Multi-cell Agent-based Simulation of the Microvasculature to Study the Dynamics of Circulating Inflammatory Cell Trafficking
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Leukocyte trafficking through the microcirculation and into tissues is central in angiogenesis, inflammation, and the immune response. Although the literature is rich with mechanistic detail describing molecular mediators of these processes, integration of signaling events and cell behaviors within a unified spatial and temporal framework at the multi-cell tissue-level is needed to achieve a fuller understanding. We have developed a novel computational framework that combines agent-based modeling (ABM) with a network flow analysis to study monocyte homing. A microvascular network architecture derived from mouse muscle was incorporated into the ABM. Each individual cell was represented by an individual agent in the simulation. The network flow model calculates hemodynamic parameters (blood flow rates, fluid shear stress, and hydrostatic pressures) throughout the simulated microvascular network. These are incorporated into the ABM to affect monocyte transit through the network and chemokine/cytokine concentrations. In turn, simulated monocytes respond to their local mechanical and biochemical environments and make behavioral decisions based on a rule set derived from independent literature. Simulated cell behaviors give rise to emergent leukocyte rolling, adhesion, and extravasation. Molecular knockout simulations were performed to validate the model, and predictions of monocyte adhesion, rolling, and extravasation show good agreement with the independently published corresponding mouse studies.
KeywordsMicrocirculation Agent-based model Network flow model Monocyte Inflammation Leukocyte adhesion
Smooth muscle cell
Wall shear stress
Tumor necrosis factor-α
Vascular cell adhesion molecule-1
Intercellular adhesion molecule-1
Leukocyte functional antigen-1
Very late antigen-4
Many vascular-associated pathologies and injury states are associated with inflammation, including atherosclerosis, stroke, chronic wounds, and peripheral vascular disease. Monocytes and other leukocytes are critical players in these diseases, where they have been shown to contribute to angiogenesis and microvascular remodeling,8,21,64 atherosclerotic lesion progression and propensity to rupture,6,7,58 as well as capillary plugging and tissue edema.32,43,99 In cases of rampant inflammation, the participation of inflammatory cells can have an overall deleterious impact on the tissue. Therefore, limiting leukocyte participation may have desired therapeutic effects.61 On the other hand, inflammatory cells also perform beneficial roles in mediating tissue recovery and regeneration,25,64 and efforts to harness their therapeutic potential have garnered considerable attention, as in the case of ischemic pre-conditioning.46,47 All of these effects are predicated on the ability of inflammatory cells to navigate through the microvasculature and preferentially home to sites of injury via interactions with the endothelium. Thus, understanding the role of inflammatory cells in vascular-associated pathologies necessitates a close study of leukocyte adhesion and the dynamics of this phenomenon as they manifest at the multi-cell tissue-level. To this end, we have developed an agent-based computational model that is underpinned by a network blood flow simulation to enable dynamic tracking of simulated inflammatory cells as they traffic through a microvascular network and home to a simulated muscle tissue bed. We then used our model to systematically interrogate the complex array of molecular signals that mediate this process with the goal of establishing a useful framework for further study of inflammatory cell participation in different disease settings.
Leukocyte–endothelial interactions are complex and dynamic—involving a cascade of molecular, mechanical, and biochemical signaling events, as well as spatially and temporally coordinated cell behaviors.105 This complexity, along with limitations in in vivo cell tracking through the circulation and interstitial tissue space, as well as an inability to dynamically visualize in vivo tissues with sub-cellular resolution, has hampered progress towards a complete understanding of this process. We submit that available experimental techniques alone do not allow for thorough study of leukocyte trafficking in its entirety, and a computational systems biology approach capable of integrating multiple factors in space and time to produce tissue-level predictions is merited.
