Toward a more accurate quantitation of the activity of recombinant retroviruses: alternatives to titer and multiplicity of infection

Abstract

In this paper, we present a mathematical model with experimental support of how several key parameters govern the adsorption of active retrovirus particles onto the surface of adherent cells. These parameters, including time of adsorption, volume of virus, and the number, size, and type of target cells, as well as the intrinsic properties of the virus, diffusion coefficient, and half-life (t(1/2)), have been incorporated into a mathematical expression that describes the rate at which active virus particles adsorb to the cell surface. From this expression, we have obtained estimates of C(vo), the starting concentration of active retrovirus particles. In contrast to titer, C(vo) is independent of the specific conditions of the assay. The relatively slow diffusion (D = 2 x 10(-8) cm(2)/s) and rapid decay (t(1/2) = 6 to 7 h) of retrovirus particles explain why C(vo) values are significantly higher than titer values. Values of C(vo) also indicate that the number of defective particles in a retrovirus stock is much lower than previously thought, which has implications especially for the use of retroviruses for in vivo gene therapy. With this expression, we have also computed AVC (active viruses/cell), the number of active retrovirus particles that would adsorb per cell during a given adsorption time. In contrast to multiplicity of infection, which is based on titer and is subject to the same inaccuracies, AVC is based on the physicochemical parameters of the transduction assay and so is a more reliable alternative.

FIG. 1

Kinetics of retrovirus adsorption. lacZ retrovirus with Polybrene was added either to an empty plate (open circles) or to a plate confluent with NIH 3T3 fibroblasts (solid circles). Adsorption was monitored with an ELISA that measured the amount of p30 remaining in the medium. The diffusion coefficient was calculated by fitting the experimental data to the Valentine and Allison equation (line) by nonlinear regression analysis. The best-fit value, D = 1.74 × 10⁻⁸ cm²/s.

FIG. 2

Recombinant retroviruses decay with a half-life of ∼6.5 h in fresh and conditioned media. Undiluted (solid circles) or diluted (1:100) lacZ retrovirus (open circles) was incubated at 37°C. At various times, 0.5-ml aliquots were taken and frozen. To test the activity of the virus, NIH 3T3 cells were plated at 6.0 × 10⁴ cells per well in six-well plates and the next day were transduced with 1.0 ml of lacZ retrovirus for 4.0 h at a final dilution of 1:500 in the presence of Polybrene. Two days later, the number of gene transfer events (CFU) was measured by X-Gal staining.

FIG. 3

Active and inactive particles adsorb, but virus decay limits the number of adsorbed active particles. (A) Simulation of the effect of various half-lives on the adsorption of active retrovirus with equation 2. Confluent monolayers of cells in a six-well plate were exposed for 48 h to 1.0 ml of retrovirus with an initial concentration of 10⁷ active particles per ml and different half-lives. Both the rate of adsorption of active particles and the steady-state levels decrease as half-life decreases. (B) Decay of virus activity has minimal effect on virus adsorption. lacZ virus was divided into two aliquots; one was decayed by incubation for 24 h at 37°C, and the other was an untreated control. (C) To measure adsorption, NIH 3T3 cells (1.5 × 10⁵ per well) were plated in a six-well dish. After 72 h, the medium was replaced with the control or with decayed virus sample containing 8 μg of Polybrene per ml. After 2 h, the virus was removed, the cells were lysed, and the lysate was analyzed for the presence of p30 capsid protein via ELISA.

FIG. 4

Effect of various volumes on the adsorption of active retrovirus. (A) Simulation of the effect of various volumes on the adsorption of active retrovirus with equation 2. Confluent monolayers of cells in a six-well plate were incubated for 48 h with different volumes of retrovirus with an initial concentration of 10⁷ active particles per ml (t_1/2 = 7.0 h). This simulation shows that for volumes which are typically used (0.5 and 1.0 ml), there is no significant difference in the number of adsorbed active particles. Beyond a critical volume, there is no significant increase in the number of adsorbed active particles. Differences only occur for exceedingly small volumes that are rarely used in six-well plates (0.2 and 0.1 ml). (B) Data from the same simulation plotted as a function of liquid depth or volume for different adsorption times to more accurately illustrate the threshold volume. The critical volume varies for different adsorption times, because the particles have additional time to diffuse greater distances. (C) The number of infectious events does not increase for volumes of retrovirus above the critical volume. NIH 3T3 cells (8.0 × 10⁴ cells/well; six-well plate) were transduced for 2.5 h the next day with different volumes of lacZ retrovirus diluted 1:500. Two days later, the number of CFU was measured by X-Gal staining. Increasing the volume of retrovirus fourfold from 0.5 to 2.0 ml did not increase the number of CFU, in agreement with the predictions of the mathematical model. A decrease in CFU occurred only with 0.25 ml of virus, a volume below the threshold volume.

FIG. 5

The number of gene transfer events is proportional to the concentration of retrovirus and the number of target cells. NIH 3T3 cells were plated at various densities (1.0 × 10⁴, 2.0 × 10⁴, 4.0 × 10⁴, and 8.0 × 10⁴ cells/well; six-well plate) and were transduced the next day (3.5 h) with 1.0 ml of lacZ retrovirus of different dilutions (1:250, 1:500, 1:1,000, and 1:2,000) in the presence of Polybrene. At the start of transduction, the number of target cells was counted in parallel wells. Two days later, the number of CFU was measured by X-Gal staining. The number of CFU is plotted as a function of virus dilution (A). CFU increases as virus concentration increases. The number of CFU is plotted as a function of cell number at the start of transduction (B). The number of CFU increases as cell number increases.

FIG. 6

Values of CFU of the same retrovirus stock are different on NIH 3T3 cells versus HuFb. Cells were plated at various densities and were transduced the next day (3.5 h) with 1.0 ml of lacZ retrovirus (diluted 1:250). At the start of transduction, the number of target cells was counted in parallel wells. Two days later, the number of CFU was measured by X-Gal staining. The number of CFU of the same virus stock is lower on human fibroblasts; however, for both cell types there is a range of cell densities where the number of CFU is linearly proportional to cell number.