Mechanics and dynamics of reconstituted cytoskeletal systems

Abstract

The intracellular cytoskeleton is an active dynamic network of filaments and associated binding proteins that control key cellular properties, such as cell shape and mechanics. Due to the inherent complexity of the cell, reconstituted model systems have been successfully employed to gain an understanding of the fundamental physics governing cytoskeletal processes. Here, we review recent advances and key aspects of these reconstituted systems. We focus on the importance of assembly kinetics and dynamic arrest in determining network mechanics, and highlight novel emergent behavior occurring through interactions between cytoskeletal components in more complex networks incorporating multiple biopolymers and molecular motors.

Biological cells are dynamic mechanical objects able to crawl, change shape, divide, and remodel. They are robust enough to withstand substantial external strains, but unlike passive soft materials, they are able to actively tune their mechanics in response to their surrounding environment. These unique active material properties are essential for cellular life, and are owed in large part to the cytoskeleton, the active and richly heterogeneous network within the cellular interior. The three primary cytoskeletal determinants of intracellular mechanics in metazoan cells are filamentous actin (F-actin), microtubules (MTs), and intermediate filaments (IFs), each with their own distinct polymerization dynamics and mechanical properties [1–5]. Together, these polymers form a diverse set of structures in the cell, the mechanics of which are determined both by the properties of the filaments themselves and by the wealth of associated filament binding proteins. However, identifying specific physical properties or interactions between individual mechanical components is difficult, and underlying details or mechanisms are often obfuscated due to the inherent complexity of the cell. Reconstituted in vitro biopolymer networks serve as experimental systems in which the complexity can be controlled by adding only a subset of cellular proteins [6]. This bottom-up approach to cytoskeletal mechanics makes it possible to dissect details of protein interactions and filament mechanics, and thus yields insights complementary to whole cell studies. Understanding the physics and mechanics of these active soft materials using model systems is the focus of this review.

The simplest reconstituted system consists of a single species of cytoskeletal filament protein. Over the past two decades, the mechanics of single-species biopolymer networks have been extensively studied [7–14], serving as a basis for our current understanding of in vitro network mechanics. The most heavily studied system is the crosslinked actin network (for a review specifically of crosslinked actin networks, see Ref. [15]). A key feature of sufficiently crosslinked semiflexible biopolymer networks is their ability to stiffen dramatically under applied strain, in some cases increasing their network elasticity by several orders of magnitude [9]. Explaining this strain stiffening and relating the network mechanics to biochemical properties, such as polymer concentration and crosslinking density, has posed a challenge due to the semiflexible nature of F-actin and intermediate filaments. In the affine network model, semiflexible polymers are treated as thermal, entropic springs [12, 16]. As individual filaments are stretched, the number of available entropic configurations of each filament is reduced, and the filament elasticity increases non-linearly. Assuming an affine network strain, strain stiffening of the bulk network is a product of the stretching of individual filaments. This model captures the experimentally observed scaling relations of elasticity with polymer concentration and the network strain stiffening in crosslinked semiflexible biopolymer networks [10, 11], and was more recently used to compare the single filament stiffness to the network elasticity using intermediate filaments [17] and F-actin networks with varying filament flexibility [18]. However, discrete network models have yielded quantitatively similar strain stiffening behavior, and have highlighted non-affine filament bending and network rearrangements as alternative origins of network strain stiffening [19, 20]. Thus, while network shear can induce the stretching of individual filaments, it also leads to network reorganization, as shown in Figure 1. These recent efforts focusing on disordered, non-affine networks provide an alternative, non-thermal explanation for the strain stiffening behavior [21, 22], and it is becoming increasingly clear that the mechanics of semiflexible biopolymer networks depend not only on the physical properties of the filaments themselves, but also on the exact network morphology [23, 24].

Figure 1.

Crosslinked actin networks subjected to external shear typically exhibit strain stiffening behavior. This is attributed to the rearrangement of filaments, as shown in panel A, which can involve both the stretching of individual network elements, as well as non-affine changes to network architecture. Confocal imaging of F-actin networks crosslinked with α-actinin before and after a 56% strain reveal structural reorganization within the sample under shear, as shown in panel B (reproduced from Ref. [25]). Scale bar is 50 µm.

