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

Features, processing states and heterologous protein interactions in the modulation of the retroviral nucleocapsid protein function

Nucleocapsid (NC) is central to retroviral replication. Nucleic acid chaperoning is a key function for NC through the action of its conserved basic amino acids and zinc-finger structures. NC manipulates genomic RNA from its packaging in the producer cell to reverse transcription into the infected host cell. This chaperone function, in conjunction with NCs aggregating properties, is up-modulated by successive NC processing events, from the Gag precursor to the fully mature protein, resulting in the condensation of the nucleocapsid within the capsid shell. Reverse transcription also depends on NC processing, whereas this process provokes NC dissociation from double-stranded DNA, leading to a preintegration complex (PIC), competent for host chromosomal integration. In addition NC interacts with cellular proteins, some of which are involved in viral budding, and also with several viral proteins. All of these properties are reviewed here, focusing on HIV-1 as a paradigmatic reference and highlighting the plasticity of the nucleocapsid architecture