Leukocyte adhesion under flow conditions has been studied experimentally using intravital microscopy of animal cremaster muscles19,63,112 and mesenteric tissue,13 as well as in in vitro flow chamber assays that allow precise manipulation of soluble chemokine levels and adhesion molecule presentation.17,53,55 This research has yielded a tremendous amount of detailed mechanistic data, and it has been demonstrated that for a generalized leukocyte population, adhesion tends to occur in sequential steps: (1) the capture of a flowing leukocyte out of the free-stream and onto the endothelium; (2) the subsequent formation and breaking of selectin bonds leading to rolling along the endothelium; (3) activation of leukocyte integrins by soluble and endothelial surface-bound chemokines; (4) firm adhesion of the leukocyte to the endothelium via activated integrins; and (5) trans-endothelial migration (for review see Ref.59). Inhibiting any one of these steps can lead to a failure of the entire process and greatly reduced trans-endothelial migration. For example, neutrophils will fail to progress through the adhesion cascade in the absence of selectins, whereas monocytes have been shown to be less dependent on selectin-mediated rolling and are able to transmigrate through integrin activation alone.26,42 Traditionally however, it is believed that selectin-mediated rolling allows an inflammatory cell to ‘survey’ the endothelium for activating stimuli, which ultimately leads to integrin activation once a theoretical ‘threshold activation level’ is reached.60 Thus, it is a unique pairing of molecular functionality that controls leukocyte adhesion: the selectins mediate the tethering and rolling of leukocytes, and the integrins utilize selectin-mediated rolling for more efficient activation and firm adhesion.
P- and E-selectins are found in endothelial cells (EC), although basal expression levels are very low. Within minutes of cell activation, both of these selectins are rapidly up-regulated and presented on the EC surface to their dominant ligand P-selectin glycoprotein-1 (PSGL-1) expressed on inflammatory cells (for a review of selectins see Ref.62). L-selectin is found only on inflammatory cells and also binds PSGL-1, although its main function is to allow circulating cells to survey and roll over each other.104 The most well-studied integrins for leukocyte–endothelium firm adhesion are the β2 integrins, MAC-1 and leukocyte functional antigen-1 (LFA1), and the α4β1 integrin, very late antigen-4 (VLA-4) (for review see Refs.66,94,113). These integrins predominantly bind to vascular cell adhesion molecule-1 (VCAM-1) and intracellular adhesion molecule (ICAM-1), both of which are expressed on the surface of ECs.85
The progression through the adhesion cascade also depends on spatially and temporally regulated chemokine/cytokine behavior59,105 and local hemodynamic forces (reviewed in Ref.39). The concentration of soluble and EC-surface-bound cytokines and chemokines has been shown to be critical in the activation of inflammatory cell integrins and modulation of adhesion molecule expression (reviewed in Refs.48,51). The mechanical influence of wall shear stress (WSS) has also been shown to modulate a rolling cell’s velocity,24 activate integrins,75,116 and promote chemokine secretion from ECs.65 Moreover, WSS values and flow velocities, if too large or small, may limit or prevent firm adhesion and/or rolling.24,30,54 We have chosen to focus on these key inputs and signals as a first step towards developing a simulation of leukocyte trafficking at the multi-cell tissue-level scale.
Our multi-cell agent-based computational model (ABM) is coupled with a network blood flow analysis to allow the simulation of circulating inflammatory cell trafficking through the microvasculature while considering the effects of fluid flow and WSS. Combining these two computational approaches allowed for complex numerical analysis while preserving spatial and temporal tissue-level properties in order to predict degrees of leukocyte infiltration under varying conditions.
We applied our modeling framework to the process of monocyte trafficking through a skeletal muscle capillary bed. Blood flow exerts WSS at varying magnitudes and spatial distributions throughout the microvascular network, which influences adhesion molecule expression, chemokine/cytokine secretion, and the probability of wall interactions and bond formation. All of these properties interact to determine the dynamics of monocyte adhesion and transmigration. Our model is ideally suited for investigation of this process. Consistent with literature, our simulations showed monocyte transmigration occurring primarily in the venules, even though no EC phenotypic differences in the vascular tree were explicitly programmed. Furthermore, simulated knockouts of L-selectin, both P- and E-selectins, and PSGL-1 preserved monocyte firm adhesion and transmigration levels, despite steep decreases in the instances of monocyte rolling. This is in agreement with in vivo experiments that indicate monocytes possess a decreased dependence on selectin-mediated rolling compared to neutrophils.26 Simulated knockouts of individual integrins predicted varying degrees of dependence of firm adhesion on them, while knocking out both VCAM-1 and ICAM-1 resulted in no firm adhesion.
Materials and Methods
Agent-based Modeling (ABM)
ABM is premised on the idea that local interactions between members of a population can lead to complex global outcomes. In ABM, a set of autonomous agents acting according to relatively simple rules give rise to, or predict, “emergent” phenomena that could not be discovered by probing the actions of one agent alone. Space and time are represented as discrete entities, and here simulations are conducted in a 2-dimensional space that is divided into a grid of stationary pixels in a Cartesian coordinate system. We use a “cells-as-agents” approach to ABM, wherein each individual agent represents one biological cell. Agents (cells) are motile within this coordinate grid and are able to survey and interact with their surrounding environment, including interactions with neighboring agents (cells) and the pixel space in which they move. Agents exhibit different behaviors (e.g., migration, division, death), and their attributes at any given time point can be described by an array of different state variables (e.g., expression levels of a particular protein, cell age).
