Multiscale Modeling of Targeted Drug Delivery

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Multiscale Modeling of Targeted Drug Delivery
Nanobiotechnology, fulfilling the promise of
nanomedicine, CEP, 2006

• Neeraj Agrawal, Joshua Weinstein
• Ravi Radhakrishnan
• Department of Bioengineering
• University of Pennsylvania

Targeted Therapeutics
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Microcarrier Arrest?
Injected microcarrier
Transport through arterial system
N (multi pass)
Circulatory System
H
Me
M
Filtered?
Y
One pass
Y
H
EndothelialCell Response
immune system interaction
Aberrant
N
Excretion
Normal
Cell Fate?
Moderate
Me
Extreme
Drug Assimilation
Other signaling
Immune response
E
H
Me
M
Intracellular uptake
Apoptosis Necrosis
Endocytotic uptake
Immunological signaling
Toxicity
E
H
M
Intracellular assimilation
Transport to microcapillaries, target tissue
Cell Death
cytokines
Me
Model
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Motivation for Modeling Targeted Drug Delivery

• Predict conditions of nanocarrier arrest on cell
  binding mechanics, receptor/ligand diffusion,
  membrane deformation, and post-attachment
  convection-diffusion transport interactions
• Determine optimal parameters for microcarrier
  design nanocarrier size, ligand/receptor
  concentration, receptor-ligand interaction,
  lateral diffusion of ligands on microcarrier
  membrane and membrane stiffness

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Parameter Space Explored in Simulations and Microcarrier Design Parameter Space Explored in Simulations and Microcarrier Design Parameter Space Explored in Simulations and Microcarrier Design Parameter Space Explored in Simulations and Microcarrier Design
Property Range and reference Experimental tenability Impact on design
Microcarrier diameter 100 nm, 1 ?m Method of sonication and filtering Small microcarriers- lower affinity, smaller amount of drug, larger surface area per volume.
Drug permeability, diffusivity, Co 10-11 - 10-9 m2/s, 5-25 wt./vol. Drug, vesicle, stress (deformation dependent. Lower permeability minimizes drug loss by diffusion. Endocytosis can affect delivery.
Receptor (anti-ICAM) density 2500-7000 ?m-2 Controlled in the protocol for tethering. Can increase affinity of the micro carrier if ICAM not saturating.
Vesicle Properties ?3?N/M, ?400kBT, M10-5 ?m/s Depends on lipid type in vesicles. (phospho vs., synthetic polymer) Impacts response time, time of microcarrier arrest, drug loss.
PEG tether attached? (Y/N) If Y, tether length ranges 30-60 nm Receptors attached on vesicle surface or via PEG linkers. Impacts the hydrodynamics, interaction with the glycocalyx.
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Parameter Space Explored in Simulations and Microcarrier Design Parameter Space Explored in Simulations and Microcarrier Design Parameter Space Explored in Simulations and Microcarrier Design Parameter Space Explored in Simulations and Microcarrier Design
Property Range and reference Experimental tenability Impact on design
Receptor, ligand characteristics, interaction CT 1000-10000 ?m-2 Diffusion coefficients vary by receptor, ligand, vesicle types. The on/off rates can be varied by protein engineering. Impacts time for microcarrier arrest and the steady state affinity.
Flow Properties Re 0.02-1,R 10-100 ?m, Sc 103 Pe 20, Ca 0.3, We 6?10-6, Fr 0.03, Et 0.5 In vivo, this largely depends on the type of the arterial microvessel Impacts the time for microcarrier arrest and drug loss.
Endothelial Cell properties ICAM-1 density 104-105 ?m-2 Depends on injury/disease type. Can be controlled by TNF-? stimulation. Allows for targeting stressed cells preferentially.
Endocytosis (collaborative) Y/N Turn off by introducing ATP toxin in cell culture expts. Compare diffusive permeability vs. internalization of vesicle
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Talk Outline

• Interaction of nanocarriers with endothelial cell
• Aim 1 Model for Glycocalyx resistance
• -- Monte Carlo Simulations to predict nanocarrier
  binding
• Aim 2 Model for Endocytosis
• -- Hybrid KMC-TDGL simulations to predict
  membrane dynamics
• Conclusions

