Mechanical diagnosis of human erythrocytes by ultra-high speed manipulation unraveled critical time window for global cytoskeletal remodeling

Abstract

Large deformability of erythrocytes in microvasculature is a prerequisite to realize smooth circulation. We develop a novel tool for the three-step "Catch-Load-Launch" manipulation of a human erythrocyte based on an ultra-high speed position control by a microfluidic "robotic pump". Quantification of the erythrocyte shape recovery as a function of loading time uncovered the critical time window for the transition between fast and slow recoveries. The comparison with erythrocytes under depletion of adenosine triphosphate revealed that the cytoskeletal remodeling over a whole cell occurs in 3 orders of magnitude longer timescale than the local dissociation-reassociation of a single spectrin node. Finally, we modeled septic conditions by incubating erythrocytes with endotoxin, and found that the exposure to endotoxin results in a significant delay in the characteristic transition time for cytoskeletal remodeling. The high speed manipulation of erythrocytes with a robotic pump technique allows for high throughput mechanical diagnosis of blood-related diseases.

Figure 1. On-chip “Catch-Load-Launch” manipulation of an erythrocyte with the aid of a robotic pump system.

(a) Schematic diagram of the manipulation. An erythrocyte is first (I) arrested at the entrance (Catch), (II) kept in the narrow path for a distinct time T (Load), and (III) released from the narrow path (Launch). (b) An example of the actual cell position x(t) (red) and the programmed position (black). (c) Magnified plot of time window of 100 ms.

Figure 2. Ultra-high speed feedback system to control the cell position inside a microchannel.

(a) Experimental setup and (b) its detailed schematic diagram. Ultra-high speed (1000 Hz) visual feedback system composed of a high-speed camera and a piezoelectric actuator connected to a syringe provides the pressure control at the channel outlet, enabling the precise cell manipulation (Δx = ± 0.24 μm) inside the narrow path (cross section: 3 μm × 3.5 μm).

Figure 3. Typical analytical representation of standard linear elastic (SLE) model in (I) Catch, (II) Load, and (III) Launch phases.

(a) Equivalent mechanical circuit that consists of two springs (spring constants: k₁, k₂) and two dampers (viscous coefficients: c₁, c₂). (b) Mathematical representation of the cell position x(t) (equation (3)). (c) Changes in cell height H(t) (equation (4)), calculated from equations (1) and (3). In the linear viscoelastic regime, the shape recovery in the launching phase (III) (red square in c) is represented by a single exponential function. For plotting, parameters are set to k₁ = 1 N/μm, k₂ = 1 N/μm, c₁ = 100 N·s/μm, c₂ = 1 N·s/μm, H(0) = 8 μm, and T = 5 s despite the arbitrariness of force unit.

Figure 4. Snapshot images of erythrocytes in “Catch-Load-Launch” process in the cases of loading times T = 5 s (left), 60 s (middle), and 300 s (right).

After the launch from the narrow path, the cell undergoes shape recovery. The shape recovery becomes drastically slower as the loading time T becomes of the order of 100 s. Scale bar is 10 μm.

Figure 5. Change in cell height H(t) over time, recorded for intact erythrocytes for the different loading times T: 5 s, 60 s, 180 s, and 300 s.

(a) Normalized cell height H(t)/H(0). The standard deviations and the fitting curves are represented by shaded areas and solid lines, respectively. Dotted lines represent H(t)/H(0) = 1 for each T. Each number of samples n is shown above the graph. Inset shows the definition of H(t), which is measured along minor axis of the shape. (b) Representative snapshot image for each T. Scale bar is 10 μm.

Figure 6. Change in cell height H(t) over time, recorded for ATP-depleted erythrocytes for the different loading times T: 5 s, 60 s, 180 s, and 300 s.

(a) Normalized cell height H(t)/H(0). The standard deviations and the fitting curves are represented by shaded areas and solid lines, respectively. Dotted lines represent H(t)/H(0) = 1 for each T. Each number of samples n is shown above the graph. (b) Representative snapshot image for each T. Scale bar is 10 μm. (c) Comparison to intact erythrocytes for each T, where H(t)/H(0) of ATP-depleted erythrocytes exhibited a remarkably faster recovery at T~T_c = 180 s. S.D. (shaded area) is defined as the maximum error coming from each S.D. of ATP-depleted and intact conditions.

Figure 7

(a) c₂/k₁, (b) τ, and (c) (c₂/k₁)/τ for intact (black) and ATP-depleted (red) erythrocytes as a function of loading time T. According to the increasing loading time, c₂/k₁ and τ exhibit a transitional increase at different T. The fact that the ratio (c₂/k₁)/τ remains almost constant suggests that the global shape recovery is dominated by the internal viscous coefficient c₂.

Figure 8. Impact of endotoxin (100 μg/ml S-LPS) on the shape recovery kinetics.

(a) Normalized cell heights H(t)/H(0) for the different loading times T = 5 s, 60 s, 180 s, and 300 s over time after the exposure to 100 μg/ml S-LPS. The standard deviations and the fitting curves are represented by shaded areas and solid lines, respectively. Dotted lines represent H(t)/H(0) = 1 for each T. Each number of samples n is shown above the graph. (b) Representative snapshot image for each T. Scale bar is 10 μm. (c) c₂/k₁, (d) τ, and (e) (c₂/k₁)/τ for erythrocytes exposed to 100 μg/ml endotoxin (blue) as a function of T. Results from intact (grey) and ATP-depleted (orange) erythrocytes are plotted for comparison.

Figure 9. Schematic diagram of characteristic time windows for loading, recovery, and cytoskeletal remodeling.

Global cytoskeletal remodeling in 100 s and the corresponding loading time T_c result in the slow shape recovery with the characteristic time τ_slow~10 s, as revealed by the present study (denoted by red). The global remodeling of entire spectrin network needs much longer time by 3 orders of magnitude compared to the local remodeling by ATP-dependent reversible dissociation-reassociation of a single node of the triangular lattice.