Table 1.
Mean Square Displacement (MSD) Curves Continue to Be Used to Drawn Ensemble Information from SPT Measurements60,65a
| qualitative diffusion type | MSD Signature | |
|---|---|---|
| normal diffusion | ⟨r(τ)2⟩ = | 2dDτ |
| confined/corralled diffusion | ⟨r(τ)2⟩ = | C1(1 − C2 exp(−C3τ)) |
| immobile/stationary | ⟨r(τ)2⟩ < | σloc2 |
| directed diffusion (constant velocity v) | ⟨r(τ)2⟩ = | 2dDτ + v2τ2 |
| anomalous subdiffusion (α < 1) | ⟨r(τ)2⟩ = | Cτα |
a
In the right column, we find the predicted theoretical MSD trend associated with ideal sampling (“ideal” is used since both infinite sample sizes and no measurement noise effects are included) where the Ci’s coincide with constants determined from the assumed dynamical model, α is an anomalous exponent, D corresponds to the normal diffusion coefficient, d to the dimension of the trajectory (e.g. such as two or three common in SPT), and σloc2 corresponds to the measurement/localization noise variance.