As the simulation steps through time, individual agents make decisions about which behaviors to execute based on their states and those of their neighbors. Agents integrate these states using a literature-based rule set to determine what behaviors they should carry out. The state of each cell is followed over time, and cell actions, interactions, and cell fate/lineage are recorded for each agent. Interactions between agents and their environment give rise to altered tissue level properties over time, such as new structures and patterns that can be quantified using standard metrics (e.g., a newly remodeled microvascular network84). These properties of ABM make it ideally suited for investigation of biological systems where temporal and spatial outcomes at the tissue-level are important, as previously described in ABM models of inflammation,3 microvascular network patterning,84 and embryogenesis.68
Theoretical Modeling Framework
Adhesion molecule expression rules
Chemokine/cytokine activation rules
Integrin activation and bond formation rules
It is important to note that our framework allows for feedback between an individual cell’s response to a changing mechanical force and the behaviors of neighboring cells, as depicted by the feedback loops between cell types and chemokine concentration levels in Fig. 1. Furthermore, the combination of adhesion molecule expression and chemokine/cytokine levels dynamically impact the probability of monocyte–EC interactions, integrin activation, and ligand–receptor binding—hence the grey arrow indicating communication between the two compartments of NetLogo in Fig. 1. Lastly, this theoretical modeling framework allows for firm adhesion to occur through different and not necessarily sequential pathways. For example, initiating firm adhesion without any selectin activity is possible, as is selectin-mediated rolling leading to integrin-mediated firm adhesion without any changes in adhesion molecule expression or circulating chemokine levels. Thus, we are able to investigate the cascade of leukocyte adhesion without prescribing the sequence of events leading to arrest.
Microvascular Network Acquisition
In silico microvascular network parameters
Avg. diameter (μm)
Avg. length (μm)
Fluid flow (mL/min)
Capillary bed size
Average EC size
20 at I-1
15 at O-1
16 at O-2
Network Blood Flow Analysis
Blood flow through the microvasculature was simulated by implementing a model of network blood flow.91,92 This model consists of two parts: solving for pressure and flows in a network (termed linear analysis by Pries and Secomb91) and applying empirically derived relationships to the solution to recalculate boundary conditions (termed “rheological analysis”91). This process is then iterated until a suitably small change in viscosity occurs. By discretizing a vascular network into nodes and elements and assuming low Reynolds number flow through a rigid and cylindrical tube, we computed the flow (Q) and pressures (P) throughout the theoretical vascular network. These assumptions allowed us to apply the finite element method to the network using Poiseuille’s law (Eq. 1), a simplification of the Navier–Stokes equations. The rheological analysis takes into account microvascular phase separation effects,92 and so viscosity was not assumed to be constant. Boundary conditions for Poiseuille’s law included inlet and outlet pressures (Table 4), along with an initial estimate of viscosity.
Integration of ABM and Network Flow Models
To integrate the ABM and network flow models, we developed an extension to NetLogo that calls the network flow analysis, implemented in MATLAB®, pauses NetLogo execution, and resumes execution in NetLogo upon receipt of the results. The NetLogo model writes relevant information about each element (length, diameter, node connectivity), known nodal pressures, and estimated blood viscosity to a file. The NetLogo model then calls MATLAB® to execute a script that reads in the file, performs flow analysis at that time-point, and writes nodal pressures, elemental flows, and WSS to a second file. Execution returns to NetLogo, which reads the output from MATLAB®, assigns fluid flows and WSS to branches of the vascular network, and pressures at each bifurcation. The model assumes that WSS at the bifurcations of the vessels is the average of WSS in neighboring vessels. It further assumes the pressure drop along each segment is linear and assigns a point pressure to each endothelial cell agent. It is this pressure differential between neighboring ECs that is used to drive leukocyte movement through blood vessels. It is important to note that the flow of plasma and circulating cells was based entirely on the inputs of experienced mechanical forces derived from the network flow model and that circulating cells are not explicitly programmed to flow through the vascular tree from arteriole to venule. The capability exists to recalculate pressure, flow, and WSS from within a running model if a change in network connectivity is detected. This feature would be important for future models that incorporate angiogenesis and result in the generation of new vessels within the microvascular network.
