Surface plasmon resonance (SPR) is an optical phenomenon used for detecting various biological substances and disease diagnostics due to its high sensitivity. SPR-based biosensors are highly sensitive optical devices and rapid detection devices, and they also have the added advantage of being label-free biosensors. Sensitivity and limit of detection are critical parameters in studying the performance of any biosensor. In plasmonic biosensors, the sensitivity and limit of detection are dependent on several parameters and a sensitivity analysis is critical to determine these parameters which can optimize our biosensor performance. Sensitivity analyses of SPR-based biosensors are important for enhancing the limit of detection (LoD), comparing performance, optimizing biosensor design, ensuring quality control, and advancing biosensing technology. In this study, we theoretically perform a sensitivity analysis on an SPR-based biosensor and consider different ways to enhance the LoD of the biosensor. The interaction we study is that of different proteins binding to gold (Au) surfaces via an electrostatic mechanism. In this study, we vary a wide range of parameters ranging from metal film thickness, and wavelengths of light incident on the biosensor and show how these parameters can be used to optimize our plasmonic biosensor in terms of sensitivity and LoD. The development of optimal biosensors is ever more critical, particularly considering recurring pandemics and disease outbreaks. Good sensitivity analysis can lead to high quality and highly effective biosensors which can be useful in the fight against disease outbreaks and pandemics.