Quantitative predictions of FtsZ protein polymerization are essential for understanding the self-regulating mechanisms in biochemical systems. Due to structural complexity and parametric uncertainty, existing kinetic models remain incomplete and their predictions error-prone. To address such challenges, we perform probabilistic uncertainty quantification and global sensitivity analysis of the concentrations of various protein species predicted with a recent FtsZ protein polymerization model. Our results yield a ranked list of modeling shortcomings that can be improved in order to develop more accurate predictions and more realistic representations of key mechanisms of such biochemical systems and their response to changes in internal or external conditions. Our conclusions and improvement recommendations can be extended to other kinetics models.