Cell Types, Adhesion Molecules, and Cytokines
Within the ABM we allowed for complex interactions between ECs and monocytes. Smooth muscle cells (SMCs) are also present, although as yet they have no behavioral rules. Each cell (agent) carries binary information regarding its instantaneous adhesion molecule expression (P-, E-, L-selectins, VCAM-1, ICAM-1, PSGL-1, VLA-4, LFA-1, MAC-1), as well as scaled chemokine and cytokine exposure (TNF-α, IL-1β, IL-4, IL-8, NO). To accommodate circulating soluble chemokine/cytokine levels we created a separate plasma agent, which carries soluble molecule concentrations through the microvascular network.
Description of Model Execution
The flowchart in Fig. 2 visually represents the logic flow through the model and the decisions made by each cell type for a given step in the simulation. At each time step, ECs survey their environment and express adhesion molecules or secrete chemokines/cytokines according to a rule set (Tables 1–3). Monocytes enter the microvascular network at an inlet node and survey their local environment. Like the EC, the monocyte then determines its expression profile and surveys the endothelium for the ligands of its adhesion molecules. If WSS is within a specified range (Table 3) and the proper selectins are present (Table 1), the monocyte begins rolling. Rolling serves to decrease monocyte travel speed through the vessel and increase the rate at which it surveys the vessel wall for adhesion molecules. Monocytes also check for integrin expression and activation to determine whether or not to arrest (Table 3).
Adhesion Molecule Expression
Expression of adhesion molecules is determined by the rules shown in Table 1. Expression is calculated at each time step and is assumed to be instantaneous. When a cell detects a cytokine or WSS level that would change adhesion molecule expression levels, it changes the expression level at that time step, with no delay for internal signaling or protein synthesis. If more than one influence on the expression of a certain molecule is present, expression is determined in a non-additive manner: the value for the cytokine with the largest influence on expression is used. A WSS modifier is applied to this value, followed by the application of a nitric oxide (NO) modifier if any NO is present. Cell surface expression is handled in a binary manner; either a cell expresses a molecule or it does not. See Table 1 for the full list of rules and citations.
Within our rule-set (Table 1), E-selectin is expressed by 3.25% of ECs and is not expressed by monocytes. Contact with Il-1β induces E-selectin expression by ECs with a probability of 100%, Il-4 induces E-selectin expression with a probability of 4%, and TNF-α induces E-selectin expression with a probability of 50%. IL-8 and varying WSS have no effect on expression levels (Table 2).
VCAM-1 is also expressed on ECs at a baseline of 3.5% of cells, although it is not expressed on monocytes. Chemokine/cytokine influences on expression are similar to those for E-selectin (Table 1), and increasing WSS values decrease expression of VCAM-1. NO also decreases the expression of VCAM-1. If NO is encountered, the likelihood of positive VCAM-1 expression is reduced by 50%, even after chemokine/cytokine and WSS influences. Expression for other adhesion molecules is carried out in a similar manner (Tables 1 and 2).
As with any computer simulation based on rules obtained from independent experimental literature, careful attention must be paid to the consistency and correctness of reported parameter values that will be incorporated into the simulation. For this reason, when possible, multiple publications were referenced for each individual rule. We then evaluated important aspects of the reported data and experimental design from each publication in order to arrive at a rule or value that accurately reflects the field’s understanding as a whole, to the best of our knowledge. For example, when determining the percent of ECs in our simulation that should express a certain adhesion molecule at baseline levels, there were often discrepancies present in the literature. If in vivo immunofluorescence data of mouse microvascular ECs showing quantifiable expression of an adhesion molecule was unavailable, we would next consider microvascular ECs from a similar species, such as rat or human. In the cases where this type of data was unavailable, we would look at in vitro data in another experimental system such as flow cytometry. Similarly, we would consider the expression data on ECs isolated from large vessels or lung microvessels only when data from microvascular skeletal muscle ECs was unavailable. Values were often averaged, and a similar approach was applied to determine all the rules incorporated into this simulation.
