Transcript aiche2006 - SEAS - University of Pennsylvania

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
University of Pennsylvania
Department of Bioengineering
Injected
microcarrier
Transport
through
arterial
system
H
immune
system
interaction
N (multi pass)
Microcarrier
Arrest?
H
Me
One pass
Circulatory
System
M
Y
Filtered?
EndothelialCell Aberrant
Normal Response
Me
Y
N
Cell
Fate?
Excretion
Moderate
Extreme
Drug
Assimilation
HE
EM
Transport to
microcapillaries,
target tissue
Me
Immune
response
M Me
Intracellular
uptake
H
Other
signaling
Apoptosis
Necrosis
Cell Death
Endocytotic
uptake
Immunological
signaling
Toxicity
Intracellular
assimilation
cytokines
Model: H: hydrodynamic; Me: mesoscale; M: molecular; E: experiment;
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represents points of drug loss
Department of Bioengineering
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
University of Pennsylvania
Department of Bioengineering
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 (antiICAM) 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,
Depends on lipid
=400kBT, M=10-5 type in vesicles.
m/s
(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
Impacts the hydrodynamics,
interaction with the
glycocalyx.
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Receptors attached
on vesicle surface or
via PEG linkers.
Department of Bioengineering
Parameter Space Explored in Simulations and Microcarrier Design
Property
Receptor, ligand
characteristics,
interaction
Range and
reference
CT =1000-10000
m-2
Experimental tenability
Impact on design
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: 10100 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
University of Pennsylvania
Department of Bioengineering
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
Cell
Antigen
Bead
Antibody
Glycocalyx
Endocytosis
Glycocalyx on EC
University of Pennsylvania
Department of Bioengineering
Effect of Glycocalyx (Experimental Data)
Binding of carriers increases about
4 fold upon infusion of heparinase.
Glycocalyx may shield beads from
binding to ICAMs
number of nanobeads bound/cell
12000
10000
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
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8000
6000
4000
2000
0
4 deg C
37 deg C
In vitro experimental data
from Dr. Muzykantov
Department of Bioengineering
Glycocalyx Morphology and Length Scales
Length Scales
Cell
10-20 μm
Antigen
20 nm
Bead
100 nm
Antibody
10 nm
Glycocalyx
100 nm1,2,3
1 Pries, A.R. et. al. Pflügers Arch-Eur J Physiol. 440:653-666, (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).
University of Pennsylvania
Department of Bioengineering
Proposed Model for Glycocalyx Resistance
1
G  presence of glycocalyx   G absence of glycoca lyx   kS 2
2
For a nanocarrier,
k = 1.6*10-6 N/m
S
S=penetration depth
Mulivor, A.W.; Lipowsky, H.H. Am J Physiol Heart Circ Physiol 283: H1282-1291, 2002
University of Pennsylvania
Department of Bioengineering
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
G( L)  G( )  1 k  L   
2
Bond formation is considered as a probabilistic event
=equilibrium bond length
L=bond length
Bell model is used to describe bond deformation
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
-7.98*10-20 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
University of Pennsylvania
Department of Bioengineering
2
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.
University of Pennsylvania
Department of Bioengineering
Effect of Antigen Diffusion
In silico experiments
Antigen: 2000 / μm2
Carriers: 80 nM
25
Antigens can diffuse
30
Antigens can't diffuse
Antigens can't diffuse
25
Multivalency
20
Multivalency
Antigens can diffuse
15
10
5
20
15
80 nM
800 nM
10
5
0
0
200 antigens /
μm2
2000 antigens /
μm2
5 beads
50 beads
For nanocarrier concentration of 800 nM, binding of nanocarriers
is not competitive for antigen concentration of 2000 antigens/ μm2
University of Pennsylvania
Department of Bioengineering
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
University of Pennsylvania
Department of Bioengineering
Effect of Glycocalyx
In silico experiments
Based on Glycocalyx spring constant = 1.6*10-7 N/m
35
No glycocalyx
with glycocalyx
30
No glycocalyx
with glycocalyx
3000
2500
2000
20
ln K
Multivalency
25
1500
15
10
1000
5
500
0
0
4 deg C
37 deg C
4 deg C
37 deg C
Presence of glycocalyx affects temperature dependence of
equilibrium constant though multivalency remains unaffected
University of Pennsylvania
Department of Bioengineering
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
University of Pennsylvania
Department of Bioengineering
Endocytosis
Ford et al., Nature, 2002
University of Pennsylvania
Department of Bioengineering
Model Components for Integrin Activated Endocytosis
Vesicle membrane motion
Hohenberg and Halperin, 1977
Nelson, Piran, Weinberg, 1987
Epsin
Ap180
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
Kinetic Monte Carlo: diffusion on a lattice
University of Pennsylvania
Clathrin
Department of Bioengineering
r*
Membrane Dynamical
Behavior
GT
No N
NVLRO
NVA
C0
R
GT: Glass transition
No N: No nucleation
NVLRO: Nucleation via long
range order
NVA: Nucleation via association
University of Pennsylvania
Department of Bioengineering
Endocytotic Vesicle Nucleation
University of Pennsylvania
Department of Bioengineering
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
University of Pennsylvania
Department of Bioengineering
Acknowledgments
Vladimir Muzykantov, Penn
Mark Goulian, Penn
David Eckmann
Portonovo Ayyaswamy
University of Pennsylvania
Department of Bioengineering
Thank You
University of Pennsylvania
Department of Bioengineering
Activation of Endocytosis as a Multiscale
Problem
Molecular
Dynamics
Extracellular
Intracellular
(MAP Kinases)
PLC
Ras
IP3
DAG
Raf
Ca++
PKC
MEK
Nucleus
Mixed Quantum
Mechanics Molecular
Mechanics
ERK
Proliferation
KMC+TDGL
University of Pennsylvania
Department of Bioengineering
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
University of Pennsylvania
Department of Bioengineering
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.
k glycocalyx= 1 k
forward
500 forward
K glycocalyx= 1 K
500
G glycocalyx= G  k T ln500
B
glycocalyx resistance  k T ln 500
B
University of Pennsylvania
Department of Bioengineering
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.
University of Pennsylvania
Department of Bioengineering