Biotechnol. Appl. Biochem. (2003) 38, 95-102 - S. Sarkar and others - Prediction of size distribution of lipid-peptide-DNA vector particles

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Biotechnology and Applied Biochemistry (2003) 38, (95–102) (Printed in Great Britain)

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Prediction of size distribution of lipid–peptide–DNA vector particles using Monte Carlo simulation techniques

Supti Sarkar*, Hu Zhang*, Susana M. Levy*, Stephen L. Hart†, Helen C. Hailes‡, Alethea B. Tabor‡ and Parviz Ayazi Shamlou*^1,2

*Department of Biochemical Engineering, University College London, Torrington Place, London, WC1E 7JE, U.K., †Institute of Child Health, UCL, Molecular Immunology Unit, Institute of Child Health, University College London Medical School, London WC1N 1EH, U.K., and ‡Department of Chemistry, UCL, University College London, Christopher Ingold Laboratories, 20 Gordon Street, London WC1H OAJ, U.K.

Key words: aggregation dynamics, formulation, lipid–peptide–DNA vector particles, Monte Carlo simulation, zeta potential.

Abbreviations used: DBD, DNA-binding domain; DLVO, Derjaugin–Landau–Verwey–Overbeel; DOPE, dioleoyl phosphatidylethanolamine; DOTMA, N-[1-(2,3-dioleyloxy)propyl]-N,N,N-trimethylammonium chloride; LPV, lipid–peptide–vector; PCS, photon correlation spectroscopy; PSD, particle size distribution; SD, spacer domain; TD, targeting domain.

Notation used: a₁, a₂, radii of primary particles 1 and 2 (m); A, Hamaker constant (J); c, ionic concentration (M); C₀ initial total particle number concentration/m³; D_H, particle hydrodynamic diameter (m); e, charge on electron (1.6×10^-19 C); H, separation distance between two primary particles (m); k, coagulation events; k_B, Boltzmann constant (1.381×10^-23 J/K); k_ij dimensionless aggregation kernel for particle i and j;

k_ij

, dimensionless emsemble average kernel; k_max, dimensionless maximum coagulation kernel; K_ij, aggregation kernel for particle i and j (m³/s); K_c intrinsic aggregation rate (m³/s); M_i, mass of particle i (kg/m³); M_k, average mass size after k aggregation events (kg/m³); M_av(0), average mass size at t=0 (kg/m³); N, constant number of particles for Monto Carlo simulation; p_ij, coagulation probability; R, random number between 0 and 1; T, absolute temperature (K); t_k, real time corresponding to k coagulation event (s); V_A, V_R and V_T, interaction energies (van der Waals' attraction, electrical repulsion and total interaction) (J); x, dimensionless [(H/a₁+a₂)]; y, dimensionless (=a₁/a₂); z, valence (charge number) of ionic species.

Greek letters used: g₁, g₂, dimensionless functions of zeta potential; z₁, z₂, zeta potentials of particles 1 and 2; e, permittivity (dimensionless); k, Debye–Hückel parameter; m(h), dynamic viscosity of liquid (kg/ms); a, adjustable constant related to zeta potential; t_c, characteristic coagulation time (s); Dt_k, time interval for k coagulation event (s)

²Present address: Lilly Research Laboratories, A Division of Eli Lilly and Company, Lilly Corporate Centre, Indianapolis, Indiana 46285, U.S.A.

Concerns with insertional mutagenesis for retrovirus and immunogenicity for adenovirus have motivated research into development of non-viral vectors that can safely deliver desired gene constructs to target cells in tissues and organs. Many non-viral vectors suffer from unacceptably poor in vivo cell transfection and low transgene expression. Evidence suggests that cell transfection is linked to particle size – vector particles below about 200 nm are considered desirable. Experimental measurements indicate, however, that vector particles are susceptible to significant aggregation under most conditions of pH and ionic strength, including physiological conditions, although there are currently no means of predicting the kinetics of aggregation. The present paper addresses this challenge by presenting a mathematical framework based on the Monte Carlo simulation techniques for modelling the dynamics of aggregation. The approach is used to simulate the evolution of particle-size distribution for an integrin-targeting lipid–peptide–DNA vector system in buffers of different pH and ionic strength. The simulations required two input parameters, including the initial-size distribution of the particles and a fitting parameter (a). Comparison of simulations with experimental data showed that a was closely related to the zeta potential of the particles in the buffer medium, making simulations fully predictive. The modelling approach may be used in other vector systems.