Classifying directed and diffusive transport in short, noisy single-molecule trajectories with wMSD

Abstract

Fluorescence imaging in combination with single-particle tracking analysis has emerged as a powerful tool to study and characterize the motion of proteins moving in biological media. One of the main challenges in this approach is to reliably distinguish between directed and diffusive transport, especially for short and often noisy trajectories showing distinct, time- and place-dependent modes of motility. In this contribution, we present a windowed Mean-Square Displacements classifier (wMSDc) that is able to reliably (i) identify periods of diffusive and directed transport, (ii) extract position-dependent diffusion coefficients and velocities, and (iii) identify the location of switches in direction or motility mode in short (< 50 time points) and noisy single-molecule trajectories. We compare the performance of this approach to a Hidden Markov Model (HMM) method and a Moment Scaling Spectrum based method (DC-MSS) previously published and show that, in most cases, its performance is superior. We present a wide range of applications: from the movement of whole organisms and cells to protein-DNA interactions in vitro and motor-protein dynamics in vivo.

IFT cargo and motors associate sequentially with IFT trains to enter cilia

“…The worm strains used in this study are listed in Table S2. The strains used have been generated before in our laboratory, using Mos-1 mediated single-copy insertion (Frokjaer-Jensen et al, 2008). Maintenance was performed using standard C. elegans techniques (Brenner, 1974), on NGM plates, seeded with HB101 E. coli.…”

“…α is a measure of the directedness of the motion, α = 2 for purely directed motion, α = 1 for purely diffusive motion and α < 1 for sub-diffusion or pausing. For each datapoint (𝑐𝑐 ∥_𝑖𝑖 ), we calculated 𝛼𝛼 in the direction parallel to the spline (𝛼𝛼 ∥_𝑖𝑖 ), using a windowed Mean Square Displacement classifier (wMSDc) approach, described in Danné et al (Danné et al, 2022). α was calculated analytically, using the following equation:…”

A small excitation window allows long-duration single-molecule imaging, with reduced background autofluorescence, inC. elegansneurons

“…For diffusive trajectories, we calculated the diffusion coefficient from the mean squared displacement (MSD) to be 0.11 μm 2 /s (for the trajectory of Figure 3H; Figure 3M). To obtain a quantitative measure for the directedness of the motion, we used an MSD-based approach [22, 23, 29] to extract the anomalous exponent (α) from MSD ( σ ) =2Γ σ α (where Γ is the generalized transport coefficient and σ is the time lag) along the track, in the direction of motion. α is a measure of the directedness of the motion, α = 2 for purely directed motion, α = 1 for purely diffusive motion and α < 1 for subdiffusion or pausing [30].…”

“…The spline was generated by interpolating a cubic spline curve on a segmented line, drawn manually over all tracks in a given dendritic section (which provides the shape of the dendrite). For each datapoint ( c ∥_ i , c ⊥_ i ), a windowed Mean Square Displacement classifier (wMSDc) approach, described in Danné et al [29], was used to extract the anomalous exponent value (α) of the time lag (τ) from MSD = 2Γ τ α (where Γ is the generalized transport coefficient), in the direction parallel ( α ∥_ i ) and perpendicular ( α ⊥_ i ) to the spline. α was calculated analytically, using the following equation: ; keeping a fixed window W = 15 time-frames.…”

Sorting at ciliary base and ciliary entry of BBSome, IFT-B and IFT-A

“…α is a measure of the directedness of the motion, α = 2 for purely directed motion, α = 1 for purely diffusive motion and α < 1 for sub-diffusion or pausing. For each datapoint ( c ∥_ i ), we calculate ⍺ in the direction parallel to the spline ( ⍺ ∥_ i ), using a windowed Mean Square Displacement classifier (wMSDc) approach, described in Danné et al 65 . α was calculated analytically, using the following equation: …”