White blood cell recruitment from the bloodstream to surrounding tissues is an essential component of the immune response. Capture Of hlood-borne Ieuk\u27Wks onto vascular endothelium proceeds via a two-step mechanism, with each step mediated by a distinct receptor-ligand pair. Cells first transiently adhere, or  roll  (via interactions between selectins and sialyl-Lewis-x), and then firmly adhere to the vascular wall (via interactions between integrins and ICAM-1). We have reported that a eomputatiokl method called Adhesive Dynamics (AD) accurately reproduces the fine scale dynamics of selectin-mediated rolling [1]. This paper extends the use of AD simulations to model the dynamics of cell adhesion when two classes of receptors are simultaneously active: one class (selectins) with weakly adhesive properties, and the other (integrins) with strongly adhesive properties. AD simulations predict synergistic functions of the two receptors in mediating adhesion. We present this relationship in a two-receptor state diagram, a map that relates the densities and properties of adhesion molecules to various adhesive behaviors that they code, such as rolling or firm adhesion. The predictions of two-receptor adhesive dynamics are validated by the ability of the model to reproduce experimental neutrophil rolling velocities

Bhatia, Sujata K.

Hammer, Daniel A

English

ScholarlyCommons@Penn

University of PennsylvaniaScholarlyCommonsDepartmental Papers (BE) Department of BioengineeringMarch 2003Dynamic Simulations of Inflammatory CellRecruitment: The State Diagram for Cell AdhesionMediated by Two ReceptorsSujata K. BhatiaUniversity of PennsylvaniaDaniel A. HammerUniversity of Pennsylvania, hammer@seas.upenn.eduFollow this and additional works at: http://repository.upenn.edu/be_papersCopyright 2003 IEEE. Reprinted from Proceedings of the 29th IEEE Annual Bioengineering Conference 2003, pages 158-159.Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=27351&page=5This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of theUniversity of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish thismaterial for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE bywriting to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is posted at ScholarlyCommons. http://repository.upenn.edu/be_papers/31For more information, please contact libraryrepository@pobox.upenn.edu.Recommended CitationBhatia, S. K., & Hammer, D. A. (2003). Dynamic Simulations of Inflammatory Cell Recruitment: The State Diagram for CellAdhesion Mediated by Two Receptors. Retrieved from http://repository.upenn.edu/be_papers/31Dynamic Simulations of Inflammatory Cell Recruitment: The StateDiagram for Cell Adhesion Mediated by Two ReceptorsAbstractWhite blood cell recruitment from the bloodstream to surrounding tissues is an essential component of theimmune response. Capture Of hlood-borne Ieuk'Wks onto vascular endothelium proceeds via a two-stepmechanism, with each step mediated by a distinct receptor-ligand pair. Cells first transiently adhere, or "roll"(via interactions between selectins and sialyl-Lewis-x), and then firmly adhere to the vascular wall (viainteractions between integrins and ICAM-1). We have reported that a eomputatiokl method called AdhesiveDynamics (AD) accurately reproduces the fine scale dynamics of selectin-mediated rolling [1]. This paperextends the use of AD simulations to model the dynamics of cell adhesion when two classes of receptors aresimultaneously active: one class (selectins) with weakly adhesive properties, and the other (integrins) withstrongly adhesive properties. AD simulations predict synergistic functions of the two receptors in mediatingadhesion. We present this relationship in a two-receptor state diagram, a map that relates the densities andproperties of adhesion molecules to various adhesive behaviors that they code, such as rolling or firmadhesion. The predictions of two-receptor adhesive dynamics are validated by the ability of the model toreproduce experimental neutrophil rolling velocities.CommentsCopyright 2003 IEEE. Reprinted from Proceedings of the 29th IEEE Annual Bioengineering Conference 2003,pages 158-159.Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=27351&page=5This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any wayimply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personaluse of this material is permitted. However, permission to reprint/republish this material for advertising orpromotional purposes or for creating new collective works for resale or redistribution must be obtained fromthe IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to allprovisions of the copyright laws protecting it.This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/be_papers/31Dynamic Simulations of Inflammatory Cell Recruitment: The State Diagram for Cell Adhesion Mediated by Two ,Receptors Sujata K. Bhatia and Daniel A. Hammer Department of Bioengineering and Chemical Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA white blood cell recruitment from the bloodstream to To clarify the relationship between the molecular surrounding tissues is an essential component of the immune properties of adhesive molecules and the macroscopic response. Capture Of hlood-borne Ieuk'Wks onto vascular behavior such as rolling or fum adhesion that thev mediate. reported that a eomputatiokl method called Adhesive Dynamics (AD) accurately reproduces the fine scale dynamics of selectin-mediated rolling 111. This paper extends the use of AD simulations to model the dynamics of cell adhesion when two classes of receptors are simultaneously active: one class (selectins) with weakly adhesive properties, and the other (integrins) with strongly adhesive properties. AD simulations predict synergistic functions of the two receptors in mediating adhesion. We present this relationship in a two-receptor state diagram, a map that relates the densities and properties of adhesion molecules to various adhesive behaviors that they code, such as rolling or firm adhesion. The predictions of two- receptor adhesive dynamics are validated by the ability of the model to reproduce experimental neutrophil rolling velocities. I. INTRODUCTlON Trafficking of blood-borne cells to tissues and organs is necessary for numerous immune functions such as inflammation [21. Leukocyte recruitment to the vessel wall and force-dependent binding kinetics [9]. The resulting Adhesive Dyna~i~ics (AD) simulation accurately reproduces the dynamics of selectin-mediated rolling [lo]. This paper extends 'AD simulations to determine the dynamics of ailhesion when two receptor-ligand systems are simultaneously active. One system is characterized by relatively weak adhesive properties, such as a low association rate and high unstressed dissociation rate which suggest a propensity for rolling interactions, as are experimentally observed with the selectin-sLe" system. The second system is characterized by relatively strong adhesive properties, such as a high association rate and low unstressed dissociation rate, as are experimentally observed with the activated integrin-ICAM-1 system. AD simulations predict that the two receptor-ligand systems have synergistic roles in promoting cell adhesion. 11. METHODS proceeds via a multi-step process, with each step mediated by distinct cell adhesion molecules. Initially, E- and P- selectin expressed on vascular endothelium interact with cell surface molecules bearing the carbohydrate sialyl-Lewis-x generates transient adhesion, or "rolling," of leukocytes Once IeUkocyteS have been Slowed by selectin-mediated :rolling, they become activated to f d y  adhere to the vessel wall [3]. Firm adhesion is The AD method has been extensively described The simulation begins with a freely moving or receptor- coated particle, modeled as a sphere with receptors disvibuted oveI its surface. A large number of adhesion a bounding wall, The tip of each. free adhesion molecule reacts with its counter-receptor with association rate ( s W .  Selectin-sLe" binding and force-driven unbinding molecules are randomly placed on the surface of the sphere the vessel diss&iationrate k, We use the Bell model [91: mediated by interactions between cell surface p2 integrins and endothelial intercellular adhesion molecule-l (ICAM- 1). Different dynamic states of adhesion are thus mediated by different classes of molecules. While the adhesive states that selectins and integtins suppon are known, the mechanism by which leukocytes go from rolling to firm' adhesion, as well as the precise molecular requirements for leukocyte arrest, remain unclear. Studies in double knockout mice show that deficiency in E- and P-selectin can eliminate the granulocyte-mediated inflammatory response, even when integrins and ICAM-1 are available for fm adhesion [41. Selectin-mediated rolling is thus necessary for integrin-mediated fum adhesion. However, grabulocyte rolling .velocities during inflammation are significantly increased in ICAMIl- deficient mice [ 5 ] ,  suggesting that ICAM-1 is also required for optimal selectin-mediated rolling. which relates the rate of.dissociation k, to the magnitude . .  