Quit

This code was developed by Dominic J Olver and Benson J.D in conjunction with the Benson J.D. Lab and the Paredes E. Lab (October 24, 2022). 
All rights reserved.

Open the sections below. Evaluate the boxes to obtain data and execute code.

General functions

(*These function are generally used in the code. *)
Needs["ErrorBarPlots`"]
adjRSquared[data_,fun_,numParameters_]:=Module[
{n,ymean,SSres,SStot,rsquared,adjrsquared},
n=Length[data];
ymean=Mean[data[[All,2]]];
SSres=Total[(#[[2]]-fun[#[[1]]])^2&/@data];
SStot=Total[(#[[2]]-ymean)^2&/@data];
rsquared=1-SSres/SStot;
adjrsquared=1-(1-rsquared)*(n-1)/(n-numParameters-1)
]

errorData[data_]:=Module[
{x,y},
x = DeleteDuplicates[data[[All,1]]];
Table[y=Select[data,#[[1]] == xi &][[All,2]];
If[Length[y]<=1,Flatten[{xi,y,0}],
{xi,Mean[y],N[StandardDeviation[y]/Length[y]^.5]}
],{xi,x}]]

errorBinData[data_,binWidth_]:=Module[
{x,y,minX,maxX},
minX=Min[data[[All,1]]];
maxX=Max[data[[All,1]]];
DeleteCases[Table[y=Select[data,xi<= #[[1]] &&#[[1]] < (xi +binWidth)&][[All,2]];
If[Length[y]==1,Flatten[{(xi+ (xi +binWidth))/2,y,0}],
If[Length[y]== 0,Null,
{(xi+ (xi +binWidth))/2,Mean[y],N[StandardDeviation[y]/Length[y]^.5]}
]
],
{xi,minX,maxX,binWidth}],Null]
]


bvhModel[data_]:=LinearModelFit[data,x,x];
(*Fit the pump leak model*)
getGridPoints[basePoints_]:=Module[{nestListGet,gridList},
gridList={};
(*this is a recursive function that takes in anoriginal list {{a1,a2,a3,...,an},{b1,b2,b3,...,bn},...,{j1,j2,j3,...jn}},
and returns all possibile comibinations of the form {ai,bi,...,ji}.
the result is a grid of n dimensions
 *)

(*this functions works by iterating over the first sublist and then sending it forward  (as the listBuilder) along with all sublists after the first sublist. 
The next step is to take what's given forward and iterate over the current first sublist 
add each element in the sublist to the list builder and send it forward.
Once there is only one sublist left, then for each element, add it to the listBuilder and append to the global GridList, then stop.
This recursive function doesn't return anything, it only builds a list by appending it to the global GridList.
*)

nestListGet[listBuilder_,nestGive_]:=If[(*Print[nestGive,"Length: ",Length[nestGive]];*)Length[nestGive]≤ 1,

Do[AppendTo[gridList,Flatten[{listBuilder,nestGive[[1,i]]}]],{i,1,Length[nestGive[[1]]]}],

Do[nestListGet[Flatten[{listBuilder,nestGive[[1,i]]}],nestGive[[2;;]]],{i,1,Length[nestGive[[1]]]}]];

nestListGet[{},basePoints];
Return[gridList]
]
minFunGen[initialBounds_,fun_,mixIt_(*,zoom_*)]:=Module[{intBorder,refinedBorder,gridPoints,gridMiddle,exteriorGrid,mid,zoom,newInitialBounds,interiorGridList,funPointsList,a,b,midl,midr,nullCatch,searchingPoints,boundingBox},
zoom=0.5 (*change this to change the amount the grid is zoomed in for each step*);
searchingPoints={};
(*take the parameter boundaries and use them to define the grid border later on*)
boundingBox={(#[[2]]-#[[1]])*0.5}&/@initialBounds;

(*get the middle points for the bounds*)
intBorder={#[[1]],0.5*(#[[1]]+#[[2]]),#[[2]]}&/@initialBounds;


(*get the intermediary parts of the border*)
refinedBorder={#[[1]],0.5*(#[[1]]+#[[2]]),#[[2]],0.5*(#[[2]]+#[[3]]),#[[3]]}&/@intBorder;

(*use the boarder to define the points in the grid. This is done by taking each parameter boundary and getting all possibilie comibinations with the other parameter boundaries*)
gridPoints=getGridPoints[(*intBorder*) refinedBorder];


(*mid=initialGuess*)
(*mid point is a uniform random point within the boundaries*) 
mid=(*0.5*(#[[1]]+#[[3]])&/@intBorder*)RandomVariate[UniformDistribution[initialBounds]];
interiorGridList=0.5*(mid+#)&/@gridPoints;

(*{gridPoints,{mid},interiorGridList}*)
(*get the function values for all the given points, that is, the static grid point defined by the boundaries, the random mid point, and the random interiorGridList defiend by the random mid point *)
funPointsList=Flatten[{fun[#],#},1]&/@(*gridPoints*)Flatten[{gridPoints,{mid},interiorGridList},1];
(*AppendTo[searchingPoints,funPointsList];*)

(*new mid point is the smallest point with respect to the function*)
mid=MinimalBy[funPointsList,First][[1,2;;]];

(*check if the new mid is on the border of the grid*)
gridMiddle=intBorder[[All,2]]; (*get the grid middle*)
exteriorGrid=DeleteCases[ 
getGridPoints[intBorder ](* get the basic grid which includes the exterior grid points.*),
gridMiddle(*remove grid middle from the grid points to be looked at*)
];

If[ (*check if mid is on the exterior*)
MemberQ[exteriorGrid,mid],
(*if it is then we won't zoom in the grid, just move it*)
newInitialBounds=Table[Flatten[{mid[[i]]-boundingBox[[i]],mid[[i]]+boundingBox[[i]]},1],{i,1,Length[boundingBox]}];,
(*if it is not on the extior grid, then we zoom in and refine the grid*)

(*define new boundaries by using the bounding box arroudn the current mid point and zoom in.*)
newInitialBounds=Table[Flatten[{mid[[i]]-zoom*boundingBox[[i]],mid[[i]]+zoom*boundingBox[[i]]},1],{i,1,Length[boundingBox]}];
(*Print["newInitialBounds: ",newInitialBounds];*)
];

(*update bounding box*)
boundingBox=(#[[2]]-#[[1]])*0.5&/@newInitialBounds;
(*Print[mid,": ",boundingBox(*,(intBorder[[1,2]]-intBorder[[1,1]])*)];*)


Do[
(*Print["newInitialBounds: ",j,newInitialBounds];*)
(*(*take the parameter boundaries and use them to define the grid border later on*)
intBorder={#[[1]],(*0.5*(#[[1]]+#[[2]]),*)#[[2]]}&/@newInitialBounds;

(*get the intermediary parts of the boarder*)
(*refinedBorder={#[[1]],0.5*(#[[1]]+#[[2]]),#[[2]],0.5*(#[[2]]+#[[3]]),#[[3]]}&/@intBorder;*)

(*use the boarder to define the points in the grid. This is done by taking each parameter boundary and getting all possibilie comibinations with the other parameter boundaries*)
gridPoints=getGridPoints[intBorder(*refinedBorder*)];


(*mid=initialGuess*)
(*mid=(*0.5*(#[[1]]+#[[3]])&/@*)RandomVariate[UniformDistribution[initialBounds]];*)
interiorGridList=0.5*(mid+#)&/@gridPoints;

(*{gridPoints,{mid},interiorGridList}*)
funPointsList=Flatten[{fun[#],#},1]&/@Flatten[{gridPoints,{mid},interiorGridList},1];

mid=MinimalBy[funPointsList,First][[1,2;;]];
Print[mid,": ",(intBorder[[1,2]]-intBorder[[1,1]])];
newInitialBounds=Table[{mid[[i]]-0.5*(intBorder[[i,2]]-intBorder[[i,1]])/2,mid[[i]]+0.5*(intBorder[[i,2]]-intBorder[[i,1]])/2},{i,1,Length[initialBounds]}];*)



(*take the parameter boundaries and use them to define the grid border later on*)
intBorder={#[[1]],0.5*(#[[1]]+#[[2]]),#[[2]]}&/@newInitialBounds;

(*get the intermediary parts of the boarder*)
refinedBorder={#[[1]],0.5*(#[[1]]+#[[2]]),#[[2]],0.5*(#[[2]]+#[[3]]),#[[3]]}&/@intBorder;

(*use the boarder to define the points in the grid. This is done by taking each parameter boundary and getting all possibilie comibinations with the other parameter boundaries*)
gridPoints=getGridPoints[(*intBorder*)refinedBorder];




mid=(*0.5*(#[[1]]+#[[3]])&/@intBorder*)RandomVariate[UniformDistribution[newInitialBounds]];
interiorGridList=0.5*(mid+#)&/@gridPoints;

(*{gridPoints,{mid},interiorGridList}*)
funPointsList=Flatten[{fun[#],#},1]&/@Flatten[{gridPoints,{mid},interiorGridList},1] (*gridPoints*);

(*mid=initialGuess*)
(*mid=0.5*(#[[1]]+#[[3]])&/@intBorder(*RandomVariate[UniformDistribution[initialBounds]]*);
interiorGridList=0.5*(mid+#)&/@gridPoints;*)
(*Print["Points to be analysed: ",Flatten[{gridPoints,{mid},interiorGridList},1]];*)
(*{gridPoints,{mid},interiorGridList}*)
(*funPointsList=Flatten[{fun[#],#},1]&/@(*gridPoints*)Flatten[{gridPoints,{mid},interiorGridList},1];*)
(*Print["Analysed: ",funPointsList];*)
(*AppendTo[searchingPoints,funPointsList];*)

mid=MinimalBy[funPointsList,First][[1,2;;]];

(*check if the new mid is on the border of the grid*)
gridMiddle=intBorder[[All,2]]; (*get the grid middle*)
exteriorGrid=DeleteCases[ 
getGridPoints[intBorder ](* get the basic grid which includes the exterior grid points.*),
gridMiddle(*remove grid middle from the grid points to be looked at*)
];

If[ (*check if mid is on the exterior*)
MemberQ[exteriorGrid,mid],
(*if it is then we won't zoom in the grid, just move it*)
newInitialBounds=Table[Flatten[{mid[[i]]-boundingBox[[i]],mid[[i]]+boundingBox[[i]]},1],{i,1,Length[boundingBox]}],
(*if it is not on the extior grid, then we zoom in and refine the grid*)
(*define new boundaries by using the bounding box arroudn the current mid point and zoom in.*)
newInitialBounds=Table[Flatten[{mid[[i]]-zoom*boundingBox[[i]],mid[[i]]+zoom*boundingBox[[i]]},1],{i,1,Length[boundingBox]}]
(*Print["newInitialBounds: ",newInitialBounds];*)];
(*Print[mid,": ",boundingBox];*)
,{j,1,mixIt}];
mid
(*searchingPoints*)
]

BvH relation

Data

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{refosmol/0.972,#}&/@Flatten[{
DeleteCases[rawdata[[5,3;;,9]],""][[;;-4]],
DeleteCases[rawdata[[5,3;;,20]],""][[;;-4]],
DeleteCases[rawdata[[5,3;;,31]],""][[;;-4]]
}],
{refosmol/0.602,#}&/@Flatten[{
DeleteCases[rawdata[[6,3;;,9]],""][[;;-4]],
DeleteCases[rawdata[[6,3;;,20]],""][[;;-4]],
DeleteCases[rawdata[[6,3;;,31]],""][[;;-4]]
}],
{refosmol/0.486,#}&/@Flatten[{
DeleteCases[rawdata[[7,3;;,9]],""][[;;-4]],
DeleteCases[rawdata[[7,3;;,21]],""][[;;-4]],
DeleteCases[rawdata[[7,3;;,32]],""][[;;-4]]
}]
},1];*)

Code

(*Export["bvh_data.csv",Prepend[bvhdata,{"Relative Inverse osmolality","Volume μm^3"}]];*)

Length@bvhrelData

(*Normalize data with respect to reference point*)
bvhrefVol=Mean[Select[bvhdata,#[[1]]==1&][[All,2]]];
bvhrelData={#[[1]],#[[2]]/bvhrefVol}&/@bvhdata;
refosmol=0.972;

(*fit BvH relation*)
bvhFit=LinearModelFit[bvhrelData,x,x];

(*get isotonic point wiso and vb*)
isotonic=1.00 (*mOsm/kg*);
bvhvb=bvhFit["BestFitParameters"][[1]];
bvhwiso=bvhFit[refosmol/isotonic]-bvhvb;

(*print results of analysis*)
Print["wiso: ",bvhwiso,", vb: ",bvhvb]
bvhFit["ParameterTable"]
Print["Durbin Watson D: ",LinearModelFit[errorData[bvhrelData][[All,{1,2}]],x,x]["DurbinWatsonD"]]

(*Plot BvH relation and plot means +/- SE*)
bvhplot=Show[ErrorListPlot[
errorData[bvhrelData],PlotRange->{{0,2.2},{0,2.5}},PlotStyle->Black,Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large,PlotMarkers->"OpenMarkers"],
Plot[{bvhFit[x]},{x,0,3},PlotRange->All,PlotStyle->Black]]

bvhFit["AdjustedRSquared"]

individual 2P model fitting

Data

Quit

(*(*cross-sectional area of oocytes exposed to 1.5 mol/kg of dmso in sea water*)
*)
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Code

(*Export["2P_model_data.csv",Prepend[Flatten[Table[Table[Flatten[{i,data[[i,j]]}],{j,1,Length[data[[i]]]}],{i,1,Length[data]}],1],{"Individual ID","Temperature Kelvin","Time seconds","Volume um^3"}]]*)

(*Transform into volume data*)
individ19C=Table[{273.1+19.5 (*temperature*),#[[1]]*60,((4 ((( #[[2]] (*cross-sectional area*)))^(3/2)))/(3 (Sqrt[π])))}&/@DeleteCases[data19C[[All,{1,i}]],{_?NumericQ,""}],{i,2,Length@data19C[[-1]]}];
individ10CR1=Table[{273.1+10(*temperature*),#[[1]],((4 (((#[[2]]))^(3/2)))/(3 (Sqrt[π])))}&/@DeleteCases[Select[data10C,#[[2]]== i&][[All,{6,7}]][[-40;;]],{_?NumericQ,"NaN"}],{i,1,Floor@Select[data10C,#[[1]]== 1&][[-1,2]]}];
individ10CR2=Table[{273.1+10 (*temperature*),#[[1]],((4 (((#[[2]]))^(3/2)))/(3 (Sqrt[π])))}&/@DeleteCases[Select[data10C,#[[2]]== i&][[All,{6,7}]][[-40;;]],{_?NumericQ,"NaN"}],{i,Floor@Select[data10C,#[[1]]== 1&][[-1,2]]+1,Floor@Select[data10C,#[[1]]== 2&][[-1,2]]}];
individ6CR1=Table[{273.1+6(*temperature*),#[[1]],((4 ((((*correctionFactor*) #[[2]]))^(3/2)))/(3 (Sqrt[π])))}&/@DeleteCases[Select[data6C,#[[2]]== i&][[All,{6,7}]][[-40;;]],{_?NumericQ,"NaN"}],{i,1,37}];
individ6CR2=Table[{273.1+6(*temperature*),#[[1]],((4 ((( (*correctionFactor*)#[[2]]))^(3/2)))/(3 (Sqrt[π])))}&/@DeleteCases[Select[data6C,#[[2]]== i&][[All,{6,7}]][[-40;;]],{_?NumericQ,"NaN"}],{i,38,Floor@data6C[[-1,2]]}];
(*individ6C = Join[individ6C1,individ6C2];*)

data=Join[individ19C,individ10CR1,individ10CR2,individ6CR1,individ6CR2];
temps={273.1+19.5 ,273.1+10 ,273.1+6};

