We report on the construction of star polymers from polystyrene beads and genetically engineered M13 bacteriophage, a long filamentous particle that forms liquid crystalline phases. The viruses anchored to the spheres undergo a radial-aligned transition at the isotropic-nematic transition of the background solvent. We measure the pair interaction potentials of star polymers using the umbrella sampling method, and investigate the influence of ionic strength and grafting density on the interactions. We found significant discrepancies between the measured interactions and the theoretical predictions based upon the second virial approximation.