Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy

Efficient multi-scale sampling methods in statistical physics

This thesis deals with the development and formalization of algorithms designed for an efficient simulation of biological systems. This work is separated into two different parts, and in each part a different algorithm is investigated. In the first part of the thesis, an algorithm that is used to simulate biological systems at the mesoscopic scale is outlined. The aforementioned algorithm is studied in detail, and several improvements, theoretical, algorithmic and technical, are presented. In the second part of the thesis, a novel sampling method is outlined, which uses deep-learning to accelerate the computation of equilibrium properties of systems defined with atomistic detail. The two parts lead to applications at different scales, and, in the future, methods and concepts developed in this thesis can be useful for the investigation of biological processes defined with mesoscopic or microscopic detail

Anomalous Diffusion and Non-classical Reaction Kinetics in Crowded Fluids

This thesis investigates the underlying mechanism and the effects of anomalous diffusion in crowded fluids by means of computer simulations. In order to elucidate the mechanism behind crowding-induced subdiffusion we discuss the average shape of tracer trajectories as a potential criterion that allows to reliably discriminate between frequently proposed models. Our simulations show that measurement errors inherent to single particle tracking generally impair the determination of the underlying random process from experimental data. We propose a particle-based model for the crowded cytoplasm that incorporates soft-core repulsion and weak attraction between globular proteins of various sizes. Under these prerequisites simulations reveal transient subdiffusion of proteins. On experimental time scales, however, diffusion is normal indicating that realistic, microscopic models of crowded fluids require further detail of the relevant interactions. In the second part of this thesis, the impact of subdiffusion on biochemical reactions is studied via mesoscopic, stochastic simulations. Due to their compact trajectories subdiffusive reactants get increasingly segregated over time. This results in anomalous kinetics that differs strongly from classical theories. Moreover, for a two-step reaction scheme relying on an intermediate dissociation-association event, subdiffusion can substantially improve the overall productivity because spatio-temporal correlations are exploited with high efficiency

Application of upscaling methods for fluid flow and mass transport in multi-scale heterogeneous media : A critical review

Physical and biogeochemical heterogeneity dramatically impacts fluid flow and reactive solute transport behaviors in geological formations across scales. From micro pores to regional reservoirs, upscaling has been proven to be a valid approach to estimate large-scale parameters by using data measured at small scales. Upscaling has considerable practical importance in oil and gas production, energy storage, carbon geologic sequestration, contamination remediation, and nuclear waste disposal. This review covers, in a comprehensive manner, the upscaling approaches available in the literature and their applications on various processes, such as advection, dispersion, matrix diffusion, sorption, and chemical reactions. We enclose newly developed approaches and distinguish two main categories of upscaling methodologies, deterministic and stochastic. Volume averaging, one of the deterministic methods, has the advantage of upscaling different kinds of parameters and wide applications by requiring only a few assumptions with improved formulations. Stochastic analytical methods have been extensively developed but have limited impacts in practice due to their requirement for global statistical assumptions. With rapid improvements in computing power, numerical solutions have become more popular for upscaling. In order to tackle complex fluid flow and transport problems, the working principles and limitations of these methods are emphasized. Still, a large gap exists between the approach algorithms and real-world applications. To bridge the gap, an integrated upscaling framework is needed to incorporate in the current upscaling algorithms, uncertainty quantification techniques, data sciences, and artificial intelligence to acquire laboratory and field-scale measurements and validate the upscaled models and parameters with multi-scale observations in future geo-energy research.© 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)This work was jointly supported by the National Key Research and Development Program of China (No. 2018YFC1800900 ), National Natural Science Foundation of China (No: 41972249 , 41772253 , 51774136 ), the Program for Jilin University (JLU) Science and Technology Innovative Research Team (No. 2019TD-35 ), Graduate Innovation Fund of Jilin University (No: 101832020CX240 ), Natural Science Foundation of Hebei Province of China ( D2017508099 ), and the Program of Education Department of Hebei Province ( QN219320 ). Additional funding was provided by the Engineering Research Center of Geothermal Resources Development Technology and Equipment , Ministry of Education, China.fi=vertaisarvioitu|en=peerReviewed

Stochastic dynamics of protein assembly

Proteine sind an allen zellulären Prozessen beteiligt und agieren dabei in der Regel in Wechselwirkung mit anderen Proteinen. In dieser Arbeit wird ein Modell für die stochastische Dynamik von Proteinkomplexen untersucht, das sich für große Systeme und lange Zeiten eignet. Jedes Protein wird als Teilchen aufgefasst, welches an seiner Oberfläche reaktive Bereiche aufweist. Ein Überlapp solcher Bereiche von zwei Modellproteinen führt zur stochastischen Ausbildung einer Bindung, die dynamisch wieder aufbrechen kann. Die Anordnung und Kinetik der Bindungsstellen kann an konkrete biologische Systeme angepasst werden. Die Dynamik des Modellsystems wird mit einer Langevin-Gleichung im überdämpften Grenzfall beschrieben. Zunächst werden drei verschiedene Detailstufen der Modellierung der bimolekularen Bindungsdynamik betrachtet. Die Zeit zum Erreichen einer reaktiven Relativposition zwischen zwei Proteinen und die Anzahl erfolgloser Annäherungen werden mit Computersimulationen und analytischen Rechnungen bestimmt. Der Effekt anisotroper Formen auf die Assemblierungsdynamik wird anhand von Ellipsoiden mit unterschiedlichen Aspektverhältnissen untersucht. Die relevante Zeitskale für anisotrope Diffusion wird analytisch bestimmt. Simulationen ergeben, dass die Annäherungsdauer im wesentlichen durch die unterschiedlichen Zugänglichkeit der reaktiven Bereiche bestimmt wird. Schließlich wird die Dynamik von Komplexen mit mehr als zwei Proteinen betrachtet. Es zeigt sich, dass die Transportprozesse zwischen Bindungsvorgängen nicht durch einfache stochastische Raten beschrieben werden können. Für die Virusassemblierung wird gezeigt, dass sie nur bei mittleren Dissoziationsraten erfolgreich verläuft