A hybrid approach combining fluctuating hydrodynamics with generalized Langevin dynamics is employed to study the motion of a neutrally buoyant nanocarrier in an incompressible Newtonian stationary fluid medium. Both hydrodynamic interactions and adhesive interactions are included, as are different receptor–ligand bond constants relevant to medical applications. A direct numerical simulation adopting an arbitrary Lagrangian–Eulerian based finite element method is employed for the simulation. The flow around the particle and its motion are fully resolved. The temperatures of the particle associated with the various degrees of freedom satisfy the equipartition theorem. The potential of mean force (or free energy density) along a specified reaction coordinate for the harmonic (spring) interactions between the antibody and antigen is evaluated for two different bond constants. The numerical evaluations show excellent comparison with analytical results. This temporal multiscale modeling of hydrodynamic and microscopic interactions mediating nanocarrier motion and adhesion has important implications for designing nanocarriers for vascular targeted drug delivery.
References
1.
Swaminathan
, T.
, Liu
, J.
, Uma
, B.
, Ayyaswamy
, P.
, Radhakrishnan
, R.
, and Eckmann
, D.
, 2011
, “Dynamic Factors Controlling Carrier Anchoring on Vascular Cells
,” IUBMB Life
, 63
(8
), pp. 640
–647
.10.1002/iub.4752.
Muzykantov
, V.
, Radhakrishnan
, R.
, and Eckmann
, D.
, 2012
, “Dynamic Factors Controlling Targeting Nanocarriers to Vascular Endothelium
,” Curr. Drug Metab.
, 113
, pp. 70
–81
.10.2174/1389200127983569163.
Calderon
, A. J.
, Muzykantov
, V.
, Muro
, S.
, and Eckmann
, D. M.
, 2009
, “Flow Dynamics, Binding and Detachment of Spherical Carriers Targeted to ICAM-1 on Endothelial Cells
,” Biorheology
, 46
, pp. 323
–341
.10.3233/BIR-2009-05444.
Calderon
, A. J.
, Bhowmick
, T.
, Leferovich
, J.
, Burman
, B.
, Pichette
, B.
, Muzykantov
, V.
, Eckmann
, D. M.
, and Muro
, S.
, 2011
, “Optimizing Endothelial Targeting by Modulating the Antibody Density and Particle Concentration of Anti-ICAM Coated Carriers
,” J. Controlled Release
, 150
(1
), pp. 37
–44
.10.1016/j.jconrel.2010.10.0255.
Munn
, L. L.
, Melder
, R. J.
, and Jain
, R. K.
, 1996
, “Role of Erythrocytes in Leukocyte-Endothelial Interactions: Mathematical Model and Experimental Validation
,” Biophys. J.
, 71
(1
), pp. 466
–478
.10.1016/S0006-3495(96)79248-26.
Liu
, J.
, Weller
, G. E. R.
, Zern
, B.
, Ayyaswamy
, P. S.
, Eckmann
, D. M.
, Muzykantov
, V. R.
, and Radhakrishnan
, R.
, 2010
, “A Computational Model for Nanocarrier Binding to Endothelium Validated Using In Vivo, In Vitro, and Atomic Force Microscopy Experiments
,” Proc. Natl. Acad. Sci. U.S.A.
, 107
, pp. 16530
–16535
.10.1073/pnas.10066111077.
Uma
, B.
, Swaminathan
, T. N.
, Ayyaswamy
, P. S.
, Eckmann
, D. M.
, and Radhakrishnan
, R.
, 2011
, “Generalized Langevin Dynamics of a Nanoparticle Using a Finite Element Approach: Thermostating With Correlated Noise
,” J. Chem. Phys.
, 135
, p. 114104
.10.1063/1.36357768.
Uma
, B.
, Swaminathan
, T. N.
, Radhakrishnan
, R.
, Eckmann
, D. M.
, and Ayyaswamy
, P. S.
, 2011
, “Nanoparticle Brownian Motion and Hydrodynamic Interactions in the Presence of Flow Fields
,” Phys. Fluids
, 23
, p. 073602
.10.1063/1.36110269.