Secretion of Soluble Factors
Simulated soluble molecules include IL-1β, Il-8, IL-4, TNF-α, and NO. We selected these key molecules from among the many cytokines that are known to play important roles in regulation of adhesion molecules. Factors affecting secretion of these molecules and their relative values are shown in Table 2. Values were taken from the literature and adjusted to an arbitrary 1000-point scale as a percent chance for a cell at that time point to sense a cytokine, based on relative potency and amounts secreted. For example, if a survey of the literature indicated that IL-4-induced secretion of IL-1β by EC was 3–5 times less effective than IL-1β-induced secretion of IL-8 by EC, it would be given an appropriate relative number on the scale (see Table 2). When assigning an effectiveness to a chemokine, the potency, time to onset, acting time, and experimental conditions were factored into the judgment to resolve any discrepancies and determine relative behaviors. These rules in particular, therefore, need to be refined as additional experimental data becomes available and further parameterization is conducted. Note that while the capability for cells to respond to IL-4 and TNF-α exists in the model, these molecules are not included in the simulations described here. The effect of IL-4 and TNF-α could be turned on by setting a baseline plasma value in the model code, or by adding a cell type that would express them along with rules for their expression.
Secretion is programmed in the same general manner for each molecule. Briefly, ECs and monocytes survey their environment, checking WSS and plasma levels of cytokines. They then calculate secretion levels in a non-additive manner, taking the maximum secretion amount from all the currently active factors influencing production (Table 2, Fig. 2). Cells secrete soluble molecules by transferring a fixed amount to the plasma agent adjacent to the cell. Plasma agents degrade all soluble factors by a fixed percentage at each time step. Rules shown in gray are less certain, and are potential targets for parameterization or further experimentation.
Secretion of NO by ECs in our model is based solely on WSS (Table 2). As WSS increases, more NO is secreted. The numeric values of WSS are divided up into four levels, and rules for each level are shown in Table 3. IL-8 secretion is induced by both high WSS and IL-1β levels. After taking the maximum of these stimuli, if the EC has encountered NO at the current time step, it reduces its secretion of IL-8 by 50%. Secretion of other soluble factors is handled in a similar manner (Table 2).
The likelihood of a cell rolling on the endothelium is determined by a combination of WSS and selectin expression at discrete locations within the network. A circulating cell first checks the magnitude of WSS it is experiencing to determine how likely it is to roll if the proper adhesion molecules are in place (Table 3). It then checks to see whether it is expressing PSGL-1 and has been in the proximity of an endothelial cell expressing either E-selectin or P-selectin. It also checks to see whether it is expressing L-selectin and has been in contact with another rolling monocyte expressing PSGL-1. If any of these conditions are met, the probability rule described above is applied, and this determines whether or not the monocyte initiates rolling on the endothelium. Rolling cells survey the endothelium at every time-step, and move to the next EC at every other time-step. Non-rolling cells move at every time-step and survey the endothelium at a rate determined by the ratio between the calculated flow velocity at their location and the literature-defined velocity of a rolling cell.41,54,93
Cell Firm Adhesion
There are three possible ligand/receptor pairs that once bound can lead to cell arrest in this model: LFA-1/ICAM-1, MAC-1/ICAM-1, and VLA-4/VCAM-1. The affinity and binding rules for these integrins are shown in Table 3. Most of the published data reports the percentage of integrins on a single cell in a high affinity state in response to different treatments. We assume that percentage of high-affinity integrins on a single cell roughly translates to percent of total cells that will adhere given a certain treatment. The probability of a monocyte firm adhering is calculated separately for each integrin (LFA-1, MAC-1, VLA-4). In this model, VLA-4 binding probability depends mainly on WSS, while LFA-1 and MAC-1, having the same ligand, can cross-activate each other, and are activated by IL-8 and/or L-selectin ligation. The probabilities of integrin activation are compared, and the maximum value is used as the likelihood that a cell will firm adhere. At WSS greater than 7 dynes/cm2, no arrest can occur in our model (Table 3). Because not all firmly adhered cells eventually complete extravasation, we assign firm adhered cells a 75% probability of re-entering the bloodstream.33 This chance is applied during the cell’s decision of whether to arrest.
Cells are assumed to extravasate from the microcirculation into the tissue after they have arrested for three time steps. This time was chosen because it has been shown33 that arrested cells can extravasate on a timescale of seconds to minutes. It has also been shown that the majority of monocytes that migrate into the tissue (approximately 75%)27,76 do not become tissue macrophages, but differentiate into another, more mobile cell type (possibly dendritic cells) and migrate out of the tissue either via the lymphatic channels or the bloodstream. This is accommodated by removing these cells from the blood (they extravasate), but excluding them from the final analysis of total tissue macrophages. Cells that survive to become tissue macrophages migrate through the interstitial space in a random walk pattern at each timestep. In this version of the model, the number of tissue macrophages is used as an output metric only.
