Computer simulations of protein diffusion in compartmentalized cell membranes

Abstract

The diffusion of proteins in the cell membrane is investigated using computer simulations of a two-dimensional model. The membrane is assumed to be divided into compartments, with adjacent compartments separated by a barrier of stationary obstacles. Each compartment contains traps represented by stationary attractive disks. Depending on their size, these traps are intended to model either smaller compartments or binding sites. The simulations are intended to model the double-compartment model, which has been used to interpret single molecule experiments in normal rat kidney cells, where five regimes of transport are observed. The simulations show, however, that five regimes are observed only when there is a large separation between the sizes of the traps and large compartments, casting doubt on the double compartment model for the membrane. The diffusive behavior is sensitive to the concentration and size of traps and the strength of the barrier between compartments suggesting that the diffusion of proteins can be effectively used to characterize the structure of the membrane.

Figure 1

Sketch (reproduced from Suzuki et al. (9)) of the time-dependent diffusion coefficient, D(t), as a function of time in the double compartment model showing the five different regimes of diffusion.

Figure 2

Model for the membrane. The barriers are represented by a sequence of blue (fence) disks of diameter σ_F = 1.5σ with a distance σ (≡ 1) between adjacent disks. The red disks are traps of diameter σ_T, which is varied from 0.5 to 3.5σ. A protein experiences a repulsive interaction when it is within a distance of σ_F/2 from a fence disk and an attractive interaction when it is within a distance of σ_T/2 from a trap disk.

Figure 3

Simulation results for the time-dependent diffusion coefficient as a function of time for ϕ_T = 0.6, V_att = 5, V_rep = 6, and σ_T = 3.5, which corresponds to the double-compartment model. Only three regimes are observed in this case, in contrast to the five regimes in Fig. 2.

Figure 4

Simulation results for (a) mean-squared displacements, 〈R²(t)〉 and (b) the time-dependent diffusion coefficient, D(t), as a function of time, for ϕ_T = 0.05, V_att = 5, V_rep = 6, and σ_T = 1. Roman numbers indicate the five regimes of protein dynamics determined by time exponents of mean-squared displacements.

Figure 5

Simulation results for D(t) for three different cases: 1), with both small and large compartments (circles); 2), with only small compartments (dashed); and 3), with only large compartments (dashed-dotted-dotted). The time-dependent diffusion coefficients calculated with only large compartments is rescaled with N_s = 10. (dotted; see the text for details) For all cases, ϕ_T = 0.05, V_att = 5, V_rep = 6, and σ_T = 1.

Figure 6

Simulation results for the time-dependent diffusion coefficient, D(t), for different concentrations of traps, ϕ_T = 0.025, 0.05, and 0.1, for V_att = 5, V_rep = 6, and σ_T = 1.

Figure 7

Simulation results for the time-dependent diffusion coefficient, D(t), for different interaction strengths of small compartments, V_att = 5, 7, and 9 for ϕ_T = 0.05, V_rep = 6, and σ_T = 1. Different values of ϕ_T are used.

Figure 8

Simulation results for the time-dependent diffusion coefficient, D(t), for different sizes of traps, σ_T = 0.5, 1, 2, and 3.5 for V_att = 5 and V_rep = 6. Values of ϕ_T are adjusted for a large compartment to contain approximately the same number of traps, i.e., ϕ_T = 0.0125, 0.05, and 0.2 for σ_T = 0.5, 1, and 2, respectively. Note that ϕ_T = 0.6 for σ_T = 3.5, because traps should be located at lattices and ϕ_T = 0.6 is the only possible number for such a case.

Figure 9

Comparison of simulation results for D(t) to experiments (9) for different values of (a) σ_T and (b) V_rep. Note that V_att = 5 and ϕ_T = 0.14 (for both a and b); and that V_rep = 3.75 (a), σ_T = 2 (b).

Figure 10

Comparison of simulation results for D(t) to experiments (9) with a variability in σ_T and V_att, values of which are chosen from a flat probability distribution, for ϕ_T = 0.14 and V_rep = 3.7. (a) No variability in σ_T or V_att; (b) variability in σ_T but not in V_att; (c) variability in both σ_T and V_att; and (d) same as for panel c, but for trajectories 10-times as long. The values of the parameters (see text for definition) are a = 0.75, σ₀ = 2, and b = 7.5.