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Tensegrity and Complex Systems Biology

Living organisms are hierarchical structures that integrate their smallest constituent parts - individual molecules including DNA, proteins and lipids - across multiple levels of organization, from organelles, to cells, tissues, organs, and the organism. Thus, a major challenge in biology and medicine today is to understand how large numbers of different molecular parts interact and self-organize into a whole system that exhibits organic properties that cannot be explained solely in terms of their component properties. A major part of our current effort is therefore to understand how interactions among different molecular components map to system-wide behaviors in living cells and tissues. As cellular biochemistry does not proceed in solution, but rather on insoluble scaffolds and structures within the cytoplasm and nucleus of living cells, we are interested in both cellular hardware (structure and mechanical properties) and software (information processing capabilities), as well as how they interplay to c ontrol cell form and function.


Our approach to understanding cellular hardware is based on cellular tensegrity theory. Tensegrity is a building principle that was first described by the architect R. Buckminster Fuller and first visualized by the sculptor Kenneth Snelson. Fuller defines tensegrity systems as structures that stabilize their shape by continuous tension or “tensional integrity” rather than by continuous compression (e.g., as used in a stone arch). Tensegrity includes two broad structural classes - prestressed and geodesic - which would both fail to act like a single entity or to maintain their shape stability when mechanically stressed without continuous transmission of tensional forces. The former hold their joints in position as the result of a “prestress” (pre-existing tensile stress or isometric tension) within a structural network that is tensed because of a subset of elements that resist being compressed. The latter triangulate their structural members and orient them along geodesics (minimal paths) to geometrically constrain movement. Our bodies provide a familiar example of a prestressed tensegrity structure: our bones act like struts to resist the pull of tensile muscles, tendons and ligaments, and the shape stability (stiffness) of our bodies varies depending on the tone (prestress) in our muscles. Examples of geodesic tensegrity structures include Fuller’s geodesic domes, carbon-based buckminsterfullerenes (buckyballs), and tetrahedral space frames, which are of great interest in astronautics because they maintain their stability in the absence of gravity and, hence, without continuous compression.

The cellular tensegrity model proposes that the whole cell is a prestressed tensegrity structure, although geodesic structures are also found in the cell at smaller size scales (e.g. clathrin-coated vesicles, viral capsids). In the model, tensional forces are borne by cytoskeletal microfilaments and intermediate filaments, and these forces are balanced by interconnected structural elements that resist compression, most notably internal microtubule struts and ECM adhesions. However, individual filaments can have dual functions and hence bear either tension or compression in different structural contexts or at different size scales (e.g. contractile microfilaments generate tension, whereas actin microfilament bundles that are rigidified by cross-links bear compression in filopodia). The tensional prestress that stabilizes the whole cell is generated actively by the contractile actomyosin apparatus. Additional passive contributions to this prestress come from cell distension through adhesions to the ECM and other cells, osmotic forces acting on the cell membrane, and forces exerted by filament polymerization. Intermediate filaments that interconnect at many points along microtubules, microfilaments and the nuclear surface provide mechanical stiffness to the cell based on their material properties and on their ability to act as suspensory cables that interconnect and tensionally stiffen the entire cytoskeleton and nuclear lattice.

Tensegrity in a Cell

See how Tensegrity Works in a Cell on the Children's Hospital 'interactive website'. You can change the length or mechanical properties of the different support elements in cells (e.g., microfilaments, microtubules, matrix adhesions) and immediately see how they influence cell shape and cytoskeletal organization.

In addition, the internal cytoskeleton interconnects at the cell periphery with a highly elastic, geodesic cytoskeletal (actin-spectrin-ankyrin) network directly beneath the plasma membrane. The efficiency of mechanical coupling between this submembranous structural network and the internal cytoskeletal lattice depends on the type of molecular adhesion complex that forms on the cell surface. The entire integrated cytoskeleton is then permeated by a viscous cytosol and enclosed by a differentially permeable surface membrane.

Importantly, working with collaborators, such as Drs. Ning Wang (Dept. of Respiratory Biology, Harvard School of Public Health) and Dimitrije Stamenovic (Dept. of Biomedical Engineering, Boston U.), we have been able to demonstrate that living mammalian cells behave mechanically like tensegrity structures. Moreover, we have developed a theoretical formulation of the tensegrity model starting from first mechanical principles that has yielded accurate qualitative and quantitative predictions of many static and dynamic cell mechanical behaviors. We are currently trying to extend and strengthen this computational approach to explain systems-wide mechanical properties in mammalian cells, and to explore their hierarchical basis.

