Mass Action Analysis of Kinetics and Extent of Fusion between Sendai Virus and Phospholipid Vesicles

The kinetics and extent of fusion between Sendai virus particles and liposomes were investigated with an assay for lipid mixing based on the relief of self-quenching of fluorescence. The measurements, which were carried out at pH 7.4 and 5.0, included liposomes of three compositions, cardiolipin (CL), CL/dioleoylphosphatidylcholine (CL/DOPC 1:1), and phosphatidylserine (PS). Liposomal lipid concentrations varied from 2.5 to 50 μM. In addition, the effect of low concentrations of the dehydrating agent poly(ethylene glycol) (PEG) on fusion between the virus and the liposomes at pH 7.4 was studied. The results were analyzed in terms of a mass action kinetic model which views the overall fusion reaction as a sequence of a second-order process of virus—liposome adhesion or aggregation, followed by the first-order fusion reaction itself. The fusion products were shown to consist of a single virus particle and several liposomes. Analytical solutions were found for the final extent of fusion and increase in fluorescence intensity following the fusion of fluorescently labeled virus particles with liposomes. The final extents of fluorescence intensity were explained by assuming an essentially irreversible binding of liposomes to inactive virus particles. The percents of active virus particles and the rate constants of fusion and aggregation were larger at pH 5 than at pH 7.4, increased when PEG was included in the medium, and varied with liposomal lipid composition according to the sequence CL > CL/DOPC > PS. At pH 5, the percents of Sendai virus particles capable of fusing with CL, CL/DOPC, and PS liposomes were 100, 80, and 30, respectively, indicating that the fusion activity is not merely a function of liposomal surface charge. The rate constant of fusion, f, exhibited the largest variation as a function of pH and liposome composition, varying from 1 to 0.005 s⁻¹, whereas the rate constant of aggregation varied from 1.8 x 10⁸ to 0.7 x 10⁸M^−1.s⁻¹. A small degree of reversibility was needed to simulate and predict the kinetics of fusion. This reversibility promoted the overall fusion rate at the later stages due to a certain degree of dissociation of liposomes bound to inactive virus particles.