of the force on the bond F. Once k, is set by Eq. 1, the association rate k, can be calculated from the B o l t "  distribution for affinity: where d is the Hookean spring constant and Ixb - hl is the deviation bond length. During each time step of the simulation, bond formation and breakage are simulated by a Monte Carlo lottery, in which random numbers are compared with the probabilities for binding and unbinding to determine whether a bond will form or break in the time interval. The bond stresses,f, are ~ .... 0-7803-7767-2103/$17.00 WOO3 IEEE 158 calculated from the distance between the end points of the attachment, L, using Hooke's law, f = rr(L - X). The stress contributed by each bond is summed to determine the total force and torque exerted by the bonds on the cell. In addition to the bonding forces, we include colloidal forces, and the external force and'torque imparted to-the cell by fluid shear to compute the net force and torque acting on the cell. 'The motion of the particle is obtained from the mobility matrix for a sphere near a plane wall in a viscous fluid [7,8]. The new positions of bond tethers at t + dr are updated from their positions at r, using the cell velocity. III. RESULTS To determine the adhesive behavior expected for a given combination of receptor densities, we calculated a state diagram for two-receptor' adhesion (Fig. l), in which observed adhesive behaviors are plotted for a range of selectin and ICAM-1 surface densities. . The boundary separating the states of rolling adhesion and fxm adhesion is parametrized by a mean velocity of 0.02VH. In this state diagram, the rate constants and mechano-chemical properties are ked, the shear rate is 100 s-', For integrin- ICAM-1 interactions, rate constants reflecting activated p2 integrin are used. The boundary separating rolling and firm adhesion is calculated for three different integrin-ICAM-1 association rates, k, ,in,rgnn = 1000, 100, and 10 s-'. The state diagram demonstrates synergistic functions of the two receptor-ligand systems in promoting cell adhesion and arrest. For example, at a selectin site density of 30 molecules/p2, the state diagram predicts rolling adhesive behavior if no ICAM-1 is present on the surface. At an .ICAM-l site density of 3 molecules/p2, the state diagram predicts rolling adhesion if no selectin is present on the surface. However, the combination of 30 molecules/p* selectin and 3 molecules/p2 ICAM-1 results in iirm adhesion, when k:,in,e8nn is greater than 100 s-I. As k&egnn decreases, the location of the firm adhesion envelope shifts to slightly higher ICAM-I densities, and the synergy between the two receptors is somewhat less pronounced though still present. Instead, at low k;,in,egnnr there are critical values of both selectin and ICAM-1 density Therefore, addition of ICAM-1 on the surface for a cell rolling on a fsed.level of-selectin facilitates f r m ~  binding, and the presence of selectin facilitates firm binding at fixed levels of integrin and ICAM-1. Clearly, the two molecular pairs work synergistically to support fxm binding. We were interested in examining the validity of our model, by comparing simulation predictions to experimental results from the literature. Kunkel and coworkers [ l l ]  used intravital microscopy to track individual leukocytes in the microcirculation of wild-type mice, CD18 (p2 integrin) 4- knockout mice, and E-selectin 4- knockout mice following TNFa induced inflammation. These investigators found that neutrophil rolling velocities in wild-type mice, were significantly lower than rolling velocities in CD18-I- or E-/- mice. AD simulations reproduce this result (Fig. 2). 0 . necessary for the transition to firm adhesion. . 159 8 I I  Wnnk.UY1-7 Fig. 1. The state diagram for adhesion mediated by WO receptm. For each rolling stafe, the boundary represents a mean velocity of 0.02V~.  - 1  1 . 