We present a theoretical and computational analysis of the rheology of networks made up of bundles of semiflexible filaments bound by transient cross-linkers. Such systems are ubiquitous in the cytoskeleton and can be formed in vitro using filamentous actin and various cross-linkers. We find that their high-frequency rheology is characterized by a scaling behavior that is quite distinct from that of networks of the well-studied single semiflexible filaments. This regime can be understood theoretically in terms of a length-scale-dependent bending modulus for bundles. Next, we observe new dissipative dynamics associated with the shear-induced disruption of the network at intermediate frequencies. Finally, at low frequencies, we encounter a region of non-Newtonian rheology characterized by power-law scaling. This regime is dominated by bundle dissolution and large-scale rearrangements of the network driven by equilibrium thermal fluctuations.
Regulation of stomata movements is crucial for plants ability to cope with their changing environment. Guard cells (GC) water potential directs water flux inside/outside this cell, which eventually is causing the stoma to open or close, respectively. Some of the osmolytes which accumulates in the GC cytoplasm and are known to play a role in stomata opening are sugars, arising from chloroplast starch degradation. During stomata closure, the accumulated osmolytes are removed from the GC cytoplasm. Surprisingly little is known about prevention of starch degradation and forming additional sugars which may interfere with osmotic changes that are necessary for correct closure of stomata. One of the early events leading to stomata closure is production of reactive oxygen species (ROS) in various sub-cellular sites and organelles of the stoma. Here we report that ROS production during abscisic acid (ABA) and methyl jasmonate (MJ) stimuli in Arabidopsis GC chloroplasts were more than tripled. Moreover, ROS were detected on the sub-organelle level in compartments that are typically occupied by starch grains. This observation leads us to suspect that ROS function in that particular location is necessary for stomata closure. We therefore hypothesize that these ROS are involved in redox control that lead to the inactivation of starch degradation that takes place in these compartments, thus contributing to the stoma closure in an additional way.
We study elasticity-driven morphological transitions of soft spherical core-shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus.
Phosphatidylinositol 5-phosphatases (5PTases) that hydrolyze the 5 position of the inositol ring are key components of membrane trafficking system. Recently, we reported that mutation in At5PTase7 gene reduced production of reactive oxygen species (ROS) and decreased expression of stress-responsive genes, resulting in increased salt sensitivity. Here, we describe an even more salt-sensitive 5ptase mutant, At5ptase9, which also hydrolyzes the 5 phosphate groups specifically from membrane-bound phosphatidylinositides. Interestingly, the mutants were more tolerant to osmotic stress. We analyzed the main cellular processes that may be affected by the mutation, such as production of ROS, influx of calcium, and induction of salt-response genes. The At5ptase9 mutants showed reduced ROS production and Ca(2+) influx, as well as decreased fluid-phase endocytosis. Inhibition of endocytosis by phenylarsine oxide or Tyrphostin A23 in wild-type plants blocked these responses. Induction of salt-responsive genes in wild-type plants was also suppressed by the endocytosis inhibitors. Thus, inhibition of endocytosis in wild-type plants mimicked the salt stress responses, observed in the At5ptase9 mutants. In summary, our results show a key non-redundant role of At5PTase7 and 9 isozymes, and underscore the localization of membrane-bound PtdIns in regulating plant salt tolerance by coordinating the endocytosis, ROS production, Ca(2+) influx, and induction of stress-responsive genes.
We determine the time- and force-dependent viscoelastic responses of reconstituted networks of microtubules that have been strongly crosslinked by biotin-streptavidin bonds. To measure the microscale viscoelasticity of such networks, we use a magnetic tweezers device to apply localized forces. At short time scales, the networks respond nonlinearly to applied force, with stiffening at small forces, followed by a reduction in the stiffening response at high forces, which we attribute to the force-induced unbinding of crosslinks. At long time scales, force-induced bond unbinding leads to local network rearrangement and significant bead creep. Interestingly, the network retains its elastic modulus even under conditions of significant plastic flow, suggesting that crosslinker breakage is balanced by the formation of new bonds. To better understand this effect, we developed a finite element model of such a stiff filament network with labile crosslinkers obeying force-dependent Bell model unbinding dynamics. The coexistence of dissipation, due to bond breakage, and the elastic recovery of the network is possible because each filament has many crosslinkers. Recovery can occur as long as a sufficient number of the original crosslinkers are preserved under the loading period. When these remaining original crosslinkers are broken, plastic flow results.
