Identifying the Rules of Engagement Enabling Leukocyte Rolling, Activation, and Adhesion

The LFA-1 integrin plays a pivotal role in sustained leukocyte adhesion to the endothelial surface, which is a precondition for leukocyte recruitment into inflammation sites. Strong correlative evidence implicates LFA-1 clustering as being essential for sustained adhesion, and it may also facilitate rebinding events with its ligand ICAM-1. We cannot challenge those hypotheses directly because it is infeasible to measure either process during leukocyte adhesion following rolling. The alternative approach undertaken was to challenge the hypothesized mechanisms by experimenting on validated, working counterparts: simulations in which diffusible, LFA1 objects on the surfaces of quasi-autonomous leukocytes interact with simulated, diffusible, ICAM1 objects on endothelial surfaces during simulated adhesion following rolling. We used object-oriented, agent-based methods to build and execute multi-level, multi-attribute analogues of leukocytes and endothelial surfaces. Validation was achieved across different experimental conditions, in vitro, ex vivo, and in vivo, at both the individual cell and population levels. Because those mechanisms exhibit all of the characteristics of biological mechanisms, they can stand as a concrete, working theory about detailed events occurring at the leukocyte–surface interface during leukocyte rolling and adhesion experiments. We challenged mechanistic hypotheses by conducting experiments in which the consequences of multiple mechanistic events were tracked. We quantified rebinding events between individual components under different conditions, and the role of LFA1 clustering in sustaining leukocyte–surface adhesion and in improving adhesion efficiency. Early during simulations ICAM1 rebinding (to LFA1) but not LFA1 rebinding (to ICAM1) was enhanced by clustering. Later, clustering caused both types of rebinding events to increase. We discovered that clustering was not necessary to achieve adhesion as long as LFA1 and ICAM1 object densities were above a critical level. Importantly, at low densities LFA1 clustering enabled improved efficiency: adhesion exhibited measurable, cell level positive cooperativity.

. Decisional processes for LFA1, PSELECTIN, MEMBRANE UNIT, LEUKOCYTE MEMBRANE, AND ICAM1. Sketched is the decisional process for the (A) LFA1, (B) PSELECTIN, (C) LEUKOCYTE MEMBRANE UNIT, (D) LEUKOCYTE MEMBRANE, and (E) ICAM1 during a simulation cycle. Black diamonds are Boolean variables that determine which behaviors are allowed during a simulation experiment, allowing us to manipulate them individually, or in combination, and to observe the overall emergent effect on LEUKOCYTES and LEUKOCYTE populations. White arrows indicate the starting point for each agent in their decisional process. Figure S2. FORCE dependence on BOND DISSOCIATION probability and force dependence on bond dissociation rates. (A) Shown is the relationship between bondforce and probability of BOND DISSOCIATION for each of the four LIGAND pairs included in the ISWBC. The effects of shear on the ligand-ligand bonds that form at the rear of the leukocyte are simulated using bondforce. BONDS within the rear row of the CONTACT ZONE experience a bondforce that is calculated by dividing the RearForce, a unitless parameter representing the effects of shear, by the total number of BONDS within the rear row. During a simulation cycle, each MEMBRANE UNIT in the rear row uses the current value of bondforce and the graphed relationship to calculate a probability that each BOND will be broken during that cycle. All BONDS elsewhere within the CONTACT ZONE experience a bondforce value of 0. UNSTRESSED (bondforce value of 0) DISSOCIATION probabilities for PSGL1/PSELECTIN, LOW-AFFINITY VLA4/VCAM1, HIGH-AFFINITY VLA4/VCAM1, LOW-AFFINITY LFA1/ICAM1, and HIGH-AFFINITY LFA1/ICAM1 were specified to be 0.14, 0.16, and 0.0035, 0.4, and 0.017 respectively. (B) The in vitro force dependence of dissociation rates for P-selectin/PSGL-1 bonds (as reported in [1]) and the high affinity VLA-4/VCAM-1 bonds (as reported in [3]) are plotted for comparison to the analogue relationships in A. The plotted values were taken from the fitted in vitro data: see Methods for details. The relationships in A are analogues of these experimentally determined relationships and are not meant to either match or fit that data. The dissociation rates of the PSGL-1/P-selectin bonds as a function of force were determined by experiments using PSGL-1-coated microbeads rolling on a P-selectin substrate in a parallel plate flow chamber [1]. The dissociation rates for the LFA-1/ICAM-1 complex were calculated from data obtained using atomic force spectroscopy [2]. The dissociation rates for the VLA-4/VCAM-1 complex were calculated from data obtained using single-molecule dynamic force spectroscopy [3]. The force dependence of dissociation rates for low affinity VLA-4/VCAM-1 data was not reported. We assumed that it is similar to PSGL-1/Pselectin relationship in A.

