In this paper, we modeled the role of ligand-induced homologous receptor desensitization in cell gradient sensing in conflicting gradients. The modeling results suggest that ligand-induced homologous receptor desensitization is important for cells to integrate signals from different chemoattractants: desensitization allows cells to preferentially respond to distant or newly emerging agonist sources in the presence of competing ligand gradients, and to undergo repositioning in complex attractant fields in response to modest changes in receptor numbers. The results derived from these studies provide a molecular explanation for previous studies of the experimental behaviors of neutrophils in competing chemoattractant gradients, and support the multi-step model of chemotactic navigation (11
). Moreover, they provide a potential explanation for the evolutionary conservation and universal expression of mechanisms of homologous receptor desensitization by G-protein coupled chemoattractant receptors.
In our model, nondesensitizable receptors mediate effective cell chemotaxis to single ligand gradients, a prediction that is consistent with experimental chemotaxis studies that have examined the effect of several nondesensitizable chemokine receptor mutants (18
). In addition, not unexpectedly, our modeling predicts that nondesensitizing ligands dominate cell orientation when in direct competition with a desensitizing attractant. However, the results emphasize further that cells expressing nondesensitizable receptors are unable to integrate attractant signals, fail to navigate effectively in complex gradient environments, and will become ‘trapped’ by local agonist sources.
Numerous settings in which multiple chemoattractants contribute in a complex manner to cell migration have been reported. For example, the neutrophil chemoattractants IL-8 and LTB4
both contribute to neutrophil recruitment to the airways in chronic obstructive pulmonary disease (COPD) (30
); chemokines CXCL12, CXCL13, CCL19 and CCL21 all contribute to regulate B cell homing to lymph nodes and Peyer’s patches, including recruitment from the blood following by chemotaxis into the follicular zones (31
); CCL17 and CCL27 participate in memory T cell homing to the skin, and CCL27 is then thought to recruit subsets of T cells to the epidermis (33
). The chemokine receptors involved in these events are universally sensitive to homologous ligand desensitization, a fact that our study suggests may be essential to the successful step-by-step migration of cells in these complex situations.
A particularly well characterized example is the finding that the balance of receptor expression for B cell zone chemokines (CXCR5 for the follicular chemokine CXCL13) and T cell zone chemokines (CCR7 for T zone chemokines CCL19 and CCL21) controls the positioning of antigen-engaged B cells at the T cell zone border (12
). As shown in our model, such balanced integration of conflicting signals requires mechanisms of homologous desensitization: desensitization allows cells to migrate down a local attractant gradient in response to a distant one. This in turn allows cells ultimately to seek an intermediate position between two chemokine sources, rather than becoming ‘trapped’ by a local high chemokine concentration. The levels of receptors expressed then will determine whether the cell moves more towards one environment or the other; and, as we have shown, modest changes in relative receptor levels can target cells to one or another adjacent chemoattractant-defined microenvironment domain. In the context of B cell positioning, resting B cells normally express both CXCR5 and CCR7, yet they selectively occupy “B cell follicles”, sites of stromal cell based CXCL13 production. Antigen activation induces a 2–3 fold increase in CCR7 expression, associated with a shift of the equilibrium position of B cells from a dispersed distribution within the follicle to the junctional region between the B cell zone and T cell zone (B/T junction); this is presumed to enhance interactions between B cells and T cells required for the immune response (12
). In a parallel but opposing manner, although many memory T cells (e.g. most ‘central’ memory cells in human tonsils) like naïve B cells co-express CXCR5 and CCR7 (37
), most resting CXCR5+ T cells are found in the T cell zone; in this case, activation causes down-regulation of CCR7 on a subset of T cells, which then home to the B cell follicles where they support the B cell germinal center response (36
). Our model raises the additional possibility that CXCR5+CCR7+ resting memory T cells can in fact access both T and B zones, migrating randomly between them until receiving a specific signal to alter expression levels of one or the other receptor. We imagine that in the physiologic setting of lymphoid tissue microenvironments, the follicular chemokine CXCL13 and the T cell zone chemokine CCL19, which are expressed by dispersed stromal cells in these microenvironments, are likely to be present as qualitatively uniform fields in the follicles and T cell zone respectively; and that a steep competing gradient of the two ligands is present at the B/T junction. Our modeling of cells expressing normal receptors in competing gradients separating uniform attractant fields show that modest changes in receptor expression levels have the potential to determine whether a cell occupies one or another domain, or instead is targeted to the junctional region, just as in the examples of lymphocyte targeting in vivo
. Key features of the model of cellular orientation required for this behavior include not only homologous receptor desensitization, but also the existence of a threshold level of differential receptor occupancy (between the front and back of the cell) below which the cell migrates randomly.