Microrheological studies of phospholipid monolayers, bilayers, and other Langmuir monolayer systems are traditionally performed by observing the thermal fluctuations of tracers attached to the membrane or interface. Measurements of this type obtain surface moduli that are orders of magnitude different from those obtained using macroscopic or active techniques. These large discrepancies can result from uncertainties in the tracers coupling to the monolayer or the local disruption of the monolayer by the tracer. To avoid such problems, we perform a microrheological experiment with the tracer particle placed at a known depth beneath the monolayer; this avoids the issues mentioned at the cost of generating a weaker, purely hydrodynamic coupling between the tracer and the monolayer. We calculate the appropriate response functions for this submerged particle microrheology and demonstrate the technique on three model monolayer systems.
We present a theory of flexural wave propagation on elastic shells having nontrivial geometry and develop an analogy to geometric optics. The transport of momentum within the shell itself is anisotropic due to the curvature, and as such complex classical effects such as birefringence are generically found. We determine the equations of reflection and refraction of such waves at boundaries between different local geometries, showing that waves are totally internally reflected, especially at boundaries between regions of positive and negative Gaussian curvature. We verify these effects by using finite element simulations and discuss the ramifications of these effects for the statistical mechanics of thin curved materials.
We studied the active transport of intracellular components along neuron processes using a new method developed in our laboratory: dispersion-relation phase spectroscopy. This method is able to quantitatively map spatially the heterogeneous dynamics of the concentration field of the cargos at submicron resolution without the need for tracking individual components. The results in terms of density correlation function reveal that the decay rate is linear in wavenumber, which is consistent with a narrow Lorentzian distribution of cargo velocity.
Plants possess remarkable ability to adapt to adverse environmental conditions. The adaptation process involves the removal of many molecules from organelles, especially membranes, and replacing them with new ones. The process is mediated by an intracellular vesicle-trafficking system regulated by phosphatidylinositol (PtdIns) kinases and phosphatases. Although PtdIns comprise a fraction of membrane lipids, they function as major regulators of stress signaling. We analyzed the role of PtdIns 5-phosphatases (5PTases) in plant salt tolerance. The Arabidopsis (Arabidopsis thaliana) genome contains 15 At5PTases. We analyzed salt sensitivity in nine At5ptase mutants and identified one (At5ptase7) that showed increased sensitivity, which was improved by overexpression. At5ptase7 mutants demonstrated reduced production of reactive oxygen species (ROS). Supplementation of mutants with exogenous PtdIns dephosphorylated at the D5 position restored ROS production, while PtdIns(4,5)P(2), PtdIns(3,5)P(2), or PtdIns(3,4,5)P(3) were ineffective. Compromised salt tolerance was also observed in mutant NADPH Oxidase, in agreement with the low ROS production and salt sensitivity of PtdIns 3-kinase mutants and with the inhibition of NADPH oxidase activity in wild-type plants. Localization of green fluorescent protein-labeled At5PTase7 occurred in the plasma membrane and nucleus, places that coincided with ROS production. Analysis of salt-responsive gene expression showed that mutants failed to induce the RD29A and RD22 genes, which contain several ROS-dependent elements in their promoters. Inhibition of ROS production by diphenylene iodonium suppressed gene induction. In summary, our results show a nonredundant function of At5PTase7 in salt stress response by regulating ROS production and gene expression.
The membranes of human red blood cells (RBCs) are a composite of a fluid lipid bilayer and a triangular network of semiflexible filaments (spectrin). We perform cellular microrheology using the dynamic membrane fluctuations of the RBCs to extract the elastic moduli of this composite membrane. By applying known osmotic stresses, we measure the changes in the elastic constants under imposed strain and thereby determine the nonlinear elastic properties of the membrane. We find that the elastic nonlinearities of the shear modulus in tensed RBC membranes can be well understood in terms of a simple wormlike chain model. Our results show that the elasticity of the spectrin network can mostly account for the area compression modulus at physiological osmolality, suggesting that the lipid bilayer has significant excess area. As the cell swells, the elastic contribution from the now tensed lipid membrane becomes dominant.
