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Mathematical Modeling and Validation of the Ergosterol Pathway in Saccharomyces cerevisiae  [PDF]
Fernando Alvarez-Vasquez, Howard Riezman, Yusuf A. Hannun, Eberhard O. Voit
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0028344
Abstract: The de novo biosynthetic machinery for both sphingolipid and ergosterol production in yeast is localized in the endoplasmic reticulum (ER) and Golgi. The interconnections between the two pathways are still poorly understood, but they may be connected in specialized membrane domains, and specific knockouts strongly suggest that both routes have different layers of mutual control and are co-affected by drugs. With the goal of shedding light on the functional integration of the yeast sphingolipid-ergosterol (SL-E) pathway, we constructed a dynamic model of the ergosterol pathway using the guidelines of Biochemical Systems Theory (BST) (Savageau., J. theor. Biol., 25, 365–9, 1969). The resulting model was merged with a previous mathematical model of sphingolipid metabolism in yeast (Alvarez-Vasquez et al., J. theor. Biol., 226, 265–91, 2004; Alvarez-Vasquez et al., Nature 433, 425–30, 2005). The S-system format within BST was used for analyses of consistency, stability, and sensitivity of the SL-E model, while the GMA format was used for dynamic simulations and predictions. Model validation was accomplished by comparing predictions from the model with published results on sterol and sterol-ester dynamics in yeast. The validated model was used to predict the metabolomic dynamics of the SL-E pathway after drug treatment. Specifically, we simulated the action of drugs affecting sphingolipids in the endoplasmic reticulum and studied changes in ergosterol associated with microdomains of the plasma membrane (PM).
Highlights of Stellar Modeling with PHOENIX  [PDF]
E. Baron,Peter H. Hauschildt,F. Allard,Eric J. Lentz,J. Aufdenberg,A. Schweitzer,T. Barman
Physics , 2002,
Abstract: We briefly describe the current version of the PHOENIX code. We then present some illustrative results from the modeling of Type Ia and Type II supernovae, hot stars, and irradiated giant planets. Good fits to observations can be obtained, when account is taken for spherically symmetric, line-blanketed, static or expanding atmospheres.
Mathematical modeling of the metastatic process  [PDF]
Jacob G. Scott,Philip Gerlee,David Basanta,Alexander G. Fletcher,Philip K. Maini,Alexander RA Anderson
Quantitative Biology , 2013,
Abstract: Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.
Mathematical Modelling of the MAP Kinase Pathway Using Proteomic Datasets  [PDF]
Tianhai Tian, Jiangning Song
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0042230
Abstract: The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.
Mathematical modeling of laser lipolysis
Serge R Mordon, Benjamin Wassmer, Jean Reynaud, Jaouad Zemmouri
BioMedical Engineering OnLine , 2008, DOI: 10.1186/1475-925x-7-10
Abstract: An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc). The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer) with a nonlinear air-tissue boundary condition including free convection.Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature.In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s) give similar skin surface temperature (max: 41°C). These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction depends on the applied energy, typically 5 cm3 for 3000 J. At last, skin retraction was observed in patients at 6-month follow up. This observation can be easily explained by mathematical modeling showing that the temperature increase inside the lower dermis is sufficient (48–50°C) to induce skin tighteningLaser lipolysis can be described by a theoretical model. Fat volume reduction observed in patients is in accordance with model calculations. Due to heat diffusion, temperature elevation is also produced inside the lower reticular dermis. This interesting
Some Reflections on the Teaching of Mathematical Modeling  [PDF]
Jon Warwick
Mathematics Educator , 2007,
Abstract: This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author’s experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve students in learning about and understanding complex problem situations the author conjectures that problems arise because insufficient time within mathematical modeling modules is spent reflecting on student work and enabling “learning to learn” about problem situations. Some suggestions for the content and delivery of mathematical modeling modules are given.
Sensitivity Analysis of CLIMEX Parameters in Modeling Potential Distribution of Phoenix dactylifera L.  [PDF]
Farzin Shabani, Lalit Kumar
PLOS ONE , 2014, DOI: 10.1371/journal.pone.0094867
Abstract: Using CLIMEX and the Taguchi Method, a process-based niche model was developed to estimate potential distributions of Phoenix dactylifera L. (date palm), an economically important crop in many counties. Development of the model was based on both its native and invasive distribution and validation was carried out in terms of its extensive distribution in Iran. To identify model parameters having greatest influence on distribution of date palm, a sensitivity analysis was carried out. Changes in suitability were established by mapping of regions where the estimated distribution changed with parameter alterations. This facilitated the assessment of certain areas in Iran where parameter modifications impacted the most, particularly in relation to suitable and highly suitable locations. Parameter sensitivities were also evaluated by the calculation of area changes within the suitable and highly suitable categories. The low temperature limit (DV2), high temperature limit (DV3), upper optimal temperature (SM2) and high soil moisture limit (SM3) had the greatest impact on sensitivity, while other parameters showed relatively less sensitivity or were insensitive to change. For an accurate fit in species distribution models, highly sensitive parameters require more extensive research and data collection methods. Results of this study demonstrate a more cost effective method for developing date palm distribution models, an integral element in species management, and may prove useful for streamlining requirements for data collection in potential distribution modeling for other species as well.
Explorations in Elementary Mathematical Modeling
Mazen Shahin
Acta Didactica Napocensia , 2010,
Abstract: In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.
Dealing with mathematical modeling in applied control
INCAS Bulletin , 2011, DOI: 10.13111/2066-8201.2011.3.2.9
Abstract: The first part of the paper presents some conjectures deduced from o long practice of systems mathematical modeling. So, it is underlined the over-emphasis developed in the sixty years history of classical control on the mathematical model. Two lessons derived from the conservativeness-versatility dualism of the mathematical models versus the mathematical theories in providing the classical control law are advanced. A third reflection concerns the spectacular decreasing of the mathematical model importance in the intelligent control. The second part of the paper shows our arguments in favor of proposed conjectures and intends especially to highlight the new intelligent control paradigm.
Mathematical modeling of formation of indoor climate  [PDF]
Yakovlev Pavel Viсtorovich,Yakovleva Ekaterina Pavlovna
Vestnik Astrahanskogo Gosudarstvennogo Tehni?eskogo Universiteta. Seria: Upravlenie, Vy?islitel?naa Tehnika i Informatika , 2012,
Abstract: The theoretical researches of heat and mass transfer processes in the area are carried out, and their impact on the climate is studied. The researches have been made, and the characteristics of the mathematical modeling of calculating velocity and temperature ranges in the rooms that have a different architectural design have been analyzed. The features of the boundary conditions and air properties are revealed.
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