Abstract: Development of drugs with adequate action on the brain is highly challenging. Quantitative understanding is needed on the highly complex processes that govern the concentration-profile of a drug (???pharmacokinetics???), such as transport of the drug from blood to brain and subsequent intra-brain distribution to the target site. The target site of a drug is the region in the brain where the drug can interact with biological target molecules are expressed on the cells, to elicit the effect of the drug.To provide such quantitative understanding we have recently developed a multi-compartmental semi-physiologically-based pharmacokinetic (semi-PBPK) brain distribution model. This model is based on a system of ordinary differential equations (ODEs) to describe the pharmacokinetics of drugs in multiple physiological brain compartments [1]. However, it is important to also take into account local brain distribution, as target expression in the brain can substantially differ between different brain regions and recent insights have shown that target association and dissociation kinetics can change local pharmacokinetics [2].To further extend our understanding of local brain drug distribution processes in the brain, we are currently exploring inclusion of partial differential equations (PDE), to include the regional brain distribution. By that we aim to integrate both the drug distribution and target interaction kinetics in a 3D manner, to ultimately improve the prediction of drug action in the brain. [1] Yamamoto, Y. et al Development of a multi-compartmental brain pharmacokinetic model and prediction of human brain target site concentrations. Submitted[2] de Witte, W.E.A. et al. (2016) In vivo Target Residence Time and Kinetic Selectivity: The Association Rate Constant as Determinant. Trends Pharmacol. Sci. xx, 1-12

Abstract: Mathematical modelling and scientific computing are powerful tools for the analysis of cell signalling (cells integrating and reacting to signals from their environment in order to effect a response) in pharmacology. ???Analytical pharmacology???, which has its roots in classical receptor theory and largely focuses on equilibrium cell responses to drugs, provides a vital theoretical basis which underpins drug classification and prediction of drug mechanism of action. Efforts towards drug development and analysis will benefit from a better quantitative understanding of how cellular responses to signals such as drugs vary over time. Systems biology methods for modelling and analysing dynamics in cell signalling are now being combined with quantitative pharmacology ideas in the emergent field of systems pharmacology, while ???mathematical pharmacology??? encompasses numerical and analytical solution methods applied to models ranging from pharmacokinetics/pharmacodynamics to intracellular signal transduction.Here we present an overview of some recent pharmacological modelling, with a focus on G-protein coupled receptors (GPCRs), which play a crucial role in the control of cellular function, and are targets for up to 60% of current pharmaceuticals. Much work to date has explored the steady-state signalling behaviour of these receptors, which we now extend to study the dynamics of their signalling systems. We will show both new results and outstanding challenges, which highlight the importance of mathematics in pharmacological research and the range of the modelling toolkit upon which we draw. In particular, we will discuss:- The robust peak-plateau dynamics of activated G-proteins.- The role of asymptotic analysis in separating time scales.- A new model reduction method for reducing complexity of signalling models.- The dynamics of biased agonism.- ODE and agent based models.- Parameter estimation challenges.- Software development.

Abstract: Modern techniques in reproductive medicine like in-vitro fertilization or intracytoplasmicsperm injection have increased the chances for successful reproduction. However, currentsuccess rates vary significantly among clinics, still reaching only about 35% even in wellfunctioning centers. This is mainly due to the usage of different treatment protocols andlimited knowledge about individual variability in the dynamics of reproductive processes.Medically-assisted reproduction requires the women to undergo hormonal treatment forseveral weeks. Even though the pharmacokinetic properties of the involved drugs arewell characterized, their pharmacodynamics is less clear and varies a lot between patients.The aim of our research is to develop a mathematical model that predicts the effect ofdrug administration on hormone blood concentrations and follicular maturation and thataccounts for the observed inter- and intra-individual variability. This model shall becomepart of a clinical decision support system for reproductive endocrinologists that enablesthe simulation and optimization of treatment strategies in-silico. The talk focuses on thedevelopment and validation of a mathematical model for the human menstrual cycle[1] ,the difficulties of parameter identification[2] , and the problem of specifying the model forindividual patients[3] . This research is joint work with the scientists involved in the EUproject PAEON[4] .[1] S. R?blitz, C. St?tzel, P. Deuflhard, H.M. Jones, D.-O. Azulay, P. van der Graaf, S.W. Martin. A mathematical model of the human menstrual cycle for the administration of GnRH analogues. Journal of Theoretical Biology 321, pp. 8-27, 2013.[2] I. Klebanov, A. Sikorski, C. Sch?tte, S. R?blitz. Prior estimation and Bayesian inference from large cohort data sets. ZIB-Report 16-09, 2016.[3] T. Mancini, I. Salvo, F. Mari, I. Melatti, A. Massini, S. Sinisi, E. Trondi, F. Davi, T. Dierkes, R. Ehrig, S. R?blitz, B. Leeners, T. Kr?ger, M. Egli, F. Ille. Patient-Specific Models from Inter-Patient Biological Models and Clinical Records. In: Formal Methods in Computer-Aided Design, 2014.[4] http://paeon.di.uniroma1.it/

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.

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.

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.

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.

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.