# Salt-Specific Suppression of the Cold Denaturation of Thermophilic Multidomain Initiation Factor 2
## 3 Discussion
### Thermodynamic Analysis of Unfolding Denaturation of Multidomain Proteins
In the case of IF2, a significant overlap in the melting transitions leads to the averaging of the melting curves. We examined the conditions when independent denaturation transitions merged, and they could not be resolved using our analysis. Using mathematical modeling of the independent transitions that systematically varied values for \(T_{\mathit{trs,\,hot}}\), \(\Delta H\), and \(\Delta c_{p}\), we could decipher the resolution of our experimental methods. To this end, it is crucial to mimic experimental conditions as much as possible, which include finite temperature steps and noise. The noise was extracted from an experimental curve, and this noise is, to a large extent, temperature independent. After calculating the first derivative of the signal for temperature, we found that even large differences in \(\Delta H\), \(\Delta c_{p}\), and \(T_{\mathit{trs,\,hot}}\) may not be enough to allow observing the distinct multiple steps of the denaturation process, particularly when denaturation enthalpies are low. Hence, under our conditions, even a 20 \({}^{\circ}\)C theoretical difference in \(T_{\mathit{trs,\,hot}}\) between unfolding G and C fragments would not result in a separate denaturation curves. When enthalpy decreases even further in the presence of salts, the resolution might be even worse. For example, in 2 M NaCl and CsCl, \(T_{\mathit{trs,\,hot}}\) of the C and G fragments differed by 20 \({}^{\circ}\)C; however, the transitions were not resolved in either the simulation or experiments. This is mostly due to the decrease in denaturation enthalpy (50 kJ/mol for G fragment and 212 kJ/mol for C fragment in the presence of NaCl; and 36 kJ/mol for G fragment and 169 kJ/mol for C fragment in the presence CsCl). As such, care must be given to the analysis when the enthalpies are low, because the analysis can be corrupted. This is because the native state is not fully reached, which affects the signal for the native state and native state baselines [32]. In the abovementioned approach, we utilize the first derivative of the signal concerning temperature, which has a clear limit due to the temperature increment over which the signal was measured, and also due to the presence of noise that had to be eliminated by averaging or by carefully performed smoothing. The major advantage of the first derivative approach is that it is model-independent and can, in principle, resolve individual transitions. Here, one interesting observation is that cold denaturation may provide a better resolution and identification of the multiple denaturation processes than hot denaturation. For example, we detected two transitions in the cold denaturation process, while during hot denaturation, there was only a single denaturation process with no transition. In the case of phosphoglycerate kinase, the authors in [41] observed two transitions during cold denaturation, while they observed only one denaturation transition on the hot side. One can conclude that the denaturation process involves a different number of steps and states on the cold and hot sides. Our analysis suggests that the number of observable transitions is not a secure diagnostic tool to conclude differences in the denaturation processes, i.e., the process can involve the same number of steps that are not resolvable due to the overlap in the transitions. Importantly, several prerequisites have to be fulfilled to reach robust conclusions on the thermodynamics of the denaturation process. First, the protein undergoes reversible denaturation IF2 and the fragments undergo reversible denaturation, as evidenced by the repeatability of the observed cold and hot denaturation (4-100 \({}^{\circ}\)C). Second, for valid two-state analysis, the cold- and heat-denatured states must be thermodynamically equivalent, which enables a description of cold and hot denaturation by a single temperature-dependent equilibrium constant. If not, these processes must be described by two distinct equilibrium constants.