(*GLOBAL PARAMETERS*)
isosmolality=1.000 * (1/(10^15)) (*L/((μm)^3)*) ; (*osmol/ ((μm)^3) *)
(*initialSalt=isosmolality; (* unless cells are preequilibrated with anisosmotic nonperm solution, this will be isosmolality *)*)
(*initialRelWaterVol=isosmolality/initialSalt;  (*initial relative water volume, should be 1 unless special case. *)*)
VbarEg=62.068/1.1135 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ; (*((μm)^3)/mol*)
VbarGly=92.09382/1.26 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
VbarDMSO=78.13 (*g·(mol^(-1))*)/1.1004 (*g (cm^(-3))*) * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
Vbar=VbarDMSO;
gasConst=0.08205 * ((10^15)/1)(* ((μm)^3) / L*); (* ((μm)^3) atm/(kelvin mol) *)
vbFraction=0.3114096329503619`;
cellCPAinit=0.0; (*initial moles of CPA --intracellular 2.5*)
extCPA=1.5 * (1/(10^15)) (*L/((μm)^3)*);(*osmol/((μm)^3) of CPA*)
extSalt=isosmolality;(* osmol/((μm)^3) of non-permeating salt*)
timeEnd=(23*60+60(*minute buffer*)); (*seconds*)

indivPwPsfitTemp[individualData_]:=Module[
{thisData,getRandomData,thisguessFit,volMax,volMin,volAvg,tmin,vtmin,dvtmin,fit1,fit2,fit1SS,fit2SS,intlpguess,intpsguess,tempKelvin,intVolRat,fitVoldata,pIndividVolume,len,tstart,vtstart,tmid,vtmid,tend,vtend,guessFit,volumeguess,lpguess,psguess},
thisData=individualData[[All,{2,3}]] (*{time (seconds), volume (μm^3)}*);
tempKelvin=individualData[[1,1]] ;
intVolRat=1.05;
intlpguess=0.002;
intpsguess=0.01;

{volMax,volMin,volAvg}={Max[thisData[[All,2]]],Min[thisData[[All,2]]],Mean[thisData[[All,2]]]};

(*define 2P model*)
pIndividVolume =ParametricNDSolveValue[{
w'[t]==-lp (*((μm)/(atm s))*)* ((6^(2/3)) (π^(1/3)) (totalIsoVol^(2/3)))(*surfaceArea*) gasConst tempKelvin * (extCPA+extSalt-((s[t]+isosmolality(totalIsoVol-vbFraction*totalIsoVol) (*nni*))/w[t])),
s'[t]== ps (*((μm)/s)*)*   ((6^(2/3)) (π^(1/3)) (totalIsoVol^(2/3)))(*surfaceArea*) (extCPA-(s[t]/w[t])),
vt'[t]==-lp (*((μm)/(atm s))*)*((6^(2/3)) (π^(1/3)) (totalIsoVol^(2/3)))(*surfaceArea*) gasConst tempKelvin * (extCPA+extSalt-((s[t]+isosmolality(totalIsoVol-vbFraction*totalIsoVol)(*nni*))/w[t]))+Vbar  ps (*((μm)/s) *) ((6^(2/3)) (π^(1/3)) (totalIsoVol^(2/3)))(*surfaceArea*) (extCPA-(s[t]/w[t])),

w[0]==(totalIsoVol-vbFraction*totalIsoVol), 
s[0]==cellCPAinit,
vt[0]==totalIsoVol
},
vt,
{t,0.,timeEnd},
{totalIsoVol,lp,ps}];

(*(*create mean data points to solve nonlinear equation to get guess fits*)
len=Length[thisData];
{tstart,vtstart}=Mean[thisData[[2;;5]]];
{tmid,vtmid}=Mean[thisData[[Floor[len/2]-1;;Floor[len/2]+2]]];
{tend,vtend}=Mean[thisData[[-3;;]]];

guessFit=FindRoot[{
pIndividVolume[totalIsoVol,lp,ps][tstart]== vtstart,
pIndividVolume[totalIsoVol,lp,ps][tmid]== vtmid,
pIndividVolume[totalIsoVol,lp,ps][tend]== vtend
},
{{totalIsoVol,volAvg,volMin,volMax*1.2},
{lp,0.001,0,.1},
{ps,0.1,0,1}},
MaxIterations->200];

{volumeguess,lpguess,psguess}={totalIsoVol,lp,ps}/.guessFit;*)

(*randomly select 3 datapoints and then solve the a nonlinear equation.
Then sort based on sum of squares with respect to the whole data set.
then select the minimum sum of squares.*)
{volumeguess,lpguess,psguess}=Sort[
Table[
getRandomData=RandomChoice[thisData,3];

thisguessFit=FindRoot[{
pIndividVolume[totalIsoVol,lp,ps][getRandomData[[1,1]]]== getRandomData[[1,2]],
pIndividVolume[totalIsoVol,lp,ps][getRandomData[[2,1]]]== getRandomData[[2,2]],
pIndividVolume[totalIsoVol,lp,ps][getRandomData[[3,1]]]== getRandomData[[3,2]]
},
{{totalIsoVol,volAvg,volMin,volMax*1.2},
{lp,0.001,0,.1},
{ps,0.1,0,1}},
MaxIterations->20];
{Sum[((pIndividVolume[totalIsoVol,lp,ps][thisData[[i,1]]]) -thisData[[i,2]])^2,{i,1,Length[thisData]}],
totalIsoVol,lp,ps}/.thisguessFit,
{i,1,10}
]][[1,{2,3,4}]];

(*

fitVoldata=thisData;
{tmin,vtmin}= Mean[SortBy[fitVoldata,Last][[;;3]]];
dvtmin=LinearModelFit[SortBy[fitVoldata,Last][[;;3]],x,x]["BestFitParameters"][[-1]];
{tend,vtend}=Mean[fitVoldata[[-3;;]]];

(*slope at tmin is dvtmin*)
fit1=FindRoot[{pIndividVolume[totalIsoVol,lp,ps][tmin]== vtmin,pIndividVolume[totalIsoVol,lp,ps]'[tmin]== dvtmin,pIndividVolume[totalIsoVol,lp,ps][tend]== vtend},{{totalIsoVol,vtmin*intVolRat,vtmin,vtmin*2},{lp,intlpguess,0,0.1},{ps,intpsguess,0,1}},MaxIterations->100];

(*slope at tmin is 0*)
fit2=FindRoot[{pIndividVolume[totalIsoVol,lp,ps][tmin]== vtmin,pIndividVolume[totalIsoVol,lp,ps]'[tmin]== 0,pIndividVolume[totalIsoVol,lp,ps][tend]== vtend},{{totalIsoVol,vtmin*intVolRat,vtmin,vtmin*2},{lp,intlpguess,0,0.1},{ps,intpsguess,0,1}},MaxIterations->100];

fit1SS = Sum[((pIndividVolume[totalIsoVol,lp,ps][fitVoldata[[i,1]]]/.fit1) -fitVoldata[[i,2]])^2,{i,1,Length[fitVoldata]}];
fit2SS = Sum[((pIndividVolume[totalIsoVol,lp,ps][fitVoldata[[i,1]]]/.fit2) -fitVoldata[[i,2]])^2,{i,1,Length[fitVoldata]}];

{volumeguess,lpguess,psguess}={totalIsoVol,lp,ps}/.If[fit1SS<fit2SS,fit1,fit2];*)


(*fit the 2P model to the data*)
thismodel= NonlinearModelFit[thisData,
{(*2P model*)
pIndividVolume[intVol,lp,ps][t],

(*contraints*)
volMin<intVol<(volMax*1.2),
(lpguess/10)<lp<(10*lpguess),
(psguess/10)<ps<(10*psguess)
},
(*Parameters*)
{{intVol,volumeguess},
{lp,lpguess },
{ps,psguess }},

(*variables*)
t(*, Method->"NMinimize"*)];
Return[
{tempKelvin,intVol,lp,ps}/.thismodel["BestFitParameters"]
]
]

modelFits=Table[
(*Print[i,"/",Length[data]];*)
indivPwPsfitTemp[data[[i]]],
{i,1,Length[data]}
]

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prunedModelFits=Table[FindAnomalies[{Log[#[[1]]],Log[#[[2]]]}&/@Select[modelFits,#[[1]]== thisTemp&][[All,{3,4}]],"AnomalyBooleanList"],{thisTemp,temps}]

prunedModelFitsBool={{False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,True,False,False,False,False,False,True,False,False,False,False,False,False,True,False,False,False},{False,False,False,False,False,False,False,False,False,False,False,False,False,False,True,False,True,False,False,False,False,False,False,True,False,False,False,False,False,False,False,False,False,True,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,True,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False},{False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,False,True,False,False,False,False,False,False,False,False,False,False,False}};

volume2P=ParametricNDSolveValue[{
w'[t]==-lp (*((μm)/(atm s))*)* ((6^(2/3)) (π^(1/3)) (totalIsoVol^(2/3)))(*surfaceArea*) gasConst tempKelvin * (extCPA+extSalt-((s[t]+isosmolality(totalIsoVol-vbFraction*totalIsoVol) (*nni*))/w[t])),
s'[t]== ps (*((μm)/s)*)*   ((6^(2/3)) (π^(1/3)) (totalIsoVol^(2/3)))(*surfaceArea*) (extCPA-(s[t]/w[t])),
vt'[t]==-lp (*((μm)/(atm s))*)*((6^(2/3)) (π^(1/3)) (totalIsoVol^(2/3)))(*surfaceArea*) gasConst tempKelvin * (extCPA+extSalt-((s[t]+isosmolality(totalIsoVol-vbFraction*totalIsoVol)(*nni*))/w[t]))+Vbar  ps (*((μm)/s) *) ((6^(2/3)) (π^(1/3)) (totalIsoVol^(2/3)))(*surfaceArea*) (extCPA-(s[t]/w[t])),

w[0]==(totalIsoVol-vbFraction*totalIsoVol), 
s[0]==cellCPAinit,
vt[0]==totalIsoVol
},
vt,
{t,0.,timeEnd},
{tempKelvin,totalIsoVol,lp,ps}];

normData=Flatten[Table[{#[[1]],#[[2]]/modelFits[[i,2]]}&/@data[[i,All,{2,3}]],{i,1,Length[prunedModelFitsBool[[1]]]}],1];

{thisTemp,meanTotVol,meanLp,meanPs}=Mean[DeleteCases[Table[If[prunedModelFitsBool[[1,i]],(*if pruned then do nothing*),modelFits[[i]]],{i,1,Length[prunedModelFitsBool[[1]]]}],Null]]

normData19C=Flatten[DeleteCases[Table[If[prunedModelFitsBool[[1,i]],(*if pruned then do nothing*),{#[[1]],#[[2]]/modelFits[[i,2]]}&/@data[[i,All,{2,3}]]],{i,1,Length[prunedModelFitsBool[[1]]]}],Null],1];
{temp19C,meanTotVol19C,meanLp19C,meanPs19C}=Mean[DeleteCases[Table[If[prunedModelFitsBool[[1,i]],(*if pruned then do nothing*),modelFits[[i]]],{i,1,Length[prunedModelFitsBool[[1]]]}],Null]]

normData10C=Flatten[DeleteCases[Table[If[prunedModelFitsBool[[2,i-Length[prunedModelFitsBool[[1]]]]],(*if pruned then do nothing*),{#[[1]],#[[2]]/modelFits[[i,2]]}&/@data[[i,All,{2,3}]]],{i,Length[prunedModelFitsBool[[1]]]+1,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]}],Null],1];
{temp10C,meanTotVol10C,meanLp10C,meanPs10C}=Mean[DeleteCases[Table[If[prunedModelFitsBool[[2,i-Length[prunedModelFitsBool[[1]]]]],(*if pruned then do nothing*),modelFits[[i]]],{i,Length[prunedModelFitsBool[[1]]]+1,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]}],Null]]

normData6C=Flatten[DeleteCases[Table[If[prunedModelFitsBool[[3,i-(Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]])]],(*if pruned then do nothing*),{#[[1]],#[[2]]/modelFits[[i,2]]}&/@data[[i,All,{2,3}]]],{i,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]+1,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]+Length[prunedModelFitsBool[[3]]]}],Null],1];
{temp6C,meanTotVol6C,meanLp6C,meanPs6C}=Mean[DeleteCases[Table[If[prunedModelFitsBool[[3,i-(Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]])]],(*if pruned then do nothing*),modelFits[[i]]],{i,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]+1,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]+Length[prunedModelFitsBool[[3]]]}],Null]]

Show[ErrorListPlot[
{errorData[normData19C],
errorBinData[normData10C,30],
errorBinData[normData6C,30]},PlotRange-> {{0,1300},{0.5,1.15}},PlotMarkers-> "OpenMarkers",PlotLegends-> {"20 °C","10 °C","6 °C"},Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],Plot[
{volume2P[temp19C,meanTotVol19C,meanLp19C,meanPs19C][t]/meanTotVol19C,
volume2P[temp10C,meanTotVol10C,meanLp10C,meanPs10C][t]/meanTotVol10C,
volume2P[temp6C,meanTotVol6C,meanLp6C,meanPs6C][t]/meanTotVol6C},{t,0,1300},PlotRange->All]]

(*getting standard error*)

StandardDeviation[DeleteCases[Table[If[prunedModelFitsBool[[1,i]],(*if pruned then do nothing*),modelFits[[i]]],{i,1,Length[prunedModelFitsBool[[1]]]}],Null]]/Length[DeleteCases[Table[If[prunedModelFitsBool[[1,i]],(*if pruned then do nothing*),modelFits[[i]]],{i,1,Length[prunedModelFitsBool[[1]]]}],Null]]^.5

{0.`,10233.571490954902`,0.00007809261754907245`*60,0.003302857547612829`*60}

StandardDeviation[DeleteCases[Table[If[prunedModelFitsBool[[2,i-Length[prunedModelFitsBool[[1]]]]],(*if pruned then do nothing*),modelFits[[i]]],{i,Length[prunedModelFitsBool[[1]]]+1,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]}],Null]]/Length[DeleteCases[Table[If[prunedModelFitsBool[[2,i-Length[prunedModelFitsBool[[1]]]]],(*if pruned then do nothing*),modelFits[[i]]],{i,Length[prunedModelFitsBool[[1]]]+1,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]}],Null]]^.5

{0.`,10845.143158726869`,0.000019609186395121656`*60,0.0004941697519687743`*60}

StandardDeviation[DeleteCases[Table[If[prunedModelFitsBool[[3,i-(Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]])]],(*if pruned then do nothing*),modelFits[[i]]],{i,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]+1,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]+Length[prunedModelFitsBool[[3]]]}],Null]]/Length[DeleteCases[Table[If[prunedModelFitsBool[[3,i-(Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]])]],(*if pruned then do nothing*),modelFits[[i]]],{i,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]+1,Length[prunedModelFitsBool[[1]]]+Length[prunedModelFitsBool[[2]]]+Length[prunedModelFitsBool[[3]]]}],Null]]^.5

(*now do the arrhenious equation*)

modelFits[[1]]

Table[Length[Select[modelFits,#[[1]]==temp&]],{temp,DeleteDuplicates[modelFits[[All,1]]]}]

