it finds many proteins and lipids on its way which are eager to bind it and thus prevent it from reaching its destination. Whilst this may first adversely affect the beneficial effect of the drug, the drug bound to the proteins is not lost and may eventually still reach its target. We discuss a class of models proposed to study the impact of proteins and lipids on the efficacy of drugs, and show that affinity plays a key role in answering the question in the title. Close

Abstract: Complexity of biological systems arises in part due to the nonlinearity of these systems. Mathematical models in biology and pharmacology often include this nonlinearity in the form of feedback mechanisms. Nonlinear models can hide interesting dynamic behaviours and as such warrant careful study. A case in point is a nonlinear model of prolactin (PRL) response to antipsychotic medication, which includes a positive feedback. Increased secretion of PRL is a side-effect of antipsychotic drugs. For repeated drug challenges, the intensity of the PRL response to the second drug challenge is lower than to the first challenge, if the duration between the two drug challenges is short. This implies that the intensity of the PRL response may be limited by a pool of PRL in a precursor compartment. The pharmacodynamics of PRL concentration in plasma has been modelled by means of a precursor-pool model which includes a positive feedback loop of plasma PRL on its own synthesis in the pool, making it a nonlinear system [1]. Even though the nonlinear model fits kinetic data from a small temporal window well, it results in unexplained multi-stationarity. We have used mathematical analysis to gain insight into this unexplained model behavior. We have shown that the nonlinearity has resulted in multiple steady states with different stability properties. Stability of each steady state, coupled with the pharmacokinetics of the drug, plays a role in determining which steady state is predicted by the model. We have been able to deduce a parametric restriction under which the desired steady state is stable [2]. The work highlights the importance of mathematical analysis in systems-pharmacological models.References:[1] Stevens J, Ploeger B, Hammarlund-Udenaes M, Osswald G, van der Graaf PH, Danhof M and de Lange ECM, Mechanism-based PKPD model for the prolactin biological system response following an acute dopamine inhibition challenge: quantitative extrapolation to humans. Journal of Pharmacokinetics and Pharmacodynamics. 2012;39(5):463-477.[2] Bakshi S, de Lange ECM, vd Graaf Piet H, Danhof M and Peletier LA, Understanding the behaviour of systems pharmacology models using mathematical analysis of differential equations - prolactin modelling as a case study. CPT: Pharmacometrics and Systems Pharmacology, 2016. Close

Abstract: Worldwide, noncompliance to drug regimens poses a significant challenge to effective treatment strategies. The WHO estimate that only 50% of patients living with chronic illness in developed countries adhere to prescribed treatment. In order to tackle this issue, an effective method of monitoring compliance is necessary.In this talk we consider reverse iontophoresis as a drug monitoring technique. This involves placing two electrodes on the skin and passing a small current between them, encouraging the movement of ions from the plasma to the skin surface where it is collected. It has been shown that prolonged systemic presence of a drug can result in a build-up of that drug in the skin which affects the reverse iontophoresis reading. We seek to determine, of the drug collected, how much has come from the skin and how much from the plasma.Our aim is to interpret reverse iontophoresis readings with particular interest in inferring the recent drug taking history of the patient. In order to do this a three model system is created: the first model predicts the systemic levels of the drug post administration, the second model describes the reservoir formation in the stratum corneum via a combination of diffusion and advection with cell movement and the third model, which is the focus of this talk, models the extraction of the reservoir via reverse iontophoresisOur extraction model takes the form of a coupled reaction-diffusion-convection system which is analysed to explore the importance of key model parameters, most notably binding rates, on the ability to effectively monitor drug levels using reverse iontophoresis across the skin. We go on to discuss the implications of our modelling and results for drug monitoring. Close

Abstract: Drug treatment schedules significantly influence the success of pharmacological intervention. Even though quantitative systems pharmacology (QSP) models are used to understand the interplay between the pharmacological system and drug action, their ability to guide drug treatment schedules is still underutilised.Here we adopt a method widely used in electrical and control engineering to inform on the timescales of QSP models in response temporal changes in oscillatory inputs. The frequency-domain response analysis (FRA) is based on the linearization of a nonlinear model around its steady states. FRA provides insights into the presence and magnitude of time-delays, the stability and performance of QSP models. Thus, FRA enables the identification of dosing frequencies for which the response of the QSP model is either amplified or attenuated. This facilitates not only the characterisation of QSP models but also aids the understanding of the pharmacological system and the optimisation of treatment schedules or the identification of signature profiles.By providing an interactive and semi-automated application based on R and the Shiny package we make FRA easy to use and accessible to everyone without the need to understand the underlying mathematics. Close

Abstract: Renal cell carcinoma (RCC) is the 8th most common cancer in UK and the most lethal urological malignancy.Resistance to treatment is almost ubiquitous in advanced disease and urgently warrants further investigation.Five year survival is approximately 40% overall and <10% with metastasis [Nat Rev Urol 2011;8:255]. NoMethod is available to predict RCC response to targeted therapy, nor to accurately identify high-risk patientsfor entry into adjuvant trials. The current study bridges genotype and phenotype towards more effectiveclinical tools for renal cancer medicine. Genetic control is realized by complex relationships between manycomponents, including numerous uncharacterised genes and unknown context-specific functions [Cell2011;144:986]. At the single-cell level, phenotype is governed by many concurrent biochemical reactionsthat form pleiotropic networks with nested hierarchical structure, and hence modularity [Science2002;297:1551]. Systematic approaches to understand the properties of these networks and so inform controlof cell behaviour include static systems-wide functional gene networks and executable models. Modellingrestricted to prior knowledge misses components and interactions, limiting the representation scope. In orderto address this knowledge gap, we are reverse engineering context-specific modularised global genenetworks. This data driven approach spans molecular and clinical parameters.Four representative RCC cell lines were selected from a panel of sixteen for transcriptome profilingat multiple time points following exposure to sunitinib, a front line drug. These representative cell lines wereidentified by unsupervised learning with data on gene expression, mutational status and sunitinib sensitivity.Modularity analysis of the drug response time course with a novel algorithm (NetNC) identified regulatedfunctionally coherent subnetworks specific to cell line (e.g. drug-resistant) or condition (e.g. hypoxia). Thefigure shows a modularised sunitinib response network, which illuminates mechanisms of cell killing anddrug resistance. Sunitinib treatment elicits substantially fewer changed network modules in hypoxicconditions relative to 'normoxia' suggesting the action of sunitinib on canonical targets (e.g. VEGFR)simulates hypoxia in RCC, which may synergise with putative anti-angiogenic action in vivo. Interestingly,induction of an apoptosis regulation module was found only in a metastatic cell line in hypoxia, includingupregulation of canonical apoptosis inhibitors BCL2 and BCLXL. Focussed analysis of the apoptosispathway across the sunitinib response time course uncovered expression changes in regulatory genes for asecond cell line. Follow-up experiments investigated chemical abrogation of apoptosis resistance alongsidesunitinib treatment as a potentially synergistic combination therapy. Close