A method for single molecule tracking using a conventional single-focus confocal setup

Abstract

One way to achieve spatial resolution using fluorescence imaging—and track single molecules—is to use wide-field illumination and collect measurements over multiple sensors (camera pixels). Here we propose another way that uses confocal measurements and a single sensor. Traditionally, confocal microscopy has been used to achieve high temporal resolution at the expense of spatial resolution. This is because it utilizes very few, and commonly just one, sensors to collect data. Yet confocal data encode spatial information. Here we show that non-uniformities in the shape of the confocal excitation volume can be exploited to achieve spatial resolution. To achieve this, we formulate a specialized hidden Markov model and adapt a forward filtering-backward sampling Markov chain Monte Carlo scheme to efficiently handle molecular motion within a symmetric confocal volume characteristically used in fluorescence correlation spectroscopy. Our method can be used for single confocal volume applications or incorporated into larger computational schemes for specialized, multi-confocal volume, optical setups.

Pitching single-focus confocal data analysis one photon at a time with Bayesian nonparametrics

“…In addition, armed with a rigorous framework, it is now possible to extend the proof-of-principle framework we put forward to treat different effects that lie beyond the current scope of this work. In particular, we can think of extending our framework to treat multiple colors [22], triplet effects, complex biomolecule photophysics [41] (such as biomolecular blinking [89,104] and photobleaching [56,91]), more complex biomolecule motion models [103] other than free diffusion [50], complex distorted PSF models [29], or even incorporate chemical reactions among the biomolecules [8,100].…”

“…To sample the location of an active biomolecule n in 3D, (x n , y n , z n ), we use forward filtering and backward sampling (FFBS) [9,19,50,86]. In particular, we update each dimension sequentially from the following full conditional probability distributions P (x n |D, µ part , {b n , y n , z n } n , {x n } n =n , ∆t), P (y n |D, µ part , {b n , x n , z n } n , {y n } n =n , ∆t), and P (z n |D, µ part , {b n , x n , y n } n , {z n } n =n , ∆t) for x, y, and z coordinates, respectively.…”

“…While BNPs have had a deep impact on Data Sci-ence since their inception, they are relatively new to Biophysics with a handful of papers [18,47,73] published to date using BNPs in Biophysical applications [50,55,[87][88][89][90]92].…”

Computational design and interpretation of single-RNA translation experiments

“…Fluorescence Correlation Spectroscopy (FCS) 665 FCS is usually implemented by computing and comparing the auto-covariances (or 666 autocorrelations) of fluorescence intensities of one or more particles within small fixed 667 volumes [34,35], but similar correlation analyses have been used to quantify intensity 668 fluctuations for tracked single particles [2]. For our analysis, we compute the temporal 669 auto-covariance times of the FLAG fluorescence signal intensity for a moving volume 670 that is centered around the moving RNA spot.…”

“…by subtracting the average intensity of the time series, and then we normalize with 674 respect to the standard deviation. Next, we computed the covariance function of the 675 fluorescence intensity for each intensity spot according to the standard formula: 676 G(τ ) = E{(I t − µ t )(I t+τ − µ t+τ )}, (35) where τ denotes the time delay and E{v} denotes the expectation of some arbitrary 677 value v.…”