Emergent complexity of the cytoskeleton: from single filaments to tissue

Abstract

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

Keywords: 87. Biological and medical physics; 87.16.-b Subcellular structure and processes; 87.16.Ln Cytoskeleton; 87.17.-d Cell processes; 87.17.Ee Growth and division; 87.17.Jj Cell locomotion, chemotaxis; 87.17.Rt Cell adhesion and cell mechanics; 87.18-h Biological complexity; 87.18.Ed Cell aggregation; 87.18.Fx Multicellular phenomena, biofilms; 87.18.Hf Spatiotemporal pattern formation in cellular populations; 87.19.xj Cancer; cell migration; cellular mechanics; emergent properties; multifunctionality; self-assembly; self-organization.

Figure. 1.

Two examples of complex organization based on cytoskeletal elements. (a) On the subcellular level, reconstituted systems of actin filaments with molecular myosin motors form networks connected by aggregated actin centers (asters). The image was taken using fluorescence microscopy and actin was labeled with a rhodamine dye. (b) On amulticellular level, neuron-like PC12 cells form extensive networks of MT-rich neurites. The image was taken using phase contrast microscopy and cells were cultured on a laminin-coated surface. Images were taken by David Smith (a) and Steve Pawlizak (b), image (a) also appeared in [148].

Figure. 2.

Schematic of a crawling cell on a 2D substrate to show the most prominent locations for the three types of cytoskeleton biopolymers. MTs are typically nucleated at the centrosome and span most parts of the cell. IFs are most commonly around the cell nucleus whereas actin filaments form dense networks close to the cell membrane. Particularly dense and dynamic actin networks are found at the leading edge of migrating cells (forming lamellipodia and filopodia).

Figure. 3.

Actin filaments are helical polar structures with a plus and a minus-end and are built from actin monomers. Various ways have been discovered how accessory proteins modify actin filament dynamics. In this sketch, representative accessory proteins are classified according to their function into the three categories “Nucleation regulation,” “Cross-linking,” or “Polymerization regulation”.

Figure. 4.

Different perspectives of functional modularity and hierarchical reductionism. While hierarchical reduction aims at dissecting a module's function according to different physical scales, the functional modularity perspective is focused on inter-module interactions regardless of their respective level of complexity.

Figure. 5.

Cellular automata as an example for emergent behavior. The frames show the state of the system for two algorithms at different times and originate from the same initial state (initial). Squares (cells) are activated (born) when they have b neighbors and survive as long as they have s neighbors. Frames A1–A3 were obtained with Conway's Game of Life algorithm (s = 2, 3; b = 3), frames B1–B4 follow the Coagulation algorithm (s = 2, 3, 5, 6, 7, 8; b = 3, 7, 8). Images were generated with MJcell v1.5. Cells are color coded along their age with yellow for novel cells and red for old cells.

Figure. 6.

Stiffness regimes of the three major cytoskeletal components and DNA illustrating that mechanical responses highly depend on the filaments architecture. Electron microscopy images were taken from [-48] with permission from Macmillan Publishers Ltd (a), US National Academy of Sciences (b), John Wiley & Sons (c), and the American Society for Biochemistry and Molecular Biology (d).

Figure. 7.

Assembly and dynamic instability of MTs. (a) In a GTP bound state, tubulin heterodimers polymerize into an oriented sheet of usually 13 PFs which eventually closes and forms a hollow tube. Upon polymerization, GTP hydrolysis occurs. (b) As soon as the free GTP-dimer concentration drops below a critical concentration, GDP-decorated dimers disassemble and the MT shrinks (catastrophe). This process can only be reversed by an increase of GTP-tubulin providing a capping layer (rescue) (Reprint from Conde et al. [63] with permission from Macmillan Publishers Ltd: Nature Reviews Neuroscience 10, 241, ©2009).

Figure. 8.

The tube model proposes that a polymer's movement within a semi-dilute solution is confined by other filaments. These confinements restrict the polymer's movement into a tube-like region.

Figure. 9.

Tilted cuvettes filled with an actin gel allow to observe the gel's flow behavior. Left side: ATP depleted conditions lead to non-motile myosin motors that essentially function as cross-linkers. Right side: in the presence of ATP, the motors are active and increase the filament transport making the gel significantly more fluid-like [97].

