Neural decision boundaries for maximal information transmission

We consider here how to separate multidimensional signals into two categories, such that the binary decision transmits the maximum possible information about those signals. Our motivation comes from the nervous system, where neurons process multidimensional signals into a binary sequence of responses (spikes). In a small noise limit, we derive a general equation for the decision boundary that locally relates its curvature to the probability distribution of inputs. We show that for Gaussian inputs the optimal boundaries are planar, but for non-Gaussian inputs the curvature is nonzero. As an example, we consider exponentially distributed inputs, which are known to approximate a variety of signals from natural environment.     

Mechanisms of negative membrane curvature sensing and generation by ESCRT III subunit Snf7

Certain proteins have the propensity to bind to negatively curved membranes and generate negative membrane curvature. The mechanism of action of these proteins is much less studied and understood than those that sense and generate positive curvature. In this work, we use implicit membrane modeling to explore the mechanism of an important negative curvature sensing and generating protein: the main ESCRT III subunit Snf7. We find that Snf7 monomers alone can sense negative curvature and that curvature sensitivity increases for dimers and trimers. We have observed spontaneous bending of Snf7 oligomers into circular structures with preferred radius of ~20 nm. The preferred curvature of Snf7 filaments is further confirmed by the simulations of preformed spirals on a cylindrical membrane surface. Snf7 filaments cannot bind with the same interface to flat and curved membranes. We find that even when a filament has the preferred radius, it is always less stable on the flat membrane surface than on the interior cylindrical membrane surface. This provides an additional energy for membrane bending which has not been considered in the spiral spring model. Furthermore, the rings on the cylindrical spirals are bridged together by helix 4 and hence are extra stabilized compared to the spirals on the flat membrane surface.     

Understanding Nucleotide-Regulated FtsZ Filament Dynamics and the Monomer Assembly Switch with Large-Scale Atomistic Simulations

Bacterial cytoskeletal protein FtsZ assembles in a head-to-tail manner, forming dynamic filaments that are essential for cell division. Here, we study their dynamics using unbiased atomistic molecular simulations from representative filament crystal structures. In agreement with experimental data, we find different filament curvatures that are supported by a nucleotide-regulated hinge motion between consecutive FtsZ monomers. Whereas GTP-FtsZ filaments bend and twist in a preferred orientation, thereby burying the nucleotide, the differently curved GDP-FtsZ filaments exhibit a heterogeneous distribution of open and closed interfaces between monomers. We identify a coordinated Mg²⁺ ion as the key structural element in closing the nucleotide site and stabilizing GTP filaments, whereas the loss of the contacts with loop T7 from the next monomer in GDP filaments leads to open interfaces that are more prone to depolymerization. We monitored the FtsZ monomer assembly switch, which involves opening/closing of the cleft between the C-terminal domain and the H7 helix, and observed the relaxation of isolated and filament minus-end monomers into the closed-cleft inactive conformation. This result validates the proposed switch between the low-affinity monomeric closed-cleft conformation and the active open-cleft FtsZ conformation within filaments. Finally, we observed how the antibiotic PC190723 suppresses the disassembly switch and allosterically induces closure of the intermonomer interfaces, thus stabilizing the filament. Our studies provide detailed structural and dynamic insights into modulation of both the intrinsic curvature of the FtsZ filaments and the molecular switch coupled to the high-affinity end-wise association of FtsZ monomers.     

Understanding Nucleotide-Regulated FtsZ Filament Dynamics and the Monomer Assembly Switch with Large-Scale Atomistic Simulations

Bacterial cytoskeletal protein FtsZ assembles in a head-to-tail manner, forming dynamic filaments that are essential for cell division. Here, we study their dynamics using unbiased atomistic molecular simulations from representative filament crystal structures. In agreement with experimental data, we find different filament curvatures that are supported by a nucleotide-regulated hinge motion between consecutive FtsZ monomers. Whereas GTP-FtsZ filaments bend and twist in a preferred orientation, thereby burying the nucleotide, the differently curved GDP-FtsZ filaments exhibit a heterogeneous distribution of open and closed interfaces between monomers. We identify a coordinated Mg²⁺ ion as the key structural element in closing the nucleotide site and stabilizing GTP filaments, whereas the loss of the contacts with loop T7 from the next monomer in GDP filaments leads to open interfaces that are more prone to depolymerization. We monitored the FtsZ monomer assembly switch, which involves opening/closing of the cleft between the C-terminal domain and the H7 helix, and observed the relaxation of isolated and filament minus-end monomers into the closed-cleft inactive conformation. This result validates the proposed switch between the low-affinity monomeric closed-cleft conformation and the active open-cleft FtsZ conformation within filaments. Finally, we observed how the antibiotic PC190723 suppresses the disassembly switch and allosterically induces closure of the intermonomer interfaces, thus stabilizing the filament. Our studies provide detailed structural and dynamic insights into modulation of both the intrinsic curvature of the FtsZ filaments and the molecular switch coupled to the high-affinity end-wise association of FtsZ monomers.     

