A mathematical relationship for hydromorphone loading into liposomes with trans-membrane ammonium sulfate gradients

Abstract

We have studied the loading of the opioid hydromorphone into liposomes using ammonium sulfate gradients. Unlike other drugs loaded with this technique, hydromorphone is freely soluble as the sulfate salt, and, consequently, does not precipitate in the liposomes after loading. We have derived a mathematical relationship that can predict the extent of loading based on the ammonium ion content of the liposomes and the amount of drug added for loading. We have adapted and used the Berthelot indophenol assay to measure the amount of ammonium ions in the liposomes. Plots of the inverse of the fraction of hydromorphone loaded versus the amount of hydromorphone added are linear, and the slope should be the inverse of the amount of ammonium ions present in the liposomes. The inverse of the slopes obtained closely correspond to the amount of ammonium ions in the liposomes measured with the Berthelot indophenol assay. We also show that loading can be less than optimal under conditions where osmotically driven loss of ammonium ions or leakage of drug after loading may occur.

Figure 1

The structure of hydromorphone.

Figure 2

A schematic representation of ammonium sulfate gradient loading.

Figure 3

The loading of hydromorphone into liposomes without a gradient. Each point is the mean of three values ± the standard deviation.

Figure 4

The fraction of drug loaded versus the amount of hydromorphone added for liposomes loaded with (NH₄)₂SO₄ at 120mM. The liposomes were either LUV (diamonds), SUV (circles), or MLV (squares), and were prepared as described under the Materials and Methods Section. Each point is the mean of three values ± the standard deviation.

Figure 5

The inverse of fraction loaded (1/F) versus the amount of hydromorphone added for SUV. Excess hydromorphone was removed either using dialysis (circles), or Sephadex chromatography (diamonds). Each point is the mean of three values ± the standard deviation.

Figure 6

The inverse of fraction loaded (1/F) versus the amount of hydromorphone added for LUV. LUV were loaded with (NH₄)₂SO₄ at either 120mM (upper panel) or 360mM (lower panel). Liposomes were suspended in either 0.9% (w/v) NaCl (upper panel, circles; lower panel, triangles), or 2.7% (w/v) NaCl (lower panel, circles). Each point is the mean of three values ± the standard deviation.

Figure 7

The inverse of fraction loaded (1/F) versus the amount of hydromorphone added for MLV. MLV were loaded with (NH₄)₂SO₄ at either 120mM (upper panel) or 360mM (lower panel), and were suspended in 0.9% (w/v) NaCl. Each point is the mean of three values ± the standard deviation.

Figure 8

The inverse of fraction loaded (1/F) versus the (drug added)/(loaded ammonium ions) ratio. All experiments from Figures 3–5 are plotted, except for SUV separated by dialysis, and LUV loaded with 360mM (NH₄)₂SO₄ and not tonicity matched during drug loading. For this plot the data points are individual values.