Molecular dynamics simulation of the adsorption of polypeptides with photoactive molecules on the surface of the carbon nanotube

Peculiarities of the location of adsorbed polypeptides on the surface of single-walled carbon nanotubes with molecules of rhodamine $\mathrm{6G}$ and without them are investigated by using the molecular dynamics method. The radial distribution of the atomic concentration of monomer units of the protein fragments in a vacuum, but for a model polypeptide of the links SER - in vacuum and water are obtained. It turned out that the parameters of the approximating curves for the polypeptide of the links SER — in vacuum and the water is almost the same. A model of the kinetics of diffusion-controlled bimolecular photoreaction with the $\mathrm{O}_2$ molecules participation is presented in the surface layer of fullerene-tubulene nanoparticle with adsorbed macromolecular chain. Local concentration $n_{\Delta} \left( r, t \right)$ of the electronic excitation of oxygen molecules in such a system is determined by the radial profile of the molecular donor energy centers, non-covalent associated with the units of the macromolecule. The description of the density distribution of units of the macromolecule on the surface of the cylindrical particle is made on the basis of the special mathematical model of conformational structure of the polymer, using the statistical theory of macromolecules. The radial dependence of average atomic concentration of polypeptides are well approximated by formulas
\begin{equation*} n(\bf{r}) = \textrm{const} \, \psi^2 (\bf{r}), \end{equation*}

\begin{eqnarray*} \left\{ \begin{aligned} \psi_I &= A \left( I_0 (qr) -K_0 (qr) \frac{I_0 (qR)}{K_0 (qR)} \right),\, R < r < r_0\\ \psi_{II} &= A K_0 (qr) \left( \frac{I_0 (qr_0)}{K_0 (qr_0)} - \frac{I_0 (qR)}{K_0 (qR)} \right), \, r_0 < r < \infty \end{aligned} \right. \end{eqnarray*}
where $R$ is the radius of the nanotube, $a$, $A$, $\alpha$ are constants, $I_0$ and $K_0$ Bessel functions of imaginary argument of zero order of the first and second kind, and the parameter $q$ is found from the equation:
\begin{equation*} K_0 \left( q,r_0 \right) I_0 \left( q,r_0 \right) = \frac{a^2 k_B T}{6 \alpha r_0} K_0^2 \left( q,r_0 \right) \frac{I_0 \left(qR \right)}{K_0 \left(qR \right)}. \end{equation*}
The obtained results can be used to describe the features of kinetic mode of molecular reactions in axially-symmetric nanostructures, like nanotubes are considered. This, in turn, may be important in the creation of the active element of precision fluorescent-optical device for measuring of molecular oxygen concentration or of a sensor of singlet oxygen for biomedical applications, as well as in the synthesis of efficient sensitizers of singlet oxygen generation for photodynamic therapy.