Plants activate a number of defense reactions in response to pathogen attack. One of the major pathways involves biosynthesis of Salicylic Acid (SA), which acts as a signaling molecule that regulates local defense reaction at the infection site and in induction of systemic acquired resistance (SAR). SA is sensed and transduced by NPR1 protein, which is a redox sensitive protein that acts as a central transcription activator of many pathogenesis related and defense related genes. In its uninduced state NPR1 exists as an oligomer in the cytoplasm. Following pathogen attack and SAR induction, cells undergo a biphasic change in cellular redox, resulting in reduction of NPR1 to a monomeric form,which moves to the nucleus. Recently, it was shown that pathogen attack or SA treatment cause S-nitrosylation of NPR1, promoting NPR1 oligomerization and restricting it in the cytoplasm. We used A. thaliana mutants in cytosolic ASCORBATE PEROXIDASE, apx1, and plants expressing antisense CATALASE gene, as well as the CATALASE inhibitor 3-amino-1,2,4-triazole, to examine the effect of H2O2 on the pathogen-triggered translocation of the NPR1 to the nucleus. Our results show that the pathogen-triggered or SA-induced nuclear translocation is prevented by accumulation of H2O2 in the cytosol. Moreover, we show that increased accumulation of cytoplasmic ROS in apx1 mutants reduced the NPR1-dependent gene expression. We suggest that H2O2 has a signaling role in pathogenesis, acting as a negative regulator of NPR1 translocation to the nucleus, limiting the NPR1-dependent gene expression.
This paper explores the effects of filament length polydispersity on the mechanical properties of semiflexible crosslinked polymer networks. Extending previous studies on monodisperse networks, we compute numerically the response of crosslinked networks of elastic filaments of bimodal and exponential length distributions. These polydisperse networks are subject to the same affine to nonaffine (A/NA) transition observed previously for monodisperse networks, wherein the decreases in either crosslink density or bending stiffness lead to a shift from affine, stretching-dominated deformations to nonaffine, bending-dominated deformations. We find that the onset of this transition is generally more sensitive to changes in the density of longer filaments than shorter filaments, meaning that longer filaments have greater mechanical efficiency. Moreover, in polydisperse networks, mixtures of long and short filaments interact cooperatively to generally produce a nonaffine mechanical response closer to the affine prediction than comparable monodisperse networks of either long or short filaments. Accordingly, the mechanical affinity of polydisperse networks is dependent on the filament length composition. Overall, length polydispersity has the effect of sharpening and shifting the A/NA transition to lower network densities. We discuss the implications of these results on experimental observation of the A/NA transition, and on the design of advanced materials.
Neuronal network behavior results from a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a simplified model, based on the proposal of Feldman and Del Negro (FDN) [Nat. Rev. Neurosci. 7, 232 (2006)], of the preBötzinger Complex, a small neuronal network that participates in the control of the mammalian breathing rhythm through periodic firing bursts. The dynamics of this randomly connected network of identical excitatory neurons differ from those of a uniformly connected one. Specifically, network connectivity determines the identity of emergent leader neurons that trigger the firing bursts. When neuronal desensitization is controlled by the number of input signals to the neurons (as proposed by FDN), the networks collective desensitization--required for successful burst termination--is mediated by k-core clusters of neurons.
The collapse dynamics of giant folds in a catanionic monolayer at the air-water interface are examined. A monolayer of dioctadecyldimethylammonium bromide (DODAB) and sodium dodecyl sulfate (SDS) in a 1:1 ratio is the system of study that previously was found to fold upon compression in a Langmuir trough. Carboxylate-coated polystyrene beads (1 microm diameter) are deposited and bound to the monolayer. Displacement of the beads is measured with epifluorescence microscopy and particle image velocimetry, yielding a measurement of the velocity of the monolayer around the fold. Reversibility is confirmed by measuring the amount of monolayer material entering and leaving the fold. Material near folds are found to have a maximum relative velocity on the order of 0.1 mm/s, and fold depths are found to be on the order of 1 mm. The folds exhibit regular unfolding behavior, which can be explained qualitatively by a simple mechanical model.
