Modeling Confined Cell Migration Mediated by Cytoskeleton Dynamics

Cell migration is an important biological process that has generated increasing interest during the last several years. This process is based on three phases: protrusion at the front end of the cell, de-adhesion at the rear end and contraction of the cell body, all of them coordinated due to the polymerization/depolymerization of certain cytoskeletal proteins. The aim of this work is to present a mathematical model to simulate the actin polymerization/depolymerization process that regulates the final outcome of cell migration process, considering all the above phases, in a particular case: when the cell is confined in a microfluidic channel. Under these specific conditions, cell migration can be approximated by using one-dimensional simulations. We will propose a system of reaction-diffusion equations to simulate the behavior of the cytoskeletal proteins responsible for protrusion and contraction in the cell, coupled with the mechanical response of the cell, computing its deformations and stresses. Furthermore, a numerical procedure is presented in order to simulate the whole process in a moving and deformable domain corresponding to the cell body

A discrete approach for modeling cell-matrix adhesions

During recent years the interaction between the extracellular matrix and the cytoskeleton of the cell has been object of numerous studies due to its importance in cell migration processes. These interactions are performed through protein clutches, known as focal adhesions. For migratory cells these focal adhesions along with force gener- ating processes in the cytoskeleton are responsible for the for- mation of protrusion structures like lamellipodia or filopodia. Much is known about these structures: the different proteins that conform them, the players involved in their formation or their role in cell migration. Concretely, growth-cone filopo- dia structures have attracted significant attention because of their role as cell sensors of their surrounding environment and its complex behavior. On this matter, a vast myriad of math- ematical models has been presented to explain its mechan- ical behavior. In this work, we aim to study the mechani- cal behavior of these structures through a discrete approach. This numerical model provides an individual analysis of the proteins involved including spatial distribution, interaction between them, and study of different phenomena, such as clutches unbinding or protein unfolding

Homogenization in clay barriers and seals: Two case studies

AbstractThe paper presents two case studies that provide information on the process of homogenization of initially heterogeneous clay barriers and seals. The first case is the canister retrieval test performed in the Aspö Hard Rock Laboratory (Sweden). The heterogeneity arises from the use of a combination of blocks and pellets to construct the engineered barrier. The degree of homogenization achieved by the end of the tests is evaluated from data obtained during the dismantling of the test. To assist in the interpretation of the test, a fully coupled thermo-hydro-mechanical (THM) analysis has been carried out. The second case involves the shaft sealing test performed in the HADES underground research laboratory (URL) in Mol (Belgium). Here the seal is made up of a heterogeneous mixture of bentonite pellets and bentonite powders. In addition to the full scale test, the process of homogenization of the mixture has also been observed in the laboratory using X-ray tomography. Both field test and laboratory tests are successfully modelled by a coupled hydro-mechanical (HM) analysis using a double structure constitutive law. The paper concludes with some considerations on the capability of highly expansive materials to provide a significant degree of homogenization upon hydration

EFICIENCIA REPRODUCTIVA Y PERFIL ENDÓCRINO EN OVEJAS PRIMALAS EN BUENA CONDICIÓN CORPORAL SUPLEMENTADAS CON GRASA DE SOBREPASO