1  I I I I "amraarrm, Fig. 2. Comparison of twwezeptor adhesive dynamic simulatims to expnimental data Irom KunLel and coworkers [ I  I]. This calculation is paformed at b,<UgM = loo0 s-1.IV. DISCUSSION Using two-receptor adhesive dynamics, we have constructed a state diagram for two-receptor adhesion. The state diagram illustrates that selectin-sLe" interactions and integrin-ICAM-1 interactions have synergistic functions in promoting cell adhesion and arrest. The predictions of two- receptor adhesive dynamics are validated by the ability of the model to reproduce, h t h  qualitatively and quantitatively, in vivo neutrophil rolling velocities. neutrophil' rolling velocities .from E-/- . and C D l W  knockout mice can be combined to reproduce the two- receptor-mediated rolling of neutrophils in wild-type mice. REFERENCES Simulation parameters that independently reproduce ... . .  . .  [I] K. C. Chang ernl.. Proc. Natl. Aud. Sci. USA, &I. 97. 11262 (2ooo). (21 T. A. Springer, Cell, vol. 76,301 (1994). 131' M. B .  Lawrence. T. A. Springer. Cell, vol. 65.859 (1991). 141 D.C. Bullardetal.. 3. Erp. Mcd. vol. 183.2329(1996). I51 D. A. Steeberetal.. 3. Imunol . ,  vol. 163.2175 (1999). I61 D. A. Hammer, S. M. Ape, Biophys. 3.. vol. 62.35 (1992). I71 A. 1. Goldman ernl.. Chem Eng. Sci.. vol. 22,637 (1%7). 181 A. J. Goldmanrral.. Chcm Dig. Sci.. vol. 22,653 (1967). 191 G. 1. Bell,Scienee, vol. 200, 618 (1978). [IO] K. C. Chang, D. A Ha"er.Biophys.~J.. vol. 79, 1891 (2ooo). 1111 E. J. Kunkeletol.. 3. Immunol., vol. 164,3301 (2000). 1121 S. K Bhatia. M. R. King. D. A. "mer, Bi0ph.w. 3.. in p m  (2003). 

Dynamic Simulations of Inflammatory Cell Recruitment: The State Diagram for Cell Adhesion Mediated by Two Receptors

Kosmopolis

University of Pennsylvania
ScholarlyCommons
Departmental Papers (BE) Department of Bioengineering
March 2003
Dynamic Simulations of Inflammatory Cell
Recruitment: The State Diagram for Cell Adhesion
Mediated by Two Receptors
Sujata K. Bhatia
University of Pennsylvania
Daniel A. Hammer
University of Pennsylvania, hammer@seas.upenn.edu
Follow this and additional works at: http://repository.upenn.edu/be_papers
Copyright 2003 IEEE. Reprinted from Proceedings of the 29th IEEE Annual Bioengineering Conference 2003, pages 158-159.
Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=27351&page=5
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the
University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this
material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by
writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
This paper is posted at ScholarlyCommons. http://repository.upenn.edu/be_papers/31
For more information, please contact libraryrepository@pobox.upenn.edu.
Recommended Citation
Bhatia, S. K., & Hammer, D. A. (2003). Dynamic Simulations of Inflammatory Cell Recruitment: The State Diagram for Cell
Adhesion Mediated by Two Receptors. Retrieved from http://repository.upenn.edu/be_papers/31
Dynamic Simulations of Inflammatory Cell Recruitment: The State
Diagram for Cell Adhesion Mediated by Two Receptors
Abstract
White blood cell recruitment from the bloodstream to surrounding tissues is an essential component of the
immune response. Capture Of hlood-borne Ieuk'Wks onto vascular endothelium proceeds via a two-step
mechanism, with each step mediated by a distinct receptor-ligand pair. Cells first transiently adhere, or "roll"
(via interactions between selectins and sialyl-Lewis-x), and then firmly adhere to the vascular wall (via
interactions between integrins and ICAM-1). We have reported that a eomputatiokl method called Adhesive
Dynamics (AD) accurately reproduces the fine scale dynamics of selectin-mediated rolling [1]. This paper
extends the use of AD simulations to model the dynamics of cell adhesion when two classes of receptors are
simultaneously active: one class (selectins) with weakly adhesive properties, and the other (integrins) with
strongly adhesive properties. AD simulations predict synergistic functions of the two receptors in mediating
adhesion. We present this relationship in a two-receptor state diagram, a map that relates the densities and
properties of adhesion molecules to various adhesive behaviors that they code, such as rolling or firm
adhesion. The predictions of two-receptor adhesive dynamics are validated by the ability of the model to
reproduce experimental neutrophil rolling velocities.
