Fig 1.
A schematic representation of GPVI signal transduction in a platelet.
GPVI is present as a complex associated with Fc receptor (FcR) γ-chain and Src family kinases (SFK) that phosphorylate an immunoreceptor tyrosine based activation motif (ITAM) in the FcR γ-chain. This allows recruitment and activation of the cytosolic tyrosine kinase Syk that leads to phosphorylation of adaptor proteins such as LAT (linker for Activation of T-cells), PI3K (phosphoinositide 3-kinase) and ultimately activation of PLCγ2 (phospholipase C). These molecules participate in triggering the downstream processes of calcium release, shape change and granule secretion that all form part of platelet activation. Arrows are not intended to imply direct phosphorylation or activation.
Fig 2.
A schematic diagram of the reactions captured in each of our mathematical models.
In all models GPVI, its associated Fc receptor γ-chain and Src family kinase, are treated as one unit. A ligand binds to this receptor bundle, which is subsequently phosphorylated, allowing for recruitment and activation of the cytosolic tyrosine kinase Syk. Binding to the receptor leads to auto-phosphorylation of Syk on tyrosine 525 (Y525), allowing the receptor to signal downstream. Model A incorporates a simple phosphatase that is able to dephosphorylate Syk on Y525, returning the receptor complex to an inactive state. In Model B an additional Syk phosphorylation site is incorporated (Y323), to which the newly introduced protein c-Cbl can bind. This allows Syk to set off a series of reactions, that include ubiquitination and the binding of the phosphatase TULA-2 that is able to dephosphorylate Syk on Y525, returning the receptor complex to an inactive state. In Model C two modifications are incorporated: the modification H1 allows TULA-2 to dephosphorylate not only the Syk molecule to which it is bound but also any nearby bound Syk molecule; in the second modification (H2) phosphorylation of Y525 results in an enhanced rate of Y323 phosphorylation. Model C, H3 incorporates H1 and H2 simultaneously.
Fig 3.
A network diagram of Model A (top panel), B (middle panel) and C (lower panels).
Variables are represented by square boxes and the parameter associated with each processes is placed next to the relevant arrow. In all panels, from left to right, a ligand (l) binds to a free receptor (g) on the cell surface forming a receptor complex (G) that phosphorylates (Gp). In Model A Syk (s) binds to the receptor complex () and activates (
). The active receptor can then signal downstream. In the middle and lower panels, the components encased in the red box represent Syk phosphorylation on Y525 (equation S6) and those in the green box represent Syk phosphorylation on Y323 (equation S7). See Tables 1 and 2 for a description of the variables and parameters.
Table 1.
The variables described in the top five rows are common to all models while the following two rows describe variables unique to Model A and the remaining rows describe variables unique to Model B and C. represents eight variables where i and j indicate phosphorylation on Y323 and Y525 respectively (0, unphosphorylated; 1, phosphorylated) and k denotes the sequential processes of (b), binding of Syk; (c), binding of c-Cbl; (u), ubiquitination and (r), binding of TULA-2.
Table 2.
A summary of model parameters.
Their definitions, units, and values utilised in simulations. N/A indicates that the parameter plays no role in the specified model. Further details of the parameter values, their sources in literature and how they were obtained from the parameter fitting process are available in S1 Text.
Fig 4.
Model A profiles compared to experimental observations of Syk phosphorylation on Y525.
Model profiles (black lines) compared to experimental observations (circles). The model accurately describes the steady state seen in experimental observations but is unable to describe the early peak in Syk Y525 phosphorylation. Experimental data of Syk phosphorylation (molecules per platelet) is the mean of three samples +/- S.E.M., phosphorylated (circles). Model simulations (solid lines) utilise parameter values from Table C in S1 Text (parameter set 1).
Fig 5.
Profiles obtained from fitting Model B to experimental observations.
