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Abstract
Microtubules (tubulin) or bundles of microfilaments (actin) are thought to cause movement, in some instances, by disassembly or assembly of subunits. Possible examples are the pulling of a chromosome toward a pole in mitosis (anaphase) or the deformation of a cell membrane to change the shape of a cell. This paper examines the relevant elementary bioenergetic considerations when assembly or disassembly of an aggregate occurs against a resisting force. The problem is considered, in the first section, without NTPase activity. Sickle cell hemoglobin aggregation in vivo is an example. In the second section, the tubulin GTPase and actin ATPase activities are included in the analysis.
... In Section 7, the relationship = * − (Ogden, 2003) will be exploited. Hill (1981) and Hill and Kirschner (1982) recognized an analogy between the assembly and disassembly of biological microfilaments and microtubules and polymers subjected to a moveable force of either thermodynamical or mechanical origin. In their model, the force is applied at one of the polymers ends and tends to either extend or compress it so that the polymer either shortens or lengthens by losing or gaining subunits, respectively, typical examples being a shortening microtubule that pulls on a chromosome, or a lengthening bundle of microfilaments pushing on a cell membrane. ...
... Assuming the plaque to be made of individual monomers, the actual stretched length of the single monomer of initial length is approximated as̃( ) . By thermodynamics consistency (Hill, 1981;Hill and Kirschner, 1982;Shemesh et al., 2005;Cao et al., 2015Cao et al., , 2017, an infinitesimal variation of the force acting on the plaque produces an infinitesimal variation of the chemical potential of the monomers building the plaque as follows (Hill, 1981): ...
... Assuming the plaque to be made of individual monomers, the actual stretched length of the single monomer of initial length is approximated as̃( ) . By thermodynamics consistency (Hill, 1981;Hill and Kirschner, 1982;Shemesh et al., 2005;Cao et al., 2015Cao et al., , 2017, an infinitesimal variation of the force acting on the plaque produces an infinitesimal variation of the chemical potential of the monomers building the plaque as follows (Hill, 1981): ...
... Following Hill (1981), Hill and Kirschner (1982), we assume a chemical potential for the plaque, and consider that, in virtue of the thermodynamical laws, an infinitesimal variation of the force acting on the plaque, , induces an infinitesimal variation as follows ...
... In the present section, we give an account of the processes of assembly and disassembly obtained with the present model. According to Eq. (31), tensile forces will expectedly promote plaque assembly, whereas compressive forces will favor its disassembly (Tanaka and Kirschner, 1995;Hill, 1981;Heidemann and Buxbaum, 1994;Putnam et al., 2001;Geiger and Bershadsky, 2001). In the present model, the force acting on the plaque corresponds to the force developed by the mechanical model in response to the inelastic pre-stretches * and * . ...
... This section investigates the effects inherent in the mathematical structure of the growth law. In the state-of-the-art literature, the growth function is usually expressed as a linear function of the mechanical force starting from the pioneering paper by Hill (1981) under the hypothesis of small displacements, with only few exceptions Fig. 13. Force plotted as a function of ∕ for the cases of pre-contraction with underlying pre-polymerization * = 1.0222 ...
We demonstrate that several key aspects of the contractile activity of a cell interacting with the substrate can be captured by means of a non linear elastic tensegrity device made of a tensile element in parallel with a buckling-prone component, and exchanging forces with the surroundings through an extracellular matrix-focal adhesion complex. Mechanosensitivity of the focal adhesion plaque is triggered by pre-strain-driven buckling of the device induced either by pre-contraction or pre-polymerization of the constituents. The impact of pre-polymerization on the mechanical force and the implications of using linear and nonlinear elasticity for the focal adhesion plaque are assessed.
... Best known are the ATP-dependent molecular motor proteins (e.g., myosin, dynein and kinesin) that advance their bound cargo by crawling along microfilaments or microtubules. Before our discovery of a second and fundamentally different type of cytoskeletal motor [1], actin-based motility was thought to be powered by Brownian Ratchets [2][3][4][5], the latter consisting of ensembles of free-ended filaments that generate modest forces when their (+)-ends make excursions far enough from the motile surface to create sufficient space for monomer addition. As the load (i.e., the force resisting forward motion) increases, ever fewer of the (+)-ends would have gaps large enough for monomer intercalation, and Brownian Ratchets necessarily stall. ...
... For many years, Brownian Ratchet-type mechanisms, consisting of ensembles of free-ended filaments, dominated the way researchers viewed actin-based motility (See Fig. 2). Although the idea began with Hill [2], it was Peskin et al. [3] who formulated a BR theory explaining how an elongating actin filament could exert an axial force, if monomers add to its growing end in a way that allows the filament to rectify the otherwise freely diffusive motions of an object. Mogilner & Oster [4] later proposed the Elastic Brownian Ratchet (EBR) Model to the account for the elasticity of actin filaments as well as to relax the requirement for colinear structure of growing filament ends. ...
... They obtained an expression for the effective polymerization velocity of an elongating filament as a function of the load it is working against as well as its angle with respect to the load. To generate a pushing force, thermally controlled excursions of the (+)-end away from the surface are needed to create a sufficient space (~2.7 nM) for a filament to elongate against a load [2]. ...
The path to the discovery of the actoclampins began with efforts to define profilin's role in actin-based pathogen and endosome rocketing. That research identified a set of FPPPP-containing cargo proteins and FPPPP-binding proteins that are consistently stationed within the polymerization zone during episodes of active motility. The very same biophysical clues that forced us to abandon Brownian Ratchet models guided us to the Actoclampin Hypothesis, which asserts that every propulsive filament possesses a (+)-end-tracking motor that generates the forces cells need to crawl. Each actoclampin motor is a multi-arm oligomeric complex, employing one arm to recruit/deliver Profilin•Actin•ATP to a growth-site located at the (+)-end of the lagging subfilament, while a second arm maintains an affinity-modulated binding interaction with the extreme (+)-end of the other subfilament. The alternating actions of these arms define a true molecular motor, the processivity of which explains why propelling filaments maintain full possession of their cargo. The Actoclampin Hypothesis also suggests how the energetics of tracker interactions with the (+)-end determines whether a given actoclampin is a passive (low force-producing) or active (high force-producing) motor, the latter requiring the Gibbs free energy of ATP hydrolysis. Another aim of this review is to acknowledge an earlier notional model that emerged from efforts to comprehend profilin's pivotal role(s) in actin-based cell motility.
... Avec les travaux de Hill et Kirschner en 1982 fut apporté la preuve que l'énergie libre associée à la réaction de polymérisation d'un biopolymère pouvait être directement transformé en énergie mécanique dans les cellules vivantes (Hill, 1981). Par la suite, les travaux de Wang en 1985 puis de Theriot et Mitchison en 1991 ont suggéré que la polymérisation des filaments d'actine contre la membrane pouvait être responsable de la force exercée lors de la protrusion du lamellipode , . ...
... Au lieu de cela nous montrons pour la première fois que les forces exercées par la polymérisation sont largement suffisantes pour déformer aussi des structures épaisses de câbles de filaments d'actine et les faire flamber, comme cela avait été montré auparavant sur des filaments individuels . Cela fait maintenant plus de 25 ans qu'il est admis que l'énergie chimique libérée par la polymérisation des filaments d'actine peut être transduite en énergie mécanique (Hill, 1981), et que la polymérisation de l'actine permet d'exercer des forces contre une cible pour la pousser. De nombreux modèles se sont succédés pour expliquer le mécanisme physique sous-jacent, pour trouver l'ordre de grandeur des forces associées, et pour déterminer une relation liant la vitesse de polymérisation du filament en fonction de la force exercée par la cible (Peskin et al., 1993), , . ...
... Pour toute déformation rapide, le gel est vu comme un solide au comportement élastique, et résiste aux déformations(Xu et al., 2000),(Marcy et al., 2004). En revanche, pour toute déformation lente, les liaisons ont le temps de se réarranger, et le cytosquelette d'actine est alors simplement vu comme un fluide visqueux(Xu et al., 2000).IV-2/ Forces générées par la polymérisation d'un biopolymère.La polymérisation d'un filament d'actine seul peut générer des forces sur une cible, même en l'absence de moteur moléculaire, comme c'est le cas au bord du lamellipode(Hill, 1981). Cette énergie provient de la variation du potentiel chimique associé à une sous-unité d'actine entre le moment où celle-ci est libre en solution et le moment où celle-ci est insérée dans le filament. ...
