Mechanics of biological networks: from the cell cytoskeleton to connective tissue. Robyn H.
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Cited by. Back to tab navigation Download options Please wait Article type: Review Article. DOI: The experimental observations along with computational approaches used to study the mechanical properties of the individual constituents of the cytoskeleton are first presented. Various computational models are then discussed ranging from discrete filamentous models to continuum level models developed to capture the highly dynamic and constantly changing properties of the cells to external and internal stimuli. Finally, the concept of cellular mechanotransduction is discussed as an essential function of the cell wherein the cytoskeleton plays a key role.
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Liu X. Dupuis, D. Muscle Res. Cell Motil. Isambert, H. Effect of bound nucleotide, phalloidin, and muscle regulatory proteins, J. Steinmetz, M. Yasuda, R. Orlova, A. Egelman, E. Howard, J. USA 84 , — Tilney, L. Ming, D. Chu, J. Paula, D. Pfaendtner, J. Huxley, H. B , 59—62 Acta 12 , — Hanson, J. Moore, P. DeRosier, D. Holmes, K. Nature , 44—49 Kabsch, W.
Nature , 37—44 Oda, T. Wittmann, T. Mitchison, T. Janson, M. Diaz, J. Hawkins, T. Bicek, A. Methods Cell Biol. Kasas, S. Gardel, M. Free monomers of actin carry a molecule of ATP and are known as G-actin or globular-actin. The actin protein in filament form is known as F-actin filamentous-actin. Actin filaments have dif- ferent rates of growth and shrinkage at their two ends. The subunits in a filament are held together by weak, noncovalent bonds that can be broken by thermal fluctuations .
Actin subunit chains are often bound together in parallel to form a stronger double-stranded helical structure. Filament length can vary depending on cell type, but they generally are 1—20 lm long and about 8 nm wide [4, 21]. Young in muscle cells , and as short as 0. In either case, they are several orders of magnitude longer than they are wide.
Actin filaments are classified as semi-flexible polymers . A single actin filament can withstand an elongation force of about — pN before breaking, and it only stretches about 0. In comparison to stretching, actin filaments bend quite easily. This large difference in magnitude between the stretching and bending properties of actin filaments allows them to be classified as an elastic string for modeling purposes. The total number of actin filaments within a cell varies by cell type and concentration levels of actin.
In red blood cells, actin fibers form a one to two filament thick network of short filaments . This amounts to approximately ,—, short actin filaments in a red blood cell cytoskeleton. This translates to about ,, 1 lm filaments in a 10 lm diameter animal cell. Spectrin is a long nm, flexible protein found close to the intracellular side of the plasma membrane.
Two spectrin molecules link together head to head to create two actin filament binding sites that are spaced approximately 75— nm apart depending if the spectrin polymer is in a convoluted position or stretched out straight [1, 4]. This distance is quite large compared to the other proteins which bind actin bundles in tight configurations about 14—30 nm apart, and leads to large flexibility in the cytoskeleton. Filamin is another binding protein that crosslinks two filaments together almost at right-angles to one another forming a loose grid of actin polymers [1, 30].
Filamin is also found binding the actin mesh to the plasma membrane in platelets. Binding of the actin network to the plasma membrane is also accomplished by other proteins. In muscle cells, the dystrophin protein carries out this role. In red blood cells, a protein in the plasma membrane known as band 3 attaches to another protein called ankyrin which in turn attaches to the spectrin proteins on the cytoskeleton . Other adhesive proteins include ezrin, radixin, and moesin  Fig.
The size of the gaps in the actin mesh range from 10 to nm [12, 38, 40], depending on cell type. The aggregate elastic moduli of an actin network differ markedly from the single filament values. Charras et al. This is due to the fact that crosslinking proteins such as spectrin are more elastic than actin, so they make the overall mesh less stiff. The cytoskeletal network is acted upon by myosin II motor proteins that produce forces between actin filaments [1, 24, 28, 33].
Myosin II, like actin, is found in all eukaryotic cells . Myosin II is a long protein composed of two heavy chains and two light chains. Myosin II subunits join to form a filament by bundling their tails together. This creates a bipolar filament with myosin heads facing in opposite directions along the fiber. Alternating myosin heads can attach to actin and exert a force ranging from 0.
Young Fig. Actin is labelled in green. After the bleb has fully inflated frame 2 , actin that arrives in the bleb builds a new cortex leading to bleb retraction  2. A bleb is a balloon-like, cytosol-filled protrusion of the plasma membrane. Unlike lamellipodia and microvilli, this type of protrusion is not formed by active growth and rearrangement of the cytoskeleton [12, 14].
The onset of bleb formation is triggered by a contraction of the actin network, such that it detaches from the plasma membrane over some region. A gap size of 0. Once a gap is formed, the typical 20— Pa [10, 35] overpressure in the cytosol with respect to ambient leads to bleb formation in 3—7 s. Typical bleb diameters range from 1 to 10 lm . The bleb stays fully inflated for about 10—20 s. After this time interval, enough free actin monomers have begun to reorganize the cytoskeleton inside the bleb for retraction to occur . The new cortex is built to a thickness of 10—20 nm 3—4 actin filaments thick with gap sizes of approximately nm  see Fig.
