Self-organization of treadmilling filaments

The cytoskeleton is an active network of polar filaments. The activity can lead to the polymerization of filaments at one end and depolymerization at the other. This phenomenon is called treadmilling and is essential for many cellular processes, in particular, the crawling of cells on a substrate. We develop a microscopic theoretical framework for describing systems of treadmilling filaments. We show that such systems can self-organize into structures observed in cell fragments, in particular, asters and moving spots.     

Dynamics and mechanics of motor-filament systems

Motivated by the cytoskeleton of eukaryotic cells, we develop a general framework for describing the large-scale dynamics of an active filament network. In the cytoskeleton, active cross-links are formed by motor proteins that are able to induce relative motion between filaments. Starting from pair-wise interactions of filaments via such active processes, our framework is based on momentum conservation and an analysis of the momentum flux. This allows us to calculate the stresses in the filament network generated by the action of motor proteins. We derive effective theories for the filament dynamics which can be related to continuum theories of active polar gels. As an example, we discuss the stability of homogenous isotropic filament distributions in two spatial dimensions.     

Cytoskeleton Dynamics: A Continuum Cooperative Hydrolysis Model

Cytoskeleton is a network of filamentous proteins, such as actin filaments and microtubules. We propose a continuum cooperative hydrolysis model which possesses exactly analytical solution to describe the dynamics of filament.The results show that the cooperativity leads to non negative-exponential distribution of T(ATP or GTP) subunits.As an application, we investigate the treadmilling phenomenon using our model. It is shown that the cooperativity remarkably affects the length of filament.     

Driven Diffusive Systems of Active Filament Bundles

The cytoskeleton is an important subsystem of cells that is involved for example in cell division and locomotion. It consists of filaments that are cross-linked by molecular motors that can induce relative sliding between filaments and generate stresses in the network. In order to study the effects of fluctuations on the dynamics of such a system we introduce here a new class of driven diffusive systems mimicking the dynamics of active filament bundles where the filaments are aligned with respect to a common axis. After introducing the model class we first analyze an exactly solvable case and find condensation. For the general case we perform a mean-field analysis and study the behavior on large length scales by coarse-graining. We determine conditions for condensation and establish a relation between the hopping rates and the tension generated in the bundle.     

Generic theory of active polar gels: a paradigm for cytoskeletal dynamics

We develop a general theory for active viscoelastic materials made of polar filaments. This theory is motivated by the dynamics of the cytoskeleton. The continuous consumption of a fuel leads to a non equilibrium state characterized by the generation of flows and stresses. Our theory can be applied to experiments in which cytoskeletal patterns are set in motion by active processes such as those which are at work in cells.     

Asters, vortices, and rotating spirals in active gels of polar filaments

We develop a general theory for active viscoelastic materials made of polar filaments. This theory is motivated by the dynamics of the cytoskeleton. The continuous consumption of a fuel generates a nonequilibrium state characterized by the generation of flows and stresses. Our theory applies to any polar system with internal energy consumption such as active chemical gels and cytoskeletal networks which are set in motion by active processes at work in cells.     

Johnson-Kendall-Roberts theory applied to living cells

Johnson-Kendall-Roberts (JKR) theory is an accurate model for strong adhesion energies of soft slightly deformable material. Little is known about the validity of this theory on complex systems such as living cells. We have addressed this problem using a depletion controlled cell adhesion and measured the force necessary to separate the cells with a micropipette technique. We show that the cytoskeleton can provide the cells with a 3D structure that is sufficiently elastic and has a sufficiently low deformability for JKR theory to be valid. When the cytoskeleton is disrupted, JKR theory is no longer applicable.     

用表面微纳米技术研究细胞水平的生物力学

文章介绍了作者所在的实验小组近年来在用表面微纳米技术研究细胞生物学方面取得的进展.由于细胞的尺寸在数微米到数十微米之间,应用微纳米技术可以精细地调控细胞微观环境.作者所在的实验小组应用微流控系统以及表面化学修饰等方法,对细胞正常行为和病理行为进行了一系列研究.通过设计力学刺激装置,对细胞骨架的主要成分———肌动蛋白对细...     

