PMC

Analysis of the “LSPIV” image-analysis method. (A) Principle of the “LSPIV” image processing algorithm and specific parameters considered in the modeling. D_RBCapp is the size of the shadow left by an RBC, and H_t is hematocrit. ΔX_mov is the displacement of a RBC from one line to the successive one. Two lines from the spatiotemporal image separated by N_Tline lines are selected. Their intensities are then cross-correlated and the maximum of the cross-correlogram is found, giving N_Tline ΔX_mov. V_{RBC app} is the ratio of ΔX_mov by T_Line. (B) V_RBCapp^LSPIV vs. N_mov was calculated from Equation (8) for a range of N_Tline with γ_Vessel = 1, N_PxLineVessel = 50, γ_Flyback = 0.5 and V_scan = 100 mm/s. (*) The dashed line gives V_RBCapp^LSPIV. (C) ΔV_RBCapp^LSPIV/V_RBCapp^LSPIV vs. V_RBCapp^LSPIV was calculated from Equation (10) for a range of V_scan with γ_Vessel = 1, N_PxLineVessel = 50, γ_Flyback = 0.5 and N_Tline = 1. (D) ΔV_RBCapp^LSPIV/V_RBCapp^LSPIV vs. V_scan was calculated from Equation (10) for a range of γ_Vessel with V_RBCapp = 5 mm/s, N_PxLineVessel = 50, γ_Flyback = 0.5 and N_Tline = 1. (E) ΔV_RBCapp^LSPIV/V_RBCapp^LSPIV vs. N_PxLineVessel was calculated from Equation (10) for a range of N_Tline with V_RBCapp = 5 mm/s, V_scan = 100 mm/s, γ_Flyback = 0.5 and γ_Vessel = 1. (F) V_RBCapp^LSPIV_minP% and V_RBCapp^LSPIV_max were calculated vs. P_x from Equation (11) and Equation (13), respectively, for a range of γ_Vessel with forward scanning, P = 10%, N_PxLineVessel = 50, Fp = 200 kHz, J/(fτ) = 2 10^–8 s²/m, γ_Flyback = 0.5 and N_Tline = 1. (G) V_RBCapp^LSPIV_minP% and V_RBCapp^LSPIV_max were calculated vs. F_p from Equation (11) and Equation (13), respectively, for a range of γ_Vessel with forward scanning, P = 10%, N_PxLineVessel = 50, P_x = 0.5 μm, J/(fτ) = 2 10^–8 s²/m, γ_Flyback = 0.5 and N_Tline = 1. (H) V_RBCapp^LSPIV_minP% and V_RBCapp^LSPIV_max were calculated vs. N_PxLineVessel from Equation (11) and Equation (13), respectively, for a range of N_Tline with forward scanning, P = 10%, F_p = 200 kHz, P_x = 0.5 μm, J/(fτ) = 2 10^–8 s²/m, γ_Flyback = 0.5 and γ_Vessel = 1. (I–K) Respectively as (F–H) for reverse scanning.

Schematic of Mathematical Models
We consider four classes of model: (A) differentiation obeys first-order kinetics. This model is given by , , in the text. (B) Differentiation from the EPI state to the NPC state is inhibited by residual ESCs in the colony. This model is given by , , in the . (C) Differentiation is described by a hidden Markov process. This model is given by , , and in the text. A minor variation to allow reversible dynamics is given by , , and in the . (D) Differentiation is described by a continuous “conveyor-belt” process in which initial variability propagates forward at constant speed. This model is given by in the . In all panels, orange denotes cells in the ESC state; green denotes cells in the EPI state; purple denotes cells in the NPC state.

The equation listed above expresses the probability of there being a incorrect forward identifications in a particular dataset, given that n reversed peptides were identified. When this equation is solved for a range of possible values for a, a probability distribution is defined. Plotted above is the probability distribution observed for the case where 3 reversed peptide identifications have been made. The 95% confidence interval is shaded in gray.

The probability distribution function (PDF) derived from Fokker-Planck equation fits well into experimental data. (A) Curve fit of anterograde movement. We defined anterograde forward as movement from the cell body toward the distal axon point, and anterograde reverse as movement that reverses in direction toward the cell body. Anterograde reverse (right) was consistent regardless of distance from the cell body, but was significantly slower than anterograde forward. (B) Retrograde forward was defined as movement from the axonal endpoint to the cell body, and retrograde reverse was opposite of the retrograde forward. A retrogradely forward moving mitochondrion is much faster than that of reverse. (C,D) Comparison mitochondrial transport in normal axons with that of axons overexpressing parkin. (C–F) Anterograde forward movement is much slower in axon overexpressing parkin compared to that of normal axon. Anterograde reverse direction is also slower due to parkin overexpression. Retrograde forward movement shows similar velocity distribution between normal and parkin overexpression. Interestingly, however, retrograde reverse movement in axon with parkin overexpression exhibits extremely narrow velocity distribution than that of normal axon. Anterograde reverse direction is also a little slower due to parkin overexpression. Retrograde forward movement shows similar velocity distribution between normal and parkin overexpression.