Correction

Aiwei Tian, Benjamin R. Capraro, Cinzia Esposito, and Tobias Baumgart. 2009. Bending stiffness depends on curvature of ternary lipid mixture tubular membranes. Biophys. J. 97:1636–1646.

Equation 9 on page 1641 should read:

$${\kappa }_{\text{eff}}={\kappa }_0-\rho \frac{{\left(\frac{\partial {\overline{\mu }}_1}{\partial C}\right)}_0^2{\left(\frac{\partial {\overline{\mu }}_2}{\partial {\varphi }_2}\right)}_0-2{\left(\frac{\partial {\overline{\mu }}_1}{\partial C}\right)}_0{\left(\frac{\partial {\overline{\mu }}_2}{\partial C}\right)}_0{\left(\frac{\partial {\overline{\mu }}_1}{\partial {\varphi }_2}\right)}_0+{\left(\frac{\partial {\overline{\mu }}_2}{\partial C}\right)}_0^2{\left(\frac{\partial {\overline{\mu }}_1}{\partial {\varphi }_1}\right)}_0}{{\left(\frac{\partial {\overline{\mu }}_1}{\partial {\varphi }_1}\right)}_0{\left(\frac{\partial {\overline{\mu }}_2}{\partial {\varphi }_2}\right)}_0-{\left(\frac{\partial {\overline{\mu }}_1}{\partial {\varphi }_2}\right)}_0{\left(\frac{\partial {\overline{\mu }}_2}{\partial {\varphi }_1}\right)}_0},$$

i.e., the sole difference between Eqs. 6 and 9 is the interpretation of the thermodynamic factor.

Equation 10 on page 1642 should read:

$${\kappa }_{\text{eff}}={\kappa }_0-\frac{3}{4}\frac{{\left(\frac{\partial \kappa }{\partial {\varphi }_1}\right)}_0^2{\left(\frac{\partial {\overline{\mu }}_2}{\partial {\varphi }_2}\right)}_0-2{\left(\frac{\partial \kappa }{\partial {\varphi }_1}\right)}_0{\left(\frac{\partial \kappa }{\partial {\varphi }_2}\right)}_0{\left(\frac{\partial {\overline{\mu }}_1}{\partial {\varphi }_2}\right)}_0+{\left(\frac{\partial \kappa }{\partial {\varphi }_2}\right)}_0^2{\left(\frac{\partial {\overline{\mu }}_1}{\partial {\varphi }_1}\right)}_0}{\rho \left\{{\left(\frac{\partial {\overline{\mu }}_1}{\partial {\varphi }_1}\right)}_0{\left(\frac{\partial {\overline{\mu }}_2}{\partial {\varphi }_2}\right)}_0-{\left(\frac{\partial {\overline{\mu }}_1}{\partial {\varphi }_2}\right)}_0{\left(\frac{\partial {\overline{\mu }}_2}{\partial {\varphi }_1}\right)}_0\right\}}{C}^2\text{.}$$