Actin is one of the major constituents of the cytoskeleton. By dynamically assembling in cells, actin filaments are able to push the membrane out, and deform the cell leading to force generation and movement. In the last ten years, biochemical studies have unveiled many different biochemical pathways that lead to actin polymerization and assembly. However, the mechanism of force generation is still under debate. The main issue is how the microscopic properties of individual filaments are integrated at the scale of a cell to produce forces. In addition, little is known about the dynamic formation and disassembly of actin filaments cables (an organisation of actin filaments in parallel/or antiparrallel bundles). Recently, formins have been shown to be an essential family of proteins for the initiation of such actin-based structures.
This manuscript highlights the work that we conduct to understand the mechanism of action of formins at a molecular level. Most of formins are processive nucleators; indeed they are promoting fast actin filament elongation while remaining attached to the growing end of the filament. We have shown by the original evanescent wave microscopy technique that Arabidopsis Thaliana FORMIN1 represents a new kind of formin, which moves to the side of the actin filament after nucleation. From the side of the pre-existing filament, FORMIN1 is able to nucleate a new filament, promoting the assembly of actin filaments into actin cables. We next combine biomimetic assays with TIRF microscopy, to address the mechanism of the dynamic of polymerization and depolymerization of actin filaments induced by ADF/cofilin. We visualized for the first time individual actin filament stochastic dynamics in real time, and proposed a selection process for the formation of large actin based structures initiated by formin.
... The formation of membrane protrusions through polymerization of an actin network suggests that actin polymerization induces forces. Thermodynamic estimations revealed that actin polymerization, more precisely addition of an actin monomer, can produce a force in the pico-newton range [Hill, 1981]. Several theories have emerged from this idea [Mogilner, 2006]: at the microscopic level, the "elastic ratchet" and "tethered-ratchet" theories propose respectively that thermal fluctuations of the actin filament or transient attachments to the membrane allow the insertion of an actin monomer that results in a pushing force against a load, and at the macroscopic level, the elastic propulsion model considers the actin network as a continuum able to accumulate stresses upon growth at the membrane surface. ...
... -2D cell motility: crawling), the resisting force of the membrane at the tip of actin bundles has been estimated as F ∼ 10-50 pN Peskin et al., 1993;. Experiments on in vitro actin filaments have estimated F perpendicular ∼ 1 pN [Footer et al., 2007;Kovar and Pollard, 2004] while it has been calculated that the thermodynamic limit corresponds to a polymerization force ∼ 9 pN for physiological conditions [Hill, 1981]. Therefore, with F perpendicular ∼ 1-9 pN and F ∼ 10-50 pN, a bundle of around 10 filaments can initiate a protrusion (Fig. 1.12 C). ...
Cell membrane deformations are essential to ensure cellular processes such as motility, division, intracellular transport and signalling. These deformations range from global shape changes such as cell rounding or elongation during cell division, to protrusions and invaginations, which allow the cell to probe its environment and uptake external components, respectively. Strikingly, membrane deformations rely on the activity of the cytoskeleton, and in particular actin, a biopolymer that forms a dynamical network. The precise role of actin and its implication in the different mechanisms at work during cell shape changes still need to be elucidated. To address this, I take an alternative approach to the complexity of cells and I use an in vitro reconstituted system to mimic shape changes with a minimal set of components: lipids and purified proteins. A branched actin network is grown at the surface of giant unilamellar vesicles, thereafter called liposomes. With this biomimetic system, I control experimental parameters such as membrane tension, varied by applying an osmotic shock, and actin network architecture, varied by modifying the protein composition. In the first part of my work, actin dynamics occur at the outer surface of the liposome and I obtain a wide variety of cell-like membrane deformations, from global shape changes of liposomes to micron scale deformations that are reminiscent of dendritic filopodia and endocytic intermediates in cells. Combining experiments and theoretical modelling, our results unveil the mechanisms of actin-driven membrane deformations, and more precisely the role of tension and network architecture. In the second part, I encapsulate the actin machinery in a liposome in an attempt to reproduce the invasion of the bacteria Shigella flexneri. To push further in the knowledge of the details of the initiation of membrane deformations, I present, in the third part, a microfluidic device, still in development, to follow precisely in real time all the steps of actin polymerization and cell-like shape changes. Once optimized, this device will provide a useful tool for other dynamical studies where micron-size objects need to be isolated.
... L'idée que la polymérisation des filaments pouvait générer les forces nécessaires à la protrusion du lamellipode fut initialement proposée au début des année 80 (Hill, 1981). En effet, à cette époque, on pensait que les forces présentes au niveau du lamellipodes étaient principalement dues aux myosines. ...
... Bien qu'indispensable à la compréhension du fonctionnement des structures protrusives, la mesure des forces générées par l'allongement d'un filament d'actine est restée longtemps théorique. Ainsi, la force maximale générée par la polymérisation fut assez vite estimée de manière théorique à 9 pN, mais une mesure directe de cette force restait essentielle Hill, 1981). ...
La motilité cellulaire est un processus intégré essentiel à de nombreux phénomènes physiologiques tels que la formation du cône de croissance et la plasticité synaptique. Des dérégulations de la motilité cellulaire peuvent être à l’origine de la formation de métastases ou de pathologies neuropsychiatriques comme la schizophrénie et l'autisme. La compréhension des mécanismes régulant la migration cellulaire est donc un enjeu majeur. La motilité cellulaire repose sur la formation de diverses structures constituées de réseaux d’actine branchés telles que le lamellipode. La formation du lamellipode nécessite l’intervention de protéines régulatrices de l’actine telles que Rac1 et les complexes Wave et Arp2/3. Grâce à l’utilisation de suivi de protéine unique, nous avons pu comprendre comment la coordination spatio-temporelle de ces régulateurs contrôle la formation et la morphologie des lamellipodes de cellules migrantes. Nous avons ainsi découvert que l’activation et la localisation du complexe Wave étaient régulées de manière enzymatique mais également mécanique. Dans une première étude, nous avons montré que la RhoGTPase Rac1 active le complexe Wave spécifiquement à l’extrémité du lamellipode. Dans une seconde étude, nous avons révélé que la localisation du complexe Wave est régulée par la dynamique des filaments des réseaux branchés d’actine. Ces données soulignent l’importance du complexe Wave dans la formation du lamellipode et révèlent l’existence d’une régulation mécanique de la localisation du complexe Wave.
... We assumed that actin filaments assemble only at the barbed end, and implemented a Brownian ratchet model as previously described (Hill, 1981). Assuming a concentration A 1 of free actin monomers, the polymerization rate k + and depolymerization rate kfor a free actin end is: k + = k on A 1 ; k À = k off such that k off /k on = A 1 * is the critical G-actin concentration. ...
... k + = k on A 1 e Àfd=k B T ; k À = k off in which d z2.8 nm is the extension provided by the addition of one monomer. From there, we can define f 0 = k B T log(A 1 /A 1 *) / d as the stall force of actin assembly (Hill, 1981). Using k on = 400 s -1 , k off = 1.4 s -1 and the free actin concentration measured in vivo in fission yeast A 1 = 40 mM (Wu and Pollard, 2005), one finds f 0 $9 pN (Dmitrieff and Né dé lec, 2016). ...
Clathrin-mediated endocytosis is an essential cellular function in all eukaryotes that is driven by a self-assembled macromolecular machine of over 50 different proteins in tens to hundreds of copies. How these proteins are organized to produce endocytic vesicles with high precision and efficiency is not understood. Here, we developed high-throughput superresolution microscopy to reconstruct the nanoscale structural organization of 23 endocytic proteins from over 100,000 endocytic sites in yeast. We found that proteins assemble by radially ordered recruitment according to function. WASP family proteins form a circular nanoscale template on the membrane to spatially control actin nucleation during vesicle formation. Mathematical modeling of actin polymerization showed that this WASP nano-template optimizes force generation for membrane invagination and substantially increases the efficiency of endocytosis. Such nanoscale pre-patterning of actin nucleation may represent a general design principle for directional force generation in membrane remodeling processes such as during cell migration and division.
... We assumed that actin filaments assemble only at the barbed end, and implemented a Brownian ratchet model as previously described (Hill, 1981). Assuming a concentration A 1 of free actin monomers, the polymerization rate k + and depolymerization rate kfor a free actin end is: ...
... in which d z2.8 nm is the extension provided by the addition of one monomer. From there, we can define f 0 = k B T log(A 1 /A 1 *) / d as the stall force of actin assembly (Hill, 1981). Using k on = 400 s -1 , k off = 1.4 s -1 and the free actin concentration measured in vivo in fission yeast A 1 = 40 mM (Wu and Pollard, 2005), one finds f 0 $9 pN (Dmitrieff and Né dé lec, 2016). ...
