Network-based approaches to quantify multicellular development

A quantitative morphospace of multicellular organ design in the plant Arabidopsis

Organ function emerges from the interactions between their constituent cells. The investigation of cellular organization can provide insight into organ function following structure-function relationships. Here, we investigate the extent to which properties in cellular organization can arise "for free" as an emergent property of embedding cells in space versus those that are actively generated by patterning processes. Default cellular configurations were established using three-dimensional (3D) digital tissue models. Network-based analysis of these synthetic cellular assemblies established a quantitative topological baseline of cellular organization, granted by virtue of passive spatial packing and the minimal amount of order that emerges for free in tessellated tissues. A 3D cellular-resolution digital tissue atlas for the model plant species Arabidopsis was generated, and the extent to which the organs in this organism conform to the default configurations was established through statistical comparisons with digital tissue models. Cells in different tissues of Arabidopsis do not conform to random packing arrangements to varying degrees. Most closely matching the random models was the undifferentiated shoot apical meristem (SAM) from which aerial organs emanate. By contrast, leaf and sepal tissue showed the greatest deviation from this baseline, suggesting these to be the most "complex" tissues in Arabidopsis. Investigation of the patterning principles responsible for the gap between these tissues and default patterns revealed cell elongation and the introduction of air spaces to contribute toward additional organ patterning complexity. This work establishes a quantitative morphospace to understand the principles of organ construction and its diversity within a single organism.

Tissues as networks of cells: towards generative rules of complex organ development

Network analysis is a well-known and powerful tool in molecular biology. More recently, it has been introduced in developmental biology. Tissues can be readily translated into spatial networks such that cells are represented by nodes and intercellular connections by edges. This discretization of cellular organization enables mathematical approaches rooted in network science to be applied towards the understanding of tissue structure and function. Here, we describe how such tissue abstractions can enable the principles that underpin tissue formation and function to be uncovered. We provide an introduction into biologically relevant network measures, then present an overview of different areas of developmental biology where these approaches have been applied. We then summarize the general developmental rules underpinning tissue topology generation. Finally, we discuss how generative models can help to link the developmental rule back to the tissue topologies. Our collection of results points at general mechanisms as to how local developmental rules can give rise to observed topological properties in multicellular systems.

Composition, structure and robustness of Lichen guilds

Symbiosis is a major engine of evolutionary innovation underlying many extant complex organisms. Lichens are a paradigmatic example that offers a unique perspective on the role of symbiosis in ecological success and evolutionary diversification. Lichen studies have produced a wealth of information regarding the importance of symbiosis, but they frequently focus on a few species, limiting our understanding of large-scale phenomena such as guilds. Guilds are groupings of lichens that assist each other's proliferation and are intimately linked by a shared set of photobionts, constituting an extensive network of relationships. To characterize the network of lichen symbionts, we used a large data set ([Formula: see text] publications) of natural photobiont-mycobiont associations. The entire lichen network was found to be modular, but this organization does not directly match taxonomic information in the data set, prompting a reconsideration of lichen guild structure and composition. The multiscale nature of this network reveals that the major lichen guilds are better represented as clusters with several substructures rather than as monolithic communities. Heterogeneous guild structure fosters robustness, with keystone species functioning as bridges between guilds and whose extinction would endanger global stability.

The Random Plots Graph Generation Model for Studying Systems with Unknown Connection Structures

We consider the problem of modeling complex systems where little or nothing is known about the structure of the connections between the elements. In particular, when such systems are to be modeled by graphs, it is unclear what vertex degree distributions these graphs should have. We propose that, instead of attempting to guess the appropriate degree distribution for a poorly understood system, one should model the system via a set of sample graphs whose degree distributions cover a representative range of possibilities and account for a variety of possible connection structures. To construct such a representative set of graphs, we propose a new random graph generator, Random Plots, in which we (1) generate a diversified set of vertex degree distributions and (2) target a graph generator at each of the constructed distributions, one-by-one, to obtain the ensemble of graphs. To assess the diversity of the resulting ensembles, we (1) substantialize the vague notion of diversity in a graph ensemble as the diversity of the numeral characteristics of the graphs within this ensemble and (2) compare such formalized diversity for the proposed model with that of three other common models (Erdős–Rényi–Gilbert (ERG), scale-free, and small-world). Computational experiments show that, in most cases, our approach produces more diverse sets of graphs compared with the three other models, including the entropy-maximizing ERG. The corresponding Python code is available at GitHub.

