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Solving the chemical master equation for monomolecular reaction systems analytically the date of receipt and acceptance should be inserted later Abstract The stochastic dynamics of a well-stirred mixture of molecular species interacting through different biochemical reactions can be accurately modelled by the chemical master equation (CME). Research in the biology and scientific computing community has concentrated mostly on the development of numerical techniques to approximate the solution of the CME via many realizations of the associated Markov jump process. The domain of exact and/or efficient methods for directly solving the CME is still widely open, which is due to its large dimension that grows exponentially with the number of molecular species involved. In this article, we present an exact solution formula of the CME for arbitrary initial conditions in the case where the underlying system is governed by monomolecular reactions. The solution can be expressed in terms of the convolution of multinomial and product Poisson distributions with time-dependent parameters evolving according to the traditional reaction-rate equations. This very structured representation allows to deduce any property of the solution. The model class includes many interesting examples and may also be used as the starting point for the design of new numerical methods for the CME of more complex reaction systems.

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In the past years it has become evident that stochastic effects in regulatory networks play an important role, leading to an increasing in stochastic modelling attempts. In contrast, metabolic networks involving large numbers of molecules are most often modelled deterministically. Going towards the integration of different model systems, gen-regulatory networks become part of a larger model system including signalling pathways and metabolic networks. Thus, the question arises of how to efficiently and accurately simulation such coupled or hybrid systems. We present an algorithmic approach for the simulation of hybrid stochastic and deterministic reaction models that allows for adaptive step-size integration of the deterministic equations while at the same time accurately tracing the stochastic reaction events. We present a mathematical derivation of the hybrid system on the stochastic process level, and present numerical examples that outline the power of hybrid simulations.Résumé. Au cours des dernières années, il est devenu clair que les effets aléatoires jouaient un rôle important dans les réseaux de régulation, et les modèles employés aujourd'hui pour décrire ces réseaux sont de nature stochastique. En revanche, les réseaux métaboliques, qui mettent en jeu un grand nombre de molécules, sont le plus souvent décrits par des modèles déterministes. Dans la modélisation de systèmes complexes, réseaux régulateurs de gènes, chemins de signaux et réseaux métaboliques sont intégrés dans un même modèle. Se pose alors la question de simuler efficacement et avec précision de tels modèles couplés (on parle aussi de modèles hybrides). Nous présentons ici une approche pour la simulation de modèles de réactions hybrides stochastiques/déterministes permettantà la fois d'avoir recoursà des pas de temps adaptatifs dans l'intégration deséquations déterministes et de simuler précisément les réactions décrites par des processus stochastiques. Des simulations numériques illustrent la puissance de ces simulations hybrides.

Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window.