... On using the normalization condition (Eq. S39 in the Supplementary Information) in Eq. 32 we find that The stall force, corresponding to zero mean velocity, is obtained by putting V N (f) = 0 in Eq. 39, and is given as For constant on-rate case, the stall force scales linearly with the number of filaments, similar to earlier predictions 6,9,36 . But the mathematical dependence of stall force on the on-rate and off-rate differ, the difference clearly arising from the continuum treatment in this paper as opposed to the discrete approach in van Doorn et al. 9 . ...
... But the mathematical dependence of stall force on the on-rate and off-rate differ, the difference clearly arising from the continuum treatment in this paper as opposed to the discrete approach in van Doorn et al. 9 . The corresponding prediction of the discrete model 6,9,36 is ...
Polymerising filaments generate force against an obstacle, as in, e.g., microtubule-kinetochore interactions in the eukaryotic cell. Earlier studies of this problem have not included explicit three-dimensional monomer diffusion, and consequently, missed out on two important aspects: (i) the barrier, even when it is far from the polymers, affects free diffusion of monomers and reduces their adsorption at the tips, while (ii) parallel filaments could interact through the monomer density field ("diffusive coupling"), leading to negative interference between them. In our study, both these effects are included and their consequences investigated in detail. A mathematical treatment based on a set of continuum Fokker-Planck equations for combined filament-wall dynamics suggests that the barrier-induced monomer depletion reduces the growth velocity and also the stall force, while the total force produced by many filaments remains additive. However, Brownian dynamics simulations show that the linear force-number scaling holds only when the filaments are far apart; when they are arranged close together, forming a bundle, sublinear scaling of force with number appears, which could be attributed to diffusive interaction between the growing polymer tips.
... to k B T ln(C/C*)/δ = ∼9 pN (Hill, 1981). Within such limits, the force developed by polymerization will depend on the conditions of assembly. ...
... (A) During polymerization, the addition of one actin monomer (orange) corresponds to an elongation (δ) at the barbed end of an actin filament (red) and is associated with a change of free energy (ΔG p = −k b T ln(C/C*)). (B) The work required to push a load over a distance (h) with a force (f) is f × h, and thus assembly remains favorable as long as ΔG p + f × h < 0. In the case where polymerization occurs straight against a load (h = δ), the maximal force (f a ) is f a = k b T ln(C/C*)/δ (Hill, 1981). (C) If the filament encounters the load with an angle (θ), then h = δ sinθ and the maximal force is consequently increased: f θ = f a /sinθ. ...
The actin cytoskeleton drives many essential processes in vivo, using molecular motors and actin assembly as force generators. We discuss here the propagation of forces caused by actin polymerization, highlighting simple configurations where the force developed by the network can exceed the sum of the polymerization forces from all filaments.
... Au vu d'une telle observation, sachant que la solution est exempte de moteurs moléculaires et que les billes sont inertes vis-à-vis des microtubules (aucune interaction chimique), on peut alors s'interroger sur les processus qui gouvernent le mouvement des billes. Il est connu que les microtubules isolés peuvent générer une force de poussée sur des objets inertes [Roberts and Hyams 1979, Hill 1981, Hill and Kirschner 1982. D'autres mécanismes sont pourtant à envisager, en particulier le fait que des ondes de concentration puisse déplacer des objets inertes. ...
... Étant donné que le mouvement des particules est lié à la réactivité du système et qu'il se fait dans la même direction que les microtubules, on est en droit de supposer qu'il est induit par la poussée directe des microtubules en croissance sur les billes. Les microtubules sont effectivement capables d'exercer une forte poussée sur des objets inertes [Roberts and Hyams 1979, Hill 1981, Hill and Kirschner 1982. Selon une telle hypothèse, les caractéristiques quantitatives du mouvement des particules devraient donc changer en fonction de leur diamètre : plus les particules ont un diamètre élevé, plus la surface exposée aux microtubules est élevée, donc, dans ce cas, le nombre de microtubules pouvant y exercer une poussée, augmente. ...
This work is concerned with the physical chemical processes underlying biological self-organisation by which an initially homogenous solution of reacting chemicals spontaneously self-organises so as to give rise to a preparation of macroscopic order and form. Theoreticians have predicted that self-organisation can arise from a coupling of reactive processes with molecular diffusion. In addition, the presence or absence of an external field, such as gravity, at a critical moment early in the self-organising process may determine the morphology that subsequently develops. The formation in-vitro of microtubules, a major element of the cellular skeleton, shows this type of behaviour. The microtubule preparations spontaneously self-organise by way of reaction and diffusion and the morphology of the state that forms depends upon the presence of gravity at a critical moment early in the process. In our experiments, I have shown that an associated phenomenon in living cells, the transport and organisation of subcellular particles, arises when microtubules self-organise in vitro. The principal objective of the experiments presented is the effect of weak external fields on microtubule self-organisation. I have shown that it is possible to reproduce the results of experiment carried in space using ground-based apparatus. Under these conditions there is no self-organisation. Self-organisation can be restablished with other external fields and factors. In addition, we have developed a numerical reaction-diffusion scheme, based on the chemical dynamics of a population of microtubules, that simulates the experimental self-organisation. In this work we outline the main features of these simulations and discuss the manner by which a permanent dialogue with experiment has helped develop a microscopic understanding of the collective behaviour. The numerical simulations predict the major features of the experimental observations.
... THE Three major theories or combinations of theories are currently in vogue (reviewed in reference 1,19,41,52). Force production by the polymerization and depolymerization of biological polymers (18, 19, 22, 35, 36; and thermodynamically formalized by Hill,16), remains the simplest model. While it is clear that polymerization and depolymerization of microtubules is a major feature of the structural changes in the mitotic spindle during mitosis, it is difficult to rule out force production by a parallel mechanochemical transducer that requires the integrity of the spindle fibers. ...
... While it is clear that polymerization and depolymerization of microtubules is a major feature of the structural changes in the mitotic spindle during mitosis, it is difficult to rule out force production by a parallel mechanochemical transducer that requires the integrity of the spindle fibers. Further, while force production as a result of polymerization of actin or tubulin (for pushing) is widely accepte, d (see reference 16), the depolymerization of polymers such as microtubules (for pulling) has not been readily embraced as a v/able mechaaochemical transducer. ...
Antibody against cytoplasmic myosin, when microinjected into actively dividing cells, provides a physiological test for the role of actin and myosin in chromosome movement. Anti-Asterias egg myosin, characterized by Mabuchi and Okuno (1977, J. Cell Biol., 74:251), completely and specifically inhibits the actin activated Mg++ -ATPase of myosin in vitro and, when microinjected, inhibits cytokinesis in vivo. Here, we demonstrate that microinjected antibody has no observable effect on the rate or extent of anaphase chromosome movements. Neither central spindle elongation nor chromosomal fiber shortening is affected by doses up to eightfold higher than those require to uniformly inhibit cytokinesis in all injected cells. We calculate that such doses are sufficient to completely inhibit myosin ATPase activity in these cells. Cells injected with buffer alone, with myosin-absorbed antibody, or with nonimmune gamma-globulin, proceed normally through both mitosis and cytokinesis. Control gamma-globulin, labeled with fluorescein, diffuses to homogeneity throughout the cytoplasm in 2-4 min and remains uniformly distributed. Antibody is not excluded from the spindle region. Prometaphase chromosome movements, fertilization, pronuclear migration, and pronuclear fusion are also unaffected by microinjected antimyosin. These experiments demonstrate that antimyosin blocks the actomyosin interaction thought to be responsible for force production in cytokinesis but has no effect on mitotic or meiotic chromosome motion. They provide direct physiological evidence that myosin is not involved in force production for chromosome movement.
... where k p and h p denote the plaque stiffness and height, respectively. We assume a chemical potential μ p for the plaque and consider that, by virtue of the thermodynamical laws, an infinitesimal variation of the force acting on the plaque, F p , induces an infinitesimal variation dμ p as follows [42,43]: ...
The mechanical response of a contractile cell anchored to the substrate through focal adhesions is studied by means of an asymmetric pre-strained tensegrity structure obeying a neo-Hookean stress-strain law. The aim is to assess the influence of overall asymmetric contraction on the cell durotaxis and on the growth of the focal adhesion plaque. The asymmetric kinematics of the system is obtained in two ways, that is by assuming a gradient of the substrate stiffness and through asymmetric buckling. Equivalent springs are purposely considered to represent the stiffness of the ensemble formed by the substrate, the focal adhesion plaque and the integrin ligands. Then, contraction results from elastic strains induced by competing polymerization and actomyosin contraction. The cell mechanical response in terms of durotaxis and its coupling with focal adhesion plaque growth is finally analysed with respect to the effects of asymmetry, gaining some insights into how this asymmetry could participate to redirect cell migration, both in terms of durotaxis and mollitaxis.
