# Problem with fitting

So I have a very simple question related to a simple topic, but also directly related to a fitting problem. I see that my question is related to this question but I don't manage to make the bridge between them.

The basic question is how to make a function that would look like :

list = {{1, 2}, 2, {3, 4, 8, 12}, 4, {2, 2, 2, 2, 2}}
F[x_] = list[[x]]

And I want to use it in the following context :

err[Vinitphi_?NumberQ, l_?NumberQ, nc_?NumberQ, tauC_?NumberQ,
tauG_?NumberQ, D0_?NumberQ, k_] =
With[{model = (Rad /. pfun)[Vinitphi, l, nc, tauC, tauG, D0]},

fit = FindMinimum[{Sum[
err[Vinitphi/2^(i - 1), l, nc, tauC, tauG, D0, i], {i, 1, 6, 1}],
3*10^7 < Vinitphi < 9*10^7, 15 < l < 30, 0.05 < tauC < 0.5,
0.2 < nc < 0.8,
4*10^(10) < D0 < 2*10^(11)}, {{Vinitphi, 4.5*10^7}, {l, 25}, {nc,
0.5}, {tauC, 0.2}, {tauG, 30}, {D0, 6*10^(10)}}]

where I get the error :

Part::pkspec1: The expression k cannot be used as a part specification.

Could you help please ?

I write in the following appendix the ParametricNDSolve I'm taking care of :

Appendix :

