Estimation of diffusion constants from single molecular measurement without explicit tracking

Abstract

BackgroundTime course measurement of single molecules on a cell surface provides detailed information about the dynamics of the molecules that would otherwise be inaccessible. To extract the quantitative information, single particle tracking (SPT) is typically performed. However, trajectories extracted by SPT inevitably have linking errors when the diffusion speed of single molecules is high compared to the scale of the particle density.MethodsTo circumvent this problem, we develop an algorithm to estimate diffusion constants without relying on SPT. The proposed algorithm is based on a probabilistic model of the distance to the nearest point in subsequent frames. This probabilistic model generalizes the model of single particle Brownian motion under an isolated environment into the one surrounded by indistinguishable multiple particles, with a mean field approximation.ResultsWe demonstrate that the proposed algorithm provides reasonable estimation of diffusion constants, even when other methods suffer due to high particle density or inhomogeneous particle distribution. In addition, our algorithm can be used for visualization of time course data from single molecular measurements.ConclusionsThe proposed algorithm based on the probabilistic model of indistinguishable Brownian particles provide accurate estimation of diffusion constants even in the regime where the traditional SPT methods underestimate them due to linking errors.Electronic supplementary materialThe online version of this article (10.1186/s12918-018-0526-5) contains supplementary material, which is available to authorized users.

Practical considerations for feature assignment in high-speed AFM of live cell membranes

“…In defining spatial ‘assignment’ we seek to determine the maximum distance, ξ, that a single q-type molecule identified in one movie frame, may travel before we are unsure that it is the same molecule in the next consecutive movie frame, taken after a time interval Δt [ 5 , 65 – 67 ]. In the ‘diffusion-like’ regime we can answer the question of spatial assignment quite simply by analytically evaluating the integral form of the probability density function (Eqn.…”

“…12c to the two nearest shells. In a similar manner to the single particle case, when defining spatial ‘assignment’ for a particle in a high-density arrangement, we seek to determine the maximum distance, ξ, that a single q-type molecule may travel before we are unsure that it is the same molecule in the next frame after a time interval Δt [ 5 , 67 ]. For the present case an equivalent way of stating this problem is to say that we wish to calculate a conditional probability, P res (ξ,ρ q ,t 2 ), where t 2 =Δt ret (Eqn.…”

“…1 ). Although this question has been extensively considered in the field of single particle tracking conducted using optical microscope procedures [ 3 – 5 ], the same type of problem has been less-well investigated in atomic force microscopy (AFM) measurements [ 6 – 8 ]. As continual scientific and technological developments produce ever faster AFM scan rates [ 9 , 10 ] the potential use of AFM devices to track the motion of slowly moving diffusible components in the cell membrane, such as protein receptors and membrane channels [ 11 ], is becoming tantalizingly extant.…”

A theoretical high-density nanoscopy study leads to the design of UNLOC, an unsupervised algorithm

“…S1 and Note S1) and as the number of fluorescent particles per µm² per frame. is linked to the inter-particle distance distribution (36) that is implicitly related to the probability of finding a single particle at a radius for randomly distributed particles, as determined using the following equation:…”