Numerical solutions of random mean square Fisher-KPP models with advection

[EN] This paper deals with the construction of numerical stable solutions of random mean square Fisher-Kolmogorov-Petrosky-Piskunov (Fisher-KPP) models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique transforms the original continuous problem into a nonlinear inhomogeneous system of random differential equations. Then, by extending to the random framework, the ideas of the exponential time differencing method, a full vector discretization of the problem addresses to a random vector difference scheme. A sample approach of the random vector difference scheme, the use of properties of Metzler matrices and the logarithmic norm allow the proof of stability of the numerical solutions in the mean square sense. In spite of the computational complexity, the results are illustrated by comparing the results with a test problem where the exact solution is known.Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-PCasabán Bartual, MC.; Company Rossi, R.; Jódar Sánchez, LA. (2020). Numerical solutions of random mean square Fisher-KPP models with advection. Mathematical Methods in the Applied Sciences. 43(14):8015-8031. https://doi.org/10.1002/mma.5942S801580314314FISHER, R. A. (1937). THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES. Annals of Eugenics, 7(4), 355-369. doi:10.1111/j.1469-1809.1937.tb02153.xBengfort, M., Malchow, H., & Hilker, F. M. (2016). The Fokker–Planck law of diffusion and pattern formation in heterogeneous environments. Journal of Mathematical Biology, 73(3), 683-704. doi:10.1007/s00285-016-0966-8Okubo, A., & Levin, S. A. (2001). Diffusion and Ecological Problems: Modern Perspectives. Interdisciplinary Applied Mathematics. doi:10.1007/978-1-4757-4978-6SKELLAM, J. G. (1951). RANDOM DISPERSAL IN THEORETICAL POPULATIONS. Biometrika, 38(1-2), 196-218. doi:10.1093/biomet/38.1-2.196Aronson, D. G., & Weinberger, H. F. (1975). Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. Partial Differential Equations and Related Topics, 5-49. doi:10.1007/bfb0070595Aronson, D. ., & Weinberger, H. . (1978). Multidimensional nonlinear diffusion arising in population genetics. Advances in Mathematics, 30(1), 33-76. doi:10.1016/0001-8708(78)90130-5Weinberger, H. F. (2002). On spreading speeds and traveling waves for growth and migration models in a periodic habitat. Journal of Mathematical Biology, 45(6), 511-548. doi:10.1007/s00285-002-0169-3Weinberger, H. F., Lewis, M. A., & Li, B. (2007). Anomalous spreading speeds of cooperative recursion systems. Journal of Mathematical Biology, 55(2), 207-222. doi:10.1007/s00285-007-0078-6Liang, X., & Zhao, X.-Q. (2006). Asymptotic speeds of spread and traveling waves for monotone semiflows with applications. Communications on Pure and Applied Mathematics, 60(1), 1-40. doi:10.1002/cpa.20154E. Fitzgibbon, W., Parrott, M. E., & Webb, G. (1995). Diffusive epidemic models with spatial and age dependent heterogeneity. Discrete & Continuous Dynamical Systems - A, 1(1), 35-57. doi:10.3934/dcds.1995.1.35Kinezaki, N., Kawasaki, K., & Shigesada, N. (2006). Spatial dynamics of invasion in sinusoidally varying environments. Population Ecology, 48(4), 263-270. doi:10.1007/s10144-006-0263-2Jin, Y., Hilker, F. M., Steffler, P. M., & Lewis, M. A. (2014). Seasonal Invasion Dynamics in a Spatially Heterogeneous River with Fluctuating Flows. Bulletin of Mathematical Biology, 76(7), 1522-1565. doi:10.1007/s11538-014-9957-3Faou, E. (2009). Analysis of splitting methods for reaction-diffusion problems using stochastic calculus. Mathematics of Computation, 78(267), 1467-1483. doi:10.1090/s0025-5718-08-02185-6Doering, C. R., Mueller, C., & Smereka, P. (2003). Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality. Physica A: Statistical Mechanics and its Applications, 325(1-2), 243-259. doi:10.1016/s0378-4371(03)00203-6Siekmann, I., Bengfort, M., & Malchow, H. (2017). Coexistence of competitors mediated by nonlinear noise. The European Physical Journal Special Topics, 226(9), 2157-2170. doi:10.1140/epjst/e2017-70038-6McKean, H. P. (1975). Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov. Communications on Pure and Applied Mathematics, 28(3), 323-331. doi:10.1002/cpa.3160280302Berestycki, H., & Nadin, G. (2012). Spreading speeds for one-dimensional monostable reaction-diffusion equations. Journal of Mathematical Physics, 53(11), 115619. doi:10.1063/1.4764932Cortés, J. C., Jódar, L., Villafuerte, L., & Villanueva, R. J. (2007). Computing mean square approximations of random diffusion models with source term. Mathematics and Computers in Simulation, 76(1-3), 44-48. doi:10.1016/j.matcom.2007.01.020Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Casabán, M.-C., Cortés, J.-C., & Jódar, L. (2016). Solving linear and quadratic random matrix differential equations: A mean square approach. Applied Mathematical Modelling, 40(21-22), 9362-9377. doi:10.1016/j.apm.2016.06.017Sarmin, E. N., & Chudov, L. A. (1963). On the stability of the numerical integration of systems of ordinary differential equations arising in the use of the straight line method. USSR Computational Mathematics and Mathematical Physics, 3(6), 1537-1543. doi:10.1016/0041-5553(63)90256-8Sanz-Serna, J. M., & Verwer, J. G. (1989). Convergence analysis of one-step schemes in the method of lines. Applied Mathematics and Computation, 31, 183-196. doi:10.1016/0096-3003(89)90118-5Calvo, M. P., de Frutos, J., & Novo, J. (2001). Linearly implicit Runge–Kutta methods for advection–reaction–diffusion equations. Applied Numerical Mathematics, 37(4), 535-549. doi:10.1016/s0168-9274(00)00061-1Cox, S. M., & Matthews, P. C. (2002). Exponential Time Differencing for Stiff Systems. Journal of Computational Physics, 176(2), 430-455. doi:10.1006/jcph.2002.6995De la Hoz, F., & Vadillo, F. (2016). Numerical simulations of time-dependent partial differential equations. Journal of Computational and Applied Mathematics, 295, 175-184. doi:10.1016/j.cam.2014.10.006Company, R., Egorova, V. N., & Jódar, L. (2018). Conditional full stability of positivity-preserving finite difference scheme for diffusion–advection-reaction models. Journal of Computational and Applied Mathematics, 341, 157-168. doi:10.1016/j.cam.2018.02.031Kaczorek, T. (2002). Positive 1D and 2D Systems. Communications and Control Engineering. doi:10.1007/978-1-4471-0221-2Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences. doi:10.1007/978-1-4612-5561-

