Simple mechanical cues could explain adipose tissue morphology

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

A Lifshitz-Slyozov type model for adipocyte size dynamics: limit from Becker-Döring system and numerical simulation

Biological data show that the size distribution of adipose cells follows a bimodal distribution. In this work, we introduce a Lifshitz-Slyozov type model, based on a transport partial differential equation, for the dynamics of the size distribution of adipose cells. We prove a new convergence result from the related Becker-Döring model, a system composed of several ordinary differential equations, toward mild solutions of the Lifshitz-Slyozov model using distribution tail techniques. Then, this result allows us to propose a new advective-diffusive model, the second-order diffusive Lifshitz-Slyozov model, which is expected to better fit the experimental data. Numerical simulations of the solutions to the diffusive Lifshitz-Slyozov model are performed using a well-balanced scheme and compared to solutions to the transport model. Those simulations show that both bimodal and unimodal profiles can be reached asymptotically depending on several parameters. We put in evidence that the asymptotic profile for the second-order system does not depend on initial conditions, unlike for the transport Lifshitz-Slyozov model.

Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix

The mechanical interaction between cells and the extracellular matrix (ECM) is fundamental to coordinate collective cell behavior in tissues. Relating individual cell-level mechanics to tissue-scale collective behavior is a challenge that cell-based models such as the cellular Potts model (CPM) are well-positioned to address. These models generally represent the ECM with mean-field approaches, which assume substrate homogeneity. This assumption breaks down with fibrous ECM, which has nontrivial structure and mechanics. Here, we extend the CPM with a bead-spring model of ECM fiber networks modeled using molecular dynamics. We model a contractile cell pulling with discrete focal adhesion-like sites on the fiber network and demonstrate agreement with experimental spatiotemporal fiber densification and displacement. We show that at high network cross-linking, contractile cell forces propagate over at least eight cell diameters, decaying with distance with power law exponent n= 0.35 - 0.65 typical of viscoelastic ECMs. Further, we use in silico atomic force microscopy to measure local cell-induced network stiffening consistent with experiments. Our model lays the foundation for investigating how local and long-ranged cell-ECM mechanobiology contributes to multicellular morphogenesis.

Adipose-tissue plasticity in health and disease

Adipose tissue, colloquially known as "fat," is an extraordinarily flexible and heterogeneous organ. While historically viewed as a passive site for energy storage, we now appreciate that adipose tissue regulates many aspects of whole-body physiology, including food intake, maintenance of energy levels, insulin sensitivity, body temperature, and immune responses. A crucial property of adipose tissue is its high degree of plasticity. Physiologic stimuli induce dramatic alterations in adipose-tissue metabolism, structure, and phenotype to meet the needs of the organism. Limitations to this plasticity cause diminished or aberrant responses to physiologic cues and drive the progression of cardiometabolic disease along with other pathological consequences of obesity.

Conditioning the microenvironment for soft tissue regeneration in a cell free scaffold

The use of cell-free scaffolds for the regeneration of clinically relevant volumes of soft tissue has been challenged, particularly in the case of synthetic biomaterials, by the difficulty of reconciling the manufacturing and biological performance requirements. Here, we investigated in vivo the importance of biomechanical and biochemical cues for conditioning the 3D regenerative microenvironment towards soft tissue formation. In particular, we evaluated the adipogenesis changes related to 3D mechanical properties by creating a gradient of 3D microenvironments with different stiffnesses using 3D Poly(Urethane-Ester-ether) PUEt scaffolds. Our results showed a significant increase in adipose tissue proportions while decreasing the stiffness of the 3D mechanical microenvironment. This mechanical conditioning effect was also compared with biochemical manipulation by loading extracellular matrices (ECMs) with a PPAR-γ activating molecule. Notably, results showed mechanical and biochemical conditioning equivalency in promoting adipose tissue formation in the conditions tested, suggesting that adequate mechanical signaling could be sufficient to boost adipogenesis by influencing tissue remodeling. Overall, this work could open a new avenue in the design of synthetic 3D scaffolds for microenvironment conditioning towards the regeneration of large volumes of soft and adipose tissue, with practical and direct implications in reconstructive and cosmetic surgery.

