Fig 1.
Schematic representation of ligand-receptor interactions.
Representations of monovalent and multivalent ligand-receptor interactions: the receptor is shown as a monomer: (A) soluble monovalent ligand (B) soluble divalent and tetravalent ligands (C) soluble monovalent or divalent ligand and a cytosolic crosslinker (D) monovalent membrane ligand (E) multivalent immobilised ligand.
Fig 2.
Interaction of monovalent, divalent and tetravalent ligands with a monomeric receptor.
(A) The concentration-occupancy relationship at equilibrium of a monovalent ligand (L) and a monomeric receptor (R). The ligand is maintained at a constant concentration (red). The following parameters have been used: KD = 1 μM, k1 = 1 μM-1s-1, k-1 = 1 s-1. (B) The concentration-occupancy relationship at equilibrium for a soluble divalent ligand [L2] and monomeric receptor, varying the second association rate constant (k2): the following values have been used: k1 = 1 μM-1s-1, k-1 and k-2 = 1 s-1 (i) k2 = 0.1 μM-1s-1 (ii) k2 = 1 μM-1s-1 (iii) k2 = 10 μM-1s-1. L2R and L2RR reflects a divalent ligand bound to 1 and 2 receptors, respectively. (C) The concentration-occupancy relationship at equilibrium for a soluble tetravalent ligand (L4) and monomeric receptor varying the concentration of (i) ligand and (ii) receptor; the concentration of L4 in (ii) was 1 μM. The other parameters are: kn = 1 μM-1s-1 and k-n = 1 s-1. The receptor concentration in (A, B and C) is 1 μM. The graphs were generated with the MATLAB code: https://github.com/zeemaqsood/TAPAS_ESR9_Modelling_Project. The selected parameters are for illustrative purposes.
Fig 3.
The effect of monovalent, divalent and tetravalent Nb2 on platelet aggregation.
(A) Representative traces of platelets incubated with (i) Nb2-2 (ii) Nb2, 5 min before collagen (3 μg/mL) (iii) Nb2-2, 5 min before collagen (3 μg/mL); (iv) concentration-response relationship of inhibition of aggregation (Agg) to collagen by Nb2 and Nb2-2, results shown as mean + s.d. (B) (i) Representative traces of platelets stimulated by Nb2-4 (ii) concentration response curves with results shown as mean ± s.d. aggregation (%) after 5 min. (iii) Representative traces of platelets incubated with vehicle (0.1% DMSO), PP2 (20 μM), PRT-060318 (10 μM) or Nb2 (100 nM) for 5 min before stimulation with Nb2-4 (16 nM) (iv) histogram showing mean ± s.d. aggregation (%) after 5 min; all five treatment groups were compared using one way ANOVA analysis, followed by Tukey test: **(P < 0.01); n = 3.
Fig 4.
Parameter values and symbols used for agent-based modelling.
(A) The symbols used to represent species in the agent-based model Figures are shown. The number of receptors (R), crosslinkers (S) and divalent ligands (LL) per box is 100 unless stated. (B) The default values for on-rates and off-rates are shown in ticks (arbitrary unit of time), with one tick corresponding to the ‘go’ function within each run. These represent the probability of a reaction to occur out of 100 runs. These are arbitrary values selected for illustrative purposes. They have been chosen to give a low basal level of dimerisation and phosphorylation to correspond to a resting platelet. Two sets of values have been chosen to reflect a moderate and high affinity crosslinker in regulating cluster formation; the latter takes into account that the affinity of a ‘moderate’ affinity crosslinker can be increased by its co-localisation in the membrane as is the case for the majority of SH2-domain containing proteins. A ‘low’ value was selected for the affinity of the ligand to reflect the affinity of individual epitopes in endogenous ligands for platelet glycoprotein receptors, noting that this can be increased by avidity. The selection of a relatively low value enables illustration of how variables can combine to drive clustering. The rate of movement of receptors is constant at 1 patch per tick patch is an arbitrary unit of area (there are 441 patches per box). The default values give rise to to a basal value of 10% receptor dimerisation and 10% receptor phosphorylation in the absence of crosslinker. The crosslinker can only bind to a phosphorylated receptor: the probability of each epitope of the crosslinker to bind to a phosphorylated receptor is shown as an average frequency per 100 ticks. Assuming that both epitopes are occupied, the ‘moderate’ affinity crosslinker will remain bound to two receptors for 16 out of 100 ticks on average. The ‘high’ affinity crosslinker will remain bound to the receptor for 81 out of 100 ticks, on average. The probability of each epitope of the divalent ligand to attach to a receptor upon collision was set to 20 out of 100 ticks and to dissociate to 20 out of 100 ticks. Assuming that both epitopes of the divalent ligand are bound at the same time, a fully occupied divalent ligand will remain bound to both receptors for an average 4 out of 100 ticks.
