Negative feedback loops are important mechanisms for generating biological rhythms. In this talk, we investigate a genetic negative feedback loop model incorporating protein-sequestration-based repression. Using Hopf bifurcation analysis combined with numerical computations, we study the existence and stability of periodic solutions. We further analyze the stoichiometric conditions associated with oscillation generation. We approximate the stoichiometry by a quantity evaluated at the bifurcation point. We also discuss the effects of differential degradation rates on the existence and stability of periodic solutions, as well as on stoichiometric balance.