Map[Length,prunedModelFits]

prunedModelFits={{{-6.7440105491506435`,-2.7321605297382354`},{-6.224089180735264`,-2.608168422530666`},{-6.089387568250579`,-2.7506006544247206`},{-6.146225621823198`,-3.0415782878459416`},{-6.503915973179043`,-2.768755702177625`},{-6.497906524704223`,-2.8787965490601652`},{-6.417137653264665`,-2.7410652731849705`},{-6.9232161981726135`,-2.9688898344743784`},{-6.80907243563599`,-3.044178068842381`},{-6.960399172896502`,-3.283535386349909`},{-6.350925942518414`,-2.6740847496860467`},{-6.177131579844852`,-2.021710822865478`},{-5.978828284762242`,-2.3108103303225374`},{-6.657712090652529`,-2.886359036005498`},{-6.2397313566549375`,-2.063402763980341`},{-6.157642351375336`,-2.557673418639458`},{-6.193014603358273`,-2.400715399824365`},{-5.974999959003579`,-2.6439449245115867`},{-6.214639138390529`,-2.388593422907367`},{-6.09059461111666`,-2.441970475757034`},{-6.078175965173237`,-2.635283224502716`},{-6.09332043345083`,-2.6454257864771713`},{-5.769915714600242`,-2.1166780344914646`},{-6.077714305300262`,-2.5899297914876653`},{-5.704787432407925`,-2.147951994804486`},{-6.160081412637387`,-2.5357124411149665`},{-6.176207061968381`,-2.5280158940655366`},{-5.8756042887383515`,-2.4432897963247986`},{-6.499942835234048`,-2.3776558388828226`},{-6.047383417214718`,-2.554608307932452`},{-6.102118768784633`,-2.4501570618816952`},{-6.365893624275426`,-2.5840887633337206`},{-6.33240201727933`,-2.322715402556342`},{-6.029374574299109`,-2.5804063129254495`},{-6.54997109345444`,-2.5551950227657816`},{-6.4195341023041035`,-2.746827848862301`},{-6.131669005353493`,-2.597751296972138`},{-6.167163051951868`,-2.697071213160286`},{-6.536680571889855`,-2.1022786542628125`},{-5.568719548956941`,-1.9950020207645542`},{-6.156377961006003`,-2.5169346337829555`},{-6.146886419350706`,-2.3245468980560724`},{-6.055600884726018`,-2.5242236291599767`},{-6.595667135506043`,-2.0740665243138703`},{-6.767194023241209`,-2.4090347094603213`},{-6.239945499156253`,-2.1868430960914687`},{-6.308655079306923`,-2.5479301105985668`},{-6.4927776089737685`,-1.9258223584082927`},{-6.236172274637146`,-2.5695714532050733`},{-6.310150087892197`,-2.647061294111817`},{-5.983388288268629`,-2.3654624701737887`},{-6.489166234042473`,-2.6671594066457276`},{-6.6158943430346175`,-2.238514488874217`}},{{-7.592030657686387`,-3.9077567711234193`},{-7.046964235349158`,-4.956123012822024`},{-7.322383776466654`,-3.668037109019615`},{-7.155082195314521`,-5.455286937312314`},{-7.234547831842777`,-4.643951355192055`},{-7.218052074108469`,-4.8670365207871615`},{-7.032455541136299`,-5.515032182730999`},{-7.1823537872787`,-4.727361021912248`},{-7.330216384347115`,-4.394613436654598`},{-7.513987859680243`,-4.946824422685922`},{-7.289240257615079`,-3.9730643375526986`},{-7.2103824066782565`,-4.923153518768986`},{-7.578934258398076`,-4.331844248882937`},{-7.1691318745415025`,-4.682578891196071`},{-7.3248080717530835`,-4.578785263063137`},{-7.546488015712755`,-4.060472866556783`},{-7.4833227348268805`,-4.307627623282007`},{-7.123299532469197`,-4.9693878188461085`},{-7.005130394195056`,-4.644806273099794`},{-7.739635375774626`,-3.8848615514965696`},{-7.076248507279186`,-5.095237894314728`},{-7.7149890369913345`,-4.680608865810477`},{-8.19597843094193`,-4.341801855507581`},{-7.775652166949779`,-4.9043854172045815`},{-7.663398081095296`,-4.403386481946326`},{-7.291045446940799`,-4.861731466478353`},{-8.15589873302663`,-4.446021097952063`},{-7.669083613369884`,-5.161155217084716`},{-7.407740626214474`,-4.453080728549475`},{-6.917164814241275`,-5.025685665605691`},{-7.38657004591829`,-4.256819674935594`},{-6.890798724409022`,-5.518943786053945`},{-6.993788892383486`,-4.933347302290366`},{-7.239299288811461`,-5.239306051266591`},{-7.193987424792149`,-5.419466826653372`},{-7.302641138502363`,-4.318775758511755`},{-7.30264113850238`,-4.318775758511733`},{-7.234281890728871`,-5.16351374102585`},{-7.51764195345149`,-4.149035969124231`},{-7.1252087936765225`,-4.571145172873097`},{-7.108039147790808`,-4.779059852474294`},{-7.673271288169633`,-4.686071782232138`},{-7.04646137676058`,-4.868643813892077`},{-6.903894701553287`,-4.9491063640933435`},{-7.516845420754647`,-4.691913665536308`},{-7.089797666517962`,-4.918028576135925`},{-7.154167766749741`,-5.053329067546195`},{-7.210604729190172`,-4.923957609253733`},{-7.1614384330439815`,-5.223156576107503`},{-6.976501265901588`,-4.941782806543945`},{-7.259655656428391`,-5.063146927047013`},{-7.187234001645936`,-4.783911934898315`},{-7.241224752250817`,-4.830980242144928`},{-7.631237260698166`,-4.480320744090045`},{-7.142490674911826`,-5.204368563616437`},{-7.210604729196685`,-4.923957609241825`},{-7.06246538376557`,-5.356710439252041`},{-7.239160288611194`,-3.9789415365249097`},{-7.0111524714279625`,-4.782990396751671`},{-7.286274193353096`,-4.9961757771642565`},{-7.031013345614704`,-4.892383057703856`},{-7.070885045852676`,-4.695349306857715`},{-7.166502091746847`,-5.099349522910383`},{-7.040622951609836`,-5.0330717818966`},{-7.093954667293765`,-4.89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gasR= 1.987*10^-3(* kcal mol^-1 K^-1*);
arrheniusData=Flatten[Table[{1000/temps[[i]],#[[1]],#[[2]]}&/@prunedModelFits[[i]],{i,1,Length[temps]}],1];
lpArrheniusFit=LinearModelFit[arrheniusData[[All,{1,2}]],x /(1000*gasR),x];
psArrheniusFit=LinearModelFit[arrheniusData[[All,{1,3}]],x /(1000*gasR),x];

Print["Fit Lp:"]
lpArrheniusFit["ParameterTable"]
Print["Fit Ps:"]
psArrheniusFit["ParameterTable"]
Show[
ErrorListPlot[{errorData[arrheniusData[[All,{1,2}]]],errorData[arrheniusData[[All,{1,3}]]]},PlotRange-> All,PlotStyle->Black,Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large,PlotMarkers->"OpenMarkers"],
Plot[{lpArrheniusFit[temp],psArrheniusFit[temp]},{temp,0,4},PlotRange->All,PlotStyle-> {{Black,Thick},{Black,Dashed}},PlotLegends->{"Lp","Ps"}]
]

gasR= 1.987*10^-3(* kcal mol^-1 K^-1*);
lpA =16.06038610207711`
 lpE=-6.555277296921298`*1000*gasR
psA =41.83189898749541`
 psE=-13.04594344564523`*1000*gasR

Osmotic Damage

Data

{NaCldata,SucrosandROedata}={{{0.`,90.`,0.8549222797927462`},{0.`,90.`,0.9151515151515152`},{0.`,90.`,0.975`},{0.`,90.`,0.9230769230769231`},{0.5`,2.`,0.9433962264150944`},{0.5`,2.`,0.9652173913043478`},{0.5`,2.`,0.9155844155844156`},{0.5`,6.`,0.9439252336448598`},{0.5`,6.`,0.9073170731707317`},{0.5`,6.`,0.9702970297029703`},{0.5`,15.`,0.912`},{0.5`,15.`,0.912568306010929`},{0.5`,15.`,0.9099099099099099`},{0.5`,30.`,0.8834355828220859`},{0.5`,30.`,0.9096385542168675`},{0.5`,50.`,0.88`},{0.5`,50.`,0.835820895522388`},{0.5`,50.`,0.926829268292683`},{0.5`,75.`,0.8597560975609756`},{0.5`,75.`,0.755`},{0.5`,75.`,0.7405405405405405`},{0.5`,90.`,0.5185185185185185`},{0.5`,90.`,0.646875`},{1.`,2.`,0.8917525773195877`},{1.`,2.`,0.792332268370607`},{1.`,2.`,0.7478632478632479`},{1.`,6.`,0.3754646840148699`},{1.`,6.`,0.3607305936073059`},{1.`,6.`,0.2863849765258216`},{1.`,15.`,0.09170305676855896`},{1.`,15.`,0.07352941176470588`},{1.`,15.`,0.14012738853503184`},{1.`,30.`,0.0044444444444444444`},{1.`,30.`,0.04807692307692308`},{1.`,30.`,0.01680672268907563`},{1.`,50.`,0.014184397163120567`},{1.`,50.`,0.`},{1.`,50.`,0.`},{1.`,75.`,0.`},{1.`,75.`,0.`},{1.`,75.`,0.`},{1.`,90.`,0.`},{1.`,90.`,0.`},{1.`,90.`,0.`},{1.5`,2.`,0.3116883116883117`},{1.5`,2.`,0.1349206349206349`},{1.5`,2.`,0.21714285714285714`},{1.5`,6.`,0.`},{1.5`,6.`,0.`},{1.5`,6.`,0.01282051282051282`},{1.5`,15.`,0.`},{1.5`,15.`,0.006369426751592357`},{1.5`,15.`,0.`},{1.5`,30.`,0.`},{1.5`,30.`,0.`},{1.5`,30.`,0.008`},{1.5`,50.`,0.`},{1.5`,50.`,0.`},{1.5`,50.`,0.`},{1.5`,75.`,0.`},{1.5`,75.`,0.`},{1.5`,75.`,0.`},{1.5`,90.`,0.`},{1.5`,90.`,0.`},{1.5`,90.`,0.`}},{{1.`,0.`,90.`,1.`},{1.`,0.`,90.`,0.9504132231404959`},{1.`,0.`,90.`,0.95`},{1.`,0.`,90.`,0.9952380952380953`},{1.`,0.5`,2.`,0.954954954954955`},{1.`,0.5`,2.`,0.968`},{1.`,0.5`,2.`,0.9401709401709402`},{1.`,0.5`,6.`,0.9617224880382775`},{1.`,0.5`,6.`,0.8677685950413223`},{1.`,0.5`,6.`,0.9144736842105263`},{1.`,0.5`,15.`,0.7988505747126436`},{1.`,0.5`,15.`,0.9466666666666667`},{1.`,0.5`,15.`,0.9140625`},{1.`,0.5`,30.`,0.7397260273972602`},{1.`,0.5`,30.`,0.7023255813953488`},{1.`,0.5`,30.`,0.753731343283582`},{1.`,0.5`,50.`,0.2517482517482518`},{1.`,0.5`,50.`,0.41358024691358025`},{1.`,0.5`,50.`,0.3`},{1.`,0.5`,75.`,0.13218390804597702`},{1.`,0.5`,75.`,0.14912280701754385`},{1.`,0.5`,75.`,0.12745098039215685`},{1.`,0.5`,90.`,0.08536585365853659`},{1.`,0.5`,90.`,0.1297709923664122`},{1.`,0.5`,90.`,0.11242603550295859`},{1.`,1.`,3.`,0.21348314606741572`},{1.`,1.`,3.`,0.18128654970760233`},{1.`,1.`,3.`,0.19230769230769232`},{1.`,1.`,6.`,0.16666666666666666`},{1.`,1.`,6.`,0.057803468208092484`},{1.`,1.`,6.`,0.0821256038647343`},{1.`,1.`,15.`,0.019704433497536946`},{1.`,1.`,15.`,0.05228758169934641`},{1.`,1.`,15.`,0.046875`},{1.`,1.`,30.`,0.`},{1.`,1.`,30.`,0.`},{1.`,1.`,30.`,0.012738853503184714`},{1.`,1.`,50.`,0.`},{1.`,1.`,50.`,0.006289308176100629`},{1.`,1.`,50.`,0.`},{1.`,1.`,75.`,0.006060606060606061`},{1.`,1.`,75.`,0.00641025641025641`},{1.`,1.`,75.`,0.0045871559633027525`},{1.`,1.`,90.`,0.`},{1.`,1.`,90.`,0.`},{1.`,1.`,90.`,0.`},{1.`,1.5`,3.`,0.021052631578947368`},{1.`,1.5`,3.`,0.`},{1.`,1.5`,3.`,0.01`},{1.`,1.5`,6.`,0.`},{1.`,1.5`,6.`,0.`},{1.`,1.5`,6.`,0.`},{1.`,1.5`,15.`,0.`},{1.`,1.5`,15.`,0.`},{1.`,1.5`,15.`,0.06896551724137931`},{1.`,1.5`,30.`,0.`},{1.`,1.5`,30.`,0.`},{1.`,1.5`,30.`,0.`},{1.`,1.5`,50.`,0.`},{1.`,1.5`,50.`,0.`},{1.`,1.5`,50.`,0.`},{1.`,1.5`,75.`,0.`},{1.`,1.5`,75.`,0.`},{1.`,1.5`,75.`,0.`},{1.`,1.5`,90.`,0.0072992700729927005`},{1.`,1.5`,90.`,0.005681818181818182`},{1.`,1.5`,90.`,0.`},{1.`,2.`,5.`,0.`},{1.`,2.`,5.`,0.`},{1.`,2.`,5.`,0.`},{1.`,2.`,9.`,0.`},{1.`,2.`,9.`,0.`},{1.`,2.`,9.`,0.`},{1.`,2.`,15.`,0.`},{1.`,2.`,15.`,0.`},{1.`,2.`,15.`,0.`},{1.`,2.`,30.`,0.`},{1.`,2.`,30.`,0.`},{1.`,2.`,30.`,0.`},{1.`,2.`,50.`,0.`},{1.`,2.`,50.`,0.`},{1.`,2.`,75.`,0.`},{1.`,2.`,75.`,0.`},{1.`,2.`,75.`,0.`},{1.`,2.`,90.`,0.`},{1.`,2.`,90.`,0.`},{1.`,2.`,90.`,0.`},{1.`,0.`,90.`,0.8322147651006712`},{1.`,0.`,90.`,0.6716417910447762`},{1.`,0.`,90.`,0.8`},{1.`,0.`,90.`,0.7846153846153846`},{0.8`,0.`,2.`,0.7873563218390804`},{0.8`,0.`,2.`,0.7906976744186046`},{0.8`,0.`,2.`,0.8432835820895522`},{0.8`,0.`,6.`,0.78125`},{0.8`,0.`,6.`,0.8106060606060606`},{0.8`,0.`,6.`,0.8062015503875969`},{0.8`,0.`,15.`,0.837037037037037`},{0.8`,0.`,15.`,0.8472906403940886`},{0.8`,0.`,15.`,0.8692307692307693`},{0.8`,0.`,30.`,0.7759562841530054`},{0.8`,0.`,30.`,0.7588235294117647`},{0.8`,0.`,30.`,0.6124031007751938`},{0.8`,0.`,50.`,0.7322834645669292`},{0.8`,0.`,50.`,0.8194444444444444`},{0.8`,0.`,50.`,0.1641025641025641`},{0.8`,0.`,75.`,0.7062937062937062`},{0.8`,0.`,75.`,0.7213114754098361`},{0.8`,0.`,75.`,0.7851239669421488`},{0.8`,0.`,90.`,0.572289156626506`},{0.8`,0.`,90.`,0.6242424242424243`},{0.8`,0.`,90.`,0.5128205128205128`},{0.7`,0.`,2.`,0.8378378378378378`},{0.7`,0.`,2.`,0.837037037037037`},{0.7`,0.`,2.`,0.7643312101910829`},{0.7`,0.`,6.`,0.8779342723004695`},{0.7`,0.`,6.`,0.8273809523809523`},{0.7`,0.`,6.`,0.7906976744186046`},{0.7`,0.`,15.`,0.400990099009901`},{0.7`,0.`,15.`,0.7699115044247787`},{0.7`,0.`,15.`,0.6909090909090909`},{0.7`,0.`,30.`,0.5769230769230769`},{0.7`,0.`,30.`,0.6626984126984127`},{0.7`,0.`,30.`,0.5512820512820513`},{0.7`,0.`,50.`,0.26811594202898553`},{0.7`,0.`,50.`,0.20930232558139536`},{0.7`,0.`,50.`,0.427536231884058`},{0.7`,0.`,75.`,0.5636363636363636`},{0.7`,0.`,75.`,0.3275862068965517`},{0.7`,0.`,75.`,0.46987951807228917`},{0.7`,0.`,90.`,0.34972677595628415`},{0.7`,0.`,90.`,0.3181818181818182`},{0.7`,0.`,90.`,0.3888888888888889`},{0.6`,0.`,2.`,0.6377952755905512`},{0.6`,0.`,2.`,0.8127659574468085`},{0.6`,0.`,2.`,0.6239316239316239`},{0.6`,0.`,6.`,0.7137096774193549`},{0.6`,0.`,6.`,0.7214611872146118`},{0.6`,0.`,6.`,0.6758241758241759`},{0.6`,0.`,15.`,0.6384615384615384`},{0.6`,0.`,15.`,0.5906432748538012`},{0.6`,0.`,15.`,0.7684729064039408`},{0.6`,0.`,30.`,0.5238095238095238`},{0.6`,0.`,30.`,0.4897959183673469`},{0.6`,0.`,30.`,0.5751295336787565`},{0.6`,0.`,50.`,0.4388888888888889`},{0.6`,0.`,50.`,0.4117647058823529`},{0.6`,0.`,50.`,0.3356164383561644`},{0.6`,0.`,75.`,0.09375`},{0.6`,0.`,75.`,0.062146892655367235`},{0.6`,0.`,75.`,0.13043478260869565`},{0.6`,0.`,90.`,0.05555555555555555`},{0.6`,0.`,90.`,0.08024691358024691`},{0.6`,0.`,90.`,0.0364963503649635`},{0.5`,0.`,2.`,0.7365269461077845`},{0.5`,0.`,2.`,0.6183574879227053`},{0.5`,0.`,2.`,0.7202797202797203`},{0.5`,0.`,6.`,0.6484375`},{0.5`,0.`,6.`,0.7668393782383419`},{0.5`,0.`,6.`,0.6686746987951807`},{0.5`,0.`,15.`,0.5989583333333334`},{0.5`,0.`,15.`,0.6502732240437158`},{0.5`,0.`,15.`,0.6416184971098265`},{0.5`,0.`,30.`,0.34074074074074073`},{0.5`,0.`,30.`,0.39634146341463417`},{0.5`,0.`,30.`,0.4228187919463087`},{0.5`,0.`,50.`,0.18518518518518517`},{0.5`,0.`,50.`,0.0728476821192053`},{0.5`,0.`,50.`,0.13970588235294118`},{0.5`,0.`,75.`,0.040983606557377046`},{0.5`,0.`,75.`,0.11612903225806452`},{0.5`,0.`,75.`,0.06206896551724138`},{0.5`,0.`,90.`,0.04838709677419355`},{0.5`,0.`,90.`,0.1271186440677966`},{0.5`,0.`,90.`,0.049689440993788817`}}};

