Effects of strangeness on the chiral pseudocritical line

Within a 2+1 flavor Nambu\textendash Jona-Lasinio model, we calculate the curvature coefficients and check them against available lattice QCD estimations. With the observation that the flavor mixing due to the `t Hooft determinant term significantly affects the ${\kappa }_2^S$, we explore the effect of ${\mu }_S$ on the $T-{\mu }_B$ crossover lines. With the novel determination of negative ${\kappa }_2^B$ at large ${\mu }_S$, we advocate the importance of studying the same in lattice QCD.