*4.6. Rotational Correlation Time Corrections*

The τ*<sup>c</sup>* of a molecule in solution is related with the solution viscosity, η, the molecular hydrodynamic volume, V, the Boltzmann constant, kB, and the absolute temperature, *T*, as [35,70]:

$$
\pi\_{\mathcal{E}} = \frac{\eta \mathcal{V}}{\mathbf{k}\_{\mathcal{B}} T} \tag{9}
$$

Based on Equation (9), τ<sup>c</sup> can be corrected for different temperatures, considering that the molecular volume does not change significantly in a small temperature interval (±5 ◦C; i.e., V and kB are constants), using [70]:

$$\frac{T\_\text{a}\tau\_{\text{c,a}}}{\eta\_\text{a}} = \frac{T\_\text{b}\tau\_{\text{c,b}}}{\eta\_\text{b}} \Leftrightarrow \tau\_{\text{c,b}} = \tau\_{\text{c,a}} \frac{\eta\_\text{b}T\_\text{a}}{\eta\_\text{a}T\_\text{b}} \tag{10}$$

where the indexes 'a' and 'b' represent a different condition of *T* and η, taking into account the variation of η with *T* [37]. The η values were assumed to be those of pure H2O or 10% D2O in the case of the corrections for the NMR-based values (those from the literature). In this way, Table 5 below shows the values employed on the calculations [37]:

**Table 5.** Values for η employed in this work, derived from the references and Equations above.


#### *4.7. Temperature Denaturation Measurements via Circular Dichroism (CD) Spectroscopy*

Circular dichroism spectroscopy measurements were carried out in a JASCO J-815 (Tokyo, Japan), using 0.1 cm path length quartz cuvettes, data pitch of 0.5 nm, velocity of 200 nm/min, data integration time (DIT) of 1 s and performing 3 accumulations. Spectra were acquired in the far UV region, between 200 and 260 nm, with 1 nm bandwidth. The temperature was controlled by a JASCO PTC-423S/15 Peltier equipment. It was varied between 0 and 96 ◦C, in steps of 2 ◦C, increasing at a rate of 8 ◦C/min and waiting 100 s after crossing 5 times the target temperature, *T*. Then, the system was allowed, at least, 120 s to equilibrate (sufficient time for a stable CD signal). Before and after denaturation, spectra were acquired at 25 ◦C, to determine the reversibility of thermal denaturation. DENV C monomer concentration was 20 μM in 50 mM KH2PO4, 200 mM KCl, pH 6.0 or pH 7.5, with 220 μL of total volume. Spectra were smoothed through the means-movement method (using 7 points) and normalized to mean residue molar ellipticity, [θ] (in deg cm2 dmol−<sup>1</sup> Res<sup>−</sup>1).

For the CD temperature denaturation data treatment, we assumed a dimer to monomer denaturation model [71–73] in which the folded dimer, F2, separates into unfolded monomers, U, in a single step described by reaction R1:

$$\text{F}\_2 \Leftrightarrow 2\text{U} \tag{\text{R1}}$$

In this system, the total protein concentration, [Pm], in monomer equivalents, is described as:

$$\mathbb{E}\left[\mathbf{P}\_{\mathbf{m}}\right] = \mathbf{2}[\mathbf{F}\_2] + \left[\mathbf{U}\right] \tag{11}$$

Hereafter, concentrations are treated as dimensionless, being divided by the standard concentration of 1 M, in order to be at standard thermodynamic conditions. The fractions of monomer in the folded, fF, and unfolded, fU, states are calculated by [71,72]:

$$\mathbf{f\_{F}} = \frac{2[\mathbf{F\_{2}}]}{[\mathbf{P\_{m}}]} \tag{12}$$

$$\mathbf{f}\_{\mathbf{U}} = \frac{[\mathbf{U}]}{[\mathbf{P}\_{\mathbf{m}}]} \tag{13}$$

$$\mathbf{f\_F} + \mathbf{f\_U} = 1\tag{14}$$

and the concentrations of folded dimer and unfolded monomer can be written in terms of fU:

$$\mathbf{f}[\mathbf{U}] = \mathbf{f}\_{\mathbf{U}}[\mathbf{P}\_{\mathbf{m}}] \tag{15}$$

$$\mathbf{f}\left[\mathbf{F}\_2\right] = \frac{\mathbf{f}\_\mathbf{F}\left[\mathbf{P}\_\mathbf{m}\right]}{2} = \frac{(\mathbf{1} - \mathbf{f}\_\mathbf{U})\left[\mathbf{P}\_\mathbf{m}\right]}{2} \tag{16}$$

