Session Z03: Patterns II: Patterns in Biological Systems from Plants to Tissues to Organs

Patterns of growth and thickness in the cerebral cortex

Between individuals and across species, brain morphology is strikingly consistent in some significant ways. One example is a characteristic pattern of cortical thickness in gyrencephalic, or folded, brains - thick outer folds, or gyri, and thin inner folds, or sulci. This raises the question: which factors (genetic, biochemical, physical, and/or others) lead to this morphological consistency? In this talk, I will cover both our models of cortical folding and our analysis of folded cortical geometries.

The former includes explorations of both the physical forces generated during folding and heterogeneous cortical growth, and examines the resulting pattern of cortical thickness. The latter includes fully three-dimensional topological analysis of local shape (curvature and depth) and thickness, in humans and several non-human primate species. Through comparisons between our models and imaging data, we can gain a deeper understanding of the factors that contribute to the variable, yet highly characteristic, patterns of thickness throughout the cortex.   

Aortic Shape Space Topology

The human aorta is the largest pressurized blood vessel in the body. Aortic pathology is inherently mechanical, ranging from through thickness fracture, aortic rupture, to intra-lamellar fracture, termed aortic dissection. While aortic rupture is immediately life-threatening, the stability of aortic dissections is poorly understood. Traditional metrics focus on singular scalar measurements of maximum aortic size. However these do not predict which dissected aortas are stable for observation versus require operative intervention. We have pioneered a differential geometry approach to classify the stability of aortic dissections. Using over 150 computed tomography scans from patients with normal and dissected aortas, we show that aortic classification is optimally performed in a scale space defined by topologic invariants rather than geometric ones. We prove that all aortas prior to rupture are globally topologically a 2-torus, T². However, dissected aortas separate from normal aortas by studying the gradients of the local aortic topology, which are calculated as spatial fluctuation of the Euler characteristic, χ. As aortic shapes become more distorted, δχ diverges with a characteristic power law, which is a hallmark of an impending topologic transition, mechanically rupture.   

Agent-based modelling of Vasculogenesis

Vasculogensis is the first stage of blood vessel formation where anigioblasts differentiate into endothelial and other auxiliary cells leading to de novo formation of vascular networks in the presence of growth factors. Efficient transportation of nutrients to tissues and organs require optimized and robust vascular networks, but it is unclear how single cell behavior affects the self-assembled formation of such networks. We present an agent-based model of vascular network formation in which single cell properties like cellular adhesion, anisotropic propulsion and the presence of multiple cell types and proliferation can lead to a variety of network morphologies that we compare quantitatively with in vitro experiments. We also explore feedback between the vascular network properties and single cell parameters to gain insight into the evolution of vascular networks.    

Optimizing multicellular network formation on elastic substrates

Cells probe their local environment by exerting forces on the surrounding medium. During tissue morphogenesis, cells are driven by these matrix-mediated, mechanical interactions, and align into functional, ordered structures. By combining a linear elastic model for substrate-mediated cell-cell mechanical interactions and an agent-based model for cell movement, we show that force dipoles modeling contractile cells on elastic substrates form branched networks that percolate when the interactions are strong enough. This suggests a mechanics-driven mechanism for the morphogenesis of multicellular networks such as endothelial cell networks during vasculogenesis. Motivated by the transport functions of biological networks, we characterize our simulated force dipole networks in terms of a percolation order parameter and morphological features such as junctions, branches, and rings and show how they depend on substrate mechanics, cell density and noise. Consistent with experiments, we find that percolating networks form at an optimal range of substrate stiffness. Lastly, we find networks are robust to low levels of activity and confinement can help induce network formation.   

Flow facilitated hierarchical pattern formation in biological transport networks

From leaf venation patterns to blood vasculature, hierarchical networks of tubes are ubiquitous in nature. We study a model where tube radius grows in proportional to local fluid flow velocity, shear rate, or flux, and show that it may facilitate the formation of hierarchical network patterns, reminiscent of some biological networks. By tuning the model parameters we observe a phase transition from homogenization (where flow is uniform) to channelization (where flow is supported by a small subset of tubes).   

