Modeling and simulation of cancer immunoprevention vaccine

Modeling immune system control of atherogenesis

MOTIVATION

Atherosclerosis is a disease that is present in almost all humans, typically beginning in early adolescence. It is a human disease broadly investigated, that is amenable to quantitative analysis. Oxidized low-density lipoproteins (LDLs) and their autoantibodies are involved in the development of atherosclerosis in animal models, but their role in humans is still not clear. Computer models may represent a virtual environment to perform experiments not possible in human volunteers that can provide a useful instrument for monitoring both the evolution of atherosclerotic lesions and to quantify the efficacy of treatments, including vaccines, oriented to reduce the LDLs and their oxidized fraction.

RESULTS

We report the application of an agent-based model to model both the immune response to atherogenesis and the atheromatous plaque progression in a generic artery wall. The level of oxidized LDLs, the immune humoral response with production of autoantibodies, the macrophages activity and the formation of foam cells are in good agreement with available clinical data, including the formation of atheromatous plaques in patients affected by hypercholesterolemia.

AVAILABILITY

The model is available at http://www.immunogrid.eu/atherogenesis/

Complex multicellular systems and immune competition: new paradigms looking for a mathematical theory

This chapter deals with the modeling and simulation of large systems of interacting entities whose microscopic state includes not only geometrical and mechanical variables (typically position and velocity), but also biological functions or specific activities. The main issue looks at the development of a biological mathematical theory for multicellular systems. The first part is devoted to the derivation of mathematical structures to be properly used to model a variety of biological phenomena with special focus on immune competition. Then, some specific applications are proposed referring to the competition between neoplastic and immune cells. Finally, the last part is devoted to research perspectives towards the objective of developing a mathematical-biological theory. A critique is presented of what has already been achieved towards the above target and what is still missing with special focus on multiscale systems.

The evolution of mathematical immunology

The types of mathematical models used in immunology and their scope have changed drastically in the past 10 years. Classical models were based on ordinary differential equations (ODEs), difference equations, and cellular automata. These models focused on the 'simple' dynamics obtained between a small number of reagent types (e.g. one type of receptor and one type of antigen or two T-cell populations). With the advent of high-throughput methods, genomic data, and unlimited computing power, immunological modeling shifted toward the informatics side. Many current applications of mathematical models in immunology are now focused around the concepts of high-throughput measurements and system immunology (immunomics), as well as the bioinformatics analysis of molecular immunology. The types of models have shifted from mainly ODEs of simple systems to the extensive use of Monte Carlo simulations. The transition to a more molecular and more computer-based attitude is similar to the one occurring over all the fields of complex systems analysis. An interesting additional aspect in theoretical immunology is the transition from an extreme focus on the adaptive immune system (that was considered more interesting from a theoretical point of view) to a more balanced focus taking into account the innate immune system also. We here review the origin and evolution of mathematical modeling in immunology and the contribution of such models to many important immunological concepts.

Analysis of vaccine’s schedules using models

We present a further, yet important, step in applying Catania Mouse Model & simulator (SimTriplex) of immune system response to vaccination. In particular we show that, as immune response can induce toxicity, one can calibrate the vaccine administrations in such a way to avoid toxicity effects, keeping immunoprevention from cancer. This result increases the model's potential applications.

Modelling the human immune system by combining bioinformatics and systems biology approaches

Over the past decade a number of bioinformatics tools have been developed that use genomic sequences as input to predict to which parts of a microbe the immune system will react, the so-called epitopes. Many predicted epitopes have later been verified experimentally, demonstrating the usefulness of such predictions. At the same time, simulation models have been developed that describe the dynamics of different immune cell populations and their interactions with microbes. These models have been used to explain experimental findings where timing is of importance, such as the time between administration of a vaccine and infection with the microbe that the vaccine is intended to protect against. In this paper, we outline a framework for integration of these two approaches. As an example, we develop a model in which HIV dynamics are correlated with genomics data. For the first time, the fitness of wild type and mutated virus are assessed by means of a sequence-dependent scoring matrix, derived from a BLOSUM matrix, that links protein sequences to growth rates of the virus in the mathematical model. A combined bioinformatics and systems biology approach can lead to a better understanding of immune system-related diseases where both timing and genomic information are of importance.

Discovery of cancer vaccination protocols with a genetic algorithm driving an agent based simulator

BACKGROUND

Immunological prevention of cancer has been obtained in HER-2/neu transgenic mice using a vaccine that combines 3 different immune stimuli (Triplex vaccine) that is repeatedly administered for the entire lifespan of the host (Chronic protocol). Biological experiments leave open the question of whether the Chronic protocol is indeed the minimal vaccination schedule affording 100% protection, or whether shorter protocols could be applied that would result in the same efficacy. A biological solution would require an enormous number of experiments, each lasting at least one year. Therefore we approached this problem by developing a simulator (SimTriplex) which describes the immune response activated by Triplex vaccine. This simulator, tested against in vivo experiments on HER-2/neu mice, reproduces all the vaccination protocols used in the in vivo experiments. The simulator should describe any vaccination protocol within the tested range. A possible solution to the former open question using a minimal search strategy based on a genetic algorithm is presented. This is the first step toward a more general approach of biological or clinical constraints for the search of an effective vaccination schedule.

RESULTS

The results suggest that the Chronic protocol included a good number of redundant vaccine administrations, and that maximal protection could still be obtained with a number of vaccinations approximately 40% less than with the Chronic protocol.

CONCLUSION

This approach may have important connotations with regard to translation of cancer immunopreventive approaches to human situations, in which it is desirable to minimize the number of vaccinations. We are currently setting up experiments in mice to test whether the actual effectiveness of the vaccination protocol agrees with the genetic algorithm.

Modelling vaccination schedules for a cancer immunoprevention vaccine

We present a systematic approach to search for an effective vaccination schedule using mathematical computerized models. Our study is based on our previous model that simulates the cancer vs immune system competition activated by tumor vaccine. This model accurately reproduces in-vivo experiments results on HER-2/neu mice treated with the immuno-prevention cancer vaccine (Triplex) for mammary carcinoma. In vivo experiments have shown the effectiveness of Triplex vaccine in protection of mice from mammary carcinoma. The full protection was conferred using chronic (prophylactic) vaccination protocol while therapeutic vaccination was less effcient.

In the present paper we use the computer simulations to systematically search for a vaccination schedule which prevents solid tumor formation. The strategy we used for defining a successful vaccination schedule is to control the number of cancer cells with vaccination cycles. We found that, applying the vaccination scheme used in in-vivo experiments, the number of vaccine injections can be reduced roughly by 30%.