Then, the equilibrium constant, Keq, of R1 is defined in terms of [U] and [F2], or fU and [Pm]:

$$\mathbf{K\_{eq}} = \frac{\left[\mathbf{U}\right]^2}{\left[\mathbf{F\_2}\right]} = \frac{\left(\mathbf{f\_{U}}[\mathbf{P\_m}]\right)^2}{(1 - \mathbf{f\_U})\left[\mathbf{P\_m}\right]/2} = \frac{2\left[\mathbf{P\_m}\right] \times \mathbf{f\_U}^2}{(1 - \mathbf{f\_U})}\tag{17}$$

which can be solved in order to fU, with the only solution in which fU ∈ [0; 1] being:

$$\text{rf}\_{\text{U}} = \frac{\sqrt{8[\text{P}\_{\text{m}}]\text{K}\_{\text{eq}} + \text{K}\_{\text{eq}}\text{e}^{2}} - \text{K}\_{\text{eq}}}{4[\text{P}\_{\text{m}}]} \tag{18}$$

The [θ] signal as a function of temperature [71,72,74], [θ]*T*, can be described as a linear combination of the signal of the folded, [θ]*T*,F, and unfolded states, [θ]*T*,U, weighted by fU:

$$[\boldsymbol{\theta}]\_T = [\boldsymbol{\theta}]\_{T, \mathbf{F}} (\mathbf{1} - \mathbf{f}\_{\mathbf{U}}) + [\boldsymbol{\theta}]\_{T, \mathbf{U}} \mathbf{f}\_{\mathbf{U}} \tag{19}$$

where [θ]*T*,F and [θ]*T*,U have a variation with *T* described here by a straight line (*i* can be F or U) [72,74]:

$$\left[\boldsymbol{\theta}\right]\_{T,i} = \mathfrak{m}\_i \ltimes T + \left[\boldsymbol{\theta}\right]\_{0,i} \tag{20}$$

Equation (19) can be re-written to evidence fU and then substitute it by Equation (18) [71,72]:

$$\begin{aligned} [\boldsymbol{\theta}]\_{\mathcal{T}} &= [\boldsymbol{\theta}]\_{\mathcal{T},\mathcal{F}} + \left( [\boldsymbol{\theta}]\_{\mathcal{T},\mathcal{U}} - [\boldsymbol{\theta}]\_{\mathcal{T},\mathcal{F}} \right) \frac{\sqrt{8 [\mathcal{P}\_{\rm m}] \mathcal{K}\_{\rm eq} + \mathcal{K}\_{\rm eq} \mathcal{Z}} - \mathcal{K}\_{\rm eq}}{4 [\mathcal{P}\_{\rm m}]} \end{aligned} \tag{21}$$

Keq can also be described by the standard Gibbs free-energy, Δ*G*◦ , of the reaction R1:

$$\mathbf{K}\_{\text{eq}} = \mathbf{e}^{-\frac{\Lambda G^{\circ}}{RT}} \tag{22}$$

where R is the rare gas constant and *T* is the absolute temperature. The Δ*G*◦ function used to fit the data contains both the enthalpic, Δ*H*◦ , and entropic, Δ*S* ◦ , variations with temperature, which take into account Δ*H*◦ *T* ◦ <sup>m</sup> , the specific heat capacity at constant pressure, <sup>Δ</sup>*C*◦ *<sup>p</sup>*, and the standard conditions' denaturation temperature, *T* ◦ m, according to [74]:

$$
\Delta G^{\circ} = \Delta H^{\circ}\_{\,\,T\_{\rm m}} \left( 1 - \frac{T}{T\_{\rm m}^{\circ}} \right) - \Delta C\_p^{\circ} \left( T\_{\rm m}^{\circ} - T + T \ln \left( \frac{T}{T\_{\rm m}^{\circ}} \right) \right) \tag{23}
$$

In our data, ΔC◦ <sup>p</sup> was statistically equal to 0 and, thus, Equation (23) can be simplified to:

$$
\Delta \text{G}^{\circ} = \Delta H^{\circ}\_{T\_{\text{m}}} \left( 1 - \frac{T}{T\_{\text{m}}^{\circ}} \right) \tag{24}
$$

