# Probing Globular Protein Self-Assembling Dynamics by Heterodyne Transient Grating Experiments
## 3 Results and Discussion
After 55 \({}^{\circ}\)C, the trend of the damping rate became almost linear with the temperature, recovering the expected behavior of the solvent, D\({}_{2}\)O. Another slight deviation from the quasi-linear T-dependence occurred around 70 \({}^{\circ}\)C. This could again be related to the unfolding of a residual fraction of HEWL proteins less affected b the acid addition [6]. Figure 4b reports the temperature trend of the damping rate for the 240 mg/mL HEWL solution. In this experimental condition, the damping rate behavior was totally different with respect to that of the diluted solution. In particular, in the 23-45 \({}^{\circ}\)C temperature range, \(\Gamma_{A}\) decreased due to the reduction of solution viscosity. Above 45 \({}^{\circ}\)C, the damping of the acoustic wave oscillation increased strongly with temperature, which could be due to the formation of protein aggregates. Indeed, at 45 \({}^{\circ}\)C the percentage of proteins in the unfolded state was high enough to promote both the deviation of the acoustic damping rate from the linear T-dependence (visible from Figure 4a) and to promote the aggregation process (visible from Figure 4b). From the literature, it is well known that even a relatively low percentage of unfolded proteins promote aggregation processes [45]. Figure 4c reports the temperature behavior of the gel system. The damping rate showed a linear temperature dependence from 23 \({}^{\circ}\)C to 45 \({}^{\circ}\)C, and at above 45 \({}^{\circ}\)C remained almost constant. We interpreted this trend with the breaking of the gel network, which implied the transition to the liquid state. In other words, according to our results the gel-sol transition takes place at 45 \({}^{\circ}\)C.  
Figure 4: Temperature dependence of the acoustic damping rate measured on the samples for the 2.1 \(\upmu\)m\({}^{-1}\)\(q\)-vector. (**a**) The diluted (120 mg/mL) lysozyme solution, (**b**) the concentrated (240 mg/mL) lysozyme solution, and (**c**) the gel system. The shaded band underlines the temperature zones characterized by different dynamic regimes. According to our investigations, the ultrasonic velocities and attenuation processes were both sensitive to the aggregation phenomena. Nevertheless, it seemed that the attenuation processes were more sensitive to the self-assembling even from its earlier stages of the process, in agreement with other investigations [17]. For both the solution samples, the deviation in the damping rates occurred around 45 \({}^{\circ}\)C, where the aggregates started to form without necessarily modifying the overall elasticity of the sample. Afterward, the increase of temperature induces the formation of a great amount of lysozyme aggregates [17; 46]. For the low concentrated solution, the unfolding of the native lysozyme stabilized the damping rate, whereas, in the highly concentrated solution, the unfolded species promoted aggregate formation, which produced a strong increase of the attenuation phenomena. This could be due to a different level of coordination between the lysozyme aggregated species or to their different structure and/or dimensions. Our outcomes were in agreement with previous studies on other protein solutions [16; 27]. The authors found that the protein's conformational rearrangements and the aggregate's formation highly affect the attenuation of the acoustic waves. Instead, the sound speed seemed to be less sensitive to these phenomena, which turn to be important only at 55 \({}^{\circ}\)C, where the aggregation extent was high enough to largely affect the sample elasticity. For the gel system, we must consider a different scenario. In fact, both the ultrasonic parameters, speed and damping, were affected by the gel-solution transition of the system taking place at 45 \({}^{\circ}\)C. According to our results, the speed of longitudinal ultrasonic acoustic waves of the gel system was dominated by the solvent proprieties (Figure 3c), whereas the damping rate showed clear differences from solvent features.