^{1,2}, D. Markelov

^{1,2}, I. Neelov

^{1,3}and A. Darinskii

^{1}

### Abstract

Poly-L-lysine (PLL) dendrimers are promising systems for biomedical applications due to their biocompatibility. These dendrimers have a specific topology: two spacers of different lengths come out of each branching point and thus the branching is asymmetric. Because of this asymmetry terminal groups are located at branches of different lengths, unlike dendrimers with a symmetric branching. This paper presents the results of the first systematic molecular dynamics simulation of such asymmetric PLL dendrimers. It is shown that PLL dendrimers are porous molecules with all terminal groups equally accessible to water. We have found that in spite of an asymmetry of branching the general structural characteristics of PLL dendrimers are rather similar to those of dendrimers with symmetric branching. We have also found that the structural characteristics of PLL dendrimers obey the general laws for dendrimers and that their electrostatic properties agree with the predictions of a general analytic theory.

This work was supported by the Russian Foundation of Basic Research (Grants 12-03-31243, 13-03-00524, and 16.523.12.3001). The simulations have been performed using the computational resources of the Institute of Macromolecular Compounds, Russian Academy of Sciences, and the Chebyshev and Lomonosov supercomputers at Moscow State University.

I. INTRODUCTION

II. MODEL AND METHOD

A. Optimization

B. Equilibration and productive runs

III. RESULTS AND DISCUSSION

A. Shape and size

B. Hydrodynamic radius

C. Internal structure

D. Distribution of terminal groups

E. Water penetration

F. Availability of terminal groups to water

G. Effective charge

IV. CONCLUSIONS

### Key Topics

- Peptides
- 13.0
- Electrostatics
- 6.0
- Computer simulation
- 5.0
- Molecular dynamics
- 5.0
- Hydrodynamics
- 4.0

##### C08

## Figures

Chemical structure of the G1 PLL dendrimer. The black line shows the core, the green line shows an inner lysine residue, and the red line shows a terminal lysine residue.

Chemical structure of the G1 PLL dendrimer. The black line shows the core, the green line shows an inner lysine residue, and the red line shows a terminal lysine residue.

Solvent accessible surfaces of the dendrimers of G = 1 to G = 5 generations.

Solvent accessible surfaces of the dendrimers of G = 1 to G = 5 generations.

Asphericity δ as a function of dendrimer molecular mass M.

Asphericity δ as a function of dendrimer molecular mass M.

Dependence of gyration radius R g on the product MG 2 (M is the molecular mass and G is the generation number).

Dependence of gyration radius R g on the product MG 2 (M is the molecular mass and G is the generation number).

Dendrimer hydrodynamic radius R h as a function of molecular mass (double log scale). Experimental data 18 (black triangles) and estimates from MD simulation: through 5% water density decay (red circles) and through (blue diamonds). Statistical errors are within 5%.

Dendrimer hydrodynamic radius R h as a function of molecular mass (double log scale). Experimental data 18 (black triangles) and estimates from MD simulation: through 5% water density decay (red circles) and through (blue diamonds). Statistical errors are within 5%.

Density profiles for dendrimers of generations G from 1 to 5. r COM is the distance from the center of mass.

Density profiles for dendrimers of generations G from 1 to 5. r COM is the distance from the center of mass.

Number of terminal groups N at a given distance r from the dendrimer center in the case of fully stretched spacers for different generations G. The dashed lines are eye guides.

Number of terminal groups N at a given distance r from the dendrimer center in the case of fully stretched spacers for different generations G. The dashed lines are eye guides.

Distribution density p of terminal groups, r is the distance from the dendrimer center.

Distribution density p of terminal groups, r is the distance from the dendrimer center.

Average number of water molecules ⟨N wat ⟩ within a sphere of radius equal to hydrodynamic radius R h .

Average number of water molecules ⟨N wat ⟩ within a sphere of radius equal to hydrodynamic radius R h .

Number of water molecules ⟨n wat ⟩ in the first coordination sphere of terminal groups as a function of the contour length L c of the corresponding branch.

Number of water molecules ⟨n wat ⟩ in the first coordination sphere of terminal groups as a function of the contour length L c of the corresponding branch.

(a) Charge distribution density p q (r/R g ). (b) Integral charge Q of the sphere with radius r (in units of R g ) for different generations G.

(a) Charge distribution density p q (r/R g ). (b) Integral charge Q of the sphere with radius r (in units of R g ) for different generations G.

Ratio between uncompensated charge Q obtained from simulation (Q max ) or analytic theory (Q*) and the dendrimer charge Q tot as a function of the distance from the dendrimer center of mass R max where negative charges of counterions compensate positive dendrimer charges.

Ratio between uncompensated charge Q obtained from simulation (Q max ) or analytic theory (Q*) and the dendrimer charge Q tot as a function of the distance from the dendrimer center of mass R max where negative charges of counterions compensate positive dendrimer charges.

## Tables

Parameters of simulated dendrimers.

Parameters of simulated dendrimers.

Radii of gyration R g .

Radii of gyration R g .

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