- Optimization of immunoglobulin substitution therapy by a stochastic immune response model (2009)
- Background: The 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. Methodology: We 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. Conclusions: 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. 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.
- Deriving a germinal center lymphocyte migration model from two-photon data (2008)
- Recently, two-photon imaging has allowed intravital tracking of lymphocyte migration and cellular interactions during germinal center (GC) reactions. The implications of two-photon measurements obtained by several investigators are currently the subject of controversy. With the help of two mathematical approaches, we reanalyze these data. It is shown that the measured lymphocyte migration frequency between the dark and the light zone is quantitatively explained by persistent random walk of lymphocytes. The cell motility data imply a fast intermixture of cells within the whole GC in approximately 3 h, and this does not allow for maintenance of dark and light zones. The model predicts that chemotaxis is active in GCs to maintain GC zoning and demonstrates that chemotaxis is consistent with two-photon lymphocyte motility data. However, the model also predicts that the chemokine sensitivity is quickly down-regulated. On the basis of these fi ndings, we formulate a novel GC lymphocyte migration model and propose its verifi cation by new two-photon experiments that combine the measurement of B cell migration with that of specifi c chemokine receptor expression levels. In addition, we discuss some statistical limitations for the interpretation of two-photon cell motility measurements in general.
- Geometrically repatterned immunological synapses uncover formation mechanisms (2006)
- The interaction of T cells and antigen-presenting cells is central to adaptive immunity and involves the formation of immunological synapses in many cases. The surface molecules of the cells form a characteristic spatial pattern whose formation mechanisms and function are largely unknown. We perform computer simulations of recent experiments on geometrically repatterned immunological synapses and explain the emerging structure as well as the formation dynamics. Only the combination of in vitro experiments and computer simulations has the potential to pinpoint the kind of interactions involved. The presented simulations make clear predictions for the structure of the immunological synapse and elucidate the role of a self-organizing attraction between complexes of T cell receptor and peptide–MHC molecule, versus a centrally directed motion of these complexes.
- Deceleration of fusion–fission cycles improves mitochondrial quality control during aging (2012)
- Mitochondrial dynamics and mitophagy play a key role in ensuring mitochondrial quality control. Impairment thereof was proposed to be causative to neurodegenerative diseases, diabetes, and cancer. Accumulation of mitochondrial dysfunction was further linked to aging. Here we applied a probabilistic modeling approach integrating our current knowledge on mitochondrial biology allowing us to simulate mitochondrial function and quality control during aging in silico. We demonstrate that cycles of fusion and fission and mitophagy indeed are essential for ensuring a high average quality of mitochondria, even under conditions in which random molecular damage is present. Prompted by earlier observations that mitochondrial fission itself can cause a partial drop in mitochondrial membrane potential, we tested the consequences of mitochondrial dynamics being harmful on its own. Next to directly impairing mitochondrial function, pre-existing molecular damage may be propagated and enhanced across the mitochondrial population by content mixing. In this situation, such an infection-like phenomenon impairs mitochondrial quality control progressively. However, when imposing an age-dependent deceleration of cycles of fusion and fission, we observe a delay in the loss of average quality of mitochondria. This provides a rational why fusion and fission rates are reduced during aging and why loss of a mitochondrial fission factor can extend life span in fungi. We propose the ‘mitochondrial infectious damage adaptation’ (MIDA) model according to which a deceleration of fusion–fission cycles reflects a systemic adaptation increasing life span.