Time steps in the model are relative to one another, but arbitrary with respect to the actual amount of time required for cell transit through the circulation, ligand binding, etc. Because keeping track of prior activating influences on a cell and integrating them over time is computationally intensive, we have assumed instantaneous expression based on a cell’s current environment and state. The output of the model can be viewed as a non-dimensionalized version of extravasation in which the behaviors of the individual cells represent a response to their time-averaged expression levels. Each model was run for 1500 time steps.
Simulations of Trafficking/Model Validation
We developed the rules for this model by considering data derived from in vitro and in vivo experiments. These data combine to constitute our rule-set, which governs individual cells’ behavioral responses when confronted with environmental/neighbor–neighbor changes. For validation, we performed in silico knockout experiments and compared the tissue-level outcomes (specifically, the number of tissue macrophages) and degree of rolling predicted to those seen in in vivo knockout mice studies that are published in independent literature. In our model, we systematically and sequentially knocked out the following molecules and combinations of molecules: (1) E- and P-selectin, (2) L-selectin, (3) PSGL-1, (4) VCAM-1, and (5) ICAM-1. We also assessed the sensitivity of our model to changes in plasma protein degradation rates, frequency of surveying the endothelium when monocytes were located in the free stream and not rolling, and varying WSS levels. Each simulation was repeated five times.
The NetLogo model file, the NetLogo extension, and the Matlab script have been placed online at http://www.bme.virginia.edu/peirce. Also at this location are expanded versions of Tables 1–3, including explanations for the derivation of rules, citation summaries, and justifications for the resolution of discrepancies between sources.
All results are presented in the form of mean ± standard deviation. All comparisons were made using the statistical analysis tools provided by SigmaPlot 5.0 (Systat, Inc., Point Richmond, CA). Data were tested for normality and analyzed by one-way ANOVA followed by non-paired Tukey’s T-test. Where unequal variances prevented analysis of a set of experiments as a whole, Student’s T-test was used to compare individual experiments to control. Statistical significance was asserted at p ≤ 0.05.
Communication between Network Flow and ABM Simulations
The network blood flow model calculated fluid flow velocities, pressure distributions, and WSS values in a simulated microvascular network (Table 4). Phase separation effects were not ignored as they play a critical role in determining blood viscosity throughout small diameter vessels. By accounting for changes in viscosity and assuming it to be variable with vessel length, diameter, and connectivity, the simulation was able to more accurately determine the mechanical parameters. The inputs for the network flow model were taken directly from the ABM drawing program in NetLogo, and the accurate segment length and nodal connectivity indicate successful communication between the two models.
Computational Model Allows Input of In Vivo Microvascular Architecture
Monocytes Extravasate Predominantly at Venules
Our simulations predicted leukocyte firm adhesion and transmigration occurring predominantly in the venule bed of the microvascular network, although these behaviors were also exhibited in both the capillary and arteriole beds (Fig. 4c). Figure 4c is a plot of the locations of monocyte extravasation divided into three areas: arteriole bed, capillary bed, and venule bed. Cells that firmly adhered without rolling are depicted as blue diamonds, while cells that progressed from rolling to firm adhesion are shown as pink squares. All simulations, including the selectin knockout trials, showed higher numbers of extravasated monocytes in the venule compartments, even after the elimination of selectin-mediated rolling (in the PSGL-1 and double E- and P-selectins knockouts). This is consistent with the current understanding that the majority of leukocyte adhesion occurs in activated venules where WSS values are lower and the proper adhesion molecules are presented to circulating cells. It is important to note that this prediction was not pre-programmed in the rule-set (e.g., a forgone conclusion), but emerged independently as a result of the actions and interactions of the agents responding to their dynamic simulated mechanical and biochemical environments.
Simulation Predicts Low Dependence of Monocytes on Selectins for Firm Adhesion
The in silico knockouts of both ICAM-1 and VCAM-1 showed a significant reduction in the number of extravasated monocytes compared to control, (Fig. 5). Similarly, in silico ICAM-1 knockouts showed a 42% increase in rolling, while VCAM-1 knockouts showed no significant difference (Fig. 6). The in silico knockout of ICAM-1 and VCAM-1 showed no firm adhesion or transmigration, while selectin-mediated rolling was greatly increased (data not shown). This is likely due to the fact that because the integrins are required for firm adhesion, simulated cells are continuing to roll for longer time periods. These data suggest that integrins have a dominant role over selectins in the monocyte adhesion cascade.