Figure. 10.

State diagram showing variations of elasticity due to changes of the actin concentration or changes of the cross-linker density (c_s represents the concentration of the cross-linker scruin). By varying these factors, the elastic modulus can be varied by more than three orders of magnitude. The elasticity can be distinguished in two different regimes: a linear regime arises for small values of R and c_A up to large strains without any stiffening effects (blue plane). A nonlinear regime arises for large values of R and c_A even under small deformations (red plane). The elasticity increases under increasing strain. Reprint from Gardel et al. [14] with permission from AAAS.

Figure. 11.

Actin stress fibers in living cells (left side: a fibroblast with labeled myosin (green) and actin (red), right side: a fibroblast with labeled actin) fulfill important tasks like mechanical stabilization. The development of cellular stress fibers is preferred by 2D cell cultures. Images were taken by Thomas Fuhs and Daniel Koch.

Figure. 12.

Actin bundles formed by α-actinin are time-dependent mechanically stabilized in their deformed position due to rearrangements of the dynamic cross-linker within the bundled structure (scale bar 5 μm). For a deformation time of 5 s, the bundle relaxes to its original position since the time is not sufficient for considerable rearrangements while for a 1000 s deformation, the bundle is observably stabilized in the deformed state [128].

Figure. 13.

Depending on the filament density different dynamic patterns emerge when actin filaments move over a myosin-coated surface. Few characteristic examples are shown here: swirl (a), swarm (b), and waves (c). Figure was adapted from [5] (with permission from Volker Schaller and Macmillan Publishers Ltd: Nature Reviews Neuroscience 467, ©2010).

Figure. 14.

The interplay between MTs and respective motor proteins can be modeled on different scales. Microscopic models (left panel) allow tracing back the network level behavior to molecular interactions but do not reach the level of abstraction needed for a fully analytical description. Macroscopic models (right panel) are much more phenomenological in their origin but they are able to deliver analytical descriptions. A certain kind of compromise is presented by mesoscopic models (center panel) that start from the molecular level but use strong coarse-graining, (d) was adapted from [161], (e) was taken from [159] (with permission from Igor Aronson), (f) was inspired by [157].

Figure. 15.

Counterion-induced formation of aster-based actin bundle networks in confined droplets. Left side: snapshots showing the transition from an actin filament solution (at dt = 0 s) to a stable actin bundle network following a slight increase in counterions above their critical concentration for inducing filament aggregation. Right side: aster-based bundle networks obtained by counterion-condensation appear highly regular regarding the average aster distances. Images were taken using confocal microscopy (left side) and epi-fluorescence microscopy (right side). Figure was adapted from [144].

Figure. 16.

Sketch presenting the five fundamental regulative principles we focus on. For each principle, one or more generic examples are illustrated. Figure was adapted from [166].

Figure. 17.

Basic reaction kinetics can already enable the formation of a large variety of two or more overlaying temporal gradients. In conjunction with polar structures such as MT or actin filaments, these gradients translate into spatial gradients. Figure was taken from [166].

Figure. 18.

Depending on the system of interest, the involved levels of complexity are intertwined differently. (a) The properties of individual biopolymer filaments can be explained by its respective monomer level and reconstituted biopolymer solutions forming entangled networks are understood from a single filament level (b). As soon as elements start to bridge more levels of complexity, the situation quickly becomes more complicated. (c) Cross-linked actin networks, for instance, are more difficult to model than entangled solutions. Closed feedback loops across multiple levels (d), such as transiently cross-linked actin networks, inhibit further coarse-graining and hence make it a demanding task for theoretical modeling.

Figure. 19.

Fluorescently labeled cytoskeleton of three different types of adhering cells with actin marked in red and MTs marked in green. (a) Fish keratocytes, (b) fibroblast, and (c) neuronal growth cone. These three cell types illustrate the large diversity of cytoskeletal architectures which is likely to result in very different mechanical characteristics. The cytoskeleton architecture of the respective cells is further illustrated below the fluorescence images. Similar figure already appeared in [372].

Figure 20.