Gene expression profiling revealed novel mechanism of action of Taxotere and Furtulon in prostate cancer cells

BACKGROUND: Both Taxotere and Capecitabine have shown anti-cancer activity against various cancers including prostate cancer. In combination, Taxotere plus Capecitabine has demonstrated higher anti-cancer activity in advanced breast cancers. However, the molecular mechanisms of action of Taxotere and Capecitabine have not been fully elucidated in prostate cancer. METHODS: The total RNA from PC3 and LNCaP prostate cells untreated and treated with 2 nM Taxotere, 110 μM Furtulon (active metabolite of Capecitabine), or 1 nM Taxotere plus 50 μM Furtulon for 6, 36, and 72 hours, was subjected to Affymetrix Human Genome U133A Array analysis. Real-time PCR and Western Blot analysis were conducted to confirm microarray data. RESULTS: Taxotere and Furtulon down-regulated some genes critical for cell proliferation, cell cycle progression, transcription factor, cell signaling, and oncogenesis, and up-regulated some genes related to the induction of apoptosis, cell cycle arrest, and differentiation in both cell lines. Taxotere and Furtulon also up-regulated some genes responsible for chemotherapeutic resistance, suggesting the induction of cancer cell resistance to these agents. CONCLUSIONS: Taxotere and Furtulon caused the alternation of a large number of genes, many of which may contribute to the molecular mechanisms by which Taxotere and Furtulon inhibit the growth of prostate cancer cells. This information could be utilized for further mechanistic research and for devising optimized therapeutic strategies against prostate cancer

Differentially expressed profiles in the larval testes of Wolbachia infected and uninfected Drosophila

BACKGROUND: Wolbachia are endosymbiotic bacteria that are frequently found in arthropods and nematodes. These maternally inherited bacteria manipulate host reproduction by several mechanisms including cytoplasmic incompatibility (CI). CI is the most common phenotype induced by Wolbachia and results in the developmental arrest of embryos derived from crosses between Wolbachia-infected males and uninfected females. Although the molecular mechanisms of CI are currently unknown, several studies suggest that host sperm is modified by Wolbachia during spermatogenesis. RESULTS: We compared the gene expression of Drosophila melanogaster larval testes with and without the wMel strain of Wolbachia to identify candidate genes that could be involved in the interaction between Wolbachia and the insect host. Microarray, quantitative RT-PCR and in situ hybridization analyses were carried out on D. melanogaster larval testes to determine the effect of Wolbachia infection on host gene expression. A total of 296 genes were identified by microarray analysis to have at least a 1.5 fold change [q-value < 5%] in expression. When comparing Wolbachia-infected flies to uninfected flies, 167 genes were up-regulated and 129 genes down-regulated. Differential expression of genes related to metabolism, immunity, reproduction and other functions were observed. Quantitative RT-PCR (qRT-PCR) confirmed 12 genes are differentially expressed in the testes of the 3rd instar larvae of Wolbachia-infected and uninfected flies. In situ hybridization demonstrated that Wolbachia infection changes the expression of several genes putatively associated with spermatogenesis including JH induced protein-26 and Mst84Db, or involved in immune (kenny) or metabolism (CG4988-RA). CONCLUSIONS: Wolbachia change the gene expression of 296 genes in the larval testes of D. melanogaster including genes related to metabolism, immunity and reproduction. Interestingly, most of the genes putatively involved in immunity were up-regulated in the presence of Wolbachia. In contrast, most of the genes putatively associated with reproduction (especially spermatogenesis) were down-regulated in the presence of Wolbachia. These results suggest Wolbachia may activate the immune pathway but inhibit spermatogenesis. Our data provide a significant panel of candidate genes that may be involved in the interaction between Wolbachia and their insect hosts. This forms a basis to help elucidate the underlying mechanisms of Wolbachia-induced CI in Drosophila and the influence of Wolbachia on spermatogenesis