Furthermore, the exact morphology of the final network, and therefore the network mechanics, is highly dependent on the kinetics of network formation and deformation history [25]. This becomes particularly apparent in crosslinked networks, as network crosslinking often occurs rapidly before the system reaches thermal equilibrium. Initially, filaments are polymerized and form bundles, but further evolution of the network is gradually halted through dynamic arrest, trapping the network in a metastable state not in thermal equilibrium, as illustrated in Figure 2. Such behavior is observed for the intermediate filament protein keratin, an essential structural component of epithelial tissue, which forms filaments by the compaction and annealing of self-assembled unit-length filaments [26]. Even in the absence of any other cellular components or regulating factors, simply tuning the assembly kinetics to favor elongation or bundling allows keratin to polymerize into a range of different structures [27]. The dynamics of network formation can also be altered by filament binding partners which change the rates of bundle formation, changing the relative rates of bundling and elongation and driving the network into different final structural states [28]. In networks of actin and the actin-bundling protein α-actinin, actin filament elongation and α-actinin-induced bundling occur concomitantly but are not independent of each other, and as filaments form and are crosslinked the dynamics of the network are dampened and inhibits further bundling. Thus, the final network state is highly dependent on the competing kinetics of filament elongation and α-actinin-induced bundling [29], resulting in a range of heterogeneous network structures [30]. Importantly, these networks do not reach thermal equilibrium as their evolution is halted by crosslinking, and a rich phase space of network morphologies is accessible across biochemically identical samples simply by altering the assembly kinetics. As a result, internal stress in the networks accumulates locally during network formation [31] and is not able to be released without crosslinker dissociation [32]. Thus, biopolymers assembled and crosslinked in vitro polymerize into diverse structures far from thermal equilibrium even in the absence of active components such as molecular motors.

Figure 2.

Actin bundles form rapidly at concentrations typically used in reconstituted actin networks. Here, 12 µM actin is mixed with 1.2 µM crosslinker and immediately imaged by fluorescence confocal microscopy. Initially, actin bundles grow and change orientation as filaments polymerize and are crosslinked. The subsequent network formation is a dynamic process that gradually arrests, as crosslinking prevents the relaxation of internal stresses that develop during polymerization. Each frame is 100 µm.

The strong dependence of the final network structure on network formation kinetics leads to unexpected behavior in in vitro reconstituted networks consisting of multiple species of biopolymers. Emergent behavior in such composite biopolymer networks is not simply attributable to the properties of the individual polymers, but is strongly dependent on interactions between polymer species with very different mechanical and dynamical characteristics. For example, the addition of microtubules to sparsely crosslinked F-actin networks has been found to promote strain stiffening, as the stiff microtubules suppresses strain inhomogeneities in the network [33]. Passive microrheological studies of F-actin-microtubule composite networks showed that microtubules unexpectedly confer an increased local compressibility to F-actin networks [34]. The presence of a second polymer species in a semiflexible biopolymer network can also influence the final dynamically arrested network state. For example, since the IF protein vimentin forms networks significantly faster than actin under similar buffer conditions, rapidly forming IFs can sterically interfere with actin filaments before these have time to fully crosslink. Counterintuitively, the additional vimentin polymer can therefore result in a weaker overall composite network, as steric interactions lead to a loss of F-actin crosslinking, as shown schematically in Figure 3 [35]. Notably, these emergent behaviors occur without direct biological or chemical crosslinkers between the different polymer species, supporting observations in cells suggesting that steric interactions between polymers greatly affect their mechanical behavior. For example, microtubules in cells can withstand large compressive loads with reduced buckling due to the lateral reinforcement of the surrounding elastic cytoskeleton [36]. Beyond such steric polymer interactions, cytoskeletal crosstalk in cells between the different polymer species also involves direct crosslinking by cytolinkers [37–41], an aspect not explored in reconstituted biopolymer systems. Overall, there are many unexplored aspects of composite biopolymer network mechanics and dynamics, and in vitro reconstituted systems offer a promising avenue for further investigating the physical interplays between cytoskeletal elements.

Figure 3.

Composite networks of crosslinked actin and vimentin IF demonstrate complicated emergent behavior. In some cases, the presence of vimentin can impede the actin crosslinking, thereby weakening the overall network structure. The addition of vimentin restricts F-actin fluctuations before dynamic arrest, as indicated by the shaded regions. When crosslinkers are abundant, potential crosslinking sites remain within reach, as illustrated in panels A and B. However, when crosslinkers are sparse, the additional constraint can lead to a loss of F-actin crosslinking, as shown in panels C and D. Figure is reproduced from Ref. [35].

In addition to the passive mechanical properties of the filaments themselves, the cytoskeleton is rich in active processes, most notably filament polymerization and depolymerization, and motor activity. This activity makes the cytoskeleton greatly different from passive mechanical systems. First of all, the constant activity ensures that the cellular interior is always far from thermal equilibrium, and equilibrium thermodynamics principles do not apply to the cytoskeleton [42]. Secondly, the activity of F-actin- and microtubule-associated motors impact cytoskeletal mechanics by generating internal forces in the networks. Molecular motors are known to stir the cytoplasm and enhance intracellular dynamics [43], amplifying the motion of intracellular organelles even when these are not undergoing active transport. While this enhanced motion appears diffusive due to the stochastic nature of the motor activity in the network, the energy in the network far exceeds thermal energy, and can be traced back to motor activity by combining active and passive microrheology techniques to extract a force spectrum of the cellular interior [44]. Motors also add substantial tension to the stress fibers of the cell. Intracellular ablation using laser nano-scissors has revealed that stress fibers behave as viscoelastic tension-bearing cables tensed mostly by myosin motors [45]. The internal tension of the fibers not only changes the basic mechanical properties of the filaments [12, 46], but is also crucial in maintaining the mechanical shape and integrity of the cell [47]. Furthermore, microfilament tension alters the affinities of binding proteins [48, 49], and can directly serve as a mechanism of mechanotransduction by exposing previously inaccessible cryptic binding sites [50].

