Critical motor number for fractional steps of cytoskeletal filaments in gliding assays

In gliding assays, filaments are pulled by molecular motors that are immobilized on a solid surface. By varying the motor density on the surface, one can control the number [Formula: see text] of motors that pull simultaneously on a single filament. Here, such gliding assays are studied theoretically using Brownian (or Langevin) dynamics simulations and taking the local force balance between motors and filaments as well as the force-dependent velocity of the motors into account. We focus on the filament stepping dynamics and investigate how single motor properties such as stalk elasticity and step size determine the presence or absence of fractional steps of the filaments. We show that each gliding assay can be characterized by a critical motor number, [Formula: see text]. Because of thermal fluctuations, fractional filament steps are only detectable as long as [Formula: see text]. The corresponding fractional filament step size is [Formula: see text] where [Formula: see text] is the step size of a single motor. We first apply our computational approach to microtubules pulled by kinesin-1 motors. For elastic motor stalks that behave as linear springs with a zero rest length, the critical motor number is found to be [Formula: see text], and the corresponding distributions of the filament step sizes are in good agreement with the available experimental data. In general, the critical motor number [Formula: see text] depends on the elastic stalk properties and is reduced to [Formula: see text] for linear springs with a nonzero rest length. Furthermore, [Formula: see text] is shown to depend quadratically on the motor step size [Formula: see text]. Therefore, gliding assays consisting of actin filaments and myosin-V are predicted to exhibit fractional filament steps up to motor number [Formula: see text]. Finally, we show that fractional filament steps are also detectable for a fixed average motor number [Formula: see text] as determined by the surface density (or coverage) of the motors on the substrate surface.     

Structural characterization of the interactions between palladin and α-actinin

The interaction between α-actinin and palladin, two actin-cross-linking proteins, is essential for proper bidirectional targeting of these proteins. As a first step toward understanding the role of this complex in organizing cytoskeletal actin, we have characterized binding interactions between the EF-hand domain of α-actinin (Act-EF34) and peptides derived from palladin and generated an NMR-derived structural model for the Act-EF34/palladin peptide complex. The critical binding site residues are similar to an α-actinin binding motif previously suggested for the complex between Act-EF34 and titin Z-repeats. The structure-based model of the Act-EF34/palladin peptide complex expands our understanding of binding specificity between the scaffold protein α-actinin and various ligands, which appears to require an α-helical motif containing four hydrophobic residues, common to many α-actinin ligands. We also provide evidence that the Family X mutation in palladin, associated with a highly penetrant form of pancreatic cancer, does not interfere with α-actinin binding.     

Actin‐induced dimerization of palladin promotes actin‐bundling

A subset of actin binding proteins is able to form crosslinks between two or more actin filaments, thus producing structures of parallel or networked bundles. These actin crosslinking proteins interact with actin through either bivalent binding or dimerization. We recently identified two binding sites within the actin binding domain of palladin, an actin crosslinking protein that plays an important role in normal cell adhesion and motility during wound healing and embryonic development. In this study, we show that actin induces dimerization of palladin. Furthermore, the extent of dimerization reflects earlier comparisons of actin binding and bundling between different domains of palladin. On the basis of these results we hypothesized that actin binding may promote a conformational change that results in dimerization of palladin, which in turn may drive the crosslinking of actin filaments. The proximal distance between two actin binding sites on crosslinking proteins determines the ultrastructural properties of the filament network, therefore we also explored interdomain interactions using a combination of chemical crosslinking experiments and actin cosedimentation assays. Limited proteolysis data reveals that palladin is less susceptible to enzyme digestion after actin binding. Our results suggest that domain movements in palladin are necessary for interactions with actin and are induced by interactions with actin filaments. Accordingly, we put forth a model linking the structural changes to functional dynamics.     

Robustness and information propagation in attractors of random boolean networks

Attractors represent the long-term behaviors of Random Boolean Networks. We study how the amount of information propagated between the nodes when on an attractor, as quantified by the average pairwise mutual information ([Formula: see text]), relates to the robustness of the attractor to perturbations ([Formula: see text]). We find that the dynamical regime of the network affects the relationship between [Formula: see text] and [Formula: see text]. In the ordered and chaotic regimes, [Formula: see text] is anti-correlated with [Formula: see text], implying that attractors that are highly robust to perturbations have necessarily limited information propagation. Between order and chaos (for so-called "critical" networks) these quantities are uncorrelated. Finite size effects cause this behavior to be visible for a range of networks, from having a sensitivity of 1 to the point where [Formula: see text] is maximized. In this region, the two quantities are weakly correlated and attractors can be almost arbitrarily robust to perturbations without restricting the propagation of information in the network.     

