First passage events in biological systems with non-exponential inter-event times

It is often possible to model the dynamics of biological systems as a series of discrete transitions between a finite set of observable states (or compartments). When the residence times in each state, or inter-event times more generally, are exponentially distributed, then one can write a set of ordinary differential equations, which accurately describe the evolution of mean quantities. Non-exponential inter-event times can also be experimentally observed, but are more difficult to analyse mathematically. In this paper, we focus on the computation of first passage events and their probabilities in biological systems with non-exponential inter-event times. We show, with three case studies from Molecular Immunology, Virology and Epidemiology, that significant errors are introduced when drawing conclusions based on the assumption that inter-event times are exponentially distributed. Our approach allows these errors to be avoided with the use of phase-type distributions that approximate arbitrarily distributed inter-event times

Dynamics of HIV-1 Assembly and Release

Assembly and release of human immunodeficiency virus (HIV) occur at the plasma membrane of infected cells and are driven by the Gag polyprotein. Previous studies analyzed viral morphogenesis using biochemical methods and static images, while dynamic and kinetic information has been lacking until very recently. Using a combination of wide-field and total internal reflection fluorescence microscopy, we have investigated the assembly and release of fluorescently labeled HIV-1 at the plasma membrane of living cells with high time resolution. Gag assembled into discrete clusters corresponding to single virions. Formation of multiple particles from the same site was rarely observed. Using a photoconvertible fluorescent protein fused to Gag, we determined that assembly was nucleated preferentially by Gag molecules that had recently attached to the plasma membrane or arrived directly from the cytosol. Both membrane-bound and cytosol derived Gag polyproteins contributed to the growing bud. After their initial appearance, assembly sites accumulated at the plasma membrane of individual cells over 1–2 hours. Assembly kinetics were rapid: the number of Gag molecules at a budding site increased, following a saturating exponential with a rate constant of ∼5×10−3 s−1, corresponding to 8–9 min for 90% completion of assembly for a single virion. Release of extracellular particles was observed at ∼1,500±700 s after the onset of assembly. The ability of the virus to recruit components of the cellular ESCRT machinery or to undergo proteolytic maturation, or the absence of Vpu did not significantly alter the assembly kinetics

Cryo Electron Tomography of Native HIV-1 Budding Sites

The structure of immature and mature HIV-1 particles has been analyzed in detail by cryo electron microscopy, while no such studies have been reported for cellular HIV-1 budding sites. Here, we established a system for studying HIV-1 virus-like particle assembly and release by cryo electron tomography of intact human cells. The lattice of the structural Gag protein in budding sites was indistinguishable from that of the released immature virion, suggesting that its organization is determined at the assembly site without major subsequent rearrangements. Besides the immature lattice, a previously not described Gag lattice was detected in some budding sites and released particles; this lattice was found at high frequencies in a subset of infected T-cells. It displays the same hexagonal symmetry and spacing in the MA-CA layer as the immature lattice, but lacks density corresponding to NC-RNA-p6. Buds and released particles carrying this lattice consistently lacked the viral ribonucleoprotein complex, suggesting that they correspond to aberrant products due to premature proteolytic activation. We hypothesize that cellular and/or viral factors normally control the onset of proteolytic maturation during assembly and release, and that this control has been lost in a subset of infected T-cells leading to formation of aberrant particles

Function of a retrotransposon nucleocapsid protein

Long terminal repeat (LTR) retrotransposons are not only the ancient predecessors of retroviruses, but they constitute significant fractions of the genomes of many eukaryotic species. Studies of their structure and function are motivated by opportunities to gain insight into common functions of retroviruses and retrotransposons, diverse mechanisms of intracellular genomic mobility and host factors that diminish or enhance retrotransposition. This review focuses on the nucleocapsid (NC) protein of a Saccharomyces cerevisiae LTR retrotransposon, the metavirus, Ty3. Retrovirus NC promotes genomic (g)RNA dimerization and packaging, tRNA primer annealing, reverse transcription strand transfers, and host protein interactions with gRNA. Studies of Ty3 NC have revealed key roles for Ty3 NC in formation of retroelement assembly sites (retrosomes), and in chaperoning primer tRNA to both dimerize and circularize Ty3 gRNA. We speculate that Ty3 NC, together with P-body and stress-granule proteins, plays a role in transitioning Ty3 RNA from translation template to gRNA, and that interactions between the acidic spacer domain of Ty3 Gag3 and the adjacent basic NC domain control condensation of the virus-like particle