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In this study, we investigated optical performance of a biosensor based on the phenomenon of localized surface plasmon resonance (LSPR) in spherical Au nanoparticles, covered by a dense monolayer of globular biomolecules. Theoretical approaches used include Mie theory for a coated spherical particle, electron relaxation time correction for nanoparticle's optical constants, and symmetrical Bruggeman effective medium theory for characterization of a biomolecular layer. LSPR biosensor response (LSPR extinction peak wavelength shift) dependences on optical and geometrical parameters of spherical gold nanoparticles covered by globular biomolecules are calculated and discussed here. We found that LSPR response has a complex behavior that is dependent on the size of the Au nanoparticle core and the biomolecular shell layer and, therefore, also dependent on the contribution of scattering to the total light extinction. It was shown for the first time that the LSPR response for small nanoparticles (with a radius up to 5 nm) could be positive (LSPR extinction peak red shifts) or negative (blue shift) and that the spherical Au nanoparticles are sensitive to large overlayer thicknesses; however, the LSPR response for thicker overlayer grows slower with an increase in overlayer thickness compared to the same increase in that of a thinner overlayer. Additionally, we have derived equations for the number of molecules and surface concentration of saturated biomolecular monolayer.