Construction of a large scale integrated map of macrophage pathogen recognition and effector systems

<p>Abstract</p> <p>Background</p> <p>In an effort to better understand the molecular networks that underpin macrophage activation we have been assembling a map of relevant pathways. Manual curation of the published literature was carried out in order to define the components of these pathways and the interactions between them. This information has been assembled into a large integrated directional network and represented graphically using the modified Edinburgh Pathway Notation (mEPN) scheme.</p> <p>Results</p> <p>The diagram includes detailed views of the toll-like receptor (TLR) pathways, other pathogen recognition systems, NF-kappa-B, apoptosis, interferon signalling, MAP-kinase cascades, MHC antigen presentation and proteasome assembly, as well as selected views of the transcriptional networks they regulate. The integrated pathway includes a total of 496 unique proteins, the complexes formed between them and the processes in which they are involved. This produces a network of 2,170 nodes connected by 2,553 edges.</p> <p>Conclusions</p> <p>The pathway diagram is a navigable visual aid for displaying a consensus view of the pathway information available for these systems. It is also a valuable resource for computational modelling and aid in the interpretation of functional genomics data. We envisage that this work will be of value to those interested in macrophage biology and also contribute to the ongoing Systems Biology community effort to develop a standard notation scheme for the graphical representation of biological pathways.</p

Health promotion through self-care and community participation: Elements of a proposed programme in the developing countries

BACKGROUND: The concepts of health promotion, self-care and community participation emerged during 1970s, primarily out of concerns about the limitation of professional health system. Since then there have been rapid growth in these areas in the developed world, and there is evidence of effectiveness of such interventions. These areas are still in infancy in the developing countries. There is a window of opportunity for promoting self care and community participation for health promotion. DISCUSSION: A broad outline is proposed for designing a health promotion programme in developing countries, following key strategies of the Ottawa Charter for health promotion and principles of self care and community participation. Supportive policies may be framed. Self care clearinghouses may be set up at provincial level to co-ordinate the programme activities in consultation with district and national teams. Self care may be promoted in the schools and workplaces. For developing personal skills of individuals, self care information, generated through a participatory process, may be disseminated using a wide range of print and audio-visual tools and information technology based tools. One such potential tool may be a personally held self care manual and health record, to be designed jointly by the community and professionals. Its first part may contain basic self care information and the second part may contain outlines of different personally-held health records to be used to record important health and disease related events of an individual. Periodic monitoring and evaluation of the programme may be done. Studies from different parts of the world indicate the effectiveness and cost-effectiveness of self care interventions. The proposed outline has potential for health promotion and cost reduction of health services in the developing countries, and may be adapted in different situations. SUMMARY: Self care, community participation and health promotion are emerging but dominant areas in the developed countries. Elements of a programme for health promotion in the developing countries following key principles of self care and community participation are proposed. Demonstration programmes may be initiated to assess the feasibility and effectiveness of this programme before large scale implementation

Modeling of Molecular Interaction between Apoptin, BCR-Abl and CrkL - An Alternative Approach to Conventional Rational Drug Design

In this study we have calculated a 3D structure of apoptin and through modeling and docking approaches, we show its interaction with Bcr-Abl oncoprotein and its downstream signaling components, following which we confirm some of the newly-found interactions by biochemical methods. Bcr-Abl oncoprotein is aberrantly expressed in chronic myelogenous leukaemia (CML). It has several distinct functional domains in addition to the Abl kinase domain. The SH3 and SH2 domains cooperatively play important roles in autoinhibiting its kinase activity. Adapter molecules such as Grb2 and CrkL interact with proline-rich region and activate multiple Bcr-Abl downstream signaling pathways that contribute to growth and survival. Therefore, the oncogenic effect of Bcr-Abl could be inhibited by the interaction of small molecules with these domains. Apoptin is a viral protein with well-documented cancer-selective cytotoxicity. Apoptin attributes such as SH2-like sequence similarity with CrkL SH2 domain, unique SH3 domain binding sequence, presence of proline-rich segments, and its nuclear affinity render the molecule capable of interaction with Bcr-Abl. Despite almost two decades of research, the mode of apoptin’s action remains elusive because 3D structure of apoptin is unavailable. We performed in silico threedimensional modeling of apoptin, molecular docking experiments between apoptin model and the known structure of Bcr- Abl, and the 3D structures of SH2 domains of CrkL and Bcr-Abl. We also biochemically validated some of the interactions that were first predicted in silico. This structure-property relationship of apoptin may help in unlocking its cancer-selective toxic properties. Moreover, such models will guide us in developing of a new class of potent apoptin-like molecules with greater selectivity and potency