Inside view of cell locomotion through single-molecule: fast F-/G-actin cycle and G-actin regulation of polymer restoration

The actin cytoskeleton drives cell locomotion and tissue remodeling. The invention of live-cell fluorescence single-molecule imaging opened a window for direct viewing of the actin remodeling processes in the cell. Since then, a number of unanticipated molecular functions have been revealed. One is the mechanism of F-actin network breakdown. In lamellipodia, one third of newly polymerized F-actin disassembles within 10 seconds. This fast F-actin turnover is facilitated by the filament severing/disrupting activity involving cofilin and AIP1. Astoundingly fast dissociation kinetics of the barbed end interactors including capping protein suggests that F-actin turnover might proceed through repetitive disruption/reassembly of the filament near the barbed end. The picture of actin polymerization is also being revealed. At the leading edge of the cell, Arp2/3 complex is highly activated in a narrow edge region. In contrast, mDia1 and its related Formin homology proteins display a long-distance directional molecular movement using their processive actin capping ability. Recently, these two independently-developed projects converged into a discovery of the spatiotemporal coupling between mDia1-mediated filament nucleation and actin disassembly. Presumably, the local concentration fluctuation of G-actin regulates the actin nucleation efficiency of specific actin nucleators including mDia1. Pharmacological perturbation and quantitative molecular behavior analysis synergize to reveal hidden molecular linkages in the actin turnover cycle and cell signaling.     

Measurement of fiber diameter using an edge diode beam of light

The possibility of utilizing an edge diode as a source of light in shadow technique for filament diameter measurement is presented. The diode light beam is scanned across a filament by means of an oscillating optical assembly. The displacement of the scanning assembly when the beam intercepts the filament and casts a shadow on a photodetector is a measure of the outside diameter of the filament. The metrological properties of the method are presented. The inaccuracy of the technique is smaller than ±0.6 μm, in an acceptable range of the fiber lateral displacement equal to about 1 mm.     

Filamin cross-linked semiflexible networks: fragility under strain

The semiflexible F-actin network of the cytoskeleton is cross-linked by a variety of proteins including filamin, which contains Ig domains that unfold under applied tension. We examine a simple filament network model cross-linked by such unfolding linkers that captures the main mechanical features of F-actin networks cross-linked by filamin proteins and show that, under sufficient strain, the network spontaneously self-organizes so that an appreciable fraction of the filamin cross-linkers are at the threshold of domain unfolding. We propose and test a mean-field model to account for this effect. We also suggest a qualitative experimental signature of this type of network reorganization under applied strain that may be observable in intracellular microrheology experiments of Crocker et al.     

Physics of cell elasticity,shape and adhesion

We review recent theoretical work that analyzes experimental measurements of the shape, fluctuations and adhesion properties of biological cells. Particular emphasis is placed on the role of the cytoskeleton and cell elasticity and we contrast the shape and adhesion of elastic cells with fluid-filled vesicles. In red blood cells (RBC), the cytoskeleton consists of a two-dimensional network of spectrin proteins. Our analysis of the wavevector and frequency dependence of the fluctuation spectrum of RBC indicates that the spectrin network acts as a confining potential that reduces the fluctuations of the lipid bilayer membrane. However, since the cytoskeleton is only sparsely connected to the bilayer, one cannot regard the composite cytoskeleton–membrane as a polymerized object with a shear modulus. The sensitivity of RBC fluctuations and shapes to ATP concentration may reflect topological defects induced in the cytoskeleton network by ATP. The shapes of cells that adhere to a substrate are strongly determined by the cytoskeletal elasticity that can be varied experimentally by drugs that depolymerize the cytoskeleton. This leads to a tension-driven retraction of the cell body and a pearling instability of the resulting ray-like protrusions. Recent experiments have shown that adhering cells exert polarized forces on substrates. The interactions of such “force dipoles” in either bulk gels or on surfaces can be used to predict the nature of self-assembly of cell aggregates and may be important in the formation of artificial tissues. Finally, we note that cell adhesion strongly depends on the forces exerted on the adhesion sites by the tension of the cytoskeleton. The size and shape of the adhesion regions are strongly modified as the tension is varied and we present an elastic model that relates this tension to deformations that induce the recruitment of new molecules to the adhesion region. In all these examples, cell shape and adhesion differ from vesicle shape and adhesion due to the presence of the elastic cytoskeleton and to the fact that active processes (ATP, molecular motors) within the cell modify cytoskeletal elasticity and tension.     

