We investigate computationally the self-organization and contraction of an initially random actomyosin ring. In the framework of a detailed physical model for a ring of cross-linked actin filaments ...and myosin-II clusters, we derive the force balance equations and solve them numerically. We find that to contract, actin filaments have to treadmill and to be sufficiently cross linked, and myosin has to be processive. The simulations reveal how contraction scales with mechanochemical parameters. For example, they show that the ring made of longer filaments generates greater force but contracts slower. The model predicts that the ring contracts with a constant rate proportional to the initial ring radius if either myosin is released from the ring during contraction and actin filaments shorten, or if myosin is retained in the ring, while the actin filament number decreases. We demonstrate that a balance of actin nucleation and compression-dependent disassembly can also sustain contraction. Finally, the model demonstrates that with time pattern formation takes place in the ring, worsening the contractile process. The more random the actin dynamics are, the higher the contractility will be.
Phase plane dynamics of ERK phosphorylation Shvartsman, Stanislav Y.; McFann, Sarah; Wühr, Martin ...
The Journal of biological chemistry,
11/2023, Letnik:
299, Številka:
11
Journal Article
Recenzirano
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The extracellular signal–regulated kinase (ERK) controls multiple critical processes in the cell and is deregulated in human cancers, congenital abnormalities, immune diseases, and neurodevelopmental ...syndromes. Catalytic activity of ERK requires dual phosphorylation by an upstream kinase, in a mechanism that can be described by two sequential Michaelis-Menten steps. The estimation of individual reaction rate constants from kinetic data in the full mechanism has proved challenging. Here, we present an analytically tractable approach to parameter estimation that is based on the phase plane representation of ERK activation and yields two combinations of six reaction rate constants in the detailed mechanism. These combinations correspond to the ratio of the specificities of two consecutive phosphorylations and the probability that monophosphorylated substrate does not dissociate from the enzyme before the second phosphorylation. The presented approach offers a language for comparing the effects of mutations that disrupt ERK activation and function in vivo. As an illustration, we use phase plane representation to analyze dual phosphorylation under heterozygous conditions, when two enzyme variants compete for the same substrate.
Quartz crystal microbalance with dissipation monitoring (QCM-D) has become a major tool enabling accurate investigation of the adsorption kinetics of nanometric objects such as DNA fragments, ...polypeptides, proteins, viruses, liposomes, polymer, and metal nanoparticles. However, in liquids, a quantitative analysis of the experimental results is often intricate because of the complex interplay of hydrodynamic and adhesion forces varying with the physicochemical properties of adsorbates and functionalized QCM-D sensors. In the present paper, we dissect the role of hydrodynamics for the analytically tractable case of stiff contact, whereas the adsorbed rigid particles oscillate with the resonator without rotation. Under the assumption of the low surface coverage, we theoretically study the excess shear force exerted on the resonator, which has two contributions: (i) the fluid-mediated force due to flow disturbance created by the particle and (ii) the force exerted on the particle by the fluid and transmitted to the sensor via contact. The theoretical analysis enables an accurate interpretation of the QCM-D impedance measurements. It is demonstrated inter alia that for particles of the size comparable with protein molecules, the hydrodynamic force dominates over the inertial force and that the apparent mass derived from QCM independently of the overtone is about 10 times the Sauerbrey (inertial) mass. The theoretical results show excellent agreement with the results of experiments and advanced numerical simulations for a wide range of particle sizes and oscillation frequencies.
The Arp2/3 complex nucleates the formation of the dendritic actin network at the leading edge of motile cells, but it is still unclear if the Arp2/3 complex plays a critical role in lamellipodia ...protrusion and cell motility. Here, we differentiated motile fibroblast cells from isogenic mouse embryonic stem cells with or without disruption of the ARPC3 gene, which encodes the p21 subunit of the Arp2/3 complex. ARPC3(-/-) fibroblasts were unable to extend lamellipodia but generated dynamic leading edges composed primarily of filopodia-like protrusions, with formin proteins (mDia1 and mDia2) concentrated near their tips. The speed of cell migration, as well as the rates of leading edge protrusion and retraction, were comparable between genotypes; however, ARPC3(-/-) cells exhibited a strong defect in persistent directional migration. This deficiency correlated with a lack of coordination of the protrusive activities at the leading edge of ARPC3(-/-) fibroblasts. These results provide insights into the Arp2/3 complex's critical role in lamellipodia extension and directional fibroblast migration.
Myosin-powered force generation and contraction in nonmuscle cells underlies many cell biological processes and is based on contractility of random actin arrays. This contractility must rely on a ...microscopic asymmetry, the precise mechanism of which is not completely clear. A number of models of mechanical and structural asymmetries in actomyosin contraction have been posited. Here, we examine a contraction mechanism based on a finite size of myosin clusters and anisotropy of force generation by myosin heads at the ends of the myosin clusters. We use agent-based numerical simulations to demonstrate that if average lengths of actin filaments and myosin clusters are similar, then the proposed microscopic asymmetry leads to effective contraction of random 1D actomyosin arrays. We discuss the model’s implication for mechanics of contractile rings and stress fibers.