Schematic principle of the optical stretcher. (a) Two opposing laser fibers emit a non-focused Gaussian beam acting as an optical trap for dielectric objects (cells) with refractive index higher than the surrounding medium. The cell is centered between the laser fibers. (b) At increased laser power, the cell is deformed along the laser axis due to mechanical stress induced at its surface. (c) The stress at the cell surface is caused by a momentum transfer occurring when light with a momentum p₀ is transmitted from a medium with refractive index n₀ into the cell medium with refractive index n₁ > n₀, where it has a momentum p₁ > p₀. Momentum conservation demands that a momentum p_x1 perpendicular away from the surface acts on it. At exit, another momentum transfer p_x2 occurs, again directed perpendicular away from the surface.

Figure 21.

Characteristic measurement curves for four selected rheological techniques as an example for active probing methods on suspended (a), adherent (b, c) and for a passive method on adherent cells (d). (a) Example graph of a step-stress compliance experiment with the optical stretcher. Cells are held at trap power for 1 s, then stretched with 1.2 W for 2 s and subsequently monitored at trap power for another 2 s. Shown here is the relative deformation of cells along the laser axis over time. This graph is an average of 167 cells. (b) Shear moduli extracted from magnetic twisting rheology plotted versus twisting frequency [243]. (c) Frequency dependence of the storage modulus G′ (filled symbols) and the loss modulus G″ (open symbols) measured on A549 cells (N = 12) at different oscillation frequencies using an SFM [238]. (d) Mean square displacement of a single particle (solid symbols) and two particles (open symbols). With the two particles method superdiffusive behavior is found [256]. Data were reproduced with permission from Ben Fabry (b), Jordi Alcaraz (c), and Tom Lubensky (d).

Figure. 22.

Comparison of different archetypes of response to applied step stress. Viscoelastic behavior is characterized by combining both elastic and viscous properties. The simple phenomenological descriptions by linear viscoelastic models (here: Voigt element) as well as the soft glassy rheology model (power-law) show viscoelastic behavior.

Figure. 23.

Different phenomenological models commonly used to describe cell mechanics. (a) Voigt element as one possible representation of mechanical equivalent circuits that combine springs and dashpots in various arrangements. (b) The tensegrity model describes the cell as a pre-stressed network consisting of cables and struts. (c) The soft glassy rheology models assume a complex energy landscape with wells of different depth ΔE such that spontaneous transitions form one to another well have a very low probability.

Figure. 24.

Fluorescence images of cell division phases: interphase, prophase, metaphase, late anaphase, and cytokinesis (EMBL, Heidelberg).

Figure 25.

(a) Prophase. Duplicated centrosomes migrate around the nucleus. (Centrosomes, consisting of a pair of previously replicated centrioles surrounded by pericentriolar material, nucleate MT assembly and organize spindle poles.) (b) Prometaphase. The nuclear envelope breaks down allowing MTs to move chromosomes to the equator (e) in a process termed congression. (c) Metaphase. Sister chromatids (double arrowheads) face opposite poles (p). MTs are oriented with their plus-ends distal to the poles, and are organized into four sets, namely: astral MTs linking spindle poles to the cell cortex; chromosomal MTs linking chromosome arms to poles; kMTs linking poles to kinetochores; and ipMTs linking the two poles. (d) Anaphase A. Chromatids are moved to opposite poles (segregation). (e) Anaphase B. Pole–pole spacing increases. During late anaphase, the division plane is determined by a mechanism involving spindle–cortex interactions and the cleavage furrow containing a contractile ring assembles from actomyosin II and begins to contract. (f) Telophase/cell–cell scission. Nuclear envelopes reassemble around decondensing segregated sisters. The contractile ring contracts (furrow ingression) developing a barrier between the daughter cells and constricting the spindle mid-zone (the array of ipMTs lying between separated chromatids) into a structure called midbody (the remnant of the mid-zone). During abscission, the furrow “seals” and separates the daughter cells, apparently involving vesicle transport/exocytosis. Reprint from Scholey et al. [294] with permission from Macmillan Publishers Ltd: Nature 422, ©2003.

Figure. 26.

(a) Anterior and (b) posterior optically induced centrosome disintegration. MTs asters were visualized by indirect immune-fluorescence to tubulin (red) in the left panels and γ-tubulin in the right panels. DNA is stained blue. Arrows point to aster fragments, arrowheads to unirradiated centrosomes. Reprint from Grill et al. [315] with permission from AAAS.

Figure. 27.

