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

Abstract

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.

Illuminating the Reaction Pathways of Viromimetic Assembly

“…For f + = 0.10, we observe only partial encapsulation as insufficient protein is available to neutralize the available charges on the template chains in the solution (Figure 2c), which is consistent with theoretical predictions. 11 At perfect stoichiometry ( f + = 0.50), almost complete coverage is achieved. Interestingly, further increasing the protein content decreases the encapsulation efficiency.…”

Real-time assembly of an artificial virus elucidated at the single-particle level

“…In bulk, the nucleation and growth of the VLP particles obeys the same simple kinetic model that was earlier shown to describe the nucleation and growth of TMV particles (9,21,22). These artificial capsid polypeptides, which can be easily modified, are therefore an ideal model system for studying viral assembly pathways.…”

“…These rod-shaped VLPs consist of a single DNA molecule coated with multiple copies of the artificial capsid polypeptide. The sequence of the artificial capsid polypeptide was designed to mimic the co-assembly mechanism of the Tobacco Mosaic Virus (TMV) capsid protein with its nucleic acid template (21)(22)(23). The polypeptide, referred to as C-S 10 -B, consists of three blocks that each encode a specific physico-chemical functionality, mimicking corresponding functionalities of viral capsid proteins (Fig.…”

Modeling Coronavirus Spread Rate Utilizing Dimensional Analysis via an Irredundant Set of Fundamental Quantities

“…Future work might be suggested in a variety of possible directions. An immediate sequel of the present work might cast equation (9a) in an explicit form by using curve fitting to experimental data [58][59][60]. Another direction of research is to apply Dimensional Analysis in epidemiological studies that mainly involve differential equations [61][62][63][64][65] and to the transmission or spread of pathogenic viruses (other than the present coronavirus one) such as the human immunodeficiency virus (HIV) [66], influenza virus [67], dengue virus [68], hepatitis C virus [69], Zika virus [70] and yellow fever virus [71].…”