Its been previously shown that the rate of hypo-osmotic shock dictates the survival probability (3). To investigate how a single channel contributes to survival, we queried survival at several shock rates with varying MscL copy number. In the main text of this work, we separated our experiments into arbitrary bins of "fast" (\(\geq\) 1.0 Hz) and "slow" (\(<\) 1.0 Hz) shock rates. In this section, we discuss our rationale for coarse graining our data into these two groupings.
As is discussed in the main text and in the supplemental section Logistic Regression, we used a bin-free method of estimating the survival probability given the MscL channel copy number as a predictor variable. While this method requires no binning of the data, it requires a data set that sufficiently covers the physiological range of channel copy number to accurately allow prediction of survivability. Fig. 4 shows the results of the logistic regression treating each shock rate as an individual data set. The most striking feature of the plots shown in Fig. 4 is the inconsistent behavior of the predicted survivability from shock rate to shock rate. The appearance of bottle necks in the credible regions for some shock rates (0.2Hz, 0.5Hz, 2.00Hz, and 2.20 Hz) appear due to a high density of measurements within a narrow range of the channel copy number at the narrowest point in the bottle neck. While this results in a seemingly accurate prediction of the survival probability at that point, the lack of data in other copy number regimes severely limits our extrapolation outside of the copy number range of that data set. Other shock rates (0.018 Hz, 0.04 Hz, and 1.00 Hz) demonstrate completely pathological survival probability curves due to either complete survival or complete death of the population.
Ideally, we would like to have a wide range of MscL channel copy numbers at each shock rate shown in Fig. 4. However, the low-throughput nature of these single-cell measurements prohibits completion of this within a reasonable time frame. It is also unlikely that thoroughly dissecting the shock rate dependence will change the overall finding from our work that several hundred MscL channels are needed to convey survival under hypo-osmotic stress.
Given the data shown in Fig. 4, we can try to combine the data sets into several bins. Fig. 5 shows the data presented in Fig. 4 separated into "slow" (\(<\) 0.5 Hz, A), "intermediate" (0.5 - 1.0 Hz, B), and "fast" (\(>\) 1.0 Hz, C) shock groups. Using these groupings, the full range of MscL channel copy numbers are covered for each case, with the intermediate shock rate sparsely sampling copy numbers greater than 200 channels per cell. In all three of these cases, the same qualitative story is told -- several hundred channels per cell are necessary for an appreciable level of survival when subjected to an osmotic shock. This argument is strengthened when examining the predicted survival probability by considering all shock rates as a single group, shown in Fig. 5D. This treatment tells nearly the same quantitative and qualitative story as the three rate grouping shown in this section and the two rate grouping presented in the main text. While there does appear to be a dependence on the shock rate for survival when only MscL is expressed, the effect is relatively weak with overlapping credible regions for the logistic regression across the all curves. To account for the sparse sampling of high copy numbers observed in the intermediate shock group, we split this set and partitioned the measurements into either the "slow" (\(<\) 1.0 Hz) or "fast" (\(\geq\) 1.0 Hz) groups presented in the main text of this work.
