Approximate Bayesian Computation (ABC) is a widely applicable and popular approach to estimating unknown parameters of mechanistic models. As ABC analyses are computationally expensive, ...parallelization on high-performance infrastructure is often necessary. However, the existing parallelization strategies leave resources unused at times and thus do not optimally leverage them yet. We present look-ahead scheduling, a wall-time minimizing parallelization strategy for ABC Sequential Monte Carlo algorithms, which utilizes all available resources at practically all times by proactive sampling for prospective tasks. Our strategy can be integrated in e.g. adaptive distance function and summary statistic selection schemes, which is essential in practice. Evaluation of the strategy on different problems and numbers of parallel cores reveals speed-ups of typically 10-20% and up to 50% compared to the best established approach. Thus, the proposed strategy allows to substantially improve the cost and run-time efficiency of ABC methods on high-performance infrastructure.
The mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We describe periodic coherent structures of the CGLE, called ...modulated amplitude waves (MAWs). MAWs of various periods P occur in phase chaotic states. A bifurcation study of the MAWs reveals that for sufficiently large period, pairs of MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation, incoherent near-MAW structures evolve towards defects. This leads to our main result: the transition from phase to defect chaos takes place when the periods of MAWs in phase chaos are driven beyond their saddle-node bifurcation.
The transition from phase chaos to defect chaos in the complex Ginzburg–Landau equation (CGLE) is related to saddle-node bifurcations of modulated amplitude waves (MAWs). First, the spatial period
P ...of MAWs is shown to be limited by a maximum
P
SN which depends on the CGLE coefficients; MAW-like structures with period larger than
P
SN evolve to defects. Second, slowly evolving near-MAWs with average phase gradients
ν≈0 and various periods occur naturally in phase chaotic states of the CGLE. As a measure for these periods, we study the distributions of spacings
p between neighbouring peaks of the phase gradient. A systematic comparison of
p and
P
SN as a function of coefficients of the CGLE shows that defects are generated at locations where
p becomes larger than
P
SN. In other words, MAWs with period
P
SN represent “critical nuclei” for the formation of defects in phase chaos and may trigger the transition to defect chaos. Since rare events where
p becomes sufficiently large to lead to defect formation may only occur after a long transient, the coefficients where the transition to defect chaos seems to occur depend on system size and integration time. We conjecture that in the regime where the maximum period
P
SN has diverged, phase chaos persists in the thermodynamic limit.
We analyze the Eckhaus instability of plane waves in the one-dimensional complex Ginzburg–Landau equation (CGLE) and describe the nonlinear effects arising in the Eckhaus unstable regime. Modulated ...amplitude waves (MAWs) are quasi-periodic solutions of the CGLE that emerge near the Eckhaus instability of plane waves and cease to exist due to saddle-node (SN) bifurcations. These MAWs can be characterized by their average phase gradient
ν and by the spatial period
P of the periodic amplitude modulation. A numerical bifurcation analysis reveals the existence and stability properties of MAWs with arbitrary
ν and
P. MAWs are found to be stable for large enough
ν and intermediate values of
P. For different parameter values they are unstable to splitting and attractive interaction between subsequent extrema of the amplitude. Defects form from perturbed plane waves for parameter values above the SN of the corresponding MAWs. The break-down of phase chaos with average phase gradient
ν≠0 (“wound-up phase chaos”) is thus related to these SNs. A lower bound for the break-down of wound-up phase chaos is given by the necessary presence of SNs and an upper bound by the absence of the splitting instability of MAWs.
The cell is the central functional unit of life. Cell behaviors, such as cell division, movements, differentiation, cell death as well as cell shape and size changes, determine how tissues change ...shape and grow during regeneration and development. However, a generally applicable framework to measure and describe the behavior of the multitude of cells in a developing tissue is still lacking. Furthermore, the specific contribution of individual cell behaviors, and how exactly these cell behaviors collectively lead to the morphogenesis and growth of tissues are not clear for many developmental and regenerative processes.
A promising strategy to fill these gaps is the continuing effort of making developmental biology a quantitative science. Recent advances in methods, especially in imaging, enable measurements of cell behaviors and tissue shapes in unprecedented detail and accuracy. Consequently, formalizing hypotheses in terms of mathematical models to obtain testable quantitative predictions is emerging as a powerful tool. Tests of the hypotheses involve the comparison of model predictions to experimentally observed data. The available data is often noisy and based on only few samples. Hence, this comparison of data and model predictions often requires very careful use of statistical inference methods. If one chooses this quantitative approach, the challenges are the choice of observables, i.e. what to measure, and the design of appropriate data-driven models to answer relevant questions.
In this thesis, I applied this data-driven modeling approach to vertebrate morphogenesis, growth and regeneration. In particular, I study spinal cord and muscle regeneration in axolotl, muscle development in zebrafish, and neuron development and maintenance in the adult human brain. To do so, I analyzed images to quantify cell behaviors and tissue shapes. Especially for cell behaviors in post-embryonic tissues, measurements of some cell behavior parameters, such as the proliferation rate, could not be made directly. Hence, I developed mathematical models that are specifically designed to infer these parameters from indirect experimental data. To understand how cell behaviors shape tissues, I developed mechanistic models that causally connect the cell and tissue scales.
