University of Pennsylvania Modeling of Targeted Drug Delivery Neeraj Agrawal

University of Pennsylvania Targeted Drug Delivery Drug Carriers injected near the diseased cells Mostly drug carriers are in µm to nm scale Carriers functionalized with molecules specific to the receptors expressed on diseased cells Leads to very high specificity and low drug toxicity

University of Pennsylvania 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 Glycocalyx Morphology and Length Scales 100 nm 1,2,3 Glycocalyx 10 nmAntibody 100 nmBead 20 nmAntigen μmCell Length Scales 1 Pries, A.R. et. al. Pflügers Arch-Eur J Physiol. 440: , (2000). 2 Squire, J.M., et. al. J. of structural biology, 136, , (2001). 3 Vink, H. et. al., Am. J. Physiol. Heart Circ. Physiol. 278: H , (2000).

University of Pennsylvania Effect of Glycocalyx (Experimental Data) Mulivor, A.W.; Lipowsky, H.H. Am J Physiol Heart Circ Physiol 283: H , 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

University of Pennsylvania Proposed Model for Glycocalyx Resistance S S=penetration depth The glycocalyx resistance is a combination of osmotic pressure (desolvation or squeezing out of water shells), electrostatic repulsion steric repulsion between the microcarrier and glycoprotein chains of the glycocalyx entropic (restoring) forces due to confining or restricting the glycoprotein chains from accessing many conformations.

University of Pennsylvania Parameter for Glycocalyx Resistance Mulivor, A.W.; Lipowsky, H.H. Am J Physiol Heart Circ Physiol 283: H , 2002 For a nanocarrier, k = 1.6*10 -6 N/m

University of Pennsylvania 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 1. Muro, et. al. J. Pharma. And expt. Therap , Eniola, A.O. Biophysical Journal, 89 (5): System size 1  1  0.5 μm Nanocarrier size100 nm Number of antibodies per nanocarrier212 Equilibrium bond energy-7.98 × J/molecule [1] Bond spring constant100 dyne/cm [2]  =equilibrium bond length L=bond length

University of Pennsylvania Select a nanocarrier at random. Check if it’s within bond-formation distance Select an antibody on this nanocarrier at random. Check if it’s within bond-formation distance. Select an antigen at random. Check if it’s within bond-formation distance. For the selected antigen, antibody; bond formation move is accepted with a probability If selected antigen, antibody are bonded with each other, then bond breakage move accepted with a probability Monte-Carlo moves for bond-formation

University of Pennsylvania Computational Details Program developed in-house. Mersenne Twister random number generator (period of ) Implemented using Intel C++ and MPICH used for parallelization System reach steady state within 200 million monte-carlo moves. Relatively low computational time required (about 4 hours on multiple processors)

University of Pennsylvania 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.

University of Pennsylvania 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

University of Pennsylvania 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

University of Pennsylvania 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

University of Pennsylvania 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 Work in Progress For larger glycocalyx resistance, importance sampling does not give accurate picture Implementation of umbrella sampling protocol Near Future Work To include membrane deformation using Time-dependent Ginzburg-Landau equation.

University of Pennsylvania Acknowledgments Vladimir Muzykantov Weining Qiu David Eckmann Andres Calderon Portonovo Ayyaswamy

University of Pennsylvania 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.

University of Pennsylvania 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 , Elsevier, Pierres, A.; Benoliel, A.-M.; Bongrand, P. Cell-cell interactions. In Physical chemistry of biological interfaces (A. Baszkin and W. Nord, Eds.), pp , Marcel Dekker, Glycocalyx thickness Squrie et. al.50 – 100 nm Vink et. al.300 – 500 nm Viscosity of glycocalyx phase ~ times higher than that of water Lee, G.M.; JCB 120: (1993).

University of Pennsylvania Bell Model Bell (Science, 1978) we can loosely associate with

University of Pennsylvania Umbrella Sampling A biasing potential added to the system along the desired coordinate to make overall potential flatter Probability distribution along the bottleneck-coordinate calculated New biasing potential = -ln (P) For efficient sampling, system divided into smaller windows. WHAM (weighted histogram analysis method) used to remove the artificial biasing potential at the end of the simulation to get free energy profile along the coordinate.

University of Pennsylvania Additional Simulation Parameters ICAM size19 nm × 3 nm R 6.5 size15 nm Chemical cut-off1.3 nm

University of Pennsylvania Determination of reaction free energy change Muro, et. al. J. Pharma. And expt. Therap , 1161.

University of Pennsylvania Glycocalyx morphology Weinbaum, S. et. al. PNAS 2003, 100, 7988.

University of Pennsylvania Fitting to Lipowsky data B is constant in a flow experiment