Statistical thermodynamics of virus assembly

This thesis is about the study of bacteriophages and HIV (Human Immunodeficiency Virus). Chapter 1 provides introduction to both bacteriophages and HIV. Bacteriophages have drawn interest from the biophysical community because they have simple structures.;In Chapter 2, the physics of genome translocation of bacteriophages in the presence of Mg+2 counterions is studied. Experiments have shown that MgSO4 salt inhibits DNA ejection from bacteriophages nonmonotonically. There is a MgSO4 concentration where the minimum amount of DNA is ejected. We propose that this is the result of DNA overcharging by Mg+2 ions. The concept of charge inversion of the double stranded DNA (dsDNA) as bacteriophages genome is used to solve this problem. This explains why Mg+2 counterions cannot condense DNA in solution.;In Chapter 3, the problem of DNA-DNA interaction mediated by divalent counterions is studied using computer simulations. Condensation of DNA in the presence of multivalent counterions draws attention because DNA ejection shows non-monotonic behavior in with counterion. Our simulation shows that if DNA configurational entropy is restricted, divalent counterions can cause DNA reentrant condensation similar to that caused by tri- or tetra-valent counterions. DNA-DNA interaction is strongly repulsive at small or large concentration and is negligible or slightly attractive for concentrations in between. This study supports the conclusion of non-monotonic behavior of bacteriophage DNA ejection obtained in Chapter 2.;Understanding the capsid assembly process of HIV, the causative agent of Acute Immune Deficiency Syndrome (AIDS), is very important because of recent interest in capsid oriented viral therapy. The unique conical shapes of mature HIV-1 capsid have drawn significant interest in the biological community and have started to attract attention from physicists. To understand HIV-1 capsid assembly, three problems are focused on in this thesis: a study of diversity of in vivo assembled HIV-1 capsids, radial distribution of RiboNucleic Acid (RNA) genomes packaged inside spherical viruses, and RNA condensation in the presence of a single nucleocapsid (NC) protein. These will be discussed in Chapter 4, Chapter 5, and Chapter 6 respectively.;In Chapter 4, how the viral membrane affects the structure of in vivo assembled HIV-1 capsid is studied. Previous studies showed that in a free assembly process, the HIV-1 conical shape is not thermodynamically stable. The viral envelope membrane present during assembly imposes constraints on the length of the capsid. An elastic continuum shell theory is used to approximate the energies of various HIV-1 capsid shapes (spherical, cylindrical and conical) numerically and analytically. It is shown that conical and cylindrical shapes are both thermodynamically stable with the viral envelope membrane constraint.;In Chapter 5, the problem of RNA genomes packaged inside spherical viruses is studied. The viral capsid is modeled as a hollow sphere. The attraction between the inner viral capsid and RNA molecules occurs at the inner capsid surface only and plays an important role in the RNA packaging process. For weak attraction, RNA concentration is maximum at the center of the capsid to maximize configurational entropy. For stronger attraction, RNA concentration peaks near the capsid surface. In the latter case, competition between the branching of RNA secondary structure and its adsorption to the inner capsid results in formation of a dense layer of RNA near the capsid surface. A mean-field approach depending on the adsorption strength of RNA molecules and the inner viral capsid is used to determine how RNA molecules are packaged inside the viral capsid.;In Chapter 6, the condensation of RNA molecules by a single retrovirus NC protein is studied. The core of HIV is composed of a complex of genomic RNA and NC proteins, surrounded by a shell of capsid proteins. The interaction between RNA molecules and NC proteins is important in the reverse transcription of viral RNA, which relates to the viral infectivity. We model a single NC protein as an infinite well at the origin representing the attractive RNA-NC protein interaction. For weak adsorption of the NC protein, only a small portion of RNA is condensed near the NC protein and the boundary distance r0 between a dilute and a condensed phase of RNA concentration is linearly proportional to the adsorption strength. For strong adsorption, there is more condensed RNA so that r0 is extended much farther than for the weak adsorption case. The latter shows that condensed RNA screens the NC protein.