(left) Centrosomal and cytoplasmic Aurora B complexes are transported to the midzone along midzone MTs and astral MTs, respectively (middle). There, Aurora B is involved in the Rho A flux, a constant activation and deactivation of Rho A leading to an accumulation of Rho A at the equatorial plane. The effectors of Rho A – formins and Rho kinase are key players in the formation of the contractile actin ring (right).

Figure. 28.

Scheme of contractile ring in cytokinesis and contractile units postulated by Pollard. Reprint from [330] with permission from Elsevier.

Figure. 29.

Illustration of the “standard model” of crawling cell migration on flat substrates [6,370]. It commonly is reduced to three processes taking place in parallel: (1) A comparatively thin actin gel protrusion extends the leading edge and adheres to the substrate. (2) The rear end actively retracts and detaches from the substrate. (3) The cell body is pulled forward.

Figure. 30.

Sketch of a crawling fibroblast-like cell. The local protrusion rate (v_protrusion) of the leading edge is the vectorial sum of retrograde flow (v_retro) and gel growth velocity (v_growth).

Figure. 31.

Actin network growth from a polystyrene bead functionalized with an Arp2/3 activator (VCA). Functionalized beads were immersed in a solution that besides actin and Arp2/3 contained few other regulative proteins (here: gelsolin, cofilin, and profilin). The bead size was about 2 μm and images were taken with phase contrast (left) and fluorescence microscopy (right). Actin was labeled with a rhodamine dye. Images were taken by Björn Stuhrmann.

Figure. 32.

Model picture of the self-organizing actin network within lamellipodia. ATP-hydrolysis acts as a timer mechanism resulting in distinguishable zones dominated by different actin accessory proteins. Branching and hence nucleation of new filaments is driven by Arp2/3 at the front while in the middle zone debranching and depolymerization dominate. At the rear of the network filaments, start to be hindered from fast depolymerization by tropomyosin binding. Illustration was taken from [57] with permission of Marie-France Carlier.

Figure. 33.

Comparison of experimental data from migrating keratocytes (taken from [387] with theoretical result obtained from computer simulation (taken from [180]) and mathematical modeling (taken from [179]). The depicted curves show concentration profiles of F-actin as well as cofilin and tropomyosin along the lamellipodial network starting at the leading edge (x = 0). For both F-actin and cofilin, theory and experiments are in good agreement.

Figure. 34.

Sketch of a crawling keratocyte. The front region is characterized by fast actin gel growth, whereas the part further back disassembles and contracts. The flanks of the cell display particularly strong contractions that to a large extent depend on myosin motor activity.

Figure. 35.

Different cell types do not only differ in morphology and cytoskeletal architecture (illustrated on the left side) but further display distinct migration characteristics. Kymographs of the leading edge of three different cell types are shown on the right (b, d, f) with the signature of persistent forward motion in the case of keratocytes (f) and significant edge fluctuations for neuronal growth cones (b) and fibroblasts (d). Image was adapted from [372].

Figure. 36.

The movements of growth cone filopodia on compliant substrates (a and b) observed by Chan and Odde [444] can be explained by a motor-clutch model (c). Images were taken from Chan and Odde [444] with permission from AAAS.

Figure. 37.

Emerging neurite of an NG-108 15 neuronal cell with overlapping growth cones. Actin networks and bundles (red) form the lamellipodium and filopodia of the cone, respectively. MTs (green) are bundled in the neurite shaft and explore the periphery of the growth cone, most likely to target adhesion sites. Confocal laser scanning image, scale bar: 10 μm.

Figure. 38.

Schematic illustrating the interplay of the actin cytoskeleton with focal adhesions. A feedback loop including trans-membrane receptors that are connected via a rather complex adhesion module to intracellular signaling pathways relates ECM properties (chemistry, mechanics) to cytoskeleton regulation. Receptor modules (e.g. integrins) transmit signals to protein complexes responsible for signaling or actin dynamics. In turn the cytoskeleton influences the maturation and configuration of focal adhesion complexes. Image inspired by Geiger et al. [440].

Figure 39.