Fig 5.
An agent-based model showing that the degree of receptor dimerisation increases with receptor number and rate of association.
The effect of receptor number and rates of association and dissociation on receptor dimerisation (Eq 4.1) was modelled using an agent-based model. Unless stated, the parameter values and key are as described in Fig 4. (A) The effect of receptor number on formation of receptor dimers (i) representative runs at steady-state with the number of receptors shown in the upper right-hand corner (ii) the level of receptor dimerisation at steady-state (iii) the time course of receptor dimerisation. Results are shown as mean + s.d. of 30 simulations at 3,000 ticks. (B) The effect of varying the rate of receptor dimerisation (i) the rate of association is shown in the upper right-hand corner, for further details see part (A). (C) The effect of varying the off-rate of receptor dimerisation (i) the off-rate of association is shown in the upper right-hand corner, for further details see part (A).
Fig 6.
An agent-based model showing the clustering of receptors in the presence of a high affinity crosslinker.
Agent-based modelling of the effect of changing the basal level of receptor phosphorylation and dimerisation, and the number of a high affinity crosslinker on receptor clustering. Unless stated, the parameter values and key are as described in Fig 4. (A) The effect of the number of high affinity crosslinkers on the proportion of receptor dimers for a receptor that is unable to dimerise (monomeric receptor) (i) representative runs at steady-state, the number of high affinity crosslinkers is shown in the upper right-hand corner (ii) number of receptors that are phosphorylated at steady-state (iii) number of receptor dimers (R = 2), trimers (R = 3), tetramers (R = 4) and higher order structures (R>4) at steady-state. Results are shown as mean + s.d. of 30 simulations at 3,000 ticks. (B) The effect of the number of high affinity crosslinker on clustering of a receptor with a basal level of dimerisation (10%) (i) the number of crosslinkers is shown in the upper right-hand corner, for further details see (A). (C) The effect of the basal level of receptor phosphorylation on clustering of receptors in the presence of a high affinity crosslinker (100 per box) (i) the rate of receptor phosphorylation per box is shown in ticks in the upper right-hand corner, for further details see (A). (D) The effect of the basal level of receptor dimerisation on clustering of receptors in the presence of a high affinity crosslinker (100 per box) (i) the rate of receptor dimerisation is shown in ticks in the upper right-hand corner, for further details see (A). (E) The effect of the number of high affinity crosslinkers on clustering of receptors in the presence of a high basal level of receptor dimerisation and phosphorylation. The rate of phosphorylation and degree of dimerisation are set to the highest values in (C) and (D) achieving ~80% and ~75% phosphorylation and dimerisation, respectively (i) The number of high affinity crosslinkers is shown in the upper right-hand corner, for further details see (A).
Fig 7.
An agent-based model showing that the effect of a divalent ligand on receptor dimerisation and higher order clustering.