Complex Systems Biology

Systems Biology is a new field that focuses on the problem of how specialized behaviors emerge from collective interactions within complex molecular networks. The common approach is to work from the “bottom-up” by accumulating huge data sets with massively-parallel techniques or molecular analytical approaches, and then use computational modeling to “reverse engineer” network topology and behavior. Our work on tensegrity revealed that great insight could be gained by viewing the system as a whole and working from the “top-down”. Specifically, we found that when trying to understand collective mechanical behavior within supramolecular assemblies, higher-order architecture and physical forces must also be considered. Tensegrity also explains how hierarchical structures may be comprised of systems within systems (molecules within cells within tissues within organs) and yet still exhibit integrated mechanical behavior. In addition, it reveals how robust behaviors, such as persistence, mechanical adaptability, and shape stability, can be generated using “sloppy” parts (e.g., flexible molecular filaments), a key feature of both complex networks and living systems. Thus, tensegrity may represent the “hardware” behind living systems.

But what about the software? This leads us to the problem of how structural networks affect information processing networks at the level of the whole cell where tensegrity and the cytoskeleton seem to exert their effects on signal integration. Experiments show that while individual cells may receive multiple simultaneous inputs, they are able to rapidly integrate these signals so as to produce just one of a few possible outputs or phenotypes (e.g., growth, quiescence, differentiation, apoptosis). But studies on mechanoregulation raise a fundamental question: how can a gradual change in a physical parameter over a broad continuum, such as cell shape (distortion from round to spread), be translated into just a few, discrete cell fates?

Signal transduction has historically been viewed in terms of linear signaling pathways that lead from a specific input to a particular outcome. However, the information conveyed by the signal transduction machinery is often distributed among numerous pathways, and the same stimulus can generate different responses depending on the setting. Activation of a single signaling receptor can induce scores of genes, and the same signaling molecule may elicit entirely different effects (e.g., growth versus apoptosis) depending on the cell type, the activity state of other regulatory proteins, and the physical context in which it acts. For example, we have shown that the soluble angiogenic mitogen, FGF, produces growth in spread endothelial cells, differentiation (capillary tube formation) in partially retracted cells, and death in fully retracted cells. Thus, the concept of linear signaling pathways may be insufficient. Instead, the characteristic phenotypes that cells exhibit during development represent emergent and intrinsically robust behaviors that arise within a complex signaling network comprised of many interacting components.

The observation that gradual variations in a single control parameter (cell shape) can switch cells between distinct gene programs (cell fates) is reminiscent of a phase transition in physics. Gradual changes in temperature, for example, similarly produce abrupt macroscopic changes between qualitatively discrete stable states (e.g., liquid versus gas or solid). Dr. Sui Huang in our group is currently exploring the possibility that cell fates may be viewed as stable high-dimensional “attractor” states in gene activation state space. A natural consequence of this model, is that switches occur between these characteristic states upon changes in environmental conditions or in response to multiple perturbations. Such switches are manifest as abrupt phenotypic changes, and hence, may represent some kind of biological "phase transition”.

But what is the molecular basis for the existence of these discrete, stable phenotypic states and associated all-or-nothing transitions between them? Generic computer models of the dynamics of large systems of interacting genes studied by Stuart Kauffman for almost 30 years revealed that, for a subset of network architectures, a few stable states spontaneously emerge as a result of the constraints imposed by the regulatory interactions. Most network states are unstable and are "attracted" to the stable states, known as the "attractor" states. To visualize attractors in cell regulatory networks, think of a ball traveling on a complex landscape where stable cell states are represented by valleys (“basins of attraction”), separated by unstable transition regions or “mountainous” terrain. A ball (or cellular state) located at the nadir of one of these valleys (the attractors) will tend to remain there. Displacement to another part of the landscape will move the ball away from the valley, but with small perturbations it will generally “roll back down” to its own starting point in the same valley. Under the influence of a larger perturbation, however, the ball could traverse a mountainous peak in the landscape. At this point it is irrevocably committed to rolling down the other side of the hill until it reaches another attractor in a neighboring valley and hence, takes on a different stable phenotype.

In summary, the dynamics predicted by this "attractor landscape" metaphor is precisely reflected in the cell fate switching behavior that is observed in living cells within multicellular organisms. Unfortunately, the emphasis in the past decades on the characterization of individual pathway modules that were assumed to have specific functions has side-lined the notion that physiologically relevant cell behaviors are regulated at the level of cell-wide regulatory networks. With the advent of genomics and proteomics technologies which can provide specific information on signaling cascades, we can now move from generic network models to studying nominal molecular pathways in the context of complexity and network theories.

Thus, we view the cell’s molecular signaling machinery as a dynamic information processing network, and suggest that cell fates represent common end-programs or "attractors" that self-organize within these networks. In this manner, we are able to describe the collective behavior of the cell's signaling molecules and their relationship to cell fate switching without having to elucidate the functions of individual molecular components. Importantly, recent experimental work from our laboratory based on dynamic whole-genome profiling of cells during the course of a cell fate switch provides direct support for the attractor hypothesis. We have developed Gene Expression Dynamics Inspector (GEDI) software ( to facilitate analysis of dynamic network behavior, and to relate these changes to specific sets of molecules that contribute to changes in cellular phenotype.

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