- 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.
- 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.
- Emergence of the mitochondrial reticulum from fission and fusion dynamics (2012)
- Mitochondria form a dynamic tubular reticulum within eukaryotic cells. Currently, quantitative understanding of its morphological characteristics is largely absent, despite major progress in deciphering the molecular fission and fusion machineries shaping its structure. Here we address the principles of formation and the large-scale organization of the cell-wide network of mitochondria. On the basis of experimentally determined structural features we establish the tip-to-tip and tip-to-side fission and fusion events as dominant reactions in the motility of this organelle. Subsequently, we introduce a graph-based model of the chondriome able to encompass its inherent variability in a single framework. Using both mean-field deterministic and explicit stochastic mathematical methods we establish a relationship between the chondriome structural network characteristics and underlying kinetic rate parameters. The computational analysis indicates that mitochondrial networks exhibit a percolation threshold. Intrinsic morphological instability of the mitochondrial reticulum resulting from its vicinity to the percolation transition is proposed as a novel mechanism that can be utilized by cells for optimizing their functional competence via dynamic remodeling of the chondriome. The detailed size distribution of the network components predicted by the dynamic graph representation introduces a relationship between chondriome characteristics and cell function. It forms a basis for understanding the architecture of mitochondria as a cell-wide but inhomogeneous organelle. Analysis of the reticulum adaptive configuration offers a direct clarification for its impact on numerous physiological processes strongly dependent on mitochondrial dynamics and organization, such as efficiency of cellular metabolism, tissue differentiation and aging.
- Immunologische Experimente am Computer : theoretische Immunologie schließt Wissenslücken (2006)
- Mathematische Methoden in der Biologie haben sich in den vergangenen 25 Jahren zunehmend etabliert. Etwa in den Bereichen der Entwicklung von Organen und Organismen sind große Anstrengungen in der Mathematik unternommen worden, die grundlegenden Mechanismen der Entwicklung aufzudecken. Der einfache Gedanke, auf dem diese Methode aufbaut, ist ein reduktionistischer: Man verwendet einen minimalen Satz von in der Biologie beobachteten Wechselwirkungen – etwa zwischen den Zellen, die das betrachtete Gewebe aufbauen –, übersetzt sie in ein mathematisches System von dynamischen Gleichungen, löst diese auf dem Computer und prüft, ob sich in der Lösung die erwartete Struktur zeigt. Wenn dies allein aufgrund experimenteller Daten aus der Biologie nicht möglich ist, ergibt sich der größte Nutzen der mathematischen Beschreibung: Dann sind neue Hypothesen im mathematischen Modell notwendig, um das reale System beschreiben zu können. Damit sagen die Theoretiker Zusammenhänge voraus, die aus der Biologie alleine nicht ableitbar sind. Diese können durch neue gezielte Experimente verifiziert werden. Ein ähnlicher Ansatz wurde in jüngerer Zeit von unserer Gruppe am Frankfurter Instute for Advanced Studies (FIAS) in der Immunologie verwendet.
- 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.
- QCD-Summenregeln mit Massen (1993)