The Seventh q-bio Summer School: Viral Dynamics

This series of lectures focus on viral and immune systems dynamics at the cellular population level, that is the modeling of interactions of immune cells and viruses within an individual. There will be a basic introduction to the biology of these systems, followed by lectures on modeling specific issues/processes/immune systems. We will cover both modeling of the healthy immune system, and viral infections such as human immunodeficiency (HIV), hepatitis (B and C), and influenza. Particular attention will be given to the evolutionary processes shaping these viruses in vivo, including the topic of phylogenetics. The approach to all these subjects will include discussions of the mathematical framework, the types of available data and how to link models and data to generate new hypotheses, estimate parameters and gain the most biological insight from restricted datasets. Group projects will include journal club presentations, small simulations projects, and there will be scope for research-type projects if enough student interest is manifested.

This section of the summer school is organized by Ruy Ribeiro. Please address all questions about this section of the summer school to its organizer.

Topics

• Introduction to viruses and the immune system (What is a virus? Viral lifecycles. Viral spread. A simple primer to immunity. Virus and the immune system: a predator-prey system.)

• How to model a viral infection within the host (Data and model generation, Models for drug treatment, Model interpretation)

• Spatial models of the immune response (Tracking single cell behavior, Understanding empirical data using models)

• Stochastic models of viral infection (When are stochastic models appropriate, Extinction dynamics, Co-infection)

• Viral evolution (Introduction to phylogenetics, Tracing HIV evolution)

Lectures / Tutorials

Introduction to viruses and immune system modeling – Ruy Ribeiro (LANL)

This series of lectures focus on viral and immune systems dynamics at the cellular population level, that is the modeling of interactions of immune cells and viruses within an individual. The first lecture will be an introduction to the series and a basic introduction to the biology of viruses and their interaction with the immune system.

How to model a viral infection – Alan Perelson (LANL)

I will show how one goes from empirical data to generating and testing a model of viral infection within a single individual. To showcase the methods I will use two examples, HIV and hepatitis C virus infection. Both viral infections are major health problems in the world today and I will show how modeling has influenced the way people think about the events going on in infected individuals and how modeling has influenced how people are treated for these infections.

Spatial models of the immune response – Rob de Boer (University of Utrecht, Netherlands)

The visualization of the dynamic behavior of immune cells using time-lapse video microscopy plays an important role in modern immunology. To draw robust conclusions, quantification of such cell migration data is required. This is far from trivial because imaging experiments are associated with various artifacts that can affect the estimated positions of the immune cells under analysis. We develop methods to correct for these artifacts and employ the most robust measures for determining cell motility and directed migration. These methods are tested on spatially explicit models of T cell migration in lymph nodes (LNs). We show that several dynamical properties of T cells are a consequence of the densely packed LN environment. Because imaging is typically restricted to experiments lasting 1 h, and because T cell-DC conjugates frequently move into and out of the imaged volume, it is difficult to estimate the true duration of interactions from contact data. We propose a method to properly make such an estimate of the average of the contact durations. We also use these techniques to analyze the migration of antigen specific CD8 T cells in the skin after localized infection with herpes simplex virus. This provided evidence for directed migration towards the infection.

Introduction to phylogenetics – Tanmoy Bhattacharya (LANL)

Nothing in biology makes sense except in the light of evolution, this is turning out to be ever truer every day. A solid understanding of what methodologically separates the biological and other sciences that are strongly affected by historical contingencies from the physical sciences discovering universal natural laws, is an important component in the training of quantitative biologists. This lecture will cover the basics of why, what, and how of phylogenetics to get students to understand this important fact.

Applying phylogenetics to understanding virus epidemics – Thomas Leitner (LANL)

In this lecture I will introduce the use of phylogenetics to track infectious diseases, known as molecular epidemiology or phylodynamics. The main examples will come from the worldwide HIV epidemic. I will show how phylogenetics have been used 1) to systematically classify the virus (including recombination), 2) to find and time it's origin in African primates, 3) to trace its pandemic spread, 4) how to infer the actual human spread rate from virus genetics, and 5) how it can be used to trace individual transmissions. The students will see how recombinant virus cannot be accurately placed in a phylogenetic tree and how they may be detected. The students will be introduced to the concept of the molecular clock, how it can be estimated and used to track epidemics. I will try to make this an interactive session, and depending on time, we may touch upon the use of genetics to trace geographical origins, ie phylogeography.

Visualization of sequence diversity and evolution – TBD

In recent years, new DNA sequencing technologies have led to a vast increase in the number of sequenced genomes. We use these technologies to study the evolution of viral populations of HIV within individual patients, following the development of immune escape through acute and later stages of infection. Large datasets enable unprecedented sensitivity for detecting early mutations and calculating viral dynamics, but require substantial investments in software (error processing) and visualization. I will discuss the application of deep sequencing techniques to the evolution of immune escape and drug resistance, as well as possible implications for vaccines.

Stochastic modelling in viral and immunological systems - Mario Castro (UP Commilas, Madrid)

Modelling population dynamics has been one of the most effective ways to quantitatively approach prediction in biological systems (specially in virus dynamics). In particular, ordinary differential equations have been widely studied to accommodate to different biological setups. However, there are some scenarios where such modelling approach cannot capture the main ingredients of the system. Specifically, when the populations are small or in the proximity of a bifurcation point (for instance close to the epidemic threshold or close to extinction) the fluctuations are large and specific stochastic modelling is required. In this tutorial session participants will be introduced to basic concepts in stochastic methods, both analytical and numerical, and focus on two case studies in which this sort of modelling approach provides different answers than ordinary differential equations.

Break-out sessions

• Journal clubs
• Project development
• Students' presentations

Projects

Information on projects can be found at Projects QB4.