Measuring Intercellular Interface Area in Plant Tissues Using Quantitative 3D Image Analysis

The cells which make up plant tissues remain fixed together through shared cell walls. Cell-to-cell communication principally takes place through these shared interfaces through a combination of plasmodesmata, transporters, and the apoplastic space. To better understand the capacity for intercellular communication in plant tissues, this chapter outlines a method which can be used to quantify the surface area of shared intercellular interfaces using whole mount imaging and quantitative 3D image analysis. This method allows the potential for intercellular communication as prescribed by cellular architecture to be measured at single cell resolution.

Small subpopulations of β-cells do not drive islet oscillatory [Ca2+] dynamics via gap junction communication

The islets of Langerhans exist as multicellular networks that regulate blood glucose levels. The majority of cells in the islet are excitable, insulin-producing β-cells that are electrically coupled via gap junction channels. β-cells are known to display heterogeneous functionality. However, due to gap junction coupling, β-cells show coordinated [Ca²⁺] oscillations when stimulated with glucose, and global quiescence when unstimulated. Small subpopulations of highly functional β-cells have been suggested to control [Ca²⁺] dynamics across the islet. When these populations were targeted by optogenetic silencing or photoablation, [Ca²⁺] dynamics across the islet were largely disrupted. In this study, we investigated the theoretical basis of these experiments and how small populations can disproportionality control islet [Ca²⁺] dynamics. Using a multicellular islet model, we generated normal, skewed or bimodal distributions of β-cell heterogeneity. We examined how islet [Ca²⁺] dynamics were disrupted when cells were targeted via hyperpolarization or populations were removed; to mimic optogenetic silencing or photoablation, respectively. Targeted cell populations were chosen based on characteristics linked to functional subpopulation, including metabolic rate of glucose oxidation or [Ca²⁺] oscillation frequency. Islets were susceptible to marked suppression of [Ca²⁺] when ~10% of cells with high metabolic activity were hyperpolarized; where hyperpolarizing cells with normal metabolic activity had little effect. However, when highly metabolic cells were removed from the model, [Ca²⁺] oscillations remained. Similarly, when ~10% of cells with either the highest frequency or earliest elevations in [Ca²⁺] were removed from the islet, the [Ca²⁺] oscillation frequency remained largely unchanged. Overall, these results indicate small populations of β-cells with either increased metabolic activity or increased frequency are unable to disproportionately control islet-wide [Ca²⁺] via gap junction coupling. Therefore, we need to reconsider the physiological basis for such small β-cell populations or the mechanism by which they may be acting to control normal islet function.

Many biological systems can be studied using network theory. How heterogeneous cell subpopulations come together to create complex multicellular behavior is of great value in understanding function and dysfunction in tissues. The pancreatic islet of Langerhans is a highly coupled structure that is important for maintaining blood glucose homeostasis. β-cell electrical activity is coordinated via gap junction communication. The function of the insulin-producing β-cell within the islet is disrupted in diabetes. As such, to understand the causes of islet dysfunction we need to understand how different cells within the islet contribute to its overall function via gap junction coupling. Using a computational model of β-cell electrophysiology, we investigated how small highly functional β-cell populations within the islet contribute to its function. We found that when small populations with greater functionality were introduced into the islet, they displayed signatures of this enhanced functionality. However, when these cells were removed, the islet, retained near-normal function. Thus, in a highly coupled system, such as an islet, the heterogeneity of cells allows small subpopulations to be dispensable, and thus their absence is unable to disrupt the larger cellular network. These findings can be applied to other electrical systems that have heterogeneous cell populations.

High-throughput image segmentation and machine learning approaches in the plant sciences across multiple scales

Agriculture has benefited greatly from the rise of big data and high-performance computing. The acquisition and analysis of data across biological scales have resulted in strategies modeling inter- actions between plant genotype and environment, models of root architecture that provide insight into resource utilization, and the elucidation of cell-to-cell communication mechanisms that are instrumental in plant development. Image segmentation and machine learning approaches for interpreting plant image data are among many of the computational methodologies that have evolved to address challenging agricultural and biological problems. These approaches have led to contributions such as the accelerated identification of gene that modulate stress responses in plants and automated high-throughput phenotyping for early detection of plant diseases. The continued acquisition of high throughput imaging across multiple biological scales provides opportunities to further push the boundaries of our understandings quicker than ever before. In this review, we explore the current state of the art methodologies in plant image segmentation and machine learning at the agricultural, organ, and cellular scales in plants. We show how the methodologies for segmentation and classification differ due to the diversity of physical characteristics found at these different scales. We also discuss the hardware technologies most commonly used at these different scales, the types of quantitative metrics that can be extracted from these images, and how the biological mechanisms by which plants respond to abiotic/biotic stresses or genotypic modifications can be extracted from these approaches.

