Real quantities can undergo such a wide variety of dynamics that the mean is often a meaningless reference point for measuring variability. Despite their widespread application, techniques like the Coefficient of Variation are not truly proportional and exhibit pathological properties. The non-parametric measure Proportional Variability (PV) [1] resolves these issues and provides a robust way to summarize and compare variation in quantities exhibiting diverse dynamical behaviour. Instead of being based on deviation from an average value, variation is simply quantified by comparing the numbers to each other, requiring no assumptions about central tendency or underlying statistical distributions. While PV has been introduced before and has already been applied in various contexts to population dynamics, here we present a deeper analysis of this new measure, derive analytical expressions for the PV of several general distributions and present new comparisons with the Coefficient of Variation, demonstrating cases in which PV is the more favorable measure. We show that PV provides an easily interpretable approach for measuring and comparing variation that can be generally applied throughout the sciences, from contexts ranging from stock market stability to climate variation.

Helicase motif VI is a short arginine-rich motif within the NTPase/helicase domain of the non-structural protein 3 (NS3) of the hepatitis C virus (HCV). We previously demonstrated that it reduces the catalytic activity and intracellular shuttling of protein kinase C (PKC). Thus, NS3-mediated PKC inhibition may be involved in HCV-associated hepatocellular carcinoma (HCC). In this study, we expand on our earlier results, which were obtained in experiments with short fragments of NS3, to show for the first time that the catalytically active, longer C-terminal NTPase/helicase of NS3 acts as a potent PKC inhibitor in vitro. PKC inhibition assays with the NTPase-inactive mutant NS3h-D1316A revealed a mixed type kinetic inhibition pattern. A broad range of 11 PKC isotypes was tested and all of the PKC isotypes were inhibited with IC50-values in the low micromolar range. These findings were confirmed for the wild-type NTPase/helicase domain in a non-radiometric PKC inhibition assay with ATP regeneration to rule out any effect of ATP hydrolysis caused by its NTPase activity. PKCα was inhibited with a micromolar IC50 in this assay, which compares well with our result for NS3h-D1316A (IC50 = 0.7 μM). In summary, these results confirm that catalytically active NS3 NTPase/helicase can act in an analogous manner to shorter NS3 fragments as a pseudosubstrate inhibitor of PKC.

We extend a recently proposed model [Chaudhuri et al., Europhys. Lett. 87, 20003 (2009)] aiming to describe the formation of fascicles of axons during neural development. The growing axons are represented as paths of interacting directed random walkers in two spatial dimensions. To mimic turnover of axons, whole paths are removed and new walkers are injected with specified rates. In the simplest version of the model, we use strongly adhesive short-range inter-axon interactions that are identical for all pairs of axons. We generalize the model to adhesive interactions of finite strengths and to multiple types of axons with type-specific interactions. The dynamic steady state is characterized by the position-dependent distribution of fascicle size and fascicle composition. With distance in the direction of axon growth, the mean fascicle size and emergent time scales grow monotonically, while the degree of sorting of fascicles by axon type has a maximum at a finite distance. To understand the emergence of slow time scales, we develop an analytical framework to analyze the interaction between neighboring fascicles.

Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been proposed to generate this type of behavior. Stochastic versions of these models can produce similarly looking time series, often with noise-driven mechanisms different from those of the deterministic models. We present a suite of measures which, when applied to the time series, serves to distinguish models and classify routes to producing MMOs, such as noise-induced oscillations or delay bifurcation. By focusing on the subthreshold oscillations, we analyze the interspike interval density, trends in the amplitude, and a coherence measure. We develop these measures on a biophysical model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and apply them on related models. The analysis highlights the influence of model parameters and resets and return mechanisms in the context of a novel approach using noise level to distinguish model types and MMO mechanisms. Ultimately, we indicate how the suite of measures can be applied to experimental time series to reveal the underlying dynamical structure, while exploiting either the intrinsic noise of the system or tunable extrinsic noise.

Mixed mode oscillations (MMO's) composed of subthreshold oscillations (STO's) and spikes appear via a variety of mechanisms in models of neural dynamics. Two key elements that can influence the prominence of the STO's are multiple time scales and time varying parameters near critical points. These features can lead to dynamics associated with bifurcation delay, and we consider three systems with this behavior. While it is well known that bifurcation delay related to a slow time scale is sensitive to noise, we compare other aspects of the noise-sensitivity in the context of MMO's, where not only bifurcation delay, but also coherence resonance and dynamics in the interspike interval play a role. Noise can play a role in amplifying the STO's but it can also drive the system into repetitive spiking without STO's. In particular we compare integrate and fire models with models that capture both spike and STO dynamics. The interplay of the underlying bifurcation structure and the modeling of the return mechanism following the spike are major factors in the robustness and noise sensitivity of the STO's in the context of multiple time scales.