Mature mammalian oocytes are poised for completing meiosis II (MII) on fertilization by positioning the spindle close to an actomyosin-rich cortical cap. Here, we show that the Arp2/3 complex ...localizes to the cortical cap in a Ran-GTPase-dependent manner and nucleates actin filaments in the cortical cap and a cytoplasmic actin network. Inhibition of Arp2/3 activity leads to rapid dissociation of the spindle from the cortex. Live-cell imaging and spatiotemporal image correlation spectroscopy analysis reveal that actin filaments flow continuously away from the Arp2/3-rich cortex, driving a cytoplasmic streaming expected to exert a net pushing force on the spindle towards the cortex. Arp2/3 inhibition not only diminishes this actin flow and cytoplasmic streaming but also enables a reverse streaming driven by myosin-II-based cortical contraction, moving the spindle away from the cortex. Thus, the asymmetric MII spindle position is dynamically maintained as a result of balanced forces governed by the Arp2/3 complex.
Mammalian oocyte meiosis encompasses two rounds of asymmetric divisions to generate a totipotent haploid egg and, as by-products, two small polar bodies. Two intracellular events, asymmetric spindle ...positioning and cortical polarization, are critical to such asymmetric divisions. Actin but not microtubule cytoskeleton has been known to be directly involved in both events. Recent work has revealed a positive feedback loop between chromosome-mediated cortical activation and the Arp2/3-orchestrated cytoplasmic streaming that moves chromosomes. This feedback loop not only maintains meiotic II spindle position during metaphase II arrest, but also brings about symmetry breaking during meiosis I. Prior to an Arp2/3-dependent phase of fast movement, meiotic I spindle experiences a slow and non-directional first phase of migration driven by a pushing force from Fmn2-mediated actin polymerization. In addition to illustrating these molecular mechanisms, mathematical simulations are presented to elucidate mechanical properties of actin-dependent force generation in this system.
Movement of meiosis I (MI) chromosomes from the oocyte centre to a subcortical location is the first step in the establishment of cortical polarity. This is required for two consecutive rounds of ...asymmetric meiotic cell divisions, which generate a mature egg and two polar bodies. Here we use live-cell imaging and genetic and pharmacological manipulations to determine the force-generating mechanism underlying this chromosome movement. Chromosomes were observed to move toward the cortex in a pulsatile manner along a meandering path. This movement is not propelled by myosin-II-driven cortical flow but is associated with a cloud of dynamic actin filaments trailing behind the chromosomes/spindle. Formation of these filaments depends on the actin nucleation activity of Fmn2, a formin-family protein that concentrates around chromosomes through its amino-terminal region. Symmetry breaking of the actin cloud relative to chromosomes, and net chromosome translocation toward the cortex require actin turnover.
Theory of axisymmetric pendular rings Rubinstein, Boris Y.; Fel, Leonid G.
Journal of colloid and interface science,
03/2014, Letnik:
417, Številka:
417
Journal Article
Recenzirano
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•A full spectrum of solutions of Young-Laplace equation for liquid menisci is found.•The possible transitions between these menisci are described.•The menisci do not exist if their ...geometric parameters do not fit a specific region.
We present the theory of liquid bridges between two solids, sphere and plane, with prescribed contact angles. We give explicit expressions for curvature, volume and surface area of pendular ring as functions of the filling angle ψ for all available types of menisci: catenoid, sphere, cylinder, nodoid and unduloid (the meridional profile of the latter may have inflection points). There exists a rich set of solutions of the Young-Laplace equation for the shape of an axisymmetric meniscus of constant mean curvature. In case when the solids do not contact each other, these solutions extend Plateau’s sequence of meniscus evolution observed with increase of the liquid volume to include the unduloids at small filling angle, unduloids with multiple inflection points and multiple catenoids.
The Young-Laplace equation with boundary conditions can be viewed as a nonlinear eigenvalue problem. Its unduloid solutions, menisci shapes and curvatures Hns(ψ), exhibit a discrete spectrum and are enumerated by two indices: the number n of inflection points on the meniscus meridional profile M and the convexity index s=±1 determined by the shape of a segment of M contacting the solid sphere: the shape is either convex, s=1, or concave, s=-1.
For the fixed contact angles the set of the functions Hns(ψ) behaves in such a way that in the plane {ψ,H} there exists a bounded domain where Hns(ψ) do not exist for any distance between solids. The curves Hns(ψ) may be tangent to the boundary of domain which is a smooth closed curve. This topological representation allows to classify possible curves and introduce a saddle point notion. We observe several types of saddle points, and give their classification.
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