Unifying Time to Contact Estimation and Collision Avoidance across Species

The [Formula: see text]-function and the [Formula: see text]-function are phenomenological models that are widely used in the context of timing interceptive actions and collision avoidance, respectively. Both models were previously considered to be unrelated to each other: [Formula: see text] is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, [Formula: see text] has a maximum before ttc. Furthermore, it is not clear how both functions could be implemented at the neuronal level in a biophysically plausible fashion. Here we propose a new framework - the corrected modified Tau function - capable of predicting both [Formula: see text]-type ("[Formula: see text]") and [Formula: see text]-type ("[Formula: see text]") responses. The outstanding property of our new framework is its resilience to noise. We show that [Formula: see text] can be derived from a firing rate equation, and, as [Formula: see text], serves to describe the response curves of collision sensitive neurons. Furthermore, we show that [Formula: see text] predicts the psychophysical performance of subjects determining ttc. Our new framework is thus validated successfully against published and novel experimental data. Within the framework, links between [Formula: see text]-type and [Formula: see text]-type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain.     

Architecture of the Outer Membrane of Escherichia coli III. Protein-Lipopolysaccharide Complexes in Intramembraneous Particles

In a previous paper (A. Verkleij, L. van Alphen, J. Bijvelt, and B. Lugtenberg, Biochim. Biophys. Acta 466:269-282, 1977) we have hypothesized that particles on the outer fracture face of the outer membrane ([Formula: see text]), with corresponding pits on the inner fracture face of the outer membrane ([Formula: see text]), consist of lipopolysaccharide (LPS) aggregates stabilized by divalent cations and that they might contain protein and/or phospholipid. In the present paper the roles of LPS, cations, and proteins in these [Formula: see text] particles are described more extensively, using a strain that lacks the major outer membrane proteins, b, c, and d (b(-) c(-) d(-)), and has a reduction in the number of [Formula: see text] particles of 75%. To study the role of divalent cations in the formation of [Formula: see text] particles, these b(-) c(-) d(-) cells were grown or incubated with Ca(2+), Mg(2+), or putrescine. The presence of Ca(2+) resulted in the appearance of many [Formula: see text] particles and [Formula: see text] pits. Mg(2+) and putrescine were less effective than Ca(2+). Introduction of these particles was not accompanied by alterations in the relative amounts of LPS and cell envelope proteins. Ca(2+) treatment of a heptoseless derivative of a b(-) c(-) d(-) strain did not result in morphological changes. Incubation of Ca(2+)-treated cells with ethylenediaminetetraacetate caused the disappearance of the introduced particles as well as the release of more than 60% of the cellular LPS. These results strongly support the hypothesis that LPS is involved in the formation of [Formula: see text] particles and [Formula: see text] pits. The roles of various outer membrane proteins in the formation of [Formula: see text] particles were studied by comparing the freeze-fracture morphology of b(-) c(-) d(-) cells with that of cells which contain one of the outer membrane proteins b, c, d, and e or the receptor protein for bacteriophage lambda. The results showed that the presence of any of these five proteins in a b(-) c(-) d(-) background resulted in a large increase in the number of [Formula: see text] particles and [Formula: see text] pits, indicating that these proteins are, independent of each other, involved in the formation of [Formula: see text] particles and [Formula: see text] pits. The simplest explanation for the results is that in wild-type cells each particle consists of LPS complexed with some molecules of a single protein species, stabilized by either divalent cations or polyamines. It is hypothesized that the outer membrane of the wild-type cell contains a heterogeneous population of particles, of which 75% consists of protein b-LPS, protein c-LPS, and protein d-LPS particles. A function of these particles as aqueous pores is proposed.     

Mapping of redox state of mitochondrial cytochromes in live cardiomyocytes using Raman microspectroscopy

This paper presents a nonivasive approach to study redox state of reduced cytochromes [Formula: see text], [Formula: see text] and [Formula: see text] of complexes II and III in mitochondria of live cardiomyocytes by means of Raman microspectroscopy. For the first time with the proposed approach we perform studies of rod- and round-shaped cardiomyocytes, representing different morphological and functional states. Raman mapping and cluster analysis reveal that these cardiomyocytes differ in the amounts of reduced cytochromes [Formula: see text], [Formula: see text] and [Formula: see text]. The rod-shaped cardiomyocytes possess uneven distribution of reduced cytochromes [Formula: see text], [Formula: see text] and [Formula: see text] in cell center and periphery. Moreover, by means of Raman spectroscopy we demonstrated the decrease in the relative amounts of reduced cytochromes [Formula: see text], [Formula: see text] and [Formula: see text] in the rod-shaped cardiomyocytes caused by H(2)O(2)-induced oxidative stress before any visible changes. Results of Raman mapping and time-dependent study of reduced cytochromes of complexes II and III and cytochrome [Formula: see text] in cardiomyocytes are in a good agreement with our fluorescence indicator studies and other published data.     

