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The folding pathways and mechanisms of IgG binding domain of protein L composed of 62 residues are simulated by an over-damped Langevin dynamics with a coarse-grained chain representation. Physical oriented effective energy functions (EEFs) are employed for sequence-specific interactions as well as topology induced energies to bias overall energies to native basin. We observed the preferential formation of N terminal hairpin and the break of structural symmetry during folding. In the free energy profile calculated from equilibrium sampling and histogram method, it clearly shows two state folding scenario with transition state (TS). In the TS regime, N terminal hairpin already forms whereas C terminal hairpin and alpha helix are not structured yet. The predicted results are fully consistent with experimental data. Moreover, we found that hydrophobicity and secondary local propensity among many physical interactions determine the overall folding routes significantly by reduced model studies.