Author Correction: Thermoring basis for the TRPV3 bio-thermometer

Correction to: Scientific Reports 10.1038/s41598-023-47100-0, published online 07 December 2023

The original version of this Article contained errors.

In the original version of this Article, the calculated heat capacity of homotetrameric TRPV3 was incorrectly calculated.

As a result, Table 1

Construct	Wild-type mTRPV3
∆H1/2, kcal/mol	1	− 0.5			2	2.5
∆S1/2, cal/mol-K	3.03	− 1.52			6.18	7.73
∆Cp, kcal/mol-K	604	670			14.4	35.1
Systemic thermal instability (Ti)	1.88	1.95	1.20	1.25	1.21	1.33
Calculated Ω10, min at Emin = 0.5 kcal/mol	10.1	9.78			1.27	3.28
Calculated Ω10, mean at Emean = 1.0 kcal/mol	20.8	19.3			2.69	6.92
Calculated Ω10, max at Emax = 3.0 kcal/mol	65.2	56.6			8.81	22.7
Measured Q10,	20.6				2.32
Ref. for measured Tth or Q10	19		19,33		19,24

now reads,

Construct	Wild-type mTRPV3
∆H1/2, kcal/mol	4	− 2			8	10
∆S1/2, cal/mol-K	12.1	− 6.07			24.7	30.9
∆Cp, kcal/mol-K	8.68	9.71			0.762	1.83
Systemic thermal instability (Ti)	1.88	1.95	1.20	1.25	1.21	1.33
Calculated Ω10, min at Emin = 0.5 kcal/mol	10.1	9.78			1.27	3.28
Calculated Ω10, mean at Emean = 1.0 kcal/mol	20.8	19.3			2.69	6.92
Calculated Ω10, max at Emax = 3.0 kcal/mol	65.2	56.6			8.81	22.7
Measured Q10,	20.6				2.32
Ref. for measured Tth or Q10	19		19,34		19,24

In addition, in the Results section

“Assuming the channel open probability (P_o) was 0.5 at T_1/2 of 50.5 °C (323.5 K), which was close to the experimental value¹⁹, the change in molar enthalpy at 323.5 K (ΔH_1/2) would be 2 kcal/mol (Table 1). Thus, the change in molar entropy at 323.5 K (ΔS_1/2) was 6.18 cal/mol-K (Table 1). Assuming mTRPV3 was fully open at 61 °C, the change in molar Gibbs free energy (ΔG) would be − 2.5 kcal/mol (Table 1). Based on the Gibbs–Helmholtz equation, the change in molar heat capacity (ΔC_p) was about 14.4 kcal/mol-K for one subunit (Table 1). When the gating pathway was extended beyond the PC-dependent minimal gating pathway, the ΔC_p value increased to 35.1 kcal/mol-K (Table 1).

In contrast, for channel gating from the closed and reduced state at 52 °C to the open and oxidized one until the maximal activity temperature around 61 °C, the total noncovalent interactions and grid sizes along the PC-dependent minimal gating pathway decreased from 51 and 96 to 49 and 59, respectively (Table 1). If P_o was 0.5 at T_1/2 of 56.5 °C (329.5 K), which was still near the experimental value¹⁹, ΔH_1/2 and ΔS_1/2 at 329.5 K would be 1 kcal/mol and 3.03 cal/mol-K, respectively (Table 1). If mTRPV3 completely opened at 61 °C, ΔG would be − 18.5 kcal/mol (Table 1). Using the same Gibbs–Helmholtz equation, ΔC_p was calculated as large as 604 kcal/mol-K for one subunit (Table 1). The value increased to 670 kcal/mol-K along with the extended gating pathway from F377 to W742 (Table 1).”

now reads,

“Assuming the apparent channel open probability (P_o) was 0.5 at T_1/2 of 50.5 °C (323.5 K), which was close to the experimental value¹⁹, the change in molar enthalpy at 323.5 K (ΔH_1/2) upon the total broken non-covalent interactions would be 8 kcal/mol (Table 1). Thus, the change in molar entropy at 323.5 K (ΔS_1/2) was 24.7 cal/mol-K (Table 1). Assuming mTRPV3 was allosterically open at 61 °C, the change in molar Gibbs free energy (ΔG) would be − 2.5 kcal/mol (Table 1). Based on the modified Gibbs–Helmholtz equation, the change in molar heat capacity (ΔC_p) was about 0.762 kcal/mol-K for one channel (Table 1). When the gating pathway was extended beyond the PC-dependent minimal gating pathway, the ΔC_p value increased to 1.83 kcal/mol-K (Table 1).

