mathematical pharmacology  (MP) Session 1

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 Close

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. Close

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/ Close