Specificity of Hpa II and Hae III DNA methylases

The methylases M.HaeIII and M.HpaII recognize the tetranucleotide sequences [Formula: see text] and [Formula: see text] respectively, in DNA, and transfer a methyl group from S-adenosylmethionine to the 5-position of cytosine on each strand as indicated by the asterisks. Restriction endonuclease R.HaeIII does not cleave the methylated sequence [Formula: see text] but can cleave [Formula: see text] in which methylation is introduced on the unnatural external cytosine positions. Similarly, R.HpaII does not cleave [Formula: see text] but can cleave [Formula: see text].Images     

Limits to the rate of adaptive substitution in sexual populations

In large populations, many beneficial mutations may be simultaneously available and may compete with one another, slowing adaptation. By finding the probability of fixation of a favorable allele in a simple model of a haploid sexual population, we find limits to the rate of adaptive substitution, [Formula: see text], that depend on simple parameter combinations. When variance in fitness is low and linkage is loose, the baseline rate of substitution is [Formula: see text], where [Formula: see text] is the population size, [Formula: see text] is the rate of beneficial mutations per genome, and [Formula: see text] is their mean selective advantage. Heritable variance [Formula: see text] in log fitness due to unlinked loci reduces [Formula: see text] by [Formula: see text] under polygamy and [Formula: see text] under monogamy. With a linear genetic map of length [Formula: see text] Morgans, interference is yet stronger. We use a scaling argument to show that the density of adaptive substitutions depends on [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] only through the baseline density: [Formula: see text]. Under the approximation that the interference due to different sweeps adds up, we show that [Formula: see text], implying that interference prevents the rate of adaptive substitution from exceeding one per centimorgan per 200 generations. Simulations and numerical calculations confirm the scaling argument and confirm the additive approximation for [Formula: see text]; for higher [Formula: see text], the rate of adaptation grows above [Formula: see text], but only very slowly. We also consider the effect of sweeps on neutral diversity and show that, while even occasional sweeps can greatly reduce neutral diversity, this effect saturates as sweeps become more common-diversity can be maintained even in populations experiencing very strong interference. Our results indicate that for some organisms the rate of adaptive substitution may be primarily recombination-limited, depending only weakly on the mutation supply and the strength of selection.     

Analysis of turnover dynamics of the submembranous actin cortex

The cell cortex is a thin network of actin, myosin motors, and associated proteins that underlies the plasma membrane in most eukaryotic cells. It enables cells to resist extracellular stresses, perform mechanical work, and change shape. Cortical structural and mechanical properties depend strongly on the relative turnover rates of its constituents, but quantitative data on these rates remain elusive. Using photobleaching experiments, we analyzed the dynamics of three classes of proteins within the cortex of living cells: a scaffold protein (actin), a cross-linker (α-actinin), and a motor (myosin). We found that two filament subpopulations with very different turnover rates composed the actin cortex: one with fast turnover dynamics and polymerization resulting from addition of monomers to free barbed ends, and one with slow turnover dynamics with polymerization resulting from formin-mediated filament growth. Our data suggest that filaments in the second subpopulation are on average longer than those in the first and that cofilin-mediated severing of formin-capped filaments contributes to replenishing the filament subpopulation with free barbed ends. Furthermore, α-actinin and myosin minifilaments turned over significantly faster than F-actin. Surprisingly, only one-fourth of α-actinin dimers were bound to two actin filaments. Taken together, our results provide a quantitative characterization of essential mechanisms under­lying actin cortex homeostasis.     

(13)C NMR Reveals No Evidence of n-π* Interactions in Proteins

An [Formula: see text] interaction between neighboring carbonyl groups has been postulated to stabilize protein structures. Such an interaction would affect the [Formula: see text]C chemical shielding of the carbonyl groups, whose paramagnetic component is dominated by [Formula: see text] and [Formula: see text] excitations. Model compound calculations indicate that both the interaction energetics and the chemical shielding of the carbonyl group are instead dominated by a classical dipole-dipole interaction. A set of high-resolution protein structures with associated carbonyl [Formula: see text]C chemical shift assignments verifies this correlation and provides no evidence for an inter-carbonyl [Formula: see text] interaction.     

