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A model of cardiac tissue as an excitable medium with two interacting pacemakers having refractory time

Alexander Loskutov, Sergei Rybalko, Ekaterina Zhuchkova (2003)

Banach Center Publications

A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase.

Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

Amelia B. Kreienkamp, Lucy Y. Liu, Mona S. Minkara, Matthew G. Knepley, Jaydeep P. Bardhan, Mala L. Radhakrishnan (2013)

Molecular Based Mathematical Biology

We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins¶a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions...

Application of coupled neural oscillators for image texture segmentation and modeling of biological rhythms

Paweł Strumiłło, Michał Strzelecki (2006)

International Journal of Applied Mathematics and Computer Science

The role of relaxation oscillator models in application fields such as modeling dynamic systems and image analysis is discussed. A short review of the Van der Pol, Wilson-Cowan and Terman-Wang relaxation oscillators is given. The key property of such nonlinear oscillators, i.e., the oscillator phase shift (called the Phase Response Curve) as a result of external pulse stimuli is indicated as a fundamental mechanism to achieve and sustain synchrony in networks of coupled oscillators. It is noted...

Computer Simulation of Protein-Protein Association in Photosynthesis

I.B. Kovalenko, A.M. Abaturova, A.N. Diakonova, O.S. Knyazeva, D.M. Ustinin, S.S. Khruschev, G.Yu. Riznichenko, A.B. Rubin (2011)

Mathematical Modelling of Natural Phenomena

The paper is devoted to the method of computer simulation of protein interactions taking part in photosynthetic electron transport reactions. Using this method we have studied kinetic characteristics of protein-protein complex formation for four pairs of proteins involved in photosynthesis at a variety of ionic strength values. Computer simulations describe non-monotonic dependences of complex formation rates on the ionic strength as the result of...

Dynamics of Biomembranes: Effect of the Bulk Fluid

A. Bonito, R.H. Nochetto, M.S. Pauletti (2011)

Mathematical Modelling of Natural Phenomena

We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow:...

Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation

Weihua Geng, Shan Zhao (2013)

Molecular Based Mathematical Biology

The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and stably solve the nonlinear PB equation in a pseudo-transient continuation approach. The operator splitting...

High Resolution Tracking of Cell Membrane Dynamics in Moving Cells: an Electrifying Approach

R.A. Tyson, D.B.A. Epstein, K.I. Anderson, T. Bretschneider (2010)

Mathematical Modelling of Natural Phenomena

Cell motility is an integral part of a diverse set of biological processes. The quest for mathematical models of cell motility has prompted the development of automated approaches for gathering quantitative data on cell morphology, and the distribution of molecular players involved in cell motility. Here we review recent approaches for quantifying cell motility, including automated cell segmentation and tracking. Secondly, we present our own novel...

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