Drug Release from Liposomes: Role of Mechanism Based Models
Bradley D. Anderson
University of Kentucky
Why liposomes? l i p o s o m e
Drug solubilization Tumor targeting – EPR effect Controlled release potential Safety/reduction of drug toxicity Commercial products
N
N
O
OH
Si
O
OOH
Xiang and Anderson, Adv. Drug Delivery Rev. 58, 357–1378 (2006)
AR-67
Rakesh K. Jain et.al. Nature Reviews Cancer 2, 266-276 (2002)
EPR effect (enhanced permeability & retention) Particle size cut-off for extravasation
Pegylation and particle size effects on liposome clearance and tissue uptake
Ishida et al., Int. J. Pharm., 190, 49-56 (1999)
Tunable release kinetics?
• Nanoparticle accumulation in tumor may require up to12-24 hrs to reach optimum
• Free drug concentration profile in tumor determines efficacy
• What release rate is optimal? • Can mechanistic models enable the
design of optimal release rates?
NCI Alliance for Nanotechnology in Cancer
t1/2 = 57 h
t1/2 = 14 h
Vehicle CPT-11 50 mg/kg
Liposomal CPT-11 50 mg/kg
Drummond et al., Cancer Res., 66, 3271 (2006)
NCI Alliance for Nanotechnology in Cancer
Antitumor efficacy of CPT-11 in a colon cancer model depends on liposome
release kinetics
“As long as the release process is still not fully understood it is difficult and speculative to make improvements to the existing formulation or devise new compounds.”
Predictive Models Must Account for the Driving Force, Membrane Permeability
and Environmental Factors • Prediction of: Driving Force Contributions
What species are transported? pH gradients and their role? Membrane binding Drug precipitation & self-association Role of environmental factors (pH, temperature, media composition)
Membrane Permeability Barrier domain for lipid bilayer transport. What governs membrane selectivity to permeant structure?
How do we predict chemical selectivity? How do we predict permeant size selectivity?\ Temperature effects
from the Doxil® package insert
• 2 mg/mL doxorubicin HCl • 16 mg/mL lipid
– 3.19 mg/mL cholesterol
– 9.58 mg/mL HSPC – 3.19 mg/mL MPEG-
DSPE • ~0.6 mg/mL NH4SO4
• pH 6.5 buffer(histidine) • sucrose for isotonicity
Equilibria and kinetic processes governing DXR release rates
from actively loaded liposomes using dynamic dialysis OH
OH3C
OHNH3
OH
O
OH
OH
OHO
OOCH3
Cl
Doxorubicin (DXR)
DXR actively-loaded - low intravesicular pH
Extravesicular pH 7.2-7.8
Physical processes included in a mechanistic model for Doxil
• Acid-base dissociation equilibria (i.e., DXR pKa) for DRX inside and outside the liposomes;
• Acid-base dissociation equilibria (i.e., pKa) for Ammonia inside and outside the liposomes;
• Acid-base dissociation equilibria (pKa) for sulfate inside and outside (if present) the liposomes;
• Precipitation equilibrium (i.e., Ksp) for DRX+ and SO42- inside the liposomes;
• Binding equilibria for DRX and DRX+ onto outer and inner bilayer leaflets;
• Forward/reverse rate constants for DRX bilayer and dialysis membrane transport
• Forward and reverse rate constants for ammonia bilayer and dialysis membrane transport
Csuhai et al., J. Pharm. Sci., 104, 1087 (2015)
Separation of drug-loaded liposomes by
gel filtration
Liposomal fraction
Unentrapped ‘free’ drug
PD MiniTrap G25 Gel filtration columns
-2
0
2
4
6
8
10
12
14
0 5 10 15
Dox
con
c( µ
g/m
l)
Volume (ml)
ENCAP
FREE
Gel filtration: Dox spiked (90%) human plasma/pH 7.4 buffer (10%)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 20 40 60 80
2 ug/mL Dox5 ug/mL Dox10 ug/mL Dox15 ug/mL Dox20 ug/mL Dox
Enc
apsu
late
d D
ox (
ug/m
L)
Time (h)
Representative blank liposomal uptake profiles (pH 5.5,3 mg/ml lipid w/250 mM (NH4)2SO4)
Which is the permeable DXR species?