On the role of membrane anisotropy and BAR proteins in the stability of tubular membrane structures

Recent studies have demonstrated that actin filaments are not crucial for the short-term stability of tubular membrane protrusions originating from the cell surface. It has also been demonstrated that prominin nanodomains and curvature inducing I-BAR proteins could account for the stability of the membrane protrusion. Here we constructed an axisymmetric model of a membrane protrusion that excludes actin filaments in order to investigate the contributions of prominin nanodomains (rafts) and I-BAR proteins to the membrane protrusion stability. It was demonstrated that prominin nanodomains and I-BAR proteins can stabilize the membrane protrusion only over a specific range of spontaneous curvature. On the other hand, high spontaneous curvature and/or high density of I-BAR proteins could lead to system instability and to non-uniform contraction in the radial direction of the membrane protrusion. In agreement with previous studies, it was also shown that the isotropic bending energy of lipids is not sufficient to explain the stability of the observed tubular membrane protrusion without actin filaments.     

Distribution of an asymmetrical copepod, Hatschekia plectropomi, on the gills of Plectropomus leopardus

Hatschekia plectropomi , an ectoparasitic copepod found on the gills, infected Plectropomus leopardus from Heron Island Reef with 100% prevalence ( n  = 32) and a mean ±  s . e . infection intensity of 131·9 ± 22·1. The distribution of 4222 adult female parasites across 32 individual host fish was investigated at several organizational levels ranging from the level of holobranch pairs to that of individual filaments. Parasites demonstrated a site preference for the two central holobranchs (2 and 3). Along the lengths of hemibranchs, filaments near the dorsal and ventral ends and those in the proximity of the bend region were rarely occupied. The probability of coming into contact with a suitable attachment site and the ability to withstand ventilation forces at that site were proposed as the major factors affecting distribution. Two H. plectropomi morphotypes were identified based on the direction of body curvature. Regardless of morphotype, 99·9% of individuals were attached such that the convex side of the body was oriented towards the oncoming ventilating water currents. Further, 93·3% of individuals attached to the posterior faces of filaments, leading to a predictable pattern of attachment for this species. It is suggested that the direction of body curvature develops in response to the direction of the ventilating water currents.     

Measurement of the persistence length of cytoskeletal filaments using curvature distributions

Cytoskeletal filaments, such as microtubules and actin filaments, play important roles in the mechanical integrity of cells and the ability of cells to respond to their environment. Measuring the mechanical properties of cytoskeletal structures is crucial for gaining insight into intracellular mechanical stresses and their role in regulating cellular processes. One of the ways to characterize these mechanical properties is by measuring their persistence length, the average length over which filaments stay straight. There are several approaches in the literature for measuring filament deformations, such as Fourier analysis of images obtained using fluorescence microscopy. Here, we show how curvature distributions can be used as an alternative tool to quantify biofilament deformations, and investigate how the apparent stiffness of filaments depends on the resolution and noise of the imaging system. We present analytical calculations of the scaling curvature distributions as a function of filament discretization, and test our predictions by comparing Monte Carlo simulations with results from existing techniques. We also apply our approach to microtubules and actin filaments obtained from in vitro gliding assay experiments with high densities of nonfunctional motors, and calculate the persistence length of these filaments. The presented curvature analysis is significantly more accurate compared with existing approaches for small data sets, and can be readily applied to both in vitro and in vivo filament data through the use of the open-source codes we provide.     

