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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 computing 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 avoids idle times of computing units by preemptive sampling of subsequent generations. This allows to utilize all available resources. The strategy can be integrated with e.g. adaptive distance function and summary statistic selection schemes, which is essential in practice. Our key contribution is the theoretical assessment of the strategy of preemptive sampling and the proof of unbiasedness. Complementary, we provide an implementation and evaluate the strategy on different problems and numbers of parallel cores, showing speed-ups of typically 10-20% and up to 50% compared to the best established approach, with some variability. Thus, the proposed strategy allows to improve the cost and run-time efficiency of ABC methods on high-performance infrastructure., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Alamoudi et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Motivation: Biological tissues are dynamic and highly organized. Multi-scale models are helpful tools to analyse and understand the processes determining tissue dynamics. These models usually depend on parameters that need to be inferred from experimental data to achieve a quantitative understanding, to predict the response to perturbations, and to evaluate competing hypotheses. However, even advanced inference approaches such as approximate Bayesian computation (ABC) are difficult to apply due to the computational complexity of the simulation of multi-scale models. Thus, there is a need for a scalable pipeline for modeling, simulating, and parameterizing multi-scale models of multi-cellular processes., Results: Here, we present FitMultiCell, a computationally efficient and user-friendly open-source pipeline that can handle the full workflow of modeling, simulating, and parameterizing for multi-scale models of multi-cellular processes. The pipeline is modular and integrates the modeling and simulation tool Morpheus and the statistical inference tool pyABC. The easy integration of high-performance infrastructure allows to scale to computationally expensive problems. The introduction of a novel standard for the formulation of parameter inference problems for multi-scale models additionally ensures reproducibility and reusability. By applying the pipeline to multiple biological problems, we demonstrate its broad applicability, which will benefit in particular image-based systems biology., Availability and Implementation: FitMultiCell is available open-source at https://gitlab.com/fitmulticell/fit., (© The Author(s) 2023. Published by Oxford University Press.)

Hepatocytes form bile canaliculi that dynamically respond to the signalling activity of bile acids and bile flow. Little is known about their responses to intraluminal pressure. During embryonic development, hepatocytes assemble apical bulkheads that increase the canalicular resistance to intraluminal pressure. Here, we investigate whether they also protect bile canaliculi against elevated pressure upon impaired bile flow in adult liver. Apical bulkheads accumulate upon bile flow obstruction in mouse models and patients with primary sclerosing cholangitis (PSC). Their loss under these conditions leads to abnormally dilated canaliculi, resembling liver cell rosettes described in other hepatic diseases. 3D reconstruction reveals that these structures are sections of cysts and tubes formed by hepatocytes. Mathematical modelling establishes that they positively correlate with canalicular pressure and occur in early PSC stages. Using primary hepatocytes and 3D organoids, we demonstrate that excessive canalicular pressure causes the loss of apical bulkheads and formation of rosettes. Our results suggest that apical bulkheads are a protective mechanism of hepatocytes against impaired bile flow, highlighting the role of canalicular pressure in liver diseases., (© 2023 The Authors. Published under the terms of the CC BY 4.0 license.)

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed through a distinct interface. To help investigators find and use simulation tools, we developed BioSimulators (https://biosimulators.org), a central registry of the capabilities of simulation tools and consistent Python, command-line and containerized interfaces to each version of each tool. The foundation of BioSimulators is standards, such as CellML, SBML, SED-ML and the COMBINE archive format, and validation tools for simulation projects and simulation tools that ensure these standards are used consistently. To help modelers find tools for particular projects, we have also used the registry to develop recommendation services. We anticipate that BioSimulators will help modelers exchange, reproduce, and combine simulations., (© The Author(s) 2022. Published by Oxford University Press on behalf of Nucleic Acids Research.)