In previous works, we demonstrated a potent inhibition of diverse protein kinase C (PKC) functions by a fragment of nonstructural protein 3 (NS3) of hepatitis C virus (HCV), mainly mediated by the Arg-rich amino acid motif HCV(1487-1500). This sequence is localized on the surface of Domain 2 of the NS3 NTPase/helicase in direct vicinity to a flexible loop that is localized between Val1458 and Thr1476. Here, we assessed the regulation of the accessibility of the Arg-rich amino acid motif for PKC by this loop, using two variants of domain 2. The first construct, termed NS3d2Delta, comprises the complete domain, HCV(1361-1503), devoid the loop. The second variant, NS3d2wt corresponds to wild type domain 2. The results indicated an enhanced inhibitory potential of NS3d2Delta towards rat brain PKC and towards the majority of PKC isoforms. This effect and the accompanying change of the mode of inhibition from a mixed mode, exerted by NS3d2wt to a competitive mode, exerted by NS3d2Delta are caused by the deletion of the loop. Accordingly, the presence of the intact loop abolished the binding of domain 2 to the tailed duplex RNA used as helicase substrate, without affecting the binding of dsDNA. Furthermore, a direct competition of dsRNA and PKC for the same binding site HCV(1487-1500), could be documented. The binding of dsRNA to NS3d2Delta previously overlaid with PPKCalpha was reduced to 30% and completely abolished in case of NS3d2Delta overlaid with cAMP-dependent protein kinase A (PKA).

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations -- both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations--both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.

We investigate the slow time scales that arise from aging of the paths during the process of path aggregation. This is studied using Monte Carlo simulations of a model aiming to describe the formation of fascicles of axons mediated by contact axon-axon interactions. The growing axons are represented as interacting directed random walks in two spatial dimensions. To mimic axonal turnover, random walkers are injected and whole paths of individual walkers are removed at specified rates. We identify several distinct time scales that emerge from the system dynamics and can exceed the average axonal lifetime by orders of magnitude. In the dynamical steady state, the position-dependent distribution of fascicle sizes obeys a scaling law. We discuss our findings in terms of an analytically tractable, effective model of fascicle dynamics.

The NTPase/helicase of Flauiviridae viruses is one of the essential components of their replication complex. The enzyme is defined by the presence of seven highly conserved amino acid motifs. Random screening of numerous hepatitis C virus (HCV) derived peptides, revealed a basic amino acid stretch corresponding to motif VI of the HCV NTPase/helicase (amino acids 1487-1500 of the HCV polyprotein). This peptide inhibited the unwinding activity of the enzyme with an IC50 = 0.2 mu M. Peptides corresponding to motif VI of HCV, West Nile virus (WNV) and Japanese encephalitis virus (JEV) were synthesized and tested as inhibitors of NTPase and unwinding reactions mediated by the viral enzymes. Peptides distinguished in regard to their length and structure. Between the peptides tested HCV(14871500) reproducing the sequence of motif VI was the most potent inhibitor of helicase activities of investigated enzymes. Other respective peptides were rather modest inhibitors. The examined peptides inhibited the Flauiviridae helicases in the following order of potency: HCV(1487-1500) > WNV(1959-1572) > JEV(1962-1975). Interestingly, the susceptibility of the helicase activity to the inhibition by the peptides was similar and in the row: HCV > WNV > JEV.The inhibition results from binding and blockade of the active site of the enzyme lyes beyond the NTP-binding and hydrolyzing site. The kinetic analyses indicated that the binding of the peptides do not interfere with the NTPase activity of the enzymes. The peptide may serve as effective and selective tool to reduce the virus propagation. (c) 2008 Elsevier Inc. All rights reserved.

We investigate the slow time scales that arise from aging of the paths during the process of path aggregation. This is studied using Monte-Carlo simulations of a model aiming to describe the formation of fascicles of axons mediated by contact axon-axon interactions. The growing axons are represented as interacting directed random walks in two spatial dimensions. To mimic axonal turnover, random walkers are injected and whole paths of individual walkers are removed at specified rates. We identify several distinct time scales that emerge from the system dynamics and can exceed the average axonal lifetime by orders of magnitude. In the dynamical steady state, the position-dependent distribution of fascicle sizes obeys a scaling law. We discuss our findings in terms of an analytically tractable, effective model of fascicle dynamics.

We study the stochastic kinetics of a signaling module consisting of a two-state stochastic point process with negative feedback. In the active state, a product is synthesized which increases the active-to-inactive transition rate of the process. We analyze this simple autoregulatory module using a path-integral technique based on the temporal statistics of state flips of the process. We develop a systematic framework to calculate averages, autocorrelations, and response functions by treating the feedback as a weak perturbation. Explicit analytical results are obtained to first order in the feedback strength. Monte Carlo simulations are performed to test the analytical results in the weak feedback limit and to investigate the strong feedback regime. We conclude by relating some of our results to experimental observations in the olfactory and visual sensory systems.