Landau
, L. D.
, and Lifshitz
, E. M.
, 1959
, Fluid Mechanics
, Pergamon Press
, London
.10.
Hauge
, E. H.
, and Martin-Löf
, A.
, 1973
, “Fluctuating Hydrodynamics and Brownian Motion
,” J. Stat. Phys.
, 7
(3
), pp. 259
–281
.10.1007/BF0103030711.
Serrano
, M.
, and Español
, P.
, 2001
, “Thermodynamically Consistent Mesoscopic Fluid Particle Model
,” Phys. Rev. E
, 64
(4
), p. 046115
.10.1103/PhysRevE.64.04611512.
Sharma
, N.
, and Patankar
, N. A.
, 2004
, “Direct Numerical Simulation of the Brownian Motion of Particles by Using Fluctuating Hydrodynamic Equations
,” J. Comput. Phys.
, 201
(2
), pp. 466
–486
.10.1016/j.jcp.2004.06.00213.
Serrano
, M.
, Gianni
, D.
, Español
, P.
, Flekkøy
, E.
, and Coveney
, P.
, 2002
, “Mesoscopic Dynamics of Voronoi Fluid Particles
,” J. Phys. A: Math. General
, 35
(7
), pp. 1605
–1625
.10.1088/0305-4470/35/7/31014.
Donev
, A.
, Vanden-Eijnden
, E.
, Garcia
, A. L.
, and Bell
, J. B.
, 2010
, “On the Accuracy of Explicit Finite-Volume Schemes for Fluctuating Hydrodynamics
,” Commun. Appl. Math. Comput. Sci.
, 5
(2
), pp. 149
–197
.10.2140/camcos.2010.5.14915.
Ladd
, A. J. C.
, 1993
. “Short-Time Motion of Colloidal Particles: Numerical Simulation via a Fluctuating Lattice-Boltzmann Equation
,” Phys. Rev. Lett.
, 70
(9
), pp. 1339
–1342
.10.1103/PhysRevLett.70.133916.
Ladd
, A. J. C.
, 1994
, “Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation. Part 1. Theoretical Foundation
,” J. Fluid Mech.
, 271
, pp. 285
–309
.10.1017/S002211209400177117.
Ladd
, A. J. C.
, 1994
, “Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation. Part 2. Numerical Results
,” J. Fluid Mech.
, 271
, pp. 311
–339
.10.1017/S002211209400178318.
Patankar
, N. A.
, 2002
, “Direct Numerical Simulation of Moving Charged, Flexible Bodies With Thermal Fluctuations
,” Technical Proceedings of the 2002 International Conference on Computational Nanoscience and Nanotechnology
, Vol. 2
, Nano Science and Technology Institute
, pp. 93
–96
.19.
Adhikari
, R.
, Stratford
, K.
, Cates
, M. E.
, and Wagner
, A. J.
, 2005
, “Fluctuating Lattice–Boltzmann
,” EPL
, 71
(3
), pp. 473
–479
.10.1209/epl/i2004-10542-520.
Dünweg
, B.
, and Ladd
, A. J. C.
, 2008
, “Lattice Boltzmann Simulations of Soft Matter Systems
,” Adv. Polym. Sci.
, 221
, pp. 89
–166
.10.1007/978-3-540-87706-6_221.
Nie
, D.
, and Lin
, J.
, 2009
, “A Fluctuating Lattice-Boltzmann Model for Direct Numerical Simulation of Particle Brownian Motion
,” Particuology
, 7
(6
), pp. 501
–506
.10.1016/j.partic.2009.06.01222.
Español
, P.
, and Zúñiga
, I.
, 2009
, “On the Definition of Discrete Hydrodynamic Variables
,” J. Chem. Phys.
, 131
, p. 164106
.10.1063/1.324758623.
Español
, P.
, Anero
, J.
, and Zúñiga
, I.
, 2009
, “Microscopic Derivation of Discrete Hydrodynamics
,” J. Chem. Phys.
, 131
, p. 244117
.10.1063/1.327422224.
Atzberger
, P. J.
, Kramer
, P. R.