Morphogenesis, wound healing, and some cancer metastases depend upon the migration of cell collectives that need to be guided to their destination as well as coordinated with other cell movements. During zebrafish gastrulation, the extension of the embryonic axis is led by the mesendodermal polster that migrates toward the animal pole, followed by the axial mesoderm that undergoes convergence and extension. Here, we investigate how polster cells are guided toward the animal pole. Using a combination of precise laser ablations, advanced transplants, and functional as well as in silico approaches, we establish that each polster cell is oriented by its immediate follower cells. Each cell perceives the migration of followers, through E-cadherin/α-catenin mechanotransduction, and aligns with them. Therefore, directional information propagates from cell to cell over the whole tissue. Such guidance of migrating cells by followers ensures long-range coordination of movements and developmental robustness., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2022 Elsevier Inc. All rights reserved.)

Physiological liver cell replacement is central to maintaining the organ's high metabolic activity, although its characteristics are difficult to study in humans. Using retrospective radiocarbon ( 14 C) birth dating of cells, we report that human hepatocytes show continuous and lifelong turnover, allowing the liver to remain a young organ (average age <3 years). Hepatocyte renewal is highly dependent on the ploidy level. Diploid hepatocytes show more than 7-fold higher annual birth rates than polyploid hepatocytes. These observations support the view that physiological liver cell renewal in humans is mainly dependent on diploid hepatocytes, whereas polyploid cells are compromised in their ability to divide. Moreover, cellular transitions between diploid and polyploid hepatocytes are limited under homeostatic conditions. With these findings, we present an integrated model of homeostatic liver cell generation in humans that provides fundamental insights into liver cell turnover dynamics., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2022 The Author(s). Published by Elsevier Inc. All rights reserved.)

The human amygdala is involved in processing of memory, decision-making, and emotional responses. Previous studies suggested that the amygdala may represent a neurogenic niche in mammals. By combining two distinct methodological approaches, lipofuscin quantification and 14 C-based retrospective birth dating of neurons, along with mathematical modelling, we here explored whether postnatal neurogenesis exists in the human amygdala. We investigated post-mortem samples of twelve neurologically healthy subjects. The average rate of lipofuscin-negative neurons was 3.4%, representing a substantial proportion of cells substantially younger than the individual. Mass spectrometry analysis of genomic 14 C-concentrations in amygdala neurons compared with atmospheric 14 C-levels provided evidence for postnatal neuronal exchange. Mathematical modelling identified a best-fitting scenario comprising of a quiescent and a renewing neuronal population with an overall renewal rate of >2.7% per year. In conclusion, we provide evidence for postnatal neurogenesis in the human amygdala with cell turnover rates comparable to the hippocampus., (© 2022. The Author(s).)

Simulations of tissue-specific effects of primary acute viral infections like COVID-19 are essential for understanding disease outcomes and optimizing therapies. Such simulations need to support continuous updating in response to rapid advances in understanding of infection mechanisms, and parallel development of components by multiple groups. We present an open-source platform for multiscale spatiotemporal simulation of an epithelial tissue, viral infection, cellular immune response and tissue damage, specifically designed to be modular and extensible to support continuous updating and parallel development. The base simulation of a simplified patch of epithelial tissue and immune response exhibits distinct patterns of infection dynamics from widespread infection, to recurrence, to clearance. Slower viral internalization and faster immune-cell recruitment slow infection and promote containment. Because antiviral drugs can have side effects and show reduced clinical effectiveness when given later during infection, we studied the effects on progression of treatment potency and time-of-first treatment after infection. In simulations, even a low potency therapy with a drug which reduces the replication rate of viral RNA greatly decreases the total tissue damage and virus burden when given near the beginning of infection. Many combinations of dosage and treatment time lead to stochastic outcomes, with some simulation replicas showing clearance or control (treatment success), while others show rapid infection of all epithelial cells (treatment failure). Thus, while a high potency therapy usually is less effective when given later, treatments at late times are occasionally effective. We illustrate how to extend the platform to model specific virus types (e.g., hepatitis C) and add additional cellular mechanisms (tissue recovery and variable cell susceptibility to infection), using our software modules and publicly-available software repository., Competing Interests: I have read the journal's policy and the authors of this manuscript have the following competing interests: JAG is the owner/operator of Virtual Tissues for Health, LLC, which develops applications of multiscale tissue models in medical applications and is a shareholder in Gilead Life Sciences.

