Aleksandr N. Bugay

Localized modulated waves in microtubules

In the present paper, we study nonlinear dynamics of microtubules (MTs). As an analytical method, we use semi-discrete approximation and show that localized modulated solitonic waves move along MT. This is supported by numerical analysis. Both cases with and without viscosity effects are studied.

Localized modulated waves and longitudinal model of microtubules

We here study nonlinear dynamics of microtubule (MT). A so-called u - model is explained in detail. A single longitudinal degree of freedom per MT subunits is assumed. It is known that a continuum approximation of a basic discrete dynamical equation of motion enables existence of kink and antikink solitons along MT. In this paper we use semi-discrete approximation for this equation and show that modulated solitonic waves could propagate as well. We suggest possible biological implications of these waves. Also, a detailed parameter analysis is performed.

Modeling nucleotide excision repair and its impact on UV-induced mutagenesis during SOS-response in bacterial cells

A model of the UV-induced mutation process in Escherichia coli bacteria has been developed taking into account the whole sequence of molecular events starting from initial photo-damage and finishing with the fixation of point mutations. The wild-type phenotype bacterial cells are compared with UV-sensitive repair-deficient mutant cells. Attention is mainly paid to excision repair system functioning as regards induced mutagenesis.

Nonlinear dynamics of C-terminal tails in cellular microtubules.

The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico, as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano-electrical waves elicited in the rows of very flexible C-terminal tails which decorate the outer surface of each microtubule. The fact that C-terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule-associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink-waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process.

On nonlinear reflection of optical pulse from low-frequency few cycle pulse

The features of the reflection of quasi-monochromatic optical pulse from intensive low frequency few cycle pulse in various nonlinear media are analyzed. The reflection effects are studied for the interaction of the optical pulse with low frequency solitons and breathers. A signal pulse experiences frequency shift, and its velocity changes correspondingly resulting in a time delay. The restrictions on the group velocity detuning and dispersion parameters are obtained and approved by numerical simulation.

Three-dimensional light bullets in anisotropic microdispersive media

Three-dimensional light bullets in Kerr media are known to be unstable. Different schemes were proposed to overcome this obstacle. One of them is to use a nonlinear parametric interaction. Such a type of interaction can be achieved in anisotropic micro-dispersive media where space dispersion is of importance. These media allow us to reach a simultaneous approximate fulfillment of group and phase matching. To study the general (3+1)D case we apply both an approximate analytical approach and numerical simulations. We suggest that nonlinear refraction manifests itself earlier than diffraction and dispersion. Both the general (3+1)D case and axial-symmetry case are studied. With the help of averaged Lagrangian method analytical solutions are derived provided that the fixed relation between the negative coefficients of the group velocity dispersion on both harmonics holds. We demonstrate that a spatiotemporal light bullet propagates for at least 300 nonlinear lengths in anisotropic media at second harmonic generation.

Mathematical Analysis of Regulatory Networks and Damage Repair Efficiency in Bacterial Cells

An extended mathematical model of the UV-induced mutation process in E. coli bacterial cells has been developed. It describes the whole sequence of molecular events involved in nucleotide excision repair of initial damage, replication kinetics and postreplication repair. The model provides ab initio calculation of the number of mismatches as a result of translesion synthesis for both wild type and repair-deficient mutant cells. A comparison of efficiency of different repair systems has been carried out.

Modeling the induced mutation process in bacterial cells with defects in excision repair system

A mathematical model of the UV-induced mutation process in Escherichia coli cells with defects in the uvrA and polA genes has been developed. The model describes in detail the reaction kinetics for the excision repair system. The number of mismatches as a result of translesion synthesis is calculated for both wild-type and mutant cells. The effect of temporal modulation of the number of single-stranded DNA during postreplication repair has been predicted. A comparison of effectiveness of different repair systems has been conducted.

Resonant generation of terahertz radiation in anisotropic media with permanent dipole moment

The generation of terahertz broadband pulses by optical rectification in nonlinear crystal under condition of laser pulse interaction with quantum particles with permanent dipole moment is examined. If the permanent dipole moment is larger than transition dipole moment, the resonant method is more efficient than nonresonant optical rectification. Estimated conversion efficiency in organics and semiconductor nanostructures can reach 0.1% and higher on order of magnitude.

Long-short-wave optical solitons in uniaxial crystals

On the base of numerical experiments we demonstrate in that the process of THz generation in nonlinear optical crystal with uniaxial anisotropy can result to formation of (2+1)-dimensional half-cycle pulses at sufficiently long distance of propagation. We also observed the formation of nonsolitonic few-cycle THz pulses, which accompanies the formation of solitons.