Rate constant vs pH for DXR monomer uptake into blank liposomes containing 250 mM (NH4)2SO4 at 37 °C.
pKa = 8.13 ± 0.20
)1( npnn fPfPSAk −+=
)/][1/(1 an KHf ++=
Suspension concentration: 3 mg lipid/mL (HPLC with ELSD detection)
Pn = 8.5 x 10-4 cm/h Pp ~ 0
Neutral form is the permeable species Csuhai et al., J. Pharm. Sci., 104, 1087 (2015)
DXR self-association
DXR uptake vs. time at varying DXR concentrations in 242 mM Na2SO4 at pH 6.5 (10 mM phosphate), 37 ºC. Dotted lines represent simultaneous fits to the isodesmic self-association model.
Top view
Side view
Anti parallel stacking
Agrawal et al., Eur. J. Med. Chem., 44, 1437 (2009)
Csuhai et al., J. Pharm. Sci., 104, 1087 (2015)
Rate of liposomal uptake (- - -) and fraction of DXR monomer ( ̶̶̶ ̶ ̶ ) vs.
DXR concentration (3 mg lipid/mL, 240 mM Na2SO4 pH 6.5, 37°C)
DXRmon = DXRTotal{2/[1 + (4KnDXRTotal + 1)0.5]}2
Kn = 7030 ± 900 M-1
Csuhai et al., J. Pharm. Sci., 104, 1087 (2015)
Ksp determination for (DXR)2SO4
DXR Solubility (mg/mL)*
T (°C) 250 mM (NH4)2SO4 150 mM (NH4)2SO4 100 mM (NH4)2SO4
50 mM (NH4)2SO4 Apparent Ksp (M3) (Eq. 7)
5 ± 1 0.17 ± 0.01 0.23 ± 0.01 0.27 ± 0.01 0.36 ± 0.02 2.1± 0.2 x 10-9
25 ± 1 0.23 ± 0.01 0.29 ± 0.01 0.35 ± 0.01 0.46 ± 0.01 3.6 ± 0.3 x 10-8
37 ± 0 0.63 ± 0.01 0.81 ± 0.04 1.00 ± 0.05 1.31 ± 0.03 2.9 ± 0.2 x 10-7
*n=3; average values ± SD
Pooled DXR solubility data at 5 ± 1°C, 25 ± 1°C, and 37 ± 0°C, in the presence of 250, 150, 100, or 50 mM (NH4)2SO4.
DXR solubility vs pH and (NH4)2SO4 concentration at 37 ± 0 °C. Error bars represent standard deviations.
Csuhai et al., J. Pharm. Sci., 104, 1087 (2015)
Influence of membrane binding on liposomal uptake rate constant
DXR uptake versus lipid concentration at 10 µg/mL DXR, 37◦C, pH 6.5, with 250 mM intraliposomal (NH4)2SO4. The model fit assumes only the monomeric, neutral species is membrane permeable.
A: liposomal surface area per ml P1: neutral monomer permeability fn: fraction neutral monomer fubo: fraction unbound c & d: aqueous & outer bilayer leaflet volume ratios
Intravesicular membrane binding is amplified due to the high internal surface/volume ratio.
OH
OH3C
OHNH3
OH
O
OH
OH
OHO
OOCH3
Cl
Doxorubicin (DXR)
DXR actively-loaded - low intravesicular pH
Extravesicular pH 7.2-7.8
• Mechanistic model accounts for all equilibria and kinetic processes below
• Dynamic intravesicular pH calculation is critical.
Implicit eqn. for pH calculation (from charge balance
Fugit et al., J. Control. Release, 217, 82 (2015)
Mechanistic model simulations in various release conditions (e.g., external pH and [NH3])
Intravesicular pH governed by external [NH3]
Low internal pH driven by NH3 release when [NH3] = 0 in media
Fugit et al., J. Control. Release, 217, 82 (2015)
Intravesicular pH modulates the driving force for DXR release –
model simulations pH 7.4 0 mM NH3
pH 7.0 50 mM NH3
pH 7.4 50 mM NH3
pH 7.8 50 mM NH3
Fugit et al., J. Control. Release, 217, 82 (2015)
DXR release vs time (expt. vs. prediction)
0
20
40
60
80
100
0 12 24 36 48 60 72
% D
XR R
emai
ning
Time (hours)
1 2 3 4 56 7 8 9 1011 12 13 14 15
0
20
40
60
80
100
0 12 24 36 48 60 72
% D
XR R
emai
ning
Time (hours)
1 2 3 4 56 7 8 9 1011 12 13 14 15
Experimental Prediction
NH
4+ 0-1
00 m
M
x1
x2
x3
pH 7.0 – 7.8
Fugit et al., J. Control. Release, 217, 82 (2015)
-15
0
15
30
45
60
75
1.5 2.5 3.5 4.5 5.5 6.5 7.5
% D
XR R
elea
sed
Afte
r 19
hr
Calculated Intravesicular pH
Observed Simulated
Empirical model Mechanistic model
Superiority of the mechanistic model
Fugit et al., J. Control. Release, 217, 82 (2015)
Dox uptake vs. Temperature pH 6.0, 30 mM phosphate,
265 mM NaCl, 10 ug/mL Dox, 3 mg/mL lipid
y = 0.1815x + 0.0404
y = 1.1401x + 0.0808
y = 3.2346x + 0.0359
y = 27.097x - 0.8234
y = 61.674x + 1.5721
0
1
2
3
4
5
6
7
0 2 4
DXR
Sus
p. C
onc.