Parameter Sensitivity Analysis
We also examined the sensitivity to knockout of the chemokine IL-8 and NO. As expected, IL-8 knockout produces a significant decrease (p = 0.008, data not shown) in the number of extravasated monocytes, while producing no change in the rolling behavior. At the current implementation state of NO, removal produces no significant change in either extravasation or rolling (data not shown).
We have developed an agent-based simulation of leukocyte trafficking through the microcirculation that spans multi-cell to tissue levels of biological scale in order to study the molecular mediators of the circulating cell adhesion cascade. Circulating monocytes and microvascular ECs are simulated on an individual-cell basis, and cells are programmed to respond to local mechanical and biochemical cues that drive monocyte rolling, adhesion, and transmigration into the tissue. The initial geometry and anatomy of the simulated microvascular network were obtained from a real microvascular network in a mouse spinotrapezius muscle. Individual cell behaviors are a dynamic response to a rule-set that was derived from independent literature, and the simulation output is the emergent accumulation of circulating monocyte-derived macrophages in the tissue. This process is relevant to many different disease states where inflammation is a key factor in the injury and recovery responses of the tissue.
The agent-based computational model is underpinned by a network flow analysis that calculates theoretical flow rates and pressures throughout the microvascular tree, while considering a variable blood viscosity. These predicted values, in turn, dictate how monocytes flow through the network and impact adhesion molecule expression and chemokine secretion. Our network blood flow model is based on Pries and Secomb’s early work, although an important next step in the evolution of our computational framework is to incorporate aspects of an improved version of this model published in 2005.90 Here, the authors modified their equations slightly to take into effect an endothelial cell surface layer (ESL) that served to reduce observed in vivo vessel diameters by a variable ESL thickness. Additionally, the incorporation of flow disturbances and capillary plugging caused by individual or small populations of leukocytes flowing through small vessels will likely be added to future models that consider ischemic interventions, mechanical wounding, and/or systemic or local inflammatory responses.
It should be re-emphasized here that SMCs are included for visual effect only, and have no behavioral rules. Because of this limitation, our implementation of the effects and production of NO is demonstrably incomplete. Incorporation of the behaviors of SMCs and additional sources and effects of NO are an important future target in our modeling process.
Another point that will be addressed as the model evolves is the assumption that cell surface expression of adhesion molecules is binary: either on or off. We acknowledge that this is not the case in vivo, and that varying levels of protein expression are important. However, it is technically challenging to accurately measure the levels of a receptor in vivo, and elucidating the response of a single cell to both varying levels of receptor expression and varying ligand concentrations in vivo is currently impossible with the available assays. MacGabhann and Popel have pioneered a computational approach to this problem70,71 which may be examined in future models. For the present work, considering cell surface protein expression as binary preserves the connections between molecules and provides high enough resolution to predict outcomes of selectin and integrin knockouts that are in agreement with the literature.
As a first step toward validating this integrated model, we performed a series of in silico knockout experiments, wherein individual and combinations of molecules were removed from the simulation by systematically altering the rule-set. The impacts these perturbations had on the number of extravasated macrophages in the tissue, the number of rolling cells, and the number of adherent cells were quantified. The data indicated a prominent role for ICAM-1 and VCAM-1 in monocyte rolling and adhesion, and a less important role for the selectins in these processes. These results are consistent with independent experimental studies performed in the corresponding set of knockout mice,26,42 suggesting that our simulation is capable of independently predicting key events during monocyte trafficking.