Comments
Copyright 2003 IEEE. Reprinted from Proceedings of the 29th IEEE Annual Bioengineering Conference 2003,
pages 158-159.
Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=27351&page=5
This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way
imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal
use of this material is permitted. However, permission to reprint/republish this material for advertising or
promotional purposes or for creating new collective works for resale or redistribution must be obtained from
the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all
provisions of the copyright laws protecting it.
This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/be_papers/31
Dynamic Simulations of Inflammatory Cell Recruitment: 
The State Diagram for Cell Adhesion Mediated by Two ,Receptors 
Sujata K. Bhatia and Daniel A. Hammer 
Department of Bioengineering and Chemical Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA 
white blood cell recruitment from the bloodstream to To clarify the relationship between the molecular 
surrounding tissues is an essential component of the immune properties of adhesive molecules and the macroscopic 
response. Capture Of hlood-borne Ieuk'Wks onto vascular behavior such as rolling or fum adhesion that thev mediate. 
reported that a eomputatiokl method called Adhesive 
Dynamics (AD) accurately reproduces the fine scale dynamics 
of selectin-mediated rolling 111. This paper extends the use of 
AD simulations to model the dynamics of cell adhesion when 
two classes of receptors are simultaneously active: one class 
(selectins) with weakly adhesive properties, and the other 
(integrins) with strongly adhesive properties. AD simulations 
predict synergistic functions of the two receptors in mediating 
adhesion. We present this relationship in a two-receptor state 
diagram, a map that relates the densities and properties of 
adhesion molecules to various adhesive behaviors that they 
code, such as rolling or firm adhesion. The predictions of two- 
receptor adhesive dynamics are validated by the ability of the 
model to reproduce experimental neutrophil rolling velocities. 
I. INTRODUCTlON 
Trafficking of blood-borne cells to tissues and organs is 
necessary for numerous immune functions such as 
inflammation [21. Leukocyte recruitment to the vessel wall 
and force-dependent binding kinetics [9]. The resulting 
Adhesive Dyna~i~ics (AD) simulation accurately reproduces 
the dynamics of selectin-mediated rolling [lo]. 
This paper extends 'AD simulations to determine the 
dynamics of ailhesion when two receptor-ligand systems are 
simultaneously active. One system is characterized by 
relatively weak adhesive properties, such as a low 
association rate and high unstressed dissociation rate which 
suggest a propensity for rolling interactions, as are 
experimentally observed with the selectin-sLe" system. The 
second system is characterized by relatively strong adhesive 
properties, such as a high association rate and low 
unstressed dissociation rate, as are experimentally observed 
with the activated integrin-ICAM-1 system. AD 
simulations predict that the two receptor-ligand systems 
have synergistic roles in promoting cell adhesion. 
