Computational approaches to developmental patterning

Design principles for generating robust gene expression patterns in dynamic engineered tissues

Recapitulating native tissue organization is a central challenge in regenerative medicine as it is critical for generating functional tissues. One strategy to generate engineered tissues with predictable and appropriate organization is to mimic the gene expression patterning process that organizes tissues in the developing embryo. In a developing embryo, correct organization is accomplished by tissue patterning via the generation of temporal and spatial patterns of gene expression coupled with, and leading to, extensive cellular re-organization. Methods to pattern gene expression in vitro could therefore provide both better models for understanding the cellular and molecular events taking place during tissue morphogenesis and novel strategies for engineering tissues with more realistic and complex architectures. While a few attempts have been made to genetically pattern tissues in vitro, these do not produce sharp predictable patterning. In both the embryo and an in vitro tissue, patterning often occurs during extensive cell re-organization but how the dynamics of gene induction and cell re-distribution interact to impact the final outcome of patterning and ultimately tissue organization is not known. Understanding this relationship and the system parameters that dictate robust pattern formation is critical for engineering genetic patterning in vitro to organize artificial tissues. We set out to identify key requirements for pattern formation by patterning gene expression in vitro in sheets of re-distributing cells using a drug-inducible gene expression system and patterned drug delivery to mimic morphogen gene induction. Based on our experimental observations, we develop a mathematical model that allows us to identify and experimentally verify the conditions under which generation of sharp gene expression patterns is possible in vitro. Our results highlight the importance of coordinating gene induction dynamics and cellular movement in order to achieve robust pattern formation.

Propulsion and navigation within the advancing monolayer sheet

As a wound heals, or a body plan forms, or a tumour invades, observed cellular motions within the advancing cell swarm are thought to stem from yet to be observed physical stresses that act in some direct and causal mechanical fashion. Here we show that such a relationship between motion and stress is far from direct. Using monolayer stress microscopy, we probed migration velocities, cellular tractions and intercellular stresses in an epithelial cell sheet advancing towards an island on which cells cannot adhere. We found that cells located near the island exert tractions that pull systematically towards this island regardless of whether the cells approach the island, migrate tangentially along its edge, or paradoxically, recede from it. This unanticipated cell-patterning motif, which we call kenotaxis, represents the robust and systematic mechanical drive of the cellular collective to fill unfilled space.

The effective application of a discrete transition model to explore cell-cycle regulation in yeast

Background

Bench biologists often do not take part in the development of computational models for their systems, and therefore, they frequently employ them as “black-boxes”. Our aim was to construct and test a model that does not depend on the availability of quantitative data, and can be directly used without a need for intensive computational background.

Results

We present a discrete transition model. We used cell-cycle in budding yeast as a paradigm for a complex network, demonstrating phenomena such as sequential protein expression and activity, and cell-cycle oscillation. The structure of the network was validated by its response to computational perturbations such as mutations, and its response to mating-pheromone or nitrogen depletion. The model has a strong predicative capability, demonstrating how the activity of a specific transcription factor, Hcm1, is regulated, and what determines commitment of cells to enter and complete the cell-cycle.

Conclusion

The model presented herein is intuitive, yet is expressive enough to elucidate the intrinsic structure and qualitative behavior of large and complex regulatory networks. Moreover our model allowed us to examine multiple hypotheses in a simple and intuitive manner, giving rise to testable predictions. This methodology can be easily integrated as a useful approach for the study of networks, enriching experimental biology with computational insights.

Forces in tissue morphogenesis and patterning

During development, mechanical forces cause changes in size, shape, number, position, and gene expression of cells. They are therefore integral to any morphogenetic processes. Force generation by actin-myosin networks and force transmission through adhesive complexes are two self-organizing phenomena driving tissue morphogenesis. Coordination and integration of forces by long-range force transmission and mechanosensing of cells within tissues produce large-scale tissue shape changes. Extrinsic mechanical forces also control tissue patterning by modulating cell fate specification and differentiation. Thus, the interplay between tissue mechanics and biochemical signaling orchestrates tissue morphogenesis and patterning in development.

Sharpening of expression domains induced by transcription and microRNA regulation within a spatio-temporal model of mid-hindbrain boundary formation

Background

The establishment of the mid-hindbrain region in vertebrates is mediated by the isthmic organizer, an embryonic secondary organizer characterized by a well-defined pattern of locally restricted gene expression domains with sharply delimited boundaries. While the function of the isthmic organizer at the mid-hindbrain boundary has been subject to extensive experimental studies, it remains unclear how this well-defined spatial gene expression pattern, which is essential for proper isthmic organizer function, is established during vertebrate development. Because the secreted Wnt1 protein plays a prominent role in isthmic organizer function, we focused in particular on the refinement of Wnt1 gene expression in this context.

Results

We analyzed the dynamics of the corresponding murine gene regulatory network and the related, diffusive signaling proteins using a macroscopic model for the biological two-scale signaling process. Despite the discontinuity arising from the sharp gene expression domain boundaries, we proved the existence of unique, positive solutions for the partial differential equation system. This enabled the numerically and analytically analysis of the formation and stability of the expression pattern. Notably, the calculated expression domain of Wnt1 has no sharp boundary in contrast to experimental evidence. We subsequently propose a post-transcriptional regulatory mechanism for Wnt1 miRNAs which yields the observed sharp expression domain boundaries. We established a list of candidate miRNAs and confirmed their expression pattern by radioactive in situ hybridization. The miRNA miR-709 was identified as a potential regulator of Wnt1 mRNA, which was validated by luciferase sensor assays.

Conclusion

In summary, our theoretical analysis of the gene expression pattern induction at the mid-hindbrain boundary revealed the need to extend the model by an additional Wnt1 regulation. The developed macroscopic model of a two-scale process facilitate the stringent analysis of other morphogen-based patterning processes.

