Mathematical Models of Adaptive Immunity

More than 5 million people die every year from infectious diseases, despite the availability of numerous antibiotics and vaccines. The discovery of penicillin to treat bacterial infections, along with the development of vaccines for previously incurable virus diseases such as polio and smallpox, achieved great reductions in mortality during the mid-20th century.

Recently, spectacular advances in medical imaging combined with mathematical tools for modeling the human immune system have provided a base for a new push against infectious disease. The challenges and opportunities presented by these new experimental and theoretical technologies were discussed at a recent workshop organized by the European Science Foundation (ESF), which set out an agenda for quantitative immunology.

"A better understanding of how the immune system responds to infection and of the factors that determine whether an infection results in protective immunity or disease could lead to medical advances resulting in a great reduction in human suffering," said Paul Garside, director of the Centre for Biophotonics at the University of Strathclyde, and Carmen Molina-Paris and Grant Lythe, applied mathematician at the University of Leeds, co-convenors of the ESF workshop.

The fact that a conference on immunology should be co-convened by mathematicians typifies the change in the field from a qualitative science into a quantitative one using comprehensive data sets derived from imaging. This should help answer the question of why a given infection is controlled by the immune system in some people, leading to prolonged adaptive immunity, while in others causes serious disease. The answer depends on numerous factors relating to interaction between metabolism, immune system pathways, and even external factors such as diet and microorganisms in the gut. Unraveling these factors requires mathematical modeling based on data obtained from images of the processes as they actually take place in the body, combined with chemical analysis of samples such as urine or blood.

One technology in particular, two-photon microscopy, is providing valuable data on immune processes, such as movement and interaction between cells, in real time, as they happen. Two-photon microscopy evolved from conventional light microscopy and exploits the fluorescence effect, causing the object of interest to emit light that can then be observed in high resolution. The ESF workshop focused on how modeling and imaging could help resolve the complex immunological and metabolic interactions between three key groups of cells involved in defense against disease, T cells, B cells, and dendritic cells. T cells are a type of white blood cell involved in the adaptive memory against previous infections, in destroying infected viral or tumor cells, and in mediating the immune response to avoid an attack on the host organism. B cells are another type of white blood cell, producing antibodies that identify and mark invading pathogens such as bacteria, also playing a key role in adaptive memory. Dendritic cells aid the other immune cells by processing invading pathogens at an early stage and presenting their antigens (unique surface components, including proteins and carbohydrates, identifying a pathogen) so that they are easily accessible to those other immune cells.

"Modeling the interactions of T cells, B cells and APCs (Antigen presenting cells) such as dendritic cells in the lymph node is one of the great challenges we face," said Garside, Lythe and Molina-Paris. "In particular, it is essential to understand the timescales of these interactions."

There are also broader questions identified at the ESF workshop, such as how the immune system maintains such great diversity in its repertoire of mature antibodies, providing protection against such a wide range of pathogens, while at the same time it is able to discriminate between self and non-self, and achieve a proportionate response to infection, so that collateral damage against the host is minimized. The importance of this fine regulation is emphasized when it goes wrong, for example in septic shock when the immune system over reacts to a pathogen, or in chronic autoimmune diseases such as MS or rheumatoid arthritis, when these immune cells attack the body's own tissue. Although the ESF workshop concentrated on infectious diseases, the research it will stimulate will also lead to better understanding and improved therapies for these conditions where the immune system malfunctions.

The ESF workshop, Challenges for Experimental and Theoretical Immunology, was held in Leeds, UK in September 2008.