Live-imaging and optogenetic dissection of transcriptional repression in living embryos

Transcriptional repression is essential for establishing and maintaining gene expression patterns. However, how repressors control gene expression at the single-cell level over time remains elusive. Here, we utilized optogenetics and live-imaging tools to analyze transcriptional repression in the early fruit fly embryo. Our analysis reveals that repression is achieved through all-or-nothing silencing activities controlled by a sharp response function. As a result, the repressor modulates the fraction of silenced cells rather than the mRNA production rate. We then applied optogenetic perturbations to demonstrate the reversible nature of silencing, with both silencing and reactivation occurring with an average response time of 2.5-3 minutes. Further analysis reveals that we can use a two-state model, including promoter ON and promoter OFF states, to recapitulate observed silencing/reactivation dynamics. The repressor controls the bursting frequency, which indicates that the repressor can only act on transcription when the promoter is switched off. We have provided a framework for further understanding and rational control of the eukaryotic transcriptional repression.   

Non-linear dynamics in contact-based pattern formation

Developing tissues are active matter systems in which the constituting cells exchange information to self-organize into distinct patterns. When cells communicate through direct physical contact, they form a signaling network with a topology that can be dynamic depending on the rheological properties of the system. To study patterning arising from feedback effects between signaling and cellular dynamics, we rely on a statistical physics approach. We consider spatial probability distributions that represent the chance of encountering and exchanging signals with a given cell. Complemented by a minimal model of the molecular signaling pathway [Corson et al. 2017], we obtain a set of coupled, nonlinear differential equations with a rich patterning landscape. We apply our theory to predict patterning dynamics in the zebrafish neuromast, a highly regenerative mechanosensory epithelium, in which cells are in a “fluid-like” state. To quantify patterning of this organ, we exploit 3D life fluorescence microscopy and an integrated approach combining experimental observations and theory.   

Patterning of membrane adhesion under hydraulic stress

Lumen formation is ubiquitous in developmental biology. The successful opening of fluid filled spaces within tissues is crucial for a zygote to grow into a topologically complex adult organism containing multiple cavities and networks of tubes. These cavities often form by the coarsening of microlumens. For instance, during blastulation in the early development of animals, embryos undergo a dynamic transformation from the morula, a dense ball of cells, to the blastula, a hollow sphere surrounding a pressurized fluid-filled cavity. This process starts with the accumulation of fluid due to ionic pumping in hundreds of micro-lumens that fracture cell-cell contacts. Later, these micro-lumens discharge into a dominant lumen in a coarsening process. However, how these microlumens nucleate and coarsen is still poorly understood. To address this issue, we look at the formation of microlumens and their progressive coarsening in the adhesion of giant unilamellar vesicles adhered to a supported lipid bilayer after an osmotic shock. Together with a theoretical model and a computational framework, we explore the length- and time-scales relevant to this process. We show the main ingredients leading to nucleation, the shape of the resulting lumens, and their coarsening.    

Matter exchange as a physical mechanism for pattern formation in membranes

Heterogeneous lipid composition in cell membranes is key to biological function, acting as one of the main mechanisms to exchange information between cells or between a cell and its environment. The underlying mechanisms controlling pattern formation are still under debate. In this work, we consider a theoretical phase-field model to describe the composition of a two-dimensional membrane exchanging matter with a reservoir. The model includes matter absorption and desorption in the membrane with different rates. By only assuming matter conservation in the system membrane-reservoir, we show with extensive numerical simulations that, depending on these rates, a complex patterned composition distribution emerges in the membrane. The pattern emergence is due to Spatio-temporal memory effects. With a semi-analytical argument, we compute the typical size of domains as a function of the absorption and desorption rates. We find scaling relations that are in excellent agreement with our numerical simulations. Our results show that the causes of heterogeneous lipid composition may be justified in simple physical terms.   