Stomatal closure during water stress is a major plant mechanism for reducing the loss of water through leaves. The opening and closure of stomata are mediated by endomembrane trafficking. The role of the vacuolar trafficking pathway, that involves v-SNAREs of the AtVAMP71 family (formerly called AtVAMP7C) in stomatal movements, was analysed. Expression of AtVAMP711-14 genes was manipulated in Arabidopsis plants with sense or antisense constructs by transformation of the AtVAMP711 gene. Antisense plants exhibited decreased stomatal closure during drought or after treatment with abscisic acid (ABA), resulting in the rapid loss of leaf water and tissue collapse. No improvement was seen in plants overexpressing the AtVAMP711 gene, suggesting that wild-type levels of AtVAMP711 expression are sufficient. ABA treatment induced the production of reactive oxygen species (ROS) in guard cells of both wild-type and antisense plants, indicating that correct hormone sensing is maintained. ROS were detected in nuclei, chloroplasts, and vacuoles. ABA treatment caused a significant increase in ROS-containing small vacuoles and also in plastids and nuclei of neighbouring epidermal and mesophyll cells. Taken together, our results show that VAMP71 proteins play an important role in the localization of ROS, and in the regulation of stomatal closure by ABA treatment. The paper also describes a novel aspect of ROS signalling in plants: that of ROS production in small vacuoles that are dispersed in the cytoplasm.
The human red blood cell (RBC) membrane, a fluid lipid bilayer tethered to an elastic 2D spectrin network, provides the principal control of the cells morphology and mechanics. These properties, in turn, influence the ability of RBCs to transport oxygen in circulation. Current mechanical measurements of RBCs rely on external loads. Here we apply a noncontact optical interferometric technique to quantify the thermal fluctuations of RBC membranes with 3 nm accuracy over a broad range of spatial and temporal frequencies. Combining this technique with a new mathematical model describing RBC membrane undulations, we measure the mechanical changes of RBCs as they undergo a transition from the normal discoid shape to the abnormal echinocyte and spherical shapes. These measurements indicate that, coincident with this morphological transition, there is a significant increase in the membranes shear, area, and bending moduli. This mechanical transition can alter cell circulation and impede oxygen delivery.
We study the mechanics of nematically ordered semiflexible networks showing that they, like isotropic networks, undergo an affine to nonaffine crossover controlled by the ratio of the filament length to the nonaffinity length. Deep in the nonaffine regime, however, these anisotropic networks exhibit a much more complex mechanical response characterized by a vanishing linear-response regime for highly ordered networks and a dependence of the shear modulus on shear direction at both small (linear) and finite (nonlinear) strains that is different from the affine prediction of orthotropic continuum linear elasticity. We show that these features can be understood in terms of a generalized floppy modes analysis of the nonaffine mechanics and a type of cooperative Euler buckling.
We determine the particulate transport properties of fluid membranes with nontrivial geometries that are surrounded by viscous Newtonian solvents. Previously, this problem in membrane hydrodynamics was discussed for the case of flat membranes by Saffman and Delbrück [P. G. Saffman and M. Delbrück, Proc. Natl. Acad. Sci. U.S.A. 72, 3111 (1975)]. We review and develop the formalism necessary to consider the hydrodynamics of membranes with arbitrary curvature and show that the effect of local geometry is twofold. First, local Gaussian curvature introduces in-plane viscous stresses even for situations in which the velocity field is coordinate-independent. Secondly, even in the absence of Gaussian curvature, the geometry of the membrane modifies the momentum transport between the bulk fluids and the membrane. We illustrate these effects by examining in detail the mobilities of particles bound to spherical and cylindrical membranes. These two examples provide experimentally testable predictions for particulate mobilities and membrane velocity fields on giant unilamellar vesicles and membrane tethers. Finally, we use the examples of spherical and cylindrical membranes to demonstrate how the global geometry and topology of the membrane influences the membrane velocities and the particle mobilities.
Legumes are unique in their ability to establish symbiotic interaction with rhizobacteria from Rhizobium genus, which provide them with available nitrogen. Nodulation factors (NFs) produced by Rhizobium initiate legume root hair deformation and curling that entrap the bacteria, and allow it to grow inside the plant. In contrast, legumes and non-legumes activate defense responses when inoculated with pathogenic bacteria. One major defense pathway is mediated by salicylic acid (SA). SA is sensed and transduced to downstream defense components by a redox-regulated protein called NPR1.
We present experimental measurements of the equilibrium elastic energy of protein-DNA chimeras, for two different sets of attachment points of the DNA "molecular spring" on the surface of the protein. Combining these with measurements of the enzymes activity under stress and a mechanical model of the system, we determine how the elastic energy is partitioned between the DNA and the protein. The analysis shows that the protein is mechanically stiffer than the DNA spring.
