Timing the Emergence of Resistance to Anti-HIV Drugs with Large Genetic Barriers

New antiretroviral drugs that offer large genetic barriers to resistance, such as the recently approved inhibitors of HIV-1 protease, tipranavir and darunavir, present promising weapons to avert the failure of current therapies for HIV infection. Optimal treatment strategies with the new drugs, however, are yet to be established. A key limitation is the poor understanding of the process by which HIV surmounts large genetic barriers to resistance. Extant models of HIV dynamics are predicated on the predominance of deterministic forces underlying the emergence of resistant genomes. In contrast, stochastic forces may dominate, especially when the genetic barrier is large, and delay the emergence of resistant genomes. We develop a mathematical model of HIV dynamics under the influence of an antiretroviral drug to predict the waiting time for the emergence of genomes that carry the requisite mutations to overcome the genetic barrier of the drug. We apply our model to describe the development of resistance to tipranavir in in vitro serial passage experiments. Model predictions of the times of emergence of different mutant genomes with increasing resistance to tipranavir are in quantitative agreement with experiments, indicating that our model captures the dynamics of the development of resistance to antiretroviral drugs accurately. Further, model predictions provide insights into the influence of underlying evolutionary processes such as recombination on the development of resistance, and suggest guidelines for drug design: drugs that offer large genetic barriers to resistance with resistance sites tightly localized on the viral genome and exhibiting positive epistatic interactions maximally inhibit the emergence of resistant genomes.

Quantum first-passage problem

Formulation of quantum first passage problem is attempted in terms of a restricted Feynman path integral that simulates an absorbing barrier as in the corresponding classical case. The positivity of the resulting probability density, however, remains to be demonstrated.

Serial quaternary-to-analogue converters

Circuits for realizing serial quaternary-to-analogue converters (QACs) are proposed in this paper. Three techniques are presented based on Shannon-Rack decoder, sample/hold serial digital-to-analogue converter and cyclic digital-to-analogue converter. Circuits for the generation of control signals and the multiplexer required in the realization of the QACs are also described. A comparison of the three methods is made.

A parallel-serial binary arbitration scheme for collision-free multi-access techniques

Multi-access techniques are widely used in computer networking and distributed multiprocessor systems. On-the-fly arbitration schemes permit one of the many contenders to access the medium without collisions. Serial arbitration is cost effective but is slow and hence unsuitable for high-speed multiprocessor environments supporting very high data transfer rates. A fully parallel arbitration scheme takes less time but is not practically realisable for large numbers of contenders. In this paper, a generalised parallel-serial scheme is proposed which significantly reduces the arbitration time and is practically realisable.

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Phenotypic and Functional Characterization of Human Mammary Stem/Progenitor Cells in Long Term Culture

Background: Cancer stem cells exhibit close resemblance to normal stem cells in phenotype as well as function. Hence, studying normal stem cell behavior is important in understanding cancer pathogenesis. It has recently been shown that human breast stem cells can be enriched in suspension cultures as mammospheres. However, little is known about the behavior of these cells in long-term cultures. Since extensive self-renewal potential is the hallmark of stem cells, we undertook a detailed phenotypic and functional characterization of human mammospheres over long-term passages. Methodology: Single cell suspensions derived from human breast `organoids' were seeded in ultra low attachment plates in serum free media. Resulting primary mammospheres after a week (termed T1 mammospheres) were subjected to passaging every 7th day leading to the generation of T2, T3, and T4 mammospheres. Principal Findings: We show that primary mammospheres contain a distinct side-population (SP) that displays a CD24(low)/CD44(low) phenotype, but fails to generate mammospheres. Instead, the mammosphere-initiating potential rests within the CD44(high)/CD24(low) cells, in keeping with the phenotype of breast cancer-initiating cells. In serial sphere formation assays we find that even though primary (T1) mammospheres show telomerase activity and fourth passage T4 spheres contain label-retaining cells, they fail to initiate new mammospheres beyond T5. With increasing passages, mammospheres showed an increase in smaller sized spheres, reduction in proliferation potential and sphere forming efficiency, and increased differentiation towards the myoepithelial lineage. Significantly, staining for senescence-associated beta-galactosidase activity revealed a dramatic increase in the number of senescent cells with passage, which might in part explain the inability to continuously generate mammospheres in culture. Conclusions: Thus, the self-renewal potential of human breast stem cells is exhausted within five in vitro passages of mammospheres, suggesting the need for further improvisation in culture conditions for their long-term maintenance.

