Direct tip-position control using magnetic actuation for achieving fast scanning in tapping mode atomic force microscopy

This article presents the development of a faster control loop for oscillation amplitude regulation in tapping mode operation of atomic force microscopy. Two techniques in relation to actuation and measurement are developed, that together significantly increase the bandwidth of the control loop. Firstly, magnetic actuation is employed to directly control the tip position of the cantilever to improve both the speed and the dynamics of the positioning system. Secondly, the signal path for oscillation amplitude regulation is separated from that for topography estimation in order to eliminate measurement delay that degrades the performance of the feedback loop. As a result, the phase-crossover frequency and gain margin of the control system are both increased, leading to a faster and more stable system. Two experiments are performed, one in air and the other in aqueous solution, to compare the developed control system with a commercial one and demonstrate the improvement. The results verify that the combination of the two techniques along with other existing methods eliminates all limitations associated with the instrument for the purpose of oscillation amplitude regulation, which is therewith dictated by the bandwidth of the cantilever

Quantitative characterization of cell behaviors through cell cycle progression via automated cell tracking.

Cell behaviors are reflections of intracellular tension dynamics and play important roles in many cellular processes. In this study, temporal variations in cell geometry and cell motion through cell cycle progression were quantitatively characterized via automated cell tracking for MCF-10A non-transformed breast cells, MCF-7 non-invasive breast cancer cells, and MDA-MB-231 highly metastatic breast cancer cells. A new cell segmentation method, which combines the threshold method and our modified edge based active contour method, was applied to optimize cell boundary detection for all cells in the field-of-view. An automated cell-tracking program was implemented to conduct live cell tracking over 40 hours for the three cell lines. The cell boundary and location information was measured and aligned with cell cycle progression with constructed cell lineage trees. Cell behaviors were studied in terms of cell geometry and cell motion. For cell geometry, cell area and cell axis ratio were investigated. For cell motion, instantaneous migration speed, cell motion type, as well as cell motion range were analyzed. We applied a cell-based approach that allows us to examine and compare temporal variations of cell behavior along with cell cycle progression at a single cell level. Cell body geometry along with distribution of peripheral protrusion structures appears to be associated with cell motion features. Migration speed together with motion type and motion ranges are required to distinguish the three cell-lines examined. We found that cells dividing or overlapping vertically are unique features of cell malignancy for both MCF-7 and MDA-MB-231 cells, whereas abrupt changes in cell body geometry and cell motion during mitosis are unique to highly metastatic MDA-MB-231 cells. Taken together, our live cell tracking system serves as an invaluable tool to identify cell behaviors that are unique to malignant and/or highly metastatic breast cancer cells

Illustration of temporal changes in cell area and cell shape along with cell cycle progression.

<p>After division, cell area gradually increases with change in cell shape from time point A to time point D. Thereafter, the cell becomes rounded with decreased cell area (time point F), marking the entry of mitotic stage. The cell is elongated with slightly increased area and subsequently a characteristic bottleneck structure appears and cell division occurs.</p

Calculation of mean square displacement (MSD) and determination of motion type.

<p>(A) Schematic showing the selected pairs of data point along a trajectory with different time interval for the calculation of MSD. (B) MSD calculation. (C) MSD as function of time interval to determine motion type. The linear increase of the MSD with the time interval indicates the motion type of random walk. Directional motion leads to a MSD curve deflected upward, whereas depressed motion results in a MSD curve deflected downward.</p

False tracking rate of selected MCF-10A, MCF-7, and MDA-MB-231 cells.

a<p>Total tracking event is the sum of the all cell-tracking events over the total selected cells that underwent an entire cell cycle. <b>^b</b>False association is mostly due to false detection of cell division, rapid change of cell locations among multiple interacting cells. <b>^c</b>Lost tracking is mainly due to low image contrast, abrupt motion due to rapid contraction of focal adhesion. Note that cells moving out the field-of-view were not counted as false tracking events.</p

Negative phase contrast images of MCF-10A, MCF-7, and MDA-MB-231 cells.

<p>(A) MCF-10A cells have polarized protrusion structures of leading edge versus trailing edge. (B) MCF-7 cells have multiple protrusion structures around cell boundaries. (C) MDA-MB-231 cells have protrusion structures at the two ends of the long axes.</p

Temporal change of cell area and cell axis ratio along cell cycle progression for MCF-10A, MCF-7, and MDA-MB-231 cells.

<p>The cell cycle was scaled to 0–1 to facilitate comparison among different cells within the same cell-line. Values of cell area or cell axis ratio for each cell examined (blue curves) were lined up with the scaled cell cycle and the mean value for each parameter was shown by the red curve in each figure. (A–C) A rapid increase in mean size of cell area occurred shortly after cell division, which reflects cell attachment on the substrate after cell division. Thereafter, mean size of cell area gradually increased. A rapid decrease in mean size of cell area occurred before the end of cell cycle, which reflects cells becoming rounded in preparation of cell division. (D–F) The mean axis ratio was lowest before and after cell division for the three cell lines, reflecting cells rounded up before and after cell division. Otherwise, the mean axis ratio did not change much at the interphase of cell cycle for both MCF-10A cells and MCF-7 cells. In comparison, the mean axis ratio for MDA-MB-231 cells slightly increased with cell cycle progression.</p

Correlation between direction of cell migration and cell long axis for MCF-10A and MDA-MB-231 cells.

<p>The direction of cell long axis along cell trajectories is shown with green arrows. (A) For the MCF-10A cell, the direction of cell long axis is mostly perpendicular to the direction of the cell trajectory. (B) For the MDA-MB-231 cell, the direction of cell long axis is mostly parallel to that of the cell trajectory. As shown in the inset of figure A, we used the unit vector <b><i>v</i></b>₁ and <b><i>v</i></b>₂ to indicate the direction of cell long axis and the direction of migration, respectively. (C, D) The histograms of the angle between the two unit vectors are shown for MCF-10A and MDA-MB-231 cells, respectively. The majority of data points for the MDA-MB-231 cell are close to zero degree, while the data points for the MCF-10A cell are distributed between 0 and 90 degree.</p

Cell behaviors during cell division for MCF-10A, MCF-7, and MDA-MB-231 cells.

<p>(A) MCF-10A cells divide horizontally with smooth separation after cell division. (B) Some MCF-7 cells divide vertically and remain vertically overlapping for a long time before the cell on the top slides down and gradually attaches to the substrate. (C) MDA-MB-231 cells are unique in that divided cells often underwent rapid motion and irregular geometry change, as shown with green contours from the fifth to the seventh figures.</p