Related papers: Reconstructing the kinetic chemotaxis kernel using…
In this paper, we consider the fast numerical solution of an optimal control formulation of the Keller--Segel model for bacterial chemotaxis. Upon discretization, this problem requires the solution of huge-scale saddle point systems to…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. In particular, several biochemical and biophysical cues give rise to tactic migration in the…
A wide array of biological systems can navigate in shallow gradients of chemoattractant with remarkable precision. Whilst previous approaches model such systems using coarse-grained chemical density profiles, we construct a dynamical model…
The simulation of a protein's folding process is often done via stochastic local search, which requires a procedure to apply structural changes onto a given conformation. Here, we introduce a constraint-based approach to enumerate lattice…
A microstructural theory of dense granular materials is presented, based on two main ideas. Firstly, that macroscopic shear results form activated local rearrangements at a mesoscopic scale. Secondly, that the update frequency of…
Many chemotactic bacteria inhabit environments in which chemicals appear as localized pulses and evolve by processes such as diffusion and mixing. We show that, in such environments, physical limits on the accuracy of temporal gradient…
We use density functional theory to describe the phase behaviors of rigid molecules. The construction of kernel function G(x, P, x, P) is discussed. Excluded-volume potential is calculated for two types of molecules with C_{2v} symmetry.…
Bacteria track chemical gradients using a biased random walk, a process called chemotaxis. Experiments suggest that bacteria also communicate during this process. Using a mathematical model, we find that sufficiently strong communication…
Bacterial chemotaxis in Escherichia coli is a canonical system for the study of signal transduction. A remarkable feature of this system is the coexistence of precise adaptation in population with large fluctuating cellular behavior in…
A Keller-Segel model describes macroscopic dynamics of bacterial colonies and biological cells. Bacteria secret chemical which attracts other bacteria so that they move towards chemical gradient creating nonlocal attraction between…
Bacterial colonies growing on surfaces are shaped by mechanical stresses transmitted through the community, governed by the balance between cell growth and steric and cell-substrate interactions. Using overdamped dynamics simulations of…
In response to a concentration gradient of nutrient, E. coli bacterium modulates the rotational bias of flagellar motors which control its run-and-tumble motion, to migrate towards regions of high nutrient concentration. Presence of…
Chemotaxis combines three processes: directional sensing, polarity reorientation and migration. Directed migration plays an important role in immune response, metastasis, wound healing and development. To describe chemotaxis, we extend a…
A goal in the kinetic characterization of a macromolecular system is the description of its slow relaxation processes, involving (i) identification of the structural changes involved in these processes, and (ii) estimation of the rates or…
The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However the relation between the tumbling rate and the internal state of bacteria is poorly understood. The…
Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
I present a universal method, called pivotal condensation, for calculating stoichiometric factors of chemical reactions. It can be done by hand, even for rather complicated reactions. The main trick, which I call kernel pivotal condensation…