Mechanical and structural properties of in vitro neurofilament hydrogels

Neurofilaments belong to the class of cytoskeletal intermediate filaments and are the predominant structural elements in axons. They are composed of a semiflexible backbone and highly charged anionic sidearms protruding from the surface of the filaments. Here, the rheology of in-vitro networks of neurofilaments purified from pig spinal cord was determined. The mechanical properties of these networks are qualitatively similar to other hydrogels of semiflexible polymers. The low-deformation storage modulus G'(omega) showed a concentration (c) dependence of G' approximately c (1.3) that is consistent with a model for semiflexible networks, but was also observed for polyelectrolyte brushes. A terminal relaxation was not observed in the frequency range investigated (0.007-5 Hz), supporting the notion that sidearms act as cross-links hindering slip between filaments on a time scale of many minutes. The mesh size distribution of the network was measured by analysis of Brownian motion of embedded beads. The concentration dependence of the mesh size follows the same power law behaviour as found for F-actin networks, but shows a significantly wider distribution attributable to the smaller persistence length of neurofilaments. The attractive interaction between filaments is increased by addition of Al(3+) ions resulting in a reduction of the linear response regime from strains bigger than 80% to less than 30%.     

FINE STRUCTURE AND SIZE DISTRIBUTION OF FREE THICK FILAMENTS IN EARLY FIBRILLOGENESIS OF ASCIDIAN TADPOLE

The development and the size distribution of free thick filaments which accumulate in the early stages of myofibril formation in somitic myoblasts of the ascidian tadpole were studied by electron microscopy. Such filaments appeared in the cell cortex but, rather dominantly, the aggregates of these thick filaments and filamentous structures were observed in the interior of the cell. The aggregate consisted of some of the following elements: filamentous structures (20–60 A in diameter); free thick filaments (60–220 A); dense Z-band precursor materials; bundles of thick (140–160 A) and thin (60–70 A) filaments; and ribosomal clusters. The free thick filaments were variable in diameter and showed long lateral projections (300–600 A) and tapered ends.
The variation curve in diameter of the free thick filaments indicates a continuous size distribution, suggesting the continuous growth of these filaments by polymerization of myosin molecules. Free thick filaments thicker than myosin filaments which were found within myofibrils were present; their significance is discussed in relation to myosin filament formation.     

Morphological Aspects of Ciliary Motility

In Elliptio complanatus lateral cilia, two distinct patterns of filament termination can be discerned. In one case, all nine filaments are present and all are single; in the second, at least one filament is missing but doublets are still present. These probably represent different configurations within one cilium in different stroke positions; to get from one to the other, some peripheral filaments must move with respect to others. The data are consistent with the hypothesis that the filaments themselves do not change length, but rather slide past one another to accommodate increasing curvature. The bent regions of the cilium are in the form of circular arcs. In a few cases, apparent displacement of filaments at the tip (Δl) can be shown to be accounted for if we assume that all differences are generated within these arcs. The displacement per degree of bend is 35 A. Regions of bent arc are initially confined to the base of the cilium but move up the shaft as straight regions appear below them. From the relationship between arc length and radius of curvature, a shaft length that is the unit that initially bends and slides may be defined. Quantal displacements of the length of one 14S dynein may perhaps occur at sites between filaments at opposite sides of such a unit as sliding occurs.     

Heavy meromyosin labeling of intermediate filaments in cultured connective tissue cells

Mild treatment with trypsin causes a radical change in the heavy meromyosin (HMM) binding properties of intermediate filaments in glycerinated, myosin-extracted cultured chick embryo connective tissue cells. In non-trypsin-treated cells, HMM labeling of filaments was often indistinct and variable in its distribution. By contrast, in cells treated with trypsin (under conditions which allowed most intermediate filaments to survive), virtually all filaments, including those of intermediate size, decorated with HMM to give distinct arrowhead patterns. We suggest that most intermediate filaments in such cells contain a core of F-actin masked by trypsin-labile accessory proteins.     

Vesicle size distributions measured by flow field-flow fractionation coupled with multiangle light scattering.