Mutual effects of α-actinin,calponin and filamin on actin binding

The mutual effect of three actin-binding proteins (α-actinin, calponin and filamin) on the binding to actin was analyzed by means of differential centrifugation and electron microscopy. In the absence of actin α-actinin, calponin and filamin do not interact with each other. Calponin and filamin do not interfere with each other in the binding to actin bundles. Slight interference was observed in the binding of α-actinin and calponin to actin bundles. Higher ability of calponin to depress α-actinin binding can be due to the higher stoichiometry calponin/actin in the complexes formed. The largest interference was observed in the pair filamin–α-actinin. These proteins interfere with each other in the binding to the bundled actin filaments; however, neither of them completely displaced another protein from its complexes with actin. The structure of actin bundles formed in the presence of any one actin-binding protein was different from that observed in the presence of binary mixtures of two actin-binding proteins. In the case of calponin or its binary mixtures with α-actinin or filamin the total stoichiometry actin-binding protein/actin was larger than 0.5. This means that α-actinin, calponin and filamin may coexist on actin filaments and more than mol of any actin-binding protein is bound per two actin monomers. This may be important for formation of different elements of cytoskeleton.     

Copper(I)-alkyl sulfide and -cysteine tri-nuclear clusters as models for metallo proteins: a structural density functional analysis

After having set up the computational methodology for Cu(I)-sulfur systems as models for copper proteins, namely using the simple ligands H(2)S, HS(-), CH(3)SH, and CH(3)S(-), the Cu(I)-Cysteine systems have been investigated: [Cu(I)( S -H(2)Cys) (n) ](+) (H(2)Cys, cysteine, NH(2),SH,COOH) [Cu(I)( S -HCys) (n) ](1-) (n) (NH(2),S(-),COOH). Finally, the structures for bi-nuclear [Formula: see text] (Et, CH(2)CH(3)), [Formula: see text] and tri-nuclear [Cu(I)( S -SH)](3), [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] (NH(2),SH,COOH), [Formula: see text] (NH(2),S(-),COOH, and NH(2),SH,COO(-)), as well as [Formula: see text] (NH(2),S(-),COO(-)), were also optimized to mimic the active center for a metallo-chaperone copper transport protein (CopZ). The X-ray structures for the biomolecules were matched fairly well as regards the Cu-S bond distances and Cu…Cu contact distances in the case the model cysteine S atom is deprotonated. Upon protonation of ligand S atoms, the conformation of clusters is altered and might bring about the di- and tri-nuclear core breakage. These findings suggest that subtle protonation/deprotonation steps, i.e. small and/or local pH changes play a significant role for copper transport processes.     

The regulatory action of α-actinin on actin filaments is enhanced by cofilin

We have used fluorescence recovery after photobleaching to study the effect of muscle α-actinin on the structure of actin filaments in dilute solutions. Unexpectedly we found that α-actinin partitioned filaments into two types: those with a high mobility and those with low mobility. We have determined that the high mobility (smaller sized) population is too large to be simple monomeric actin:α-actinin complexes. Although it is known that cofilin encourages the transformation of α-actinin:actin gels into large meshworks of inter-digitating actin filament bundles (Maciver et al. 1991), we have found that the presence of cofilin also increases the cross-linking of actin filaments by α-actinin and hypothesize that this is due to cofilin’s ability to alter the filament twist. This effectively makes more potential α-actinin binding sites per unit of actin filament. As expected from previous work, this effect was more marked at pH 6.5 than at pH 8.0. Both effects are likely to operate in cells to deny other actin-binding proteins access to binding these particular filaments and may explain how very different actin cytoskeletal structures may co-exist in the same cell at the same time.     

Complexity-entropy causality plane as a complexity measure for two-dimensional patterns

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to [Formula: see text] fractal landscapes generated numerically where we compare our measures with the Hurst exponent; [Formula: see text] liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; [Formula: see text] 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; [Formula: see text] and Ising surfaces where our method identified the critical temperature and also proved to be stable.     