In contrast, for channel gating from the closed and reduced state at 52 °C to the open and oxidized one until the maximal activity temperature around 61 °C, the total noncovalent interactions and grid sizes along the PC-dependent minimal gating pathway of one subunit decreased from 51 and 96 to 49 and 59, respectively (Table 1). If the apparent P_o was 0.5 at T_1/2 of 56.5 °C (329.5 K), which was still near the experimental value¹⁹, ΔH_1/2 and ΔS_1/2 at 329.5 K upon the total broken non-covalent interactions would be 4 kcal/mol and 12.1 cal/mol-K, respectively (Table 1). If mTRPV3 allosterically opened at 61 °C, ΔG would be − 18.5 kcal/mol (Table 1). Using the same Gibbs–Helmholtz equation, ΔC_p was calculated as large as 8.68 kcal/mol-K for one channel (Table 1). The value increased to 9.61 kcal/mol-K along with the extended gating pathway from F377 to W742 (Table 1).”

Furthermore, in the Discussion section

“It should be noteworthy that even if the change in molar enthalpy (ΔH) of one subunit was as small as 2 kcal/mol from a closed and reduced state to an oxidized and open one, the huge change in molar heat capacity (ΔC_p) of 604 kcal/mol-K was still enough to absorb more heat as the configurational heat capacity (love) while keeping a small change in molar entropy at T_1/2 (ΔS_1/2, 3.03 cal/mol). This observation was in agreement with the decrease in the conformational entropy as reflected by the decrease of the systematic thermal instability from 1.88 to 1.20 to stabilize the open state (Table 1). In sharp contrast, when mTRPV3 was oxidized, ΔC_p dramatically declined from 604 kcal/mol-K to 14.4 kcal/mol-K along with the decrease in the mean Ω₁₀ value from 20.8 to 2.69 and the decline in Q₁₀ from 20.6 to 2.32 (Table 1).”

now reads

“It should be noteworthy that even if the change in molar enthalpy (ΔH) of one channel upon the total broken non-covalent interactions was as small as 8 kcal/mol from a closed and reduced state to an oxidized and open one, the huge change in molar heat capacity (ΔC_p) of 8.68 kcal/mol-K was still enough to absorb more heat as the configurational heat capacity (love) while keeping a small change in molar entropy at T_1/2 (ΔS_1/2, 12.1 cal/mol). This observation was in agreement with the decrease in the entropy of compact conformations as reflected by the decrease of the systematic thermal instability from 1.88 to 1.20 to stabilize the apparent open state (Table 1). In sharp contrast, when mTRPV3 was oxidized, ΔC_p dramatically declined from 8.68 kcal/mol-K to 0.762 kcal/mol-K along with the decrease in the mean Ω₁₀ value from 20.8 to 2.69 and the decline in Q₁₀ from 20.6 to 2.32 (Table 1).”

Finally, in the Methods section

“T_1/2 was defined as a temperature at which the open probability (P_o) of mTRPV3 was 0.5. It was calculated using the following equation:

$${\text{T}}_{1/2}={\text{T}}_{\text{m},\text{c}}+{\text{(T}}_{\text{m},\text{o}}-{\text{T}}_{\text{m},\text{c}})/2$$

where, T_m,c and T_m,o were the calculated melting temperature thresholds of the biggest grids in mTRPV3 in the closed and open states, respectively. At T_1/2, the change in systematic molar Gibbs free energy (ΔG) is zero. The change in systematic molar enthalpy was calculated using the following equation:

$$\mathrm{\Delta }{\text{H}}_{1/2}={\text{(H}}_{\text{c}}-{\text{H}}_{\text{o}})/2={\text{(EN}}_{\text{c}}-{\text{EN}}_{\text{o}})/2$$

where, E is usually 1 kcal/mol. Therefore, the change in molar entropy at T_1/2 could be calculated using the following equation:

$$\mathrm{\Delta }{\text{S}}_{1/2}=\mathrm{\Delta }{\text{H}}_{1/2}/{\text{T}}_{1/2}$$

