Spatial Stochastic Model of the Pre-B Cell Receptor

Abstract

Survival and proliferation of immature B lymphocytes requires expression and tonic signaling of the pre-B cell receptor (pre-BCR). This low level, ligand-independent signaling is likely achieved through frequent, but short-lived, homo interactions. Tonic signaling is also central in the pathology of precursor B acute lymphoblastic leukemia (B-ALL). In order to understand how repeated, transient events can lead to sustained signaling and to assess the impact of receptor accumulation induced by the membrane landscape, we developed a spatial stochastic model of receptor aggregation and downstream signaling events. Our rule- and agent-based model builds on previous mature BCR signaling models and incorporates novel parameters derived from single particle tracking of pre-BCR on surfaces of two different B-ALL cell lines, 697 and Nalm6. Live cell tracking of receptors on the two cell lines revealed characteristic differences in their dimer dissociation rates and diffusion coefficients. We report here that these differences affect pre-BCR aggregation and consequent signal initiation events. Receptors on Nalm6 cells, which have a lower off-rate and lower diffusion coefficient, more frequently form higher order oligomers than pre-BCR on 697 cells, resulting in higher levels of downstream phosphorylation in the Nalm6 cell line.

Fig. 1.

3-D simulation space containing pre-BCR (red circles), pre-BCR specific domains (enclosed lines), available Lyn (blue asterisks) and Syk molecules (green circles). Pre-BCR and Lyn molecules undergo Brownian motion in the x and y planes and these planes represent the plasma membrane. Syk molecules undergo Brownian motion in the x, y and z planes and these planes represent the cytoplasm and the plasma membrane. Pre-BCR molecules are free to enter their domains in the plasma membrane but pay an exit penalty to leave the domains. Lyn and Syk molecules freely diffuse and do not observe any domains. There are 71 pre-BCR molecules in the system, 7 Lyn molecules (total number of Lyn molecules available to the receptor for binding) and 169 Syk molecules (697 cells) or 959 Syk molecules (Nalm6 cells).

Fig. 2.

Percent of receptors engaged as monomers or different-sized oligomers in 697 and Nalm6 cells (with and without domains) at steady state. All bars are the averages of 3 runs between 50 and 600 seconds. The binding radius for the two cell lines is 0.0001 μm. The dimer off-rate for 697 cells is 1.14/s, compared to 0.159/s for Nalm6 cells‥

Fig. 3.

Time evolution of the percent of Igα and Igβ phosphorylation on the pre-BCR for 697 and Nalm6 cells (with and without domains). (A) 697, Domain. (B) 697, No Domain. (C) Nalm6, Domain. (D) Nalm6, No Domain. In the model, the two phosphorylation sites on each ITAM Igα and Igβ) are lumped together such that Igα can be phosphorylated singly, doubly or unphosphorylated. Igβ can also be phosphorylated singly, doubly or unphosphorylated.

Fig. 4.

Percent of average Igα and Igβ phosphorylation status for pre-BCR (697 and Nalm6 cell lines, with and without domains) at steady state (average of 3 runs between 50 and 600 seconds, ± standard deviation). Bars reporting singly and doubly phosphorylated ITAM bars for Igα and Igβ are stacked.

Fig. 5.

Time evolution of the percent of total available Lyn bound to the receptor and activated Lyn for the 697 and Nalm6 cell line (with and without domains). (A) 697, Domain. (B) 697, No Domain. (C) Nalm6, Domain. (D) Nalm6, No Domain. The total amount of Lyn molecules available to the receptor for binding is 7 Lyn molecules for both cell lines. The total simulation time for each run was 600 seconds. Activated Lyn represents a Lyn molecule which has been phosphorylated at Y397 by another Lyn molecule.

Fig. 6.

Percent of total available Lyn bound to the receptor and activated Lyn for the 697 and Nalm6 cell line (with and without domains) at steady state (average of 3 runs between 50 and 600 seconds, ± standard deviation). (A) Percent of receptor bound Lyn. (B) Percent of Lyn phosphorylated. The amount of Lyn available to receptors is 10% of the total receptor population.

Fig. 7.

Time evolution of the percent of total Syk molecules bound to the receptor and activated Syk for the 697 and Nalm6 cell line (with and without domains). (A) 697, Domain. (B) 697, No Domain. (C) Nalm6, Domain. (D) Nalm6, No Domain. Syk phosphorylation site 1 represents Syk transphosphorylation in its catalytic domain (Y519 and Y520) by another Syk molecule. Syk phosphorylation site 2 represents Syk phosphorylated in its linker region (Y342 and Y346) by Lyn. The two phosphorylation sites on the catalytic domain of Syk (site 1) have been lumped together and can be phosphorylated or unphosphorylated, as have the two phosphorylation sites on the linker region of Syk (site 2)‥

Fig. 8.

Percent of total available Syk molecules bound to the receptor and activated Syk for the 697 and Nalm6 cell line (with and without domains) at steady state. Syk binding and phosphorylation at steady state. (A) Percent of receptor bound Syk. (B) Percent of Syk phosphorylated by Lyn. Bars report averages of 3 runs (3 runs between 50 and 600 seconds, ± standard deviation).