Code

(*Export["osmotic_damage_NaCldata.csv",Prepend[NaCldata, {"Added NaCl to Seawater osmol/kg","Time minutes","Survival (development to 4-arm-plateaus stage/total count)"}]];
Export["osmotic_damage_SucrosandROedata.csv",Prepend[SucrosandROedata,{"Osmolality of Seawater osmol/kg","Added Sucrose to Seawater osmol/kg", "Time minutes","Survival (development to 4-arm-plateaus stage/total count)"}]];*)

controlNaCl=Mean[Select[NaCldata,#[[1]]== 0&][[All,3]]];
fittingNaClData={1+#[[1]](*osmol/kg*),#[[2]]*60(*seconds*)+30 (*techician average time*),#[[3]]/controlNaCl(*normalized survival*)}&/@NaCldata;
osmolsNaCl=Sort@Select[DeleteDuplicates[fittingNaClData[[All,1]]],#>1&];
times=Sort@DeleteDuplicates[fittingNaClData[[All,2]]];
fitNaCl=Table[
Select[fittingNaClData,#[[1]]== osmol&][[All,{2,3}]],
{osmol,osmolsNaCl}
];

succontrolsurvival = Mean[{1,
0.950413223,
0.95,
0.995238095
}];
fittingSucData={#[[1]] + #[[2]] (*osmol*),#[[3]]*60(*seconds*)+45 (*techician average time*),#[[4]]/succontrolsurvival}&/@Select[SucrosandROedata,#[[1]]== 1&& #[[2]] > 0&];
osmolsSuc=DeleteDuplicates[fittingSucData[[All,1]]];

rocontrolsurvival = Mean[{0.832214765,
0.671641791,
0.8,
0.784615385
}];
relrosurv ={#[[1]],#[[3]]*60(*seconds*) +30 (*techician average time*),#[[4]]/rocontrolsurvival}&/@ Select[Select[SucrosandROedata,#[[2]] == 0&],#[[1]]<1.&];
osmolsRO=DeleteDuplicates[relrosurv[[All,1]]];

(*GLOBAL PARAMETERS*)
isosmolality=1.000 * (1/(10^15)) (*L/((μm)^3)*) ; (*osmol/ ((μm)^3) *)
(*initialSalt=isosmolality; (* unless cells are preequilibrated with anisosmotic nonperm solution, this will be isosmolality *)*)
(*initialRelWaterVol=isosmolality/initialSalt;  (*initial relative water volume, should be 1 unless special case. *)*)
VbarEg=62.068/1.1135 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ; (*((μm)^3)/mol*)
VbarGly=92.09382/1.26 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
VbarDMSO=78.13 (*g·(mol^(-1))*)/1.1004 (*g (cm^(-3))*) * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
Vbar=VbarDMSO;
gasConst=0.08205 * ((10^15)/1)(* ((μm)^3) / L*); (* ((μm)^3) atm/(kelvin mol) *)
vbFraction=0.3114096329503619`;
cellCPAinit=0.0; (*initial moles of CPA --intracellular 2.5*)
(*extCPA=1.5 * (1/(10^15)) (*L/((μm)^3)*);(*osmol/((μm)^3) of CPA*)
extSalt=isosmolality;(* osmol/((μm)^3) of non-permeating salt*)*)
timeEnd=(90*60+60(*minute buffer*)); (*seconds*)


V0=447536.1408228077`(*((μm)^3)*);
surfaceArea=4.835975862049408`*(V0^(2/3))(*((μm)^2)*);
vb=0.3114096329503619`;
W0=(1-vb)*V0(*((μm)^3)*);
nni=isosmolality*W0 (*osmols*);
S0=0 (*initial intracellular CPA *)(*mols*);

gasR= 1.987*10^-3(* kcal mol^-1 K^-1*);
lpA =16.06038610207711`;
 lpE=-6.555277296921298`*1000*gasR;
psA =41.83189898749541`;
 psE=-13.04594344564523`*1000*gasR;



(*James Benson's concentration step function*)
cEXTfunc[startπ_?NumericQ,finalπ_?NumericQ,a_?NumericQ,b_?NumericQ,t_?NumericQ]:=((finalπ/startπ-1)*LogisticSigmoid[(t-a)/b]+1)*startπ
(*Dominic Olver's concentration step function*)
conc[startπ_?NumericQ,finalπ_?NumericQ,a_?NumericQ,b_?NumericQ,t_?NumericQ]:=N[(1+Erf[(t-a)/b])(finalπ-startπ)/2+startπ,20]

(*describes extracellular osmolality as a function of time*)
πFunction[π1_?NumericQ,π2_?NumericQ,exposureStartTime_?NumericQ,returnStartTime_?NumericQ]:=Module[
(*this function brings osmolality form π1 to π2 and then returns it back to π1*)
{πFun,
a (* offset parameter for conentration function*),
b (* slope parameter for conentration function*),
mixingTime (*time for the mixing to occur*),
step1,
step2,
step3,
step4
},
a=2.5;
b=1;
mixingTime=5;(*assumed total mixing time is at most 5 seconds*)
step1=exposureStartTime;
step2=exposureStartTime+mixingTime;
step3=returnStartTime;
step4=returnStartTime+mixingTime;
πFun[t_?NumericQ]:= Piecewise[
{(*hold for π1*)
{π1,t≤ step1},
(*go from π1 ro π2*)
{conc[π1,π2,a,b,t-step1],step1<t≤ step2},
(*hold at π2*)
{π2,step2<t≤step3},
(*return to π1*)
{conc[π2,π1,a,b,t-step3],step3<t≤ step4},
(*hold at π1*)
{π1,step4<t}
}];
Return[πFun]
]


solutionResponseFunction[saltOsmol_(*osmol/kg*),cpaOsmol_(*osmol/kg*),exposureTime_(*seconds*),tempKelvin_]:=Module[
{extSaltFun,extCPAFun,isotonic,timeEnd,twoPmodel,externalSalt,externalCPA,impSols},

isotonic=1 (*mOsm/kg*)(*transform into (*mOsm/μm^3*)*)* (1/(10^15)) (*L/((μm)^3)*) ;

externalSalt=saltOsmol (*osmol/kg*)*(1/(10^15)) (*L/((μm)^3)*) ;(*osmol/((μm)^3)*)
externalCPA=cpaOsmol (*osmol/kg*)*(1/(10^15)) (*L/((μm)^3)*) ;(*osmol/((μm)^3)*)
extSaltFun=πFunction[isotonic,externalSalt,0,exposureTime];
extCPAFun=πFunction[0,externalCPA,0,exposureTime];
timeEnd=90 *60+600(*seconds*);

(*define 2P model*)
twoPmodel =NDSolve[{
w'[t]==- 2 E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * (extCPAFun[t]+extSaltFun[t]-((s[t]+nni)/w[t])),
s'[t]==  E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPAFun[t]-(s[t]/w[t])),
vt'[t]==-  2 E^(lpA + lpE/(gasR * tempKelvin))*surfaceArea *gasConst tempKelvin * (extCPAFun[t]+extSaltFun[t]-((s[t]+nni)/w[t]))+  Vbar  E^(psA + psE/(gasR * tempKelvin))  surfaceArea (extCPAFun[t]-(s[t]/w[t])),
sw[t]==s[t]/w[t] (*mols/μm^3*)  ,

w[0]==W0, 
s[0]==S0(*cellCPAinit*),
vt[0]==V0,
sw[0]== S0/W0
},
{w,s,sw,vt},
{t,0.,timeEnd},
AccuracyGoal->20];

(*save just the interpolation functions.*)
Export["wsol.wdx",w/.twoPmodel];
Export["ssol.wdx",s/.twoPmodel];
Export["swsol.wdx",sw/.twoPmodel];
Export["vtsol.wdx",vt/.twoPmodel];
impSols=Flatten[{Import["wsol.wdx"],Import["ssol.wdx"],Import["swsol.wdx"],Import["vtsol.wdx"]},1];
Return[impSols]
]

OsmoticDamageFunction[saltOsmol_?NumericQ(*osmol/kg*),cpaOsmol_?NumericQ(*osmol/kg*),exposureTime_?NumericQ(*seconds*),tempKelvin_?NumericQ,β_?NumericQ]:=Module[
{extSaltFun,extCPAFun,isotonic,timeEnd,twoPmodel,externalSalt,externalCPA,impSols},

isotonic=1 (*mOsm/kg*)(*transform into (*mOsm/μm^3*)*)* (1/(10^15)) (*L/((μm)^3)*) ;

externalSalt=saltOsmol (*osmol/kg*)*(1/(10^15)) (*L/((μm)^3)*) ;(*osmol/((μm)^3)*)
externalCPA=cpaOsmol (*osmol/kg*)*(1/(10^15)) (*L/((μm)^3)*) ;(*osmol/((μm)^3)*)
extSaltFun=πFunction[isotonic,externalSalt,0,exposureTime];
extCPAFun=πFunction[0,externalCPA,0,exposureTime];
timeEnd=exposureTime+30*60(*seconds*);


josm[timeEnd]
]

ClearAll[extSalt,extCPA,tempKelvin,tf,β]
josm=ParametricNDSolveValue[{
w'[t]==-2  E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * (
Piecewise[
{{extCPA+extSalt,t<=tf},
{1(*isotonic*),t>tf}}
]* (1/(10^15)) -((s[t]+nni)/w[t])),

s'[t]==  E^(psA + psE/(gasR * tempKelvin))* surfaceArea (
Piecewise[
{{extCPA,t<=tf},
{0(*isotonic*),t>tf}}
] * (1/(10^15))-(s[t]/w[t])),

vt'[t]==-2 E^(lpA + lpE/(gasR * tempKelvin))*surfaceArea *gasConst tempKelvin * (
Piecewise[
{{extCPA+extSalt,t<=tf},
{1(*isotonic*),t>tf}}
]* (1/(10^15)) -((s[t]+nni)/w[t]))+  Vbar  E^(psA + psE/(gasR * tempKelvin))  surfaceArea (
Piecewise[
{{extCPA,t<=tf},
{0(*isotonic*),t>tf}}
]* (1/(10^15))-(s[t]/w[t])),

jOsm'[t]== Abs[vt[t]/V0-1]^β ,

w[0]==W0, 
s[0]==S0(*cellCPAinit*),
vt[0]==V0,
jOsm[0]== 0
},
jOsm,
{t,0.,(tf+600)},
{extSalt,extCPA,tempKelvin,tf,β},
(*AccuracyGoal->30,*)
MaxSteps->Infinity];
osmoLP=0.191/60  (*μm/atm/s*)(*from Adams et al. 2003*);

josmPure=ParametricNDSolveValue[{
w'[t]==- osmoLP* surfaceArea gasConst *293(*tempKelvin*) * (
Piecewise[
{{extSalt,t<=tf},
{1(*isotonic*),t>tf}}
]* (1/(10^15)) -((nni)/w[t])),

jOsm'[t]== (1-w[t]/W0)^β ,

w[0]==W0, 
jOsm[0]== 0
},
jOsm,
{t,0.,(tf+600)},
{extSalt,tf,β},
AccuracyGoal->30,
MaxSteps->Infinity
];
josmPureSwell=ParametricNDSolveValue[{
w'[t]==- osmoLP* surfaceArea gasConst *293(*tempKelvin*) * (
Piecewise[
{{extSalt,t<=tf},
{1(*isotonic*),t>tf}}
]* (1/(10^15)) -((nni)/w[t])),

jOsm'[t]== (w[t]/W0-1)^β ,

w[0]==W0, 
jOsm[0]== 0
},
jOsm,
{t,0.,(tf+600)},
{extSalt,tf,β},
AccuracyGoal->16
];
osmoticDamage[Const_?NumericQ,β_?NumericQ,extSalt_?NumericQ,tf_?NumericQ]:=E^-(
(E^Const) josmPure[extSalt(*extSaltFun*),tf(*tf*),β(*β*)][tf+600]
)
osmoticDamageSwell[Const_?NumericQ,β_?NumericQ,extSalt_?NumericQ,tf_?NumericQ]:=E^-(
(E^Const) josmPureSwell[extSalt(*extSaltFun*),tf(*tf*),β(*β*)][tf+600]
)

Length@Select[fittingNaClData,#[[2]]<= 2000&]

thisnlmNaCl=NonlinearModelFit[Select[fittingNaClData,#[[2]]<= 2000&],{
osmoticDamage[Cbvh,β,osmo,tf]
},{{Cbvh,5.619514540375738},{β,10.67}},{osmo,tf}(*,Method-> "NMinimize"*)];

thisnlmNaCl["ParameterTable"]
thisnlmNaCl["AdjustedRSquared"]

Show[ErrorListPlot[Table[errorData[Select[fitNaCl[[i]],#[[2]]<= 2000&]],{i,Length[fitNaCl]}],PlotRange->{{0,2000},{0,1.1}},PlotMarkers->"OpenMarkers",PlotLegends->{"1.5 osmol/kg","2.0 osmol/kg","2.5 osmol/kg"}, Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[{
thisnlmNaCl[1.5,tf],
thisnlmNaCl[2.,tf],
thisnlmNaCl[2.5,tf]},{tf,0,2000},PlotRange->All]]

sucNLMlist=Table[
thisnlm=NonlinearModelFit[
Select[fittingSucData,#[[2]]<= 2000&],
{osmoticDamage[Cbvh,β,osmo,tf]},{{Cbvh,-6.481921203695049`+1.2824780842828019` *β}},{osmo,tf}];
{thisnlm["AIC"],β,Cbvh/.thisnlm["BestFitParameters"]},
{β,2,16,1}
];

