Optimization of Immunoglobulin Substitution Therapy by a Stochastic Immune Response Model

Marc Thilo Figge

doi:10.1371/journal.pone.0005685

Abstract

BackgroundThe immune system is a complex adaptive system of cells and molecules that are interwoven in a highly organized communication network. Primary immune deficiencies are disorders in which essential parts of the immune system are absent or do not function according to plan. X-linked agammaglobulinemia is a B-lymphocyte maturation disorder in which the production of immunoglobulin is prohibited by a genetic defect. Patients have to be put on life-long immunoglobulin substitution therapy in order to prevent recurrent and persistent opportunistic infections.MethodologyWe formulate an immune response model in terms of stochastic differential equations and perform a systematic analysis of empirical therapy protocols that differ in the treatment frequency. The model accounts for the immunoglobulin reduction by natural degradation and by antigenic consumption, as well as for the periodic immunoglobulin replenishment that gives rise to an inhomogeneous distribution of immunoglobulin specificities in the shape space. Results are obtained from computer simulations and from analytical calculations within the framework of the Fokker-Planck formalism, which enables us to derive closed expressions for undetermined model parameters such as the infection clearance rate.ConclusionsWe find that the critical value of the clearance rate, below which a chronic infection develops, is strongly dependent on the strength of fluctuations in the administered immunoglobulin dose per treatment and is an increasing function of the treatment frequency. The comparative analysis of therapy protocols with regard to the treatment frequency yields quantitative predictions of therapeutic relevance, where the choice of the optimal treatment frequency reveals a conflict of competing interests: In order to diminish immunomodulatory effects and to make good economic sense, therapeutic immunoglobulin levels should be kept close to physiological levels, implying high treatment frequencies. However, clearing infections without additional medication is more reliably achieved by substitution therapies with low treatment frequencies. Our immune response model predicts that the compromise solution of immunoglobulin substitution therapy has a treatment frequency in the range from one infusion per week to one infusion per two weeks.

Highlights

Adaptive immunity implies immune responses against pathogenic challenges that are antigen-specific and that are memorized by the immune system
We find that the critical value of the clearance rate, below which a chronic infection develops, is strongly dependent on the strength of fluctuations in the administered immunoglobulin dose per treatment and is an increasing function of the treatment frequency
The comparative analysis of therapy protocols with regard to the treatment frequency yields quantitative predictions of therapeutic relevance, where the choice of the optimal treatment frequency reveals a conflict of competing interests: In order to diminish immunomodulatory effects and to make good economic sense, therapeutic immunoglobulin levels should be kept close to physiological levels, implying high treatment frequencies

Summary

Introduction

Adaptive immunity implies immune responses against pathogenic challenges that are antigen-specific and that are memorized by the immune system. In order to bind to the vast amount of different antigens, the molecular structure of immunoglobulin contains a hypervariable region This region is generated by random combinations of gene segments that encode a large variety of antigen binding sites and that give rise to a highly diverse repertoire of immunoglobulin. Germinal centers are follicular structures in lymphoid organs where B-lymphocytes undergo the process of somatic hypermutation with regard to the immunoglobulin hypervariable region [3,4,5] This is followed by the complex process of Blymphocyte selection for high-affinity immunoglobulin, which we only start to unravel today [6]. Selected B-lymphocytes either differentiate into plasma cells or into long-lived memory cells The latter give rise to faster and stronger immune responses on second encounter of the same antigen. Patients have to be put on life-long immunoglobulin substitution therapy in order to prevent recurrent and persistent opportunistic infections

Methods

Results

Discussion

Conclusion