Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking

Abstract

Diffusion in the plasma membrane of living cells is often found to display anomalous dynamics. However, the mechanism underlying this diffusion pattern remains highly controversial. Here, we study the physical mechanism underlying Kv2.1 potassium channel anomalous dynamics using single-molecule tracking. Our analysis includes both time series of individual trajectories and ensemble averages. We show that an ergodic and a nonergodic process coexist in the plasma membrane. The ergodic process resembles a fractal structure with its origin in macromolecular crowding in the cell membrane. The nonergodic process is found to be regulated by transient binding to the actin cytoskeleton and can be accurately modeled by a continuous-time random walk. When the cell is treated with drugs that inhibit actin polymerization, the diffusion pattern of Kv2.1 channels recovers ergodicity. However, the fractal structure that induces anomalous diffusion remains unaltered. These results have direct implications on the regulation of membrane receptor trafficking and signaling.anomalous subdiffusion | Brownian motion | continuous time random walk | single-particle tracking T he plasma membrane is a highly complex system with a dynamic organization required to maintain many fundamental processes that include signal transduction, receptor recognition, endocytic transport, and cell-cell adhesion. The study of the diffusion pattern of transmembrane proteins and lipids grants biophysical information on membrane organization, structure, and dynamics. In particular, single-molecule tracking provides insight into the interaction of membrane proteins with their surroundings. Stochastic molecular transport is described by the probability distribution of displacements and how it evolves over time. This distribution is called a propagator, and in the case of Brownian motion it is Gaussian. Diffusion processes that deviate from Brownian motion are considered anomalous, and they involve propagators that may or may not be Gaussian. For example, diffusion in a fractal has a stretched Gaussian propagator (1).Experimental and theoretical work suggests there is a correlation between macromolecular crowding and anomalous diffusion (2-4). However, the mechanism behind hindered diffusion in living cells remains controversial. Several models have been proposed, including membrane compartmentalization, receptor and cytoskeleton binding, and membrane heterogeneity (lipid rafts). Particle trajectories are frequently characterized by their mean square displacement (MSD) (5). A Brownian particle in a 2D space yields an MSD hΔr 2 ðtÞi ¼ 4Dt. However, in many systems the MSD scales as a sublinear power law, indicating anomalous diffusion. In general hΔr 2 ðtÞi ∝ t γ , where γ is the anomaly exponent. Anomalous subdiffusion is manifested by a characteristic exponent γ < 1, and anomalous superdiffusion by γ > 1.Two biologically relevant processes are recognized to induce anomalous subdiffusion in the plasma membrane: (i) transient immobilization and (ii) geometrical i...

Nonergodic subdiffusion from transient interactions with heterogeneous partners

“…The model discussed in this paper proposes a mechanistic explanation for the nonergodic subdiffusion observed in several biological systems [3][4][5][6][7], based on the occurrence of specific, transient interactions with a heterogeneous population of interacting partners. The model displays many similarities with the long-time behavior of the heavy-tail CTRW [9] and the patch model [19].…”

“…Such anomalous diffusion can have different physical origins and a large amount of models have been proposed for its interpretation, some of the most relevant ones being recently discussed by Metzler and co-workers [2]. The detailed analysis of the particle trajectories has shown that some processes characterized by anomalous diffusion also exhibit differences between ensemble and time averaged observables, such as the mean squared displacement itself [3][4][5][6][7]. This feature, known as weakergodicity breaking [8], reflects the physical nature of specific stochastic mechanisms, for which time averages are random and thus irreproducible in spite of the large statistics.…”

Segmentation of 3D Trajectories Acquired by TSUNAMI Microscope: An Application to EGFR Trafficking

“…Other than the mechanisms in confined geometries that lead to subdiffusive behaviors (corralled, hop, and cage diffusion, as discussed in Fig. S8), mechanisms in ''unconfined'' geometries, such as continuous time random walk (93)(94)(95), fractional Brownian motion (96,97), and random walk on a fractal structure (98), can also give subdiffusive MSD curves (11,41,99). A sophisticated differentiation decision tree, such as the one proposed by Meroz's group (41), should be established and rigorously tested.…”

Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity

“…represents the ensemble average, and α > 0 is the exponent which characterizes the diffusion behavior (α < 1, α = 1, and α > 1 correspond to the subdiffusion, normal diffusion, and superdiffusion, respectively). The anomalous behavior is observed in various systems ranging from a charge carrier transport in amorphous material [1], light diffusion [2], polymeric materials [3], to biological transports [4][5][6][7][8][9], The diffusion behavior will depend on the time scale, and thus the exponent α may take several different values depending on ∆. For example, in entangled polymers, the EAMSD of a segment exhibits four different regions which reflect the crossovers between different characteristic relaxation time scales [3].…”