Mean squared displacement problem

Diffusion is the random migration of molecules or particles arising from motion due to

thermal energy. Interestingly, models of molecular diffusion can be applied to predict and

study other migration processes as well, including the migration of cells, animals, and even

the stock market.

The data tables were generated by a

"single particle tracking approach, wherein the movements of individual cancer cells were

monitored as they migrated in two different tissue mimicking contexts: a sparse collagen

matrix and a dense collagen matrix.

? Plot the trajectory of each cancer cell's movement.

? Do MatLab program to apply a Random Walk Model to the data, by calculating

the mean squared displacement of each cancer cell as a function of Tau. Analyze

only the first 1/3 of the time points.

? Use this program to generate a plot of the cell's MSD(Tau) vs. Tau.

Frame # X Y Time Interval 0 0 0 2 -1.539502 0.02749023 2.00078344 3 -1.8864746 -1.0672363 1.99689996 4 -3.6763184 -1.5496094 2.00018334 -2.9803223 -2.3796387 2.00141668 -5.6810059 -2.5630859 2.00174999 7 -6.409082 -4.2913086 1.99676669 8 -7.096875 -4.4366699 1.99548328 9 -9.2245117 -4.7128906 2.00246668 10 -9.8058105 -5.248877 1.99839997 11 -10.472559 -4.3891113 2.00326657 12 -12.173096 -4.5805664 1.99594998 13 -12.85249 -4.8554199 1.99868333 14 -13.581641 -5.6181641 2.00359988 15 -15.099756 -6.3503418 1.99966669 16 -15.662988 -6.4650391 2.00051665 17 -16.301855 -6.4077637 2.00110006 18 -16.581299 -5.4257324 1.99933338 19 -13.809814 -4.8071289 2.00093341 20 -16.577197 -4.6069824 1.99989998 21 -16.896338 -5.0918945 1.99913335 22 -16.624072 -5.5949219 2.00096655 23 -18.179346 -6.0873047 1.99886668 24 -17.036377 -6.4625977 1.99915004 25 -17.419434 -6.0692383 2.00343323 26 -18.716064 -6.7990723 2.00113344 27 -20.071387 -7.4950195 1.99711668 28 -20.755811 -7.9083984 1.99874997 29 -21.160938 -8.5795898 1.99993336 30 -23.019775 -9.0473145 2.00235009 31 -23.937842 -9.7910645 2.00241661 32 -23.850391 -9.2875977 1.99783337 33 -24.965576 -10.602686 2.00188327 34 -26.226611 -10.019482 2.00114989 35 -27.89624 -10.151123 2.00038338 36 -26.309912 -10.001025 2.00171661 37 -27.92417 -9.1178223 1.99444997