The ability for coarse-graining varies strongly among the different phenomena studied on the cellular level. (a) So far, the mechanical behavior of cells on shorter timescales is mostly described by phenomenological models. A decent microscopic understanding might already result from models originating from the underlying network level. By comparing to the subcellular level, however, one has to expect that compound and transient networks will be most relevant demanding some adaptation of even lower levels. (b) Cell division involves the interplay of numerous different proteins and includes several internal feedback loops which makes it less accessible to coarse-graining. (c + d) Various model approaches aim at further understanding cell motility. Lamellipodial motion is particularly accessible to coarse-graining and hence attracted most attention from physicists (c). Whereas some models start from the molecular level others further coarse-grain the problem to the network, i.e. the actin gel level. (d) As soon as filopodia or MTs significantly influence the cellular migration, the filament can no longer be ignored.

Figure. 40.

(a) Grafting experiments showed the effect of the homeostatic flow and the high level of versatility of Hydra tissues [496]. (b) Image of H. vulgaris depicting its most prominent parts. Hydras morphology is simple: a gastric column ends in a head (hypostome) surrounded by tentacles and a basal disk at the other side. (c) Hydra cells can be cut into pieces or even be entirely disassembled and re-aggregated to form a new organism. Within this process, first a hollow sphere is formed. This sphere passes through several phases of pulsations before a new small hydra finally emerges. Figure (a) was adapted from [496], figure (c) was inspired by [497].

Figure. 41.

Systematic grafting experiments revealed the importance of the provenience and the destination position of the tissue fragment. Head cells are supposed to segregate head inhibitors. Inserting a head fragment close to a head inhibits new head formation (a). Only at distal inserting positions a head is formed since the inhibitor level is low there (b). Grafts of distal origins also show only weak head formation even if inserted at a distal position as the activator level is small (a). (c) The activator activates head formation but at the same time raises the inhibitor level while the inhibitor in turn suppresses the activator and consequently the head formation [505,506]. Figures (a) + (b) were adapted from Müller [505] with permission from Elsevier.

Figure. 42.

Different types of cell–cell junctions allow different means of intracellular communication. Gap junctions (a) allow cells in a tissue to directly exchange signaling molecules and ions. Other junction types such as adherens junctions (b) or desmosome junctions (c) establish direct links between the cytoskeletal networks of two neighboring cells. While adherens junctions link to actin filaments, the desmosome connects IFs (keratins).

Figure. 43.

Foty and Steinberg [542] showed that cell–cell adhesion is an essential factor for cell sorting in re-aggregates. The surface tension of the cluster appears to be a linear function of the Cadherin expression level. Figures were adapted from Foty and Steinberg [542] with permission from Elsevier.

Figure. 44.

Zebrafish embryogenesis starts with a pair of cells: one animal and one vegetal (yolk) cell. The animal cell divides synchronously without much growth and follows a definite protocol for the first divisions. Left: top view of the first divisions. Right: side view of selected states: A 2-cell state, B 4-cell state, C 8-cell state, until F, where the synchronous division gets disordered and cells start behaving individually. As a consequence, the cell cluster becomes a droplet behaving similar to a fluid. Figures were taken from Kimmel et al. [490] with permission from John Wiley & Sons.

Figure. 45.

The animal cell droplet of Zebrafish further spreads over the yolk cell similar to a water droplet wetting a hydrophilic surface. Eventually, the cells show global organization as they break symmetry during epiboly (last two pictures). A complex flow scenario results in a fish embryo wrapped band-like around the yolk cell. Image was adapted from Keller et al. [548] with permission from Elsevier.

Figure 46.

Tissue remodeling requires reversible (both directions of arrows) externally triggered deformation and irreversible (only one direction of arrows) relocalization of the cells. The colored arrows indicate the cell flow at the center of the layer (red = pushing, blue = pulling). Transitions from one state to another can be reversible when a return to the original cell order is possible (e.g. by removing the external cue. Irreversible transitions, in contrast, imply a change in intrinsic cell order (a return to the original overall shape is still possible, though). Several modes are depicted here: x-contraction and y-extension (b→c) leads to tissue bending (c) and after relaxation to tissue elongation called epiboly (g) which is often combined with tissue spreading and thinning. x- and y-contraction leads to evagination (e) or may end up in tissue thickening after rearranging the cells (a) based on transversal intercalation. The inverse process leads to tissue thinning and again to a flat state (d) similar to (b) which happens often in conjunction with epiboly. Bending of tissues is always linked to an asymmetrical cellular deformation. (e, f) A deformation can be the cause or the result of the tissue bending depending if the process is triggered from the surrounding tissue or actively driven by local cells implying their cytoskeleton force generation machinery. Further transformations are possible and thinning and rearrangements can, for instance, be combined to transform a sheet to a tube (see, e.g. [550]).

