Mathematical Model of Viral Kinetics In Vitro Estimates the Number of E2-CD81 Complexes Necessary for Hepatitis C Virus Entry

Interaction between the hepatitis C virus (HCV) envelope protein E2 and the host receptor CD81 is essential for HCV entry into target cells. The number of E2-CD81 complexes necessary for HCV entry has remained difficult to estimate experimentally. Using the recently developed cell culture systems that allow persistent HCV infection in vitro, the dependence of HCV entry and kinetics on CD81 expression has been measured. We reasoned that analysis of the latter experiments using a mathematical model of viral kinetics may yield estimates of the number of E2-CD81 complexes necessary for HCV entry. Here, we constructed a mathematical model of HCV viral kinetics in vitro, in which we accounted explicitly for the dependence of HCV entry on CD81 expression. Model predictions of viral kinetics are in quantitative agreement with experimental observations. Specifically, our model predicts triphasic viral kinetics in vitro, where the first phase is characterized by cell proliferation, the second by the infection of susceptible cells and the third by the growth of cells refractory to infection. By fitting model predictions to the above data, we were able to estimate the threshold number of E2-CD81 complexes necessary for HCV entry into human hepatoma-derived cells. We found that depending on the E2-CD81 binding affinity, between 1 and 13 E2-CD81 complexes are necessary for HCV entry. With this estimate, our model captured data from independent experiments that employed different HCV clones and cells with distinct CD81 expression levels, indicating that the estimate is robust. Our study thus quantifies the molecular requirements of HCV entry and suggests guidelines for intervention strategies that target the E2-CD81 interaction. Further, our model presents a framework for quantitative analyses of cell culture studies now extensively employed to investigate HCV infection.

Rainbow Connection Number and Connectivity

The rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges, so that every pair of vertices is connected by at least one path in which no two edges are colored the same. Our main result is that rc(G) <= inverted right perpendicularn/2inverted left perpendicular for any 2-connected graph with at least three vertices. We conjecture that rc(G) <= n/kappa + C for a kappa-connected graph G of order n, where C is a constant, and prove the conjecture for certain classes of graphs. We also prove that rc(G) < (2 + epsilon)n/kappa + 23/epsilon(2) for any epsilon > 0.

Impact of Disturrance on Composition, Structure, And Floristics of Tropical Moist Forests in Uttara Kannada District, Western Ghats, India

Impact of disturbance on forest stand density, basal area, dbh class distribution of density and basal area, species richness, species diversity and similarity index was assessed through monitoring six, one-hectare, permanent forest plots after a period of 24 years in tropical moist forests of Uttara Kannada district, Western Ghats, India. It was observed that all sites lost trees due to removal by people and mortality. Loss of trees was more in sites that are easily accessible and closer to human habitation. In spite of a decrease in tree density, an increase in basal area was observed in some forest plots, which could be on account of stimulatory growth of surviving trees. Decrease in basal area in other sites indicates greater human pressure and overexploitation of trees. Preponderance of lower girth class trees, and a unimodal reverse `J-shaped' curve of density distribution as observed in majority of the sites in the benchmark year, was indicative of regenerating status of these forests. The decrease in number of species in all forest sites was due to indiscriminate removal of trees by people, without sparing species with only a few individuals, and also due to mortality of trees of rare species. Higher species richness and diversity in the lowest dbh class in most of the sites in the benchmark year is indicative of the existence of favorable conditions for sylvigenesis. The decrease in the similarity index suggests extirpation of species, favoring invasion and colonization by secondary species. To minimize human pressure on forests and to facilitate regeneration and growth, proper management planning and conservation measures are needed.

Real-time monitoring of critical nodes with minimal number of Phasor Measurement Units

This paper presents a method for placement of Phasor Measurement Units, ensuring the monitoring of vulnerable buses which are obtained based on transient stability analysis of the overall system. Real-time monitoring of phase angles across different nodes, which indicates the proximity to instability, the very purpose will be well defined if the PMUs are placed at buses which are more vulnerable. The issue is to identify the key buses where the PMUs should be placed when the transient stability prediction is taken into account considering various disturbances. Integer Linear Programming technique with equality and inequality constraints is used to find out the optimal placement set with key buses identified from transient stability analysis. Results on IEEE-14 bus system are presented to illustrate the proposed approach.

