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

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

3. University of Pennsylvania 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

4. University of Pennsylvania Department of Bioengineering Parameter Space Explored in Simulations and Microcarrier Design PropertyRange 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, C o 10 -11 - 10 -9 m 2 /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,  =400k B T, 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.

5. University of Pennsylvania Department of Bioengineering Parameter Space Explored in Simulations and Microcarrier Design PropertyRange and reference Experimental tenabilityImpact on design Receptor, ligand characteristics, interaction C T =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 PropertiesRe: 0.02-1,R: 10- 100  m, Sc: 10 3 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 10 4 -10 5  m -2 Depends on injury/disease type. Can be controlled by TNF-  stimulation. Allows for targeting stressed cells preferentially. Endocytosis (collaborative) Y/NTurn off by introducing ATP toxin in cell culture expts. Compare diffusive permeability vs. internalization of vesicle

6. 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 Glycocalyx Antibody Bead Antigen Cell Glycocalyx on EC Endocytosis

7. University of Pennsylvania Department of Bioengineering Effect of Glycocalyx (Experimental Data) Mulivor, A.W.; Lipowsky, H.H. Am J Physiol Heart Circ Physiol 283: H1282-1291, 2002 Binding of carriers increases about 4 fold upon infusion of heparinase. Glycocalyx may shield beads from binding to ICAMs Increased binding with increasing temperature can not be explained in an exothermic reaction In vitro experimental data from Dr. Muzykantov

8. University of Pennsylvania Department of Bioengineering Glycocalyx Morphology and Length Scales 100 nm 1,2,3 Glycocalyx 10 nmAntibody 100 nmBead 20 nmAntigen 10-20 μmCell Length Scales 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).

9. University of Pennsylvania Department of Bioengineering Proposed Model for Glycocalyx Resistance Mulivor, A.W.; Lipowsky, H.H. Am J Physiol Heart Circ Physiol 283: H1282-1291, 2002 For a nanocarrier, k = 1.6*10 -6 N/m S S=penetration depth

10. 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 Bond formation is considered as a probabilistic event Bell model is used to describe bond deformation Periodic boundary conditions along the cell and impenetrable boundaries perpendicular to cell are enforced Based on experimental data on binding of free antibodies to antigen (Dr. Muzykantov lab.) Eniola, A.O. Biophysical Journal, 89 (5): 3577-3588 System size 1  1  0.5 μm Nanocarrier size100 nm Number of antibodies per nanocarrier212 Equilibrium bond energy-7.98*10 -20 J/molecule Bond spring constant100 dyne/cm  =equilibrium bond length L=bond length

11. University of Pennsylvania Department of Bioengineering Binding Mechanics Multivalency: Number of antigens (or antibody) bound per nanocarrier Radial distribution function of antigens: Indicates clustering of antigens in the vicinity of bound nanobeads Energy of binding: Characterizes equilibrium constant of the reaction in terms of nanobeads These properties are calculated by averaging four different in silico experiments.

12. University of Pennsylvania Department of Bioengineering Effect of Antigen Diffusion In silico experiments For nanocarrier concentration of 800 nM, binding of nanocarriers is not competitive for antigen concentration of 2000 antigens/ μm 2 Carriers: 80 nMAntigen: 2000 / μm 2 / μm 2 80 nM 800 nM

13. University of Pennsylvania Department of Bioengineering Spatial Modulation of Antigens Diffusion of antigens leads to clustering of antigens near bound nanocarriers 500 nanocarriers (i.e. 813 nM) on a cell with antigen density of 2000/μm 2 Nanobead length scale

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

15. 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

16. University of Pennsylvania Department of Bioengineering Endocytosis Ford et al., Nature, 2002

17. University of Pennsylvania Department of Bioengineering Model Components for Integrin Activated Endocytosis 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 Clathrin Membrane Ap180 Epsin diffusion Kinetic Monte Carlo: diffusion on a lattice Vesicle membrane motion Hohenberg and Halperin, 1977 Nelson, Piran, Weinberg, 1987 Gillespie, 1977

18. University of Pennsylvania Department of Bioengineering Membrane Dynamical Behavior ** C0C0 R NVLRO NVA No N GT GT: Glass transition No N: No nucleation NVLRO: Nucleation via long range order NVA: Nucleation via association

19. University of Pennsylvania Department of Bioengineering Endocytotic Vesicle Nucleation

20. 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

21. University of Pennsylvania Department of Bioengineering Acknowledgments Vladimir Muzykantov, Penn Mark Goulian, Penn David Eckmann Portonovo Ayyaswamy

22. University of Pennsylvania Department of Bioengineering Thank You

23. University of Pennsylvania Department of Bioengineering Activation of Endocytosis as a Multiscale Problem Extracellular Intracellular (MAP Kinases) Ras Raf MEK ERK PLC  IP 3 DAG Ca ++ PKC Proliferation Nucleus Molecular Dynamics Mixed Quantum Mechanics Molecular Mechanics KMC+TDGL

24. University of Pennsylvania Department of Bioengineering Epsin-Membrane Interaction Parameters Range (R) C 0 (intrinsic curvature) Hardsphere exclusion  *, Surface Density Measurable quantities: C 0, 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

25. 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.

26. University of Pennsylvania Department of Bioengineering 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. 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).