Comment to the Paper of Michael J. Saxton: "A Biological Interpretation of Transient Anomalous Subdiffusion. I. Qualitative Model"

In a recent paper, Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient sub-diffusive regimes in mean-squared displacements (MSD) plots, calculated from experimental trajectories of molecules diffusing in living cells, acquired by Single Particle (or Molecule) Tracking techniques (SPT or SMT). In this Comment, without questioning the existence of sub-diffusive behaviors, which certainly play a key role in numbers of mechanisms in living systems, we point out that the data used by J.M. Saxton can as well be fitted by a simple law, resulting from confined diffusion at short times, with a slower free diffusion superimposed at larger times. When visualizing MSD plots, the transition from short-term diffusion confined in domains of size L, to slower, longer-term free diffusion, can be confused with anomalous diffusion over several orders of magnitude of time.Comment: To appear in Biophysical Journa

Direct membrane protein–DNA interactions required early in nuclear envelope assembly

Among the earliest events in postmitotic nuclear envelope (NE) assembly are the interactions between chromatin and the membranes that will fuse to form the NE

Probing microscopic origins of confined subdiffusion by first-passage observables

Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean square displacement (MSD). However, subdiffusive behavior can stem from different microscopic scenarios, which can not be identified solely by the MSD data. In this paper we present a theoretical framework which permits to calculate analytically first-passage observables (mean first-passage times, splitting probabilities and occupation times distributions) in disordered media in any dimensions. This analysis is applied to two representative microscopic models of subdiffusion: continuous-time random walks with heavy tailed waiting times, and diffusion on fractals. Our results show that first-passage observables provide tools to unambiguously discriminate between the two possible microscopic scenarios of subdiffusion. Moreover we suggest experiments based on first-passage observables which could help in determining the origin of subdiffusion in complex media such as living cells, and discuss the implications of anomalous transport to reaction kinetics in cells.Comment: 21 pages, 3 figures. Submitted versio

Quantitative analysis of single particle trajectories: mean maximal excursion method

An increasing number of experimental studies employ single particle tracking to probe the physical environment in complex systems. We here propose and discuss new methods to analyze the time series of the particle traces, in particular, for subdiffusion phenomena. We discuss the statistical properties of mean maximal excursions, i.e., the maximal distance covered by a test particle up to time t. Compared to traditional methods focusing on the mean squared displacement we show that the mean maximal excursion analysis performs better in the determination of the anomalous diffusion exponent. We also demonstrate that combination of regular moments with moments of the mean maximal excursion method provides additional criteria to determine the exact physical nature of the underlying stochastic subdiffusion processes. We put the methods to test using experimental data as well as simulated time series from different models for normal and anomalous dynamics, such as diffusion on fractals, continuous time random walks, and fractional Brownian motion.Comment: 10 pages, 7 figures, 2 tables. NB: Supplementary material may be found in the downloadable source file

The Chromosomal Passenger Complex Activates Polo Kinase at Centromeres

The coordinated activities at centromeres of two key cell cycle kinases, Polo and Aurora B, are critical for ensuring that the two sister kinetochores of each chromosome are attached to microtubules from opposite spindle poles prior to chromosome segregation at anaphase. Initial attachments of chromosomes to the spindle involve random interactions between kinetochores and dynamic microtubules, and errors occur frequently during early stages of the process. The balance between microtubule binding and error correction (e.g., release of bound microtubules) requires the activities of Polo and Aurora B kinases, with Polo promoting stable attachments and Aurora B promoting detachment. Our study concerns the coordination of the activities of these two kinases in vivo. We show that INCENP, a key scaffolding subunit of the chromosomal passenger complex (CPC), which consists of Aurora B kinase, INCENP, Survivin, and Borealin/Dasra B, also interacts with Polo kinase in Drosophila cells. It was known that Aurora A/Bora activates Polo at centrosomes during late G2. However, the kinase that activates Polo on chromosomes for its critical functions at kinetochores was not known. We show here that Aurora B kinase phosphorylates Polo on its activation loop at the centromere in early mitosis. This phosphorylation requires both INCENP and Aurora B activity (but not Aurora A activity) and is critical for Polo function at kinetochores. Our results demonstrate clearly that Polo kinase is regulated differently at centrosomes and centromeres and suggest that INCENP acts as a platform for kinase crosstalk at the centromere. This crosstalk may enable Polo and Aurora B to achieve a balance wherein microtubule mis-attachments are corrected, but proper attachments are stabilized allowing proper chromosome segregation

Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed-down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in 2d. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte-Carlo simulations, we show that those three scenarios have distinctive effects on the apparent affinity of the reaction. While continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hinderance by obstacles both improve it. However, only in the case of slowed-down Brownian motion, the affinity is maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.Comment: Biophysical Journal (2013