Jen Barnet
Spirulina
Image at 10 X
Scale bar = 0.496 mm
Image at 20X
scale bar = 11.0 um
Width of Spirulina = 5.8 um
Length of Spirulina = 1.77 mm
Yeast (HBT and HA2)
We counted the yeast cells in the image as a whole to determine the exact number, and then we drew a grid on the image and counted the yeast cells within each sqare (see sample image above). We used grid sizes of 2X2, 3X3, 4X4, 5X5, and 6X6 to compare the accuracy of counting the cells in only a small sample space versus the entire area.
The results in the graphs below show that counting one square in a 2X2 grid is comparable to that of the entire image for low density and high density cells. HA2 were at low density with only 99 cells/image and HBT was at high density with 532 cells/image. The counting of cells in a 3X3 grid was dramatically worse. The process of counting in a sample area and extrapolating saves time when estimating the number of cells growing in a flask or test tube.
The size of one square in the 2X2 grid is ~1.5 mm per side.
The size of one square in the 3X3 grid is ~1.0 mm per side.
Diffusion
We recorded the tracks of 2-um fluorescent beads dispersed in two fluids of differing viscosities: pure H2O, and a 2:1 (V/M) H2O:PEG (polyethylene glycol) solution, using a fluorescence microscope. Unfortunately particles were scarce and diffusion was slow in the higher viscosity H2O:PEG solution. Plotted below are the coordinates of the sole bead tracked in this experiment, as well as the x-coordinate and y-coordinate plotted separately against time. There appears to be some variation in bead location, although the resolution is too low to be sure (640x480 pixels over a 295x220 um field of view, giving one-pixel resolution of 0.5 um).
The same experiment, but in pure H2O, displayed faster-moving and more numerous beads:
From the time series above, it is apparent that ‘particle 5’ is an anomaly, and that particles 0 and 2 are actually the same particle. Seeing that particles 0, 1 and 3 persisted the longest, but appeared to drift overall (and in the same direction), we calculated the center of mass of the three particles at each time point. Subtracting the center-of-mass coordinates from the coordinates of each particle gave the diffusive component of each particle’s motion (as opposed to the bulk, directional motion due to an external factor such as tilt in the microscope slide). In the following figure, the locus of each of the three particles tracks is apparent.
However, when plotting the squared distance of each particle from its starting location versus time, the data does not form a straight line for any of the three beads:
This lack of fit might be due to the low concentration of beads on the slide, and makes estimation of the diffusion coefficient difficult. A different approach involves measuring the distance each bead moves between two successive images, squaring it, and dividing this squared distance by the time interval between the images. Doing this for each of the three beads above, for each of their 18 common time intervals, gives a distribution of 54 estimates of <R^2> / t:
Since this quantity (<R^2> / t ) is equal to 4D, we can estimate the diffusion coefficient from the histogram data. Taking a weighted average of the three most highly populated bins gives an estimate of 0.4 um^2 / sec for 4D, or D ~ 0.1 um^2 / sec.
Now we use this estimate of D to estimate the fluid
viscosity (n), using D = kT / (6*pi*n*r). Taking T = 300K (27’C, room temperature) and
bead radius r = 1um, gives a fluid viscosity of 2.2 centipoises. From the CRC Handbook of Chemistry and Physics, the viscosity of water at 27’C
is 0.85 cp, so our estimate is within a factor of about 2.5.