Population Dynamics of Borrelia burgdorferi in Lyme Disease

Many chronic inflammatory diseases are known to be caused by persistent bacterial or viral infections. A well-studied example is the tick-borne infection by the gram-negative spirochaetes of the genus Borrelia in humans and other mammals, causing severe symptoms of chronic inflammation and subsequent tissue damage (Lyme Disease), particularly in large joints and the central nervous system, but also in the heart and other tissues of untreated patients. Although killed efficiently by human phagocytic cells in vitro, Borrelia exhibits a remarkably high infectivity in mice and men. In experimentally infected mice, the first immune response almost clears the infection. However, approximately 1 week post infection, the bacterial population recovers and reaches an even larger size before entering the chronic phase. We developed a mathematical model describing the bacterial growth and the immune response against Borrelia burgdorferi in the C3H mouse strain that has been established as an experimental model for Lyme disease. The peculiar dynamics of the infection exclude two possible mechanistic explanations for the regrowth of the almost cleared bacteria. Neither the hypothesis of bacterial dissemination to different tissues nor a limitation of phagocytic capacity were compatible with experiment. The mathematical model predicts that Borrelia recovers from the strong initial immune response by the regrowth of an immune-resistant sub-population of the bacteria. The chronic phase appears as an equilibration of bacterial growth and adaptive immunity. This result has major implications for the development of the chronic phase of Borrelia infections as well as on potential protective clinical interventions

A mathematical model of T lymphocyte calcium dynamics derived from single transmembrane protein properties.

Fate decision processes of T lymphocytes are crucial for health and disease. Whether a T lymphocyte is activated, divides, gets anergic, or initiates apoptosis depends on extracellular triggers and intracellular signaling. Free cytosolic calcium dynamics plays an important role in this context. The relative contributions of store-derived calcium entry and calcium entry from extracellular space to T lymphocyte activation are still a matter of debate. Here we develop a quantitative mathematical model of T lymphocyte calcium dynamics in order to establish a tool which allows to disentangle cause-effect relationships between ion fluxes and observed calcium time courses. The model is based on single transmembrane protein characteristics which have been determined in independent experiments. This reduces the number of unknown parameters in the model to a minimum and ensures the predictive power of the model. Simulation results are subsequently used for an analysis of whole cell calcium dynamics measured under various experimental conditions. The model accounts for a variety of these conditions, which supports the suitability of the modeling approach. The simulation results suggest a model in which calcium dynamics dominantly relies on the opening of channels in calcium stores while calcium entry through calcium-release activated channels (CRAC) is more associated with the maintenance of the T lymphocyte calcium levels and prevents the cell from calcium depletion. Our findings indicate that CRAC guarantees a long-term stable calcium level which is required for cell survival and sustained calcium enhancement

A mathematical model of immune activation with a unified self-nonself concept.

The adaptive immune system reacts against pathogenic nonself, whereas it normally remains tolerant to self. The initiation of an immune response requires a critical antigen(Ag)-stimulation and a critical number of Ag-specific T cells. Autoreactive T cells are not completely deleted by thymic selection and partially present in the periphery of healthy individuals that respond in certain physiological conditions. A number of experimental and theoretical models are based on the concept that structural differences discriminate self from nonself. In this article, we establish a mathematical model for immune activation in which self and nonself are not distinguished. The model considers the dynamic interplay of conventional T cells, regulatory T cells (Tregs), and IL-2 molecules and shows that the renewal rate ratio of resting Tregs to naïve T cells as well as the proliferation rate of activated T cells determine the probability of immune stimulation. The actual initiation of an immune response, however, relies on the absolute renewal rate of naïve T cells. This result suggests that thymic selection reduces the probability of autoimmunity by increasing the Ag-stimulation threshold of self reaction which is established by selection of a low number of low-avidity autoreactive T cells balanced with a proper number of Tregs. The stability analysis of the ordinary differential equation model reveals three different possible immune reactions depending on critical levels of Ag-stimulation: a subcritical stimulation, a threshold stimulation inducing a proper immune response, and an overcritical stimulation leading to chronic co-existence of Ag and immune activity. The model exhibits oscillatory solutions in the case of persistent but moderate Ag-stimulation, while the system returns to the homeostatic state upon Ag clearance. In this unifying concept, self and nonself appear as a result of shifted Ag-stimulation thresholds which delineate these three regimes of immune activation