Then, Equation (21) was combined with Equations (20), (22) and (24), and fitted to the data using GraphPad Prism v5 software, via the non-linear least squares method, to extract both the Δ*H*◦ *T* ◦ <sup>m</sup> and *T* ◦ m, along with the respective SE values. Afterwards, Δ*S* ◦ *T* ◦ <sup>m</sup> can be obtained, since <sup>Δ</sup>*G*◦ = 0 kJ mol−<sup>1</sup> at *T* ◦ m, via the following Equation:

$$
\Delta H^{\circ}\_{\ T\_{\rm m}^{\circ}} - T\_{\rm m}^{\circ} \Delta S^{\circ}\_{\ \ T\_{\rm m}^{\circ}} = 0 \Rightarrow \Delta S^{\circ}\_{\ \ T\_{\rm m}^{\circ}} = \frac{\Delta H^{\circ}\_{\ \ T\_{\rm m}^{\circ}}}{T\_{\rm m}^{\circ}} \tag{25}
$$

The SE of Δ*S* ◦ *T* ◦ <sup>m</sup> was calculated based on <sup>Δ</sup>*H*◦ *T* ◦ <sup>m</sup> , *<sup>T</sup>* ◦ m, and the respective SE values:

$$\mathrm{SE}\_{\mathrm{\Delta S}^{\circ}\_{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\cdot}}\cdot}\right{\mathrm{\mathrm{\cdot}}}}}}}}}}}}}}}}}}\right}}\,}}\,}$$

Interestingly, for a dimer to monomer denaturation, Keq depends on [Pm] and, consequently, Δ*G*◦ also depends on [Pm]. This implies that Δ*G*◦ = 0 at *T* ◦ <sup>m</sup> (*T*<sup>m</sup> value estimated if [Pm] = 1M), which is considerably higher than the observed *T*<sup>m</sup> (that occurs when fU = 0.5). The dependence of *T*<sup>m</sup> with [Pm] is [72]:

$$
\Delta G^{\circ}\_{\text{ f}\_{\text{U}}=0.5} = -\text{RT}\_{\text{m}} \ln \left( \left[ \text{P}\_{\text{m}} \right] \right) \Rightarrow T\_{\text{m}} = \frac{\Delta G^{\circ}\_{\text{f}\_{\text{U}}=0.5}}{-\text{R} \ln \left( \left[ \text{P}\_{\text{m}} \right] \right)} \tag{27}
$$

$$T\_{\rm m} = \frac{\Delta H^{\circ}\_{\rm T\_{\rm m}}}{\Delta S^{\circ}\_{\rm T\_{\rm m}} - \text{R } \ln([\rm P\_{\rm m}])} \tag{28}$$

The SE of *T*m was based on the percentual SE value of *T* ◦ m.

Values obtained for both pH conditions were statistically evaluated via F-tests to compare two possible fits, one assuming a given parameter as being different for the distinct data sets, and another assuming that parameter to be equal between data sets (while maintaining the other parameters different). No statistically significant difference (*p* < 0.05) was observed.

**Author Contributions:** Conceptualization, A.F.F., N.C.S. and I.C.M.; In silico studies, A.F.F., V.A., A.S.M., N.K. and I.C.M.; Recombinant protein production, A.F.F., A.S.M., F.J.E. and I.C.M.; Time-resolved fluorescence anisotropy studies, A.F.F. and J.C.R.; Circular dichroism studies, A.F.F. and I.C.M.; Formal analysis, A.F.F., J.C.R. and I.C.M.; Resources, I.C.M., F.J.E., N.C.S.; Writing-original draft preparation, A.F.F., N.K., and I.C.M.; Writing-review and editing, A.F.F., A.S.M., N.K., N.C.S. and I.C.M.; Supervision, N.C.S. and I.C.M.; Project administration, N.C.S. and I.C.M.; Funding acquisition, N.C.S. and I.C.M.

**Funding:** This work was supported by "Fundação para a Ciência e a Tecnologia–Ministério da Ciência, Tecnologia e Ensino Superior" (FCT-MCTES, Portugal) project PTDC/SAU-ENB/117013/2010, Calouste Gulbenkian Foundation (FCG, Portugal) project Science Frontiers Research Prize 2010. A.F.F., A.S.M. and J.C.R. also acknowledge FCT-MCTES fellowships SFRH/BD/77609/2011, PD/BD/113698/2015 and SFRH/BD/95856/2013, respectively. I.C.M. acknowledges FCT-MCTES Programs "Investigador FCT" (IF/00772/2013) and "Concurso de Estímulo ao Emprego Científico" (CEECIND/01670/2017). This work was also supported by UID/BIM/50005/2019, project funded by Fundação para a Ciência e a Tecnologia (FCT)/ Ministério da Ciência, Tecnologia e Ensino Superior (MCTES) through Fundos do Orçamento de Estado.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