... Differential equations are a critical tool for modelling biophysical phenomena by describing the relationship between independent variables and their derivatives (Wang, 2013). In the case of bundled actin filaments, mechanical loads placed due to stress on the actin polymers modulate their assembly, and an ordinary differential equation-based model (ODE) was developed to explore bioenergetics of polymerisation and depolymerisation reactions (Hill, 1981) (Supplementary text, Section 3.2.1). It showed that adding monomers at the filament tip promoted surface propulsion, with monomer binding influenced by the maximum transition energy available from depolymerisation. ...
Life on Earth has evolved to thrive in the Earth's natural gravitational field; however, as space technology advances, we must revisit and investigate the effects of unnatural conditions on human health, such as gravitational change. Studies have shown that microgravity has a negative impact on various systemic parts of humans, with the effects being more severe in the human immune system. Increasing costs, limited experimental time, and sample handling issues hampered our understanding of this field. To address the existing knowledge gap and provide confidence in modelling the phenomena, in this review, we highlight experimental works in mechano-immunology under microgravity and different computational modelling approaches that can be used to address the existing problems.
... It might be doubted that a 'lifeless' polymer network like the basement membrane or any ECM can produce tissue-remodelling forces. However, there is a prominent example of force-generating polymerscytoskeleton: actin filaments and microtubules propel organelles, chromosomes, and cells by dynamically growing, collapsing, and deforming [127][128][129][130][131][132][133]. Dynamic remodelling of ECMs may also drive tissue rearrangements. ...
Extracellular matrices (ECMs) are essential for the architecture and function of animal tissues. ECMs have been thought to be highly stable structures; however, too much stability of ECMs would hamper tissue remodelling required for organ development and maintenance. Regarding this conundrum, this article reviews multiple lines of evidence that ECMs are in fact rapidly moving and replacing components in diverse organisms including hydra, worms, flies, and vertebrates. Also discussed are how cells behave on/in such dynamic ECMs, how ECM dynamics contributes to embryogenesis and adult tissue homoeostasis, and what molecular mechanisms exist behind the dynamics. In addition, it is highlighted how cutting-edge technologies such as genome engineering, live imaging, and mathematical modelling have contributed to reveal the previously invisible dynamics of ECMs. The idea that ECMs are unchanging is to be changed, and ECM dynamics is emerging as a hitherto unrecognized critical factor for tissue development and maintenance.
... 16 It can be seen that most of above works are independent to characterize (or observe) a single assembly (or disassembly) process. If we want to track an intact biological process inside cells (e.g., assembly/disassembly of microtubulin), 17 continu-ous showing of the assembly/disassembly (or disassembly/ assembly) process is needed. As we know, by conjugating a fluorescence tag to a small molecule (or biomacromolecule) to form a fluorescent conjugate, self-assembly/disassembly of its nanostructure will lead to fluorescence on/off (or off/on). ...
To track an intact biological process inside cells, continuous showing of the assembly/disassembly process is needed and fluorescence is advantageous in characterizing these processes. However, using fluorescence “on/off” to observe a sequential assembly/disassembly process in living cells has not been reported. Herein, we rationally designed a probe PEA-NBD-Yp and employed its fluorescence “on/off” to trace tandem assembly/disassembly of nanofibers in living HeLa cells. In vitro experiments validated that PEA-NBD-Yp could be efficiently dephosphorylated by ALP to yield PEA-NBD-Y, which self-assembled into nanofibers with the NBD fluorescence “on”. Also, the PEA-NBD-Y nanofiber was disassembled by GSH, accompanied by fluorescence “off”. Living cell imaging (together with ALP-inhibition or GSH-blocking) experiments sequentially showed the self-assembling nanofibers on the cell outer membrane with fluorescence “on” (On1), translocated inside cells (On2), and disassembled by GSH with fluorescence “off” (Off2). We anticipate that our strategy of one probe conferring temporal “on/off” fluorescence signals might provide people with a new tool to deeply understand a biological event in living cells in the near future.
... To allow further actin polymerization at the end of these actin filaments near the membrane, an "open" end between an actin filament and the membrane should be available of sufficient space and for sufficient time [100,101]. This can be achieved by three methods: i) stochastic/thermal movement of the membrane and polymerization in the periods of sufficient open space (racket model [102][103][104]), ii) stochastic/thermal bending of the actin filaments that allows open space [105], and iii) a combination of these two with cooperativity between adjacent actin filaments near the membrane. In each of these models actin polymerization produces a forward force leading to the growth of the pseudopod, while pseudopod growth induces counterforces, such as membrane tension and viscous drag, and counteractivities, including depletion of materials [101]. ...
The trajectory of moving eukaryotic cells depends on the kinetics and direction of extending pseudopods. The direction of pseudopods has been well studied to unravel mechanisms for chemotaxis, wound healing and inflammation. However, the kinetics of pseudopod extension–when and why do pseudopods start and stop- is equally important, but is largely unknown. Here the START and STOP of about 4000 pseudopods was determined in four different species, at four conditions and in nine mutants (fast amoeboids Dictyostelium and neutrophils, slow mesenchymal stem cells, and fungus B . d . chytrid with pseudopod and a flagellum). The START of a first pseudopod is a random event with a probability that is species-specific (23%/s for neutrophils). In all species and conditions, the START of a second pseudopod is strongly inhibited by the extending first pseudopod, which depends on parallel filamentous actin/myosin in the cell cortex. Pseudopods extend at a constant rate by polymerization of branched F-actin at the pseudopod tip, which requires the Scar complex. The STOP of pseudopod extension is induced by multiple inhibitory processes that evolve during pseudopod extension and mainly depend on the increasing size of the pseudopod. Surprisingly, no differences in pseudopod kinetics are detectable between polarized, unpolarized or chemotactic cells, and also not between different species except for small differences in numerical values. This suggests that the analysis has uncovered the fundament of cell movement with distinct roles for stimulatory branched F-actin in the protrusion and inhibitory parallel F-actin in the contractile cortex.
... The first term, −k B T ln α jn (L n ), is the free energy penalty due to compression with α jn (L n ) the ratio of the partition functions of the clamped filament in presence and in absence of the wall [15]. The second term is the free energy gain due to the self-assembly of (j n − 2) monomers to the seed to form the filament [31]. Finally, C is an irrelevant, j-independent constant (the free energy of the living filament permanent seed). ...
In various biological processes, semi-flexible filaments like F-actin exploit chemical energy associated to polymerization to perform mechanical work against a loaded external obstacle. The dynamics of fingerlike filopodial structures, characterized by the relationship between the obstacle velocity $V$ and the applied external load $F$, is generally interpreted by a brownian ratchet mechanism appropriate to fully rigid filaments. Based on the properties of the Wormlike Chain model, we propose an original and general multiscale approach to consider filament flexibility in the modelling. By stochastic dynamic simulations, we studied the dynamical relaxation of a bundle of $N_f$ supercritical semi-flexible filaments against an optical trap load ($F=-\kappa_TL$, where $L$ is the distance between the grafting wall and the obstacle mobile wall, and $\kappa_T$ the trap strength). For realistic values of the model parameters, the systematic motion of the trap is two/three orders of magnitude slower than the characteristic time between chemical events and this separation of time scales lets consider the optical trap relaxation as a sequence of non-equilibrium steady states for the bundle properties. The velocity-load relationship $V(F,\lambda)$ can then be generalized by introducing the degree of flexibility $\lambda$, defined as the ratio of the filaments contour length over the typical length beyond which flexibility effects are detectable. Our approach lets us map out the entire range of flexibility from the rigid to the escaping filament regime, in which the trap gets large enough for filaments to have a high probability to laterally escape, not participating anymore to the bundle polymerization force. We show that flexibility considerably enriches the theoretical scenario filling the gap between the multi-filaments brownian ratchet model and the mean field Perfect Load Sharing result.
... Highly cross-linked filaments are used in cells for transferring the mechanical stimulus resulting from mechanical forces applied to cell surfaces [33]. These forces generate elastic stress waves, which rapidly propagate through actin stress fibers. ...
The plasmodium of Physarum polycephalum is very sensitive to its environment, and reacts to stimuli with appropriate motions. Both the sensory and motor stages of these reactions are explained by hydrodynamic processes, based on fluid dynamics, with the participation of actin filament networks. This paper is devoted to actin filament networks as a computational medium. The point is that actin filaments, with contributions from many other proteins like myosin, are sensitive to extracellular stimuli (attractants as well as repellents), and appear and disappear at different places in the cell to change aspects of the cell structure - e.g. its shape. By assembling and disassembling actin filaments, some unicellular organisms, like Amoeba proteus, can move in response to various stimuli. As a result, these organisms can be considered a simple reversible logic gate - extracellular signals being its inputs and motions its outputs. In this way, we can implement various logic gates on amoeboid behaviours. These networks can embody arithmetic functions within p-adic valued logic. Furthermore, within these networks we can define the so-called diagonalization for deducing undecidable arithmetic functions.
