For each growth curve obtained from the above described regression model, the growth rate was calculated as the slope of each line fitted between the knots of every growth curve (Figure 1). That is, the growth rate (alternatively slope) was calculated for the curve in each of the three intervals. The slope of these line segments may be considered as the derivative of each spline between each knot for every growth curve and thus representing growth rate. We refer to these slopes (or derivatives), change in OD with respect to time, as
growth rates. The growth rates for all strains were compared using a t-distribution for each concentration of lactoferrin added to LB or Syncase broth. Growth rates outside the 95% prediction interval were considered as significantly different to those inside (Figures 2 and 3).
“spline” package in R produces scaling coefficients that can be difficult to interpret, we re-run the above mentioned regression model in STATA using the mkspline function, which gives linear coefficient estimates for each slope. Hence, to obtain linear growth estimates, regression models were fitted for all strains using the mkspline function in STATA, which provides the slope of each linear growth estimate making up the modeled curve. Both the bs function in R and the mkspline function in STATA were applied to make a linear spline with three separate, equally spaced lines joined together with two knots. These three lines represent intervals 1, 2 and 3 (See Figure 1)