ent
rapp
ed (µ
g/m
L)
Time (h)
37 C42 C47 C52 C57 C
Arrhenius plot – uptake rate vs. 1/T
Ea = 65.6 kcal/mol
(consistent with chain ordering effect on bilayer barrier properties & size selectivity)
Xiang & Anderson, Biophys. J., 72, 223 (1997)
10° ↑ => 24-fold ↑ in k
Historical Model for Structure-Transport Relationships
• “Bulk” Solubility-Diffusion theory – Graham (1866); Overton’s rule (1896, 1899, 1902)
Permeability: Po = KmemDmem/h incorrect!
Kmem = PCmembrane/water ~ PCoctanol/water
Dmem = const/MW1/2
log (Po) = const + 1.0 log PCoctanol/water/MW1/2
Not for bilayer transport! Xiang & Anderson, Adv. Drug Delivery Revs., 58, 1357 (2006)
Bulk Solubility Diffusion Theory fails to account for phase transitions
Data plotted from Xiang and Anderson, Biophys. J. 1998.
-10
-9
-8
-7
-6
-5
-4
-3
-2
3 3.1 3.2 3.3 3.4
1/T x 1000 (K)
ln P
erm
(obs
erve
d an
d pr
edic
ted)
DPPC phase transition
Formic Acid across DPPC
“Bulk” permeability
Bulk solubility-diffusion model fails to account for the amplified size
selectivity
20 140 260 380 500
V (A 3 )
10 -11
10 -10
10 -9
10 -8
10 -7
10 -6
10 -5
10 -4
P m
δ / K
or D
Decane diffusion (n=0.8)
Egg PC - liquid crystalline bilayers (n=1.48)
DPPC - gel phase bilayers (n=6.2)
log Pmδ /K = const - n log V
Permeability theory - barrier domain model
PK D
hf Pm
barrier water barrier
barriero= = ∗/
Po = from solubility-diffusion theory f = reflects chain ordering factor
f = foexp(-λas/af)
Permeant cross-sectional area
Bilayer free-surface area – decreases with increase in chain-order
Xiang & Anderson, Adv. Drug Delivery Revs., 58, 1357 (2006)
Joguparthi et al., J Pharm Sci 97:400–420, 2008
Lactone t1/2 = 3 hr
Translation from in vitro to in vivo • Release methods in blood or plasma
– Pitfalls of dynamic dialysis • see Modi & Anderson, Mol. Pharmaceutics, 10, 3076 (2013)
– Non-sink release methods • see Fugit & Anderson, Mol. Pharmaceutics, 11, 1314 (2014)
– Real-time spectroscopic methods • see Fugit et al., J. Control. Release, 197, 10 (2015)
Topotecan (TPT)
Liposomal TPT release in human plasma monitored by fluorescence excitation
spectra Dependence of TPT release t1/2 on
extravesicular ammonia concentration
Environmental factors in vivo may influence liposomal release rates
• Exchange of plasma lipid components with vesicle lipids • Disruption of pH gradients by permeable (small
molecule) plasma components – see Joguparthi & Anderson, J. Pharm. Sci., 97, 433 (2008) – accelerated
silatecan release due to plasma CO2
– see Fugit et al., J. Control. Release, 197, 10 (2015)
Liu et al., Anticancer Drugs, 13, 709 (2002)
Liposomal TPT retention in PBS vs. human plasma
NH3 in human plasma (8 donors) as rec’d from supplier
Increase in NH3 in human plasma vs storage time at various temps.
Acknowledgments Eva Csuhai Sogol Kangarlou Tian-Xiang Xiang Andre Ponta
Kyle Fugit Duhyung Choi Paul Bummer Amar Jyoti
Portions of the work presented were supported by Grant Number R25CA153954 from the National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Instittute or the National Institutes of Health.