Demonstration of chemostat operation and verification of expected statistical

I first wanted to demonstrate that the Sortostat was capable of “normal” chemostat operation by growing cells in the reactor without applying a directed selection. The

LabView software in this case simply made a random decision about whether to send cells in the sorting chamber to the waste. Under these conditions the Sortostat performs similar to the microchemostat (Figure 4-8 and 4-9).

Figure 4-8 Demonstration of operating the Sortostat as a normal chemostat

Cells expressing CFP or YFP were co-cultured in the Sortostat and grown with a constant dilution rate but random sorting in order to demonstrate that the Sortostat can operate like a“normal” chemostat. For each time point two images were captured of the sorting chamber

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and processed by automated image processing algorithms to count cells: one image was captured with a CFP emission filter to count CFP cells (blue circles) and the other was captured with a YFP emission filter to count YFP cells (green circles). The cells reach steady state growth by six hours as indicated by a leveling off of the cell counts.

Figure 4-9 Demonstration of operating the Sortostat as a normal chemostat

A segment of a longer run where sorting is allowed to proceed at random. The earlier time points including the initial rise to steady state are not shown in the plot. The data here represents a 20 hour time course. For each time point two images were captured of the sorting chamber and processed by automated image processing algorithms to count cells: one image was captured with a CFP emission filter to count CFP cells (blue dots) and the other was captured with a YFP emission filter to count YFP cells (green dots). These two counts were summed to provide a total count in the sorting chamber (red dots). The total cell count remains relatively constant over the entire segment demonstrating that the cells are in normal, steady-state chemostat growth.

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In order to better understand the performance of the Sortostat, I verified that experimental results agreed with expected theoretical statistical distributions for the cells captured in the sorting chamber. I used the data shown in figure 4-9 to conduct this analysis. First, I evaluated that the distribution of the total number of cells that were captured in the sorting chamber. Assuming that the growth chamber loop is well-mixed then the number of cells captured in the sorting chamber can be modeled as a binomial distribution where the probability of capturing W cells in the sorting chamber is given by the binomial equation:

X  W|,   W#Z_{1  }![Z _{Eq. 4.6}

Where  is the total number of cells in the reactor (3800 on average in this experiment) and  is the size of the sorting chamber relative to the total volume of the growth chamber loop (1/100). I can then solve for the probability mass function and compare it the histogram of the data (Figure 4-10). There is good agreement between the predicted distribution and the experimental data.

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Figure 4-10 Comparison of model distribution to experimental results for the number of cells captured in the sorting chamber.

There is good agreement between the predicted binomial distribution (blue curve) for the number of cells captured in the sorting chamber and the histogram of experimental data (blue bars).

I can extend this analysis to also evaluate the expected number of cells expressing CFP captured in the sorting chamber based on the average fraction of cells expressing CFP in the reactor. Since the number of cells expressing CFP in the sorting chamber ( ) will be correlated with the total number of cells in the sorting chamber (W) I will need to solve for the joint probability distribution:

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I previously solved for X  W in Eq. 4.6, so I only need to solve ]  |X  W that can be modeled as a binomial distribution:

]  |X  W  W #_{1  }Z[ _{Eq. 4.8}

Where  is the average percentage of cells expressing CFP in reactor (50%). I can then solve this distribution and compare the predicted joint distribution against the experimental data to find a good agreement (Figure 4-11).

Figure 4-11 Theoretical joint probability distribution of the total number of cells in the sorting chamber and the number of CFP expressing cells in the sorting chamber agrees with experimental data.

Comparison of (A) theoretical and (B) experimental joint probability distributions, the color bar represents the probability of capturing a particular pair of the total number of cells in the sorting chamber and the number of CFP expressing cells in the sorting chamber. There is good agreement between the predicted distribution and the experimental data.

Accurate theoretical distributions of the number of cells expressing CFP or YFP captured in the sorting chamber will support the development of more complicated models of

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the overall function of the Sortostat (Chapter 5). In particular, the strength of the selective pressure that can be applied to a subpopulation (such as CFP expressing cells) will be

dependent on the distribution of cells from that subpopulation that are captured in the sorting chamber. For example, a wider distribution of the number of CFP expressing cells in the sorting chamber would allow for a higher selective pressure to be applied to the CFP

expressing cells. To better understand the relationship between the distribution of CFP cells and the selective pressure consider the extreme case where there is no variation in the number of CFP cells captured (in other words, an infinitely narrow distribution). In that scenario I would be unable to apply any selective pressure to the CFP subpopulation as every sorting event would remove the same number of CFP cells.