Free-Knot Spline Approximation of Stochastic Processes

We study optimal approximation of stochastic processes by polynomial splines with free knots. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the $s$-fold integrated Wiener process as well as for scalar diffusion processes we determine the asymptotic behavior of the average $L_p$-distance to the splines spaces, as the (expected) number $k$ of free knots tends to infinity.Comment: 23 page

Automated Real-Time Tumor Pharmacokinetic Profiling in 3D Models: A Novel Approach for Personalized Medicine

Cancer treatment often lacks individual dose adaptation, contributing to insufficient efficacy and severe side effects. Thus, personalized approaches are highly desired. Although various analytical techniques are established to determine drug levels in preclinical models, they are limited in the automated real-time acquisition of pharmacokinetic profiles. Therefore, an online UHPLC-MS/MS system for quantitation of drug concentrations within 3D tumor oral mucosa models was generated. The integration of sampling ports into the 3D tumor models and their culture inside the autosampler allowed for real-time pharmacokinetic profiling without additional sample preparation. Docetaxel quantitation was validated according to EMA guidelines. The tumor models recapitulated the morphology of head-and-neck cancer and the dose-dependent tumor reduction following docetaxel treatment. The administration of four different docetaxel concentrations resulted in comparable courses of concentration versus time curves for 96 h. In conclusion, this proof-of-concept study demonstrated the feasibility of real-time monitoring of drug levels in 3D tumor models without any sample preparation. The inclusion of patient-derived tumor cells into our models may further optimize the pharmacotherapy of cancer patients by efficiently delivering personalized data of the target tissue

A Dual Fluorescence–Spin Label Probe for Visualization and Quantification of Target Molecules in Tissue by Multiplexed FLIM–EPR Spectroscopy

Simultaneous visualization and concentration quantification of molecules in biological tissue is an important though challenging goal. The advantages of fluorescence lifetime imaging microscopy (FLIM) for visualization, and electron paramagnetic resonance (EPR) spectroscopy for quantification are complementary. Their combination in a multiplexed approach promises a successful but ambitious strategy because of spin label-mediated fluorescence quenching. Here, we solved this problem and present the molecular design of a dual label (DL) compound comprising a highly fluorescent dye together with an EPR spin probe, which also renders the fluorescence lifetime to be concentration sensitive. The DL can easily be coupled to the biomolecule of choice, enabling in vivo and in vitro applications. This novel approach paves the way for elegant studies ranging from fundamental biological investigations to preclinical drug research, as shown in proof-of-principle penetration experiments in human skin ex vivo

Subgingival lipid A profile and endotoxin activity in periodontal health and disease.

OBJECTIVES: Regulation of lipopolysaccharide (LPS) chemical composition, particularly its lipid A domain, is an important, naturally occurring mechanism that drives bacteria-host immune system interactions into either a symbiotic or pathogenic relationship. Members of the subgingival oral microbiota can critically modulate host immuno-inflammatory responses by synthesizing different LPS isoforms. The objectives of this study were to analyze subgingival lipid A profiles and endotoxin activities in periodontal health and disease and to evaluate the use of the recombinant factor C assay as a new, lipid A-based biosensor for personalized, point-of-care periodontal therapy. MATERIALS AND METHODS: Subgingival plaque samples were collected from healthy individuals and chronic periodontitis patients before and after periodontal therapy. Chemical composition of subgingival lipid A moieties was determined by ESI-Mass Spectrometry. Endotoxin activity of subgingival LPS extracts was assessed using the recombinant factor C assay, and their inflammatory potential was examined in THP-1-derived macrophages by measuring TNF-α and IL-8 production. RESULTS: Characteristic lipid A molecular signatures, corresponding to over-acylated, bi-phosphorylated lipid A isoforms, were observed in diseased samples. Healthy and post-treatment samples were characterized by lower m/z peaks, related to under-acylated, hypo-phosphorylated lipid A structures. Endotoxin activity levels and inflammatory potentials of subgingival LPS extracts from periodontitis patients were significantly higher compared to healthy and post-treatment samples. CONCLUSIONS: This is the first study to consider structure-function-clinical implications of different lipid A isoforms present in the subgingival niche and sheds new light on molecular pathogenic mechanisms of subgingival biofilm communities. CLINICAL RELEVANCE: Subgingival endotoxin activity (determined by lipid A chemical composition) could be a reliable, bacterially derived biomarker and a risk assessment tool for personalized periodontal care

The optimal discretization of stochastic differential equations

AbstractWe study pathwise approximation of scalar stochastic differential equations. The mean squared L2-error and the expected number n of evaluations of the driving Brownian motion are used for the comparison of arbitrary methods. We introduce an adaptive discretization that reflects the local properties of every single trajectory. The corresponding error tends to zero like c·n−1/2, where c is the average of the diffusion coefficient in space and time. Our method is justified by the matching lower bound for arbitrary methods that are based on n evaluations on the average. Hence the adaptive discretization is asymptotically optimal. The new method is very easy to implement, and about 7 additional arithmetical operations are needed per evaluation of the Brownian motion. Hereby we can determine the complexity of pathwise approximation of stochastic differential equations. We illustrate the power of our method already for moderate accuracies by means of a simulation experiment