Interplay of cytoskeletal activity and lipid phase stability in dynamic protein recruitment and clustering

Abstract

Recent experiments have revealed that some membrane proteins aggregate to form clusters. This type of process has been proven to be dynamic and to be actively maintained by external kinetics. Additionally, this dynamic recruiting is cholesterol- and actin-dependent, suggesting that raft organization and cytoskeleton rearrangement play a crucial role. In the present study, we propose a simple model that provides a general framework to describe the dynamical behavior of lipid-protein assemblies. Our results suggest that lipid-mediated interactions and cytoskeleton-anchored proteins contribute to the modulation of such behavior. In particular, we find a resonant condition between the membrane protein and cytoskeleton dynamics that results in the invariance of the ratio of clustered proteins that is found in in vivo experimental observations.

Figure 1. Schematic representation of the simulation model.

The membrane is portrayed as a surface where the relative concentration of lipids ϕ(r,t) is plotted as a grey scale; areas enriched in raft-like lipids are represented as darkened regions. Cytoskeleton-anchored proteins (X) are represented by red inclusions that nucleate lipid rafts. These proteins can eventually detach after an average time τ due to the active re-polymerization of the actin meshwork. Raftophilic proteins (P) diffuse and are attracted to lipid rafts, causing transient aggregation of these proteins in areas enriched with raft-like lipids, forming protein clusters.

Figure 2. Trapping effect of static inclusions.

Simulations for a system with a single static trapping inclusion (N_X = 1) and one mobile protein (N_P = 1). The system size is 100 × 100 sites (0.25 μm²). The distance to the trapping inclusion is monitored for different cases. (a) λ = 1, α = 0.5: only a few very short trapping periods. (b) λ = 2, α = 0.5: increasing protein-lipid affinity promotes longer trapping periods. (c) λ = 2, α = 0: when the lipid mixture approaches the phase boundary, the mobile protein remains trapped most of the time. (d) Probability distribution for the P-X distance for different values of λ and α.

Figure 3. A trajectory showing STALL periods.

Trajectory of a P protein in a system with an array of fixed inclusions. The interaction parameters are λ = 2 and α = 0.5. STALL periods (green lines) occur around the static proteins (red squares). The lipid mixture is not shown for simplicity. Notice that the STALL periods are only caused by lipid-mediated interactions.

Figure 4. Trapping of proteins in a continuous description.

Protein density cross-sections, ρ(x), obtained from a continuum (coarse-grained) approach using different interaction parameters λ and α. The mean protein density average is initially fixed to 1. The X particle is placed at x = 0.

Figure 5. Transient trapping of proteins in clusters.

Sequence of snapshots corresponding to a simulated membrane of 1 μm² containing 50 nucleating active inclusions X (red) and 1000 diffusing P proteins (blue) in a lipid media (color code on the right side). The model parameters are τ = 0.5 s, λ = 3, and α = 0.5. The sequence only shows a 0.4 μm² subsection to observe the details of the cluster formation (green arrow) and destruction (red arrow) process. From left to right and top to bottom, the sequence covers the last 0.4 s of simulation (almost one time period τ).

Figure 6. Density fluctuations and cluster distribution.

(a) Distribution of protein density fluctuations, P(δρ), for N_P = 1000. Black: reference case (τ = 0.5 s, λ = 3, α = 0.5). Red: random case (no interactions). (b) Distribution of the probability of finding a protein cluster formed by n proteins, P_cl(n). Black: reference case (τ = 0.5 s, λ = 3, α = 0.5). Red: random case (no interactions). Blue: case with slower cytoskeleton dynamics (τ = 5 s, λ = 3, α = 0.5).

Figure 7. Resonant condition for the invariance of the ratio of proteins forming clusters.

Ratio of proteins in clusters, Φ, as a function of the normalized mobile protein density ρ_P for the reference case (λ = 3, α = 0.5) with different attachment/detachment kinetics: red squares (τ = 0.02 s), green diamonds (τ = 0.1 s), black circles (τ = 0.5 s), blue triangles (τ = 1 s), yellow stars (τ = 5 s), and violet plus symbols (τ = 10 s). Random case (no interactions): black empty circles.