Specifically, I first investigated the behaviors of neural stem cells that underlie the regenerative outgrowth of the spinal cord after tail amputation in the axolotl. To do so, I quantified all relevant cell behaviors. A detailed analysis of the proliferation pattern in space and time revealed that the cell cycle is accelerated between 3-4 days after amputation in a high-proliferation zone, initially spanning from 800 µm anterior to the amputation plane. The activation of quiescent stem cells and cell movements into the high-proliferation zone also contribute to spinal cord growth but I did not find contributions by cellular rearrangements or cell shape changes. I developed a mathematical model of spinal cord outgrowth involving all contributing cell behaviors which revealed that the acceleration of the cell cycle is the major driver of spinal cord outgrowth. To compare the behavior of neural stem cells with cell behaviors in the regenerating muscle tissue that surrounds the spinal cord, I also quantified proliferation of mesenchymal progenitor cells and found similar proliferation parameters. I showed that the zone of mesenchymal progenitors that gives rise to the regenerating muscle segments is at least 350 µm long, which is consistent with the length of the high-proliferation zone in the spinal cord.
Second, I investigated shape changes in developing zebrafish muscle segments by quantifying time-lapse movies of developing zebrafish embryos. These data challenged or ruled out a number of previously proposed mechanisms. Motivated by reported cellular behaviors happening simultaneously in the anterior segments, I had previously proposed the existence of a simple tension-and-resistance mechanism that shapes the muscle segments. Here, I could verify the predictions of this mechanism for the final segment shape pattern. My results support the notion that a simple physical mechanism suffices to self-organize the observed spatiotemporal pattern in the muscle segments.
Third, I corroborated and refined previous estimates of neuronal cell turnover rates in the adult human hippocampus. Previous work approached this question by combining quantitative data and mathematical modeling of the incorporation of the carbon isotope C-14. I reanalyzed published data using the published deterministic neuron turnover model but I extended the model by a better justified measurement error model. Most importantly, I found that human adult neurogenesis might occur at an even higher rate than currently believed.
The tools I used throughout were (1) the careful quantification of the involved processes, mainly by image analysis, and (2) the derivation and application of mathematical models designed to integrate the data through (3) statistical inference. Mathematical models were used for different purposes such as estimating unknown parameters from indirect experiments, summarizing datasets with a few meaningful parameters, formalizing mechanistic hypotheses, as well as for model-guided experimental planning. I venture an outlook on how additional open questions regarding cell turnover measurements could be answered using my approach. Finally, I conclude that the mechanistic understanding of development and regeneration can be advanced by comparing quantitative data to the predictions of specifically designed mathematical models by means of statistical inference methods.
Bile, the central metabolic product of the liver, is secreted by hepatocytes
into bile canaliculi (BC), tubular subcellular structures of 0.5-2 $\mu$m
diameter which are formed by the apical ...membranes of juxtaposed hepatocytes. BC
interconnect to build a highly ramified 3D network that collects and transports
bile towards larger interlobular bile ducts (IBD). The transport mechanism of
bile is of fundamental interest and the current text-book model of "osmotic
canalicular bile flow", i.e. enforced by osmotic water influx, has recently
been quantitatively verified based on flux measurements and BC contractility
(Meyer et al., 2017) but challenged in the article entitled "Intravital dynamic
and correlative imaging reveals diffusion-dominated canalicular and
flow-augmented ductular bile flux" (Vartak et al., 2020). We feel compelled to
share a series of arguments that question the key conclusions of this study
(Vartak et al., 2020), particularly because it risks to be misinterpreted and
misleading for the field in view of potential clinical applications. We
summarized the arguments in the following 8 points.
Ausgedehnte dissipative Systeme können fernab vom thermodynamischen Gleichgewicht instabil gegenüber Oszillationen bzw. Wellen oder raumzeitlichem Chaos werden. Die komplexe Ginzburg-Landau Gleichung ...(CGLE) stellt ein universelles Modell zur Beschreibung dieser raumzeitlichen Strukturen dar. Diese Arbeit ist der theoretischen Analyse komplexer Muster gewidmet. Mittels numerischer Bifurkations- und Stabilitätsanalyse werden Instabilitäten einfacher Muster identifiziert und neuartige Lösungen der CGLE bestimmt. Modulierte Amplitudenwellen (MAW) und Super-Spiralwellen sind Beispiele solcher komplexer Muster. MAWs können in hydrodynamischen Experimenten und Super-Spiralwellen in der Belousov-Zhabotinsky-Reaktion beobachtet werden. Der Grenzübergang von Phasen- zu Defektchaos wird durch den Existenzbereich der MAWs erklärt. Mittels der selben numerischen Methoden wird Bursting vom Fold-Hopf-Typ in einem Modell der Kalziumsignalübertragung in Zellen identifiziert.
Ausgedehnte dissipative Systeme können fernab vom thermodynamischen Gleichgewicht instabil gegenüber Oszillationen bzw. Wellen oder raumzeitlichem Chaos werden. Die komplexe Ginzburg-Landau Gleichung ...(CGLE) stellt ein universelles Modell zur Beschreibung dieser raumzeitlichen Strukturen dar. Diese Arbeit ist der theoretischen Analyse komplexer Muster gewidmet. Mittels numerischer Bifurkations- und Stabilitätsanalyse werden Instabilitäten einfacher Muster identifiziert und neuartige Lösungen der CGLE bestimmt. Modulierte Amplitudenwellen (MAW) und Super-Spiralwellen sind Beispiele solcher komplexer Muster. MAWs können in hydrodynamischen Experimenten und Super-Spiralwellen in der Belousov-Zhabotinsky-Reaktion beobachtet werden. Der Grenzübergang von Phasen- zu Defektchaos wird durch den Existenzbereich der MAWs erklärt. Mittels der selben numerischen Methoden wird Bursting vom Fold-Hopf-Typ in einem Modell der Kalziumsignalübertragung in Zellen identifiziert.
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