... Hence, actin filaments are instable, they can assemble and disassemble rapidly by polymerization and depolymerization respectively. For more details see [4], [5], [6], [7], [9], [10], [12], [13], [14], [15], [16]. ...
This paper is devoted to actin filament networks as a computation medium. The point is that actin filaments are sensitive to outer cellular stimuli (attractants as well as repellents) and they appear and disappear at different places of the cell to change the cell structure, e.g. its shape. Due to assembling and disassembling actin filaments, Amoeba pro-teus can move in responses to different stimuli. As a result , Amoeba proteus can be considered a simple reversible logic gate, where outer cellular signals are its inputs and the amoeba motions are its outputs. In this way, we can implement the FREDKIN logic gate on the amoeba behaviours. The actin filament networks have the same basic properties as neural networks: lateral inhibition; lateral activation ; recurrent inhibition; recurrent excitation; feedforward inhibition; feedforward excitation; convergence/divergence. These networks can embody arithmetic functions defined re-cursively and corecursively within p-adic valued logic. Furthermore , within these networks we can define the so-called diagonalization for deducing undecidable arithmetic functions .
... By tuning the trap strength κ T at fixed (N f , L R , A, µ 1 , T), one can study the equilibrium properties of bundles of filaments for different (self-adjusted) average positions of the wall. The average optical trap length L for bundles of flexible filaments in ideal conditions can be roughly estimated by Hill's polymerization force value F H [14][15][16], the exact average force for rigid filaments [6], so that we expect [5,6]: ...
We report a coarse-grained molecular dynamics simulation study of a bundle of parallel actin filaments under supercritical conditions pressing against a loaded mobile wall using a particle-based approach where each particle represents an actin unit. The filaments are grafted to a fixed wall at one end and are reactive at the other end, where they can perform single monomer (de)polymerization steps and push on a mobile obstacle. We simulate a reactive grand canonical ensemble in a box of fixed transverse area A, with a fixed number of grafted filaments N f , at temperature T and monomer chemical potential μ 1 . For a single filament case ( N f = 1 ) and for a bundle of N f = 8 filaments, we analyze the structural and dynamical properties at equilibrium where the external load compensates the average force exerted by the bundle. The dynamics of the bundle-moving-wall unit are characteristic of an over-damped Brownian oscillator in agreement with recent in vitro experiments by an optical trap setup. We analyze the influence of the pressing wall on the kinetic rates of (de)polymerization events for the filaments. Both static and dynamic results compare reasonably well with recent theoretical treatments of the same system. Thus, we consider the proposed model as a good tool to investigate the properties of a bundle of living filaments.
... Now if the mesoscopic system has a 1D position x that experiences a constant external mechanical resistant force ξ (or a rotational angle with a constant external torque) and undergoes cyclic motion, as shown in figure 1(C) [41,[60][61][62] then equation (33) ...
Nonequilibrium thermodynamics (NET) investigates processes in systems out of
global equilibrium. On a mesoscopic level, it provides a statistical dynamic
description of various complex phenomena such as chemical reactions, ion
transport, diffusion, thermochemical, thermomechanical and mechanochemical
fluxes. In the present review, we introduce a mesoscopic stochastic formulation
of NET by analyzing entropy production in several simple examples. The
fundamental role of nonequilibrium steady-state cycle kinetics is emphasized.
The statistical mechanics of Onsager's reciprocal relations in this context is
elucidated. Chemomechanical, thermomechanical, and enzyme-catalyzed
thermochemical energy transduction processes are discussed. It is argued that
mesoscopic stochastic NET provides a rigorous mathematical basis of fundamental
concepts needed for understanding complex processes in chemistry, physics and
biology, and which is also relevant for nanoscale technological advances.
... Equilibrium polymerization was first modelled quantitatively by Oosawa and Asakura (1962) and treadmilling predicted mathematically by Wegner (1976). Thermodynamics was used by Hill (1981a) to demonstrate that a polymerizing filament can generate force in the piconewton range. Later on, Peskin et al. (1993) formulated a Brownian ratchet theory for how a growing polymer could exert an axial force. ...
... It is possible that this ejection is the direct result of the dynamic instability of centrosomal MTs (14,27). Since elongating MTs can exert a push (5,8), the continuous nucleation, elongation, disassembly, and new nucleation of MTs at the centrosome could well expel ,large cellular components (e.g., chromosome fragments) to the periphery of the MT array. Indeed the in vivo elongation rate of centrosomal MTs in mammalian interphase cells at 37°C is ~3 -4 Ixm/min (29), a rate comparable to the 2 Ixm/min ejection rate of NLC asters at room temperature. ...
During mitosis a monooriented chromosome oscillates toward and away from its associated spindle pole and may be positioned many micrometers from the pole at the time of anaphase. We tested the hypothesis of Pickett-Heaps et al. (Pickett-Heaps, J. D., D. H. Tippit, and K. R. Porter, 1982, Cell, 29:729-744) that this behavior is generated by the sister kinetochores of a chromosome interacting with, and moving in opposite direction along, the same set of polar microtubules. When the sister chromatids of a monooriented chromosome split at the onset of anaphase in newt lung cells, the proximal chromatid remains stationary or moves closer to the pole, with the kinetochore leading. During this time the distal chromatid moves a variable distance radially away from the pole, with one or both chromatid arms leading. Subsequent electron microscopy of these cells revealed that the kinetochore on the distal chromatid is free of microtubules. These results suggest that the distal kinetochore is not involved in the positioning of a monooriented chromosome relative to the spindle pole or in its oscillatory movements. To test this conclusion we used laser microsurgery to create monooriented chromosomes containing one kinetochore. Correlative light and electron microscopy revealed that chromosomes containing one kinetochore continue to undergo normal oscillations. Additional observations on normal and laser-irradiated monooriented chromosomes indicated that the chromosome does not change shape, and that the kinetochore region is not deformed, during movement away from the pole. Thus movement away from the pole during an oscillation does not appear to arise from a push generated by the single pole-facing kinetochore fiber, as postulated (Bajer, A. S., 1982, J. Cell Biol., 93:33-48). When the chromatid arms of a monooriented chromosome are cut free of the kinetochore, they are immediately ejected radially outward from the spindle pole at a constant velocity of 2 micron/min. This ejection velocity is similar to that of the outward movement of an oscillating chromosome. We conclude that the oscillations of a monooriented chromosome and its position relative to the spindle pole result from an imbalance between poleward pulling forces acting at the proximal kinetochore and an ejection force acting along the chromosome, which is generated within the aster and half-spindle.
... In the last ten years there has been a resurgence of interest in polymerization reactions as sources of motive force. Several theoretical treatments have examined the thermodynamics of this possibility (Hill, 1981(Hill, , 1987Hill and Kirschner, 1982). Experimental work in vitro, has demonstrated that MT polymerization within liposomes can deform the surrounding membrane (Miyamoto and Hotani, 1988;Hotani and Miyamoto, 1990), providing compelling evidence that polymerization alone can transduce the chemical energy of MT formation into the mechanical energy necessary to distend a membrane. ...
We have developed a system for studying the motions of cellular objects attached to depolymerizing microtubules in vitro. Radial arrays of microtubules were grown from lysed and extracted Tetrahymena cells attached to a glass coverslip that formed the top of a light microscope perfusion chamber. A preparation of chromosomes, which also contained vesicles, was then perfused into the chamber and allowed to bind to the microtubule array. The concentration of tubulin was then reduced by perfusing buffer that lacked both tubulin and nucleotide triphosphates, and the resulting microtubule depolymerization was observed by light microscopy. A fraction of the bound objects detached in the flow and washed away, while others stabilized the microtubules to which they were bound. Some of the particles and chromosomes, however, moved in toward the Tetrahymena ghost as their associated microtubules shortened. The mean speeds for particles and chromosomes were 26 +/- 20 and 15 +/- 12 microns/min, respectively. These motions occurred when nucleotide triphosphate levels were very low, as a result of either dilution or by the action of apyrase. Furthermore, the motions were unaffected by 100 microM sodium orthovanadate, suggesting that these forces are not the result of ATP hydrolysis by a minus end-directed mechanoenzyme. We conclude that microtubule depolymerization provided the free energy for the motions observed. All the objects that we studied in detail moved against a stream of buffer flowing at approximately 100 microns/s, so that the force being developed was at least 10(-7) dynes. This force is large enough to contribute to some forms of motility in living cells.
