Analysis and use of CPP data

4.3.1 Chosen subset of CPP data

A subset of the available data was chosen for fitting (Table 4.3). In order to examine within-cell variation in parameters, and differences in parameters between fits to experiments with and without bubbles, all the data for Cell 4 was fit. Cell 4 was chosen as there were 6 smooth OPP curves with bubbles, and more available HPP data for this cell. In order to examine between-cell variation in parameters, a positive and negative OPP and HPP set was fit for Cells 2 and 3. Data for Cell 1 was not fit as it was a noisier data set.

Table 4.3 Subset of the data that will be fit by the models.

Cell Experiments

2 4 OPP with bubble; 4 HPP

3 4 OPP with bubble; 4 HPP

4 6 OPP with bubble, 4 OPP without bubble; 10 HPP

4.3.2 Resolution of CPP data

The time resolution of the Pfloek data was about 0.02-0.2 s, giving around 3000-6000 data points for OPP experiments, and around 500-800 data points for HPP

experiments. Use of all the data points in a parameter estimation via Matlab

optimization runs was impractical because of excess computer runtimes (which could take an hour or more) and therefore the data was culled. To this aim, the effects of culling on parameter values estimated using the classical model were analysed. For an OPP data set with 520 points in the water phase and 2127 points in the solute phase, points in both phases were culled by selecting every ith point, where i varied between 2 and 10. When the data was culled by the same amount in both water and solute phases, the parameters differed by <1% for fits between the unculled and most greatly culled data. This behaviour was verified on another OPP data set. While there was little change in the parameters, the SE’s for the estimated parameters increased with

decreasing data resolution. However, the magnitude of the SE’s when every 10th point was retained was found to be acceptable (Table 4.4), and it was decided to use this data resolution for all OPP data sets, i.e. every 10th data point in the pfloek output was retained during parameter estimation.

A similar analysis on two HPP data sets revealed that retaining every 10th point did not alter the estimated parameters, but did increase the SE in Lp.It was chosen to

retain every 2ndpoint for the HPP data sets, since there are far fewer points as

compared to OPP data and the optimization is still efficient. This brings the size of the culled HPP data sets down to that of the culled OPP data sets, and the SE in Lpto 0.01

x 10-6 m s-1 MPa-1.

Table 4.4 Showing parameters estimated with the classical model and their standard errors, for two OPP data sets. A data resolution of 1/10th has been used, giving a total of 265 points for the negative OPP and 272 points for the positive OPP data sets.

Negative OPP Positive OPP

Lp (x 10-6 m s -1 MPa-1) 1.30 ±0.01 1.49 ±0.01 ps (x 10 -6 m s-1) 3.92 ±0.02 3.84 ±0.02 σ 0.273 ±0.001 0.262 ±0.001 t0 (s) 1.04 ±0.02 0.73 ±0.02

It must be noted that when a different data resolution is used between the water and solute phases in the OPP data, points in the water and solute phases are differentially weighted, which affects the estimated parameters. It was found that the estimated parameters differed by 2-8% for fits between the unculled data and most greatly culled data – where every point in one phase was retained while every 10th point in the other phase was retained. The above results show that as long as the same data

resolution is used for the whole data set, there is little effect on the estimated parameters.

The time interval that resulted from using every 10th data point generally ranged between 0.5 and 1.5 s. The data could also be culled based on time intervals, e.g. retaining points every 0.5s apart. An exploration of this was not carried out.

4.3.3 Analysis of CPP equilibrium pressures

Initial and final equilibrium pressures were determined over periods of about 20s, depending on the amount of noise in the data. It was observed that the final equilibrium pressure often overshot the initial equilibrium pressure for the OPP experiments. An analysis of equilibrium values revealed a consistent pattern where PE

was slightly lower than P0 for the negative OPP, and PE was slightly higher than P0

for the positive OPP (Table 4.5; Fig. 4.3a). The APW change from full to half- strength, or vice-versa, was suspected to be the cause of this overshoot. This was confirmed when OPP experiments were later conducted on another Chara cell without the APW change (Cell 5), as no overshooting of PE occurred for this cell, but

instead a consistent slight undershooting was observed (Table 4.5). Possible reasons for this will be outlined in a later discussion.

Table 4.5 Mean differences between initial equilibrium pressures P0 and final equilibrium

pressures PE observed in the OPP data, for cells 2 to 5. Errors given are standard errors.

Mean P0 - PE values

Cell Positive OPP Negative OPP

2 -0.0020 ±0.0005 0.0028 ±0.0003

3 -0.0012 ±0.001 0.0031 ±0.0005

4 -0.0013 ±0.0006 0.0006 ±0.0008

5 0.0013 ±0.0001 -0.0014 ±0.0003

Sensitivity of cell turgor to the external concentration was also confirmed in the models, where the APW change had to be incorporated into the perturbation (initial) conditions in order to give a reasonable fit to the PE values of the data. As shown in

§2.2.2, the standard KK equations without an APW change predict that PE returns to

the original equilibrium pressure P0, and the value of PEis not changed by the

presence of ULs (§3.6.2).

A long-term drift in the equilibrium pressures was observed for cells 2-4 (e.g. Fig. 4.3b). Cells 2 and 3 showed a downward drift, and Cell 4 showed an upward drift. No significant drift was observed for Cell 5, which may be due to it being a larger cell (volume = 31.2 mm3_{) with more stable turgor pressures. It is possible that the lack of}

an overshoot in PE and long-term drift for Cell 5 are both related to the absence of an

APW change, however this could not be determined from the data available.

Although P0was determined individually for each experiment, a constant cell volume

V0 and cell radius r0 were used for all experiments on the one cell, corresponding to

the measured values at the beginning of all the experiments. These values were not adjusted to correspond to P0, since the corresponding changes in V0 and r0 are so

small as to make negligible impact on the fits, which are more sensitive to the value of P0.

P0- PE values for Cell 2

-0.0042 -0.0021 0.0000 0.0021 0.0042 0 2 4 6 8 10