The separation method, flow field-flow fractionation (flow FFF), is coupled on-line with multiangle laser light scattering (MALLS) for simultaneous measurement of the size and concentration of vesicles eluting continuously from the fractionator. These size and concentration data, gathered as a function of elution time, may be used to construct both number- and mass-weighted vesicle size distributions. Unlike most competing, noninvasive methods, this flow FFF/MALLS technique enables measurement of vesicle size distributions without a separate refractive index detector, calibration using particle size standards, or prior assumptions about the shape of the size distribution. Experimentally measured size distributions of vesicles formed by extrusion and detergent removal are non-Gaussian and are fit well by the Weibull distribution. Flow FFF/MALLS reveals that both the extrusion and detergent dialysis vesicle formation methods can yield nearly size monodisperse populations with standard deviations of approximately 8% about the mean diameter. In contrast to the rather low resolution of dynamic light scattering in analyzing bimodal systems, flow FFF/MALLS is shown to resolve vesicle subpopulations that differ by much less than a factor of two in mean size.     

Gravitropism and gravimorphism during regeneration from protoplasts of the moss Ceratodon purpureus (Hedw.) Brid.

Wild-type (WT) protonemata of the moss Ceratodon purpureus grow upwards in darkness (negative gravitropism), whereas protonemata of the mutant, wrong-way response (wwr-1) grow down. Since Ceratodon protoplasts regenerate to form new protonemata, we analyzed whether the direction of filament emergence was influenced by gravity (gravimorphism) and determined the cytological events that correlated with the onset of gravitropism in WT and wwr-1 filaments formed de novo. In the WT the direction of filament emergence appeared to be gravimorphic as more than 66% of the new filaments emerged above the horizontal. In contrast, the direction of filament emergence was random in wwr-1. Tip-growing cells of both genotypes became gravitropic within a total of one to two cell divisions. Gravitropic curvature in wwr-1 was opposite in direction to that of WT, and the timing of curvature was comparable, indicating that the wwr-1 mutation acts during the onset of gravitropic competence. In time-lapse studies of both genotypes, neither a plastid-free zone nor obvious and extensive plastid sedimentation characteristic of mature dark-grown protonemata was observed in the new filaments prior to gravitropic curvature. Thus, it appears that these latter two features are not required for gravitropism in new protonemal filaments from protoplasts. Received: 24 October 1997 / Accepted: 18 November 1997     

Path reconstruction as a tool for actin filament speed determination in the in vitro motility assay.

The in vitro motility assay is used to measure speed of actin filaments moving over a glass surface coated with heavy meromyosin. In this paper a new method, the path reconstruction method, is presented to evaluate observed speeds. The method is compared with the commonly used centroid method, in which the centroids of the filaments are followed from frame to frame. Instead, in the path reconstruction method speed is evaluated from determination of perimeters of the filaments in each frame and by reconstruction of the traversed paths of the filaments over a number of frames. Biases in the determination of speed occurring in the centroid method due to curvature of paths and to video noise and Brownian motion are eliminated in the path reconstruction method, allowing measurement over a range of frame rates from 5 to 25 per second. The path reconstruction method leads to a clear separation of motile and nonmotile filaments provided that filaments are analyzed over at least 10 successive frames and allows easier separation of uniform and nonuniform sliding behavior.     

Self-organization of amphiphilic polymer in vesicle bilayers composed of surfactant mixtures

Cryogenic transmission electron microscopy (cryo-TEM) and small angle neutron scattering (SANS) are used to investigate the association of amphiphilic polymers consisting of a double-chain hydrophobic tail attached onto poly(ethylene glycol) (PEG) polymer chains into two different systems of equilibrium vesicles. For cetyltrimethylammonium bromide (CTAB)/sodium perfluorohexanoate (FC(5)) vesicle bilayers, the size distribution of the vesicles slightly becomes narrow in the presence of the polymers, suggesting that the wedge-shaped polymers increase the spontaneous curvature of the vesicles. In contrast, the confinement of polymer molecules inside the CTAB/sodium perfluorooctanoate (FC(7)) vesicles that are stabilized by spontaneous curvature causes an abrupt decrease in the bilayer rigidity. By an analysis of vesicle size distribution, it is found that the membrane elasticity of CTAB/FC(7) vesicles is varied considerably from 6k(B)T to 0.3k(B)T, implying the transition of stabilization mechanism from spontaneous curvature to thermal fluctuation in the presence of polymer. The polymer incorporation mechanism into the bilayers is understood, in the comparison of the vesicle radius and size distribution before and after adding polymer, as that the polymer is anchored into the vesicle bilayer owing to hydrophobic property after the adsorption on the surface of the bilayer.     