ListPlot[sucNLMlist[[All,{2,1}]]]

Sort[sucNLMlist][[1]]

sucNLMlist=Table[
thisnlm=NonlinearModelFit[
Select[fittingSucData,#[[2]]<= 2000&],
{osmoticDamage[Cbvh,β,osmo,tf]},{{Cbvh,9.742182607046953`}},{osmo,tf}];
{thisnlm["AIC"],β,Cbvh/.thisnlm["BestFitParameters"]},
{β,13-1,13+1,0.1}
];

ListPlot[sucNLMlist[[All,{2,1}]]]
Sort[sucNLMlist][[1]]

sucNLMlist=Table[
thisnlm=NonlinearModelFit[
Select[fittingSucData,#[[2]]<= 2000&],
{osmoticDamage[Cbvh,β,osmo,tf]},{{Cbvh,9.85827474441405`}},{osmo,tf}];
{thisnlm["AIC"],β,Cbvh/.thisnlm["BestFitParameters"]},
{β,13.1-.2,13.1+.2,0.01}
];

ListPlot[sucNLMlist[[All,{2,1}]]]
Sort[sucNLMlist][[1]]

Length@Select[fittingSucData,#[[2]]<= 2000&]

thisnlmSuc=NonlinearModelFit[(*fittingSucData*) Select[fittingSucData,#[[1]]<= 2.5&&#[[2]]<= 2000&],{
osmoticDamage[Cbvh,β,osmo,tf]
},{{Cbvh,9.916184133672111},{β,13.15}},{osmo,tf}(*,Method-> "NMinimize"*)];

thisnlmSuc["ParameterTable"]
thisnlmSuc["AdjustedRSquared"]

Show[ErrorListPlot[Table[errorData[Select[fittingSucData,#[[1]]== osmo&&#[[2]]<2000&][[All,{2,3}]]],{osmo,{1.5`,2.`,2.5`}}],PlotRange->{{0,2000},{0,1.1}},PlotMarkers->"OpenMarkers",PlotLegends->{"1.5 osmol/kg","2.0 osmol/kg","2.5 osmol/kg"}, Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[{
thisnlmSuc[1.5,tf],
thisnlmSuc[2.,tf],
thisnlmSuc[2.5,tf]},{tf,0,2000},PlotRange->All]]

(*check if the fitted parameters overlap, indicating if they are significantly different or not.*)
Show[Graphics[{thisnlmNaCl["ParameterConfidenceRegion",ConfidenceLevel-> .99],thisnlmNaCl["ParameterConfidenceRegion",ConfidenceLevel-> .95],thisnlmNaCl["ParameterConfidenceRegion",ConfidenceLevel-> .9]}],Graphics[{thisnlmSuc["ParameterConfidenceRegion",ConfidenceLevel-> .99],thisnlmSuc["ParameterConfidenceRegion",ConfidenceLevel-> .95],thisnlmSuc["ParameterConfidenceRegion",ConfidenceLevel-> .9]}],ListPlot[{{Cbvh,β}/.thisnlmNaCl["BestFitParameters"],{Cbvh,β}/.thisnlmSuc["BestFitParameters"]},PlotRange->All]]

ParameterEllipsoid[{1.881086302374743`,10.87554987231552`},{1.6834496061392128`,0.10336835025869316`},{{0.5796026047408334`,0.8148992702031591`},{-0.8148992702031591`,0.5796026047408334`}}]

roNLMlist=Table[
thisnlm=NonlinearModelFit[
Select[relrosurv,#[[2]]<= 2000&],
{osmoticDamageSwell[Cbvh,β,osmo,tf]},{{Cbvh,-7.563851518121521`+0.4902766065682082`*β}},{osmo,tf}];
{thisnlm["AIC"],β,Cbvh/.thisnlm["BestFitParameters"]},
{β,2,8,1}
];

ListPlot[roNLMlist[[All,{2,1}]]]
Sort[roNLMlist][[1]]

roNLMlist=Table[
Print[β];
thisnlm=NonlinearModelFit[
Select[relrosurv,#[[2]]<= 2000&],
{osmoticDamageSwell[Cbvh,β,osmo,tf]},{{Cbvh,-7.563851518121521`+0.4902766065682082`*β}},{osmo,tf}];
{thisnlm["AIC"],β,Cbvh/.thisnlm["BestFitParameters"]},
{β,1.4,2,.1}
];

LinearModelFit[roNLMlist[[All,{2,3}]],x,x]

ListPlot[roNLMlist[[All,{2,1}]]]
Sort[roNLMlist][[1]]

roNLMlist=Table[
Print[β];
thisnlm=NonlinearModelFit[
Select[relrosurv,#[[2]]<= 2000&],
{osmoticDamageSwell[Cbvh,β,osmo,tf]},{{Cbvh,-8.37744931897547`+0.45882407211745235`*β}},{osmo,tf}];
{thisnlm["AIC"],β,Cbvh/.thisnlm["BestFitParameters"]},
{β,1.5-.2,1.5+.2,.01}
];

ListPlot[roNLMlist[[All,{2,1}]]]
Sort[roNLMlist][[1]]

Length@Select[relrosurv,#[[2]]<= 2000&]

thisROnlm=NonlinearModelFit[(*relrosurv*)
Select[relrosurv,#[[2]]<= 2000&],
{osmoticDamageSwell[Cbvh,β,osmo,tf]},{{Cbvh,-7.66334647972756},{β,1.55}},{osmo,tf}];

thisROnlm["ParameterTable"]

thisROnlm["AdjustedRSquared"]

Show[ErrorListPlot[Table[errorData[Select[relrosurv,#[[1]]== osmo&&#[[2]]<2000&][[All,{2,3}]]],{osmo,osmolsRO}],PlotRange->{{0,2000},{0,1.2}},PlotMarkers->"OpenMarkers",PlotLegends-> {"0.8 osmol/kg","0.7 osmol/kg","0.6 osmol/kg","0.5 osmol/kg"},Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[{thisROnlm[0.8,tf],
thisROnlm[0.7,tf],
thisROnlm[0.6,tf],
thisROnlm[0.5,tf]},{tf,0,2000},PlotRange->All]]

T-test between NaCl and Sucrose

transDataNaCl={#[[1]],#[[2]]-30,#[[3]]}&/@Select[fittingNaClData,1<#[[1]]<=2.5&&#[[2]]<1860&];
transDataSuc={#[[1]],#[[2]]-45,#[[3]]}&/@Select[fittingSucData,1<#[[1]]<=2.5&&#[[2]]<1860&];
timeList=DeleteDuplicates[transDataNaCl[[All,2]]];
osmoList=DeleteDuplicates[transDataSuc[[All,1]]];

{dataPairsNaCl,dataPairsSuc}=Transpose[DeleteCases[Flatten[Table[
d1=Select[transDataNaCl,#[[1]]== thisOsmo&&#[[2]]== thisTime&][[All,3]];
d2=Select[transDataSuc,#[[1]]== thisOsmo&&#[[2]]== thisTime&][[All,3]];
If[Length[d1]== 0 ||Length[d2]== 0 ,{,},{Mean[d1],Mean[d2]}],
{thisOsmo,osmoList},{thisTime,timeList}],1],{,}]]

(*get useful information*)

Length[Flatten[{dataPairsNaCl,dataPairsSuc},1]]

Median@dataPairsNaCl
MedianDeviation@dataPairsNaCl
Median@dataPairsSuc
MedianDeviation@dataPairsSuc

Mean@dataPairsNaCl
StandardDeviation@dataPairsNaCl
Mean@dataPairsSuc
StandardDeviation@dataPairsSuc

(*run test*)

(*Normality is not true for all subsets of data*)
PairedTTest[{dataPairsNaCl,dataPairsSuc},Automatic,"TestDataTable"]

(*Visually, normality isn't that bad in the historgram*)
Histogram[dataPairsNaCl-dataPairsSuc,8,PlotRange->All]

(*perform nonparameteric test*)
SignedRankTest[{dataPairsNaCl,dataPairsSuc},Automatic,"TestDataTable"]

(*nonparametric test and paired T-test agree*)

Chill injury

Data

{data4Craw,data10Craw,data19Craw}={{{2.`,0.33070866141732286`},{2.`,0.5983606557377049`},{2.`,0.6086956521739131`},{6.`,0.6243386243386243`},{6.`,0.4774193548387097`},{6.`,0.723404255319149`},{15.`,0.6878612716763006`},{15.`,0.6894409937888198`},{15.`,0.7380952380952381`},{30.`,0.7132352941176471`},{30.`,0.7721518987341772`},{30.`,0.7688172043010753`},{50.`,0.5`},{50.`,0.7465753424657534`},{75.`,0.5811965811965812`},{75.`,0.7985611510791367`},{75.`,0.49473684210526314`},{90.`,0.5208333333333334`},{90.`,0.5275590551181102`},{90.`,0.6242038216560509`}},{{2.`,0.8923766816143498`},{2.`,0.7863247863247863`},{2.`,0.7537878787878788`},{6.`,0.8495575221238938`},{6.`,0.8084112149532711`},{6.`,0.77431906614786`},{15.`,0.6972477064220184`},{15.`,0.794392523364486`},{15.`,0.851063829787234`},{30.`,0.6928104575163399`},{30.`,0.7558139534883721`},{30.`,0.6976744186046512`},{50.`,0.7416267942583732`},{50.`,0.7852760736196319`},{50.`,0.7090909090909091`},{75.`,0.6904761904761905`},{75.`,0.7987804878048781`},{75.`,0.7830882352941176`},{90.`,0.8035714285714286`},{90.`,0.8448979591836735`},{90.`,0.7028301886792453`}},{{2.`,0.9065420560747663`},{2.`,0.972972972972973`},{2.`,0.8947368421052632`},{6.`,0.8932038834951457`},{6.`,0.9262295081967213`},{6.`,0.926605504587156`},{15.`,0.8275862068965517`},{15.`,0.5315315315315315`},{15.`,0.9385964912280702`},{30.`,0.9256198347107438`},{30.`,0.85`},{30.`,0.875`},{50.`,0.9435483870967742`},{50.`,0.9433962264150944`},{50.`,0.9016393442622951`},{75.`,0.916083916083916`},{75.`,0.6129032258064516`},{75.`,0.8811881188118812`},{90.`,0.8582677165354331`},{90.`,0.7704081632653061`},{90.`,0.7924528301886793`}}};

Code

(*Export["chill_injury_data.csv",
Prepend[
Join[
{273.1+1.7285714285714289`,#[[1]],#[[2]]}&/@data4Craw,
{273.1+10,#[[1]],#[[2]]}&/@data10Craw,
{273.1+19.6,#[[1]],#[[2]]}&/@data19Craw
],{"Temperature (Kelvin)","Time (minutes)","Survival (development to 4-arm-plateaus stage/total count)"}]
]*)

iceBath=Mean[{2.3,2.6,1.1,1.6,1.2,2.3,1}]

StandardDeviation[{2.3,2.6,1.1,1.6,1.2,2.3,1}]/Length[{2.3,2.6,1.1,1.6,1.2,2.3,1}]^.5

iceBath=Mean[{2.3,2.6,1.1,1.6,1.2,2.3,1}];
temps={iceBath,10,19.5};
chilldata4C={iceBath (*temperature in Celsius*),#[[1]]*60 + 30 (*time in seconds*),#[[2]] (*survival*)}&/@ data4Craw;
chilldata10C={10,#[[1]]*60 + 30 ,#[[2]]}&/@ data10Craw;
chilldata19C={19.5,#[[1]]*60 + 30 ,#[[2]]}&/@ data19Craw;
chilldata=Join[chilldata4C,chilldata10C,chilldata19C];
meanContsurv=Mean[chilldata19C[[All,3]]];
chillreldata={#[[1]],#[[2]],#[[3]]/meanContsurv}&/@chilldata;

chillTemp[Ctemp_,tempPhys_,temp_]:=E^-(Ctemp*Piecewise[{{0,temp>= tempPhys},{tempPhys-temp,temp< tempPhys}}])
chillTime[Ctemp_,tempPhys_,temp_,t_]:=E^-(Ctemp*Piecewise[{{0,temp>= tempPhys},{tempPhys-temp,temp< tempPhys}}]*t/100)

tempNLM=NonlinearModelFit[chillreldata,{chillTemp[Ctemp,tempPhys,temp],0<tempPhys<30},{{Ctemp,1},{tempPhys,17}},
{temp,time}]
timeNLM=NonlinearModelFit[chillreldata,{chillTime[Ctemp,tempPhys,temp,time],0<tempPhys<30},{{Ctemp,0},{tempPhys,17}},
{temp,time}]

(*test for correlation at each temprature*)
TableForm@Table[{temp,Length[Select[chillreldata,#[[1]]== temp&][[All,{2,3}]]],CorrelationTest[Select[chillreldata,#[[1]]== temp&][[All,{2,3}]],0,(*"SpearmanRank",*){"TestDataTable",All}]},{temp,Reverse[temps]}]

Length@chillreldata

0.00025720288080756794`*100

timeNLM["ParameterTable"]
tempNLM["ParameterTable"]

TableForm@{{"","Ctemp","Temp Phys","adjRSquared","AIC","BIC"},
{"Time Model",100*Ctemp/.timeNLM["BestFitParameters"],tempPhys/.timeNLM["BestFitParameters"],timeNLM["AdjustedRSquared"],timeNLM["AIC"],timeNLM["BIC"]},
{"Temp Model",Ctemp/.tempNLM["BestFitParameters"],tempPhys/.tempNLM["BestFitParameters"],tempNLM["AdjustedRSquared"],tempNLM["AIC"],tempNLM["BIC"]}
}

Show[ErrorListPlot[Table[errorData[Select[chillreldata,#[[1]]== temp&][[All,{2,3}]]],{temp,Reverse[temps]}],PlotRange->{{0,5500},{0,1.2}},PlotMarkers->"OpenMarkers",PlotLegends-> {"19.5 °C","10.0 °C","1.7 °C"},Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[
{timeNLM[19.5,t],
timeNLM[10,t],
timeNLM[0.5,t]},
{t,0,5500},PlotRange-> All],
Plot[
{tempNLM[19.5,t],
tempNLM[10,t],
tempNLM[0.5,t]},
{t,0,5500},PlotRange-> All,PlotStyle->Dashed]]

Show[ErrorListPlot[errorData[chillreldata[[All,{1,3}]]],PlotRange->{{0,20},{0,1.2}},PlotMarkers->"OpenMarkers",Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[
{tempNLM[temp,100]},
{temp,0,20},PlotRange-> All]]

Show[ErrorListPlot[errorData[chillreldata[[All,{1,3}]]],PlotRange->{{0,20},{0,1.2}},PlotMarkers->"OpenMarkers",PlotStyle-> Black, Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[
{1,tempNLM[temp,100]},
{temp,0,20},PlotRange-> All,PlotStyle->{{Black,Thin},{Black,Dashed}}]]