Actin filaments assemble into force-generating systems involved in diverse cellular functions, including cell motility, adhesion, contractility and division. It remains unclear how networks of actin filaments, which individually generate piconewton forces, can produce forces reaching tens of nanonewtons. Here we use in situ cryo-electron tomography to unveil how the nanoscale architecture of macrophage podosomes enables basal membrane protrusion. We show that the sum of the actin polymerization forces at the membrane is not sufficient to explain podosome protrusive forces. Quantitative analysis of podosome organization demonstrates that the core is composed of a dense network of bent actin filaments storing elastic energy. Theoretical modelling of the network as a spring-loaded elastic material reveals that it exerts forces of a few tens of nanonewtons, in a range similar to that evaluated experimentally. Thus, taking into account not only the interface with the membrane but also the bulk of the network, is crucial to understand force generation by actin machineries. Our integrative approach sheds light on the elastic behavior of dense actin networks and opens new avenues to understand force production inside cells. Actin filaments generate force in diverse contexts, although how they can produce nanonewtons of force is unclear. Here, the authors apply cryo-electron tomography, quantitative analysis, and modelling to reveal the podosome core is a dense, spring-loaded, actin network storing elastic energy.
3D culture of cells in designer biomaterial matrices provides a biomimetic cellular microenvironment and can yield critical insights into cellular behaviours not available from conventional 2D cultures. Hydrogels with dynamic properties, achieved by incorporating either degradable structural components or reversible dynamic crosslinks, enable efficient cell adaptation of the matrix and support associated cellular functions. Herein we demonstrate that given similar equilibrium binding constants, hydrogels containing dynamic crosslinks with a large dissociation rate constant enable cell force-induced network reorganization, which results in rapid stellate spreading, assembly, mechanosensing, and differentiation of encapsulated stem cells when compared to similar hydrogels containing dynamic crosslinks with a low dissociation rate constant. Furthermore, the static and precise conjugation of cell adhesive ligands to the hydrogel subnetwork connected by such fast-dissociating crosslinks is also required for ultra-rapid stellate spreading (within 18 h post-encapsulation) and enhanced mechanosensing of stem cells in 3D. This work reveals the correlation between microscopic cell behaviours and the molecular level binding kinetics in hydrogel networks. Our findings provide valuable guidance to the design and evaluation of supramolecular biomaterials with cell-adaptable properties for studying cells in 3D cultures. 3D culture systems can provide critical insights into cellular behaviour. Here, the authors study the binding timescale of dynamic crosslinks and the conjugation stability of cell-adhesive ligands in cell–hydrogel network interactions to evaluate the impact on stem cell behaviour, mechanosensing and differentiation.
Clathrin-mediated endocytosis is an essential cellular function in all eukaryotes that is driven by a self-assembled macromolecular machine of over 50 different proteins in tens to hundreds of copies. How these proteins are organized to produce endocytic vesicles with high precision and efficiency is not understood. Here, we developed high-throughput superresolution microscopy to reconstruct the nanoscale structural organization of 23 endocytic proteins from over 100,000 endocytic sites in yeast. We found that proteins assemble by radially-ordered recruitment according to function. WASP family proteins form a circular nano-scale template on the membrane to spatially control actin nucleation during vesicle formation. Mathematical modeling of actin polymerization showed that this WASP nano-template creates sufficient force for membrane invagination and substantially increases the efficiency of endocytosis. Such nanoscale pre-patterning of actin nucleation may represent a general design principle for directional force generation in membrane remodeling processes such as during cell migration and division.
We study the model of growing filament against a wall proposed by Peskin, Odell, and Oster [Biophys. J. 65, 316 (1993)] using the ratio of chemical to diffusion timescales as a small expansion parameter. A detailed multiple-scale analysis allows us to fully describe the spatiotemporal evolution toward a steady-state distribution for the wall-tip distance, including chemical effects, in very good agreement with numerical simulations. Implications on the quasistatic approximation, where the force on the wall is allowed to vary slowly in time, are discussed. A corrected force-velocity relationship together with explicit expressions of the relevant timescales are provided.
The dynamic behavior of bundles of actin filaments growing against a loaded obstacle is investigated through a generalized version of the standard multifilament Brownian Ratchet model in which the (de)polymerizing filaments are treated not as rigid rods but as semiflexible discrete wormlike chains with a realistic value of the persistence length. By stochastic dynamic simulations, we study the relaxation of a bundle of Nf filaments with a staggered seed arrangement against a harmonic trap load in supercritical conditions. Thanks to the time scale separation between the wall motion and the filament size relaxation, mimicking realistic conditions, this setup allows us to extract a full load-velocity curve from a single experiment over the trap force/size range explored. We observe a systematic evolution of steady nonequilibrium states over three regimes of bundle lengths L. A first threshold length Λ marks the transition between the rigid dynamic regime (L < Λ), characterized by the usual rigid filament load-velocity relationship V(F), and the flexible dynamic regime (L > Λ), where the velocity V(F, L) is an increasing function of the bundle length L at a fixed load F, the enhancement being the result of an improved level of work sharing among the filaments induced by flexibility. A second critical length corresponds to the beginning of an unstable regime characterized by a high probability to develop escaping filaments which start growing laterally and thus do not participate anymore in the generation of the polymerization force. This phenomenon prevents the bundle from reaching at this critical length the limit behavior corresponding to perfect load sharing.
Cell migration is the physical movement of cells and is responsible for the extensive cellular invasion and metastasis that occur in high-grade tumors. Motivated by decades of direct observation of cell migration via light microscopy, theoretical models have emerged to capture various aspects of the fundamental physical phenomena underlying cell migration. Yet, the motility mechanisms actually used by tumor cells during invasion are still poorly understood, as is the role of cellular interactions with the extracellular environment. In this chapter, we review key physical principles of cytoskeletal self-assembly and force generation, membrane tension, biological adhesion, hydrostatic and osmotic pressures, and their integration in mathematical models of cell migration. With the goal of modeling-driven cancer therapy, we provide examples to guide oncologists and physical scientists in developing next-generation models to predict disease progression and treatment.
Previous chapters have dealt with the phenomenon centered on the structure and function of biological membranes. The lipid membrane is an essential structure that guarantees the steady state of the life in the ever-changing environment. Non-stop exchange of matters and information with the environment is a salient feature of the activity of living thing. The previous chapters describe various facts of these aspects. Voluntary movement is another remarkable feature of living things. Thus in Chap. 7, various types of biological motions are described. First, muscle contraction is briefly described, because it is one of the best known and studied example of the motor-based biological motions. Another well-studied example of the motor-based motion is the organelle transport; microscopic observations and analysis of the motion are described as examples. Motors related to the transport motility are briefly described and actin and microtubule tracks are described in some detail. The dynamism of the cell is largely depends on the dynamism of the system of actin filaments, microtubules and intermediate filaments. These filament systems are assembled or disassembled according to the needs of the cell, which is adopted in generating cellular movements. In the case of actin filaments and microtubules the movements such as lamellipodial protrusion, segregation of chromosomes and organelle transport, are driven. For these phenomena polymerization and depolymerization of the subunit of these polymers play essential roles. Thus, the polymerization/depolymerization-driven motions in the cell are one of the main theme of the last half of this chapter.
The gastrointestinal (GI) tract is composed of basic tissue types (epithelia, connective, blood, lymphatic, muscle, and nerve tissue) formed from different structural and functional units that determine fundamental life processes. This chapter provides detailed and contemporary information on the structural and functional characteristics of the cells that constitute the GI tract.
The plasmodium of Physarum polycephalum is very sensitive to its environment and reacts to stimuli by its appropriate motions. The sensitive stage as well as the motor stage of these reactions are explained by hydrodynamic processes, based on fluid dynamics, with participating of actin filament networks. This chapter is devoted to actin filament networks as a computation medium. The point is that actin filaments with a participating of many other proteins like myosin are sensitive to outer cellular stimuli (attractants as well as repellents) and they appear and disappear at different places of the cell to change the cell structure, e.g. its shape. Due to assembling and disassembling actin filaments, some unicellular organisms like Amoeba proteus can move in responses to different stimuli.
