Appendix I: Description of the ‘PfFit’ program

Background.

The PfFit program was written using MATLAB (Ver. 6.5, Release 13; from The MathWorks, Natick, MA). The executable file, installation instructions and User Guide, as well as the source files are available upon request from the corresponding author. We verified the MATLAB simulations of the external bath concentration and of the cell volume changes according to the different models using EXCEL (Microsoft Office 2000).

Program structure.

The program has three parts, (A): “IndicatorFit”, for fitting the experimentally sampled time course of concentration changes of the bath indicator, (B): “ModelMake”, for creating simulations of volume changes, bath osmoticum changes and Pf changes, and (C): “VolumeFit”, for fitting the time course of changes in cell volume calculated from the experimentally determined crossectional-areas of the cells. “ModelMake” and “VolumeFit” use parameters describing the bath concentration changes originating from “IndicatorFit”; “VolumeFit” and “IndicatorFit”can be tested on simulations created by “ModelMake”.

A: “IndicatorFit”.

Program Input. Initially, the user must supply the name of the file with “Dyet” vs. “t”, the absorbance values sampled while flushing the indicator dye through the bath, vs. the time of their sampling (Eq; 1a, Materials and Methods, illustrated in Fig. 2A. The parameters list can be filled out manually in the program’s window, or obtained from a parameter file.

The parameters to be supplied are: Coutorig and Coutend (the steady-state values of the initial and the end osmolarities in the bath, Eq. 1b in Materials and Methods, ”twidth“ and “thalf” (initial guesses - “seeds” - for two of the four parameters of the sigmoidal curve to be fitted to Dyetvs. t; twidth is related to the duration of the transition part of the sigmoid, thalf is the midpoint of the transition ), N_steady_st_pts” (the number of end samples of Dyet to be averaged for the automatic evaluation of Dyeend,the end steady-state value of dye absorbance (Important: during the exchange, the absorbance of the bath solution needs to be sampled till it attains a steady state value); and a couple of parameters related to the baseline absorbance: “t_start_wash” (the duration of baseline sampling with Coutorig in the bath), and “threshold_%” (the threshold - % of baseline value - at which the program detects departure from baseline of the indicator absorption).

Program Output. The results of the fit are 3 additional parameters describing the sigmoidal time course of bath concentration change, ”twidth“, thalf and “Coutinit“ (the asymptotic value of bath osmolarity at -∞, corresponding to “Dyeinit“, the best-fit absorbance at minus infinity, calculated without an initial guess, as a by-product, from Eq. 1a), and “lag”, or “flush_lag” (the lag between the marking of the opening of the perfusion valve and the actual entry of the new solution to the bath, extracted from fitting the indicator data using a “threshold_%”). This is actually a correction for the user-determined waiting period between the beginning of record and the actual entry of new solution to the bath. These 4 output parameters, and the two input variables, Coutorig and Coutend, serve subsequently as inputs in part B of the ‘PfFit’ program, for simulating the time course of cell volume change, or in part C of ‘PfFit’, for fitting the time course of the volume change.

Additional Output:A figure, fully documenting the data (Cout vs. t) and the fit; additionally, the values of “lag”, ”twidth“, thalf, “Coutinit“, Coutorig and Coutend are saved in an ASCII tab-delimited text file: ‘_IndResults.txt’

B: “ModelMake”.

This is a simulation program, designed to examine various hypotheses ("models”) and the realtive importance of the parameters in each of these models.

Program Input. The user needs to supply parameters to run the program, like in the case of “IndicatorFit” (except for a data file). In addition to “t_start_wash”, lag”, ”twidth“, thalf, “Coutinit“, “Coutorig“ and “Coutend“, described above, additional parameters are required as follows:

- 3 parameters related to the dynamics of the cell’s osmotic water permeability, “Pf” (the Pf value at the very start of volume change), “slopePf” (the rate of Pf change) and “delay” (the time period between the start of bath perfusion and start of volume change);

- the “model class”, defining the Pf dynamics; the models (see detailed descriptions in Results and in Materials and Methods) are lumped here into three classes: Class I (equivalent to model 1); Class II (equivalent to models 2-5)[1]; Class III (equivalent to model 6).

- The other parameters to be supplied by the users are “Radius” (the cell radius), “Num_of_points” (the number of sample points to be created in the simulation), “Duration” (the duration of the simulated cell volume change) and “Noise_%” (the amount of random noise - relative to the baseline volume[2] – to be added to the calculated simulated time courses of cell volume and cell cross-section area).