Diffusion
LFA1 DIFFUSION and TABLE S1 are mentioned in the RECEPTOR Behaviors subsection under Methods. LFA1 lateral mobility parameters were determined such that they have similar relative diffusive properties as observed in vitro. At each time step, each LFA1 object is allowed to randomly move to any of the 6 neighboring hexagonal grid sections on the LFA1GRID, for a specific number of times determined by the parameter LFA1MoveNum. We explored several parameter values for LFA1MoveNum and calculated the diffusion coefficients using Eq 1. <r 2 > is the MSD, t is the time interval, D is the time-dependent diffusion coefficient, and the α coefficient classifies the mode of anomalous diffusion.
Cairo et al. used single-particle tracking to determine the diffusion coefficients of LFA-1 on peripheral blood lymphocytes prior to and after activation with phorbol-12-myristate-13-acetate [4]. They observed in all cells before and after activation the existence of two subpopulations of LFA-1, immobile and mobile, distinguished by their diffusive properties. Diffusion coefficients have not been determined for neutrophils. We assumed neutrophil LFA-1 had similar diffusive properties. We first sought LFA1MoveNum parameter values that would allow our LFA1 objects to exhibit similar diffusive properties as those in the mobile and immobile subpopulations. In their calculations of diffusion coefficients, Cairo et al. observed values of α that were consistent with Brownian diffusion (0.7 < α < 1.2), and therefore we calculated D values using a α value of 1. We determined that a LFA1MoveNum of 10 gave similar diffusive properties to those of the immobile subpopulation, while a LFA1MoveNum of 120 yielded similar diffusive properties to the mobile subpopulation (Table S1). This section and Figure S3 are mentioned in the LFA1 CLUSTERING and LEUKOCYTE ADHESION subsection under Results. We repeated the experiments aimed at identifying the effect of ICAM1Density on LEUKOCYTE ADHESION, but changed the LFA1GridDensity parameter value (the fraction of all MEMBRANE UNITS that contain LFA1GRIDS) from 0.2 to 0.1. When LFA1GridDensity was decreased to 0.1 ( Figure. S3A), the ICAM1Density below which the influence of CLUSTERING became significant shifted from 50 to 70. The magnitude of the clustering effect increased at lower ICAM1Density values. On the other hand, when LFA1GridDensity was increased, for example from 0.2 to 0.4 (Fig. S3B), the ICAM1Density below which the influence of CLUSTERING became significant shifted from 50 to 30. That trend continued at larger LFAGridDensity values. However, in both cases, cooperative binding effects were still observed.

Appraisal of Model Specifications
This section was cited in the Other Models of Leukocyte Rolling and Adhesion subsection under Discussion.
Following the parsimony guideline, we strove to assemble a system of interacting components that would, at the margin, be complicated enough to exhibit multiple, different targeted attributes under different experimental conditions, but not so complicated that a component could be eliminated without significantly degrading behavioral similarities for the full set of targeted attributes. Some ISWBC2 components map to a conflated set of leukocyte features. Some leukocyte features have no ISWBC2 counterparts. The latter does not mean that those features were ignored or assumed unimportant. At each stage of iterative refinement, a goal was to determine the degree of biomimicry (level of biological emulation) that could be accomplished with a few components before concluding that others may be needed.
Both wet-lab experimental systems used whole blood containing red blood cells in addition to leukocytes. It is well known that smaller red blood cells can enhance leukocytesubstratum interactions by pushing the larger leukocytes from the axial flow to the vessel wall [5], [6], [7]. We do not discount the significance of such interactions under some conditions, however we chose specifically to focus on the interactions between an already attached leukocyte and its surface. At the beginning of each simulation, LEUKOCYTES were placed on the surface where interactions were allowed to form (or not). We posited that red blood cell-leukocyte interactions were similar in WT and KO mice, contributing equally to differences in wet-lab results, and so could be ignored. The flow chamber system was perfused by murine blood. The dynamics of leukocyte rolling and adhesion may have been influenced by the pulsatile blood flow. A rheological evaluation of the autoperfused flow chamber system was undertaken and reported stable flow conditions and tolerable changes in blood-flow velocity and wall shear stress. Flow through the chamber was essentially laminar and quasi-steady, as reflected by a Reynolds number less than three and a Womersley number of 0.5 [8]. In vivo, wall shear stress varies along the venular tree as vessel diameter and flow rate change. We started by specifying a constant SHEAR STRESS (REARFORCE) at all locations and times within in silico experiments. Our protocol called for retaining that parsimonious specification until falsification of a particular ISWBC2 required adopting a more fine-grained specification, which it did not. Varying REARFORCE can be implemented, as done earlier [9], when that is needed. Adhering to the parsimony guideline within the iterative refinement protocol has proven an effective tool in preventing ISWBC2s from becoming unnecessarily complicated.
