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Several single-molecule studies aim to reliably extract parameterscharacterizing molecular confinement or transient kinetic trapping fromexperimental observations. Pioneering works from single particle tracking inmembrane diffusion studies [Kusumi et al., Biophysical J., 1993] appealed toMean Square Displacement tools for extracting diffusivity and other parametersquantifying the degree of confinement. More recently, the practical utility ofsystematically treating multiple noise sources (including noise induced byrandom photon counts) through likelihood techniques have been more broadlyrealized in the SPT community. However, bias induced by finite time seriessample sizes has not received great attention. Mitigating parameter biasinduced by finite sampling is important to any scientific endeavor aiming forhigh accuracy, but correcting for bias is also often an important step in theconstruction of optimal parameter estimates. In this article, it isdemonstrated how a popular model of confinement can be corrected for finitesample bias in situations where the underlying data exhibits Brownian diffusionand observations are measured with non-negligible experimental noise (e.g.,noise induced by finite photon counts). The work of Tang and Chen [J.Econometrics, 2009] is extended to correct for bias in the estimated corralradius (a parameter commonly used to quantify confinement in SPT studies) inthe presence of measurement noise. It is shown that the approach presented iscapable of reliably extracting the corral radius using only hundreds ofdiscretely sampled observations in situations where other methods (includingMSD and Bayesian techniques) would encounter serious difficulties. The abilityto accurately statistically characterize transient confinement suggests newtechniques for quantifying confined and/or hop diffusion in complexenvironments.

physical review. e, statistical, nonlinear and soft matter physics

Correcting for Bias of Molecular Confinement Parameters Induced by Small  Time Series Sample Sizes in Single-Molecule Trajectories Containing  Measurement Noise