Fig. 5: Time and temperature-dependent microscopic dynamics.

a Temporal evolution of the relaxation time of egg yolk samples heated to temperatures in the range 63–72 °C. Four distinct dynamical regimes are identified. regime-A: accelerating motion of egg yolk-granules during heating, regime-B: equilibration of the system at the final temperature followed by protein denaturation and aggregation, regime-C: gelation of proteins, regime-D: ageing of the gel. The regime-A is denoted by the red dashed circle. The regimes B, C, and D are separated by horizontal dashed lines. The \({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} }\) and τ_B are the absolute waiting time and the equilibrium relaxation time from regime-B, respectively. The black dashed line indicates \(\sim {({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} })}^{-0.4}\). b Normalised relaxation time with respect to τ_B, as a function of t_w (= \({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} }-{t}_{{{{{{{{\rm{heating}}}}}}}}}\)) normalised with respect to t^* (sol-gel transition time). Here \({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} }\) and t_heating are the absolute waiting time and the time taken to reach the final T, respectively. The two black curves before and after t^* indicate a power-law (\(\sim {({t}_{{{{{{{{\rm{w}}}}}}}}}/{t}^{*})}^{0.3}\)) and an exponential fit (\(\sim \exp ({t}_{{{{{{{{\rm{w}}}}}}}}}/{t}^{*})\)), respectively. An Arrhenius plot of t^* with Arrhenius fit (solid line) is shown in the inset of b. The error bar in t^* is estimated using the error in the fit parameters of power-law fits of normalised scattering invariant at low-q and high-q regimes as shown in Fig. 2 (see Supplementary Note 6 for details). c Temporal evolution of the relaxation time of egg yolk heated to temperatures in the range of 75–100 °C. The regime-A is denoted by the red dashed circle. The regimes C and D are separated by horizontal dashed lines. The black dashed lines in regime-A and D indicate \(\sim {({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} })}^{-0.4}\) and \(\sim {({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} })}^{0.4}\) respectively. d Comparison of the relaxation time of egg yolk with egg yolk-plasma and yolk-granules (yolk-granule concentration is 910 mg/ml) at two temperatures as indicated in the legend. All τ are extracted for a q value of 0.0055 nm⁻¹ except for the yolk-plasma sample, where the dynamical information was not accessible at this q value. Hence we extrapolated τ at q = 0.03 nm⁻¹ to the value at q = 0.0055 nm⁻¹ using a τ ∝ 1/q relationship. Details are provided in the Supplementary Note 9. The blue vertical line indicates \({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} }\) = 70 s. The black dashed lines from bottom to top represent \(\sim {({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} })}^{-0.4}\), \(\sim {({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} })}^{1.8}\) and \(\sim {({t}_{{{{{{{{\rm{w}}}}}}}}}^{{\prime} })}^{0.4}\). a, c, d The coloured short vertical lines close to the x axis represent the time (t_heating) taken to reach a temperature T from the initial temperature of 22 °C. The error bars in τ indicate the parameter uncertainty obtained from the fits using least-squares minimisation. Source data are provided as a Source Data file.