Generalized master equation for first-passage problems in partitioned spaces

Abstract Motivated by a range of biological applications related to the transport of molecules in cells, we present a modular framework to treat first-passage problems for diffusion in partitioned spaces. The spatial domains can differ with respect to their diffusivity, geometry, and dimensionality, but can also refer to transport modes alternating between diffusive, driven, or anomalous motion. The approach relies on a coarsegraining of the motion by dissecting the trajectories on domain boundaries or when the mode of transport changes, yielding a small set of states. The time evolution of the reduced model follows a generalized master equation, which takes the form of a set of linear integro-differential equations in the occupation probabilities of the states and the corresponding probability fluxes. Further building blocks of the model are partial first-passage time (FPT) densities, which encode the transport behavior in each domain or state. The approach is exemplified and validated for a target search problem with two domains in one- and three-dimensional space, first by exactly reproducing known results for an artificially divided, homogeneous space, and second by considering the situation of domains with distinct diffusivities. Analytical solutions for the FPT densities are given in Laplace domain and are complemented by numerical backtransform yielding FPT densities over many decades in time, confirming that the geometry and heterogeneity of the space can introduce additional characteristic timescales

Ascorbate exerts anti-proliferative effects through cell cycle inhibition and sensitizes tumor cells towards cytostatic drugs

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Analysis of cellular and molecular antitumor effects upon inhibition of SATB1 in glioblastoma cells

Background: The Special AT-rich Sequence Binding Protein 1 (SATB1) regulates the expression of many genes by acting as a global chromatin organizer. While in many tumor entities SATB1 overexpression has been observed and connected to pro-tumorigenic processes, somewhat contradictory evidence exists in brain tumors with regard to SATB1 overexpression in glioblastoma and its association with poorer prognosis and tumor progression. On the functional side, initial data indicate that SATB1 may be involved in several tumor cell-relevant processes. Methods: For the detailed analysis of the functional relevance and possible therapeutic potential of SATB1 inhibition, we employ transient siRNA-mediated knockdown and comprehensively analyze the cellular and molecular role of SATB1 in glioblastoma. Results: In various cell lines with different SATB1 expression levels, a SATB1 gene dose-dependent inhibition of anchorage-dependent and –independent proliferation is observed. This is due to cell cycle-inhibitory and pro-apoptotic effects of SATB1 knockdown. Molecular analyses reveal SATB1 knockdown effects on multiple important (proto-) oncogenes, including Myc, Bcl-2, Pim-1, EGFR, β-catenin and Survivin. Molecules involved in cell cycle, EMT and cell adhesion are affected as well. The putative therapeutic relevance of SATB1 inhibition is further supported in an in vivo tumor xenograft mouse model, where the treatment with polymeric nanoparticles containing SATB1-specific siRNAs exerts antitumor effects. Conclusion: Our results demonstrate that SATB1 may represent a promising target molecule in glioblastoma therapy whose inhibition or knockdown affects multiple crucial pathways

Exactly solvable dynamics of forced polymer loops

Abstract Here, we show that a problem of forced polymer loops can be mapped to an asymmetric simple exclusion process with reflecting boundary conditions. The dynamics of the particle system can be solved exactly using the Bethe ansatz. We thus can fully describe the relaxation dynamics of forced polymer loops. In the steady state, the conformation of the loop can be approximated by a combination of Fermi–Dirac and Brownian bridge statistics, while the exact solution is found by using the fermion integer partition theory. With the theoretical framework presented here we establish a link between the physics of polymers and statistics of many-particle systems opening new paths of exploration in both research fields. Our result can be applied to the dynamics of the biopolymers which form closed loops. One such example is the active pulling of chromosomal loops during meiosis in yeast cells which helps to align chromosomes for recombination in the viscous environment of the cell nucleus

Schlussbericht

Im Rahmen des SPEAKER Projekts bestand die Aufgabenstellung im Aufbau einer Sprachassistenzplattform ”Made in Germany“. Hierbei wurde eine Plattform entwickelt, welche insbesondere im professionellen Umfeld Anwendung findet. Daher wurde die Plattform zielgerichtet den Anforderungen der Industrie und Business-to-Business (B2B) Anwendungen zugeschnitten und deren speziellen Bedürfnisse berücksichtigt. Hierzu zählen Datensouveränität, ein transparenter und sicherer Umgang mit Nutzerdaten, domänenspezifische Anpassbarkeit, Flexibilität beim Produktivbetrieb, einheitliche Schnittstellen, sowie attraktive Lizenzmodelle. Schon während der Projektlaufzeit wurde die Plattform und die Technologiemodule in verschiedenen Anwendungsfällen der Projektpartner erprobt. Datei-Upload durch TIBAs part of the SPEAKER project, the task was to create a voice assistant platform "Made in Germany". A platform was developed specifically for professional use, tailored to the requirements of the industry and business-to-business (B2B) applications, taking into account their specific needs. This includes data sovereignty, transparent and secure handling of user data, domain-specific adaptability, flexibility in productive operation, standardized interfaces, and attractive licensing models. During the project duration, the platform and technology modules were tested in various application cases with project partners