rad={{{0., 117.705}, {3., 148.255}, {6., 176.81}, {9., 183.561}, {12.,
197.419}, {15., 210.672}, {18., 211.152}, {21., 209.889}, {24.,
207.741}, {27., 204.352}, {30., 201.79}, {33., 199.976}, {36.,
199.04}, {39., 197.151}, {42., 197.584}, {45., 196.198}, {48.,
195.153}, {51., 195.711}, {54., 194.088}, {57., 193.304}, {60.,
192.474}, {63., 192.13}, {66., 192.877}, {69., 192.371}, {72.,
192.657}, {75., 190.984}, {78., 190.685}, {81., 190.449}, {84.,
189.83}, {87., 189.625}, {90., 194.855}, {93., 186.581}, {96.,
184.735}, {99., 184.586}, {102., 183.505}, {105., 181.531}, {108.,
179.925}, {111., 178.428}, {114., 176.164}, {117., 175.375}, {120.,
174.782}, {123., 172.649}, {126., 170.454}, {129.,
168.357}, {132., 168.04}, {135., 167.26}, {138., 165.657}, {141.,
164.797}, {144., 163.705}, {147., 161.214}, {150., 160.5}, {153.,
159.353}, {156., 157.873}, {159., 157.225}}, {{0., 51.7792}, {3.,
80.825}, {6., 108.913}, {9., 121.147}, {12., 130.805}, {15.,
140.562}, {18., 143.615}, {21., 146.513}, {24., 147.63}, {27.,
147.12}, {30., 146.693}, {33., 147.396}, {36., 148.256}, {39.,
147.737}, {42., 148.685}, {45., 149.043}, {48., 147.814}, {51.,
148.776}, {54., 147.959}, {57., 147.775}, {60., 148.031}, {63.,
148.284}, {66., 148.334}, {69., 148.521}, {72., 148.974}, {75.,
146.562}, {78., 145.734}, {81., 145.177}, {84., 145.588}, {87.,
144.949}, {90., 147.035}, {93., 141.755}, {96., 140.841}, {99.,
139.94}, {102., 138.25}, {105., 136.508}, {108., 135.52}, {111.,
133.758}, {114., 132.694}, {117., 131.744}, {120., 131.208}, {123.,
130.292}, {126., 127.612}, {129., 126.981}, {132.,
127.035}, {135., 125.198}, {138., 123.557}, {141., 123.946}, {144.,
120.738}, {147., 119.875}, {150., 118.828}, {153.,
118.162}, {156., 117.363}, {159., 116.712}}, {{0., 29.62}, {3.,
53.1414}, {6., 67.2233}, {9., 82.5676}, {12., 83.5019}, {15.,
92.3142}, {18., 98.9869}, {21., 102.557}, {24., 106.481}, {27.,
107.188}, {30., 107.637}, {33., 108.415}, {36., 109.622}, {39.,
110.593}, {42., 111.205}, {45., 111.396}, {48., 111.668}, {51.,
114.126}, {54., 113.3}, {57., 114.27}, {60., 114.849}, {63.,
110.808}, {66., 116.51}, {69., 118.796}, {72., 119.636}, {75.,
118.02}, {78., 116.026}, {81., 116.767}, {84., 116.994}, {87.,
119.169}, {90., 121.246}, {93., 116.291}, {96., 117.296}, {99.,
117.72}, {102., 115.814}, {105., 114.76}, {108., 114.853}, {111.,
113.886}, {114., 112.522}, {117., 112.109}, {120., 112.376}, {123.,
110.998}, {126., 109.708}, {129., 108.926}, {132.,
108.075}, {135., 107.182}, {138., 106.723}, {141., 106.562}, {144.,
103.807}, {147., 102.798}, {150., 102.333}, {153.,
101.633}, {156., 100.395}, {159., 99.889}}, {{0., 79.5768}, {3.,
86.0729}, {6., 101.334}, {9., 103.158}, {12., 104.818}, {15.,
104.534}, {18., 104.361}, {21., 105.568}, {24., 107.109}, {27.,
105.042}, {30., 105.165}, {33., 107.669}, {36., 108.182}, {39.,
108.549}, {42., 109.208}, {45., 109.714}, {48., 110.098}, {51.,
110.481}, {54., 110.373}, {57., 110.563}, {60., 111.115}, {63.,
111.766}, {66., 112.415}, {69., 113.322}, {72., 113.272}, {75.,
113.95}, {78., 113.98}, {81., 114.017}, {84., 111.879}, {87.,
114.706}, {90., 112.125}, {93., 109.696}, {96., 112.481}, {99.,
109.528}, {102., 108.22}, {105., 108.112}, {108., 107.387}, {111.,
106.369}, {114., 106.522}, {117., 105.678}, {120., 111.234}, {123.,
109.391}, {126., 104.95}, {129., 109.079}, {132., 109.363}, {135.,
100.807}, {138., 99.9696}, {141., 100.622}, {144., 99.789}, {147.,
98.5068}, {150., 99.6161}, {153., 97.4872}, {156.,
101.554}, {159., 101.406}}, {{0., 30.4597}, {3., 35.889}, {6.,
45.7724}, {9., 54.0641}, {12., 56.851}, {15., 59.1402}, {18.,
61.0664}, {21., 63.1851}, {24., 65.2428}, {27., 66.6239}, {30.,
67.5882}, {33., 68.5353}, {36., 69.885}, {39., 71.1742}, {42.,
72.485}, {45., 73.2793}, {48., 74.2798}, {51., 74.7271}, {54.,
74.8248}, {57., 75.83}, {60., 76.1228}, {63., 77.5324}, {66.,
76.4005}, {69., 77.5578}, {72., 80.4519}, {75., 80.1548}, {78.,
80.1533}, {81., 79.2626}, {84., 79.6456}, {87., 79.5882}, {90.,
78.9125}, {93., 77.5023}, {96., 80.9046}, {99., 78.125}, {102.,
78.1087}, {105., 82.0064}, {108., 80.6066}, {111., 82.9245}, {114.,
83.6384}, {117., 82.0775}, {120., 81.1198}, {123., 75.248}, {126.,
78.1893}, {129., 72.6991}, {132., 72.683}, {135., 80.5139}, {138.,
83.442}, {141., 81.0871}, {144., 80.1472}, {147., 79.3543}, {150.,
79.0979}, {153., 79.0636}, {156., 78.3953}, {159.,
77.2895}}, {{0., 27.5731}, {3., 27.4456}, {6., 37.2589}, {9.,
40.9683}, {12., 43.2509}, {15., 44.3384}, {18., 46.5891}, {21.,
48.0219}, {24., 49.6954}, {27., 51.1536}, {30., 51.7754}, {33.,
53.2019}, {36., 54.9082}, {39., 55.9732}, {42., 57.3092}, {45.,
58.6397}, {48., 58.9803}, {51., 58.6734}, {54., 60.6691}, {57.,
61.3107}, {60., 62.1459}, {63., 63.2534}, {66., 64.1169}, {69.,
64.7201}, {72., 65.4561}, {75., 65.7958}, {78., 65.9518}, {81.,
66.9163}, {84., 67.5038}, {87., 64.925}, {90., 69.8176}, {93.,
65.8334}, {96., 69.2665}, {99., 66.6777}, {102., 65.9855}, {105.,
69.4403}, {108., 70.2052}, {111., 69.9442}, {114., 70.7562}, {117.,
70.3714}, {120., 63.5385}, {123., 62.8021}, {126.,
67.0399}, {129., 61.5096}, {132., 63.1028}, {135., 70.3602}, {138.,
70.2032}, {141., 69.4146}, {144., 68.2243}, {147.,
67.9524}, {150., 67.8477}, {153., 68.2036}, {156., 68.2165}, {159.,
67.5863}}}