When the channel was fully open at T_{m, o}, the change in molar Gibbs free energy along the PC-dependent minimal gating pathway from the closed state at T_m,c to the open one at T_m,o was calculated using the following equation:

$$\mathrm{\Delta }{\text{G}}_{\text{Tm},\text{o}}={\text{(S}}_{\text{o}}-{\text{S}}_{\text{c}}\text{)E}/2$$

where, E is usually 1 kcal/mol. So, the concurrent change in molar heat capacity (ΔCp) was calculated from the Gibbs–Helmholtz equation:

$$\mathrm{\Delta }{\text{C}}_{\text{p}}=\{\mathrm{\Delta }{\text{H}}_{1/2}[1-{\text{(T}}_{\text{m},\text{o}}/{\text{T}}_{1/2})]-\mathrm{\Delta }{\text{G}}_{\text{Tm},\text{o}}\}/[({\text{T}}_{1/2}-{\text{T}}_{\text{m},\text{o}})+{\text{T}}_{\text{m},\text{o}}\ast {\text{ln(T}}_{\text{m},\text{o}}/{\text{T}}_{1/2})]\text{''}$$

now reads,

“T_1/2 was defined as a temperature at which the apparent open probability (P_o) of mTRPV3 was 0.5. It was calculated using the following equation:

$${\text{T}}_{1/2}={\text{T}}_{\text{m},\text{c}}+{\text{(T}}_{\text{m},\text{o}}-{\text{T}}_{\text{m},\text{c}})/2$$

where, T_m,c and T_m,o were the calculated melting temperature thresholds of the biggest grids in mTRPV3 in the closed and open states, respectively. At T_1/2, the change in systematic molar Gibbs free energy (ΔG_1/2) is zero, and the in systematic molar enthalpy upon the total broken non-covalent interactions was calculated using the following equation:

$$\mathrm{\Delta }{\text{H}}_{1/2}=4\ast ({\text{H}}_{\text{c}}-{\text{H}}_{\text{o}})/2=4\ast ({\text{EN}}_{\text{c}}-{\text{EN}}_{\text{o}})/2$$

where, E is usually 1 kcal/mol. Therefore, the change in molar entropy at T_1/2 could be calculated using the following equation:

$$\mathrm{\Delta }{\text{S}}_{1/2}=\mathrm{\Delta }{\text{H}}_{1/2}/{\text{T}}_{1/2}$$

When the channel was allosterically open at T_{m, o}, the change in molar Gibbs free energy along the PC-dependent minimal gating pathway from the closed state at T_m,c to the open one at T_m,o was calculated using the following equation:

$$\mathrm{\Delta }\text{G}={\text{(S}}_{\text{o}}-{\text{S}}_{\text{c}}\text{)E}/2$$

where, E is usually 1 kcal/mol. Assuming the temperatures of maximal stability (T_s) were 303.7 and 292 K for the minimal P_o of reduced and oxidized channels, respectively, and the enthalpy change at T_s, ΔH_s = – ΔG/2; the concurrent change in molar heat capacity (ΔC_p) was then calculated from the modified Gibbs–Helmholtz equation to match the maximal experimental molar enthalpy change for channel opening¹⁹:

$$\mathrm{\Delta }{\text{C}}_{\text{p}}=(\mathrm{\Delta }{\text{H}}_{\text{s}}-\mathrm{\Delta }{\text{G}}_{1/2})/[({\text{T}}_{\text{s}}-{\text{T}}_{1/2})+{\text{T}}_{1/2}+{\text{T}}_{1/2}\ast {\text{ln(T}}_{1/2}/{\text{T}}_{\text{s}})]\text{''}$$

The original Article has been corrected.