11. METHODS 
proceeds via a multi-step process, with each step mediated 
by distinct cell adhesion molecules. Initially, E- and P- 
selectin expressed on vascular endothelium interact with cell 
surface molecules bearing the carbohydrate sialyl-Lewis-x 
generates transient adhesion, or "rolling," of leukocytes 
Once IeUkocyteS have been Slowed 
by selectin-mediated :rolling, they become activated to 
f d y  adhere to the vessel wall [3]. Firm adhesion is 
The AD method has been extensively described The 
simulation begins with a freely moving or receptor- 
coated particle, modeled as a sphere with receptors 
disvibuted oveI its surface. A large number of adhesion 
a bounding wall, The tip of each. free adhesion 
molecule reacts with its counter-receptor with association 
rate 
( s W .  Selectin-sLe" binding and force-driven unbinding molecules are randomly placed on the surface of the sphere 
the vessel 
diss&iationrate k, We use the Bell model [91: 
mediated by interactions between cell surface p2 integrins 
and endothelial intercellular adhesion molecule-l (ICAM- 
1). Different dynamic states of adhesion are thus mediated 
by different classes of molecules. 
While the adhesive states that selectins and integtins 
suppon are known, the mechanism by which leukocytes go 
from rolling to firm' adhesion, as well as the precise 
molecular requirements for leukocyte arrest, remain unclear. 
Studies in double knockout mice show that deficiency in E- 
and P-selectin can eliminate the granulocyte-mediated 
inflammatory response, even when integrins and ICAM-1 
are available for fm adhesion [41. Selectin-mediated 
rolling is thus necessary for integrin-mediated fum 
adhesion. However, grabulocyte rolling .velocities during 
inflammation are significantly increased in ICAMIl- 
deficient mice [ 5 ] ,  suggesting that ICAM-1 is also required 
for optimal selectin-mediated rolling. 
which relates the rate of.dissociation k, to the magnitude . .  of 
the force on the bond F. 
Once k, is set by Eq. 1, the association rate k, can be 
calculated from the B o l t "  distribution for affinity: 
where d is the Hookean spring constant and Ixb - hl is the 
deviation bond length. 
During each time step of the simulation, bond formation 
and breakage are simulated by a Monte Carlo lottery, in 
which random numbers are compared with the probabilities 
for binding and unbinding to determine whether a bond will 
form or break in the time interval. The bond stresses,f, are 
~ .... 
0-7803-7767-2103/$17.00 WOO3 IEEE 158 
calculated from the distance between the end points of the 
attachment, L, using Hooke's law, f = rr(L - X). The stress 
contributed by each bond is summed to determine the total 
force and torque exerted by the bonds on the cell. In 
addition to the bonding forces, we include colloidal forces, 
and the external force and'torque imparted to-the cell by 
fluid shear to compute the net force and torque acting on the 
cell. 'The motion of the particle is obtained from the 
mobility matrix for a sphere near a plane wall in a viscous 
fluid [7,8]. The new positions of bond tethers at t + dr are 
updated from their positions at r, using the cell velocity. 
III. RESULTS 
To determine the adhesive behavior expected for a given 
combination of receptor densities, we calculated a state 
diagram for two-receptor' adhesion (Fig. l), in which 
observed adhesive behaviors are plotted for a range of 
selectin and ICAM-1 surface densities. . The boundary 
separating the states of rolling adhesion and fxm adhesion is 
parametrized by a mean velocity of 0.02VH. In this state 
diagram, the rate constants and mechano-chemical 
properties are ked, the shear rate is 100 s-', For integrin- 
ICAM-1 interactions, rate constants reflecting activated p2 
integrin are used. The boundary separating rolling and firm 
adhesion is calculated for three different integrin-ICAM-1 
association rates, k, ,in,rgnn = 1000, 100, and 10 s-'. 