Agent-based modelling was used to study the combination of a divalent ligand, receptor dimerisation and a cytosolic crosslinker on receptor clustering. Unless stated, the parameter values and key are as described in Fig 4. (A) The effect of a divalent ligand on clustering of a receptor that is unable to dimerise in the presence of a moderate affinity crosslinker (i) representative runs at steady-state, the number of divalent ligands is varied from 25–200 as shown in the upper right-hand corner (ii) number of receptors that are phosphorylated at steady-state (iii) number of receptor dimers (R = 2), trimers (R = 3), tetramers (R = 4) and higher order (R>4) structures at steady-state. Results are shown as mean + s.d. of 30 simulations at 3,000 ticks. (B) The effect of a divalent ligand on clustering of receptors with a low basal level of dimerisation (10%) (i) the number of divalent ligands is in the upper right-hand corner, for further details see (A). (C) (i-iii) The effect of a divalent ligand and moderate affinity crosslinking on clustering of receptors with a low basal level of dimerisation (10%) (i) the number of divalent ligands in the upper right-hand corner (iv) representative runs showing the time course of receptor clustering with the tick intervals are shown in the upper right-hand corner; the number of divalent ligands is 200, for further details see (A).
Fig 8.
The Syk inhibitor PRT-060318 inhibits rhodocytin-and AYP1-induced CLEC-2 clustering.
(A) Confocal microscope calibration using Atto-488 dye (10 nM) in water at 25°C. The axial (Zo) and lateral (Wo) radii were determined to be ~1.72+0.72 μm and ~0.23+0.03 μm respectively and the confocal volume was ~0.17+0.05 μm3. > 110 FCS calibration measurements were taken in five experiments. Data are presented as mean ± s.d. (n = 5). (B) (i) Representative confocal microscopy images showing membrane localisation of CLEC-2-eGFP in resting and stimulated cells (field of view = 52 x 52 μm) (scale bar = 5 μm). (Bii) Box plots showing the molecular brightness (cpm s-1) of CLEC-2-eGFP, centre lines represent median, box limits indicate the 25th and 75th percentiles, and whiskers extend to minimum and maximum points. Concentration of rhodocytin (30 nM), mAb AYP1 (6.6 nM), PRT (10 μM) were used. Significance was measured with Kruskal-Wallis with Dunn’s post-hoc where P ≤ 0.05. In (ii) # = significance compared to CLEC-2 alone. FCS measurements were taken in 35–48 cells; n = 3–5.
Fig 9.
Synergistic inhibition of platelet aggregation by CLEC-2 and GPVI agonists by threshold concentrations of blocking biologics and the Syk inhibitor PRT-060318.
(Ai) Representative traces of washed platelets (2x108 platelets/ml) preincubated for 10 min with threshold concentrations of PRT-060318 (2.5 nM) and/or the divalent anti-CLEC-2 antibody fragment, AYP1 F(ab)2 (2.2 nM). The arrow indicates the time of addition of rhodocytin (100nM). (Aii) The mean ± s.d. level of aggregation (%) after 10 min (n = 3). (Bi) Representative traces of washed platelets (2x108 platelets/ml) preincubated for 10 min with non-inhibitory concentrations of PRT-060318 (2.5 nM) and/or the divalent anti-GPVI nanobody, Nb2-2 (2.2 nM). The arrow indicates the time of addition of CRP (1 μg/ml). (Bii) The mean ± s.d. level of aggregation (%) after 3 min (n = 3: in one donor, 0.50 nM Nb2-2 was used due to 2.2 nM causing complete inhibition). Significance was measured using one-way ANOVA with a Tukey post-hoc test where P ≤ 0.05.
Fig 10.
A model depicting how a combination of a weakly dimerising receptor and a crosslinking agent can drive cluster formation.
The key is shown on the upper right: (A) illustrates crosslinking of two phosphorylated receptors in such a way that growth can only occur through dissociation or addition of a divalent ligands (B) ligand-induced dimerisation of two crosslinked dimers (C) cluster growth by a dimerising receptor and crosslinker. This can be further increased in the presence of a divalent ligand.