Cytotoxicity

Data

{data4Ctox,data10Ctox,data19Ctox}={{{0.`,2.`,42.`,85.`,0.33070866141732286`,""},{0.`,2.`,73.`,49.`,0.5983606557377049`,""},{0.`,2.`,98.`,63.`,0.6086956521739131`,""},{0.`,6.`,118.`,71.`,0.6243386243386243`,""},{0.`,6.`,74.`,81.`,0.4774193548387097`,""},{0.`,6.`,102.`,39.`,0.723404255319149`,""},{0.`,15.`,119.`,54.`,0.6878612716763006`,""},{0.`,15.`,111.`,50.`,0.6894409937888198`,""},{0.`,15.`,124.`,44.`,0.7380952380952381`,""},{0.`,30.`,97.`,39.`,0.7132352941176471`,""},{0.`,30.`,122.`,36.`,0.7721518987341772`,""},{0.`,30.`,143.`,43.`,0.7688172043010753`,""},{0.`,50.`,61.`,61.`,0.5`,""},{0.`,50.`,109.`,37.`,0.7465753424657534`,""},{0.`,75.`,68.`,49.`,0.5811965811965812`,""},{0.`,75.`,111.`,28.`,0.7985611510791367`,""},{0.`,75.`,94.`,96.`,0.49473684210526314`,""},{0.`,90.`,75.`,69.`,0.5208333333333334`,""},{0.`,90.`,67.`,60.`,0.5275590551181102`,""},{0.`,90.`,98.`,59.`,0.6242038216560509`,""},{0.5`,2.`,50.`,58.`,0.46296296296296297`,""},{0.5`,2.`,63.`,69.`,0.4772727272727273`,""},{0.5`,2.`,40.`,78.`,0.3389830508474576`,""},{0.5`,6.`,35.`,100.`,0.25925925925925924`,""},{0.5`,6.`,44.`,56.`,0.44`,""},{0.5`,6.`,63.`,60.`,0.5121951219512195`,""},{0.5`,15.`,49.`,116.`,0.296969696969697`,""},{0.5`,15.`,30.`,74.`,0.28846153846153844`,""},{0.5`,15.`,57.`,115.`,0.3313953488372093`,""},{0.5`,30.`,32.`,124.`,0.20512820512820512`,""},{0.5`,30.`,37.`,102.`,0.26618705035971224`,""},{0.5`,30.`,53.`,99.`,0.34868421052631576`,""},{0.5`,50.`,35.`,110.`,0.2413793103448276`,""},{0.5`,50.`,25.`,78.`,0.24271844660194175`,""},{0.5`,50.`,33.`,124.`,0.21019108280254778`,""},{0.5`,75.`,30.`,78.`,0.2777777777777778`,""},{0.5`,75.`,25.`,102.`,0.1968503937007874`,""},{0.5`,75.`,23.`,151.`,0.13218390804597702`,""},{0.5`,90.`,30.`,121.`,0.1986754966887417`,""},{0.5`,90.`,35.`,122.`,0.2229299363057325`,""},{0.5`,90.`,48.`,121.`,0.28402366863905326`,""},{1.`,2.`,65.`,116.`,0.35911602209944754`,""},{1.`,2.`,59.`,103.`,0.36419753086419754`,""},{1.`,6.`,38.`,125.`,0.2331288343558282`,""},{1.`,6.`,44.`,193.`,0.18565400843881857`,""},{1.`,6.`,62.`,115.`,0.3502824858757062`,""},{1.`,15.`,20.`,119.`,0.14388489208633093`,""},{1.`,15.`,8.`,117.`,0.064`,""},{1.`,15.`,15.`,179.`,0.07731958762886598`,""},{1.`,30.`,28.`,102.`,0.2153846153846154`,""},{1.`,30.`,30.`,109.`,0.2158273381294964`,""},{1.`,30.`,12.`,147.`,0.07547169811320754`,""},{1.`,50.`,16.`,176.`,0.08333333333333333`,""},{1.`,50.`,29.`,84.`,0.25663716814159293`,""},{1.`,50.`,59.`,102.`,0.36645962732919257`,""},{1.`,75.`,19.`,123.`,0.13380281690140844`,""},{1.`,75.`,22.`,168.`,0.11578947368421053`,""},{1.`,75.`,12.`,145.`,0.07643312101910828`,""},{1.`,90.`,8.`,126.`,0.05970149253731343`,""},{1.`,90.`,16.`,107.`,0.13008130081300814`,""},{1.`,90.`,9.`,178.`,0.0481283422459893`,""}},{{0.`,2.`,199.`,24.`,0.8923766816143498`,"Only Sea water for all of these. 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Code

(*Export["cytotoxicity_data.csv",
Prepend[
Join[
{#[[1]],273.1+1.7285714285714289`,#[[2]],#[[5]]}&/@data4Ctox,
{#[[1]],273.1+10,#[[2]],#[[5]]}&/@data10Ctox,
{#[[1]],273.1+19.6,#[[2]],#[[5]]}&/@data19Ctox
],{"Me2SO added to isotonic Seawater (osmol/kg)","Temperature (Kelvin)","Time (minutes)","Survival (development to 4-arm-plateaus stage/total count)"}]
]*)

(*normalize data to control*)
iceBath=Mean[{2.3,2.6,1.1,1.6,1.2,2.3,1}];

contSurvival19C=Mean[Select[data19Ctox,#[[1]]== 0&][[All,5]]];
reldata19C={273.1+19.6(*temp*),#[[1]](*cpaM*),#[[2]]*60 +30(*time, seconds*) ,#[[5]](*survival*)/contSurvival19C}&/@(*data19C[[;;-7]]*)Select[data19Ctox,0.1<#[[1]]≤ 1.5&&#[[2]]<= 30(*&&0.1<#[[5]]*)&];

contSurvival10C=Mean[Select[data10Ctox,#[[1]]== 0&][[All,5]]];
reldata10C={273.1+10(*temp*),#[[1]](*cpaM*),#[[2]]*60 +30(*time, seconds*) ,#[[5]](*survival*)/contSurvival10C}&/@(*data10C *)Select[data10Ctox,0.1<#[[1]]≤ 1.5&&#[[2]]<= 30(*&&.1<#[[5]]*)&];

contSurvival4C=Mean[Select[data4Ctox,#[[1]]== 0&][[All,5]]];
reldata4C={273.1+iceBath(*temp*),#[[1]](*cpaM*),#[[2]]*60+30 (*time, seconds*) ,#[[5]](*survival*)/contSurvival4C}&/@(*data4C*)Select[data4Ctox,0.1<#[[1]]≤ 1.5&&#[[2]]<=  30(*&&.1<#[[5]]*)&];

fitData= Join[reldata4C,reldata10C,reldata19C];

(*GLOBAL PARAMETERS*)
isosmolality=1.000 * (1/(10^15)) (*L/((μm)^3)*) ; (*osmol/ ((μm)^3) *)
(*initialSalt=isosmolality; (* unless cells are preequilibrated with anisosmotic nonperm solution, this will be isosmolality *)*)
(*initialRelWaterVol=isosmolality/initialSalt;  (*initial relative water volume, should be 1 unless special case. *)*)
VbarEg=62.068/1.1135 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ; (*((μm)^3)/mol*)
VbarGly=92.09382/1.26 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
VbarDMSO=78.13 (*g·(mol^(-1))*)/1.1004 (*g (cm^(-3))*) * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
Vbar=VbarDMSO;
gasConst=0.08205 * ((10^15)/1)(* ((μm)^3) / L*); (* ((μm)^3) atm/(kelvin mol) *)
vbFraction=0.3114096329503619`;
cellCPAinit=0.0; (*initial moles of CPA --intracellular 2.5*)
(*extCPA=1.5 * (1/(10^15)) (*L/((μm)^3)*);(*osmol/((μm)^3) of CPA*)
extSalt=isosmolality;(* osmol/((μm)^3) of non-permeating salt*)*)
timeEnd=(90*60+60(*minute buffer*)); (*seconds*)


V0=447536.1408228077`(*((μm)^3)*);
surfaceArea=4.835975862049408`*(V0^(2/3))(*((μm)^2)*);
vb=0.3114096329503619`;
W0=(1-vb)*V0(*((μm)^3)*);
nni=isosmolality*W0 (*osmols*);
S0=0 (*initial intracellular CPA *)(*mols*);

gasR= 1.987*10^-3(* kcal mol^-1 K^-1*);
lpA =16.06038610207711`;
 lpE=-6.555277296921298`*1000*gasR;
psA =41.83189898749541`;
 psE=-13.04594344564523`*1000*gasR;

Cshrink=1.881086302374743`;
βshrink=10.87554987231552`;
Cswell=-7.663464309343182`;
βswell=1.5476459457183478`;

(*define 2P model*)
jtox =ParametricNDSolveValue[{
w'[t]==
Piecewise[
{
{(*treatment*)
-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((extCPA+extSalt)* (1/(10^15)) -((s[t]+nni)/w[t]))
,t<=tf},
{(*return to iso*)
-E^(lpA + lpE/(gasR * 293)) * surfaceArea gasConst* 293 * (1* (1/(10^15)) -((s[t]+nni)/w[t])),t>tf}}
],

s'[t]== Piecewise[
{
{(*treatment*)
 E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* (1/(10^15)) -(s[t]/w[t])),t<=tf},
{(*return to iso*)
 E^(psA + psE/(gasR * 293))* surfaceArea (0 -(s[t]/w[t])),t<=tf}
}],


(*vt'[t]==Piecewise[
{
{(*treatment*)
-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * (extCPA+extSalt* (1/(10^15)) -((s[t]+nni)/w[t]))
,t<=tf},
{(*return to iso*)
-E^(lpA + lpE/(gasR * 293)) * surfaceArea gasConst* 293 * (1* (1/(10^15)) -((s[t]+nni)/w[t])),t>tf}}
]+  Vbar Piecewise[
{
{(*treatment*)
 E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* (1/(10^15)) -(s[t]/w[t])),t<=tf},
{(*return to iso*)
 E^(psA + psE/(gasR * 293))* surfaceArea (0 -(s[t]/w[t])),t<=tf}
}],*)

jTox'[t]==((10^15)*s[t]/(w[t]))^α (*mols/μm^3*),

w[0]==W0, 
s[0]==10.^-18(*S0*)(*cellCPAinit*),
(*vt[0]==V0,*)
jTox[0]==0
},
jTox,
{t,0.,(tf+600)},
{tempKelvin,extCPA,extSalt,tf,α},
AccuracyGoal->20,
MaxSteps->Infinity];

jtoxTemp =ParametricNDSolveValue[{
w'[t]==
Piecewise[
{
{(*treatment*)
-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((extCPA+extSalt)* (1/(10^15)) -((s[t]+nni)/w[t]))
,t<=tf},
{(*return to iso*)
-E^(lpA + lpE/(gasR * 293)) * surfaceArea gasConst* 293 * (1* (1/(10^15)) -((s[t]+nni)/w[t])),t>tf}}
],

s'[t]== Piecewise[
{
{(*treatment*)
 E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* (1/(10^15)) -(s[t]/w[t])),t<=tf},
{(*return to iso*)
 E^(psA + psE/(gasR * 293))* surfaceArea (0 -(s[t]/w[t])),t<=tf}
}],


(*vt'[t]==Piecewise[
{
{(*treatment*)
-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * (extCPA+extSalt* (1/(10^15)) -((s[t]+nni)/w[t]))
,t<=tf},
{(*return to iso*)
-E^(lpA + lpE/(gasR * 293)) * surfaceArea gasConst* 293 * (1* (1/(10^15)) -((s[t]+nni)/w[t])),t>tf}}
]+  Vbar Piecewise[
{
{(*treatment*)
 E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* (1/(10^15)) -(s[t]/w[t])),t<=tf},
{(*return to iso*)
 E^(psA + psE/(gasR * 293))* surfaceArea (0 -(s[t]/w[t])),t<=tf}
}],*)

jTox'[t]==((10^15)*s[t]/(w[t]))^(αa + αb/(tempKelvin*gasR)) (*mols/μm^3*),

w[0]==W0, 
s[0]==10.^-18(*cellCPAinit*),
(*vt[0]==V0,*)
jTox[0]==0
},
jTox,
{t,0.,(tf+600)},
{tempKelvin,extCPA,extSalt,tf,αa , αb},
AccuracyGoal->20,
MaxSteps->Infinity];


vtTemp =ParametricNDSolveValue[{
w'[t]==
Piecewise[
{
{(*treatment*)
-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((extCPA+extSalt)* (1/(10^15)) -((s[t]+nni)/w[t]))
,t<=tf},
{(*return to iso*)
-E^(lpA + lpE/(gasR * 293)) * surfaceArea gasConst* 293 * (1* (1/(10^15)) -((s[t]+nni)/w[t])),t>tf}}
],

s'[t]== Piecewise[
{
{(*treatment*)
 E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* (1/(10^15)) -(s[t]/w[t])),t<=tf},
{(*return to iso*)
 E^(psA + psE/(gasR * 293))* surfaceArea (0 -(s[t]/w[t])),t<=tf}
}],


vt'[t]==Piecewise[
{
{(*treatment*)
-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((extCPA+extSalt)* (1/(10^15)) -((s[t]+nni)/w[t]))
,t<=tf},
{(*return to iso*)
-E^(lpA + lpE/(gasR * 293)) * surfaceArea gasConst* 293 * (1* (1/(10^15)) -((s[t]+nni)/w[t])),t>tf}}
]+  Vbar Piecewise[
{
{(*treatment*)
 E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* (1/(10^15)) -(s[t]/w[t])),t<=tf},
{(*return to iso*)
 E^(psA + psE/(gasR * 293))* surfaceArea (0 -(s[t]/w[t])),t<=tf}
}],


w[0]==W0, 
s[0]==0.(*cellCPAinit*),
vt[0]==V0
},
vt,
{t,0.,(tf+600)},
{tempKelvin,extCPA,extSalt,tf},
AccuracyGoal->20,
MaxSteps->Infinity];




josmFull =ParametricNDSolveValue[{
w'[t]==
Piecewise[
{
{(*treatment*)
-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((extCPA+extSalt)* (1/(10^15)) -((s[t]+nni)/w[t]))
,t<=tf},
{(*return to iso*)
-E^(lpA + lpE/(gasR * 293)) * surfaceArea gasConst* 293 * (1* (1/(10^15)) -((s[t]+nni)/w[t])),t>tf}}
],

s'[t]== Piecewise[
{
{(*treatment*)
 E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* (1/(10^15)) -(s[t]/w[t])),t<=tf},
{(*return to iso*)
 E^(psA + psE/(gasR * 293))* surfaceArea (0 -(s[t]/w[t])),t<=tf}
}],

vt'[t]==Piecewise[
{
{(*treatment*)
-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((extCPA+extSalt)* (1/(10^15)) -((s[t]+nni)/w[t]))
,t<=tf},
{(*return to iso*)
-E^(lpA + lpE/(gasR * 293)) * surfaceArea gasConst* 293 * (1* (1/(10^15)) -((s[t]+nni)/w[t])),t>tf}}
]+  Vbar Piecewise[
{
{(*treatment*)
 E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* (1/(10^15)) -(s[t]/w[t])),t<=tf},
{(*return to iso*)
 E^(psA + psE/(gasR * 293))* surfaceArea (0 -(s[t]/w[t])),t<=tf}
}],


jOsm'[t]==If[vt[t]<=  V0,
(E^Cshrink)*(1-vt[t]/V0)^βshrink ,
(E^Cswell)*(vt[t]/V0-1)^βswell
],

w[0]==W0, 
s[0]==S0(*cellCPAinit*),
vt[0]==V0,
jOsm[0]==0
},
jOsm,
{t,0.,(tf+600)},
{tempKelvin,extCPA,extSalt,tf},
AccuracyGoal->20];


totalDamage[tempKelvin_?NumericQ,extCPA_?NumericQ,extSalt_?NumericQ,tf_?NumericQ,μa_?NumericQ,μb_?NumericQ,α_?NumericQ]:=E^-(E^(μa+μb/(gasR tempKelvin))  *jtox[tempKelvin,extCPA,extSalt,tf,α][tf+600]+Re[josmFull[tempKelvin,extCPA,extSalt,tf][tf+600]])




totalDamage2[tempKelvin_?NumericQ,extCPA_?NumericQ,extSalt_?NumericQ,tf_?NumericQ,μa_?NumericQ,μb_?NumericQ,αa_?NumericQ,αb_?NumericQ]:=E^-(E^(μa+μb/(gasR tempKelvin)) *jtoxTemp[tempKelvin,extCPA,extSalt,tf,αa,αb][tf+600]+Re[josmFull[tempKelvin,extCPA,extSalt,tf][tf+600]])



totalDamage3[tempKelvin_?NumericQ,extCPA_?NumericQ,extSalt_?NumericQ,tf_?NumericQ,μa_?NumericQ,μb_?NumericQ,αa_?NumericQ,αb_?NumericQ]:=E^-(E^(μa+μb/(gasR tempKelvin)) * extCPA^(E^(αa+αb/(gasR tempKelvin)))tf+Re[josmFull[tempKelvin,extCPA,extSalt,tf][tf+600]])

