Nanoscale Stochastic Modeling of Nanoparticle Internalization and Expulsion through Receptor-mediated Transcytosis Journal: Nanoscale Manuscript ID NR-ART-03-2019-002710.R1 Article Type: Paper Date Submitted by the 23-Apr-2019 Author: Complete List of Authors: Deng, Hua; Washington State University, School of Mechanical and Materials Engineering Dutta, Prashanta; Washington State University, School of Mechanical and Materials Engineering Liu, Jin; Washington State University, School of Mechanical and Materials Engineering Page 1 of 10 Please doNanoscale not adjust margins Nanoscale ARTICLE Stochastic Modeling of Nanoparticle Internalization and Expulsion through Receptor-mediated Transcytosis a a a Received 00th January 20xx, Hua Deng Prashnanta Dutta and Jin Liu * Accepted 00th January 20xx The receptor-mediated transcytosis (RMT) is a fundamental mechanism for the transcellular transport of nanoparticles. RMT DOI: 10.1039/x0xx00000x is a complex process, during which the nanoparticles actively interact with the membrane and the membrane profile undergoes extreme deformations for particle internalization and expulsion. In this work, we developed a stochastic model to study the endocytosis and exocytosis of nanoparticle across soft membranes. The model is based on the combination of a stochastic particle binding model with a membrane model, and accounts for both the clathrin-mediated endocytosis for internalization and the actin-mediated exocytosis for explusion. Our results showed the nanoparticle must have certain avidity with enough ligand density and ligand-receptor binding affinity to be uptaken, while too much avidity limited the particle release from the cell surface. We furhter explored the functional roles of actin during exocytosis, which has been a topic under active debates. Our simulations indicated that the membrane compression due to the actin induced tension tended to break the ligand-receptor bonds and to shrink the fusion pore. Therefore, an intermediate tension promoted the fusion pore expansion and nanoparticle release, while high tension prohibits particle release. Our model leads to new and critical mechanistic insights into RMT, and represents a powerful platform for aiding the rational design of nanocarriers for controlled drug delivery. As illustrated in Figure 1, transport of nanoparticles across a 1 Introduction cell through RMT is a complex and multi-stage process. It requires the selective binding of particle to the receptors on one The receptor-mediated transcytosis (RMT) is of significant side of the cell surface, internalization of the particles, transport importance for the understanding of the fundamental biological of the vesicle through the cytoplasm, docking to the surface on transportation of nutrients and viruses, as well as biomedical the other side of the cell, fusion with the lipid membrane and applications in drug delivery.1-5 For example, it is well known eventually expulsion of the particle from the membrane. that epithelial cells facilitate fast transcellular transport of Understanding the interactions between nanoparticle and various viruses, such as human immunodeficiency virus (HIV) membrane and the extreme deformations of membrane during influenza virus, and poliovirus.6-9 RMT is also a promising and non-invasive technique for delivery of drug carriers across endothelial cells at blood-brain barrier (BBB) for brain cancer and neurodegenerative diseases, such as Alzheimer’s disease and Parkinson’s disease.4, 10 The RMT process includes both particle internalization through receptor-mediated endocytosis (RME) and expulsion through exocytosis. Theoretical and experimental works have investigated the internalization of nanoparticles through RME.11-15 But the exocytosis process during RMT has been rarely studied. Recent investigations have demonstrated that higher endocytosis may not automatically lead to a better transcytosis capability of nanoparticle.16-18 The precise mechanism behind the efficient transport of nanoparticle through RMT is still less understood. Figure 1. Schematic of the receptor-mediated transcytosis of nanoparticle. The particle first binds with the receptors on the extracellular side of the cell, then the interactions trigger the assembly of clathrin-coated pit (CCP). CCP induces the deformation of membrane and the formation of the particle-containing vesicle. The mature vesicle is a. School of Mechanical and Materials Engineering, Washington State University, pinched off from the membrane with the assistance of dynamin and transported to the WA 99163, USA E-mail: [email protected] other side. During the transportation, clathrin coats are disassembled from the vesicle † Footnotes relating to the title and/or authors should appear here. surface. The