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Stimuli-Responsive Polymers in Nanotechnology: Deposition and Possible Effect on Drug Release

A. L. Yarin (2008)

Mathematical Modelling of Natural Phenomena

Stimuli-responsive polymers result in on-demand regulation of properties and functioning of various nanoscale systems. In particular, they allow stimuli-responsive control of flow rates through membranes and nanofluidic devices with submicron channel sizes. They also allow regulation of drug release from nanoparticles and nanofibers in response to temperature or pH variation in the surrounding medium. In the present work two relevant mathematical models are introduced to address precipitation-driven...

Stippling the Skin: Generation of Anatomical Periodicity by Reaction-Diffusion Mechanisms

D. J. Headon, K. J. Painter (2009)

Mathematical Modelling of Natural Phenomena

During vertebrate development cells acquire different fates depending largely on their location in the embryo. The definition of a cell's developmental fate relies on extensive intercellular communication that produces positional information and ultimately generates an appropriately proportioned anatomy. Here we place reaction-diffusion mechanisms in the context of general concepts regarding the generation of positional information during development and then focus on these mechanisms as parsimonious...

The EM algorithm and its implementation for the estimation of frequencies of SNP-haplotypes

Joanna Polańska (2003)

International Journal of Applied Mathematics and Computer Science

A haplotype analysis is becoming increasingly important in studying complex genetic diseases. Various algorithms and specialized computer software have been developed to statistically estimate haplotype frequencies from marker phenotypes in unrelated individuals. However, currently there are very few empirical reports on the performance of the methods for the recovery of haplotype frequencies. One of the most widely used methods of haplotype reconstruction is the Maximum Likelihood method, employing...

The Influence of Look-Ahead on the Error Rate of Transcription

Y. R. Yamada, C. S. Peskin (2010)

Mathematical Modelling of Natural Phenomena

In this paper we study the error rate of RNA synthesis in the look-ahead model for the random walk of RNA polymerase along DNA during transcription. The model’s central assumption is the existence of a window of activity in which ribonucleoside triphosphates (rNTPs) bind reversibly to the template DNA strand before being hydrolyzed and linked covalently to the nascent RNA chain. An unknown, but important, integer parameter of this model is the window...

Thermodynamics of DNA microarrays

Enrico Carlon (2008)

Banach Center Publications

DNA microarrays have been widely used in molecular biology laboratories. The main current application of these devices is the determination of the gene expression level for thousands of genes simultaneously. Here we review a recently introduced physical model for hybridization (i.e. the binding of complementary DNA strands) in Affymetrix arrays and compare it to experimental results. The experimental data follow rather well the microscopic model and the approach offers several advantages compared...

Unraveling the Tangled Complexity of DNA: Combining Mathematical Modeling and Experimental Biology to Understand Replication, Recombination and Repair

S. Robic, J. R. Jungck (2011)

Mathematical Modelling of Natural Phenomena

How does DNA, the molecule containing genetic information, change its three-dimensional shape during the complex cellular processes of replication, recombination and repair? This is one of the core questions in molecular biology which cannot be answered without help from mathematical modeling. Basic concepts of topology and geometry can be introduced in undergraduate teaching to help students understand counterintuitive complex structural transformations...

Using normal mode analysis in teaching mathematical modeling to biology students

D. A. Kondrashov (2011)

Mathematical Modelling of Natural Phenomena

Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many learning...

Weighted Elastic Net Model for Mass Spectrometry Imaging Processing

D. Hong, F. Zhang (2010)

Mathematical Modelling of Natural Phenomena

In proteomics study, Imaging Mass Spectrometry (IMS) is an emerging and very promising new technique for protein analysis from intact biological tissues. Though it has shown great potential and is very promising for rapid mapping of protein localization and the detection of sizeable differences in protein expression, challenges remain in data processing due to the difficulty of high dimensionality and the fact that the number of input variables in...

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