Stability analysis and Hopf bifurcation based on time delay neurons under electromagnetic fields

Neurons contain a large number of ions inside and outside the cell, and the transmembrane currents formed by the movement of these ions cause membrane potential fluctuations and induce electromagnetism inside and outside the cell. In addition, any change in external electromagnetic fields can cause changes in the membrane potential of the neurons. Therefore, based on the three-dimensional Hindmarsh — Rose (HR) neuron model, a five-dimensional neuron model with time delay is developed in this paper by introducing flux and electric field variables and considering the resulting time delay. First, the Hopf bifurcation theory is used to demonstrate the local stability of the system at the equilibrium point at different time delays. Then, the stability of the Hopf bifurcation and its direction are proved by using the central flow shape theorem. Finally, the existence of the Hopf bifurcation is proved using the phase diagram and the bifurcation diagram, and the effects of several important parameters on the model are investigated by numerical simulations using time series plots, ISI bifurcation plots and two-parameter bifurcation plots. The model is found to be accompanied by chaotic and chaos-free plus-periodic bifurcation structures, mixed-mode discharges and other phenomena. Also, its discharge pattern can be controlled after adding time delay. The results of this paper provide help to the pathogenic mechanism and control of neurological diseases.

Transition between Random and Periodic Electron Currents on a DNA Chain

By resorting to a model inspired to the standard Davydov and Holstein-Fröhlich models, in the present paper we study the motion of an electron along a chain of heavy particles modeling a sequence of nucleotides proper to a DNA fragment. Starting with a model Hamiltonian written in second quantization, we use the Time Dependent Variational Principle to work out the dynamical equations of the system. It can be found that, under the action of an external source of energy transferred to the electron, and according to the excitation site, the electron current can display either a broad frequency spectrum or a sharply peaked frequency spectrum. This sequence-dependent charge transfer phenomenology is suggestive of a potentially rich variety of electrodynamic interactions of DNA molecules under the action of electron excitation. This could imply the activation of interactions between DNA and transcription factors, or between DNA and external electromagnetic fields.

Dipole radiation and beyond from axion stars in electromagnetic fields

We investigate the production of photons from coherently oscillating, spatially localized clumps of axionic fields (oscillons and axion stars) in the presence of external electromagnetic fields. We delineate different qualitative behaviour of the photon luminosity in terms of an effective dimensionless coupling parameter constructed out of the axion-photon coupling, and field amplitude, oscillation frequency and radius of the axion star. For small values of this dimensionless coupling, we provide a general analytic formula for the dipole radiation field and the photon luminosity per solid angle, including a strong dependence on the radius of the configuration. For moderate to large coupling, we report on a non-monotonic behavior of the luminosity with the coupling strength in the presence of external magnetic fields. After an initial rise in luminosity with the coupling strength, we see a suppression (by an order of magnitude or more compared to the dipole radiation approximation) at moderately large coupling. At sufficiently large coupling, we find a transition to a regime of exponential growth of the luminosity due to parametric resonance. We carry out 3+1 dimensional lattice simulations of axion electrodynamics, at small and large coupling, including non-perturbative effects of parametric resonance as well as backreaction effects when necessary. We also discuss medium (plasma) effects that lead to resonant axion to photon conversion, relevance of the coherence of the soliton, and implications of our results in astrophysical and cosmological settings.

Effect of Spherical Elements of Biosensors and Bioreactors on the Physicochemical Properties of a Peroxidase Protein

External electromagnetic fields are known to be able to concentrate inside the construction elements of biosensors and bioreactors owing to reflection from their surface. This can lead to changes in the structure of biopolymers (such as proteins), incubated inside these elements, thus influencing their functional properties. Our present study concerned the revelation of the effect of spherical elements, commonly employed in biosensors and bioreactors, on the physicochemical properties of proteins with the example of the horseradish peroxidase (HRP) enzyme. In our experiments, a solution of HRP was incubated within a 30 cm-diameter titanium half-sphere, which was used as a model construction element. Atomic force microscopy (AFM) was employed for the single-molecule visualization of the HRP macromolecules, adsorbed from the test solution onto mica substrates in order to find out whether the incubation of the test HRP solution within the half-sphere influenced the HRP aggregation state. Attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) was employed in order to reveal whether the incubation of HRP solution within the half-sphere led to any changes in its secondary structure. In parallel, spectrophotometry-based estimation of the HRP enzymatic activity was performed in order to find out if the HRP active site was affected by the electromagnetic field under the conditions of our experiments. We revealed an increased aggregation of HRP after the incubation of its solution within the half-sphere in comparison with the control sample incubated far outside the half-sphere. ATR-FTIR allowed us to reveal alterations in HRP’s secondary structure. Such changes in the protein structure did not affect its active site, as was confirmed by spectrophotometry. The effect of spherical elements on a protein solution should be taken into account in the development of the optimized design of biosensors and bioreactors, intended for performing processes involving proteins in biomedicine and biotechnology, including highly sensitive biosensors intended for the diagnosis of socially significant diseases in humans (including oncology, cardiovascular diseases, etc.) at early stages.