gaussian smoother in r

Question

I'm using ggplot to plot the below data, and I'm trying to fit a smoother that captures the gaussian-like nature of the curves. I've tried standard loess and spline smoothers, but they result in huge dips in the Front line that aren't there (I tried attaching an image of the stat_smooth() result, but I don't have 10 reputation points as I'm new to stackoverflow).

I'm now trying to force a gaussian smoother by creating a formula (MyFormula) that's a gaussian shape and using that in the stat_smooth function, but I get the following error, which I think is happening because the MyFormula equation isn't being separated by FrontBack:

"Error in model.frame.default(formula = C$mean_Dye ~ max(C$mean_Dye) + : variable lengths differ (found for 'max(C$mean_Dye)')"

Is there an easier way to fit a gaussian-shaped (or any other representative) smoother to this data for both the front and back lines?

MyFormula=C$mean_Dye~max(C$mean_Dye)*exp(-0.5*((C$Meters-mean(C$Meters))/sd(C$Meters))^2)     

ggplot(C, aes(x=Meters, y=mean_Dye, color=FrontBack)) + geom_point(pch=19, size = 6, alpha=1/4) + geom_errorbar(aes(ymin=mean_Dye-seDye, ymax=mean_Dye+seDye), width=0.1) + coord_cartesian(ylim=c(-100,100), xlim=c(16,50)) + stat_smooth(method="gam", formula=MyFormula, group=C$FrontBack, se=F)

 Meters     mean_Dye   seDye    FrontBack  
 17.0      -0.005      0.05        Front
 29.0       0.036      0.05        Front
 31.5       50.78      14.3        Front
 32.5       69.82      8.04        Front
 33.0       58.53      5.72        Front
 33.5       50.93      5.29        Front
 34.5       43.15      3.70        Front
 37.0       15.51      4.02        Front
 49.0       0.069      0.03        Front
 17.0       0.111      0.023        Back
 23.0       1.92       0.278        Back
 26.0       5.98       0.743        Back
 28.0       12.13      1.186        Back
 30.0       18.99      1.419        Back
 31.0       19.04      0.916        Back
 32.0       18.17      1.416        Back
 33.0       16.51      2.143        Back
 34.0       13.99      2.178        Back
 35.0       11.85      2.136        Back
 36.0       6.63       1.751        Back
 38.0       0.97       0.689        Back
 40.0       0.099      0.116        Back
 43.0       0.004      0.039        Back
 49.0       0.041      0.040        Back

Answer 1

Answer found in previous post - works great.

f<-function(x, theta) {
    m<-theta[1]; s<-theta[2]; a<-theta[3]; b<-theta[4];
    a*exp(-0.5*((x-m)/s)^2) + b
}

fit<-nls(y~f(x,c(m,s,a,b)), data.frame(x,y), start=list(m=12, s=5, a=12, b=-2))