Recent experiments on molecular motor driven in vitro F-Actin networks have found anomalously large strain fluctuations at low frequency. In addition, the shear modulus of these active networks becomes as much as one hundred times larger than that of the same system in equilibrium. We develop a two-fluid model of a low-density semiflexible network driven by molecular motors to explore these effects and show that, relying on only simple assumptions regarding the motor activity in the system we can quantitatively understand both the low-frequency fluctuation enhancement and the nonequilibrium stiffening of the network. These results have implications for the interpretation of microrheology in such active networks including the cytoskeleton of living cells. In addition, they may form the basis for theoretical studies of biomimetic nonequilibrium gels whose mechanical properties are tunable through the control of their nonequilibrium steady-state.
Large scale, discrete element simulations are performed to study the dynamics of a rotating drum partially filled with cohesive granular particles. The continuous avalanche regime is explored using a simple model for interparticle cohesion in order to simulate the effects of granular media in the presence of a wetting fluid. The shape of the free surface for cohesionless particles ranges from flat to a concave S shape depending on the rotation rate and frictional properties between the grains and the drum side walls. The presence of interparticle cohesion reduces the concavity of the free surface and pushes the free surface towards a flat or even slightly convex shape. From contour plots of the velocity, we show how the position of the vortex core (the stationary spot in the laboratory frame) depends on the rotation speed and interparticle cohesion strength and how this relationship can be understood from considerations of the incompressibility condition on the mass flow.
Because of its ability to study specifically labeled structures, fluorescence microscopy is the most widely used technique for investigating live cell dynamics and function. Fluorescence correlation spectroscopy is an established method for studying molecular transport and diffusion coefficients at a fixed spatial scale. We propose a new approach, dispersion-relation fluorescence spectroscopy (DFS), to study the transport dynamics over a broad range of spatial and temporal scales. The molecules of interest are labeled with a fluorophore whose motion gives rise to spontaneous fluorescence intensity fluctuations that are analyzed to quantify the governing mass transport dynamics. These data are characterized by the effective dispersion relation. We report on experiments demonstrating that DFS can distinguish diffusive from advection motion in a model system, where we obtain quantitatively accurate values of both diffusivities and advection velocities. Because of its spatially resolved information, DFS can distinguish between directed and diffusive transport in living cells. Our data indicate that the fluorescently labeled actin cytoskeleton exhibits active transport motion along a direction parallel to the fibers and diffusive in the perpendicular direction.
We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double-stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single-stranded DNA chain. This construct, studied by H. Qu and G. Zocchi [Europhys. Lett. 94, 18003 (2011)], displays nonlinear strain softening associated with the local melting of the double-stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented wormlike chain model, the helix-coil wormlike chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented wormlike chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.
Leguminous plants have exclusive ability to form symbiotic relationship with soil bacteria of the genus Rhizobium. Symbiosis is a complex process that involves multiple molecular signaling activities, such as calcium fluxes, production of reactive oxygen species (ROS) and synthesis of nodulation genes. We analyzed the role of ROS in defense gene expression in Medicago truncatula during symbiosis and pathogenesis. Studies in Arabidopsis thaliana showed that the induction of pathogenesis-related (PR) genes during systemic acquired resistance (SAR) is regulated by NPR1 protein, which resides in the cytoplasm as an oligomer. After oxidative burst and return of reducing conditions, the NPR1 undergoes monomerization and becomes translocated to the nucleus, where it functions in PR genes induction. We show that ROS production is both stronger and longer during symbiotic interactions than during interactions with pathogenic, nonhost or common nonpathogenic soil bacteria. Moreover, root cells inoculated with Sinorhizobium meliloti accumulated ROS in the cytosol but not in vacuoles, as opposed to Pseudomonas putida inoculation or salt stress treatment. Furthermore, increased ROS accumulation by addition of H?O? reduced the PR gene expression, while catalase had an opposite effect, establishing that the PR gene expression is opposite to the level of cytoplasmic ROS. In addition, we show that salicylic acid pretreatment significantly reduced ROS production in root cells during symbiotic interaction.
The neurons of the neocortex show ~1-Hz synchronized transitions between an active up state and a quiescent down state. The up-down state transitions are highly coherent over large sections of the cortex, yet they are accompanied by pronounced, incoherent noise. We propose a simple model for the up-down state oscillations that allows analysis by straightforward dynamical systems theory. An essential feature is a nonuniform network geometry composed of groups of excitatory and inhibitory neurons with strong coupling inside a group and weak coupling between groups. The enhanced deterministic noise of the up state appears as the natural result of the proximity of a partial synchronization transition. The synchronization transition takes place as a function of the long-range synaptic strength linking different groups of neurons.
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