Impact of mathematical pharmacology on practice and theory: four case studies

Drug-discovery has become a complex disci- pline in which the amount of knowledge about human biology, physiology, and biochemistry have increased. In order to harness this complex body of knowledge mathe- matics can play a critical role, and has actually already been doing so. We demonstrate through four case studies, taken from previously published data and analyses, what we can gain from mathematical/analytical techniques when nonlinear concentration-time courses have to be trans- formed into their equilibrium concentration-response (tar- get or complex) relationships and new structures of drug potency have to be deciphered; when pattern recognition needs to be carried out for an unconventional response- time dataset; when what-if? predictions beyond the obser- vational concentration-time range need to be made; or when the behaviour of a semi-mechanistic model needs to be elucidated or challenged. These four examples are typical situations when standard approaches known to the general community of pharmacokineticists prove to be inadequate

New Equilibrium Models of Drug-Receptor Interactions Derived from Target-Mediated Drug Disposition

In vivo analyses of pharmacological data are traditionally based on a closed system approach not incorporating turnover of target and ligand-target kinetics, but mainly focussing on ligand-target binding properties. This study incorporates information about target and ligand-target kinetics parallel to binding. In a previous paper, steady-state relationships between target- and ligand-target complex versus ligand exposure were derived and a new expression of in vivo potency was derived for a circulating target. This communication is extending the equilibrium relationships and in vivo potency expression for (i) two separate targets competing for one ligand, (ii) two different ligands competing for a single target and (iii) a single ligand-target interaction located in tissue. The derived expressions of the in vivo potencies will be useful both in drug-related discovery projects and mechanistic studies. The equilibrium states of two targets and one ligand may have implications in safety assessment, whilst the equilibrium states of two competing ligands for one target may cast light on when pharmacodynamic drug-drug interactions are important. The proposed equilibrium expressions for a peripherally located target may also be useful for small molecule interactions with extravascularly located targets. Including target turnover, ligand-target complex kinetics and binding properties in expressions of potency and efficacy will improve our understanding of within and between-individual (and across species) variability. The new expressions of potencies highlight the fact that the level of drug-induced target suppression is very much governed by target turnover properties rather than by the target expression level as such.Analysis and Stochastic

Exosomal cancer immunotherapy is independent of MHC molecules on exosomes

Peptide-loaded exosomes are promising cancer treatment vehicles; however, moderate T cell responses in human clinical trials indicate a need to further understand exosome-induced immunity. We previously demonstrated that antigen-loaded exosomes carry whole protein antigens and require B cells for inducing antigen-specific T cells. Therefore, we investigated the relative importance of exosomal major histocompatibility complex (MHC) class I for the induction of antigen-specific T cell responses and tumour protection. We show that ovalbumin-loaded dendritic cell-derived exosomes from MHCI-/- mice induce antigen-specific T cells at the same magnitude as wild type exosomes. Furthermore, exosomes lacking MHC class I, as well as exosomes with both MHC class I and II mismatch, induced tumour infiltrating T cells and increased overall survival to the same extent as syngeneic exosomes in B16 melanoma. In conclusion, T cell responses are independent of exosomal MHC/peptide complexes if whole antigen is present. This establishes the prospective of using impersonalised exosomes, and will greatly increase the feasibility of designing exosome-based vaccines or therapeutic approaches in humans

A Flexible Nonlinear Feedback System That Captures Diverse Patterns of Adaptation and Rebound

An important approach to modeling tolerance and adaptation employs feedback mechanisms in which the response to the drug generates a counter-regulating action which affects the response. In this paper we analyze a family of nonlinear feedback models which has recently proved effective in modeling tolerance phenomena such as have been observed with SSRI’s. We use dynamical systems methods to exhibit typical properties of the response-time course of these nonlinear models, such as overshoot and rebound, establish quantitive bounds and explore how these properties depend on the system and drug parameters. Our analysis is anchored in three specific in vivo data sets which involve different levels of pharmacokinetic complexity. Initial estimates for system (kin, kout, ktol ) and drug (EC50/IC50, Emax/Imax, n ) parameters are obtained on the basis of specific properties of the response-time course, identified in the context of exploratory (graphical) data analysis. Our analysis and the application of its results to the three concrete examples demonstrates the flexibility and potential of this family of feedback models

Changing musical emotion: A computational rule system for modifying score and performance

CMERS system architecture has been implemented in the programming language scheme, and it uses the improvised music programming environment with the objective to provide researchers with a tool for testing the relationships between musical features and emotion. A music work represented in CMERS uses the music object hierarchy that is based on GTTM's grouping structure and is automatically generated from the phrase boundary markup and MIDI file. The Mode rule type of CMERS converts a note into those of the parallel mode and no change in pitch height occurs when converting to the parallel mode. It is reported that the odds of correctness with CMERS are approximately five times greater than that of DM. The repeated-measures analysis of variance for valence shows a significant difference between systems with F (1, 17) = 45.49, p < .0005 and the interaction between system and quadrant is significant with F (3, 51) = 4.23, p = .01, which indicates that CMERS is extensively more effective at correctly influencing valence than DM. c 2010 Massachusetts Institute of Technology

Feedback modeling of non-esterified fatty acids in rats after nicotinic acid infusions

A feedback model was developed to describe the tolerance and oscillatory rebound seen in non-esterified fatty acid (NEFA) plasma concentrations following intravenous infusions of nicotinic acid (NiAc) to male Sprague-Dawley rats. NiAc was administered as an intravenous infusion over 30 min (0, 1, 5 or 20 μmol kg−1 of body weight) or over 300 min (0, 5, 10 or 51 μmol kg−1 of body weight), to healthy rats (n = 63), and serial arterial blood samples were taken for measurement of NiAc and NEFA plasma concentrations. Data were analyzed using nonlinear mixed effects modeling (NONMEM). The disposition of NiAc was described by a two-compartment model with endogenous turnover rate and two parallel capacity-limited elimination processes. The plasma concentration of NiAc was driving NEFA (R) turnover via an inhibitory drug-mechanism function acting on the formation of NEFA. The NEFA turnover was described by a feedback model with a moderator distributed over a series of transit compartments, where the first compartment (M1) inhibited the formation of R and the last compartment (MN) stimulated the loss of R. All processes regulating plasma NEFA concentrations were assumed to be captured by the moderator function. The potency, IC50, of NiAc was 45 nmol L−1, the fractional turnover rate kout was 0.41 L mmol−1 min−1 and the turnover rate of moderator ktol was 0.027 min−1. A lower physiological limit of NEFA was modeled as a NiAc-independent release (kcap) of NEFA into plasma and was estimated to 0.032 mmol L−1 min−1. This model can be used to provide information about factors that determine the time-course of NEFA response following different modes, rates and routes of administration of NiAc. The proposed model may also serve as a preclinical tool for analyzing and simulating drug-induced changes in plasma NEFA concentrations after treatment with NiAc or NiAc analogues