ABSTRACT Hepatitis C virus (HCV) chronic infections represent one of the major and still unresolved health problems because of low efficiency and high cost of current therapy. Therefore, our studies centered on a viral protein, the NS3 helicase, whose activity is indispensable for replication of the viral RNA, and on its peptide inhibitor that corresponds to a highly conserved arginine-rich sequence of domain 2 of the helicase. The NS3 peptide (p14) was expressed in bacteria. Its 50% inhibitory activity in a fluorometric helicase assay corresponded to 725 nM, while the ATPase activity of NS3 was not affected. Nuclear magnetic resonance (NMR) studies of peptide-protein interactions using the relaxation filtering technique revealed that p14 binds directly to the full-length helicase and its separately expressed domain 1 but not to domain 2. Changes in the NMR chemical shift of backbone amide nuclei (1H and 15N) of domain 1 or p14, measured during complex formation, were used to identify the principal amino acids of both domain 1 and the peptide engaged in their interaction. In the proposed interplay model, p14 contacts the clefts between domains 1 and 2, as well as between domains 1 and 3, preventing substrate binding. This interaction is strongly supported by cross-linking experiments, as well as by kinetic studies performed using a fluorometric assay. The antiviral activity of p14 was tested in a subgenomic HCV replicon assay that showed that the peptide at micromolar concentrations can reduce HCV RNA replication.

The title compound (4) was synthesized by the reaction of ethyl 1-(2,3,5-tri-O-benzoyl-beta-D-ribofuranosyl)-5-formylimidazole-4-carboxylate with excess guanidine in ethanol at reflux. Compound 4 was evaluated in vitro against NTPases/helicases of four different viruses of the Flaviviridae family, including the West Nile virus (WNV), hepatitis C virus (HCV), dengue virus (DENV), and the Japanese encephalitis virus (JEV), employing both an RNA and a DNA substrate. The compound showed activity against NTPase/helicase of WNV and HCV with an IC50 of 23 and 37 mu M, respectively, when a DNA substrate was employed, while no activity was observed when an RNA substrate was used. There was no activity against the NTPase/helicase of either DENV or JEV irrespective of whether an RNA or a DNA substrate was employed. Considering that Flaviviridae are RNA viruses, the observed absence of activity against an RNA substrate, but the presence of activity against a DNA substrate is intriguing and somewhat surprising. The preliminary studies show that compound 4 does not form a tight complex with either an RNA or a DNA substrate, suggesting that its mechanism of action may involve direct interaction with the enzyme. (c) 2007 Elsevier Ltd. All rights reserved.

In this report, we demonstrate the interaction of the non-structural protein 3 (NS3) of hepatitis C virus (HCV) with alkaloide tropolone (2-hydroxy-2,4,6-heptatriene-1-one) and its derivatives. The compounds were biochemically screened separately against the ATPase and helicase activities of HCV NS3. In the investigations presented, alkaIoide tropolone and its derivatives significantly inhibited the helicase activity of the viral protein when using a DNA substrate, with 50% inhibitory concentration values within a low micromolar range. The results using the RNA substrate were unexpected--none of the tropolone derivatives excerted any modulating influence towards the unwinding activity. Surprisingly, no influence of the nucleoside triphosphatase (NTPase) turnover was observed. Evidence is presented confirming that these compounds do not act by blocking the NTP-binding site, but by occupying an additional allosteric regulatory site. Further mechanisms of action, particularly of some of the derivatives, are discussed.

To improve anti-helical activity of analogues of 1 H-benzotriazole and 1 H-benzimidazole their N-alkyl derivatives were synthesized and tested for anti-helicase activity against enzymes of selected Flaviviridae including hepatitis C virus (HCV), West Nile virus (WNV), Dengue virus (DENV) and Japanese encephalitis virus (JEV). 1- and 2-alkyl derivatives of 4,5,6,7-tetrabromo-1 H-benzotriazole were obtained by direct alkylation of 4,5,6,7-tetrabromo-1 H-benzotriazole with the use of respective alkyl halides in the presence of KOH in methanol, to give a mixture of 1- and 2- isomers, which was separated by flash column chromatography in good yield. The proportion of isomers strongly depended on the reaction time and temperature. 1- and 2-hydroxyethyl and 1- and 2-chloroethyl derivatives of the tetrabromobenzo-triazole were synthesized with the use of 2-bromoethanol and 1-bromo-2-chloroethane respectively as alkylating agents. N-alkylation of this benzotriazole compound enhanced inhibitory activity and selectivity towards the helicase activity of HCV NTPase/helicase. The most active were the 2-methyl, 2-ethyl and 2-propyl derivatives (IC 50 ∼6.5 μM in the presence of DNA as a substrate). Derivatives of the benzotriazole in which hydroxyethyl or chloroethyl replaced the alkyl substituents lost their inhibitory activity. Brominated or methylated benzotriazole N(1) ribosides also did not exert helicase inhibitory activity. Although a number of N(1) and N(2) alkyl derivatives exerted good HCV and WNV helicase inhibitory activity when DNA was used as substrate, the activity was strongly decreased or even disappeared when RNA was used as substrate. The cytotoxicity tests in Vero and HeLa Tat cells showed a substantial decrease of cytotoxicity of N-alkyl derivatives as compared to the parent benzotriazole.