There are three sources of error in the procedures described above: (1) errors associated with sampling the coordinates that comprise the outline of the polyp, (2) errors associated with the assumption that the polyp is rotationally symmetric about the axis of the focal plane, and (3) errors associated with bending of the polyp outside the focal plane.
Sampling error: Sampling errors of the polyp outline stem from two sources; the pixel resolution of the true polyp outline and the intensity of sampling of the polyp outline (i.e., the number of measurements taken to estimate area or volume). We assessed our sampling error by repeating the protocols described above for a polyp with no stolons. Since the mouth is closed after feeding, repeated measurements of area and volume of a polyp without stolons should be constant, within sampling error. We measured the area enclosed by the polyp outline using the area algorithm installed in the OPTIMAS package and used the coefficient of variation of 50 points of a post-feeding time series as our index of error for area measurements. Measures of the area of a polyp with no stolons varied 1.6%.
The optimal sampling intensity of a polyp image reflects a balance between too few measures to accurately estimate the polyp outline and too many measures that yield a large compounded error from the cumulative errors associated with each measure. Our estimates of polyp volume derive from 11 measures of width along the body column of the polyp and polyp length. Based on an exploration of the influence of varying the number of widths sampled (from n=2 to n=50) we established n=11 as the appropriate trade-off between accuracy and efficiency. The coefficient of variation for estimates of the volume of a polyp with no stolons for the same 50 point time series was 4.45% (the minimum of 3.7% occurred at n=16 widths, and comparable error values for different sampling intensities were observed over the range from n=10 to n=25).
Violations of rotational symmetry: Volume estimates are based on an assumption that the polyp is being viewed along its longitudinal axis and changes in its shape are not accompanied by changes in its orientation relative to the focal plane. Polyps do not behave so conveniently and this contributes to the error of our volume estimates. The volume of a polyp with no stolons oscillates with very low amplitide about a mean value. This indicates that as a polyp changes shape, it rotates relative to the focal plane, but that these rotations are symmetric. Measurements of amplitude of these volume oscillations for 3 periods yielded an average error for volume determinations of +/- 0.5 nl. A second set of observations were performed to confirm this error estimate. A polyp connected to a stolon of known length and radius was treated as above. In this case, as the polyp changes shape, the amplitude of any volume flux should equal the volume of the stolon. Treating the stolon as a cylinder, its maximal volume can be estimated (pi*r(squared)*L) and the difference between the observed amplitude of polyp volume and estimated stolon volume constitutes the error. Measurements of this difference for 6 periods yielded an average error of +/- 0.7 nl. The lumen of stolons are not precisely cylindrical (Van Winkle and Blackstone 1997). Estimates of volume based on this assumption are overestimates in one direction (Blackstone 1996), which may contribute to the slightly greater error (0.2 nl) detected by this method.
Polyp Behavior: Polyps display two forms of variation in shape in addition to the regular oscillations in length and volume we characterize here. The first is the well-characterized contraction pulse, a symmetric contraction of the polyp along its long axis associated with a distinctive epithelial potential (Passano and McCullough 1962, 1964, Josephson and Mackie 1965, Shibley 1969, Stokes 1974). Contraction pulses do not draw the polyp outside of the focal plane and are accurately measured by our algorithms. The second behavior is more problematic. Here the polyp contracts, as with the contraction pulse, but the contraction is asymmetric causing the polyp to rapidly bend. The above-described algorithms accommodate bending of the polyp within the focal plane, but cannot detect bends outside the focal plane. Such intermittent, rapid bends of the polyp which drew the polyp outside the focal plane were not observed in periods shortly after feeding, presumably because the food item in the gut limited the capacity of the polyp to engage in such behavior. Bends outside of the focal plane became a common feature of the records as digestion proceeded (beginning at ca. 180 and 1200 minutes post-feeding in the coupled and isolated treatments, respectively). Rapid bends drawing the polyp outside the focal plane, however, constituted only a small fraction of the overall record (5.9% and 2.6% in the coupled and isolated records, resepectively). These data points are spurious and are denoted as such by tickmarks along the abcissa in plots of the time series we present below.