Linking Genes to Shape in Plants Using Morphometrics

A transition from qualitative to quantitative descriptors of morphology has been facilitated through the growing field of morphometrics, representing the conversion of shapes and patterns into numbers. The analysis of plant form at the macromorphological scale using morphometric approaches quantifies what is commonly referred to as a phenotype. Quantitative phenotypic analysis of individuals with contrasting genotypes in turn provides a means to establish links between genes and shapes. The path from a gene to a morphological phenotype is, however, not direct, with instructive information progressing both across multiple scales of biological complexity and through nonintuitive feedback, such as mechanical signals. In this review, we explore morphometric approaches used to perform whole-plant phenotyping and quantitative approaches in capture processes in the mesoscales, which bridge the gaps between genes and shapes in plants. Quantitative frameworks involving both the computational simulation and the discretization of data into networks provide a putative path to predicting emergent shape from underlying genetic programs.

Efficient vasculature investment in tissues can be determined without global information

Cells are the fundamental building blocks of organs and tissues. Information and mass flow through cellular contacts in these structures is vital for the orchestration of organ function. Constraints imposed by packing and cell immobility limit intercellular communication, particularly as organs and organisms scale up to greater sizes. In order to transcend transport limitations, delivery systems including vascular and respiratory systems evolved to facilitate the movement of matter and information. The construction of these delivery systems has an associated cost, as vascular elements do not perform the metabolic functions of the organs they are part of. This study investigates a fundamental trade-off in vascularization in multicellular tissues: the reduction of path lengths for communication versus the cost associated with producing vasculature. Biologically realistic generative models, using multicellular templates of different dimensionalities, revealed a limited advantage to the vascularization of two-dimensional tissues. Strikingly, scale-free improvements in transport efficiency can be achieved even in the absence of global knowledge of tissue organization. A point of diminishing returns in the investment of additional vascular tissue to the increased reduction of path length in 2.5- and three-dimensional tissues was identified. Applying this theory to experimentally determined biological tissue structures, we show the possibility of a co-dependency between the method used to limit path length and the organization of cells it acts upon. These results provide insight as to why tissues are or are not vascularized in nature, the robustness of developmental generative mechanisms and the extent to which vasculature is advantageous in the support of organ function.

The helical motions of roots are linked to avoidance of particle forces in soil

Limitation to root growth results from forces required to overcome soil resistance to deformation. The variations in individual particle forces affects root development and often deflects the growth trajectory. We have developed transparent soil and optical projection tomography microscopy systems where measurements of growth trajectory and particle forces can be acquired in a granular medium at a range of confining pressures. We developed image-processing pipelines to analyse patterns in root trajectories and a stochastic-mechanical theory to establish how root deflections relate to particle forces and thickening of the root. Root thickening compensates for the increase in mean particle forces but does not prevent deflections from 5% of most extreme individual particle forces causing root deflection. The magnitude of deflections increases with pressure but they assemble into helices of conserved wavelength in response linked to gravitropism. The study reveals mechanisms for the understanding of root growth in mechanically impeding soil conditions and provides insights relevant to breeding of drought-resistant crops.

Chemically induced neurite-like outgrowth reveals a multicellular network function in patient-derived glioblastoma cells

Tumor stem cells and malignant multicellular networks have been separately implicated in the therapeutic resistance of glioblastoma multiforme (GBM), the most aggressive type of brain cancer in adults. Here, we show that small-molecule inhibition of RHO-associated serine/threonine kinase proteins (ROCKi) significantly promoted the outgrowth of neurite-like cell projections in cultures of heterogeneous patient-derived GBM stem-like cells. These projections formed de novo-induced cellular network (iNet) 'webs', which regressed after withdrawal of ROCKi. Connected cells within the iNet web exhibited long range Ca²⁺ signal transmission, and significant lysosomal and mitochondrial trafficking. In contrast to their less-connected vehicle control counterparts, iNet cells remained viable and proliferative after high-dose radiation. These findings demonstrate a link between ROCKi-regulated cell projection dynamics and the formation of radiation-resistant multicellular networks. Our study identifies means to reversibly induce iNet webs ex vivo, and may thereby accelerate future studies into the biology of GBM cellular networks.