The state diagram demonstrates synergistic functions of 
the two receptor-ligand systems in promoting cell adhesion 
and arrest. For example, at a selectin site density of 30 
molecules/p2, the state diagram predicts rolling adhesive 
behavior if no ICAM-1 is present on the surface. At an 
.ICAM-l site density of 3 molecules/p2, the state diagram 
predicts rolling adhesion if no selectin is present on the 
surface. However, the combination of 30 molecules/p* 
selectin and 3 molecules/p2 ICAM-1 results in iirm 
adhesion, when k:,in,e8nn is greater than 100 s-I. As k&egnn 
decreases, the location of the firm adhesion envelope shifts 
to slightly higher ICAM-I densities, and the synergy 
between the two receptors is somewhat less pronounced 
though still present. Instead, at low k;,in,egnnr there are 
critical values of both selectin and ICAM-1 density 
Therefore, addition of ICAM-1 on the surface for a cell 
rolling on a fsed.level of-selectin facilitates f r m ~  binding, 
and the presence of selectin facilitates firm binding at fixed 
levels of integrin and ICAM-1. Clearly, the two molecular 
pairs work synergistically to support fxm binding. 
We were interested in examining the validity of our 
model, by comparing simulation predictions to experimental 
results from the literature. Kunkel and coworkers [ l l ]  used 
intravital microscopy to track individual leukocytes in the 
microcirculation of wild-type mice, CD18 (p2 integrin) 4- 
knockout mice, and E-selectin 4- knockout mice following 
TNFa induced inflammation. These investigators found 
that neutrophil rolling velocities in wild-type mice, were 
significantly lower than rolling velocities in CD18-I- or E-/- 
mice. AD simulations reproduce this result (Fig. 2). 
0 
. necessary for the transition to firm adhesion. . 
159 
8 I I  
Wnnk.UY1-7 
Fig. 1. The state diagram for adhesion mediated by WO receptm. For each 
rolling stafe, the boundary represents a mean velocity of 0.02V~.  
- 1  1 . 1  I I I I 
"amraarrm, 
Fig. 2. Comparison of twwezeptor adhesive dynamic simulatims to 
expnimental data Irom KunLel and coworkers [ I  I]. This calculation is 
paformed at b,<UgM = loo0 s-1.
IV. DISCUSSION 
Using two-receptor adhesive dynamics, we have 
constructed a state diagram for two-receptor adhesion. The 
state diagram illustrates that selectin-sLe" interactions and 
integrin-ICAM-1 interactions have synergistic functions in 
promoting cell adhesion and arrest. The predictions of two- 
receptor adhesive dynamics are validated by the ability of 
the model to reproduce, h t h  qualitatively and 
quantitatively, in vivo neutrophil rolling velocities. 
neutrophil' rolling velocities .from E-/- . and C D l W  
knockout mice can be combined to reproduce the two- 
receptor-mediated rolling of neutrophils in wild-type mice. 
REFERENCES 
Simulation parameters that independently reproduce ... . .  
. .  
[I] K. C. Chang ernl.. Proc. Natl. Aud. Sci. USA, &I. 97. 11262 (2ooo). 
(21 T. A. Springer, Cell, vol. 76,301 (1994). 
131' M. B .  Lawrence. T. A. Springer. Cell, vol. 65.859 (1991). 
141 D.C. Bullardetal.. 3. Erp. Mcd. vol. 183.2329(1996). 
I51 D. A. Steeberetal.. 3. Imunol . ,  vol. 163.2175 (1999). 
I61 D. A. Hammer, S. M. Ape, Biophys. 3.. vol. 62.35 (1992). 
I71 A. 1. Goldman ernl.. Chem Eng. Sci.. vol. 22,637 (1%7). 
181 A. J. Goldmanrral.. Chcm Dig. Sci.. vol. 22,653 (1967). 
191 G. 1. Bell,Scienee, vol. 200, 618 (1978). 
[IO] K. C. Chang, D. A Ha"er.Biophys.~J.. vol. 79, 1891 (2ooo). 
1111 E. J. Kunkeletol.. 3. Immunol., vol. 164,3301 (2000). 
1121 S. K Bhatia. M. R. King. D. A. "mer, Bi0ph.w. 3.. in p m  (2003). 


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Dynamic Simulations of Inflammatory Cell Recruitment: The State Diagram for Cell Adhesion Mediated by Two Receptors

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