^{1}

^{2}

^{3}

The possibility of complex formation by short lysine brush and therapeutic Semax peptides was investigated using molecular dynamics method. Lysine dendrimers and polymer brushes are used for drug and other (e.g., DNA, peptides, and polysaccharides) molecules delivery to different target cells. It is known that they could penetrate blood brain barrier. Since short lysine brush is nontoxic, a system containing of such brush and 8 oppositely charged Semax peptides was studied. It was obtained that stable complexes consisting of brush and peptides formed and structures of these complexes were investigated. Such complex can be used in future for delivery of Semax peptides to brain since these peptides have significant antioxidant, antihypoxic and neuroprotective effects.

Interest to macromolecules with regular branched structure grows every year [^{−}) of peptides. Hydrogen bonds between dendrigraft and peptide and hydrophobic interactions between their nonpolar groups are also important for creation of such complexes. Due to this ability to make complexes the dendrigrafts like other dendritic molecules could be used as multifunctional nanocarriers for delivery of drug or/and other molecules [

Therapeutic Semax peptide [

In our previous paper we studied complexes of Semax peptides with lysine dendrimer [

Molecular dynamics (MD) method is currently the main method for simulation of

polymer and biopolymer systems. The method consists in numerical solution of the classical Newton equations of motion for all atoms of the all molecules in the system. It was used first in the mid-fifties of the last century [

Modeling was performed using the molecular dynamics method for systems consisting of one lysine dendrigraft of second generation containing 8 lysine residues in main chain, 48 positively charged

Snapshots of a system consisting of dendrigraft of second generation, peptides, ions and water during simulation are shown on

are far from dendrigraft. After 30 ns (

To characterize the size of the subsystem containing dendrigraft and peptides during the equilibration the square of instant gyration radius

where R―is the center mass of dendrigraft, r_{i} и m_{i}―coordinates and masses of i atom correspondingly, N―is the total number of atoms in dendrigraft, M is the total mass of dendrigraft. This function was calculated using g_gyrate function of GROMACS software [

The time dependence of radius of gyration R_{g} of dendrigraft and peptides at the beginning of calculation describes the kinetics of process of complex formation (_{g} fluctuate slightly, but its average value practically does not change with time. Therefore, we can assume that the system is in equilibrium state.

The time dependence function of distances between dendrigraft and peptides also demonstrates the formation of complex within first 20 - 30 ns of simulation. Plateau on curves of

Another quantity that can characterize the rate of complex formation is the total number of hydrogen bonds (N) between dendrigraft and peptides. The dependence of this value on time is shows on

From

The size of complex in equilibrium state is evaluated by mean square of radius of gyration averaged through the time after equilibration (2):

where Dt = t_{max} − t_{eq }, t_{max}―full time of calculation and and t_{eq}―time of equilibration and < > means averaging the through equilibrium part of MD trajectory.

In equilibrium state the size of the complex (DG2 and 8 Semax peptides) is larger than the size of dendrigraft (see

The shape of complex can be characterized by its tensor of inertia main component ratio (

The shape of complex could be roughly characterised by ratio of largest and smallest eigenvalues of inertia tensor describing our system

Information about the internal structure of the equilibrium complex could be obtained using radial density distribution (3) of different groups of atoms relatively center of inertia of system.

where m_{comp}―mass of all atoms in complex; V_{комп}―volume of complex.

The radial distribution functions (not normalized) calculated using g_rdf function of GROMACS are shown on

System | Eigenvalues | |||
---|---|---|---|---|

R_{g} (nm) | ||||

Dendrigraft (DG2) | 1.12 | 1.45 | 1.51 | 1.67 |

DG2 & 8 Semax | 1.20 | 1.40 | 1.57 | 1.75 |

System | |
---|---|

Dendrigraft | 1.35 |

Dendrigraft + 8 Semax | 1.31 |

The number of hydrogen bonds between peptides and dendrigraft shows how tightly peptides associate with dendrigraft. From equilibrium part of

The distribution function of hydrogen bonds number (

The other characteristic of interaction between dendrigraft and peptides in complex is the distribution of ion pairs number between their charged groups. ^{−}) of the glutamic acid in peptides. There is also small second peak on this dependence probably due to second neighboring charges.

To evaluate the translational mobility of our systems, the time dependence of the mean square displacements (4) of the centers of inertia (MSD), were calculated (

We have found that dependence of MSD function on time is almost linear in some interval of time t in double logarithm coordinates (not shown). It means that in this interval the motion of complex is the diffusion-like motion (see ^{2}/s.

The system consisting of second generation dendrigraft and 8 Semax molecules in water with counterions has been studied. The process of complex formation by lysine dendrigraft of second generation and therapeutic Semax peptides and the equilibrium structure of the complex was investigated for the first time by the method of molecular dynamics simulation. It was shown that dendrigraft-peptide complex formation occurs rather quickly (in first 20 - 30 ns). After this time the complex is stable and the dendrigraft atoms are mainly inside the complex, while the peptide atoms are mainly on the surface of dendrigraft. In future it is necessary to study process of complexes formation and stability of similar complexes with greater number of peptides to define maximum capacity of this particular dendrigraft for delivery of Semax peptide.

This work was partly supported by grant 074-U01 of Government of RF and RFBR

grants 16-03-00775 and 15-33-20693mol_a_ved. Computing resources on supercomputers “Lomonosov” were provided by supercomputer center of Moscow State University [

Popova, E., Okrugin, B. and Neelov, I. (2016) Molecular Dynamics Simulation of Interaction of Short Lysine Brush and Oppositely Charged Semax Peptides. Natural Science, 8, 499-510. http://dx.doi.org/10.4236/ns.2016.812051