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.     

A Mathematical Model of Rift Valley Fever with Human Host

Rift Valley Fever is a vector-borne disease mainly transmitted by mosquito. To gain some quantitative insights into its dynamics, a deterministic model with mosquito, livestock, and human host is formulated as a system of nonlinear ordinary differential equations and analyzed. The disease threshold [Formula: see text] is computed and used to investigate the local stability of the equilibria. A sensitivity analysis is performed and the most sensitive model parameters to the measure of initial disease transmission [Formula: see text] and the endemic equilibrium are determined. Both [Formula: see text] and the disease prevalence in mosquitoes are more sensitive to the natural mosquito death rate, d(m). The disease prevalence in livestock and humans are more sensitive to livestock and human recruitment rates, [Formula: see text] and [Formula: see text], respectively, suggesting isolation of livestock from humans is a viable preventive strategy during an outbreak. Numerical simulations support the analytical results in further exploring theoretically the long-term dynamics of the disease at the population level.     

Are Coiled-Coils of Dimeric Kinesins Unwound during Their Walking on Microtubule?

Dimeric kinesin motor proteins such as homodimeric kinesin-1, homodimeric Ncd and heterodimeric Kar3/Vik1are composed of two head domains which are connected together by a rod-shaped, coiled-coil stalk. Despite the extensive and intensive studies on structures, kinetics, dynamics and walking mechanism of the dimers, whether their coiled-coils are unwound or not during their walking on the microtubule is still an unclear issue. Here, we try to clarify this issue by using molecular dynamics simulations. Our simulation results showed that, for Ncd, a large change in potential of mean force is required to unwind the coiled-coil by only several pairs of residues. For both Ncd and kinesin-1, the force required to initiate the coiled-coil unwinding is larger than that required for unfolding of the single [Formula: see text]-helix that forms the coiled-coil or is larger than that required to unwind the DNA duplex, which is higher than the unbinding force of the kinesin head from the microtubule in strong microtubule-binding states. Based on these results and the comparison of the sequence between the coiled-coil of Kar3/Vik1 and those of Ncd and kinesin-1, it was deduced that the coiled-coil of the Kar3/Vik1 should also be very stable. Thus, we concluded that the coiled-coils of kinesin-1, Ncd and Kar3/Vik1 are almost impossible to unwind during their walking on the microtubule.     

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.     

The dynamics, causes and possible prevention of hepatitis e outbreaks

Rapidly spreading infectious diseases are a serious risk to public health. The dynamics and the factors causing outbreaks of these diseases can be better understood using mathematical models, which are fit to data. Here we investigate the dynamics of a Hepatitis E outbreak in the Kitgum region of northern Uganda during 2007 to 2009. First, we use the data to determine that [Formula: see text] is approximately 2.25 for the outbreak. Secondly, we use a model to estimate that the critical level of latrine and bore hole coverages needed to eradicate the epidemic is at least [Formula: see text] and [Formula: see text] respectively. Lastly, we further investigate the relationship between the co-infection factor for malaria and Hepatitis E on the value of [Formula: see text] for Hepatitis E. Taken together, these results provide us with a better understanding of the dynamics and possible causes of Hepatitis E outbreaks.     

Stochastic amplification of fluctuations in cortical up-States

Cortical neurons are bistable; as a consequence their local field potentials can fluctuate between quiescent and active states, generating slow [Formula: see text] Hz oscillations which are widely known as transitions between Up and Down States. Despite a large number of studies on Up-Down transitions, deciphering its nature, mechanisms and function are still today challenging tasks. In this paper we focus on recent experimental evidence, showing that a class of spontaneous oscillations can emerge within the Up states. In particular, a non-trivial peak around [Formula: see text] Hz appears in their associated power-spectra, what produces an enhancement of the activity power for higher frequencies (in the [Formula: see text] Hz band). Moreover, this rhythm within Ups seems to be an emergent or collective phenomenon given that individual neurons do not lock to it as they remain mostly unsynchronized. Remarkably, similar oscillations (and the concomitant peak in the spectrum) do not appear in the Down states. Here we shed light on these findings by using different computational models for the dynamics of cortical networks in presence of different levels of physiological complexity. Our conclusion, supported by both theory and simulations, is that the collective phenomenon of "stochastic amplification of fluctuations" - previously described in other contexts such as Ecology and Epidemiology - explains in an elegant and parsimonious manner, beyond model-dependent details, this extra-rhythm emerging only in the Up states but not in the Downs.     

