Inflection points (IPs) of unfolding profiles are useful parameters for assessing protein stability, along with melting temperatures (Tms). This article is about how IPs are determined from measured data. 

In order to analyze complex unfolding profiles with multiple unfolding transitions, Prometheus software uses smoothed differentiations of the data to precisely determine the inflection point for each transition in the unfolding profile (see figure below). For each profile curve, the second derivative is calculated, and its intercepts with the x-axis are determined. Relevant intercepts are determined based on the directionality of the unfolding profile. In the example depicted here, the unfolding profile curve is going upwards (redshift), and the second derivative is scanned for x-intercepts with the curve sloping downwards. This prevents the misinterpretation of irrelevant inflection points in the unfolding profile.

Figure: The left panel represents a simulated unfolding profile with two upward transitions in the fluorescence ratio. The framed part of the curve was differentiated (represented in the right panel). Here, the first and second derivatives of the curve are shown: f’ signifies the first derivative (purple line) and f’’ the second derivative (green line). Prometheus software only shows the first derivative, but uses the second derivative to determine x-axis intercepts. Only the intercept points showing an opposite direction in the second derivative compared to the original curve are extracted as relevant IPs, highlighted by arrows. Therefore, the first and third intercepts are extracted as relevant IPs (signified by grey circles), while the second intercept is disregarded as irrelevant (signified by grey crossed out circle).