Amino Acid spacings

BMS Data Plot with mean gap 17

TauNu={ {17.45,.8136}, {55.01,0.5929}, {16.31,0.7686} ,{14.58,.7271},{20.75,.7776},{18.96,0.7384},{39.14,0.7866},{14.55,0.9524},{13.26,0.7316},{10.18,0.8478},{45.60,0.8462},
{15.53,0.8695},{21.24,0.7689},{23.62,0.8077},{20.96,0.7767},{10.75,0.8467},{16.19,0.8540},{17.13,0.9325},{61.82,0.5796},
{26.70,0.7943}}

bmsdata[τ_,ν_]:=Abs[PolyGamma[1,ν]-PolyGamma[1,1]]+Abs[Log[18/τ] 1]

BMS=Table[{TauNu[[k,1]],TauNu[[k,2]],bmsdata[TauNu[[k,1]],TauNu[[k,2]]]+0.3},
{k,1,20}];

scatt=ListPointPlot3D[BMS,BoxRatios->{1,1,1},PlotRange->{{1,70},{0.49,1.31},{0,6.2} },
ViewPoint->{15,-3,15},BoxRatios->{1,1,1},PlotStyle->PointSize[Large] ];
s4=Plot3D[Abs[PolyGamma[1,ν]-PolyGamma[1,1]]+Abs[Log[18/τ] 1], 
{τ,1,70},{ν,0.49,1.31}, PlotPoints->50,Mesh->{9,5},
ViewPoint->{15,-3,15},BoxRatios->{1,1,1},PlotRange->All,
Boxed->True, Axes->True];
s5=Show[scatt,s4]

Random Simulations

MSG1=(({{21.814410480349345`, 20.565273404957054`, 1.1251695919589921`}, {18.34011090573013`, 18.248765538835244`, 1.0100361840090206`}, {19.872255489021956`, 20.15241049360088`, 0.9723896380846054`}, {18.94876660341556`, 18.10382061110822`, 1.095522793229974`}, {19.822`, 19.129196750953067`, 1.07374579354625`}, {19.64566929133858`, 20.203219052998307`, 0.9455674475654587`}, {20.87029288702929`, 20.657126939995443`, 1.020744976146723`}, {21.70152505446623`, 22.002387173605797`, 0.9728388458601751`}, {20.1046277665996`, 18.16082718003723`, 1.2255211817702756`}, {18.754253308128543`, 17.348044434484972`, 1.168687781264709`}, {20.196356275303643`, 20.235026439636048`, 0.9961815504296393`}, {19.892215568862277`, 19.47378646492349`, 1.0434352562341607`}, {20.724425887265134`, 19.379907218598962`, 1.1435670407259115`}, {21.723311546840957`, 22.13041242442661`, 0.9635473167243888`}, {18.990458015267176`, 18.359536119418227`, 1.0699105517624174`}, {19.843058350100602`, 19.67865628563805`, 1.0167784626077003`}, {19.170825335892513`, 18.40797259054983`, 1.084600256396369`}, {19.978`, 18.41444268499043`, 1.1770281747021003`}, {19.701581027667984`, 17.788634636977537`, 1.2266394500605764`}, {19.82634730538922`, 19.18092240824559`, 1.0684309060807302`}}))

dist[τ_,ν_]:=Abs[PolyGamma[1,ν]-PolyGamma[1,1]]+Abs[Log[20/τ] 1];
Data=Table[{MSG1[[k,1]],MSG1[[k,3]],dist[MSG1[[k,1]],MSG1[[k,3]]]+0.03},
{k,1,20}];
scattr=ListPointPlot3D[Data,BoxRatios->{1,1,1},PlotRange->All,
ViewPoint->{15,-3,15},BoxRatios->{1,1,1},PlotStyle->PointSize[Large] ];
s4r=Plot3D[Abs[PolyGamma[1,ν]-PolyGamma[1,1]]+Abs[Log[20/τ] 1], 
{τ,18,22},{ν,0.49,1.32}, PlotPoints->50,Mesh->{8,5},
ViewPoint->{15,-3,15},BoxRatios->{1,1,1},PlotRange->All,FaceGrids->None,
Boxed->True, Axes->True];
Show[s4r,scattr,s]