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.     

Morphology and Viscoelasticity of Actin Networks Formed with the Mutually Interacting Crosslinkers: Palladin and Alpha-actinin

Actin filaments and associated actin binding proteins play an essential role in governing the mechanical properties of eukaryotic cells. Even though cells have multiple actin binding proteins (ABPs) that exist simultaneously to maintain the structural and mechanical integrity of the cellular cytoskeleton, how these proteins work together to determine the properties of actin networks is not clearly understood. The ABP, palladin, is essential for the maintenance of cell morphology and the regulation of cell movement. Palladin coexists with [Formula: see text]-actinin in stress fibers and focal adhesions and binds to both actin and [Formula: see text]-actinin. To obtain insight into how mutually interacting actin crosslinking proteins modulate the properties of actin networks, we characterized the micro-structure and mechanics of actin networks crosslinked with palladin and [Formula: see text]-actinin. We first showed that palladin crosslinks actin filaments into bundled networks which are viscoelastic in nature. Our studies also showed that composite networks of [Formula: see text]-actinin/palladin/actin behave very similar to pure palladin or pure [Formula: see text]-actinin networks. However, we found evidence that palladin and [Formula: see text]-actinin synergistically modify network viscoelasticity. To our knowledge, this is the first quantitative characterization of the physical properties of actin networks crosslinked with two mutually interacting crosslinkers.     

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.     

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.     

Mechanical anisotropy of ankyrin repeats

Red blood cells are frequently deformed and their cytoskeletal proteins such as spectrin and ankyrin-R are repeatedly subjected to mechanical forces. While the mechanics of spectrin was thoroughly investigated in vitro and in vivo, little is known about the mechanical behavior of ankyrin-R. In this study, we combine coarse-grained steered molecular dynamics simulations and atomic force spectroscopy to examine the mechanical response of ankyrin repeats (ARs) in a model synthetic AR protein NI6C, and in the D34 fragment of native ankyrin-R when these proteins are subjected to various stretching geometry conditions. Our steered molecular dynamics results, supported by AFM measurements, reveal an unusual mechanical anisotropy of ARs: their mechanical stability is greater when their unfolding is forced to propagate from the N-terminus toward the C-terminus (repeats unfold at ~60 pN), as compared to the unfolding in the opposite direction (unfolding force ～ 30 pN). This anisotropy is also reflected in the complex refolding behavior of ARs. The origin of this unfolding and refolding anisotropy is in the various numbers of native contacts that are broken and formed at the interfaces between neighboring repeats depending on the unfolding/refolding propagation directions. Finally, we discuss how these complex mechanical properties of ARs in D34 may affect its behavior in vivo.     

(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.     

Trans-Theta Logistics: A New Family of Population Growth Sigmoid Functions

Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ([Formula: see text] L). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population (N) is divided into reproducing (P) and non-reproducing/quiescent (Q) sub-populations. The modes of the rate of change of ratio P/N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P/N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic (T [Formula: see text] L) since they exist when the [Formula: see text] L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid (TS). The [Formula: see text] L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T [Formula: see text] L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T [Formula: see text] L versus [Formula: see text] L for model growth curves.     

