Transmission electron microscope (TEM) is expensive and not available to all research facilities. Our next step involves using our HIS-TEV-Gag_RFP construct to design an economical fluorescent assay to verify nanoparticle assembly. The purpose of this modeling experiment was to determine the approximate number of RFP molecules (PDB ID: 2H5Q) that could fit inside a Gag nanoparticle. By analyzing the RFP structure on the Protein Database we decided that the best way to approximate the volume was to treat it like a cylinder since it has a beta barrel structure. The RFPs height is 40Å and the diameter is 30Å therefore the volume is approximately 1.13*105Å3.

Figure 1. Crystal structure of mCherry, a red fluorescent protein (PDB ID: 2H5Q).

    Although the outer diameter of the Gag nanoparticle could be measured using the electron microscope, the inner diameter could not. It’s necessary to determine the inner diameter so that the inner nanoparticle volume can be calculated. To determine whether there is a correlation between the outer and inner diameter we used the Virus Particle Explorer database (VIPERdb) and recorded outer and inner diameter measurements for at least one virus particle per genus. Three different pH assembly buffers were used for the formation of Gag nanoparticles. Since the average Gag nanoparticle for each buffer fell between 250 and 450 angstroms we only considered particles from VIPERdb within that range, there were 61 samples in total. For those 61 nanoparticles the ratio between the outer and inner diameter is 1.60 +/- 0.26 and the average shell thickness is 60.7Å +/- 16.9Å. Two theoretical values for the inner diameter were made, Theoretical Value 1 (TV1) was based on the ration of outer to inner diameter and Theoretical Value 2 (TV2) was based on the average shell thickness. The accuracy of these theoretical values were tested by calculating how much it differed from the measured inner diameter. The average percent difference between TV1 and the measured inner diameter was 11.0%. The average percent difference between TV2 and the measured inner diameter was 11.6%. Since the percent differences were not significantly different we calculated the theoretical inner volume (TIV) for each of the theoretical inner diameters. To calculate the approximate number of RFP protein molecules per Gag nanoparticle we divided the theoretical inner volume by the calculated RFP volume. Below are the results for the average outer diameter of the gag nanoparticles that we assembled in vitro:

Table 1. Theoretical inner diameter and inner volume values for HIS tagged Gag nanoparticles.

Assembly Buffer pH	Average Tagged Outer Diameter	TV1 Å	TV2 Å	TIV1 Å3	TIV2 Å3	Number of RFP In TIV 1	Number of RFP in TIV2
acidic	423	266	301.6	9.56*10^6	1.44*10^7	84	127
neutral	NA	NA	NA	NA	NA	NA	NA
basic	331.2	208.3	209.8	4.73*10^6	4.83*10^6	41	42

Table 2. Theoretical inner diameter and inner volume values for untagged Gag nanoparticles.

Assembly Buffer pH	Average Un tagged Outer Diameter Å	TV1 Å	TV2 Å	TIV1 Å3	TIV2 Å3	Number of RFP In TIV 1	Number of RFP in TIV2
acidic	361	227	239.6	6.13*10^6	7.20*10^6	54	63
neutral	288	181.1	166.6	3.11*10^6	2.42*10^6	27	21
basic	NA	NA	NA	NA	NA	NA	NA

    In order to properly assemble the fluorescent Gag nanoparticles it’s important to determine the number of subunits that the nanoparticle is composed of so that we can determine the appropriate ratio of Gag subunits to Gag-RFP fusion subunits. As seen in Figure 2, there does appear to be a slight correlation between number of subunits and the outer diameter length, however, because there is such a large range of diameter sizes for each subunit, it’s difficult to predict how many subunits are in a virus particle based on outer diameter size alone. Of the 61 particles from the 250Å to 450Å, 57.4% are composed of 60 subunits and 32.8% are composed of 180 subunits. The number of subunits for all of the surveyed particles from the VIPERdb are multiples of 60. As seen in tables 1 and 2 the average nanoparticle size varies based on pH as well as whether the Gag is HIS tagged. This could indicate that the number of subunits change depending on environmental factors.

Figure 2. Regression analysis between the length of outer diameter (A) to the number of subunits.

    We have a potential model for determining the number of RFP molecules that can fit within our Gag nanoparticles that were assembled in vitro. In order to obtain a more reliable estimate more Gag nanoparticle must be measured under the transmission electron microscope so that we can have a reliable average.