Self-Assembly Dynamics of Linear Virus-Like Particles: Theory and Experiment.

We experimentally and theoretically studied the self-assembly kinetics of linear virus-like particles (VLPs) consisting of double-stranded DNA and virus-like coat proteins. The polynucleotide acts as a self-assembly template for our proteins with engineered attractive protein-DNA and protein-protein interactions that imitate the physicochemical functionality of virus coat proteins. Inspired by our experimental observations, where we found that VLPs grow from one point onward, our model presumes a nucleation step before subsequent sequential cooperative binding from one of the ends of the polynucleotide. By numerically solving the pertinent reaction rate equations, we investigated the assembly dynamics as a function of the ratio between the number of available binding sites and proteins in the solution, i.e., the stoichiometry of the molecular building blocks. Depending on the stoichiometry, we found monotonic or nonmonotonic assembly kinetics. If the proteins in the solution vastly outnumber the binding sites on all of the polynucleotides, then the assembly kinetics were strictly monotonic and the assembled fraction increases steadily with time. However, if the concentration of proteins and binding sites is equal, then we found an overshoot in the concentration of fully covered polynucleotides. We compared our model with length distributions of two types of VLPs measured by atomic force microscopy imaging and found satisfactory agreement, suggesting that a relatively simple model may be useful in describing the assembly kinetics of chemically complex systems. We furthermore re-evaluated data by Hernandez-Garcia et al. (Nat. Nanotechnol. 2014, 9, 698-702) to include the effect of a finite protein concentration previously ignored. By fitting our model to the experimental data, we were able to pinpoint the sum of the protein-protein and protein-DNA interaction free energies, the binding rate of a protein to the DNA, and the nucleation free energy associated with switching a protein from the solution to the bound conformation. The values that we found for the VLPs are comparable to virus capsid binding energies of linear and spherical viruses.