How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarrete et al., eLife 2019), we introduce the concept of co-orientational order parameters, which generalize the known biaxial order parameters of the theory of liquid crystals. Applying these concepts to three-dimensional reconstructions of single cells from high-resolution imaging data of mouse liver tissue, we show that the axes of nematic cell polarity of hepatocytes exhibit local coordination and are aligned with the biaxially anisotropic sinusoidal network for blood transport. Our study characterizes liver tissue as a biological example of a biaxial liquid crystal. The general methodology developed here could be applied to other tissues and in-vitro organoids., Competing Interests: The authors have declared that no competing interests exist.

Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in itself. Research software must be sustainable in order to understand, replicate, reproduce, and build upon existing research or conduct new research effectively. In other words, software must be available, discoverable, usable, and adaptable to new needs, both now and in the future. Research software therefore requires an environment that supports sustainability. Hence, a change is needed in the way research software development and maintenance are currently motivated, incentivized, funded, structurally and infrastructurally supported, and legally treated. Failing to do so will threaten the quality and validity of research. In this paper, we identify challenges for research software sustainability in Germany and beyond, in terms of motivation, selection, research software engineering personnel, funding, infrastructure, and legal aspects. Besides researchers, we specifically address political and academic decision-makers to increase awareness of the importance and needs of sustainable research software practices. In particular, we recommend strategies and measures to create an environment for sustainable research software, with the ultimate goal to ensure that software-driven research is valid, reproducible and sustainable, and that software is recognized as a first class citizen in research. This paper is the outcome of two workshops run in Germany in 2019, at deRSE19 - the first International Conference of Research Software Engineers in Germany - and a dedicated DFG-supported follow-up workshop in Berlin., Competing Interests: No competing interests were disclosed., (Copyright: © 2021 Anzt H et al.)

The mechanisms of organ size control remain poorly understood. A key question is how cells collectively sense the overall status of a tissue. We addressed this problem focusing on mouse liver regeneration. Using digital tissue reconstruction and quantitative image analysis, we found that the apical surface of hepatocytes forming the bile canalicular network expands concomitant with an increase in F-actin and phospho-myosin, to compensate an overload of bile acids. These changes are sensed by the Hippo transcriptional co-activator YAP, which localizes to apical F-actin-rich regions and translocates to the nucleus in dependence of the integrity of the actin cytoskeleton. This mechanism tolerates moderate bile acid fluctuations under tissue homeostasis, but activates YAP in response to sustained bile acid overload. Using an integrated biophysical-biochemical model of bile pressure and Hippo signaling, we explained this behavior by the existence of a mechano-sensory mechanism that activates YAP in a switch-like manner. We propose that the apical surface of hepatocytes acts as a self-regulatory mechano-sensory system that responds to critical levels of bile acids as readout of tissue status., (© 2020 The Authors. Published under the terms of the CC BY 4.0 license.)

The Hedgehog (Hh) and Wnt/β-Catenin (Wnt) cascades are morphogen pathways whose pronounced influence on adult liver metabolism has been identified in recent years. How both pathways communicate and control liver metabolic functions are largely unknown. Detecting core components of Wnt and Hh signaling and mathematical modeling showed that both pathways in healthy liver act largely complementary to each other in the pericentral (Wnt) and the periportal zone (Hh) and communicate mainly by mutual repression. The Wnt/Hh module inversely controls the spatiotemporal operation of various liver metabolic pathways, as revealed by transcriptome, proteome, and metabolome analyses. Shifting the balance to Wnt (activation) or Hh (inhibition) causes pericentralization and periportalization of liver functions, respectively. Thus, homeostasis of the Wnt/Hh module is essential for maintaining proper liver metabolism and to avoid the development of certain metabolic diseases. With caution due to minor species-specific differences, these conclusions may hold for human liver as well., (Copyright © 2019 The Author(s). Published by Elsevier Inc. All rights reserved.)

Early disease diagnosis is key to the effective treatment of diseases. Histopathological analysis of human biopsies is the gold standard to diagnose tissue alterations. However, this approach has low resolution and overlooks 3D (three-dimensional) structural changes resulting from functional alterations. Here, we applied multiphoton imaging, 3D digital reconstructions and computational simulations to generate spatially resolved geometrical and functional models of human liver tissue at different stages of non-alcoholic fatty liver disease (NAFLD). We identified a set of morphometric cellular and tissue parameters correlated with disease progression, and discover profound topological defects in the 3D bile canalicular (BC) network. Personalized biliary fluid dynamic simulations predicted an increased pericentral biliary pressure and micro-cholestasis, consistent with elevated cholestatic biomarkers in patients' sera. Our spatially resolved models of human liver tissue can contribute to high-definition medicine by identifying quantitative multiparametric cellular and tissue signatures to define disease progression and provide new insights into NAFLD pathophysiology.

Polarity is a universal design principle of biological systems that manifests at all organizational scales, yet its coordination across scales remains poorly understood. Here, we make use of the extreme anatomical plasticity of planarian flatworms to probe the interplay between global body plan polarity and local cell polarity. Our quantitative analysis of ciliary rootlet orientation in the epidermis reveals a dynamic polarity field with head and tail as independent determinants of anteroposterior (A/P) polarization and the body margin as determinant of mediolateral (M/L) polarization. Mathematical modeling rationalizes the global polarity field and its response to experimental manipulations as superposition of separate A/P and M/L fields, and we identify the core PCP and Ft/Ds pathways as their molecular mediators. Overall, our study establishes a framework for the alignment of cellular polarity vectors relative to planarian body plan landmarks and establishes the core PCP and Ft/Ds pathways as evolutionarily conserved 2D-polarization module., (Copyright © 2019 Elsevier Inc. All rights reserved.)

Functional tissue architecture originates by self-assembly of distinct cell types, following tissue-specific rules of cell-cell interactions. In the liver, a structural model of the lobule was pioneered by Elias in 1949. This model, however, is in contrast with the apparent random 3D arrangement of hepatocytes. Since then, no significant progress has been made to derive the organizing principles of liver tissue. To solve this outstanding problem, we computationally reconstructed 3D tissue geometry from microscopy images of mouse liver tissue and analyzed it applying soft-condensed-matter-physics concepts. Surprisingly, analysis of the spatial organization of cell polarity revealed that hepatocytes are not randomly oriented but follow a long-range liquid-crystal order. This does not depend exclusively on hepatocytes receiving instructive signals by endothelial cells, since silencing Integrin-β1 disrupted both liquid-crystal order and organization of the sinusoidal network. Our results suggest that bi-directional communication between hepatocytes and sinusoids underlies the self-organization of liver tissue., Competing Interests: HM, HN, AS, FS, Wd, KM, RB, VK, LB, YK, BF, MZ No competing interests declared, FJ Reviewing editor, eLife, (© 2019, Morales-Navarrete et al.)

The secretion of osmolytes into a lumen and thereby caused osmotic water inflow can drive fluid flows in organs without a mechanical pump. Such fluids include saliva, sweat, pancreatic juice and bile. The effects of elevated fluid pressure and the associated mechanical limitations of organ function remain largely unknown since fluid pressure is difficult to measure inside tiny secretory channels in vivo. We consider the pressure profile of the coupled osmolyte-flow problem in a secretory channel with a closed tip and an open outlet. Importantly, the entire lateral boundary acts as a dynamic fluid source, the strength of which self-organizes through feedback from the emergent pressure solution itself. We derive analytical solutions and compare them to numerical simulations of the problem in three-dimensional space. The theoretical results reveal a phase boundary in a four-dimensional parameter space separating the commonly considered regime with steady flow all along the channel, here termed "wet-tip" regime, from a "dry-tip" regime suffering ceased flow downstream from the closed tip. We propose a relation between the predicted phase boundary and the onset of cholestasis, a pathological liver condition with reduced bile outflow. The phase boundary also sets an intrinsic length scale for the channel which could act as a length sensor during organ growth.

Chemical reaction networks are ubiquitous in biology, and their dynamics is fundamentally stochastic. Here, we present the software library pSSAlib, which provides a complete and concise implementation of the most efficient partial-propensity methods for simulating exact stochastic chemical kinetics. pSSAlib can import models encoded in Systems Biology Markup Language, supports time delays in chemical reactions, and stochastic spatiotemporal reaction-diffusion systems. It also provides tools for statistical analysis of simulation results and supports multiple output formats. It has previously been used for studies of biochemical reaction pathways and to benchmark other stochastic simulation methods. Here, we describe pSSAlib in detail and apply it to a new model of the endocytic pathway in eukaryotic cells, leading to the discovery of a stochastic counterpart of the cut-out switch motif underlying early-to-late endosome conversion. pSSAlib is provided as a stand-alone command-line tool and as a developer API. We also provide a plug-in for the SBMLToolbox. The open-source code and pre-packaged installers are freely available from http://mosaic.mpi-cbg.de.

The polarization of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganization in response to an opposing instructive cue, which we here consider using the example of experimentally inducible body axis inversions in planarian flatworms. We define a dynamically diluted alignment model linking three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours, and cell turnover replacing polarized cells by initially unpolarized cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganization, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganization depends linearly on this effective parameter and no abrupt transitions are observed. This allows us to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic 8-Potts model with annealed site-dilution and makes testable predictions regarding the polarization of dynamic systems, such as the planarian epithelium., (© 2017 The Author(s).)

Bile, the central metabolic product of the liver, is transported by the bile canaliculi network. The impairment of bile flow in cholestatic liver diseases has urged a demand for insights into its regulation. Here, we developed a predictive 3D multi-scale model that simulates fluid dynamic properties successively from the subcellular to the tissue level. The model integrates the structure of the bile canalicular network in the mouse liver lobule, as determined by high-resolution confocal and serial block-face scanning electron microscopy, with measurements of bile transport by intravital microscopy. The combined experiment-theory approach revealed spatial heterogeneities of biliary geometry and hepatocyte transport activity. Based on this, our model predicts gradients of bile velocity and pressure in the liver lobule. Validation of the model predictions by pharmacological inhibition of Rho kinase demonstrated a requirement of canaliculi contractility for bile flow in vivo. Our model can be applied to functionally characterize liver diseases and quantitatively estimate biliary transport upon drug-induced liver injury., (Copyright © 2017 The Author(s). Published by Elsevier Inc. All rights reserved.)

Axolotls are unique in their ability to regenerate the spinal cord. However, the mechanisms that underlie this phenomenon remain poorly understood. Previously, we showed that regenerating stem cells in the axolotl spinal cord revert to a molecular state resembling embryonic neuroepithelial cells and functionally acquire rapid proliferative divisions (Rodrigo Albors et al., 2015). Here, we refine the analysis of cell proliferation in space and time and identify a high-proliferation zone in the regenerating spinal cord that shifts posteriorly over time. By tracking sparsely-labeled cells, we also quantify cell influx into the regenerate. Taking a mathematical modeling approach, we integrate these quantitative datasets of cell proliferation, neural stem cell activation and cell influx, to predict regenerative tissue outgrowth. Our model shows that while cell influx and neural stem cell activation play a minor role, the acceleration of the cell cycle is the major driver of regenerative spinal cord outgrowth in axolotls., Competing Interests: The authors declare that no competing interests exist.

Background: Salamanders regenerate their tails after amputation anywhere along their length. How the system faithfully reconstitutes the original number of segments and length is not yet known., Methods: To gain quantitative insight into how the system regenerates the appropriate length, we amputated tails at 4 or 16 myotomes post-cloaca and measured blastema size, cell cycle kinetics via cumulative Bromodeoxyuridine (BrdU) incorporation and the method of Nowakowski, and myotome differentiation rate., Results: In early stages until day 15, blastema cells were all proliferative and divided at the same rate at both amputation levels. A larger blastema was formed in 4th versus 16th myotome amputations indicating a larger founding population. Myotome differentiation started at the same timepoint in the 4th and 16 th level blastemas. The rate of myotome formation was more rapid in 4th myotome blastemas so that by day 21 the residual blastema from the two amputation levels achieved equivalent size. At that time point, only a fraction of blastema cells remain in cycle, with the 4th myotome blastema harboring double the number of cycling cells as the 16th myotome blastema allowing it to grow faster and further reconstitute the larger number of missing myotomes., Conclusions: These data suggest that there are two separable phases of blastema growth. The first is level-independent, with cells displaying unrestrained proliferation. In the second phase, the level-specific growth is revealed, where differing fractions of cells remain in the cell cycle over time.

Living matter equals water, to a first approximation, and water transport across barriers such as membranes and epithelia is vital. Water serves two competing functions. On the one hand, it is the fundamental solvent enabling random mobility of solutes and therefore biochemical reactions and intracellular signal propagation. Homeostasis of the intracellular water volume is required such that messenger concentration encodes the stimulus and not inverse volume fluctuations. On the other hand, water flow is needed for transport of solutes to and away from cells in a directed manner, threatening volume homeostasis and signal transduction fidelity of cells. Feedback regulation of fluid transport reconciles these competing objectives. The regulatory mechanisms often span across multiple spatial scales from cellular interactions up to the architecture of organs. Open questions relate to the dependency of water fluxes and steady state volumes on control parameters and stimuli. We here review selected mathematical models of feedback regulation of fluid transport at the cell scale and identify a general "core-shell" structure of such models. We propose that fluid transport models at other spatial scales can be constructed in a generalised core-shell framework, in which the core accounts for the biophysical effects of fluid transport whilst the shell reflects the regulatory mechanisms. We demonstrate the applicability of this framework for tissue lumen growth and suggest future experiments in zebrafish to test lumen size regulation mechanisms., (Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.)

The muscle segments of fish have a folded shape, termed a chevron, which is thought to be optimal for the undulating body movements of swimming. However, the mechanism shaping the chevron during embryogenesis is not understood. Here, we used time-lapse microscopy of developing zebrafish embryos spanning the entire somitogenesis period to quantify the dynamics of chevron shape development. By comparing such time courses with the start of movements in wildtype zebrafish and analysing immobile mutants, we show that the previously implicated body movements do not play a role in chevron formation. Further, the monotonic increase of chevron angle along the anteroposterior axis revealed by our data constrains or rules out possible contributions by previously proposed mechanisms. In particular, we found that muscle pioneers are not required for chevron formation. We put forward a tension-and-resistance mechanism involving interactions between intra-segmental tension and segment boundaries. To evaluate this mechanism, we derived and analysed a mechanical model of a chain of contractile and resisting elements. The predictions of this model were verified by comparison with experimental data. Altogether, our results support the notion that a simple physical mechanism suffices to self-organize the observed spatiotemporal pattern in chevron formation., (© 2014. Published by The Company of Biologists Ltd.)

Morpheus is a modeling environment for the simulation and integration of cell-based models with ordinary differential equations and reaction-diffusion systems. It allows rapid development of multiscale models in biological terms and mathematical expressions rather than programming code. Its graphical user interface supports the entire workflow from model construction and simulation to visualization, archiving and batch processing.