exocytosis starts with the fusion between the vesicle and the cell Electronic Supplementary Information (ESI) available: [details of any supplementary membrane. The post-fusion pore opening is mediated by the actin network activity. information available should be included here]. See DOI: 10.1039/x0xx00000x Please do not adjust margins Please doNanoscale not adjust margins Page 2 of 10 ARTICLE Nanoscale both internalization and expulsion is critical for the transcellular During endocytosis, the clathrin coated pit is modeled as transport of nanoparticle through RMT. additional intrinsic curvature and modified bending rigidity. Many nanoparticle properties, such as the particle size, Therefore, the total energy with clathrin can be expressed as: shape, ligand density/type, etc. and biological factors, such as 휅 휅 ∬ 2 ∬ 푐푙푎 2 the assembly of clathrin and actin as mentioned above, will 퐸 = [2(2퐻) + 휎]푑퐴 + [ 2 (2퐻 ― 퐻푐푙푎) ]푑퐴 (2) impact the membrane deformation during the transcytosis. Therefore, a numerical model, which is able to incorporate the where 휅푐푙푎 and 퐻푐푙푎 are the bending rigidity and intrinsic effects from key biological components, is desirable for curvature of the clathrin coat. In our model, the ligand and studying the receptor-mediated transcytosis of nanoparticle. receptor binding trigger the recruitment of clathrin lattices; The receptor-mediated endocytosis and internalization of each new binding introduces a curvature field representing the particles have been well-characterized and a variety of accumulated clathrin. The ligand-receptor interactions are computational models exist in the literature,11, 13, 19-22 but the modeled by the Bell model:30 exocytosis and expulsion of nanoparticles have been less 1 2 23-26 explored. Alternative translocation pathways through ∆퐺푟(푑) = ∆퐺0 + 2푘푑 (3) membrane rupture and penetration have also been studied 푑 through coarse-grained molecular simulations. 27, 28 In this work, Here is the distance between the binding tips of the ∆퐺 we developed a stochastic model for the RMT and applied this interacting ligand and receptor, 0 is the equilibrium free 푑 = 0 푘 model to study the internalization and expulsion of ligand- energy change at , and is the interaction bond force ∆퐺 coated nanoparticle. Our model is a combination of receptor- constant. In our model, 0 is obtained from the dissociation 퐾 ∆퐺 = ― 푘 푇푙푛퐾 푘 mediated endocytosis and exocytosis. The effects of assembly constant 푑 via 0 퐵 푑, where 퐵 is the Boltzmann 푇 of clathrin-coated pit (CCP) and actin have been taken into constant and is the thermodynamic temperature. Ligand and account in endocytosis and exocytosis processes respectively. receptor pairs are allowed to form bonds within the reaction 푑 31 Using our model, we systematically investigate the effects of cut-off distance 푐. The bonds are reversible, they may break ligand density and ligand-receptor binding affinity on the overall due to nanoparticle and receptor movements or membrane 푘 ∆퐺 푑 effectiveness of transcytosis. In addition, we also explore the deformation. will be determined from 0 and 푐. For a functional roles of filamentous actin assembly during fusion bonded receptor, it is allowed to bend and rotate. This flexural pore expansion and particle release. The results are consistent movement of receptor represents the entropy change during with available experiments and provide deeper understanding binding. Under the assumption of small deformations, we of the fundamental mechanisms involved in this complex model the flexure of a receptor as bending a beam from process. equilibrium (normal to membrane surface) position, and the bending energy is calculated as: ∆퐺 (휃) = (2퐸퐼/퐿)휃2 2 Model and Methods 푓 (4) 2.1 Clathrin-mediated Endocytosis Model where 퐸퐼 is the receptor flexural rigidity, 퐿 is the receptor length and 휃 represents the bending angle from the normal In our model, the nanoparticle is treated as a rigid sphere with direction of the local membrane. Therefore, the total binding ligands uniformly coated on its surface. The nanoparticle is able energy change for each interaction is the difference between to translate and rotate. The ligands and receptors are modeled the energy reduction by ligand-receptor interaction and the as cylinders with one end attached to the particle/membrane energy increase through receptor bending. More details surface and the other free end as binding tip. The membrane regarding the endocytosis model can be found from our surface is modeled with Helfrich Hamiltonian29 using a three- previous publication.22 dimensional curvilinear triangulate system. The total energy E of membrane is: 2.2 Exocytosis Model 휅 ∬ 2 Our exocytosis model mimics the expansion of the fusion pore 퐸 = [2(2퐻 ― 퐻0) + 휅퐾 + 휎]푑퐴 (1) and