Biophysics in reverse: Using blood cells to accurately calibrate force-microscopy cantilevers
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Overview of the experimental setup and procedure. [(a) and (b)] The core components of the horizontal AFM are arranged perpendicular to the optical axis of an inverted microscope, providing a side view of the cantilever and allowing for easy integration of a micropipette setup. The double arrow denotes pipette translation to/from the cantilever by closed-loop piezoactuation. (The sketches are not to scale.) [(c)–(f)] Videomicrographs show how a preswollen (at ) red blood cell is first picked up in a pipette (cylindrical tip, ID [(c) and (d)]), then manipulated close to the tip of the cantilever (e), and repeatedly pushed against the flat of the cantilever (f). (The side view of the -wide cantilever creates a blurry diffraction pattern; only the cantilever tip appears more or less in focus.)
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Scope and repeatability of the force measurements. Two control parameters were varied between experiments: the pipette-aspiration pressure [(a) the -values are given below the graph] and (b) the contact position along the length of the cantilever. A total of 23 cantilever-deflection curves are shown as a function of time. They were aligned so that the time corresponded to the moment of first contact between the approaching cell and the stationary cantilever. Nearly indistinguishable results were obtained for each parameter set (three to five individual curves are plotted on top of each other as indicated). Illustrative videomicrographs are included at the bottom . Note that the recorded cantilever deflection refers to the displacement at the point of cell contact. The conversion from position-detector voltage to cantilever deflection depends on the contact location and had to be separately calibrated for each position. This was done by deflecting the cantilever at each cell-contact position with a rigid needle whose translation speed was precisely known (demonstrated at the lower left).
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Comparison of the measured red-cell deformation with theoretical predictions provides the spring constant of the cantilever. (a) All raw data (cf. Fig. 2) were converted to give the red-cell indentation as a function of the cantilever deflection . For each pipette-aspiration pressure , the figure contains at least three nearly indistinguishable graphs, for a total of 20 curves. All six sets of measurements could be well simultaneously matched by our theoretical predictions (bright solid lines) with only one adjustable parameter, the cantilever spring constant . (b) Examples of numerically computed red-cell contours predicted for the compression experiment of (a). (c) For all measured values of and , the tip spring constant was calculated as a function of the total cantilever length according to (Eq. (1) thin orange lines). The mean values are shown as a thick blue line, flanked by black lines marking the range. Our ultimate choice of (red circle) corresponded to the value (vertical red line) that gave the smallest standard deviation. Also shown are the results of other common calibration methods.
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