, and Peskin
, C. S.
, 2007
, “A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales
,” J. Comput. Phys.
, 224
(2
), pp. 1255
–1292
.10.1016/j.jcp.2006.11.01525.
Ermak
, D. L.
, and McCammon
, J. A.
, 1978
, “Brownian Dynamics With Hydrodynamic Interactions
,” J. Chem. Phys.
, 69
(4
), pp. 1352
–1360
.10.1063/1.43676126.
Brady
, J. F.
, and Bossis
, G.
, 1988
, “Stokesian Dynamics
,” Ann. Rev. Fluid Mech.
, 20
(1
), pp. 111
–157
.10.1146/annurev.fl.20.010188.00055127.
Foss
, D. R.
, and Brady
, J. F.
, 2000
, “Structure, Diffusion and Rheology of Brownian Suspensions by Stokesian Dynamics Simulation
,” J. Fluid Mech.
, 407
, pp. 167
–200
.10.1017/S002211209900755728.
Banchio
, A. J.
, and Brady
, J. F.
, 2003
, “Accelerated Stokesian Dynamics: Brownian Motion
,” J. Chem. Phys.
, 118
(22
), pp. 10323
–10332
.10.1063/1.157181929.
Iwashita
, T.
, Nakayama
, Y.
, and Yamamoto
, R.
, 2008
, “A Numerical Model for Brownian Particles Fluctuating in Incompressible Fluids
,” J. Phys. Soc. Jpn
, 77
(7
), p. 074007
.10.1143/JPSJ.77.07400730.
Iwashita
, T.
, and Yamamoto
, R.
, 2009
, “Short-Time Motion of Brownian Particles in a Shear Flow
,” Phys. Rev. E
, 79
(3
), p. 031401
.10.1103/PhysRevE.79.03140131.
Kubo
, R.
, 1966
, “The Fluctuation-Dissipation Theorem
,” Rep. Prog. Phys.
, 29
(1
), pp. 255
–284
.10.1088/0034-4885/29/1/30632.
Kubo
, R.
, Toda
, M.
, and Hashitsume
, N.
, 1991
, Nonequilibrium Statistical Mechanics
, 2nd ed., Springer-Verlag
, Berlin
.33.
Uma
, B.
, Eckmann
, D. M.
, Ayyaswamy
, P. S.
, and Radhakrishnan
, R.
, 2012
, “A Hybrid Formalism Combining Fluctuating Hydrodynamics and Generalized Langevin Dynamics for the Simulation of Nanoparticle Thermal Motion in an Incompressible Fluid Medium
,” Mol. Phys.
, 110
, pp. 1057
–1067
.10.1080/00268976.2012.66351034.
Bell
, G.
, Dembo
, M.
, and Bongrand
, P.
, 1984
, “Cell Adhesion. Competition Between Nonspecific Repulsion and Specific Bonding
,” Biophys. J.
, 45
(6
), pp. 1051
–1064
.10.1016/S0006-3495(84)84252-635.
Hanley
, W.
, McCarty
, O.
, Jadhav
, S.
, Tseng
, Y.
, Wirtz
, D.
, and Konstantopoulos
, K.
, 2003
, “Single Molecule Characterization of P-Selectin/Ligand Binding
,” J. Biol. Chem.
, 278
(12
), pp. 10556
–10561
.10.1074/jbc.M21323320036.
Radhakrishnan
, R.
, Uma
, B.
, Liu
, J.
, Ayyaswamy
, P.
, and Eckmann
, D.
, “Temporal Multiscale Approach for Nanocarrier Motion With Simultaneous Adhesion and Hydrodynamic Interactions in Targeted Drug Delivery
,” J. Comput. Phys.
, Special Issue on Multiscale Modeling and Simulation of Biological Systems (in press).37.
Uma
, B.
, Radhakrishnan
, R.
, Eckmann
, D.
, and Ayyaswamy
, P.
, “Fluctuating Hydrodynamics Approach for the Simulation of Nanoparticle Brownian Motion in a Newtonian Fluid
,” Proceedings of the 21st National and 10th ISHMT-ASME Heat and Mass Transfer Conference
(in press).38.
