This paper demonstrates a proof-of-principle for a new signal transduction method for protein detection called Bead Assembly Magnetorotation (BAM). In this paper, we chose to focus on the protein thrombin, a popular choice for proof-of-principle work in this field. BAM is based on using the protein target to mediate the formation of aptamer-coated 1 μm magnetic beads into a bead assembly, formed at the bottom of a 1 μL hanging droplet. The size, shape and fractal dimension of this bead assembly all depend on the protein concentration. The protein concentration can be measured in two ways: by magnetorotation, in which the rotational period of the assembly correlates with the protein concentration, or by fractal analysis. Additionally, a microscope-free magnetorotation detection method is introduced, based on a simple laser apparatus built from standard laboratory components.

We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest-Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70–1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles.