Lars Hufnagel

Forecast and control of epidemics in a globalized world

The rapid worldwide spread of severe acute respiratory syndrome demonstrated the potential threat an infectious disease poses in a closely interconnected and interdependent world. Here we introduce a probabilistic model that describes the worldwide spread of infectious diseases and demonstrate that a forecast of the geographical spread of epidemics is indeed possible. This model combines a stochastic local infection dynamics among individuals with stochastic transport in a worldwide network, taking into account national and international civil aviation traffic. Our simulations of the severe acute respiratory syndrome outbreak are in surprisingly good agreement with published case reports. We show that the high degree of predictability is caused by the strong heterogeneity of the network. Our model can be used to predict the worldwide spread of future infectious diseases and to identify endangered regions in advance. The performance of different control strategies is analyzed, and our simulations show that a quick and focused reaction is essential to inhibiting the global spread of epidemics.

On the mechanism of wing size determination in fly development

A fundamental and unresolved problem in animal development is the question of how a growing tissue knows when it has achieved its correct final size. A widely held view suggests that this process is controlled by morphogen gradients, which adapt to tissue size and become flatter as tissue grows, leading eventually to growth arrest. Here, we present evidence that the decapentaplegic (Dpp) morphogen distribution in the developing Drosophila wing imaginal disk does not adapt to disk size. We measure the distribution of a functional Dpp-GFP transgene and the Dpp signal transduced by phospho-Mad and show that the characteristic length scale of the Dpp profile remains approximately constant during growth. This finding suggests an alternative scenario of size determination, where disk size is determined relative to the fixed morphogen distribution by a certain threshold level of morphogen required for growth. We propose that when disk boundary reaches the threshold the arrest of cell proliferation throughout the disk is induced by mechanical stress in the tissue. Mechanical stress is expected to arise from the nonuniformity of morphogen distribution that drives growth. This stress, through a negative feedback on growth, can compensate for the nonuniformity of morphogen, achieving uniform growth with the rate that vanishes when disk boundary reaches the threshold. The mechanism is demonstrated through computer simulations of a tissue growth model that identifies the key assumptions and testable predictions. This analysis provides an alternative hypothesis for the size determination process. Novel experimental approaches will be needed to test this model.

Multiview light-sheet microscope for rapid in toto imaging

We present a multiview selective-plane illumination microscope (MuVi-SPIM), comprising two detection and illumination objective lenses, that allows rapid in toto fluorescence imaging of biological specimens with subcellular resolution. The fixed geometrical arrangement of the imaging branches enables multiview data fusion in real time. The high speed of MuVi-SPIM allows faithful tracking of nuclei and cell shape changes, which we demonstrate through in toto imaging of the embryonic development of Drosophila melanogaster.

Collective and single cell behavior in epithelial contact inhibition

Control of cell proliferation is a fundamental aspect of tissue physiology central to morphogenesis, wound healing, and cancer. Although many of the molecular genetic factors are now known, the system level regulation of growth is still poorly understood. A simple form of inhibition of cell proliferation is encountered in vitro in normally differentiating epithelial cell cultures and is known as “contact inhibition.” The study presented here provides a quantitative characterization of contact inhibition dynamics on tissue-wide and single cell levels. Using long-term tracking of cultured Madin-Darby canine kidney cells we demonstrate that inhibition of cell division in a confluent monolayer follows inhibition of cell motility and sets in when mechanical constraint on local expansion causes divisions to reduce cell area. We quantify cell motility and cell cycle statistics in the low density confluent regime and their change across the transition to epithelial morphology which occurs with increasing cell density. We then study the dynamics of cell area distribution arising through reductive division, determine the average mitotic rate as a function of cell size, and demonstrate that complete arrest of mitosis occurs when cell area falls below a critical value. We also present a simple computational model of growth mechanics which captures all aspects of the observed behavior. Our measurements and analysis show that contact inhibition is a consequence of mechanical interaction and constraint rather than interfacial contact alone, and define quantitative phenotypes that can guide future studies of molecular mechanisms underlying contact inhibition.

Improving the efficiency of FP-LAPW calculations

Abstract The full-potential linearized augmented-plane wave (FP-LAPW) method is well known to enable most accurate calculations of the electronic structure and magnetic properties of crystals and surfaces. The implementation of atomic forces has greatly increased its applicability, but it is still generally believed that FP-LAPW calculations require substantial higher computational effort compared to the pseudopotential plane wave (PPW) based methods. In the present paper we analyze the FP-LAPW method from a computational point of view. Starting from an existing implementation (WIEN95 code), we identified the time consuming parts and show how some of them can be formulated more efficiently. In this context also the hardware architecture plays a crucial role. The remaining computational effort is mainly determined by the setup and diagonalization of the Hamiltonian matrix. For the latter, two different iterative schemes are compared. The speed-up gained by these optimizations is compared to the runtime of the “original” version of the code, and the PPW approach. We expect that the strategies described here, can also be used to speed up other computer codes, where similar tasks must be performed.

Quantitative fluorescence imaging of protein diffusion and interaction in living cells

Diffusion processes and local dynamic equilibria inside cells lead to nonuniform spatial distributions of molecules, which are essential for processes such as nuclear organization and signaling in cell division, differentiation and migration. To understand these mechanisms, spatially resolved quantitative measurements of protein abundance, mobilities and interactions are needed, but current methods have limited capabilities to study dynamic parameters. Here we describe a microscope based on light-sheet illumination that allows massively parallel fluorescence correlation spectroscopy (FCS) measurements and use it to visualize the diffusion and interactions of proteins in mammalian cells and in isolated fly tissue. Imaging the mobility of heterochromatin protein HP1α (ref. 4) in cell nuclei we could provide high-resolution diffusion maps that reveal euchromatin areas with heterochromatin-like HP1α-chromatin interactions. We expect that FCS imaging will become a useful method for the precise characterization of cellular reaction-diffusion processes.

Mechanical Stress Inference for Two Dimensional Cell Arrays

Many morphogenetic processes involve mechanical rearrangements of epithelial tissues that are driven by precisely regulated cytoskeletal forces and cell adhesion. The mechanical state of the cell and intercellular adhesion are not only the targets of regulation, but are themselves the likely signals that coordinate developmental process. Yet, because it is difficult to directly measure mechanical stress in vivo on sub-cellular scale, little is understood about the role of mechanics in development. Here we present an alternative approach which takes advantage of the recent progress in live imaging of morphogenetic processes and uses computational analysis of high resolution images of epithelial tissues to infer relative magnitude of forces acting within and between cells. We model intracellular stress in terms of bulk pressure and interfacial tension, allowing these parameters to vary from cell to cell and from interface to interface. Assuming that epithelial cell layers are close to mechanical equilibrium, we use the observed geometry of the two dimensional cell array to infer interfacial tensions and intracellular pressures. Here we present the mathematical formulation of the proposed Mechanical Inverse method and apply it to the analysis of epithelial cell layers observed at the onset of ventral furrow formation in the Drosophila embryo and in the process of hair-cell determination in the avian cochlea. The analysis reveals mechanical anisotropy in the former process and mechanical heterogeneity, correlated with cell differentiation, in the latter process. The proposed method opens a way for quantitative and detailed experimental tests of models of cell and tissue mechanics.

Spatial constraints control cell proliferation in tissues

Significance Spatiotemporal coordination of cell growth underlies tissue development and disease. Mechanical feedback between cells has been proposed as a regulatory mechanism for growth control both in vivo and in cultured cells undergoing contact inhibition of proliferation. Evidence beyond theoretical and correlative observations falls short. In this study, we probe the impact of mechanical tissue perturbations on cell cycle progression by monitoring cell cycle dynamics of cells in tissues subject to acute changes in boundary conditions, as well as tissue stretching and compression. Taken together, we conclude that the ability of tissues to support cell cycle progression adapts to the available space through a memory-free control mechanism, which may coordinate proliferation patterns to maintain tissue homeostasis. Control of cell proliferation is a fundamental aspect of tissue formation in development and regeneration. Cells experience various spatial and mechanical constraints depending on their environmental context in the body, but we do not fully understand if and how such constraints influence cell cycle progression and thereby proliferation patterns in tissues. Here, we study the impact of mechanical manipulations on the cell cycle of individual cells within a mammalian model epithelium. By monitoring the response to experimentally applied forces, we find a checkpoint at the G1–S boundary that, in response to spatial constraints, controls cell cycle progression. This checkpoint prevents cells from entering S phase if the available space remains below a characteristic threshold because of crowding. Stretching the tissue results in fast cell cycle reactivation, whereas compression rapidly leads to cell cycle arrest. Our kinetic analysis of this response shows that cells have no memory of past constraints and allows us to formulate a biophysical model that predicts tissue growth in response to changes in spatial constraints in the environment. This characteristic biomechanical cell cycle response likely serves as a fundamental control mechanism to maintain tissue integrity and to ensure control of tissue growth during development and regeneration.

Quantitative cell polarity imaging defines leader-to-follower transitions during collective migration and the key role of microtubule-dependent adherens junction formation

The directed migration of cell collectives drives the formation of complex organ systems. A characteristic feature of many migrating collectives is a ‘tissue-scale’ polarity, whereby ‘leader’ cells at the edge of the tissue guide trailing ‘followers’ that become assembled into polarised epithelial tissues en route. Here, we combine quantitative imaging and perturbation approaches to investigate epithelial cell state transitions during collective migration and organogenesis, using the zebrafish lateral line primordium as an in vivo model. A readout of three-dimensional cell polarity, based on centrosomal-nucleus axes, allows the transition from migrating leaders to assembled followers to be quantitatively resolved for the first time in vivo. Using live reporters and a novel fluorescent protein timer approach, we investigate changes in cell-cell adhesion underlying this transition by monitoring cadherin receptor localisation and stability. This reveals that while cadherin 2 is expressed across the entire tissue, functional apical junctions are first assembled in the transition zone and become progressively more stable across the leader-follower axis of the tissue. Perturbation experiments demonstrate that the formation of these apical adherens junctions requires dynamic microtubules. However, once stabilised, adherens junction maintenance is microtubule independent. Combined, these data identify a mechanism for regulating leader-to-follower transitions within migrating collectives, based on the relocation and stabilisation of cadherins, and reveal a key role for dynamic microtubules in this process.

Inverted light-sheet microscope for imaging mouse pre-implantation development

Despite its importance for understanding human infertility and congenital diseases, early mammalian development has remained inaccessible to in toto imaging. We developed an inverted light-sheet microscope that enabled us to image mouse embryos from zygote to blastocyst, computationally track all cells and reconstruct a complete lineage tree of mouse pre-implantation development. We used this unique data set to show that the first cell fate specification occurs at the 16-cell stage.