Kinetic Modeling of Virus Growth in Cells

Abstract

When a virus infects a host cell, it hijacks the biosynthetic capacity of the cell to produce virus progeny, a process that may take less than an hour or more than a week. The overall time required for a virus to reproduce depends collectively on the rates of multiple steps in the infection process, including initial binding of the virus particle to the surface of the cell, virus internalization and release of the viral genome within the cell, decoding of the genome to make viral proteins, replication of the genome, assembly of progeny virus particles, and release of these particles into the extracellular environment. For a large number of virus types, much has been learned about the molecular mechanisms and rates of the various steps. However, in only relatively few cases during the last 50 years has an attempt been made-using mathematical modeling-to account for how the different steps contribute to the overall timing and productivity of the infection cycle in a cell. Here we review the initial case studies, which include studies of the one-step growth behavior of viruses that infect bacteria (Qβ, T7, and M13), human immunodeficiency virus, influenza A virus, poliovirus, vesicular stomatitis virus, baculovirus, hepatitis B and C viruses, and herpes simplex virus. Further, we consider how such models enable one to explore how cellular resources are utilized and how antiviral strategies might be designed to resist escape. Finally, we highlight challenges and opportunities at the frontiers of cell-level modeling of virus infections.

Keywords: DNA virus; RNA virus; bacteriophages; biophysics; computational biology; computer modeling; growth modeling; kinetics; mathematical modeling; molecular biology.

FIG 1

Modeling integrates diverse data to predict virus growth in cells. Descriptions of the molecular functions encoded by the viral genome are used to write equations that describe how levels of viral mRNA, protein, and genomes change over the course of infection. The equations integrate kinetic and other biochemical and biophysical data as parameter values. They are typically solved computationally by numerical integration to yield predicted concentrations of intermediates and final product (virus) levels over the course of infection.

FIG 2

Most virus genomes encode fewer than 100 proteins. Virus genomes are relatively small, with most being fewer than 100 kb long, encoding about 100 proteins; 1 kb of sequence encodes about one protein. The first genome of any organism to be sequenced was that of phage phiX174 (5.39 kb), completed in 1977.

FIG 3

To replicate, all viruses must make mRNA and protein. Single-stranded positive-sense RNA genomes, designated (+)ssRNA, are of the same sense as mRNA, so they can immediately serve as templates for protein synthesis.

FIG 4

Each step of virus reproduction can be described by a differential equation. (1) Binding. A free virus particle initially adsorbs to the surface of a living host cell, a process that is usually mediated by proteins on the surface of the virus particle and specific receptor proteins on the surface of the host cell. The equation expresses the binding event as a mass action process that depends on levels of free (unbound) virus and free (unoccupied) receptors. Further, the equation describes how levels of bound virus fall as they enter the cell. Here, for simplicity, we neglect the possible dynamics of the receptor, which can recycle to the surface or be internalized. (2) Entry. The genome of the virus, often accompanied by copackaged viral proteins, is delivered into the host cell, where it gains access to the protein synthesis machinery and other resources of the cell. The equation accounts for the appearance of genomes that are supplied by viral entry as well as the increase in genome level owing to replication and their depletion owing to their decay. (3) Transcription. The virus genome is used as a template to produce different viral mRNA transcripts. Different mRNAs (denoted by the subscripted variable i in the equation) are accounted for by potentially different rates of transcription (promoter strengths), and they depend on genome levels. For positive-sense RNA viruses, the transcription step is not included because the viral genome serves as the template for translation. (4) Translation. The viral mRNAs recruit the protein synthesis machinery of the host cell to produce different viral proteins. (5) Assembly. Virus proteins self-assemble to form aggregates (procapsids). (6) Encapsidation. The packaging of progeny viral genomes into viral procapsids yields intact viral progeny. The equation accounts for the dependence of ith protein synthesis on the level of ith mRNA and also for depletion of free proteins by processes that assemble them into capsids and processes that cause them to decay. (7) Release. Viral progeny are liberated from the host cell, and encounters between the viral progeny and other susceptible host cells initiate further rounds of growth. Concurrent processes (not shown, for simplicity) include a diverse range of cellular responses to infection, such as activation of cellular defenses (restriction or clustered regularly interspaced short palindromic repeat [CRISPR]-Cas responses in bacteria or interferon-mediated innate immune signaling in mammalian host cells), induction of cell suicide (apoptosis) responses, and shutdown of host biosynthetic functions.

FIG 5

Drug targeting of viral gene regulation. The model of phage T7 intracellular development was expanded to incorporate effects of antisense drugs targeting different virus-specific functions. (A) Drug targeting of mRNA that encodes the major capsid (coat) protein of T7, a major protein component of the progeny phage. As the potency (or affinity) of the drug for this target increased, coat protein production was correspondingly reduced, ultimately inhibiting the production of virus progeny. Viruses that spontaneously generate mutations can attenuate the drug potency (or affinity between the drug and its target) and thereby reduce the inhibitory effects of drug on virus growth, as shown, for example, by the path for virus populations moving from point 1 to point 2. More rapid growth by drug-resistant viruses than by wild-type viruses allows such viruses to become enriched and enables the resulting virus population to escape from the drug. (B) When a drug targets mRNA that encodes the RNA polymerase of T7 (RNA Pol), a different behavior ensues owing to the negative feedback of RNA Pol on its own synthesis. In this case, more potent drugs do not necessarily have greater inhibitory effects on virus growth. Instead, drugs of intermediate potency can have larger inhibitory effects on virus production because they exploit the contributions of the feedback to the overall growth behavior. Mutations that reduce drug potency enable virus populations to move from point 1 to point 2, creating viruses that are more growth inhibited than the wild type. Such mutants would not be expected to become enriched over the wild-type virus. By accounting for the overall effects of drugs on such regulatory loops, the model provides an opportunity to identify potential “evolutionary traps” that select against established mechanisms of drug escape (68).