Stable Single α-Helices Are Constant Force Springs in Proteins

Single α-helix (SAH) domains are rich in charged residues (Arg, Lys, and Glu) and stable in solution over a wide range of pH and salt concentrations. They are found in many different proteins where they bridge two functional domains. To test the idea that their high stability might enable these proteins to resist unfolding along their length, the properties and unfolding behavior of the predicted SAH domain from myosin-10 were characterized. The expressed and purified SAH domain was highly helical, melted non-cooperatively, and was monomeric as shown by circular dichroism and mass spectrometry as expected for a SAH domain. Single molecule force spectroscopy experiments showed that the SAH domain unfolded at very low forces (<30 pN) without a characteristic unfolding peak. Molecular dynamics simulations showed that the SAH domain unfolds progressively as the length is increased and refolds progressively as the length is reduced. This enables the SAH domain to act as a constant force spring in the mechanically dynamic environment of the cell.     

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     

Application of DFT methods to the study of the coordination environment of the VO2+ ion in V?proteins

Density functional theory (DFT) methods were used to simulate the environment of vanadium in several V proteins, such as vanadyl-substituted carboxypeptidase (sites A and B), vanadyl-substituted chloroplast F(1)-ATPase (CF(1); site 3), the reduced inactive form of vanadium bromoperoxidase (VBrPO; low- and high-pH sites), and vanadyl-substituted imidazole glycerol phosphate dehydratase (IGPD; sites α, β, and γ). Structural, electron paramagnetic resonance, and electron spin echo envelope modulation parameters were calculated and compared with the experimental values. All the simulations were performed in water within the framework of the polarizable continuum model. The angular dependence of [Formula: see text] and [Formula: see text] on the dihedral angle θ between the V=O and N-C bonds and on the angle φ between the V=O and V-N bonds, where N is the coordinated aromatic nitrogen atom, was also found. From the results it emerges that it is possible to model the active site of a vanadium protein through DFT methods and determine its structure through the comparison between the calculated and experimental spectroscopic parameters. The calculations confirm that the donor sets of sites B and A of vanadyl-substituted carboxypeptidase are [[Formula: see text], H(2)O, H(2)O, H(2)O] and [N(His)(||), N(His)(⊥), [Formula: see text], H(2)O], and that the donor set of site 3 of CF(1)-ATPase is [[Formula: see text], OH(Thr), H(2)O, H(2)O, [Formula: see text]]. For VBrPO, the coordination modes [N(His)(||), N(His)(∠), OH(Ser), H(2)O, H(2)O(ax)] for the low-pH site and [N(His)(||), N(His)(∠), OH(Ser), OH(-), H(2)O(ax)] or [N(His)(||), N(His)(∠), [Formula: see text], H(2)O] for the high-pH site, with an imidazole ring of histidine strongly displaced from the equatorial plane, can be proposed. Finally, for sites α, β, and γ of IGPD, the subsequent deprotonation of one, two, and three imidazole rings of histidine and the participation of a carboxylate group of a glutamate residue ([N(His)(||), [Formula: see text], H(2)O, H(2)O], [N(His)(||), N(His)(||), [Formula: see text], H(2)O], and [N(His)(||), N(His)(||), [Formula: see text], OH(-), [Formula: see text]], respectively) seems to be the most plausible hypothesis.     

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.     

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.     

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.     

Stochastic simulations of pattern formation in excitable media

We present a method for mesoscopic, dynamic Monte Carlo simulations of pattern formation in excitable reaction-diffusion systems. Using a two-level parallelization approach, our simulations cover the whole range of the parameter space, from the noise-dominated low-particle number regime to the quasi-deterministic high-particle number limit. Three qualitatively different case studies are performed that stand exemplary for the wide variety of excitable systems. We present mesoscopic stochastic simulations of the Gray-Scott model, of a simplified model for intracellular Ca[Formula: see text] oscillations and, for the first time, of the Oregonator model. We achieve simulations with up to [Formula: see text] particles. The software and the model files are freely available and researchers can use the models to reproduce our results or adapt and refine them for further exploration.