Non-Markovian master equation for quantum transport of fermionic carriers.

We propose a simple, yet feasible, model for quantum transport of fermionic carriers across tight-binding chain connecting two reservoirs maintained at arbitrary temperatures and chemical potentials. The model allows for elementary derivation of the master equation for the reduced single particle density matrix (SPDM) in a closed form in both Markov and Born approximations. In the Markov approximation the master equation is solved analytically, whereas in the Born approximation the problem is reduced to an algebraic equation for the SPDM in the Redfield form. The non-Markovian equation is shown to lead to resonant transport similar to Landauer's conductance. It is shown that in the deep non-Markovian regime the transport current can be matched with that obtained by the non-equilibrium Green's function method.

Manifestation of Majorana modes overlap in the Aharonov-Bohm effect.

One of the key features of the Majorana bound states emerging in topological superconducting (SC) wires is increasing oscillations of their energy under the growth of magnetic field or chemical potential due to concomitant enhancement of hybridization of the Majorana mode wave functions initially localized at the opposite edges of the structure. In this study we found that the other consequence of it is a shift of Aharonov-Bohm (AB) oscillations of linear-response conductance in an interference device where two ends of the SC wire connected with a normal contact via non-SC wires (arms). In addition, it is accompanied by an oscillation period doubling. The numerical calculations for the spinful system are supported by the analytical results for different spinless models allowing to track the conductance evolution as the hybridization of the Majorana modes increases. It is shown that since the coupling between the different arms and normal contact is implemented only via the different-type Majoranas the AB oscillations acquire a fundamentalπ/2 shift in comparison with the effect for an analogous system of zero-energy quantum dots.

Fano effect in Aharonov-Bohm ring with topologically superconducting bridge.

Taking into account an inner structure of the arms of the Aharonov-Bohm ring (AB ring) we have analyzed the transport features related to the topological phase transition which is induced in a superconducting wire (SC wire) with strong spin-orbit interaction (SOI). The SC wire acts as a bridge connecting the arms. The in-plane magnetic-field dependence of linear-response conductance obtained using the nonequilibrium Green's functions in the tight-binding approximation revealed the Breit-Wigner and Fano resonances (FRs) if the wire is in the nontrivial phase. The effect is explained by the presence of two interacting transport channels in the system. As a result, the FRs are attributed to bound states in continuum (BSCs). The BSC lifetime is determined by both hopping parameters between subsystems and the SC-wire properties. It is established that the FR width and position are extremely sensitive to the type of the lowest-energy excitation in the SC wire, the Majorana or Andreev bound state (MBS or ABS, respectively). Moreover, it is shown that in the specific case of the AB ring, the T-shape geometry, the FR disappears for the transport via the MBS and the conductance is equal to one quantum. It doubles in the local transport regime. On the contrary, in the ABS case the local conductance vanishes. The influence of the mean-field Coulomb interactions and diagonal disorder in the SC wire on the FR is investigated.

Dynamics of the inducing signal for the SOS regulatory system in Escherichia coli after ultraviolet irradiation.

SOS response in Escherichia coli is induced by various DNA-damaging treatments, for example by ultraviolet irradiation, to help a cell to recover from the damage. During induction of the SOS regulatory system, generation of the inducing signal for the system is the early step. In the present study a model for quantitative description of the signal dynamics is developed. We derive the inducing signal, in terms of concentration of single-stranded DNA, as a function of time since the moment of ultraviolet irradiation. Simulation of the signal level after irradiation with two doses of 5 and 20 J m-2 is presented. This provides quantitative description of the event that controls various cellular physiological reactions induced in the course of the SOS response. The dynamics of the signal level are then used as an input for a dynamical equation description of the SOS regulatory system that we proposed earlier. This allows for a quantitative analysis of the subsequent step in the SOS induction: cleavage of LexA protein, a negative regulator of the SOS system. The model is verified against available experimental data for LexA protein level in ultraviolet radiation-induced Escherichia coli cells.

Induction of the SOS Response in Ultraviolet-Irradiated Escherichia coli Analyzed by Dynamics of LexA, RecA and SulA Proteins.

The SOS response in Escherichia coli is induced after DNA-damaging treatments including ultraviolet light. Regulation of the SOS response is accomplished through specific interaction of the two SOS regulator proteins, LexA and RecA. In ultraviolet light-treated cells, nucleotide excision repair is the major system that removes the induced lesions from the DNA. Here, induction of the SOS response in Escherichia coli with normal and impaired excision repair function is studied by simulation of intracellular levels of regulatory LexA and RecA proteins, and SulA protein. SulA protein is responsible for SOS-inducible cell division inhibition. Results of the simulations show that nucleotide excision repair influences time-courses of LexA, RecA and SulA induction by modulating the dynamics of RecA protein distribution between its normal and SOS-activated forms.

Mathematical model of the SOS response regulation of an excision repair deficient mutant of Escherichia coli after ultraviolet light irradiation.

A mathematical model for the development of the SOS signal in nucleotide-excision repair deficient Escherichia coli cells subjected to ultraviolet light irradiation is proposed, in which regions of single-stranded DNA (gaps) are created during replication of a damaged chromosome when the strand elongation stops at pyrimidine dimers. The concentration of single-stranded DNA of gaps as a function of time is obtained. The model for the interaction of the LexA and RecA proteins, a well-established key event in SOS regulation, is presented, resulting in a system of differential equations for the concentrations of LexA, RecA and activated RecA proteins. The simulated LexA protein kinetic curves agree with the experimental data for two excision repair deficient mutants: uvrA6 and dnaC28 uvrB(del), which is also a temperature-sensitive DNA replication initiation mutant. It is shown that the model can be used to quantitatively describe the kinetics of SOS response through the amount of the SOS signal (concentration of single-stranded DNA) in a cell as a function of time.