Plant behaviour in response to the environment: information processing in the solid state

Information processing and storage underpins many biological processes of vital importance to organism survival. Like animals, plants also acquire, store and process environmental information relevant to their fitness, and this is particularly evident in their decision-making. The control of plant organ growth and timing of their developmental transitions are carefully orchestrated by the collective action of many connected computing agents, the cells, in what could be addressed as distributed computation. Here, we discuss some examples of biological information processing in plants, with special interest in the connection to formal computational models drawn from theoretical frameworks. Research into biological processes with a computational perspective may yield new insights and provide a general framework for information processing across different substrates. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Multicellular Systems Biology: Quantifying Cellular Patterning and Function in Plant Organs Using Network Science

Organ function is at least partially shaped and constrained by the organization of their constituent cells. Extensive investigation has revealed mechanisms explaining how these patterns are generated, with less being known about their functional relevance. In this paper, a methodology to discretize and quantitatively analyze cellular patterning is described. By performing global organ-scale cellular interaction mapping, the organization of cells can be extracted and analyzed using network science. This provides a means to take the developmental analysis of cellular organization in complex organisms beyond qualitative descriptions and provides data-driven approaches to inferring cellular function. The bridging of a structure-function relationship in hypocotyl epidermal cell patterning through global topological analysis provides support for this approach. The analysis of cellular topologies from patterning mutants further enables the contribution of gene activity toward the organizational properties of tissues to be linked, bridging molecular and tissue scales. This systems-based approach to investigate multicellular complexity paves the way to uncovering the principles of complex organ design and achieving predictive genotype-phenotype mapping.

Global Topological Order Emerges through Local Mechanical Control of Cell Divisions in the Arabidopsis Shoot Apical Meristem

The control of cell position and division act in concert to dictate multicellular organization in tissues and organs. How these processes shape global order and molecular movement across organs is an outstanding problem in biology. Using live 3D imaging and computational analyses, we extracted networks capturing cellular connectivity dynamics across the Arabidopsis shoot apical meristem (SAM) and topologically analyzed the local and global properties of cellular architecture. Locally generated cell division rules lead to the emergence of global tissue-scale organization of the SAM, facilitating robust global communication. Cells that lie upon more shorter paths have an increased propensity to divide, with division plane placement acting to limit the number of shortest paths their daughter cells lie upon. Cell shape heterogeneity and global cellular organization requires KATANIN, providing a multiscale link between cell geometry, mechanical cell-cell interactions, and global tissue order.

Information Processing and Distributed Computation in Plant Organs

The molecular networks plant cells evolved to tune their development in response to the environment are becoming increasingly well understood. Much less is known about how these programs function in the multicellular context of organs and the impact this spatial embedding has on emergent decision-making. Here I address these questions and investigate whether the computational control principles identified in engineered information processing systems also apply to plant development. Examples of distributed computing underlying plant development are presented and support the presence of shared mechanisms of information processing across these domains. The coinvestigation of computation across plant biology and computer science can provide novel insight into the principles of plant development and suggest novel algorithms for use in distributed computing.

Fluorescein Transport Assay to Assess Bulk Flow of Molecules Through the Hypocotyl in Arabidopsis thaliana

The bulk transport of molecules through plant tissues underpins growth and development. The stem acts as a conduit between the upper and low domains of the plant, facilitating transport of solutes and water from the roots to the shoot system, and sugar plus other elaborated metabolites towards the non-photosynthetic organs. In order to perform this function efficiently, the stem needs to be optimized for transport. This is achieved through the formation of vasculature that connects the whole plant but also through connectivity signatures that reduce path length distributions outside the vascular system. This protocol was devised to characterize how cell connectivity affects the bulk flow of molecules traversing the stem. This is achieved by exposing young seedlings to fluorescein, for which no specific transporter is assumed to be present in A. thaliana, and assessing the relative concentration of this fluorescent compound in individual cells of the embryonic stem (hypocotyl) using confocal microscopy and quantitative 3D image analysis after a given exposure time.