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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 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; University of Pennsylvania 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 =3N/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. University of Pennsylvania 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: 610-6, 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 University of Pennsylvania 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 110.5 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