({{μa->-80.55238281488882`}, {μb->41.01389808202523`}, {αa->22.206291494178927`}, {αb->-11.527831847336365`}})

E^(αa+αb/(gasR tempKelvin))/.{αa->22.206291494178927`,αb->-11.527831847336365`,tempKelvin-> 293}
E^(αa+αb/(gasR tempKelvin))/.{αa->22.206291494178927`,αb->-11.527831847336365`,tempKelvin-> 283}
E^(αa+αb/(gasR tempKelvin))/.{αa->22.206291494178927`,αb->-11.527831847336365`,tempKelvin-> 273+1.7}

E^(μa+μb/(gasR tempKelvin)) * extCPA^(E^(αa+αb/(gasR tempKelvin)))

Length@fitData
Length@Select[fitData,#[[3]]<=2000&]

toxmodel3=NonlinearModelFit[fitData,{totalDamage3[tempKelvin,extCPA,1(*extSalt*),tf,μa,μb,αa,αb]},
{{μa,-80.5523836734053},
{μb,41.01389855664423},
{αa,22.206291677990723},
{αb,-11.527831947449103}},
{tempKelvin,extCPA,tf}];
toxmodel3["AdjustedRSquared"]
toxmodel3["AIC"]
toxmodel3["BIC"]
toxmodel3["BestFitParameters"]

toxmodel2=NonlinearModelFit[fitData,{totalDamage2[tempKelvin,extCPA,1(*extSalt*),tf,μa,μb,αa,αb]},
{{μa,-44.87674340642502},
{μb,21.552332836930567},
{αa,36.96990574177566},
{αb,-19.751256348590296}},
{tempKelvin,extCPA,tf}];
toxmodel2["AdjustedRSquared"]
toxmodel2["AIC"]
toxmodel2["BIC"]
toxmodel2["BestFitParameters"]

toxmodel1=NonlinearModelFit[fitData,{totalDamage[tempKelvin,extCPA,1(*extSalt*),tf,μa,μb,α]},
{{μa,-128.78894561155033},
{μb,70.21580550473658},
{α,4.710260125822662}},
{tempKelvin,extCPA,tf}];
toxmodel1["AdjustedRSquared"]
toxmodel1["AIC"]
toxmodel1["BIC"]
toxmodel1["BestFitParameters"]

TableForm@{{"","Fitted Parameters","RSquared","AIC","BIC"},
{"Model 1",
toxmodel1["BestFitParameters"],
toxmodel1["AdjustedRSquared"],
toxmodel1["AIC"],
toxmodel1["BIC"]
},
{"Model 2",
toxmodel2["BestFitParameters"],
toxmodel2["AdjustedRSquared"],
toxmodel2["AIC"],
toxmodel2["BIC"]
},
{"Model 3",
toxmodel3["BestFitParameters"],
toxmodel3["AdjustedRSquared"],
toxmodel3["AIC"],
toxmodel3["BIC"]}
}

toxmodel1["ParameterTable"]
toxmodel2["ParameterTable"]
toxmodel3["ParameterTable"]

Show[ErrorListPlot[
Table[
errorData[Select[reldata19C,#[[2]] == osmo&][[All,{3,4}]]],{osmo,DeleteDuplicates[reldata19C[[All,2]]]}],
PlotRange->{{0,2000},{0,1.2}},PlotMarkers->"OpenMarkers",PlotLegends->{"0.5 osmol/kg","1.0 osmol/kg","1.5 osmol/kg"},Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[{
toxmodel1[292.70000000000005,0.5,t],
toxmodel1[292.70000000000005,1.0,t],
toxmodel1[292.70000000000005,1.5,t]},{t,0,2000},PlotRange->All(*,PlotStyle->Thick*)],
Plot[{
toxmodel2[292.70000000000005,0.5,t],
toxmodel2[292.70000000000005,1.0,t],
toxmodel2[292.70000000000005,1.5,t]},{t,0,2000},PlotRange->All,PlotStyle->Thin],
Plot[{
toxmodel3[292.70000000000005,0.5,t],
toxmodel3[292.70000000000005,1.0,t],
toxmodel3[292.70000000000005,1.5,t]},{t,0,2000},PlotRange->All,PlotStyle->Dashed]]

Show[ErrorListPlot[
Table[
errorData[Select[reldata10C,#[[2]] == osmo&][[All,{3,4}]]],{osmo,DeleteDuplicates[reldata10C[[All,2]]]}],
PlotRange->{{0,2000},{0,1.2}},PlotMarkers->"OpenMarkers",PlotLegends->{"0.5 osmol/kg","1.0 osmol/kg","1.5 osmol/kg"},Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[{
toxmodel1[283.1,0.5,t],
toxmodel1[283.1,1.0,t],
toxmodel1[283.1,1.5,t]},{t,0,2000},PlotRange->All(*,PlotStyle->Thick*)],
Plot[{
toxmodel2[283.1,0.5,t],
toxmodel2[283.1,1.0,t],
toxmodel2[283.1,1.5,t]},{t,0,2000},PlotRange->All,PlotStyle->Thin],
Plot[{
toxmodel3[283.1,0.5,t],
toxmodel3[283.1,1.0,t],
toxmodel3[283.1,1.5,t]},{t,0,2000},PlotRange->All,PlotStyle->Dashed]]

Show[ErrorListPlot[
Table[
errorData[Select[reldata4C,#[[2]] == osmo&][[All,{3,4}]]],{osmo,DeleteDuplicates[reldata4C[[All,2]]]}],
PlotRange->{{0,2000},{0,1.2}},PlotMarkers->"OpenMarkers",PlotLegends->{"0.5 osmol/kg","1.0 osmol/kg"},Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
Plot[{
toxmodel1[274.8285714285715,0.5,t],
toxmodel1[274.8285714285715,1.0,t]},{t,0,2000},PlotRange->All(*,PlotStyle->Thick*)],
Plot[{
toxmodel2[274.8285714285715,0.5,t],
toxmodel2[274.8285714285715,1.0,t]},{t,0,2000},PlotRange->All,PlotStyle->Thin],
Plot[{
toxmodel3[274.8285714285715,0.5,t],
toxmodel3[274.8285714285715,1.0,t]},{t,0,2000},PlotRange->All,PlotStyle->Dashed]]

22*60

Plot[{
vtTemp[273+0,1.5(*extCPA*),1(*extSalt*),1320 (*tf*)][t]/V0,
vtTemp[273+5,1.5(*extCPA*),1(*extSalt*),1320 (*tf*)][t]/V0,
vtTemp[273+10,1.5(*extCPA*),1(*extSalt*),1320 (*tf*)][t]/V0,
vtTemp[273+15,1.5(*extCPA*),1(*extSalt*),1320 (*tf*)][t]/V0,
vtTemp[273+20,1.5(*extCPA*),1(*extSalt*),1320 (*tf*)][t]/V0
},{t,0,1320},PlotRange->All]

Optimized loading Code

Functions

getShrinkjTotValue[vgoal_,sbywgoal_,tempKelvin_]:=Module[{msInt,tInt,tFinal,volume2P,vCall,dvCall,extCPAInt,timeInt,ms,sbyw2P,getsbyw,josmshrink,jtoxshrink,tempDamage,jtot,fullShrinkFunction,
wLtoμm3Const,
isosmolality,
(*initialSalt=isosmolality; (* unless cells are preequilibrated with anisosmotic nonperm solution, this will be isosmolality *)*)
(*initialRelWaterVol=isosmolality/initialSalt;  (*initial relative water volume, should be 1 unless special case. *)*)
VbarEg,
VbarGly,
VbarDMSO,
Vbar,
gasConst,
vbFraction,
cellCPAinit,
(*extCPA=1.5 * wLtoμm3Const(*L/((μm)^3)*);(*osmol/((μm)^3) of CPA*)
extSalt=isosmolality;(* osmol/((μm)^3) of non-permeating salt*)*)
timeBounder,


V0,
surfaceArea,
vb,
W0,
nni,
S0,

gasR,
lpA ,
lpE,
psA ,
 psE,

Cshrink,
βshrink,
Cswell,
βswell,

μa,
μb,
αa,
αb,

Ctemp,
tempPhys,
loadingExtSalt},

(*GLOBAL PARAMETERS*)
wLtoμm3Const=(10.^(-15))(*L/((μm)^3)*) ;
isosmolality=1.000 * wLtoμm3Const(*L/((μm)^3)*) ; (*osmol/ ((μm)^3) *)
(*initialSalt=isosmolality; (* unless cells are preequilibrated with anisosmotic nonperm solution, this will be isosmolality *)*)
(*initialRelWaterVol=isosmolality/initialSalt;  (*initial relative water volume, should be 1 unless special case. *)*)
VbarEg=62.068/1.1135 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ; (*((μm)^3)/mol*)
VbarGly=92.09382/1.26 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
VbarDMSO=78.13 (*g·(mol^(-1))*)/1.1004 (*g (cm^(-3))*) * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
Vbar=VbarDMSO;
gasConst=0.08205 * ((10^15)/1)(* ((μm)^3) / L*); (* ((μm)^3) atm/(kelvin mol) *)
vbFraction=0.3114096329503619`;
cellCPAinit=0.0; (*initial moles of CPA --intracellular 2.5*)
(*extCPA=1.5 * wLtoμm3Const(*L/((μm)^3)*);(*osmol/((μm)^3) of CPA*)
extSalt=isosmolality;(* osmol/((μm)^3) of non-permeating salt*)*)
timeBounder=20000; (*seconds*)


V0=447536.1408228077`(*((μm)^3)*);
surfaceArea=4.835975862049408`*(V0^(2/3))(*((μm)^2)*);
vb=0.3114096329503619`;
W0=(1-vb)*V0(*((μm)^3)*);
nni=isosmolality*W0 (*osmols*);
S0=0 (*initial intracellular CPA *)(*mols*);

gasR= 1.987*10^-3(* kcal mol^-1 K^-1*);
lpA =16.06038610207711`;
lpE=-6.555277296921298`*1000*gasR;
psA =41.83189898749541`;
 psE=-13.04594344564523`*1000*gasR;

Cshrink=1.881086302374743`;
βshrink=10.87554987231552`;
Cswell=-7.663464309343182`;
βswell=1.5476459457183478`;

μa=-80.55238281488882;
μb=41.01389808202523;
αa=22.206291494178927;
αb=-11.527831847336365;

Ctemp=0.025295141078064486;
tempPhys=14.326439389183086+273.15;

loadingExtSalt=0 (*osmol/kg*);



volume2P =ParametricNDSolveValue[{
w'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((extCPA+extSalt)*wLtoμm3Const-((s[t]+nni)/w[t])),

s'[t]== E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* wLtoμm3Const -(s[t]/w[t])),

vt'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((extCPA+extSalt)* wLtoμm3Const -((s[t]+nni)/w[t]))+ Vbar E^(psA + psE/(gasR * tempKelvin))* surfaceArea (extCPA* wLtoμm3Const-(s[t]/w[t])),


(*jOsm'[t]==If[vt[t]<=  V0,
(E^Cshrink)*(1-vt[t]/V0)^βshrink ,
(E^Cswell)*(vt[t]/V0-1)^βswell
],*)

w[0]==W0, 
s[0]==S0(*cellCPAinit*),
vt[0]==V0(*,
jOsm[0]==0*)
},
vt,
{t,0.,tf},
{(*tempKelvin,*)extCPA,extSalt,tf},(*
AccuracyGoal->20,*)MaxSteps->Infinity];

vCall[msInt_?NumericQ,tInt_?NumericQ]:=volume2P[msInt,loadingExtSalt,tInt][tInt]/V0;
dvCall[msInt_?NumericQ,tInt_?NumericQ]:=volume2P[msInt,loadingExtSalt,tInt]'[tInt];
(*get initial shrink values*)
{extCPAInt,timeInt}={msInt,tInt}/.FindRoot[{vCall[msInt,tInt]== vgoal,dvCall[msInt,tInt]==  0},{{msInt,10,0,Infinity},{tInt,60,0,Infinity}}];
(*Print[{extCPAInt,timeInt}];*)

(*shrunken volume*)
ms[wt_?NumericQ,st_?NumericQ,extSalt_?NumericQ,t_?NumericQ]:=Piecewise[{
{(*First step is to have constant ms that gets you to the desired volume,*)
extCPAInt,t≤  timeInt},
{
(*now hold the volume constant*)
(((wLtoμm3Const)^(-1)) (E^(lpA+(lpE/(gasR tempKelvin)))) gasConst nni tempKelvin+((wLtoμm3Const)^(-1)) (E^(lpA+(lpE/(gasR tempKelvin)))) gasConst tempKelvin st-((wLtoμm3Const)^(-1)) (E^(psA+(psE/(gasR tempKelvin)))) Vbar st-(E^(lpA+(lpE/(gasR tempKelvin)))) extSalt   gasConst tempKelvin wt)/(((E^(lpA+(lpE/(gasR tempKelvin)))) gasConst tempKelvin-(E^(psA+(psE/(gasR tempKelvin)))) Vbar)wt),timeInt<t}
}];
sbyw2P=ParametricNDSolveValue[{
w'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((ms[w[t],s[t],loadingExtSalt,t](*extCPA*)+loadingExtSalt)* wLtoμm3Const-((s[t]+nni)/w[t])),

s'[t]== E^(psA + psE/(gasR * tempKelvin))* surfaceArea (ms[w[t],s[t],loadingExtSalt,t](*extCPA*)* wLtoμm3Const -(s[t]/w[t])),

sbyw[t]== Vbar s[t]/(Vbar s[t] + w[t]),
(*jOsm'[t]==If[vt[t]<=  V0,
(E^Cshrink)*(1-vt[t]/V0)^βshrink ,
(E^Cswell)*(vt[t]/V0-1)^βswell
],*)
(*WhenEvent[Vbar s[t]/(Vbar s[t] + w[t])== sbywgoal,Sow[t]],*)

w[0]==W0, 
s[0]==S0(*cellCPAinit*)(*,
vt[0]==V0*)(*,
jOsm[0]==0*)
},
sbyw,
(*{w,s,vt},*)
{t,0.,(tf)},
{(*tempKelvin,*)(*extCPA,*)(*extSalt,*)tf},
MaxSteps->Infinity];

(*now get the time needed for loading*)
getsbyw[tf_?NumericQ]:=sbyw2P[tf][tf];
(*Print["Results of the roots: ",FindRoot[getsbyw[tf]==sbywgoal,{tf,1000,1,Infinity}]];*)
tFinal=tf/.FindRoot[getsbyw[tf]==sbywgoal,{tf,10,1,Infinity}];

(*tFinal=Flatten[Reap[w[loadingExtSalt,20000][20000]/.sbyw2P]][[2]];*)
(*Print["tFinal: ",tFinal];*)

fullShrinkFunction=ParametricNDSolve[{
w'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((ms[w[t],s[t],loadingExtSalt,t](*extCPA*)+loadingExtSalt)* wLtoμm3Const-((s[t]+nni)/w[t])),

s'[t]== E^(psA + psE/(gasR * tempKelvin))* surfaceArea (ms[w[t],s[t],loadingExtSalt,t](*extCPA*)* wLtoμm3Const-(s[t]/w[t])),

vt'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((ms[w[t],s[t],loadingExtSalt,t](*extCPA*)+loadingExtSalt)*wLtoμm3Const-((s[t]+nni)/w[t]))+ Vbar E^(psA + psE/(gasR * tempKelvin))* surfaceArea (ms[w[t],s[t],loadingExtSalt,t](*extCPA*)*wLtoμm3Const-(s[t]/w[t])),