With their Adhesive Dynamics (AD) model of leukocyte rolling and adhesion, King and Hammer demonstrated that only bonds at the trailing edge of the contact zone were under stress and that increases in instantaneous velocity correlated with breakage of trailing edge bonds [10]. They state that it is reasonable to simplify the force and torque balances such that only bonds at the trailing edge of the contact zone experience force [11]. Therefore, we have implemented the model specification that only bonds at the rear of the leukocyte experiences force, and that this is shared equally among all bonds at the rear.
Our approach has been focused on simulating a targeted set of system-level properties. It was not our intention to discover ISWBC parameterizations that would yield simulation results that tightly fit specific sets of experimental data. Therefore, we did not, for example, attempt an explicit mapping between the shear force and the amount of force experienced by bonds at the rear of the leukocyte. Leukocytes are notoriously deformable and therefore we elected to avoid a mapping such as the Goldman equation [12], which has been used in the AD models to calculate the amount of force a sphere experiences from an applied shear force by assuming that the sphere is solid. In addition, the mapping from the force on the cell to the force on the rear bonds can be quite complex as PSGL-1 and VLA-4 are both ligands that are concentrated at the tips of stretchy and heterogeneous microvilli. It should be noted that an estimate of 124.4 ± 26.1 pN per dyn/cm 2 wall shear stress for selectin tethers at the rear of neutrophils has been calculated previously using the Goldman equation [13].
To account for the effect of an applied force on the kinetics of bond dissociation in their AD simulations, Hammer and co-workers employed both the Bell model and Dembo Hookean Spring model (see [14]). The Bell Model predicts the bond dissociation rate as a function of applied force, whereas the Dembo model treats bonds as Hookean springs and relates bond dissociation rate to the length of the stretched bond. Use of a similar fine-grained representation of bond dissociation may have yielded more precise simulation results, but that level of resolution and precision was not needed to meet the simulation objectives in Table 1. We used a simple model to relate the probability of bond dissociation with bond force (Fig. S2A); it was motivated by in vitro experiments by Park et al. [15], and Zhang et al. [16]. We previously determined that this implementation was sufficient [9].
Many molecular level details are believed to impact effective bond formation and breakage within small portions of a leukocyte membrane and the corresponding portion of the surface. Examples include contact irregularities, local dynamics and ligand relocation within the membrane, force history of bond loading, and bond compliance. All of these factors are aggregated and controlled in the ISWBC by an event probability. When explanation of system level behaviors requires a more detailed representation, one or more of these factors can be specifically represented, without compromising the function of other ISWBC components. The probability parameters will remain, but their values and explanation will have changed.
There are many adhesion molecules present on the endothelial surface with varying site densities. Additionally, there is an endothelial surface layer. Studies have shown that the endothelial surface layer may slow plasma flow and may limit the exposure of adhesion molecules [17]. We specified two classes of ENDOTHELIAL ADHESION objects. One maps to Pselectin and any other molecules that behave similarly under the referent wet-lab conditions. The other maps to ICAM-1 and any similarly behaving molecules. We also specified two classes of LEUKOCYTE ADHESION objects. One maps to PSGL-1 and any other molecules that behave similarly under the referent wet-lab conditions. The other maps to LFA-1 and any similarly behaving molecules. We specified one class of CHEMOKINE RECEPTOR objects. It maps to CXCR2 and any other chemokine receptors behaving similarly under the referent wet-lab conditions.
We started by specifying simply that LEUKOCYTES would interact with a layer of randomly distributed RECEPTOR and CHEMOKINE objects. The nature of the actual surface to which those objects are attached was not specified. The RECEPTOR and CHEMOKINE objects map to reactive counterparts that are sufficiently exposed to react. We did not encounter nonmatching simulation results that would have triggered revising that specification. Consequently, ISWBC2 systems map equally well to those having engineered and endothelial surfaces.
CXCL1 is not a proinflammatory chemokine. We can therefore posit that ISWBC2 system surfaces map to inactive endothelial cells having a basal expression of adhesion molecules [18]. Again, when it is needed, it is straightforward to add objects that map to endothelial surface features without having to reengineer other features of the ISWB2 system.