eps = 1;
phic = 0.85;
v = 80
a = 0
phi0 = 0.63;
L = 5000;
nL0 = 1;

pfun = ParametricNDSolve[{Derivative[1][V][
t] == -((
D0 (E^(-((L + t v)^2/(4 D0 t)))) (-L + t v) Vinitphi )/((D0 t)^(
3/2)*4*Sqrt[Pi]*phi0)) + (
2 Vphi[t] (phic - Vphi[t]/V[t]) (-2 + phic +
2 (1 - Vphi[t]/V[t])) (1 - (1 - Vphi[t]/V[t])^2))/((1 -
phic)^2 tauC V[t]^(
1/3)) - (-nc V[t] - (
4 l L nL0 \[Pi] Csch[((E^(((a Vphi[t])/(
2 V[t])))) ((3/\[Pi])^(1/3)) (V[t]^(1/3)) )/(
2^(2/3) l)] (-E^(-((a Vphi[t])/V[t]))
l^2 Sinh[((E^(((a Vphi[t])/(2 V[t])))) ((3/\[Pi])^(
1/3)) (V[t]^(1/3)) )/(2^(2/3) l)] + (
E^(-((a Vphi[t])/(2 V[t]))) l (3/\[Pi])^(1/3)
Cosh[((E^(((a Vphi[t])/(2 V[t])))) ((3/\[Pi])^(1/3)) (
V[t]^(1/3)) )/(2^(2/3) l)] V[t]^(1/3))/(2^(
2/3)) ))/ (-L Coth[((E^(((a Vphi[t])/(
2 V[t])))) ((3/\[Pi])^(1/3)) (V[t]^(1/3)) )/(
2^(2/3) l)] + ((3/\[Pi])^(1/3)
Coth[((E^(((a Vphi[t])/(2 V[t])))) ((3/\[Pi])^(1/3)) (
V[t]^(1/3)) )/(2^(2/3) l)] V[t]^(1/3))/2^(2/3) - l))/
tauG, V[eps] == 4*Pi/3*2^3,
Derivative[1][Vphi][
t] == -((D0 (E^(-((L + t v)^2/(4 D0 t)))) (-L + t v) Vinitphi )/(
4*Sqrt[Pi]*phi0 (D0 t)^(3/2))) + ((
Vphi[t] (-nc V[t] - (
4 l L nL0 \[Pi] Csch[((E^(((a Vphi[t])/(
2 V[t])))) ((3/\[Pi])^(1/3)) (V[t]^(1/3)) )/(
2^(2/3) l)] (-E^(-((a Vphi[t])/V[t]))
l^2 Sinh[((E^(((a Vphi[t])/(2 V[t])))) ((3/\[Pi])^(
1/3)) (V[t]^(1/3)) )/(2^(2/3) l)] + (
E^(-((a Vphi[t])/(2 V[t]))) l (3/\[Pi])^(1/3)
Cosh[((E^(((a Vphi[t])/(2 V[t])))) ((3/\[Pi])^(1/3)) (
V[t]^(1/3)) )/(2^(2/3) l)] V[t]^(1/3))/(2^(
2/3)) ))/ (-L Coth[((E^(((a Vphi[t])/(
2 V[t])))) ((3/\[Pi])^(1/3)) (V[t]^(1/3)) )/(
2^(2/3) l)] + ((3/\[Pi])^(1/3)
Coth[((E^(((a Vphi[t])/(2 V[t])))) ((3/\[Pi])^(1/3)) (
V[t]^(1/3)) )/(2^(2/3) l)] V[t]^(1/3))/2^(2/3) - l)))/
V[t]) /tauG, Vphi[eps] ==4*Pi/3*2^3*phi0,