In many animals, regenerative processes can replace lost body parts. Organ and tissue regeneration consequently also hold great medical promise. The regulation of regenerative processes is achieved through concerted actions of multiple organizational levels of the organism, from diffusing molecules and cellular gene expression patterns up to tissue mechanics. Our intuition is usually not adapted well to this degree of complexity and the quantitative aspects of the regulation of regenerative processes remain poorly understood. One way out of this dilemma lies in the combination of experimentation and mathematical modeling within an iterative process of model development/refinement, model predictions for novel experimental conditions, quantitative experiments testing these predictions, and subsequent model refinement. This interdisciplinary approach has already provided key insights into smaller scale processes during embryonic development and a so-far limited number of more complex regeneration processes. This review discusses selected theoretical and interdisciplinary studies and is structured along the three phases of regeneration: (1) initiation of a regeneration response, (2) tissue patterning during regenerate growth, (3) arresting the regeneration response. Moreover, we highlight the opportunities provided by extensions of mathematical models from developmental processes toward the study of related regenerative processes., (© 2014 Elsevier Inc. All rights reserved.)

The Hedgehog (Hh) signalling cascade is highly conserved and involved in development and disease throughout evolution. Nevertheless, in comparison with other pathways, our mechanistic understanding of Hh signal transduction is remarkably incomplete. In the absence of ligand, the Hh receptor Patched (Ptc) represses the key signal transducer Smoothened (Smo) through an unknown mechanism. Hh binding to Ptc alleviates this repression, causing Smo redistribution to the plasma membrane, phosphorylation and opening of the Smo cytoplasmic tail, and Smo oligomerisation. However, the order and interdependence of these events is as yet poorly understood. We have mathematically modelled and simulated Smo activation for two alternative modes of pathway activation, with Ptc primarily affecting either Smo localisation or phosphorylation. Visualising Smo activation through a novel, fluorescence-based reporter allowed us to test these competing models. Here, we show that Smo localisation to the plasma membrane is sufficient for phosphorylation of the cytoplasmic tail in the presence of Ptc. Using fluorescence cross-correlation spectroscopy (FCCS), we also demonstrate that inactivation of Ptc by Hh induces Smo clustering irrespective of Smo phosphorylation. Our observations therefore support a model of Hh signal transduction whereby Smo subcellular localisation and not phosphorylation is the primary target of Ptc function.

Background: Replacement of dysfunctional β-cells in the islets of Langerhans by transdifferentiation of pancreatic acinar cells has been proposed as a regenerative therapy for diabetes. Adult acinar cells spontaneously revert to a multipotent state upon tissue dissociation in vitro and can be stimulated to redifferentiate into β-cells. Despite accumulating evidence that contact-mediated signals are involved, the mechanisms regulating acinar-to-islet cell transdifferentiation remain poorly understood., Results: In this study, we propose that the crosstalk between two contact-mediated signaling mechanisms, lateral inhibition and lateral stabilization, controls cell fate stability and transdifferentiation of pancreatic cells. Analysis of a mathematical model combining gene regulation with contact-mediated signaling reveals the multistability of acinar and islet cell fates. Inhibition of one or both modes of signaling results in transdifferentiation from the acinar to the islet cell fate, either by dedifferentiation to a multipotent state or by direct lineage switching., Conclusions: This study provides a theoretical framework to understand the role of contact-mediated signaling in pancreatic cell fate control that may help to improve acinar-to-islet cell transdifferentiation strategies for β-cell neogenesis.

The cell fate decision of multi-potent pancreatic progenitor cells between the exocrine and endocrine lineages is regulated by Notch signalling, mediated by cell-cell interactions. However, canonical models of Notch-mediated lateral inhibition cannot explain the scattered spatial distribution of endocrine cells and the cell-type ratio in the developing pancreas. Based on evidence from acinar-to-islet cell transdifferentiation in vitro, we propose that lateral stabilization, i.e. positive feedback between adjacent progenitor cells, acts in parallel with lateral inhibition to regulate pattern formation in the pancreas. A simple mathematical model of transcriptional regulation and cell-cell interaction reveals the existence of multi-stability of spatial patterns whose simultaneous occurrence causes scattering of endocrine cells in the presence of noise. The scattering pattern allows for control of the endocrine-to-exocrine cell-type ratio by modulation of lateral stabilization strength. These theoretical results suggest a previously unrecognized role for lateral stabilization in lineage specification, spatial patterning and cell-type ratio control in organ development.