Fattening chips: hypertrophy, feeding, and fasting of human white adipocytes in vitro

Adipose is a distributed organ that performs vital endocrine and energy homeostatic functions. Hypertrophy of white adipocytes is a primary mode of both adaptive and maladaptive weight gain in animals and predicts metabolic syndrome independent of obesity. Due to the failure of conventional culture to recapitulate adipocyte hypertrophy, technology for production of adult-size adipocytes would enable applications such as in vitro testing of weight loss therapeutics. To model adaptive adipocyte hypertrophy in vitro, we designed and built fat-on-a-chip using fiber networks inspired by extracellular matrix in adipose tissue. Fiber networks extended the lifespan of differentiated adipocytes, enabling growth to adult sizes. By micropatterning preadipocytes in a native cytoarchitecture and by adjusting cell-to-cell spacing, rates of hypertrophy were controlled independent of culture time or differentiation efficiency. In vitro hypertrophy followed a nonlinear, nonexponential growth model similar to human development and elicited transcriptomic changes that increased overall similarity with primary tissue. Cells on the chip responded to simulated meals and starvation, which potentiated some adipocyte endocrine and metabolic functions. To test the utility of the platform for therapeutic development, transcriptional network analysis was performed, and retinoic acid receptors were identified as candidate drug targets. Regulation by retinoid signaling was suggested further by pharmacological modulation, where activation accelerated and inhibition slowed hypertrophy. Altogether, this work presents technology for mature adipocyte engineering, addresses the regulation of cell growth, and informs broader applications for synthetic adipose in pharmaceutical development, regenerative medicine, and cellular agriculture.

Structural Elements of the Biomechanical System of Soft Tissue

In living organisms, forces are constantly generated and transmitted throughout tissue. Such forces are generated through interaction with the environment and as a result of the body’s endogenous movement. If these internally or externally originating forces exceed the ability of tissues to cope with the applied forces, (i.e. “tissue thresholds”), they will cause force-related tissue harm. However, biotensegrity systems act to prevent these forces from causing structural damage to cells and tissues. The mechanism and structure of soft tissues that enable them to maintain their integrity and prevent damage under constantly changing forces is still not fully understood. The current anatomical and physical knowledge is insufficient to assess and predict how, why, where, and when to expect force-related tissue harm.

When including the concept of tensegrity and the related principles of the hierarchical organisation of the elements of the subcellular tensional homeostatic structure into current biomechanical concepts, it increases our understanding of the events in force handling in relation to the onset of force-related tissue harm: Reducing incident forces in tissue to a level that is not harmful to the involved structures is achieved by dissipation, transduction and transferring the force in multiple dimensions. To enable this, the biomechanical systems must function in a continuous and consistent way from the cellular level to the entire body to prevent local peak forces from causing harm. In this article, we explore the biomechanical system with a focus on biotensegrity concepts across several organisational levels, describing in detail how it may function and reflecting on how this might be applied to patient management.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

Extra-cellular matrix rigidity may dictate the fate of injury outcome

After injury, while regeneration can be observed in hydra, planaria and some vertebrates, regeneration is rare in mammals and particularly in humans. In this paper, we investigate the mechanisms by which biological tissues recover after injury. We explore this question on adipose tissue, using the mathematical framework recently developed in Peurichard et al., J. Theoret. Biol. 429 (2017), pp. 61-81. Our assumption is that simple mechanical cues between the Extra-Cellular Matrix (ECM) and differentiated cells can explain adipose tissue morphogenesis and that regeneration requires after injury the same mechanisms. We validate this hypothesis by means of a two-dimensional Individual Based Model (IBM) of interacting adipocytes and ECM fiber elements. The model successfully generates regeneration or scar formation as functions of few key parameters, and seems to indicate that the fate of injury outcome could be mainly due to ECM rigidity.

Are Tumor Cell Lineages Solely Shaped by Mechanical Forces?

This paper investigates cell proliferation dynamics in small tumor cell aggregates using an individual-based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM model is based on the hypothesis that cells are incompressible objects that grow in size and divide once a threshold size is reached, and that newly born cell adhere to the existing cell cluster. We performed comparisons between the simulation model and experimental data by using several statistical indicators. The results suggest that the emergence of particular morphologies can be explained by simple mechanical interactions.