Figure 47.

The canonical (yellow background) and non-canonical (red background) Wnt/β-catenin signaling pathways are related to mechanical elements and actions responsible for cell polarization, migration and tissue organization. Blue background stands for membrane bound receptors. β-catenin is a major player and is permanently created and degraded by the APC complex. It is important for linking the cytoskeleton to the cell membrane and to neighboring cells but also as a gene transcription factor. If it is over-expressed or if APC is not working properly developmental genes are activated and the cell is less adhesive and the epithelial-mesenchymal transition is induced with cell migration and proliferation. These are features of malignant tumors. The Wnt pathway is further directly linked to pathways controlling the activity and structure of the cytoskeleton: Rac, Cdc42, and Rho. It was recently discovered that IPGAP1 has a major regulatory function for actin and MT cytoskeleton. This is also the case for the APC-Asef complex. The illustration combines different sources as indicated by numbers on a white background. 1: [560], 2: [561], 3:[559], 4: [562,563], 5: [564].

Figure 48.

During the regeneration of H. vulgaris, a cellular cluster first establishes a spherical arrangement consisting of a hollow cellular double layer. This spheroid's regeneration can be described by three phases with saw tooth like oscillations – the radius and the second, third Fourier modes are depicted in (a). The transition from phase II to III shows a transition to non-uniform tissue elasticity as the pressurized cell ball is stronger deformed (red line) as the relaxed one (blue line). (b) Orientation of the hydra head with respect to the direction of a temperature gradient across the cell aggregate. During the transition from phase I to II, the axis is locked. Small temperature gradients applied from the beginning are sufficient to significantly affect the orientation of the head (yellow squares, red triangles) which is a signature of the system's critical state. Later, application of a temperature gradient does no longer result in an overall reorientation (blue circles). Images were adapted from [584] (a) and [497] (b) (with permission from Albrecht Ott).

Figure. 49.

Cell biomechanics could be very useful for cancer diagnosis, e.g. using the optical stretcher, illustrated in (A). Average deformation and relaxation curves of benign cells and breast tumor cells from early and late stage tumors (G1 and G3) are shown in (B). With increasing tumor aggressiveness, the cells become more compliant. Despite the higher deformability, i.e. weaker elastic strength, late stage tumor cells show a stronger relaxation behavior. This relaxation behavior of softer tumor cells can only be explained by increased cell contractility since the passive viscoelastic properties only permit a weaker relaxation behavior. Illustration in (A) by courtesy of Steve Pawlizak, data in (B) kindly provided by Franziska Wetzel.

Figure 50.

Tissue organization includes a tremendous variety of different phenomena. Some show a very high complexity with feedback-loops ranging from the molecular scale up to the multicellular level (a). This includes examples involving complex signaling cascades or gene regulation. Gene regulation, for instance, is able to alter cytoskeletal components, which will affect its network architecture and thereby cellular properties and behavior. At the same time, the resulting interactions on a cellular level or above can involve signaling cascades down to the molecular or genetic level hence forming a multi-scale feedback-loop. In such cases, coarse-graining becomes a very difficult endeavor. Other examples, however, demonstrate nicely that very prominent phenomena on the tissue level can even be described on the cellular scale such as cell sorting in cellular aggregates [542], collective cell migration [536] or epithelial tissue dynamics [554,614].

Figure. 51.

Possible level hierarchy from molecules to consciousness. A detailed picture of the levels’ connections is likely to result in a highly intertwined structure.

Figure. 52.

A given system comprised of several levels of complexity can only be reduced further, i.e. split into smaller subsystems if no loss of lower level details occurs. (a) For strictly hierarchical order, further reduction is possible without apparent loss of causal understanding. If interactions bridge one or more levels, the reduction becomes difficult but remains possible (b) as long as no inherent multi-level feedbacks occur (c). The bridging interactions in (b) must be included in form of suitable modifications of the bridged level. Here, filaments* is a modified form of filaments that, for instance, considers “sticky” filaments to account for molecular cross-linkers.