In various cellular processes, biofilaments like F-actin and F-tubulin are able to exploit chemical energy associated to polymerization to perform mechanical work against an external load. The force-velocity relationship quantitatively summarizes the nature of this process. By a stochastic dynamical model, we give, together with the evolution of a staggered bundle of $N_f$ rigid living filaments facing a loaded wall, the corresponding force--velocity relationship. We compute systematically the simplified evolution of the model in supercritical conditions $\rho_1=U_0/W_0>1$ at $\epsilon=d^2W_0/D=0$, where $d$ is the monomer size, $D$ is the obstacle diffusion coefficient, $U_0$ and $W_0$ are the polymerization and depolymerization rates. Moreover, we see that the solution at $\epsilon=0$ is valid for a good range of small non-zero $\epsilon$ values. We consider two classical protocols: the bundle is opposed either to a constant load or to an optical trap set-up, characterized by a harmonic restoring force. The constant force case leads, for each $F$ value, to a stationary velocity $V^{stat}(F;N_f,\rho_1)$ after a relaxation with characteristic time $\tau_{micro}(F)$. When the bundle (initially taken as an assembly of filament seeds) is subjected to a harmonic restoring force (optical trap load), the bundle elongates and the load increases up to stalling (equilibrium) over a characteristic time $\tau^{OT}$. Extracted from this single experiment, the force-velocity $V^{OT}(F;N_f,\rho_1)$ curve is found to coincide with $V^{stat}(F;N_f,\rho_1)$, except at low loads. We show that this result follows from the adiabatic separation between $\tau_{micro}$ and $\tau^{OT}$, i.e. $\tau_{micro}\ll\tau^{OT}$.
Making the right catch
Tension reveals cryptic vinculin-binding sites on α-catenin and talin at cadherin-based cell-cell and integrin-based cell-matrix adhesions, respectively. The enrichment of vinculin at cellular adhesions is thus an indicator of load-induced reinforcement of the cytoskeletal linkage. Huang et al. used a single-molecule optical trap assay to measure the binding lifetimes of vinculin to single actin filaments under load. The vinculin-F-actin interaction formed a directional catch bond—one that is very weak at low force but that greatly increases in lifetime with increasing force. This explains vinculin's role as a reinforcing linker at both cell-cell and cell-matrix adhesions.
Science , this issue p. 703
One of the major recurring themes in this symposium on Tissue Engineering is that to design effective artificial tissues, we must first understand the critical chemical and structural determinants that control tissue development. Current tissue engineering approaches commonly use cell attachment scaffolds that are complex composites of naturally occuring extracellular matrix (ECM) molecules (e.g., collagens, glycosaminoglycans). Unfortunately, these “artificial ECMs” are restricted from an engineering standpoint: they exhibit a limited range of structural and chemical properties and are not easily chemically modified. Also, their large-scale fabrication can be limited by “batch to batch” variability during purification of the individual ECM molecules. An alternative approach for cell transplantation is to develop a completely synthetic attachment foundation that can support a high degree of cell function and yet be highly biocompatible (Vacanti et al., 1988; Cima et al., 1991). To accomplish this objective, recent advances in ECM biology must be merged with new developments in bioengineering and polymer chemistry.
In the first six chapters of this book, we have examined a simple aggregation process that involves physical interactions only. There is no chemistry. These are termed “equilibrium aggregates.” Chapters 7 and 8 are more complicated in that we study the aggregation of enzyme molecules: in addition to the intermolecular (i.e., interenzyme) forces that produce the aggregation, the subunits of the polymer may be engaged in enzymatic activity. Such polymers are called1 “steady-state aggregates.”
We establish the statistical mechanics framework for a bundle of Nf living and uncrosslinked actin filaments in a supercritical solution of free monomers pressing against a mobile wall. The filaments are anchored normally to a fixed planar surface at one of their ends and, because of their limited flexibility, they grow almost parallel to each other. Their growing ends hit a moving obstacle, depicted as a second planar wall, parallel to the previous one and subjected to a harmonic compressive force. The force constant is denoted as the trap strength while the distance between the two walls as the trap length to make contact with the experimental optical trap apparatus. For an ideal solution of reactive filaments and free monomers at fixed free monomer
chemical potential
μ
1, we obtain the general expression for the grand potential from which we derive averages and distributions of relevant physical quantities, namely, the obstacle position, the bundle polymerization force, and the number of filaments in direct contact with the wall. The grafted living filaments are modeled as discrete Wormlike chains, with F-actin persistence length ℓp, subject to discrete contour length variations ±d (the monomer size) to model single monomer (de)polymerization steps. Rigid filaments (ℓp = ∞), either isolated or in bundles, all provide average values of the stalling force in agreement with Hill’s predictions FsH=NfkBTln(ρ1/ρ1c)/d, independent of the average trap length. Here ρ
1 is the density of free monomers in the solution and ρ
1c its critical value at which the filament does not grow nor shrink in the absence of external forces. Flexible filaments (ℓp < ∞) instead, for values of the trap strength suitable to prevent their lateral escape, provide an average bundle force and an average trap length slightly larger than the corresponding rigid cases (few percents). Still the stalling force remains nearly independent on the average trap length, but results from the product of two strongly L-dependent contributions: the fraction of touching filaments ∝〈L〉O.T.2 and the single filament buckling force ∝〈L〉O.T.−2.
The mitotic spindle is responsible for organized chromosome movement during cell division. The spindle is composed largely of microtubules (MTs) and their associated proteins, but the mechanisms by which these components interact to produce mitosis with a low frequency of error in chromosome segregation is still a subject of intensive investigation.
Neutrophils are defensive cells that are recruited from the blood into damaged or inflamed tissues by chemotactic agents. Ligand-receptor interactions at the cell surface elicit adhesion, locomotion, granule exocytosis, and the respiratory burst [Baggiolini and Kernen, 1992]. In vitro analysis shows that these responses are controlled at several levels of intracellular signal transduction processes. In this introduction we first review some of the biochemical events associated with these responses.
Thermodynamics and mechanics of active cell motion is a relatively recent area of research which is experiencing a transition that is brought by the rapid development of the field during the past decade. Roughly speaking, the transition is from collection of biological information from experiments and postulation of physical mechanisms through verbal arguements to quantitation of working hypotheses via mathematical equations and numerical computation of physical parameters. In this paper various biophysical and biochemical bases of active cell motions are briefly reviewed and some particular models are described.
IntroductionTemperature-Jump Strategy for Polymerization of Actin Encapsulated in VesiclesManipulation of Deformed VesiclesFuture Perspectives: Evolving Model Systems
Living cells are soft bodies of a characteristic form, but endowed with a capacity for a steady turnover of their structures. This dynamic character is the main difference between cells and most objects engineers are concerned with. Despite these dynamics, an overall shape can be maintained and structural continuity assures continuity of force transmission throughout ontogeny. Dynamics is the basis for the high reactivity of cells to internal and external signals. For instance, migrating cells colliding with others may either immediately change their direction of locomotion or they may adhere to each other and start to form an epithelium. Both events require structural reorganization. This is determined by three factors: (1) the commitment of the cell to a certain pattern of behavior controlled by the genetic material, (2) the mechanical constraints inherent in the cell structure itself, and (3) mechanical interaction of the cell with its environment. Therefore, continuity of tension transmission can be regarded as a form of information processing (Albrecht-Bühler 1985 and Chap. IV.2). A historical overview of the development of ideas on the “skeletal structures” in cells is given by Stossel et al. (Chap. II.5). The most consequent approach to such an understanding of cell architecture, at the present, is that of Ingber and Jamieson (1985) describing cells as tensegrity structures, i.e., structures which generate their own tensional forces and exhibit an architectural integrity independent of gravity. A discussion of whether their model holds true in detail for a description of cell architecture would excess the scope of these introductory remarks.
To explain how biological tissues form and function, we must first understand how different types of regulatory signals, both chemical and mechanical, integrate inside the cell. A clue to the mechanism of signal integration comes from recognition that the action of a force on any mass, regardless of scale, will result in a change in three dimensional structure. This is critical because recent studies reveal that many of the molecules that mediate signal transduction and stimulus-response coupling are physically bound to insoluble structural scaffoldings within the cytoskeleton and nucleus (Ingber 1993a). In this type of “solid-state” regulatory system, mechanically-induced structural arrangements could provide a mechanism for regulating cellular biochemistry and hence, efficiently integrating structure and function. However, this is a difficult question to address using conventional molecular biological approaches because this problem is not based on changes in chemical composition or local binding interactions. Rather, it is a question of architecture. As a result of this challenge, a new scientific discipline of “Molecular Cell Engineering” is beginning to emerge which combines elements of molecular cell biology, bioengineering, architecture, and biomechanics.
