Mean Squared Displacement: Difference between revisions
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Finding the MSD was not a trivial task. | |||
<HTML><embed src="http://bradleymonk.com/media/MSD.mp4" height="500" width="640" autoplay="false"></HTML> | |||
{{Box|font=120%|width=95%|float=left|text=12px|MEAN SQUARED DISPLACEMENT| | |||
;Brownian Motion Mean Squared Displacement | |||
* The goal of this calculation is to relate the simulated particle diffusion to real world values, namely velocity. | |||
*Particle velocity will be a function of MSD {{Button|''x'' units ²⁄s}} which scales on space (units) and time (s) parameters. | |||
* Space and time in the model are defined arbitrarily as '''Step_Size''' and '''Step''' where each Step a particle moves a distance randomly chosen from a normal distribution (µ{{=}}1,σ{{=}}.2) | |||
*a step size of {{Button|1 unit/step}} will produce a brownian motion MSD of {{Button|~0.52 ±0.2 units ²/s}} | |||
*empirical observations show that reasonable values for MSD are: | |||
** PSD 0.01 µm ²/s | |||
** synaptic 0.05 µm ²/s | |||
** extrasynaptic 0.1 µm ²/s | |||
*given an MSD of {{Button|0.52 ±0.2 units ²/s}} at the current parameters: 1 step {{=}} 1 unit (at µ{{=}}1,σ{{=}}.2), the model will need to be scaled such that particles move at an extrasynaptic rate of 0.1 µm ²/s. | |||
*spines are on average 1 to 10 µm apart, if the model is comparing two spines 1 µm apart, they should be separated by 5 units of model space. This is because the current particle diffusion rate of the model is .5 µm ²/s and the empirical MSD is .1 µm ²/s | |||
}} | |||
{{Article|Michalet|2010|Phys Rev E Stat Nonlin Soft Matter Phys - [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3055791/ PDF]|PMC3055791|Mean Square Displacement Analysis of Single-Particle Trajectories with Localization Error: Brownian Motion in Isotropic Medium}} | {{Article|Michalet|2010|Phys Rev E Stat Nonlin Soft Matter Phys - [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3055791/ PDF]|PMC3055791|Mean Square Displacement Analysis of Single-Particle Trajectories with Localization Error: Brownian Motion in Isotropic Medium}} | ||
{{ExpandBox|Expand to view experiment summary| | {{ExpandBox|Expand to view experiment summary| | ||
We examine the capability of mean square displacement analysis to extract reliable values of the diffusion coefficient D of single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least square fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points is used for the fit. We discuss the practical implications of these results for data analysis in single-particle tracking experiments. | |||
}}<!-- END ARTICLE --> | }}<!-- END ARTICLE --> | ||
Revision as of 19:27, 4 August 2013
Finding the MSD was not a trivial task.
<HTML><embed src="http://bradleymonk.com/media/MSD.mp4" height="500" width="640" autoplay="false"></HTML>
MEAN SQUARED DISPLACEMENT
Michalet • 2010 • Phys Rev E Stat Nonlin Soft Matter Phys - PDF
Expand to view experiment summary
We examine the capability of mean square displacement analysis to extract reliable values of the diffusion coefficient D of single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least square fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points is used for the fit. We discuss the practical implications of these results for data analysis in single-particle tracking experiments.