Scale-free foraging by primates emerges from their interaction with a complex environment

Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce, randomly distributed resources, but a less explored alternative is that this behaviour may result from the interaction of foraging animals with a particular distribution of resources. We introduce a simple foraging model where individual primates follow mental maps and choose their displacements according to a maximum efficiency criterion, in a spatially disordered environment containing many trees with a heterogeneous size distribution. We show that a particular tree-size frequency distribution induces non-Gaussian movement patterns with multiple spatial scales (Lévy walks). These results are consistent with field observations of tree-size variation and spider monkey (Ateles geoffroyi) foraging patterns. We discuss the consequences that our results may have for the patterns of seed dispersal by foraging primates.     

Mechanism of membrane curvature sensing by amphipathic helix containing proteins

There are several examples of membrane-associated protein domains that target curved membranes. This behavior is believed to have functional significance in a number of essential pathways, such as clathrin-mediated endocytosis, which involve dramatic membrane remodeling and require the recruitment of various cofactors at different stages of the process. This work is motivated in part by recent experiments that demonstrated that the amphipathic N-terminal helix of endophilin (H0) targets curved membranes by binding to hydrophobic lipid bilayer packing defects which increase in number with increasing membrane curvature. Here we use state-of-the-art atomistic simulation to explore the packing defect structure of curved membranes, and the effect of this structure on the folding of H0. We find that not only are packing defects increased in number with increasing membrane curvature, but also that their size distribution depends nontrivially on the curvature, falling off exponentially with a decay constant that depends on the curvature, and crucially that even on highly curved membranes defects large enough to accommodate the hydrophobic face of H0 are never observed. We furthermore find that a percolation model for the defects explains the defect size distribution, which implies that larger defects are formed by coalescence of noninteracting smaller defects. We also use the recently developed metadynamics algorithm to study in detail the effect of such defects on H0 folding. It is found that the comparatively larger defects found on a convex membrane promote H0 folding by several kcal/mol, while the smaller defects found on flat and concave membrane surfaces inhibit folding by kinetically trapping the peptide. Together, these observations suggest H0 folding is a cooperative process in which the folding peptide changes the defect structure relative to an unperturbed membrane.     

Motor Regulation Results in Distal Forces that Bend Partially Disintegrated Chlamydomonas Axonemes into Circular Arcs

The bending of cilia and flagella is driven by forces generated by dynein motor proteins. These forces slide adjacent microtubule doublets within the axoneme, the motile cytoskeletal structure. To create regular, oscillatory beating patterns, the activities of the axonemal dyneins must be coordinated both spatially and temporally. It is thought that coordination is mediated by stresses or strains, which build up within the moving axoneme, and somehow regulate dynein activity. During experimentation with axonemes subjected to mild proteolysis, we observed pairs of doublets associating with each other and forming bends with almost constant curvature. By modeling the statics of a pair of filaments, we show that the activity of the motors concentrates at the distal tips of the doublets. Furthermore, we show that this distribution of motor activity accords with models in which curvature, or curvature-induced normal forces, regulates the activity of the motors. These observations, together with our theoretical analysis, provide evidence that dynein activity can be regulated by curvature or normal forces, which may, therefore, play a role in coordinating the beating of cilia and flagella.     

Motor Regulation Results in Distal Forces that Bend Partially Disintegrated Chlamydomonas Axonemes into Circular Arcs

The bending of cilia and flagella is driven by forces generated by dynein motor proteins. These forces slide adjacent microtubule doublets within the axoneme, the motile cytoskeletal structure. To create regular, oscillatory beating patterns, the activities of the axonemal dyneins must be coordinated both spatially and temporally. It is thought that coordination is mediated by stresses or strains, which build up within the moving axoneme, and somehow regulate dynein activity. During experimentation with axonemes subjected to mild proteolysis, we observed pairs of doublets associating with each other and forming bends with almost constant curvature. By modeling the statics of a pair of filaments, we show that the activity of the motors concentrates at the distal tips of the doublets. Furthermore, we show that this distribution of motor activity accords with models in which curvature, or curvature-induced normal forces, regulates the activity of the motors. These observations, together with our theoretical analysis, provide evidence that dynein activity can be regulated by curvature or normal forces, which may, therefore, play a role in coordinating the beating of cilia and flagella.