Last, we discuss the basis and limitations of our model. In our model, parameter values such as the total receptor number (50,000 in most of our analyses), the dissociation constant (4.4nM) and other kinetic rates are adapted from experimental studies of formyl peptide receptors on neutrophils (25
). The values of some key parameters are similar in other chemoattractant receptor systems as well (e.g. 75,000 total receptors and kd
=4nM for chemokine IL-8 on human neutrophils). In our model, changing the total receptor number or kd
alone by up to 10-fold does not alter the fundamental importance of homologous receptor desensitization for cell positioning in competing gradients as shown in our examples. Recycling of desensitized receptors, however, is required to maintain sufficient signaling receptor-ligand complexes at equilibrium for orientation in our model, and the relative rate of receptor internalization and recycling compared with receptor desensitization will affect cell orientation as shown in : if insufficient unoccupied receptors are recycled to the surface, the cells lose the ability to orient at equilibrium. Similarly, the rate of receptor desensitization relative to receptor internalization and recycling is also important for robust orientation to the distant gradient in competing gradients. The threshold of signaling receptor occupancy difference required for chemotactic orientation is set to 10 in our model based on 1) the minimal receptor occupancy difference (~10) calculated to be required for orientation by neutrophils, which can chemotax directionally in response to a ~1% ligand concentration difference across the cell length (26
); and on 2) considerations mentioned above regarding predicted stochastic fluctuations in receptor-ligand binding near the kd
). The physiologic threshold for effective orientation is likely to be influenced by a number of factors, including the kd
of the receptor, the local ligand concentration (determining the number of receptors remaining on the cell surface, as well as the level of stochastic variation in receptor-ligand complexes), and the dimensions of the cell. Moreover, a physiologic “threshold” is not expected to be absolute as modeled here; the efficiency of orientation is not a step function, but rather would improve as ΔLR* increases until an optimum is achieved.
The ligand gradient in our model is generated by a power function and a nonlinear profile is chosen with n=3, so that agonist concentration changes with the cube of the distance. This profile is an approximation of the nonlinear gradients generated in some in-vitro
migration assays (e.g. the under agarose assay (11
), or the micropipette-based assay (39
for simple gradient modeling is set arbitrarily at 17.6 nM so that the mean concentration in the gradient region modeled equals the kd
(4.4 nM). Additionally, we consider that nonlinear gradients are likely to be the rule in vivo
. In the simplest in-vivo
scenario, a single cell produces a finite amount of freely diffusing ligand at a constant rate into an environment, resulting in concentration decreasing nonlinearly as a function of the distance from the cell. If as is likely the ligand is degraded everywhere with first order kinetics, nonlinear gradients with n>2 will be expected. In addition, most chemokines bind with low affinity to glycosaminoglycan (GAG) on cells and in tissue stroma. Reversible interactions with stromal elements are expected to have the effect of steepening gradients even further. For these reasons, we chose to focus on a gradient with a nonlinear profile as presented rather than modeling the gradient based on free diffusion as such a gradient will become uniform or linear at equilibrium. Quantitative aspects of cell orientation in competing gradients may also be sensitive to gradient profiles, but this issue is not addressed here.
Previous studies have shown that there is an intracellular signaling hierarchy in which end-target chemoattractants such as C5a and f
MLP dominate host-derived chemoattractants such as IL-8 and LTB4
in attracting neutrophils in competing gradients, an effect mediated by heterologous receptor desensitization and/or, as shown in recent studies, by alterations in intracellular orientation signals used by host chemokines (11
). Since heterologous receptor desensitization in essence eliminates the contribution of the competing distant host ligand, orientation in this context is equivalent to orientation to a single local ligand gradient. Thus we have limited our modeling here to host-derived non-cross-desensitizing chemoattractants, which trigger common downstream signaling pathways in cells through their binding receptors.
In addition, our model is limited to chemotactic orientation and does not describe cell migration. Numerous studies indicate that, regardless of gradient configuration, and even in uniform ligand fields, cells are motile when in the presence of ligand. Thus, orientation as modeled here would determine the direction of this continuous migration, and regions in which there is insufficient ΔLR* to support orientation are considered zones of random migration. Furthermore, we consider only fixed 1-D ligand gradients and point cellular units, avoiding complications such as time-dependent gradient shape and ligand concentration, and diffusion of receptors on the cell surface. Ligand-induced receptor modifications at the front and the back unit are considered local events, as well. While this is likely a simplification of the reality of receptor cycling, during which signaling events may influence preferential receptor cycling to the front of the cell (40
), we consider that there is not adequate data available on this point for modeling. Moreover, the effects of preferential recycling to the front would be to enhance orientation at equilibrium and thus would not alter our conclusions qualitatively.
In summary, the current model provides a theoretical framework that has allowed us to consider the role of ligand-induced homologous receptor desensitization in cell gradient sensing in competing ligand gradients. Our results suggest a critical role for ligand-dependent receptor desensitization in the orientation and positioning of cells in complex physiologic settings.