(*jOsm'[t]==If[vt[t]<=  V0,
(E^Cshrink)*(1-vt[t]/V0)^βshrink ,
(E^Cswell)*(vt[t]/V0-1)^βswell
],*)
(*WhenEvent[Vbar s[t]/(Vbar s[t] + w[t])== sbywgoal,Sow[t]],*)

w[0]==W0, 
s[0]==S0(*cellCPAinit*),
vt[0]==V0(*,
jOsm[0]==0*)
},
{w,s,vt},
{t,0.,tf},
{(*tempKelvin,*)(*extCPA,*)(*extSalt,*)tf},
MaxSteps->Infinity];

(*now define damage models*)
josmshrink=NDSolveValue[{
w'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((ms[w[t],s[t],loadingExtSalt(*extSalt*),t](*extCPA*)+loadingExtSalt)* wLtoμm3Const-((s[t]+nni)/w[t])),

s'[t]== E^(psA + psE/(gasR * tempKelvin))* surfaceArea (ms[w[t],s[t],loadingExtSalt,t](*extCPA*)* wLtoμm3Const-(s[t]/w[t])),

vt'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((ms[w[t],s[t],loadingExtSalt,t](*extCPA*)+loadingExtSalt)* wLtoμm3Const-((s[t]+nni)/w[t]))+ Vbar E^(psA + psE/(gasR * tempKelvin))* surfaceArea (ms[w[t],s[t],loadingExtSalt,t](*extCPA*)* wLtoμm3Const-(s[t]/w[t])),

(*sbyw[t]==Vbar s[t]/(Vbar s[t] + w[t]),*)

jOsm'[t]==If[vt[t]<=  V0,
(E^Cshrink)*(1-vt[t]/V0)^βshrink ,
(E^Cswell)*(vt[t]/V0-1)^βswell
],

w[0]==W0, 
s[0]==S0(*cellCPAinit*),
vt[0]==V0,
jOsm[0]== 0
},
jOsm,
{t,0.,tFinal},
MaxSteps->Infinity];

jtoxshrink=NDSolveValue[{
w'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((ms[w[t],s[t],loadingExtSalt,t](*extCPA*)+loadingExtSalt)* wLtoμm3Const-((s[t]+nni)/w[t])),

s'[t]== E^(psA + psE/(gasR * tempKelvin))* surfaceArea (ms[w[t],s[t],loadingExtSalt,t](*extCPA*)* wLtoμm3Const-(s[t]/w[t])),

(*vt'[t]==-E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((ms[w[t],s[t],loadingExtSalt,t](*extCPA*)+loadingExtSalt)* wLtoμm3Const-((s[t]+nni)/w[t]))+ Vbar E^(psA + psE/(gasR * tempKelvin))* surfaceArea (ms[w[t],s[t],loadingExtSalt,t](*extCPA*)* wLtoμm3Const-(s[t]/w[t])),*)

(*sbyw[t]==Vbar s[t]/(Vbar s[t] + w[t]),*)

jtox'[t]== E^(μa+μb/(gasR tempKelvin)) * (ms[w[t],s[t],loadingExtSalt,t])^(E^(αa+αb/(gasR tempKelvin))),

w[0]==W0, 
s[0]==S0(*cellCPAinit*),
(*vt[0]==V0,*)
jtox[0]== 0
},
jtox,
{t,0.,tFinal},
MaxSteps->Infinity];

tempDamage[temp_?NumericQ]:=Ctemp*Piecewise[{{0,temp>= tempPhys},{tempPhys-temp,temp< tempPhys}}];


(*get damage*)
jtot= josmshrink[tFinal]+jtoxshrink[tFinal]+tempDamage[tempKelvin];

Return[jtot]
]

getSwelljTotValue[vgoal_,sbywgoal_,tempKelvin_]:=Module[{msInt,tInt,tFinal,volume2P,vCall,dvCall,extCPAInt,timeInt,ms,sbyw2P,getsbyw,josm,jtox,tempDamage,jtot,
initialSwellVolume2P,loadingms,mn,swellLoading,initSwellTime,dehydrationStartTime,fullSwellLoading,
thisVolTemp,thisVolFun,thisMSFun,jOsmFun,MSFun,tempFun,jOsmDamage,jToxDamage,jToxFun,thisWaterTemp,thisCPATemp,thisWaterFun,thisCPAFun,msFun,dehydrationendTimeLimit,
wLtoμm3Const,
isosmolality,
(*initialSalt=isosmolality; (* unless cells are preequilibrated with anisosmotic nonperm solution, this will be isosmolality *)*)
(*initialRelWaterVol=isosmolality/initialSalt;  (*initial relative water volume, should be 1 unless special case. *)*)
VbarEg,
VbarGly,
VbarDMSO,
Vbar,
gasConst,
vbFraction,
cellCPAinit,
(*extCPA=1.5 * wLtoμm3Const(*L/((μm)^3)*);(*osmol/((μm)^3) of CPA*)
extSalt=isosmolality;(* osmol/((μm)^3) of non-permeating salt*)*)
timeBounder,

V0,
surfaceArea,
vb,
W0,
nni,
S0,

gasR,
lpA ,
lpE,
psA ,
 psE,

Cshrink,
βshrink,
Cswell,
βswell,

μa,
μb,
αa,
αb,

Ctemp,
tempPhys,
loadingExtSalt,
intLoadingExtCPA,
gets,finishingTimeGuess,dehydrationendTimeGuess,
oldW,
oldS,
newW,
newS,
currentT,
Δt,checkForInitialSwellTime,checkForDehydrationStartTime,phase,mss,mnn,
newJosm,newJtox,Cswellprop,toxExponent,toxProportionality
},

(*GLOBAL PARAMETERS*)

wLtoμm3Const=(10.^(-15))(*L/((μm)^3)*) ;
isosmolality=1.000 * wLtoμm3Const(*L/((μm)^3)*) ; (*osmol/ ((μm)^3) *)
(*initialSalt=isosmolality; (* unless cells are preequilibrated with anisosmotic nonperm solution, this will be isosmolality *)*)
(*initialRelWaterVol=isosmolality/initialSalt;  (*initial relative water volume, should be 1 unless special case. *)*)
VbarEg=62.068/1.1135 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ; (*((μm)^3)/mol*)
VbarGly=92.09382/1.26 * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
VbarDMSO=78.13 (*g·(mol^(-1))*)/1.1004 (*g (cm^(-3))*) * (10^12)(*((μm)^(3 ))/ (cm^3)*) ;(*((μm)^3)/mol*)
Vbar=VbarDMSO;
gasConst=0.08205 * ((10^15)/1)(* ((μm)^3) / L*); (* ((μm)^3) atm/(kelvin mol) *)
vbFraction=0.3114096329503619`;
cellCPAinit=0.0; (*initial moles of CPA --intracellular 2.5*)
(*extCPA=1.5 * wLtoμm3Const(*L/((μm)^3)*);(*osmol/((μm)^3) of CPA*)
extSalt=isosmolality;(* osmol/((μm)^3) of non-permeating salt*)*)
timeBounder=8000; (*seconds*)


V0=447536.1408228077`(*((μm)^3)*);
surfaceArea=4.835975862049408`*(V0^(2/3))(*((μm)^2)*);
vb=0.3114096329503619`;
W0=(1-vb)*V0(*((μm)^3)*);
nni=isosmolality*W0 (*osmols*);
S0=0 (*initial intracellular CPA *)(*mols*);

gasR= 1.987*10^-3(* kcal mol^-1 K^-1*);
lpA =16.06038610207711`;
lpE=-6.555277296921298`*1000*gasR;
psA =41.83189898749541`;
 psE=-13.04594344564523`*1000*gasR;

Cshrink=1.881086302374743`;
βshrink=10.87554987231552`;
Cswell=-7.663464309343182`;
βswell=1.5476459457183478`;

μa=-80.55238281488882;
μb=41.01389808202523;
αa=22.206291494178927;
αb=-11.527831847336365;

Ctemp=0.025295141078064486;
tempPhys=14.326439389183086+273.15;

loadingExtSalt=0 (*osmol/kg*);
intLoadingExtCPA=0 (*osmol/kg*);


(*Now get total loading time*)
oldW=W0;
oldS=S0;
newJosm=0;
newJtox=0;
Cswellprop=E^Cswell;

toxExponent=E^(αa+αb/(gasR tempKelvin));
toxProportionality=E^(μa+μb/(gasR tempKelvin));

currentT=0;
Δt=0.1;
initSwellTime=0;
dehydrationStartTime=0;

(*swelling phase*)
mnn=0;
mss=0;
While[(oldW/V0+vbFraction)< vgoal&&currentT<100000,
newW=oldW+-Δt*E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((mss(*extCPA*)+mnn(*extSalt*))* wLtoμm3Const-((oldS+nni)/oldW));
newS=oldS+Δt* E^(psA + psE/(gasR * tempKelvin))* surfaceArea (mss(*extCPA*)* wLtoμm3Const-(oldS/oldW));

oldW=newW;
oldS=newS;

newJosm=newJosm+Δt*(Cswellprop*Abs[(newW/V0+vbFraction-1)]^βswell);
(*newJtox=newJtox+Δt *(toxProportionality*mss^toxExponent);*)

currentT=currentT+Δt(*;
If[(oldW/V0+vbFraction)≥vgoal,Break[]],
{time,0,100000,Δt}*)];
initSwellTime=currentT;


(*loading phase*)
mnn=0;
While[sbywgoal>(oldS Vbar/W0)&&currentT<100000,

mss=(((wLtoμm3Const)^(-1)) (E^(lpA+(lpE/(gasR tempKelvin)))) gasConst nni tempKelvin+((wLtoμm3Const)^(-1)) (E^(lpA+(lpE/(gasR tempKelvin)))) gasConst tempKelvin oldS-((wLtoμm3Const)^(-1)) (E^(psA+(psE/(gasR tempKelvin)))) Vbar oldS-(E^(lpA+(lpE/(gasR tempKelvin)))) loadingExtSalt   gasConst tempKelvin oldW)/(((E^(lpA+(lpE/(gasR tempKelvin)))) gasConst tempKelvin-(E^(psA+(psE/(gasR tempKelvin)))) Vbar)oldW);

newW=oldW+-Δt*E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((mss(*extCPA*)+mnn(*extSalt*))* wLtoμm3Const-((oldS+nni)/oldW));
newS=oldS+Δt* E^(psA + psE/(gasR * tempKelvin))* surfaceArea (mss(*extCPA*)* wLtoμm3Const-(oldS/oldW));
oldW=newW;
oldS=newS;

newJosm=newJosm+Δt*(Cswellprop*Abs[(newW/V0+vbFraction-1)]^βswell);
newJtox=newJtox+Δt *(toxProportionality*mss^toxExponent);

currentT=currentT+Δt(*;
If[(sbywgoal W0/ Vbar)≥  oldS,Break[]],
{time,0,100000,Δt}*)];
dehydrationStartTime=currentT;

(*dehydration phase*)
mnn=10;
While[(Vbar oldS/(Vbar oldS + oldW))<sbywgoal&&currentT<100000,
mss=oldS/oldW  ((wLtoμm3Const)^(-1));
newW=oldW+-Δt*E^(lpA + lpE/(gasR * tempKelvin)) * surfaceArea gasConst tempKelvin * ((mss(*extCPA*)+mnn(*extSalt*))* wLtoμm3Const-((oldS+nni)/oldW));
newS=oldS+Δt* E^(psA + psE/(gasR * tempKelvin))* surfaceArea (mss(*extCPA*)* wLtoμm3Const-(oldS/oldW));
oldW=newW;
oldS=newS;

newJosm=newJosm+Δt*(Cswellprop*Abs[(newW/V0+vbFraction-1)]^βswell);
newJtox=newJtox+Δt *(toxProportionality*mss^toxExponent);

currentT=currentT+Δt(*;
If[(Vbar oldS/(Vbar oldS + oldW))≥ sbywgoal,Break[]],
{time,0,100000,Δt}
*)];
tFinal=currentT;

tempFun[temp_?NumericQ]:=Ctemp*Piecewise[{{0,temp>= tempPhys},{tempPhys-temp,temp< tempPhys}}];

(*Get damages for protocol*)
jOsmDamage=newJosm;
jToxDamage=newJtox;
tempDamage=tempFun[tempKelvin];

(*get total damage*)
jtot= (jOsmDamage+jToxDamage+tempDamage);

Return[jtot]
]
getDamage[vgoal_,sbywgoal_,tempKelvin_]:=If[vgoal<=  1,getShrinkjTotValue[vgoal,sbywgoal,tempKelvin],getSwelljTotValue[vgoal,sbywgoal,tempKelvin]]

Numerical search for maxima

Table[Flatten[{vbyv,NMaximize[{
E^-getDamage[vload,vbyv,temp],
0.5<vload<3,
273<temp≤ 293}
,{vload,temp}]},1],{vbyv,0.01,.21,.01}]

Results and Figures

maxSurvivalList={{0.01`,0.9979338488068317`,{vload->1.1299786465766288`,temp->293.`}},{0.02`,0.9943865006052048`,{vload->1.1866598415004557`,temp->292.987750160777`}},{0.03`,0.9884635753896116`,{vload->1.245121628724048`,temp->292.9919449229656`}},{0.04`,0.9793973678756437`,{vload->1.3029492965693539`,temp->292.9963948263466`}},{0.05`,0.966411583992255`,{vload->1.3582729372285016`,temp->292.9952238628876`}},{0.060000000000000005`,0.9488355171842175`,{vload->1.4192492384795468`,temp->292.99581737070883`}},{0.06999999999999999`,0.9260071873726994`,{vload->1.4811126999371504`,temp->292.9978709513413`}},{0.08`,0.896982443681475`,{vload->1.5479758663843506`,temp->292.995132282517`}},{0.09`,0.8602859721116762`,{vload->1.6101915845493058`,temp->292.9961885760747`}},{0.09999999999999999`,0.8118852616866483`,{vload->1.6693696269559088`,temp->292.9920277867449`}},{0.11`,0.7426563494163609`,{vload->1.7367370191517804`,temp->292.9886091406724`}},{0.12`,0.6340568889275988`,{vload->1.7949717680260993`,temp->292.9640485090359`}},{0.13`,0.4644857109354347`,{vload->1.8593195133542288`,temp->292.99239599818213`}},{0.14`,0.26807789680459154`,{vload->1.9209953161024416`,temp->291.27186245184544`}},{0.15000000000000002`,0.11939714035221226`,{vload->1.9500397628117883`,temp->289.8737608705695`}},{0.16`,0.03874316141200599`,{vload->2.0334543882227454`,temp->288.49313220476614`}},{0.17`,0.008449875070049764`,{vload->2.104624975798205`,temp->287.4825142122767`}},{0.18000000000000002`,0.0011195759302233628`,{vload->2.1613626925663225`,temp->286.47023202766246`}},{0.19`,0.00008618461617285642`,{vload->2.210401087912254`,temp->285.73150936679014`}},{0.2`,3.5574966108442204`*^-6,{vload->2.3033189839037362`,temp->285.2589345914029`}},{0.21000000000000002`,7.07595757344673`*^-8,{vload->2.3484597689169457`,temp->284.40627080356694`}}};

flatMaxSurv=Table[Join[maxSurvivalList[[i,{1,2}]],{vload,temp}/.maxSurvivalList[[i,3]]],{i,1,Length[maxSurvivalList]}]

Table[Flatten[{vbyv,NMaximize[{
E^-getDamage[vload,vbyv,temp],
0.5<vload<3,
273<temp≤ 293}
,{vload,temp}]},1],{vbyv,{0.4,0.5}}]

Show[ListLinePlot[maxSurvivalList[[All,{1,2}]],PlotRange->All,PlotStyle->Black,Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large],
ListPlot[maxSurvivalList[[All,{1,2}]],PlotRange->All,(*Joined->True,InterpolationOrder->1,*)(*Mesh->All,*)PlotStyle->Black,Frame->True,FrameTicksStyle->Directive[Black,24],ImageSize -> Large]]

(*below is survival for 0.1 CPA v/v as a function of loading volume and temperature*)

ddd=Flatten[Table[{vol,temp,E^-getDamage[vol,0.1,temp]},{vol,1.01,3,.1},{temp,280,293,1}],1];

MaximalBy[ddd,Last]

ListPlot3D[ddd,PlotRange->All]