Withdrawn

The seedcoat of common millet (Panicum miliaceum) has a unique jigsaw puzzle-like microstructure. The epidermis cells on the seedcoat articulate via wavy intercellular sutures, forming a compact layer to protect the kernel inside. The intercellular boundaries of the cells are joined by thin, wavy suture interfaces. Previous studies have shown that this tessellation design can have amplified strength, toughness, and can have auxetic properties under higher stiffness ratios.

The goal of this study is to quantify the functionally graded mechanical properties of the seedcoat under different levels of humidity. Nanoindentation mechanical experiments are performed at selected locations on the surface of the seedcoat in a humidity chamber. The effective stiffness at different locations under different levels humidity are determined. The relationship between the complexity of local suture tessellation and the corresponding mechanical properties are explored. With the experimental input, finite element models of suture tessellations at different locations are developed to reveal the mechanics of the functionally graded property of the seedcoat.   

Contact-breaking, pore-space patterning and network formation in spongy mesophyll development

Morphogenesis, or the emergence of spatial structure and heterogeneity during biological development, is driven by cell growth, proliferation, and changes in cell properties, which gives rise to patterns and ultimately function in young tissues. Schizogeny, or the formation of pore space via separation of formerly adherent cells, occurs frequently during plant tissue morphogenesis. While schizogeny is known to pattern pore space in developing roots, here we study more poorly understood schizogeny during the development of the spongy mesophyll tissue of leaves and flowers. We develop a two-dimensional computational model of discrete, deformable particles to mimic the developmental process from confluent mesophyll progenitor cells to porous, network-like mature cells with highly non-spherical shapes. We show that proper development of the spongy mesophyll requires a careful balance of cell-cell adhesion, contact breaking, and the aging of elasticity in the cell wall. We discuss the impact of cell boundary-driven stress on global tissue morphology and anisotropy, as well as extensions to three spatial dimensions.   

Discretizing the Dragonfly Wing: Fluid Flow and Strucutral Analysis

Transport networks are ubiquitous in the world around us, from engineered infrastructure to biology. Notable examples include the xylem in plant leaves, cytoplasm transport in slime molds, and blood flow in the human body. Among biological transport networks, hemolymph flow in insect wings is of particular importance. These systems are large and complex, often containing thousands of elements, and play a vital role in both transport and mechanical rigidity. Here, I study the interplay between flow and mechanics. On the relevant scale, flow is laminar, and pressure driven, resulting in relatively simple flow dynamics for any individual edge. However, complex flow behavior emerges when the system is analyzed as a whole. Structural analysis of the wing under an aerodynamic load is also possible when the wing network is discretized in this manner. As hemolymph composes a large percentage of total wing weight, interaction between fluid flow and wing structure is potentially relevant. Through this simulation, insight is gained into the role of hemolymph flow in insect wings   

Circular and spiral-like crack patterns of desiccated bacterial deposits

Desiccation cracks are ubiquitous and play a key role in a plethora of applications such as coating and printing. Here, we report desiccation crack patterns of drying suspensions of Escherichia coli (E. coli) with different swimming behaviors. Drops of bacterial suspensions with a volume of 2.5 µL and a volume fraction of 10-20% are deposited onto glass substrates for drying. We observe circular cracks in the consolidating film of wild-type E. coli with run-and-tumbling motions, whereas spiral-like cracks are observed in the film of mutant E. coli with tumbling motions. Using fracture mechanics, we show that the circular cracks arise from the locally ordered structure driven by the collective motion of wild-type bacteria and the tensile nature of the radial drying stress. In comparison, the spiral-like cracks are induced by film delamination due to the strong bending moment, which propagates along the azimuthal direction with increasing drying time. Our results elucidate the role of bacteria swimming behavior in desiccation cracks and further enhance the understanding of the rich mechanical instabilities in consolidating bacteria films.