The IspA protease's involvement in the regulation of the sporulation process of Bacillus thuringiensis is revealed by proteomic analysis

We have observed that the process of sporulation of the ispA-deficient mutant was delayed under phase-contrast microscopy. The protein profiles of the ispA-deficient mutant have been analyzed using two-dimensional gel electrophoresis. The results of a proteomic analysis using MALDI-TOF MS indicated that a sporulation-associated protein, pro- [Formula: see text], was upregulated, while two other sporulation-associated proteins, SpoVD and SpoVR, were downregulated in the ispA-deficient mutant. It has been known that pro- [Formula: see text] is a precursor of [Formula: see text] and is required for gene expression related to the late stage of sporulation. Moreover, SpoVD and SpoVR are known to be involved in the formation of the spore cortex. Based on these observations, we propose that the delay in the sporulation process observed in the ispA-deficient mutant may be due to a failure of [Formula: see text] to signal sporulation. This phenomenon may be further enhanced by insufficient amount of SpoVD and SpoVR for cortex formation. In this study, we have revealed for the first time a possible pathway for the regulation of sporulation-associated proteins via IspA.     

Morphogenesis of liposomes encapsulating actin depends on the type of actin-crosslinking

To study the morphogenesis of cells caused by the organization of their internal cytoskeletal network, we characterized the transformation of liposomes encapsulating actin and its crosslinking proteins, fascin, alpha-actinin, or filamin, using real-time high-intensity dark-field microscopy. With increasing temperature, the encapsulated G-actin polymerized into actin filaments and formed bundles or gels, depending on the type of actin-crosslinking protein that was co-encapsulated, causing various morphological changes of liposomes. The differences in morphology among transformed liposomes indicate that actin-crosslinking proteins determine liposome shape by organizing their specific actin networks. Morphological analysis reveals that the crosslinking manner, i.e. distance and angular flexibility between adjacent crosslinked actin filaments, is essential for the morphogenesis rather than their binding affinity and stoichiometry to actin filaments.     

Kinetics of Bulge Bases in Small RNAs and the Effect of Pressure on It

Due to their self-catalytic properties, small RNAs with bulge bases are hypothesized to be primordial molecules which could form elementary translation systems. Using molecular dynamics simulations, we study the binding propensity of small RNAs by calculating the free energy barrier corresponding to the looped out conformations of bulge bases, which presumably act as the binding sites for ligands in these small RNAs. We find that base flipping kinetics can proceed at atmospheric pressure but with a very small propensity. Furthermore, the free energy barrier associated with base flipping depends on the stacking with neighboring bases. Next, we studied the base flipping kinetics with pressure. We find that the free energy associated with base looping out increases monotonically as the pressure is increased. Furthermore, we calculate the mean first-passage time of conformational looping out of the bulge base using the diffusion of reaction coordinate associated with the base flipping on the underlying free energy surface. We find that the mean first-passage time associated with bulge looping out increases slowly upon increasing pressures [Formula: see text] up to [Formula: see text] atm but changes dramatically for [Formula: see text] atm. Finally, we discuss our results in the light of the role of hydration shell of water around RNA. Our results are relevant for the RNA world hypothesis.     

The biosynthesis of 4-hydroxycoumarin and dicoumarol by Aspergillus fumigatus Fresenius

A strain of Aspergillus fumigatus Fresenius, isolated from spoiled hay, converts melilotic acid (o-hydroxyphenylpropionic acid) and o-coumaric acid into 4-hydroxycoumarin and dicoumarol. The sequence is shown to be melilotic acid (I) [Formula: see text] coumaric acid (IV) [Formula: see text] beta-hydroxymelilotic acid (II) [Formula: see text] beta-oxomelilotic acid (III) [Formula: see text] 4-hydroxycoumarin (VI), on the basis of (1) studies on the formation of postulated intermediates, (2) experiments with isotopically labelled materials and (3) sequential enzyme induction. In the presence of semicarbazide, o-coumaraldehyde is formed from o-coumaric acid: there is no evidence, however, that this lies on the normal metabolic pathway.     

α-Actinin and Filamin Cooperatively Enhance the Stiffness of Actin Filament Networks

Background

The close subcellular proximity of different actin filament crosslinking proteins suggests that these proteins may cooperate to organize F-actin structures to drive complex cellular functions during cell adhesion, motility and division. Here we hypothesize that α-actinin and filamin, two major F-actin crosslinking proteins that are both present in the lamella of adherent cells, display synergistic mechanical functions.

Methodology/Principal Findings

Using quantitative rheology, we find that combining α-actinin and filamin is much more effective at producing elastic, solid-like actin filament networks than α-actinin and filamin separately. Moreover, F-actin networks assembled in the presence of α-actinin and filamin strain-harden more readily than networks in the presence of either α-actinin or filamin.

Significance

These results suggest that cells combine auxiliary proteins with similar ability to crosslink filaments to generate stiff cytoskeletal structures, which are required for the production of internal propulsive forces for cell migration, and that these proteins do not have redundant mechanical functions.