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

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.475
2.
Muzykantov
,
V.
,
Radhakrishnan
,
R.
, and
Eckmann
,
D.
,
2012
, “
Dynamic Factors Controlling Targeting Nanocarriers to Vascular Endothelium
,”
Curr. Drug Metab.
,
113
, pp.
70
81
.10.2174/138920012798356916
3.
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-2009-0544
4.
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.2010.10.025
5.
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)79248-2
6.
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.1006611107
7.
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
.10.1063/1.3635776
8.
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
.10.1063/1.3611026
9.
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/BF01030307
11.
Serrano
,
M.
, and
Español
,
P.
,
2001
, “
Thermodynamically Consistent Mesoscopic Fluid Particle Model
,”
Phys. Rev. E
,
64
(
4
), p.
046115
.10.1103/PhysRevE.64.046115
12.
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.2004.06.002
13.
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
.10.1088/0305-4470/35/7/310
14.
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.2010.5.149
15.
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.70.1339
16.
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/S0022112094001771
17.
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/S0022112094001783
18.
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/i2004-10542-5
20.
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_2
21.
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.2009.06.012
22.
Español
,
P.
, and
Zúñiga
,
I.
,
2009
, “
On the Definition of Discrete Hydrodynamic Variables
,”
J. Chem. Phys.
,
131
, p.
164106
.10.1063/1.3247586
23.
Español
,
P.
,
Anero
,
J.
, and
Zúñiga
,
I.
,
2009
, “
Microscopic Derivation of Discrete Hydrodynamics
,”
J. Chem. Phys.
,
131
, p.
244117
.10.1063/1.3274222
24.
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.2006.11.015
25.
Ermak
,
D. L.
, and
McCammon
,
J. A.
,
1978
, “
Brownian Dynamics With Hydrodynamic Interactions
,”
J. Chem. Phys.
,
69
(
4
), pp.
1352
1360
.10.1063/1.436761
26.
Brady
,
J. F.
, and
Bossis
,
G.
,
1988
, “
Stokesian Dynamics
,”
Ann. Rev. Fluid Mech.
,
20
(
1
), pp.
111
157
.10.1146/annurev.fl.20.010188.000551
27.
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/S0022112099007557
28.
Banchio
,
A. J.
, and
Brady
,
J. F.
,
2003
, “
Accelerated Stokesian Dynamics: Brownian Motion
,”
J. Chem. Phys.
,
118
(
22
), pp.
10323
10332
.10.1063/1.1571819
29.
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.77.074007
30.
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.79.031401
31.
Kubo
,
R.
,
1966
, “
The Fluctuation-Dissipation Theorem
,”
Rep. Prog. Phys.
,
29
(
1
), pp.
255
284
.10.1088/0034-4885/29/1/306
32.
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
.10.1080/00268976.2012.663510
34.
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)84252-6
35.
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.M213233200
36.
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/jp074514x
40.
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.2011.05.063
41.
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.56.6620
42.
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.56.6633
43.
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)00100-7
44.
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_13
45.
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)00068-2
46.
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.2000.6592
47.
Zwanzig
,
R.
, and
Bixon
,
M.
,
1970
, “
Hydrodynamic Theory of the Velocity Correlation Function
,”
Phys. Rev. A
,
2
(
5
), pp.
2005
2012
.10.1103/PhysRevA.2.2005
48.
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-I
49.
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)73987-8
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