Exploring the mechanical features of biological cells, including their architecture and stability, this textbook is a pedagogical introduction to the interdisciplinary fields of cell mechanics and soft matter physics from both experimental and theoretical perspectives. This second edition has been greatly updated and expanded, with new chapters on complex filaments, the cell division cycle, the mechanisms of control and organization in the cell, and fluctuation phenomena. The textbook is now in full color which enhances the diagrams and allows the inclusion of new microscopy images. With more than 280 end-of-chapter exercises exploring further applications, this textbook is ideal for advanced undergraduate and graduate students in physics and biomedical engineering. A website hosted by the author contains extra support material, diagrams and lecture notes, and is available at www.cambridge.org/Boal.
We report here recent findings that multiple cytoskeletal filaments (assumed rigid) pushing an obstacle typically generate more force than just the sum of the forces due to individual ones. This interesting phenomenon, due to the hydrolysis process being out of equilibrium, escaped attention in previous experimental and theoretical literature. We first demonstrate this numerically within a constant force ensemble, for a well known model of cytoskeletal filament dynamics with random mechanism of hydrolysis. Two methods of detecting the departure from additivity of the collective stall force, namely from the force-velocity curve in the growing phase, and from the average collapse time versus force curve in the bounded phase, is discussed. Since experiments have already been done for a similar system of multiple microtubules in a harmonic optical trap, we study the problem theoretically under harmonic force. We show that within the varying harmonic force ensemble too, the mean collective stall force of N filaments is greater than N times the mean stall force due to a single filament; the actual extent of departure is a function of the monomer concentration.
The field of cell mechanics involves problems at the interface of mechanics, molecular transport, biochemical kinetics, thermodynamics and cell biology. We argue that chemical engineering training is uniquely suited for fruitful research in the field by discussing three examples in the research area. Cell mechanics is already well represented in many chemical engineering departments and promises to be a vibrant sub-area in the profession.
Colchicine blocks microtubule polymerization by an unusual substoichiometric poisoning mechanism. We have investigated the mechanism by which this poisoning occurs with several experimental approaches, and have found that colchicine acts by addition to microtubule ends as a colchicine-tubulin complex.
The basic kinetic and bioenergetic theory is outlined for two kinds of translocation on DNA: (i) helicases that use ATP to move along single-stranded DNA or to move on and invade double-stranded DNA at a replication fork; and (ii) DNA-binding proteins (not ATPases) that form bound aggregates on single-stranded DNA and facilitate replication by steady-state treadmilling of molecules between the ends of the aggregate. The respective resemblances to myosin--actin in muscle and to steady-state treadmilling in solution of actin or tubulin are pointed out.
In this report, we examine how the cell can selectively stabilize anchored filaments and suppress spontaneous filament assembly. Because microtubules and actin filaments have an organized distribution in cells, the cell must have a mechanism for suppressing spontaneous and random polymerization. Though the mechanism for suppressing spontaneous polymerization is unknown, an unusual property of these filaments has been demonstrated recently, i.e., under steady-stae conditions, in vitro actin filaments and microtubules can exhibit a flux of subunits through the polymers called "treadmilling." In vivo, however, most, if not all, of these polymers are attached at one end to specific structures and treadmilling should not occur. The function of treadmilling in vivo is, therefore, unclear at present. However, as shown here, the same physicochemical property of coupling assembly to ATP or GTP hydrolysis that leads to treadmilling in vitro can act to selectively stabilize anchored polymers in vivo. I show here that the theory of treadmilling implies that the concentration of subunits necessary for assembly of the nonanchored polymer will in general be higher than the concentration necessary for the assembly of polymers anchored with a specific polarity. This disparity in the monomer concentrations required for assembly can lead to a selective stabilization of anchored polymers and complete suppression of spontaneous polymerization at apparent equilibrium in vivo. It is possible, therefore, that the phenomenon of treadmilling is an in vitro manifestation of a mechanism designed to use ATP or GTP hydrolysis to control the spatial organization of filaments in the cell.
Microtubules are polar structures, and this polarity is reflected in their biased directional growth. Following a convention established previously (G. G. Borisy, 1978, J. Mol. Biol. 124:565--570), we define the plus (+) and minus (-) ends of a microtubule as those equivalent in structural orientation to the distal and proximal ends, respectively, of the A subfiber of flagellar outer doublets. Rates of elongation were obtained for both ends using flagellar axonemes as seeds and porcine brain microtubule protein as subunits. Since the two ends of a flagellar seed are distinguishable morphologically, elongation of each end may be analyzed separately. By plotting rates of elongation at various concentrations of subunit protein, we have determined the association and dissociation rate constants for the plus and minus ends. Under our conditions at 30 degrees C, the association constants were 7.2 X 10(6) M-1 s-1 and 2.25 X 10(6) M-1 s-1 for the plus and minus ends, respectively, and the dissociation constants were 17 s-1 and 7 s-1. From these values and Wegner's equations (1976, J. Mol. Biol. 108:139--150), we identified the plus end of the microtubule as its head and calculated "s," the head-to-tail polymerization parameter. Surprisingly small values (s = 0.07 +/- 0.02) were found. The validity of models of mitosis based upon head-to-tail polymerization (Margolis et al., 1978, Nature (Lond.) 272:450--452) are discussed in light of a small value for s.
Actins and myosins similar to the major proteins of muscle are the major molecular components of intricate mechanochemical systems that perform numerous vital motility and structural functions in all eukaryotic cells. In this article, after a brief summary of the morphological distribution and ultrastructure of actin, myosin, and interrelated proteins of nonmuscle cells, our present knowledge of their biochemistry is critically appraised from the perspective that understanding complex cellular processes depends ultimately on the identification, purification, and biochemical characterization of the proteins involved. Although few conclusions are reached, possible molecular mechanisms for cellular regulation of actin polymerization, filament association, actomyosin ATPase activity, and mechanochemical coupling are discussed and a number of potentially fruitful directions for further research are suggested. These include comparative biochemical investigations and the study of the interaction of heterologous proteins, but particular emphasis is given to the need for quantitative studies at the molecular level of motility proteins purified from a single cellular source.
The exchange of subunits at the ends of actin filaments was followed after addition of radioactively labelled actin monomers to solutions of polymeric actin. The incorporation and release of subunits can be explained by a polymerization mechanism in which the filaments grow at one end and shorten simultaneously at the other (head to tail polymerization). It is found that the net result of four association and four dissociation steps is a lengthening of the filament by one protomer at one end and a corresponding shortening at the other.The head to tail polymerization is made possible by the irreversible ATP dephosphorylation which is connected with the polymerization cycles of actin. This eliminates the restriction which is valid for a completely reversible association mechanism where the direction of growth is either outwards from or inwards to the centre at both ends of the aggregate.
In a previous paper, bioenergetic aspects of head-to-tail polymerization for a two-state actin ATPase cycle were discussed. In section 2, here, the steady-state polymer length distribution for this case is derived. The distribution has the same mathematical form as at equilibrium, but the parameters are different. In section 3, both bioenergetic topics and the polymer length distribution are considered for the more general and realistic case of a three-state actin ATPase cycle. Again, the mathematical form of the steady-state distribution is the same as at equilibrium, but the parameters are more complicated. In section 4, the question is examined of how much the mean and variance of a polymer length distribution, obtained from a finite experimental sample of polymer (aggregate) molecules, would be expected to deviate from the true mean and variance (from an infinite sample). Also considered briefly in section 4 is the effect of hard polymer-polymer interactions on the equilibrium polymer length distribution, at finite polymer concentrations.
Wegner's theory of steady-state head-to-tail polymerization of actin (or microtubules) is extended somewhat in order to show the explicit role of the ATP (or GTP) free energy of hydrolysis (X) in the steady-state kinetics. The monomer flux and the ATP flux can both be expressed in terms of X and rate constants of the model. Both fluxes approach zero as X leads to 0 (by variation of the concentrations of ATP, ADP, and Pi); this limit corresponds to ATP equilibrium. The dependence of rate constants on these concentrations is examined. Free energy levels of the monomer kinetic cycle and the rate of free energy dissipation are discussed. The steady-state polymer length distribution is derived for a special case.
corresponds to Ap. in the previous section, but Ap. is negative for values of c of interest
- Again Ap
Again Ap.. corresponds to Ap. in the previous section, but Ap.
is negative for values of c of interest. In fact,
Ap.+ Ap. = Apr.
[32]
- T L Hill
Hill, T. L. (1977) Free Energy Transduction in Biology (Academic, New York).
- A Wegner
Wegner, A. (1976)J. Mol Biol 108, 139-150.
26 becomes TdaS/dt = Jm(Ap.u + IF) + j 1() AFT (C C c)
- Eq Apa
ApA, Eq. 26 becomes
TdaS/dt = Jm(Ap.u + IF) + j 1() AFT (C C c). [3]