Reaction Kinetics under Anomalous Diffusion

Die vorliegende Arbeit befasst sich mit der Verallgemeinerung von Reaktions-Diffusions-Systemen auf Subdiffusion. Die subdiffusive Dynamik auf mesoskopischer Skala wurde mittels Continuous-Time Random Walks mit breiten Wartezeitverteilungen modelliert. Die Reaktion findet auf mikroskopischer Skala, d.h. während der Wartezeiten, statt und unterliegt dem Massenwirkungsgesetz. Die resultierenden Integro-Differentialgleichungen weisen im Integralkern des Transportterms eine Abhängigkeit von der Reaktion auf. Im Falle der Degradation A->0 wurde ein allgemeiner Ausdruck für die Lösungen beliebiger Dirichlet-Randwertprobleme hergeleitet. Die Annahme, dass die Reaktion dem Massenwirkungsgesetz unterliegt, ist eine entscheidende Voraussetzung für die Existenz stationärer Profile unter Subdiffusion. Eine nichtlineare Reaktion stellt die irreversible autokatalytische Reaktion A+B->2A unter Subdiffusion dar. Es wurde ein Analogon zur Fisher-Kolmogorov-Petrovskii-Piscounov-Gleichung (FKPP) aufgestellt und die resultierenden propagierenden Fronten untersucht. Numerische Simulationen legten die Existenz zweier Regimes nahe, die sowohl mittels eines Crossover-Argumentes als auch durch analytische Berechnungen untersucht wurden. Das erste Regime ist charakterisiert durch eine Front, deren Breite und Geschwindigkeit sich mit der Zeit verringert. Das zweite, fluktuationsdominierte Regime liegt nicht im Geltungsbereich der kontinuierlichen Gleichung und weist eine stärkere Abnahme der Frontgeschwindigkeit sowie eine atomar scharf definierte Front auf. Ein anderes Szenario, bei dem eine Spezies A in ein mit immobilen B-Partikeln besetztes Medium hineindiffundiert und gemäß dem Schema A+B->(inert) reagiert, wurde ebenfalls betrachtet. Diese Anordnung wurde näherungsweise als ein Randwertproblem mit einem beweglichen Rand (Stefan-Problem) formuliert. Die analytisch gewonnenen Ergebnisse bzgl. der Position des beweglichen Randes wurden durch numerische Simulationen untermauert.The present work studies the generalization of reaction-diffusion schemes to subdiffusion. The subdiffusive dynamics was modelled by means of continuous-time random walks on a mesoscopic scale with a heavy-tailed waiting time pdf lacking the first moment. The reaction was assumed to take place on a microscopic scale, i.e. during the waiting times, obeying the mass action law. The resultant equations are of integro-differential form, and the reaction explicitly affects the transport term. The long ranged memory of the subdiffusion kernel is modified by a factor accounting for the reaction of particles during the waiting times. The degradation A->0 was considered and a general expression for the solution to arbitrary Dirichlet Boundary Value Problems was derived. For stationary solutions to exist in reaction-subdiffusion, the assumption of reactions according to classical rate kinetics is essential. As an example for a nonlinear reaction-subdiffusion system, the irreversible autocatalytic reaction A+B->2A under subdiffusion is considered. A subdiffusive analogue of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation was derived and the resultant propagating fronts were studied. Two different regimes were detected in numerical simulations, and were discussed using both crossover arguments and analytic calculations. The first regime is characterized by a decaying front velocity and width. The fluctuation dominated regime is not within the scope of the continuous description. The velocity of the front decays faster in time than in the continuous regime, and the front is atomically sharp. Another setup where reactants A penetrate a medium initially filled with immobile reactants B and react according to the scheme A+B->(inert) was also considered. This problem was approximately described in terms of a moving boundary problem (Stefan-problem). The theoretical predictions concerning the moving boundary were corroborated by numerical simulations

Generalized master equation for first-passage problems in partitioned spaces

Abstract Motivated by a range of biological applications related to the transport of molecules in cells, we present a modular framework to treat first-passage problems for diffusion in partitioned spaces. The spatial domains can differ with respect to their diffusivity, geometry, and dimensionality, but can also refer to transport modes alternating between diffusive, driven, or anomalous motion. The approach relies on a coarse-graining of the motion by dissecting the trajectories on domain boundaries or when the mode of transport changes, yielding a small set of states. The time evolution of the reduced model follows a generalized master equation (GME) for non-Markovian jump processes; the GME takes the form of a set of linear integro-differential equations in the occupation probabilities of the states and the corresponding probability fluxes. Further building blocks of the model are partial first-passage time (FPT) densities, which encode the transport behavior in each domain or state. After an outline of the general framework for multiple domains, the approach is exemplified and validated for a target search problem with two domains in one- and three-dimensional space, first by exactly reproducing known results for an artificially divided, homogeneous space, and second by considering the situation of domains with distinct diffusivities. Analytical solutions for the FPT densities are given in Laplace domain and are complemented by numerical backtransforms yielding FPT densities over many decades in time, confirming that the geometry and heterogeneity of the space can introduce additional characteristic time scales.</jats:p