Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway

Kinetic-transport equations are, by now, standard models to describe the dynamics of populations of bacteria moving by run-and-tumble. Experimental observations show that bacteria increase their run duration when encountering an increasing gradient of chemotactic molecules. This led to a first class of models which heuristically include tumbling frequencies depending on the path-wise gradient of chemotactic signal. More recently, the biochemical pathways regulating the flagellar motors were uncovered. This knowledge gave rise to a second class of kinetic-transport equations, that takes into account an intra-cellular molecular content and which relates the tumbling frequency to this information. It turns out that the tumbling frequency depends on the chemotactic signal, and not on its gradient. For these two classes of models, macroscopic equations of Keller-Segel type, have been derived using diffusion or hyperbolic rescaling. We complete this program by showing how the first class of equations can be derived from the second class with molecular content after appropriate rescaling. The main difficulty is to explain why the path-wise gradient of chemotactic signal can arise in this asymptotic process. Randomness of receptor methylation events can be included, and our approach can be used to compute the tumbling frequency in presence of such a noise

Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient

Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for nutrients availability which can differ depending on the situation under consideration, in vivo or in vitro. Numerical solutions exhibit, as expected from medical observations, a proliferative rim and a necrotic core. However, their precise profiles are rather complex, both in one and two dimensions.Comment: 25 page

Derivation of a Hele-Shaw type system from a cell model with active motion

We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the novelty of the present paper. This new ingredient is considered here as a standard diffusion process. The free boundary model is derived from a description at the cell level using the asymptotic of a stiff pressure limit. Compared to the case when active motion is neglected, the pressure satisfies the same complementarity Hele-Shaw type formula. However, the cell density is smoother (Lipschitz continuous), while there is a deep change in the free boundary velocity, which is no longer given by the gradient of the pressure, because some kind of 'mushy region' prepares the tumor invasion

Process Optimization and Downscaling of a Single Electron Single Dot Memory

This paper presents the process optimization of a single-electron nanoflash electron memory. Self-aligned single dot memory structures have been fabricated using a wet anisotropic oxidation of a silicon nanowire. One of the main issue was to clarify the process conditions for the dot formation. Based on the process modeling, the influence of various parameters (oxidation temperature, nanowire shape) has been investigated. The necessity of a sharp compromise between these different parameters to ensure the presence of the memory dot has been established. In order to propose an aggressive memory cell, the downscaling of the device has been carefully studied. Scaling rules show that the size of the original device could be reduced by a factor of 2. This point has been previously confirmed by the realization of single-electron memory devices

An Eco-Friendly Lifestyle In Your Hands

Society has begun to be more conscious about the products they consume on a daily basis. People are changing to plant-based diets or vegan lifestyles. The high demand of this market, motivated the idea to develop an eco-friendly and user-friendly app that will make people’s life easier. By combining two concepts that are popular amongst this generation, an app was developed. This app contains all the sources and information one looks for during the transition into an eco-friendly lifestyle

Low 60Fe abundance in Semarkona and Sahara 99555

Iron-60 (t1/2=2.62 Myr) is a short-lived nuclide that can help constrain the astrophysical context of solar system formation and date early solar system events. A high abundance of 60Fe (60Fe/56Fe= 4x10-7) was reported by in situ techniques in some chondrules from the LL3.00 Semarkona meteorite, which was taken as evidence that a supernova exploded in the vicinity of the birthplace of the Sun. However, our previous MC-ICPMS measurements of a wide range of meteoritic materials, including chondrules, showed that 60Fe was present in the early solar system at a much lower level (60Fe/56Fe=10-8). The reason for the discrepancy is unknown but only two Semarkona chondrules were measured by MC-ICPMS and these had Fe/Ni ratios below ~2x chondritic. Here, we show that the initial 60Fe/56Fe ratio in Semarkona chondrules with Fe/Ni ratios up to ~24x chondritic is 5.4x10-9. We also establish the initial 60Fe/56Fe ratio at the time of crystallization of the Sahara 99555 angrite, a chronological anchor, to be 1.97x10-9. These results demonstrate that the initial abundance of 60Fe at solar system birth was low, corresponding to an initial 60Fe/56Fe ratio of 1.01x10-8.Comment: The Astrophysical Journal, in press. 28 pages, 2 tables, 3 figure