Uma
, B.
, Radhakrishnan
, R.
, Eckmann
, D.
, and Ayyaswamy
, P.
, “A Hybrid Approach for the Simulation of the Thermal Motion of a Nearly Neutrally Buoyant Nanoparticle in an Incompressible Newtonian Fluid Medium
,” ASME J. Heat Transfer
(in press).39.
Agrawal
, N.
, and Radhakrishnan
, R.
, 2007
, “The Role of Glycocalyx in Nanocarrier-Cell Adhesion Investigated Using a Thermodynamic Model and Monte Carlo Simulations
,” J. Phys. Chem. C
, 111
(43
), pp. 15848
–15856
.10.1021/jp074514x40.
Liu
, J.
, Agrawal
, N.
, Calderon
, A.
, Ayyaswamy
, P.
, Eckmann
, D.
, and Radhakrishnan
, R.
, 2011
, “Multivalent Binding of Nanocarrier to Endothelial Cells Under Shear Flow
,” Biophys. J.
, 101
(2
), pp. 319
–326
.10.1016/j.bpj.2011.05.06341.
Grmela
, M.
, and Öttinger
, H.
, 1997
, “Dynamics and Thermodynamics of Complex Fluids. I. Development of a General Formalism
,” Phys. Rev. E
, 56
(6
), pp. 6620
–6632
.10.1103/PhysRevE.56.662042.
Öttinger
, H.
, and Grmela
, M.
, 1997
, “Dynamics and Thermodynamics of Complex Fluids. II. Illustrations of a General Formalism
,” Phys. Rev. E
, 56
(6
), pp. 6633
–6655
.10.1103/PhysRevE.56.663343.
Patankar
, N. A.
, Singh
, P.
, Joseph
, D. D.
, Glowinski
, R.
, and Pan
, T. W.
, 2000
, “A New Formulation of the Distributed Lagrange Multiplier/Fictitious Domain Method for Particulate Flows
,” Int. J. Multiphase Flow
, 26
, pp. 1509
–1524
.10.1016/S0301-9322(99)00100-744.
Chen
, Y.
, Sharma
, N.
, and Patankar
, N.
, 2006
, “Fluctuating Immersed Material (FIMAT) Dynamics for the Direct Simulation of the Brownian Motion of Particles
,” Proceedings of the IUTAM Symposium on Computational Approaches to Multiphase Flow, S.
Balachandar
and A.
Prosperetti
, eds., Springer
, Dordrecht, The Netherlands, pp. 119
–129
.10.1007/1-4020-4977-3_1345.
Hu
, H.
, 1996
, “Direct Simulation of Flows of Solid-Liquid Mixtures
,” Int. J. Multiphase Flow
, 22
(2
), pp. 335
–352
.10.1016/0301-9322(95)00068-246.
Hu
, H. H.
, Patankar
, N. A.
, and Zhu
, M. Y.
, 2001
, “Direct Numerical Simulations of Fluid-Solid Systems Using the Arbitrary Langrangian-Eulerian Technique
,” J. Comput. Phys.
, 169
(2
), pp. 427
–462
.10.1006/jcph.2000.659247.
Zwanzig
, R.
, and Bixon
, M.
, 1970
, “Hydrodynamic Theory of the Velocity Correlation Function
,” Phys. Rev. A
, 2
(5
), pp. 2005
–2012
.10.1103/PhysRevA.2.200548.
Roux
, B.
, 1995
, “The Calculation of the Potential of Mean Force Using Computer Simulations
,” Comput. Phys. Commun.
, 91
(1–3
), pp. 275
–282
.10.1016/0010-4655(95)00053-I49.
Zhang
, X.
, Wojcikiewicz
, E.
, and Moy
, V.
, 2002
, “Force Spectroscopy of the Leukocyte Function-Associated Antigen-1/Intercellular Adhesion Molecule-1 Interaction
,” Biophys. J.
, 83
(4
), pp. 2270
–2279
.10.1016/S0006-3495(02)73987-8Copyright © 2013 by ASME
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