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The dynamics of bio-conjugated magnetic nanoparticles suspended in buffer-saline solutions containing target proteins (i.e., analytes) is investigated numerically on a mesoscopic level. To simulate the dispersion of magnetic nanoparticles the dissipative particle dynamics is employed, which allows to study rather large systems, while still retaining important microscopic nanoparticle properties. In addition, the method is coupled to the Landau-Lifshitz-Gilbert equation, describing the dynamics of the magnetic nanocrystals within the macrospin approximation. The binding of multivalent analytes to the recognition ligands of the nanoparticles leads to the formation of clusters of magnetic nanoparticles, which in turn drastically changes the macroscopic magnetic response of the solution. Such colloidal changes are experimentally observable, allowing to explore new approaches to quantify the analyte amount. The ratio of the concentrations between the analytes (biomarkers) and the recognition ligands on the nanoparticles is found to play an important role in the formation and hydrodynamic size of the clusters. The proposed computational framework has great potential to be integrated with experimental efforts to advance the development of nanoparticle-based biosensors for disease diagnostics and other biomedical applications.