Model profiles obtained from fitting Model B to experimental observation describing Syk phosphorylation on Y525 and Y323 (top row) faithfully represent the steady state seen in experimental data but fail to capture early transient peaks in both sets of data. Model B fitted to a restricted set of experimental observation (bottom row), describing Syk phosphorylation on Y525, closely replicates observations describing Y525 but model predictions for Y323 phosphorylation are nearly three fold higher than that seen in experimental data. In all panels experimental data of Syk phosphorylation (molecules per platelet) is the mean of three samples +/- S.E.M., phosphorylated (circles). Model simulations (solid lines) shown in panels a and b utilise parameter values from Table G in S1 Text (parameter set 1) and simulations shown in panels c and d utilise values from Table F in S1 Text (parameter set 1).
Fig 6.
Profiles obtained from fitting Model C to experimental observations.
Model profiles obtained from fitting Model C to experimental observation describing Syk phosphorylation on Y525 and Y323 are shown in panels a and b. Model C with H3 implemented (solid lines) faithfully represents the experimental data. Model C with H1 or H2 implemented (broken and dotted lines respectively) fail to describe the full dynamics displayed in the data. Model C fitted to a restricted set of experimental observation, describing Syk phosphorylation on Y525 closely replicates observations describing Y525 (panel c) but model predictions for Y323 phosphorylation (panel d) are nearly three fold higher than that seen in experimental data. In all panels experimental data of Syk phosphorylation (molecules per platelet) is the mean of three samples +/- S.E.M., phosphorylated (circles). Model simulations (H1, broken lines; H2, dotted lines; H3, solid lines) shown in panels a and b utilise parameter values from Table J in S1 Text (parameter set 1) and simulations shown in panels c and d utilise values from Table I in S1 Text (parameter set 1).
Fig 7.
Model profiles compared to experimental data from taken from nine donors.
Experimental values are mean (solid red line) +/- 95% C.I. (shaded region) and of all data. Model profile (solid black line) utilises Model C (H3). Parameter values and initial conditions are taken from Tables J (parameter set H3,1) and D in S1 Text respectively.
Table 3.
Model comparisons based on the Akaike’s Information Criterion (AIC) and its corrected form (AICc).
Fig 8.
Model predictions for regulatory protein participation.
Simulations utilise the five best parameter sets (Table J in S1 Text) obtained from fitting the final model (i.e. Model C, H3) to experimental data: the variation in model predictions is low and all simulations predict that very few of the regulatory proteins, c-Cbl and TULA-2, are required to control Syk activity.
Fig 9.
Model predictions of the effect of ligand depletion (left) show close agreement to experimental data (right).
Model profiles of Syk activity are the result of a series of simulations where the ligand is decreased from 100% through to 1% of its original value. Experimental observations (right) are the result of a series of experiments where the agonist (CRP) is decreased from 100% through to 1% of its original value. Model profile (solid black line) utilises Model C (H3). Parameter values and initial conditions are taken from Tables J (parameter set H3,1) and D in S1 Text respectively.
Fig 10.
Syk activity in a hypothetical population.
The results of 200 simulations are shown (each simulation representing a hypothetical donor). Two markers of each simulation (peak Syk Y525 phosphorylation and time-to-peak) are denoted graphically by a circle. Two distinct populations are shown: a healthy population (green) where protein composition were varied across their normal range and a population with 75% deficiency in levels of GPVI. In all simulations parameter values are held fixed to those shown in Table J in S1 Text, set H3,1. The initial conditions of GPVI, Syk and c-Cbl are randomly selected from a range (healthy population: GPVI, +/-12%; Syk +/-22%, c-Cbl +/-25%; GPVI deficient population: GPVI, -25%+/-12%; Syk +/-22%, c-Cbl +/-25%) from the values given in Table D in S1 Text while TULA-2 is held steady to the value shown as there is no variation data for this protein. The large black circle indicates an individual with the mean protein levels that were obtained experimentally (GPVI, 5000; Syk, 2763; c-Cbl, 2581).