Endocytosis
Glycocalyx on EC
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Effect of Glycocalyx (Experimental Data)
Binding of carriers increases about 4 fold upon
infusion of heparinase.
Glycocalyx may shield beads from binding to ICAMs
Mulivor, A.W. Lipowsky, H.H. Am J Physiol Heart
Circ Physiol 283 H1282-1291, 2002
Increased binding with increasing temperature can
not be explained in an exothermic reaction
In vitro experimental data from Dr. Muzykantov
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Glycocalyx Morphology and Length Scales
Length Scales
1 Pries, A.R. et. al. Pflügers Arch-Eur J
Physiol. 440653-666, (2000). 2 Squire, J.M., et.
al. J. of structural biology, 136, 239-255,
(2001). 3 Vink, H. et. al., Am. J. Physiol. Heart
Circ. Physiol. 278 H285-289, (2000).
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Proposed Model for Glycocalyx Resistance
For a nanocarrier, k 1.610-6 N/m
S
Spenetration depth
Mulivor, A.W. Lipowsky, H.H. Am J Physiol Heart
Circ Physiol 283 H1282-1291, 2002
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Simulation Protocol for Nanocarrier Binding
Equilibrium binding simulated using Metropolis
Monte Carlo.
New conformations are generated from old ones
by -- Translation and Rotation of nanocarriers --
Translation of Antigens on endothelial cell
surface
Bond formation is considered as a probabilistic
event Bell model is used to describe bond
deformation
?equilibrium bond length Lbond length
Periodic boundary conditions along the cell and
impenetrable boundaries perpendicular to cell are
enforced
System size 1??1?0.5 µm
Nanocarrier size 100 nm
Number of antibodies per nanocarrier 212
Equilibrium bond energy -7.9810-20 J/molecule
Bond spring constant 100 dyne/cm
Based on experimental data on binding of free
antibodies to antigen (Dr. Muzykantov
lab.) Eniola, A.O. Biophysical Journal, 89 (5)
3577-3588
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Binding Mechanics
Multivalency Number of antigens (or antibody)
bound per nanocarrier
Energy of binding Characterizes equilibrium
constant of the reaction in terms of nanobeads
Radial distribution function of antigens
Indicates clustering of antigens in the vicinity
of bound nanobeads
These properties are calculated by averaging
four different in silico experiments.
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Effect of Antigen DiffusionIn silico experiments
Carriers 80 nM
Antigen 2000 / µm2
80 nM
800 nM
/ µm2
/ µm2
For nanocarrier concentration of 800 nM, binding
of nanocarriers is not competitive for antigen
concentration of 2000 antigens/ µm2
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Spatial Modulation of Antigens
500 nanocarriers (i.e. 813 nM) on a cell with
antigen density of 2000/µm2
Nanobead length scale
Diffusion of antigens leads to clustering of
antigens near bound nanocarriers
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Effect of GlycocalyxIn silico experiments
Based on Glycocalyx spring constant 1.610-7 N/m
Presence of glycocalyx affects temperature
dependence of equilibrium constant though
multivalency remains unaffected
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Conclusions

• Antigen diffusion leads to higher nanocarrier
  binding affinity
• Diffusing antigens tend to cluster near the bound
  nanocarriers
• Glycocalyx represents a physical barrier to the
  binding of nanocarriers
• Presence of Glycocalyx not only reduces binding,
  but may also reverse the temperature dependence
  of binding

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Endocytosis
Ford et al., Nature, 2002
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Model Components for Integrin Activated
Endocytosis
Ap180
Epsin
Vesicle membrane motion
Hohenberg and Halperin, 1977 Nelson, Piran,
Weinberg, 1987
Membrane
z(x,y,t) membrane coordinates ? interfacial
tension ? bending rigidity M membrane mobility,
? Langevin noise F elastic free energy C(x,y)
is the intrinsic mean curvature of the membrane
Epsin diffusion
Gillespie, 1977
Clathrin
Kinetic Monte Carlo diffusion on a lattice
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Membrane Dynamical Behavior
GT Glass transition No N No nucleation NVLRO
Nucleation via long range order NVA Nucleation
via association
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Endocytotic Vesicle Nucleation
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Conclusions

• The hybrid multiscale approach is successful in
  describing the dynamic processes associated with
  the interaction of proteins and membranes at a
  coarse-grained level
• Membrane-mediated protein-protein repulsion and
  attraction effects short- and long-ranged
  ordering
• Two modes of vesicle nucleation observed
• The mechanism of nucleation assisted by accessory
  proteins has to be compared to that in their
  absence

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Acknowledgments
Vladimir Muzykantov, Penn Mark Goulian,
Penn David Eckmann Portonovo Ayyaswamy
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Thank You
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Activation of Endocytosis as a Multiscale Problem
Molecular Dynamics
Extracellular
Intracellular
(MAP Kinases) Ras
Mixed Quantum Mechanics Molecular Mechanics
PLC?
IP3
DAG
Raf
MEK
Ca
PKC
Nucleus
ERK
Proliferation
KMCTDGL
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Epsin-Membrane Interaction Parameters
Range (R)
r, Surface Density
Hardsphere exclusion
C0 (intrinsic curvature)
Measurable quantities C0, D, ??, ? Micropipette,
FRAP, Microscopy
C(x,y) is the mean intrinsic curvature of the
membrane determined by epsins adsorbed on the
membrane. C(x,y) is dynamically varying because
of lateral diffusion of epsins
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Calculation of Glycocalyx spring constant
Forward rate (association) modeled as second
order reaction Backward rate (dissociation)
modeled as first order reaction
Rate constants derived by fitting Lipowsky data
to rate equation. Presence of glycocalyx effects
only forward rate contant.
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Glycocalyx thickness
Squrie et. al. 50 100 nm
Vink et. al. 300 500 nm
Viscosity of glycocalyx phase 50-90 times
higher than that of water Lee, G.M. JCB 120
25-35 (1993).

• Review chapters on glycocalyx
• Robert, P. Limozin, L. Benoliel, A.-M.
  Pierres, A. Bongrand, P. Glycocalyx regulation
  of cell adhesion. In Principles of Cellular
  engineering (M.R. King, Ed.), pp. 143-169,
  Elsevier, 2006. 
• Pierres, A. Benoliel, A.-M. Bongrand, P.
  Cell-cell interactions. In Physical chemistry of
  biological interfaces (A. Baszkin and W. Nord,
  Eds.), pp. 459-522, Marcel Dekker, 2000.