Agent-Based Modelling of Viral Infection

by Dimitri Perrin

The three phases of the macroscopic evolution of the HIV infection are well known, but it is still difficult to understand how the cellular-level interactions come together to create this characteristic pattern and, in particular, why there are such differences in individual responses. An 'agent-based' approach is chosen as a means of inferring high-level behaviour from a small set of interaction rules at the cellular level. Here the emphasis is on cell mobility and viral mutations.

One of the most characteristic aspects of the HIV infection is its evolution: in the initial short acute phase the original viral strains are destroyed, in the second year-long latency period, the number of strains slowly increases and, in the final phase, Acquired ImmunoDeficiency Syndrome (AIDS) develops when the immune system is no longer able to cope with the multiplying strains and is overcome. The principal aim of this work, based at Dublin City University, is to try to understand why the range of experience with respect to HIV infection is so diverse. In particular, the work aims to address questions relating to variation in the length of the individual latency period. This may be very long (for relatively low success of antipathetic mutation) in one individual, compared to another with much higher mutation levels.

The indications are that the observed variation lies in the priming and initial level of fitness of the immune response of the individual, together with the various factors that influence this. If such 'priming patterns' can be recognized or even predicted, then in the long term we may have a way of 'typing' an individual and targeting intervention appropriately. Unfortunately, understanding how the immune system is primed by experience of antigenic invasion and diversity is non-trivial. The challenge is to determine what assumptions can be made about the nature of the experience, and then modelled, tested against clinical data and hence argued plausibly. The aim is to understand how the cell interactions lead to the observed endpoints. What exactly is involved in antigenic diversity? How variable is the mutation rate and the viral load? What is the importance of cell mobility and how realistic is this in terms of cross-infection and subsystem involvement? How important then is the cross-reactivity?

The immune response is dynamic and includes growth and replenishment of cells and in-built adaptability, through mutation of its defences to meet new threats. It also includes aspects of cell mobility, which may be captured by means of defining the movement and affinity of cell-types in a defined spatial framework. In particular, this will enable us to study the variation in viral load and the way in which the host response may lead to degradation of protection.
To investigate these questions, an 'agent-based' approach is chosen as a means of inferring high-level behaviour from a small set of interaction rules at the cellular level. Such behaviour cannot be extracted analytically from the set of rules, but emerges as a result of stochastic events, which play an important part in the immune response.

The lymph node (adapted from N. Levy, Pathology of lymph nodes, 1996) is modelled as a matrix in which each element is a physical neighbourhood and can contain several agents of each type.

The initial model consists of agents (or functional units) with designated properties that mimic the operation of a single lymph node (as a test case). This prototype, however, includes all known interactions contributing to cell-mediated immunity and the local evolution of the virions. The antibody-mediated response has not been considered initially, because the cell-mediated arm plays a dominant role in repelling attack. The agents implemented represent Th (helper) and Tc (cytotoxic) lymphocytes, Antigen Presenting Cells and virions. They inherit from a common C++ class designed to deal with features such as mobility. Each class then implements through attributes and methods the specific properties of each cell type, such as the activation of a Tc cell by a Th cell. The lymph node is modelled as a matrix in which each element is a physical neighbourhood able to contain various agents of each type.

The next step is to increase of the number of lymph nodes. This extension involves millions of agents and requires major computational effort, so that parallelization methods are inevitable. The use of these methods is a natural consequence and advantage of the multi-agent approach. A human body contains hundreds of lymph nodes. The aim here is to extend the size and complexity of the systems that can be modelled to something approaching reality.

The representation of the innate response as a common background and the adaptive part as a characterized set of features will be the next step. This will allow the development of a large system to be studied over a longer period, in order to focus on disease progression endpoints and intervention effects.

The author would like to thank the Irish Research Council for Science, Engineering and Technology for the funding made available through the Embark Initiative.

Please contact:
Dimitri Perrin, Dublin City University/IUA, Ireland