Zebrafish models for ectopic mineralization disorders: practical issues from morpholino design to post-injection observations

Zebrafish (ZF, Danio rerio) has emerged as an important and popular model species to study different human diseases. Key regulators of skeletal development and calcium metabolism are highly conserved between mammals and ZF. The corresponding orthologs share significant sequence similarities and an overlap in expression patterns when compared to mammals, making ZF a potential model for the study of mineralization-related disorders and soft tissue mineralization. To characterize the function of early mineralization-related genes in ZF, these genes can be knocked down by injecting morpholinos into early stage embryos. Validation of the morpholino needs to be performed and the concern of aspecific effects can be addressed by applying one or more independent techniques to knock down the gene of interest. Post-injection assessment of early mineralization defects can be done using general light microscopy, calcein staining, Alizarin red staining, Alizarin red-Alcian blue double staining, and by the use of transgenic lines. Examination of general molecular defects can be done by performing protein and gene expression analysis, and more specific processes can be explored by investigating ectopic mineralization-related mechanisms such as apoptosis and mitochondrial dysfunction. In this paper, we will discuss all details about the aforementioned techniques; shared knowledge will be very useful for the future investigation of ZF models for ectopic mineralization disorders and to understand the underlying pathways involved in soft tissue calcification.

Wnt signaling in skin development, homeostasis, and disease

The skin and its appendages constitute the largest organ of the body. Its stratified epithelia offer protection from environmental stresses such as dehydration, irradiation, mechanical trauma, and pathogenic infection, whereas its appendages, like hair and sebaceous glands, help regulate body temperature as well as influence animal interaction and social behavior through camouflage and sexual signaling. To respond to and function effectively in a dynamic external environment, the skin and its appendages possess a remarkable ability to regenerate in a carefully controlled fashion. When this finely tuned homeostatic process is disrupted, skin diseases such as cancers may result. At present, the molecular signals that orchestrate cell proliferation, differentiation, and patterning in the skin remain incompletely understood. It is increasingly apparent that many morphogenetic pathways with key roles in development are also important in regulating skin biology. Of these, Wnt signaling has emerged as the dominant pathway controlling the patterning of skin and influencing the decisions of embryonic and adult stem cells to adopt the various cell lineages of the skin and its appendages, as well as subsequently controlling the function of differentiated skin cells. Here we will review established concepts and present recent advances in our understanding of the diverse roles that Wnt signaling plays in skin development, homeostasis, and disease.

Spatiotemporal order, disorder, and propagating defects in homogeneous system of relaxation oscillators

A variety of complex spatial patterns relevant to chemical and biological systems can be generated through reaction-diffusion mechanisms. In this paper, we show that diffusive coupling through the inactivating component in a system of relaxation oscillators extends such complexity to the temporal domain, generating remarkable spatiotemporal phenomena. We provide analytic explanations of the antiphase synchronization and spatially patterned oscillatory death regimes. We report a chimera state where patches with distinct dynamics coexist and also observe propagating phase defects resembling persistent structures in cellular automata that may be used for computation.

Divergent lymphocyte signalling revealed by a powerful new tool for analysis of time-lapse microscopy

We describe a new approach for interactive analysis of time-lapse microscopy, and apply this approach to elucidating whether polarity regulation is conserved between epithelial cells and lymphocytes. A key advantage of our analysis platform, 'TACTICS', is the capacity to visualize individual data points in the context of large data sets, similar to standard approaches in flow cytometry. Scatter plots representing microscopic parameters or their derivations such as polarity ratios are linked to the original data such that clicking on each dot enables a link to images and movies of the corresponding cell. Similar to flow cytometric analysis, subsets of the data can be gated and reanalyzed to explore the relationships between different parameters. TACTICS was used to dissect the regulation of polarization of the cell fate determinant, Numb, in migrating lymphocytes. We show here that residues of Numb that are phosphorylated by atypical protein kinase C (aPKC) to mediate apicobasal polarity in epithelial cells are not required for polarization of Numb in T cells, indicating that the role of aPKC is not conserved between lymphocytes and epithelia.

The mechanics behind cell polarity

The generation of cell polarity is one of the most intriguing symmetry-breaking events in biology. It is involved in almost all physiological and developmental processes and, despite the differences between plant and animal cell structures, cell polarity is generated by a similar core mechanism that comprises the extracellular matrix (ECM), Rho GTPase, the cytoskeleton, and the membranes. Several recent articles show that mechanical factors also contribute to the establishment and robustness of cell polarity, and the different molecular actors of cell polarity are now viewed as integrators of both biochemical and mechanical signals. Although cell polarity remains a complex process, some level of functional convergence between plants and animals is revealed. Following comparative presentation of cell polarity in plants and animals, we will discuss the theoretical background behind the role of mechanics in polarity and the relevant experimental tests, focusing on ECM anchorage, cytoskeleton behavior, and membrane tension.

Curvature-driven effective attraction in multicomponent membranes

We study closed liquid membranes that segregate into three phases due to differences in the chemical and physical properties of its components. The shape and in-plane membrane arrangement of the phases are coupled through phase-specific bending energies and line tensions. We use simulated annealing Monte Carlo simulations to find low-energy structures, allowing both phase arrangement and membrane shape to relax. The three-phase system is the simplest one in which there are multiple interface pairs, allowing us to analyze interfacial preferences and pairwise distinct line tensions. We observe the system's preference for interface pairs that maximize differences in spontaneous curvature. From a pattern selection perspective, this acts as an effective attraction between phases of most disparate spontaneous curvature. We show that this effective attraction is robust enough to persist even when the interface between these phases is the most penalized by line tension. This effect is driven by geometry and not by any explicit component-component interaction.