Rainbow connection number and connected dominating sets

The rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this article we show that for every connected graph on n vertices with minimum degree delta, the rainbow connection number is upper bounded by 3n/(delta + 1) + 3. This solves an open problem from Schiermeyer (Combinatorial Algorithms, Springer, Berlin/Hiedelberg, 2009, pp. 432437), improving the previously best known bound of 20n/delta (J Graph Theory 63 (2010), 185191). This bound is tight up to additive factors by a construction mentioned in Caro et al. (Electr J Combin 15(R57) (2008), 1). As an intermediate step we obtain an upper bound of 3n/(delta + 1) - 2 on the size of a connected two-step dominating set in a connected graph of order n and minimum degree d. This bound is tight up to an additive constant of 2. This result may be of independent interest. We also show that for every connected graph G with minimum degree at least 2, the rainbow connection number, rc(G), is upper bounded by Gc(G) + 2, where Gc(G) is the connected domination number of G. Bounds of the form diameter(G)?rc(G)?diameter(G) + c, 1?c?4, for many special graph classes follow as easy corollaries from this result. This includes interval graphs, asteroidal triple-free graphs, circular arc graphs, threshold graphs, and chain graphs all with minimum degree delta at least 2 and connected. We also show that every bridge-less chordal graph G has rc(G)?3.radius(G). In most of these cases, we also demonstrate the tightness of the bounds.

Cubicity, degeneracy, and crossing number

A $k$-box $B=(R_1,...,R_k)$, where each $R_i$ is a closed interval on the real line, is defined to be the Cartesian product $R_1\times R_2\times ...\times R_k$. If each $R_i$ is a unit length interval, we call $B$ a $k$-cube. Boxicity of a graph $G$, denoted as $\boxi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-boxes. Similarly, the cubicity of $G$, denoted as $\cubi(G)$, is the minimum integer $k$ such that $G$ is an intersection graph of $k$-cubes. It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan: Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/ 0607092, 2006.] that, for a graph $G$ with maximum degree $\Delta$, $\cubi(G)\leq \lceil 4(\Delta +1)\log n\rceil$. In this paper, we show that, for a $k$-degenerate graph $G$, $\cubi(G) \leq (k+2) \lceil 2e \log n \rceil$. Since $k$ is at most $\Delta$ and can be much lower, this clearly is a stronger result. This bound is tight. We also give an efficient deterministic algorithm that runs in $O(n^2k)$ time to output a $8k(\lceil 2.42 \log n\rceil + 1)$ dimensional cube representation for $G$. An important consequence of the above result is that if the crossing number of a graph $G$ is $t$, then $\boxi(G)$ is $O(t^{1/4}{\lceil\log t\rceil}^{3/4})$ . This bound is tight up to a factor of $O((\log t)^{1/4})$. We also show that, if $G$ has $n$ vertices, then $\cubi(G)$ is $O(\log n + t^{1/4}\log t)$. Using our bound for the cubicity of $k$-degenerate graphs we show that cubicity of almost all graphs in $\mathcal{G}(n,m)$ model is $O(d_{av}\log n)$, where $d_{av}$ denotes the average degree of the graph under consideration. model is O(davlogn).

Coulomb-hole summations and energies for GW calculations with limited number of empty orbitals: a modified static remainder approach

Ab initio GW calculations are a standard method for computing the spectroscopic properties of many materials. The most computationally expensive part in conventional implementations of the method is the generation and summation over the large number of empty orbitals required to converge the electron self-energy. We propose a scheme to reduce the summation over empty states by the use of a modified static remainder approximation, which is simple to implement and yields accurate self-energies for both bulk and molecular systems requiring a small fraction of the typical number of empty orbitals.

Queuing of concurrent movement plans by Basal Ganglia

How the brain converts parallel representations of movement goals into sequential movements is not known. We tested the role of basal ganglia (BG) in the temporal control of movement sequences by a convergent approach involving inactivation of the BG by muscimol injections into the caudate nucleus of monkeys and assessing behavior of Parkinson's disease patients, performing a modified double-step saccade task. We tested a critical prediction of a class of competitive queuing models that explains serial behavior as the outcome of a selection of concurrently activated goals. In congruence with these models, we found that inactivation or impairment of the BG unmasked the parallel nature of goal representations such that a significantly greater extent of averaged saccades, curved saccades, and saccade sequence errors were observed. These results suggest that the BG perform a form of competitive queuing, holding the second movement plan in abeyance while the first movement is being executed, allowing the proper temporal control of movement sequences.

Optimal design of timer-based, distributed selection with unknown number of nodes

The timer-based selection scheme is a popular, simple, and distributed scheme that is used to select the best node from a set of available nodes. In it, each node sets a timer as a function of a local preference number called a metric, and transmits a packet when its timer expires. The scheme ensures that the timer of the best node, which has the highest metric, expires first. However, it fails to select the best node if another node transmits a packet within Delta s of the transmission by the best node. We derive the optimal timer mapping that maximizes the average success probability for the practical scenario in which the number of nodes in the system is unknown but only its probability distribution is known. We show that it has a special discrete structure, and present a recursive characterization to determine it. We benchmark its performance with ad hoc approaches proposed in the literature, and show that it delivers significant gains. New insights about the optimality of some ad hoc approaches are also developed.

