Figure 1.
Schematic depiction of the initial distribution of proteins.
(A) depicts the membrane with clustered proteins, with Lat and pZAP-70 molecules initially located in non-overlapping clusters. Lat molecules are confined to diffuse only within their initial cluster domain, while ZAP-70 molecules can diffuse anywhere on the membrane. (B) depicts the homogeneously distributed system, with Lat and pZAP-70 molecules homogeneously distributed initially. In both cases, phosphatase molecules that can deactivate pZAP-70 can diffuse through all domains and are homogeneously distributed initially.
Figure 2.
Fraction of phosphorylated Lat as a function of time without phosphatase.
The fraction of phosphorylated Lat (pLat) measures the ratio of the number of phosphorylated Lat molecules to the total number of Lat molecules. Solid lines (dark) correspond to the homogeneous system and dashed lines (lighter) correspond to the system with clustered proteins. Dashed red curves have 5 ZAP-70 and 5 Lat clusters, and dashed blue curves have 20 ZAP-70 and 20 Lat clusters. Each cluster initially contains 20 proteins. The homogeneous systems have the same number of molecules but in a homogeneous initial configuration.
Figure 3.
Fraction of phosphorylated Lat as a function of time with phosphatase.
Solid lines correspond to the homogeneous system and dashed lines correspond to the system with clustered proteins. (A) The effect of increasing the number of clusters at fixed phosphatase concentration (800 phosphatase molecules per π µm2). Dashed red curves have 5 ZAP-70 and 5 Lat clusters, and dashed blue curves have 20 ZAP-70 and 20 Lat clusters. Each cluster contains 20 molecules, with solid lines (dark) corresponding to the equivalent homogeneously distributed initial conditions. (B) The effect of increasing the initial concentration of active ZAP-70. The results are shown for 5 ZAP-70 and 5 Lat clusters. Blue curves have 100 pZAP-70 per cluster, red curves have 20 pZAP-70 per cluster, and the concentration of phosphatase is 800 per π µm2. (C) The effect of decreasing the concentration of phosphatase. Results are shown for 5 ZAP-70 and 5 Lat clusters, each of which contains 20 molecules. Red curves have 800 phosphatase per π µm2 and blue curves have 200 phosphatase per π µm2.
Figure 4.
Steady-state fraction of pLat for various conditions.
Each system contains 800 phosphatases of pZAP-70. We obtain the fraction of pLat over 60 different configurations of clusters with 25 trajectories for each configuration. The homogenous system produces larger quantities of pLat at all conditions. (A) compares the steady state fraction of pLat for various numbers of pZAP-70 per cluster. In the system with clustered proteins, 20 Lat molecules and a variable number of pZAP-70 molecules are initially located inside each cluster. Solid curves with squares and dashed curves with circles represent the homogenous systems and the cluster systems, respectively. Colors correspond to the following conditions: 20 ZAP-70 and 20 Lat clusters (blue), 10 ZAP-70 and 10 Lat clusters (green), 5 ZAP-70 and 5 Lat clusters (red). (B) shows the difference between the fraction of pLat in the homogenous system and the fraction of pLat in the cluster system for various diameters of clusters. Each system contains 400 Lat, and 400 pZAP-70 molecules. “5Z/5L” stands for the cluster system that contains 5 pZAP-70 and 5 Lat clusters, each of which initially contains 80 molecules.
Figure 5.
The mean distance from a Lat molecule to the kth nearest pZAP-70.
Results are averaged over 1000 initial configurations. Note that in both figures, blue and green data points are nearly indistinguishable. (A) Results for 10 Lat clusters, each of which contains 40 molecules (400 Lat molecules are distributed homogeneously in the green results). There are 400 pZAP-70 molecules, either homogeneously distributed or distributed into 10 clusters. (B) Results for 20 Lat clusters, each of which contains 20 molecules. There are 400 pZAP-70 molecules, either homogeneously distributed or distributed into 20 clusters. To avoid edge effects, numerical results were obtained by considering only Lat molecules near the center of the system.
Figure 6.
The effect of distributing a fixed number of Lat molecules in different numbers of clusters.
Simulation results for 400 Lat molecules placed in 10 clusters (red), 20 clusters (blue), or homogeneously (geen). In all cases, 400 pZAP-70 molecules are homogeneously distributed initially and can diffuse through all domains. No phosphatase is present. (A) and (B) display the fraction of pLat as a function of time for D = 0.0033 µm2/s and D = 0.33 µm2/s, respectively. (C) and (D) measure the number of ZAP-70 bound to Lat as a function of time and correspond to the diffusivities of (A) and (B), respectively. The differences between the different initial configurations are more pronounced at slower diffusion rates.
Figure 7.
The number of unique neighboring pZAP-70 per Lat molecule.
Results are averaged over 1000 initial configurations. (A) Results for 10 Lat clusters, each of which contains 40 molecules (400 Lat molecules are homogeneously distributed in the green results). There are 400 pZAP-70 molecules, either homogeneously distributed or distributed into 10 clusters. (B) Results for 20 Lat clusters, each of which contains 20 molecules. There are 400 pZAP-70 molecules, either homogeneously distributed or distributed into 20 clusters.