Objective: To evaluate the effect of the addition of bypass fat in primiparous ewes in good body condition (CC 3) on the reproductive variables and serum levels of insulin (INS) and progesterone (P4).Design/methodology/approach: A completely randomized design was used. Forty-four primiparous ewes were randomly distributed in two experimental groups: 1) In the AGS group (n=22) ewes added with 75 g of bypass fat during a period of 25 d; 2) in the SGS group (n=22) ewes without additional fat. Estrus synchronization was performed using the CIDR device for 11 d, and ewes in estrus were served. To determine serum concentrations of P4 and INS, blood samples were collected every 48 h during supplementation.Results: Estrus onset and presentation were not different. No differences were found in gestation and prolificacy, nor changes for the mean P4 in serum. Serum INS concentrations showed differences during the synchronization d 8-14.Limitations of the study: The addition of 75 g of bypass fat in ewes with BC 3 does not have effects on reproductive variables, therefore, is recommended to use it in ewes with low BC.Findings/conclusions: The addition of bypass fat in primiparous ewes in BC 3 does not change P4 concentrations; however, it causes variations in the concentrations of INS in blood serum without modifying the response in the reproductive variables.Objetivo: Evaluar el efecto de la adición de grasa de sobrepaso en ovejas primalas en buena condición corporal (CC 3) sobre las variables reproductivas y niveles séricos de insulina (INS) y progesterona (P4).Diseño/metodología/aproximación: El diseño experimental fue completamente al azar. Se utilizaron 44 ovejas distribuidas aleatoriamente: 1) En el grupo AGS (n=22) las ovejas recibieron 75 g de grasa de sobrepaso 2) En el grupo SGS (n=22) las ovejas permanecieron sin la adición de grasa. Se realizó la sincronización del estro con CIDR por 11 d, y las ovejas en estro recibieron monta. Para evaluar las concentraciones de P4 e INS en suero, se colectaron muestras de sangre cada 48 h, durante la suplementación.Resultados: La presentación e inicio del estro no fueron diferentes. No se encontraron diferencias en porcentaje de gestación, prolificidad, ni concentración de P4 en suero. Las concentraciones de INS presentaron diferencias durante los d 8 a 14 de la sincronización.Limitaciones del estudio/implicaciones: La adición de 75 g de grasa de sobrepaso en ovejas con CC 3 no afecta las variables reproductivas, se recomienda utilizarla en ovejas con baja CC.Hallazgos/conclusiones: La adición de grasa de sobrepaso en ovejas primalas en CC 3 no cambia las concentraciones de P4; sin embargo, causa variaciones en las concentraciones de INS en suero sanguíneosin modificar la respuesta en las variables reproductivas

Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems

[EN] In this paper, a parametric family of seventh-order of iterative method to solve systems of nonlinear equations is presented. Its local convergence is studied and quadratic polynomials are used to investigate its dynamical behavior. The study of the fixed and critical points of the rational function associated to this class allows us to obtain regions of the complex plane where the method is stable. By depicting parameter planes and dynamical planes we obtain complementary information of the analytical results. These results are used to solve some nonlinear problems. (C) 2017 Elsevier Inc. All rights reserved.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P and by Generalitat Valenciana PROMETEO/2016/089.Amiri, A.; Cordero Barbero, A.; Darvishi, M.; Torregrosa Sánchez, JR. (2018). Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems. Applied Mathematics and Computation. 323:43-57. https://doi.org/10.1016/j.amc.2017.11.040S435732

Preserving the order of convergence: Low-complexity Jacobian-free iterative schemes for solving nonlinear systems

[EN] In this paper, a new technique to construct a family of divided differences for designing derivative-free iterative methods for solving nonlinear systems is proposed. By using these divided differences any kind of iterative methods containing a Jacobian matrix in its iterative expression can be transformed into a "Jacobian-free" scheme preserving the order of convergence. This procedure is applied on different schemes, showing theoretically their order and error equation. Numerical experiments confirm the theoretical results and show the efficiency and performance of the new Jacobian-free schemes. (C) 2018 Published by Elsevier B.V.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P, MTM2015-64013-P and Generalitat Valenciana PROMETEO/2016/089.Amiri, A.; Cordero Barbero, A.; Darvishi, M.; Torregrosa Sánchez, JR. (2018). Preserving the order of convergence: Low-complexity Jacobian-free iterative schemes for solving nonlinear systems. Journal of Computational and Applied Mathematics. 337:87-97. https://doi.org/10.1016/j.cam.2018.01.004S879733

A fast algorithm to solve systems of nonlinear equations

[EN] A new HSS-based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved. Spectral properties of the new method are investigated. Performance profile for the new scheme is computed and compared with HSS algorithm. Besides, by a numerical example in which a two-dimensional nonlinear convection diffusion equation is solved, we compare the new method and the Newton-HSS method. Numerical results show that the new scheme solves the problem faster than the NewtonHSS scheme in terms of CPU -time and number of iterations. Moreover, the application of the new method is found to be fast, reliable, flexible, accurate, and has small CPU time.This research was partially supported by Ministerio de Economia y Competitividad, Spain under grants MTM2014-52016-C2-2-P and Generalitat Valenciana, Spain PROMETEO/2016/089.Amiri, A.; Cordero Barbero, A.; Darvishi, M.; Torregrosa Sánchez, JR. (2019). A fast algorithm to solve systems of nonlinear equations. Journal of Computational and Applied Mathematics. 354:242-258. https://doi.org/10.1016/j.cam.2018.03.048S24225835