The mechanisms underlying atrial fibrillation (AF), the most common sustained cardiac rhythm disturbance, remain elusive. Atrial fibrosis plays an important role in the development of AF and rotor dynamics. Both electrical wavelength (WL) and the degree of atrial fibrosis change as AF progresses. However, their combined effect on rotor core location remains unknown. The aim of this study was to analyze the effects of WL change on rotor core location in both fibrotic and non-fibrotic atria. Three patient specific fibrosis distributions (total fibrosis content: 16.6, 22.8, and 19.2%) obtained from clinical imaging data of persistent AF patients were incorporated in a bilayer atrial computational model. Fibrotic effects were modeled as myocyte-fibroblast coupling + conductivity remodeling; structural remodeling; ionic current changes + conductivity remodeling; and combinations of these methods. To change WL, action potential duration (APD) was varied from 120 to 240ms, representing the range of clinically observed AF cycle length, by modifying the inward rectifier potassium current (IK1) conductance between 80 and 140% of the original value. Phase singularities (PSs) were computed to identify rotor core locations. Our results show that IK1 conductance variation resulted in a decrease of APD and WL across the atria. For large WL in the absence of fibrosis, PSs anchored to regions with high APD gradient at the center of the left atrium (LA) anterior wall and near the junctions of the inferior pulmonary veins (PVs) with the LA. Decreasing the WL induced more PSs, whose distribution became less clustered. With fibrosis, PS locations depended on the fibrosis distribution and the fibrosis implementation method. The proportion of PSs in fibrotic areas and along the borders varied with both WL and fibrosis modeling method: for patient one, this was 4.2–14.9% as IK1 varied for the structural remodeling representation, but 12.3–88.4% using the combination of structural remodeling with myocyte-fibroblast coupling. The degree and distribution of fibrosis and the choice of implementation technique had a larger effect on PS locations than the WL variation. Thus, distinguishing the fibrotic mechanisms present in a patient is important for interpreting clinical fibrosis maps to create personalized models.

When an inhomogeneous RNA-polymerase (RNAP) binds to an inhomogeneous DNA at the physiological temperature, we propose a spin-like model of DNA nonlinear dynamics with long-range interactions (LRI) between adjacent and distant base pairs to study RNAP-DNA dynamics. Using Holstein-Primakoff's representation and Glauber's coherent state representation, we show that the model equation is a completely integrable nonlinear Schrödinger equation whose dispersive coefficient depends on LRI's parameter. Inhomogeneities have introduced perturbation terms in the equation of motion of RNAP-DNA dynamics. Considering the homogeneous part of that equation, a detailed study of the solution shows that the number of base pairs which form the bubble, the height, and the width of that bubble depend on the long-range parameter. The results of the perturbation analysis show that the inhomogeneities due to the DNA and RNAP structures do not alter the velocity and amplitude of the soliton, but introduce some fluctuations in the localized region of the soliton. The events that happen in the present study may represent binding of an RNAP to a promoter site in the DNA during the transcription process.

The effects of long-range interactions between peptides on the protein–DNA dynamics in the long-wave limit are studied. The investigation, done at the physiological temperature, is based on a coupled spin system of DNA molecule which includes the helicoidal geometry of DNA molecule and the Kac–Baker long-range interaction between the peptides of the protein molecule. By using the Holstein–Primakoff bosonic representation of the spin operators, we show that the original discrete equations for the protein–DNA interaction dynamics can be reduced to the nonlinear Schrödinger (NLS) equation of which the dispersive and the nonlinear coefficients depend among other things on the protein long-range interaction parameter and on the helicoidal coupling coefficient. Furthermore, we find that the amplitude and the width of the resulting breather solution, in the form of the bubble moving along the DNA molecule, are strongly influenced by the long-range and helicoidal interactions. This result shows a relevant length scale for real protein–DNA interaction.