Myosin II, present in this new cytoskeleton, creates contractions which pull the blebbed membrane inward to be reattached to the base cytoskeleton [11, 24]. Homogenized models of the cytoskeleton treated as a continuum are of limited utility since the elastic properties change in time as new links are formed and broken between actin filaments at a microscopic level. There are about one-micron long filaments in a typical cell . The filaments are crosslinked and the typical length of a filament segment between crosslinks is on the order of nm . This means there are approximately filament segments in the cytoskeleton and roughly 5 9 crosslink protein complexes.
Time steps on the order of s are required to capture all mentioned phenomena, leading to 3 9 time steps over the s duration of a typical bleb. A more complete review is available in the book by Kamm and Mofrad . Simplification of the network geometry has been investigated by Boey et al. Palmer et al. To elucidate whether this is an acceptable hypothesis several research groups have undertaken the task of thoroughly modeling a small portion of the cytoskeleton to understand its mechanical response to various stresses.
Kwon et al. The model performs well for isotropic and nearly isotropic systems, but exhibits large errors when the distribution of filament orientations is far from uniform. In a similar study, Huisman et al. The filaments were found to reorient themselves in the direction of applied shear, and the computed shear stiffening was compared to experimental findings. They conclude that the response of the network is highly dependent upon the topology of the filament mesh.
Head et al. Young networks, dependent on crosslink density and filament length. They distinguish two distinct regimes, one where strains are uniformly distributed affine defor- mation and another in which strains are non-uniformly distributed non-affine deformation. Buxton et al. The filaments can also undergo capping, severing and crosslinking.
The network develops until it reaches a sta- tistical steady state and is then placed under shear stress in order to examine its mechanical response. Different networks were built based on different actin dynamics rates, and the mechanical responses of these networks were compared.
The networks upon which these simulations were carried out typically consisted of approximately — filaments of lengths 2—9 lm, with about crosslinks connecting them. Each simulation took about h of CPU time. This model consists of two types of prestressed elements: interconnected tension- bearing elements which represent the actin filaments of the cytoskeleton and compression-bearing elements, which represent microtubules .
The model is successful at capturing the strain-hardening observed in cells spreading over a substrate. Stamenovic et al. They compare their results against experimental data, finding that the empirical moduli in general fall within their theoretically derived bounds. There is also a body of research dedicated to the treatment of the cytoskeleton as a continuum. Alt and Dembo  use a two-phase fluid description of the cytoplasm in ameboid cells.
The cytosol water-like substance within the cell is represented as a Newtonian fluid, and the cytoskeleton is represented as a highly viscous, polymeric fluid. This characterization is used under the assumption that the crosslinks in the cytoskel- eton are constantly rearranging, allowing the network to adapt and move easily like a fluid.
This model is used to simulate the formation of a lamellipodium during cell migration. During this phenomenon, the cytoskeleton undergoes many structural rearrangements. They demonstrate experimentally that localized contractions of the actin mesh can create local pressure increases that do not instantaneously equilibrate across the cell. Their theoretical model was developed to explain the cellular phenomenon of bleb formation. While homeostatic behavior might reasonably be captured by coarse grained models, there is significant interest in large changes in cytoskeleton configuration since such changes are often associated with diseased states.
Elucidating cytoskeleton behavior in such situations might suggest therapeutic approaches. The continuum models of Alt and Dembo  and Charras et al. This consti- tutive law is complex and time-varying, and dependent on the microstructure of the medium. Without representing this microstructure in some way, the models in  and  do not reflect the changes and rearrangements occurring in the cyto- skeleton that lead to varying mechanical properties. The detailed microscopic models that treat small portions of the cytoskeleton provide a great deal of insight into the mechanical response of small patches of actin networks, but do not apply to the entire cellular network due to the inhomogeneity and anisotropy of the cytoskeleton.
Huisman et al.
These protein levels can certainly vary in different parts of the cortex as the cell undergoes locomotion and shape change. The detailed micro- scopic models also highlight the consequences of increasing anisotropy as the cytoskeleton is observed at smaller scales, especially the non-affine distribution of strain. The cytoskeleton rearrangement response is at time scales comparable to those arising from continuum level unsteady forces during pro- trusion and blebbing. There is no time scale separation and the microscopic configuration of the cytoskeleton is not at equilibrium.
In this work we apply a general multiscale interaction procedure, the time- parallel continuum—kinetic—molecular tP-CKM algorithm . This algorithm is specially constructured to treat processes not at equilibrium at the microscale. A short overview of the algorithm is presented here, with further details available in .
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The algorithm is constructed from three solvers for each length scale, and procedures for interscale communication. The three solvers are as follows. Continuum-level solver. This may be any numerical approximation procedure for PDEs, e. A finite volume procedure is exemplified here. Kinetic-level solver. The p. Molecular-level solver. The spatial dependence on x is suppressed for simplicity of presentation. The following steps are taken in the algorithm: 1. A new p. The Fig.