Neeraj Agrawal University of Pennsylvania 1 Modeling of Targeted Drug Delivery and Endocytosis Neeraj Agrawal Clathrin

Neeraj Agrawal University of Pennsylvania 2 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

Neeraj Agrawal University of Pennsylvania 3 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

Neeraj Agrawal University of Pennsylvania 4 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).

Neeraj Agrawal University of Pennsylvania 5 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

Neeraj Agrawal University of Pennsylvania 6 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.

Neeraj Agrawal University of Pennsylvania 7 Parameter for Glycocalyx Resistance Mulivor, A.W.; Lipowsky, H.H. Am J Physiol Heart Circ Physiol 283: H , 2002 For a nanocarrier, k = 3.9*10 9 J/m 4

Neeraj Agrawal University of Pennsylvania 8 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 System size 1  1  0.5 μm Nanocarrier size100 nm Number of antibodies per nanocarrier212 Equilibrium bond energy-7.98 × J/molecule Bond spring constant1000 dyne/cm Antigen Flexural Rigidity700 pN-nm 2  =equilibrium bond length L=bond length

Neeraj Agrawal University of Pennsylvania 9 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 Select a nanocarrier at random. Check if it’s within bond-formation distance

Neeraj Agrawal University of Pennsylvania 10 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.

Neeraj Agrawal University of Pennsylvania 11 Effect of Antigen Diffusion In silico experiments Increasing antigen concentration diminishes the effect of antigen diffusion.

Neeraj Agrawal University of Pennsylvania 12 Effect of Antigen Flexure In silico experiments Allowing antigens to flex leads to higher multivalency.

Neeraj Agrawal University of Pennsylvania 13 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

Neeraj Agrawal University of Pennsylvania 14 Effect of Glycocalyx In silico experiments Presence of glycocalyx affects temperature dependence of equilibrium constant. Based on Glycocalyx spring constant = 1.6*10 -7 N/m

Neeraj Agrawal University of Pennsylvania 15 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

Neeraj Agrawal University of Pennsylvania 16 Multiscale Modeling of Protein-Mediated Membrane Dynamics: Integrating Cell Signaling with Trafficking Neeraj Agrawal Clathrin

Neeraj Agrawal University of Pennsylvania 17 Endocytosis: The Internalization Machinery in Cells Detailed molecular and physical mechanism of the process still evading. Endocytosis is a highly orchestrated process involving a variety of proteins. Attenuation of endocytosis leads to impaired deactivation of EGFR – linked to cancer Membrane deformation and dynamics linked to nanocarrier adhesion to cells Short-term Quantitative dynamic models for membrane invagination: Development of a multiscale approach to describe protein-membrane interaction at the mesoscale (  m) Long-term Integrating with signal transduction Minimal model for protein-membrane interaction in endocytosis on the mesoscale

Neeraj Agrawal University of Pennsylvania 18 Endocytosis of EGFR A member of Receptor Tyrosine Kinase (RTK) family Transmembrane protein Modulates cellular signaling pathways – proliferation, differentiation, migration, altered metabolism Multiple possible pathways of EGFR endocytosis – depends on ambient conditions –Clathrin Dependent Endocytosis –Clathrin Independent Endocytosis

Neeraj Agrawal University of Pennsylvania 19 Clathrin Dependent Endocytosis One of the most common internalization pathway Kirchhausen lab. AP - 2 epsin AP - 2 clathrin AP-2 epsin AP - 2 clathrin AP - 2 epsin clathrin. EGF Membrane Common theme: –Cargo Recognition – AP2 –Membrane bending proteins – Clathrin, epsin AP2 Clathrin polymerization

Neeraj Agrawal University of Pennsylvania 20 Wiley, H.S., Trends in Cell biology, vol 13, Trafficking Mechanism of EGFR

Neeraj Agrawal University of Pennsylvania 21 Overview Protein diffusion models Membrane models Model Integration Preliminary Results Tale of three elastic models Random walker

Neeraj Agrawal University of Pennsylvania 22 Linearized Elastic Model For Membrane: Monge-TDGL Helfrich membrane energy accounts for membrane bending and membrane area extension. Force acting normal to the membrane surface (or in z-direction) drives membrane deformation Spontaneous curvatureBending modulus Frame tension Splay modulus Consider only those deformations for which membrane topology remains same. z(x,y) The Monge gauge approximation makes the elastic model amenable to Cartesian coordinate system In Monge notation, for small deformations, the membrane energy is

Neeraj Agrawal University of Pennsylvania 23 Curvature-Inducing Protein Epsin Diffusion on the Membrane Each epsin molecule induces a curvature field in the membrane Membrane in turn exerts a force on epsin Epsin performs a random walk on membrane surface with a membrane mediated force field, whose solution is propagated in time using the kinetic Monte Carlo algorithm Bound epsin position KMC-move Metric epsin(a)  epsin(a+a 0 ) where a 0 is the lattice size, F is the force acting on epsin

Neeraj Agrawal University of Pennsylvania 24 Hybrid Multiscale Integration Regime 1: Deborah number De<<1 or (a 0 2 /D)/(z 2 /M) << 1 Regime 2: Deborah number De~1 or (a 2 /D)/(z 2 /M) ~ 1 KMC TDGL #=1/De #=  /  t Surface hopping switching probability Relationship Between Lattice & Continuum Scales Lattice  continuum: Epsin diffusion changes C 0 (x,y) Continuum  lattice: Membrane curvature introduces an energy landscape for epsin diffusion R

Neeraj Agrawal University of Pennsylvania 25 Applications Monge TDGL (linearized model) –Radial distribution function –Orientational correlation function Surface Evolution  validation, computational advantage. Local TDGL  vesicle formation. Integration with signaling –Clathrin Dependent Endocytosis Interaction of Clathrin, AP2 and epsin with membrane –Clathrin Independent Endocytosis –Targeted Drug Delivery Interaction of Nanocarriers with fluctuating cell membrane.

Neeraj Agrawal University of Pennsylvania 26 Local-TDGL (No Hydrodynamics) A new formalism to minimize Helfrich energy. No linearizing assumptions made. Applicable even when membrane has overhangs Exact solution for infinite boundary conditions TDGL solutions for 1×1 µm 2 fixed membrane At each time step, local coordinate system is calculated for each grid point. Monge-TDGL for each grid point w.r.to its local coordinates. Rotate back each grid point to get overall membrane shape.

Neeraj Agrawal University of Pennsylvania 27 Potential of Mean Force PMF is dictated by both energetic and entropic components Epsin experience repulsion due to energetic component when brought close. Second variation of Monge Energy (~ spring constant). Non-zero H 0 increases the stiffness of membrane  lower thermal fluctuations Test function Bound epsin experience entropic attraction. x0

Neeraj Agrawal University of Pennsylvania 28 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).