Instabilities of isotropic solutions of active polar filaments

We study the dynamics of an isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for constant motor concentration taking into account excluded volume and an estimate of entanglement. At low filament density the system develops a density instability, while at high density entanglement drives the instability of orientational fluctuations.     

Steady state dynamics of a moving model cell

Crawling cell motility results due to treadmilling of a polymerized actin network at the leading edge. Steady state dynamics of a moving cell are governed by actin concentration profiles across the cell. Branching of new filaments implicating Arp2/3 and capping of existing filaments with capZ or Gelsolin are central to the robust functioning of the actin network. Using computer simulations, steady state concentration profiles of globular actin (G actin) and filamentous actin (F actin) are computed. The profiles are in agreement with experimentally observed ones. Simulations unveil that there is an optimal capping and branching rate for which the velocity of the model cell is maximum. Our simulations also indicate that the capping of actin filaments results in an increase in nucleation of new filaments by Arp2/3-induced branching and is in agreement with a recently observed monomer gating model. We observe that Arp2/3 and capping protein exhibit a functional antagonism with respect to the actin network treadmilling.     

Motor-driven bacterial flagella and buckling instabilities

Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff’s elastic-rod theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum in space and show that it buckles under the thrust force at a critical motor torque. Buckling becomes visible as a supercritical Hopf bifurcation in the thrust force. A second buckling transition occurs at an even higher motor torque. We attach the flagellum to a spherical cell body and also observe the first buckling transition during locomotion. By changing the size of the cell body, we vary the necessary thrust force and thereby obtain a characteristic relation between the critical thrust force and motor torque. We present a elaborate analytical model for the buckling transition based on a helical rod which quantitatively reproduces the critical force-torque relation. Real values for motor torque, cell body size, and the geometry of the helical filament suggest that buckling should occur in single bacterial flagella. We also find that the orientation of pulling flagella along the driving torque is not stable and comment on the biological relevance for marine bacteria.     

Thermal and non-thermal fluctuations in active polar gels

We discuss general features of noise and fluctuations in active polar gels close to and away from equilibrium. We use the single-component hydrodynamic theory of active polar gels built by Kruse and coworkers to describe the cytoskeleton in cells. Close to equilibrium, we calculate the response function of the gel to external fields and introduce Langevin forces in the constitutive equations with correlation functions respecting the fluctuation-dissipation theorem. We then discuss the breakage of the fluctuation-dissipation theorem due to an external field such as the activity of the motors. Active gels away from equilibrium are considered at the scaling level. As an example of application of the theory, we calculate the density correlation function (the dynamic structure factor) of a compressible active polar gel and discuss possible instabilities.     

Elementary excitations of biomembranes: Differential geometry of undulations in elastic surfaces

Biomembrane undulations are elementary excitations in the elastic surfaces of cells and vesicles. As such they can provide surprising insights into the mechanical processes that shape and stabilize biomembranes. We explain how naturally these undulations can be described by classical differential geometry. In particular, we apply the analytical formalism of differential-geometric calculus to the surfaces generated by a cell membrane and underlying cytoskeleton. After a short derivation of the energy due to a membrane's elasticity, we show how undulations arise as elementary excitations originating from the second derivative of an energy functional. Furthermore, we expound the efficiency of classical differential-geometric formalism to understand the effect of differential operators that characterize processes involved in membrane physics. As an introduction to concepts the paper is self-contained and rarely exceeds calculus level.     

Formalising the Pathways to Life Using Assembly Spaces

Assembly theory (referred to in prior works as pathway assembly) has been developed to explore the extrinsic information required to distinguish a given object from a random ensemble. In prior work, we explored the key concepts relating to deconstructing an object into its irreducible parts and then evaluating the minimum number of steps required to rebuild it, allowing for the reuse of constructed sub-objects. We have also explored the application of this approach to molecules, as molecular assembly, and how molecular assembly can be inferred experimentally and used for life detection. In this article, we formalise the core assembly concepts mathematically in terms of assembly spaces and related concepts and determine bounds on the assembly index. We explore examples of constructing assembly spaces for mathematical and physical objects and propose that objects with a high assembly index can be uniquely identified as those that must have been produced using directed biological or technological processes rather than purely random processes, thereby defining a new scale of aliveness. We think this approach is needed to help identify the new physical and chemical laws needed to understand what life is, by quantifying what life does.