A common pitfall in the design of ABMs is the fallacy of “programming the proof,” or claiming that an outcome that was hardwired into the model from the start represents a validation of the model. In that case, the outcome is not a validation; the model simply outputs exactly what it was programmed to output. With this in mind, we developed a model of monocyte trafficking in skeletal muscle that preserves multiple levels of complexity with direct and indirect effects. For example, our rule-set states that E-selectin ligation has no direct effect on the activation of the β2 integrins (MAC-1 and LFA-1). Simply put, there is no intracellular cross talk between the binding partner of E-selectin (PSGL-1) and the β2 integrins that would lead to affinity changes. This does not exclude other indirect and potentially powerful effects of E-selectin on integrin activation through other pathways. Through studying the biology and the theoretical framework of our model, the existence of at least one alternate pathway is readily apparent: (1) selectin knockout leads to decreased rolling of monocytes along the endothelium; (2) a lack of cell rolling impacts velocity and leads to decreased wall surveying; (3) decreased wall surveying translates to fewer opportunities for integrin activation to occur (e.g., affinity changes induced by IL-8 exposure are less frequent); and (4) lower average integrin affinity decreases firm adhesion. Therefore, because of this and other pathways, the decreased dependence on selectins for monocyte capture, arrest, and extravasation is a non-intuitive result that was not programmed into the model, and a qualitative validation against in vivo data is possible.
Several other groups have modeled varying aspects of leukocyte–endothelium interactions, although none have integrated adhesion molecule expression with mechanical and biochemical signaling throughout the entire adhesion cascade. Krasik et al. elegantly integrated two types of modeling, mechanics-based and signaling-based, to elucidate and predict how integrin activating stimuli (e.g., E-selectin ligation) translated into neutrophil adhesion dynamics such as rolling time and distance traveled.50 Other computational models have demonstrated that there are numerous determinants of cell rolling velocities, in addition to a receptor’s affinity for its ligand.49 Previous work has predicted the effects of leukocyte deformability on adhesion kinetics,18,39 as well as the kinetics of integrin and L-selectin mediated neutrophil aggregation under flow.107 All of these computational models are highly detailed and mechanistically informative, but they neglect the overall spatial and temporal dynamics within entire tissues. Thus, our model fills a critical gap and provides a tool to interrogate the individual and combined effects of molecules, cell behaviors, and mechanical forces. Useful extensions of this approach include combining it with intracellular signaling network models82 such that each cell is underpinned by its own signaling network,83 in order to expand the range of biological scales accounted for and to provide more fine-grained resolution of molecular signaling details within each cell. Furthermore, building onto the current framework through modular additions of other computational analysis techniques, including probabilistic models, neural networks, or more rigorous differential equations would allow for more powerful analysis.
Even though intracellular levels of detail are sacrificed in this first-attempt, we have shown that this computational approach can interrogate inflammatory cell trafficking mechanisms (and combinations of mechanisms) on a tissue-level scale. Although we only consider monocyte trafficking in a simulation that does not include an exhaustive list of adhesion molecules and chemokines/cytokines, the potential to expand the simulation is great. With this computational framework in place, the ability to extend the list of biochemical activators is immediately feasible, as new molecules and interactions are identified and new questions arise. Moreover, the ability to modify the simulation so as to incorporate additional cell types, including neutrophils, lymphocytes, and even circulating stem/progenitor cells, is promising. A new population of cells would likely respond to a similar set of rules, but differ in their population density, expression levels, and sensitivity to biochemical stimuli. With this incorporation, it would be possible to compare the dependence of monocytes on the selectins to the dependence of neutrophils on the selectins.
By adding a simulated population of circulating stem/progenitor cells, either therapeutically delivered intravenously or mobilized from the bone marrow, it would be possible to test hypotheses regarding stem cell trafficking and incorporation into injured tissues. In this way, our simulation could be adapted to address a major question in regenerative medicine which centers on the role of circulating progenitor cells in angiogenesis: what signals and combinations thereof orchestrate their dynamic trafficking to injured tissues? By providing rules for EC proliferation (capillary sprouting) and by allowing intermittent hemodynamic flow/WSS updates from the network flow simulation during the execution of the agent-based simulation, an angiogenic microvascular network could be simulated. Then, the dynamic trafficking of circulating stem/progenitor cells during angiogenesis could be assessed and systematically manipulated within the setting of a simulated angiogenic microvascular network.
In summary, we have developed a computational model that captures the multi-cell tissue-level dynamics of monocyte trafficking within a microvascular network bed. Our model enables individual simulated cell tracking in space and time, which is currently not possible in experimental models. With the added ability to target specific molecules individually (e.g., by augmenting or decreasing their expression/functionality) we anticipate that this tool will serve as a platform not only for hypothesis testing, but also for hypothesis generation in a field that is of central importance to human disease and regenerative medicine.
We are very grateful for the contributions of Kelly Benedict (University of Virginia, Department of Biomedical Engineering) for her help in the development of the network blood flow model. We are also grateful to Melissa Yingling for her contributions in the early developmental stages of this approach.
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