Multiscale Modeling of Targeted Drug Delivery Nanobiotechnology, fulfilling the promise of nanomedicine, CEP, 2006 Multiscale Modeling of Targeted Drug Delivery Neeraj Agrawal, Joshua Weinstein & Ravi Radhakrishnan Department of Bioengineering University of Pennsylvania Targeted Therapeutics

Microcarrier Arrest? Injected microcarrier Transport through arterial system N (multi pass) Circulatory System H Me M One pass Y Filtered? Y H immune system interaction EndothelialCell Response Aberrant N Normal Excretion Me Cell Fate? Moderate Extreme Drug Assimilation Other signaling Immune response H E M Me Intracellular uptake Apoptosis Necrosis Endocytotic uptake Immunological signaling Toxicity H E M Transport to microcapillaries, target tissue Intracellular assimilation Cell Death cytokines Me Model: H: hydrodynamic; Me: mesoscale; M: molecular; E: experiment; represents points of drug loss

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

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, M=10-5 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.

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

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 Cell Glycocalyx on EC Antigen Bead Antibody Glycocalyx

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

Glycocalyx Morphology and Length Scales 100 nm1,2,3 Glycocalyx 10 nm Antibody 100 nm Bead 20 nm Antigen 10-20 μm Cell 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).

Proposed Model for Glycocalyx Resistance 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

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 L=bond 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 -7.98*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

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.

Effect of Antigen Diffusion In 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

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

Effect of Glycocalyx In silico experiments Based on Glycocalyx spring constant = 1.6*10-7 N/m Presence of glycocalyx affects temperature dependence of equilibrium constant though multivalency remains unaffected

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

Endocytosis Ford et al., Nature, 2002

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

Membrane Dynamical Behavior NVLRO NVA No N GT Membrane Dynamical Behavior GT: Glass transition No N: No nucleation NVLRO: Nucleation via long range order NVA: Nucleation via association

Endocytotic Vesicle Nucleation

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

Vladimir Muzykantov, Penn Acknowledgments Vladimir Muzykantov, Penn Mark Goulian, Penn David Eckmann Portonovo Ayyaswamy

Thank You

Activation of Endocytosis as a Multiscale Problem Extracellular Molecular Dynamics Intracellular (MAP Kinases) Ras Mixed Quantum Mechanics Molecular Mechanics PLC IP3 DAG Raf Ca++ PKC MEK Nucleus ERK Proliferation KMC+TDGL

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

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.

Viscosity of glycocalyx phase ~ 50-90 times higher than that of water 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.