On the Chern number of I-admissible filtrations of ideals

Let I be an m-primary ideal of a Noetherian local ring (R, m) of positive dimension. The coefficient e(1)(I) of the Hilbert polynomial of an I-admissible filtration I is called the Chern number of I. A formula for the Chern number has been derived involving the Euler characteristic of subcomplexes of a Koszul complex. Specific formulas for the Chern number have been given in local rings of dimension at most two. These have been used to provide new and unified proofs of several results about e(1)(I).

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

Contrasting fire regimes in a seasonally dry tropical forest and a savanna ecosystem in the western Ghats, India

Tropical dry forests and savannas constitute more than half of all tropical forests and grasslands, but little is known about forest fire regimes within these two extensive types of ecosystems. Forest fire regimes in a predominantly dry forest in India, the Nilgiri landscape, and a predominantly savanna ecosystem in the Sathyamangalam landscape, were examined. Remote sensing data were applied to delineate burned areas, determine fire size characteristics, and to estimate fire-rotation intervals. Belt transects (0.5 ha) were used to estimate forest structure, diversity, and fuel loads. Mean area burned, mean number of fires, and mean fire size per year were substantially higher in the Nilgiri landscape compared to the Sathyamangalam landscape. Mean fire-rotational interval was 7.1 yr in the Nilgiri landscape and 44.1 yr in the Sathyamangalam landscape. Tree (>= 10 cm diameter at breast height) species diversity, tree density, and basal area were significantly higher in the Nilgiri landscape compared to the Sathyamangalam landscape. Total fuel loads were significantly higher in tropical dry and moist deciduous forests in the Nilgiri landscape, but total fuel loads were higher in the tropical dry thorn forests of the Sathyamangalam landscape. Thus, the two landscapes revealed contrasting fire regimes and forest characteristics, with more and four-fold larger fires in the Nilgiri landscape. The dry forests and savannas could be maintained by a combination of factors, such as fire, grazing pressures, and herbivore populations. Understanding the factors maintaining these two ecosystems will be critical for their conservation.

Effect of steady rotation on low Reynolds number vortex shedding behind a circular cylinder

In this paper control of oblique vortex shedding in the wake behind a straight circular cylinder is explored experimentally and computationally. Towards this, steady rotation of the cylinder about its axis is used as a control device. Some limited studies are also performed with a stepped circular cylinder, where at the step the flow is inevitably three-dimensional irrespective of the rotation rate. When there is no rotation, the vortex shedding pattern is three dimensional as described in many previous studies. With a non-zero rotation rate, it is demonstrated experimentally as well as numerically that the shedding pattern becomes more and more two-dimensional. At sufficiently high rotation rates, the vortex shedding is completely suppressed.

Effect of myonuclear number and mitochondrial fusion on Drosophila indirect flight muscle organization and size

Mechanisms involved in establishing the organization and numbers of fibres in a muscle are not completely understood. During Drosophila indirect flight muscle (IFM) formation, muscle growth is achieved by both incorporating hundreds of nuclei, and hypertrophy. As a result, IFMs provide a good model with which to understand the mechanisms that govern overall muscle organization and growth. We present a detailed analysis of the organization of dorsal longitudinal muscles (DLMs), a subset of the IFMs. We show that each DLM is similar to a vertebrate fascicle and consists of multiple muscle fibres. However, increased fascicle size does not necessarily change the number of constituent fibres, but does increase the number of myofibrils packed within the fibres. We also find that altering the number of myoblasts available for fusion changes DLM fascicle size and fibres are loosely packed with myofibrils. Additionally, we show that knock down of genes required for mitochondrial fusion causes a severe reduction in the size of DLM fascicles and fibres. Our results establish the organization levels of DLMs and highlight the importance of the appropriate number of nuclei and mitochondrial fusion in determining the overall organization, growth and size of DLMs. (C) 2013 Elsevier Inc. All rights reserved.

EFFICIENT QUANTUM RANDOM NUMBER GENERATION USING QUANTUM INDISTINGUISHABILITY

In this paper, we propose a quantum method for generation of random numbers based on bosonic stimulation. Randomness arises through the path-dependent indeterministic amplification of two competing bosonic modes. We show that the process provides an efficient method for macroscopic extraction of microscopic randomness.