127 research outputs found
Adaptive finite element method assisted by stochastic simulation of chemical systems
Stochastic models of chemical systems are often analysed by solving the corresponding\ud
Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability\ud
distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with non-negligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the probability density
Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis
This paper is concerned with a non-homogeneous in space and non-local in time
random walk model for anomalous subdiffusive transport of cells. Starting with
a Markov model involving a structured probability density function, we derive
the non-local in time master equation and fractional equation for the
probability of cell position. We show the structural instability of fractional
subdiffusive equation with respect to the partial variations of anomalous
exponent. We find the criteria under which the anomalous aggregation of cells
takes place in the semi-infinite domain.Comment: 18 pages, accepted for publicatio
Coarse-grained brownian dynamics simulation of rule-based models
International audienceStudying spatial effects in signal transduction, such as co-localization along scaffold molecules, comes at a cost of complexity. In this paper, we propose a coarse-grained, particle-based spatial simulator, suited for large signal transduction models. Our approach is to combine the particle-based reaction and diffusion method, and (non-spatial) rule-based modeling: the location of each molecular complex is abstracted by a spheric particle, while its internal structure in terms of a site-graph is maintained explicit. The particles diffuse inside the cellular compartment and the colliding complexes stochastically interact according to a rule-based scheme. Since rules operate over molecular motifs (instead of full complexes), the rule set compactly describes a combinatorial or even infinite number of reactions. The method is tested on a model of Mitogen Activated Protein Kinase (MAPK) cascade of yeast pheromone response signaling. Results demonstrate that the molecules of the MAPK cascade co-localize along scaffold molecules, while the scaffold binds to a plasma membrane bound upstream component, localizing the whole signaling complex to the plasma membrane. Especially we show, how rings stabilize the resulting molecular complexes and derive the effective dissociation rate constant for it
Mathematical description of bacterial traveling pulses
The Keller-Segel system has been widely proposed as a model for bacterial
waves driven by chemotactic processes. Current experiments on {\em E. coli}
have shown precise structure of traveling pulses. We present here an
alternative mathematical description of traveling pulses at a macroscopic
scale. This modeling task is complemented with numerical simulations in
accordance with the experimental observations. Our model is derived from an
accurate kinetic description of the mesoscopic run-and-tumble process performed
by bacteria. This model can account for recent experimental observations with
{\em E. coli}. Qualitative agreements include the asymmetry of the pulse and
transition in the collective behaviour (clustered motion versus dispersion). In
addition we can capture quantitatively the main characteristics of the pulse
such as the speed and the relative size of tails. This work opens several
experimental and theoretical perspectives. Coefficients at the macroscopic
level are derived from considerations at the cellular scale. For instance the
stiffness of the signal integration process turns out to have a strong effect
on collective motion. Furthermore the bottom-up scaling allows to perform
preliminary mathematical analysis and write efficient numerical schemes. This
model is intended as a predictive tool for the investigation of bacterial
collective motion
Provenance and paleoenvironmental context of the Late Pleistocene thin aeolian silt mantles in southwestern Poland – A widespread parent material for soils
Thin loess deposits are widespread soil parent materials and important archives for paleoenvironmental reconstruction. The origin of loess in SW Poland is attributed to the Great Odra Valley (GOV), following the general concept that large rivers play a major role in regional silt supply. Yet, the precise provenance (glacier sources and/or local rocks) of silts, possibly deflated from dry GOV braided riverbeds, is not clear. Our study of thin and thick loess mantles in SW Poland for the first time indicates the provenance of thin loess based on mineralogical (MLA-SEM) and isotopic analyses (143Nd/144Nd, 87Sr/86Sr). Luminescence ages of five localities point to thin loess mantle formation during and shortly (23.0 to 17.7 ka yr) after the Last Glacial Maximum (LGM). Our isotopic data indicate that thin loess deposits in SW Poland are the mixtures of two main components – local Sudetic and Scandinavian, the latter delivered by the Fennoscandian ice sheet (FIS). Also, detailed analyses of heavy minerals show that a single mineral (e.g., hornblende) may come from both Sudetic and Scandinavian sources. This research highlights the role of the (Pleistocene) GOV in collecting and homogenizing materials, while supplying the region with fine particles to be deflated by paleowinds from open surfaces. Anomalies in mineralogy and isotopic composition are connected with influence of Sudetic mountain rivers and locally blowing silt material by katabatic winds. Regional grain size differentiation of thin loess mantles explains transport distance and altitude. © 2021 The Author
Recommended from our members
Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell
Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area
Singular Cucker-Smale Dynamics
The existing state of the art for singular models of flocking is overviewed,
starting from microscopic model of Cucker and Smale with singular communication
weight, through its mesoscopic mean-filed limit, up to the corresponding
macroscopic regime. For the microscopic Cucker-Smale (CS) model, the
collision-avoidance phenomenon is discussed, also in the presence of bonding
forces and the decentralized control. For the kinetic mean-field model, the
existence of global-in-time measure-valued solutions, with a special emphasis
on a weak atomic uniqueness of solutions is sketched. Ultimately, for the
macroscopic singular model, the summary of the existence results for the
Euler-type alignment system is provided, including existence of strong
solutions on one-dimensional torus, and the extension of this result to higher
dimensions upon restriction on the smallness of initial data. Additionally, the
pressureless Navier-Stokes-type system corresponding to particular choice of
alignment kernel is presented, and compared - analytically and numerically - to
the porous medium equation
Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows
The three-dimensional equations of compressible magnetohydrodynamic
isentropic flows are considered. An initial-boundary value problem is studied
in a bounded domain with large data. The existence and large-time behavior of
global weak solutions are established through a three-level approximation,
energy estimates, and weak convergence for the adiabatic exponent
and constant viscosity coefficients
- …