Gap junctions exhibit nonlinear electrical properties that have been hypothesized to be relevant to arrhythmogenicity in a structurally remodeled tissue. Large-scale implementation of gap junction dynamics in 3D propagation models remains challenging. We aim to quantify the impact of nonlinear diffusion during episodes of arrhythmias simulated in a left atrial model. Homogenization of conduction properties in the presence of nonlinear gap junctions was performed by generalizing a previously developed mathematical framework. A monodomain model was solved in which conductivities were time-varying and depended on transjunctional potentials. Gap junction conductances were derived from a simplified Vogel–Weingart model with first-order gating and adjustable time constant. A bilayer interconnected cable model of the left atrium with 100 $\mu$ m resolution was used. The diffusion matrix was recomputed at each time step according to the state of the gap junctions. Sinus rhythm and atrial fibrillation episodes were simulated in remodeled tissue substrates. Slow conduction was induced by reduced coupling and by diffuse or stringy fibrosis. Simulations starting from the same initial conditions were repeated with linear and nonlinear gap junctions. The discrepancy in activation times between the linear and nonlinear diffusion models was quantified. The results largely validated the linear approximation for conduction velocities >20 cm/s. In very slow conduction substrates, the discrepancy accumulated over time during atrial fibrillation, eventually leading to qualitative differences in propagation patterns, while keeping the descriptive statistics, such as cycle lengths, unchanged. The discrepancy growth rate was increased by impaired conduction, fibrosis, conduction heterogeneity, lateral uncoupling, fast gap junction time constant, and steeper action potential duration restitution.

We consider a novel approach to mathematically define a graphing method to represent amino acid sequences of proteins in two-dimensional plane and characterize them numerically. The amino acids are represented by their relative magnitude of their hydrophobicity. Each amino acid is compared with a vector and moves in relative direction which generates a graph. Applications are shown in Zaire Ebola Virus to conclude how this plotting can be more useful than base sequence plotting. Also, superimposition graph of SARS and SARS-CoV-2 shows that these sequences are strongly related and Various other applications are shown too to explain it's fruitfulness.