Program Output. The simulations are saved in 4 ASCII tab-delimited text files for further display or tests of the analysis program:

- (1) ‘_MODEL_T_areas.txt’ (the simulated time course of changing cell’s surface area): a 2-column matrix, including time, t, and surface area values, without or with added random noise[3];

- (2) ‘_MODEL_T_SIMvolumes.txt’ (the simulated time course of changing volume): a 3-column matrix including time, t, the simulated volume (without or with added random noise[4]) and the simulated volume without noise;

- (3) ‘_MODEL_T_Pfabs_Pfscaled.txt’ (the simulated time course of Pf), : a 3-column matrix including time, t, the simulated Pf in absolute values and the simulated Pf in relative values, scaled for optimised display on the figure;

- (4) ‘_MODEL_T_Cout_Cin_delC.txt’ (the time courses of concentrations): a 4-column matrix, comprised of time, t, bath concentration, Cout, intracellular concentration Cin and the difference between the last two, delC.

An additional Output:A figure showing the simulated data (all 3 concentrations vs. t, Volume vs. t and Pfvs. t), along with the values of all of the input parameters.

C: “VolumeFit”.

Program Input. The user needs to BROWSE for a data file - the time course of changing cell surface area - and supply the values of “t_start_wash”, lag”, ”twidth“, thalf, “Coutinit“, “Coutorig“ and “Coutend“, described above.

Additionally, a choice of “model CLASS” is required. The models are categorized into three types, as in ‘ModelMake’, with the same basic differences with regard to the Pf dynamics (as details in Results). However, rather than being related strictly to the values of “slopePf” and “delay”, the model numbers are defined here more broadly, differing with respect to which parameters are being fixed and which are being adjusted (i.e., freely variable) during the fitting procedure.

Class I, model 1 – only Pf is free to vary, slopePf and delay can be zero or non zero, but their values remain fixed;

Class II, model 2 – only Pf is free to vary; model 3 – Pf and slopePf are free to vary, delay is fixed; model 4 – Pf and delay are free to vary, slopePf is fixed; model 5 – all three are allowed to vary;

Class III, model 6 – all three parameters vary; models 7 and 8, not described before, are based on model 6; model 7 – slopePf and delay are free to vary, Pf is fixed; model 8 – slopePf is fixed and Pf and delay vary.

Program Output. A figure shows the data (Volume vs. t and Pfvs. t) and the fit (to volume-t), along with the values of various input and output parameters including the fit error; 5 ASCII tab-delimited text files allow replotting the data and simulations in user-preferred formats, or tabulating various values for further analyses:

- (1) ‘_EXPTl_T_volumes.txt’ (the experimentally determined time course of cell’s volume): a 2-column matrix, including time and volume;

- (2) ‘_FIT_T_volumes.txt’ (the simulated best-fit time course of volume): a 2-column matrix including time and the simulated volume;

- (3) ‘_FIT_T_Pfabs_Pfscaled.txt’ (the simulated time course of Pf): a 3-column matrix including time, the simulated Pf in absolute values and the simulated Pf in relative values, scaled for optimised display on the figure;

- (4) ‘_FIT_T_Cout_Cin_delC.txt’ (the time courses of concentrations, reconstructed, like in ModelMaker, based on parameters from IndicatorFit): a 4-column matrix, comprised of time, t, bath concentration, Cout, intracellular concentration Cin and of the difference between the last two, delC;

(5) ‘_FIT_Vol_Results.txt‘ (the list of fit results): ‘key’ (model number), cell radius, ‘C’ (difference between the initial and final bath concentrations, in mM), Pf, slopePf, delay, ‘FVAL’ (fit error, normalized to the # of fitted data points and to the baseline volume value), ‘V_%’ (the final relative change in cell volume), ‘A_%’ (the final relative change in cell surface area), finalPf, ‘V_gro_dur’ (the duration of the post-delay period of swelling or shrinking).

[1] The distinction among models 2-5, while not indicated explicitly in the input or the output of ModelMake, is implicit in the values of “slopePf“ and “delay”: it is model 2 if both slopePf anddelay = 0; model 3 if only delay = 0, model 4 if only slopePf =0 and model 5 if both slopePf anddelay ≠0 .

[2] The noise is distributed normally around a zero mean, with the user-defined ‘Noise_%’ = SD relative to the volume baseline.

[3] See footnote 11: noise

[4] See footnote 11: noise definition