Because of the dominant role of active processes in the cell, the incorporation of motors into reconstituted in vitro systems has received considerable attention over the past decade. Two-dimensional reconstituted systems of myosin motors and F-actin on a lipid membrane have been used to mimic the actin cortex of the cell [51], and showed that motor activity induces both tension and compression in actin, which can cause both contraction and induce filament buckling and breaking. In three-dimensional reconstituted networks of F-actin, motor activity causes a temporal coarsening and development of a variety of mesoscopic structures [52–54], and enhances the non-equilibrium fluctuations in the network [55], reminiscent of the motor-driven enhanced motion seen in cells [44]. Clustered in vitro acto-myosin structures can exhibit dynamic reorganization, and are able to either fuse into larger structures or rupture into smaller ones [56, 57]; however, this dynamic behavior is dependent on the crosslinking and motor concentrations in the network. On the one hand, if the actin is highly crosslinked by a separate F-actin crosslinking protein or by inactive myosin at low ATP concentrations, myosin motor activity can serve to generate internal tension in the network. This internal tension in turn stiffens the network, analogous to strain stiffening in passive networks under an externally applied strain [9, 58], and suggests that internal network tension generated by motor activity can serve as a mechanism for regulating network elasticity, as shown in Figure 4. On the other hand, at low crosslinking densities, the lack of network connectivity causes the motors to fluidize the network, rather than contract it into clusters. Robust network contraction is thus dependent on the interplay between crosslinking to maintain network connectivity, and motorgenerated forces which tend to both tense and fluidize the network [57, 59]. The right concentration range of crosslinkers is required to ensure that the network is fully connected, yet not so dynamically arrested that motor forces are insufficient to induce contraction [60]. In this regime, in which the network is balanced between full fluidity and static crosslinking, motor activity allows for a rich dynamic behavior and constant remodeling of heterogeneous structures around a steady-state equilibrium of cluster sizes [56, 57]. The degree of crosslinking and motor activity also dictates whether contraction occurs globally or locally within the network, and since many crosslinkers respond to tension, the motor activity can dynamically affect the connectivity of the network, leading to different mesoscopic structures [61].

Figure 4.

Acto-myosin networks stiffen due to internally generated tension, reminiscent of the stiffening observed in networks under external shear, as discussed in Ref. [58]. The network tension is generated by myosin, as shown schematically in panel A, and can increase the network elasticity by several orders of magnitude as compared to an unstressed F-actin network. Myosin activity in an actin/α-actinin network can also cause both network contraction and local structural rearrangements, as shown by confocal fluorescence in panels B and C (reproduced from Ref. [59]). Scale bar is 2 µm.

The bottom-up cytoskeletal model systems discussed here contain at most a few cytoskeletal elements, such as one or two biopolymer species, and a filament crosslinking protein. However, even with a relatively limited number of components, these soft biological materials display a wealth of unique behavior very different from more traditional, well-studied solids, and in many cases begin to capture qualitatively similar mechanics to that of the cytoskeleton. While the mechanics of the individual cytoskeletal polymers and single-species networks have been quite well studied, composite networks have shown additional surprising emergent properties, and the addition of motors to reconstituted biopolymer systems further introduces novel mechanics and dynamics, the details of which are still not fully explored. A hallmark of these active soft matter systems, and of living systems in general, is their highly non-equilibrium nature. While cytoskeletal polymers undergo turnover on the order of tens of seconds in cellular regions such as the leading edge of motile cells [62], the gradual onset of dynamic arrest occurs on a similar time scale as illustrated in Figure 2, and regions of cells undergoing slower polymer turnover could experience arrested network evolution similar to observations in reconstituted networks. ATP-dependent processes contribute greatly to the dynamic behavior of the cytoskeleton, and reconstituted networks incorporating these elements, such as molecular motors, have already yielded insights into potential cellular mechanisms. The addition of motors to more complex reconstituted network systems is an exciting avenue of future research. For example, since the structure of biopolymer networks is dependent on the formation kinetics pathway, incorporating additional cytoskeletal elements into active networks is likely to alter both the network mechanics and active dynamical properties. For example, introducing a second biopolymer species to a contractile acto-myosin network would likely affect the contractile behavior and marginal stability of the composite structure. As future studies incorporate additional cytoskeletal components, these reconstituted systems will continue to provide additional insights into intracellular behavior, while also serving to broaden our knowledge of basic physical properties of active soft matter.

Highlights.

• Reconstituted networks are used to study fundamental physics of cytoskeletal systems

• Filament properties and assembly kinetics determine network morphology and mechanics

• Systems with multiple components and motors exhibit novel emergent behavior