Conformation of the flexible bent helix of Leu1-zervamicin in crystal C and a possible gating action for ion passage

The membrane channel-forming polypeptide, Leu(1)-zervamicin, Ac-Leu-Ile-Gln-Iva-Ile(5)-Thr-Aib-Leu-Aib-Hyp(10) -Gln-Aib-Hyp-Aib-Pro(15)-Phol (Aib: alpha-aminoisobutyric acid; Iva: isovaline; Hyp: 4-hydroxyproline; Phol: phenylalininol) has been analyzed by x-ray diffraction in a third crystal form. Although the bent helix is quite similar to the conformations found in crystals A and B, the amount of bending is more severe with a bending angle approximate to 47 degrees, The water channel formed by the convex polar faces of neighboring helices is larger at the mouth than in crystals A and B, and the water sites have become disordered. The channel is interrupted in the middle by a hydrogen bond between the OH of Hyp(10) and the NH2 of the Gln(11) of a neighboring molecule. The side chain of Gln(11) is wrapped around the helix backbone in an unusual fashion in order that it can augment the polar side of the helix. In the present crystal C there appears to be an additional conformation for the Gln(11) side chain (with approximate to 20% occupancy) that opens the channel for possible ion passage. Structure parameters for C85H140N18O22.xH(2)O.C2H5OH are space group P2(1)2(1)2(1), a = 10.337 (2) Angstrom, b = 28.387 (7) Angstrom, c = 39.864 (11) Angstrom, Z = 4, agreement factor R = 12.99% for 3250 data observed > 3 sigma(F), resolution = 1.2 Angstrom. (C) 1994 John Wiley & Sons, Inc.

First passage probability during random vibration

The probability that a random process crosses an arbitrary level for the first time is expressed as a Gram—Charlier series, the leading term of which is the Poisson approximation. The coefficients of this series are related to the moments of the number of level crossings. The results are applicable to both stationary and non-stationary processes. Some numerical results are presented for the response process of a linear single-degree-of-freedom oscillator under Gaussian white noise excitation.

Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

First passage distributions for long memory processes

We study the distribution of first passage time for Levy type anomalous diffusion. A fractional Fokker-Planck equation framework is introduced.For the zero drift case, using fractional calculus an explicit analytic solution for the first passage time density function in terms of Fox or H-functions is given. The asymptotic behaviour of the density function is discussed. For the nonzero drift case, we obtain an expression for the Laplace transform of the first passage time density function, from which the mean first passage time and variance are derived.

Mutual inhibition and capacity sharing during parallel preparation of serial eye movements

Many common activities, like reading, scanning scenes, or searching for an inconspicuous item in a cluttered environment, entail serial movements of the eyes that shift the gaze from one object to another. Previous studies have shown that the primate brain is capable of programming sequential saccadic eye movements in parallel. Given that the onset of saccades directed to a target are unpredictable in individual trials, what prevents a saccade during parallel programming from being executed in the direction of the second target before execution of another saccade in the direction of the first target remains unclear. Using a computational model, here we demonstrate that sequential saccades inhibit each other and share the brain's limited processing resources (capacity) so that the planning of a saccade in the direction of the first target always finishes first. In this framework, the latency of a saccade increases linearly with the fraction of capacity allocated to the other saccade in the sequence, and exponentially with the duration of capacity sharing. Our study establishes a link between the dual-task paradigm and the ramp-to-threshold model of response time to identify a physiologically viable mechanism that preserves the serial order of saccades without compromising the speed of performance.

Carboxyl terminal domain basic amino acids of mycobacterial topoisomerase I bind DNA to promote strand passage

Bacterial DNA topoisomerase I (topoI) carries out relaxation of negatively supercoiled DNA through a series of orchestrated steps, DNA binding, cleavage, strand passage and religation. The N-terminal domain (NTD) of the type IA topoisomerases harbor DNA cleavage and religation activities, but the carboxyl terminal domain (CTD) is highly diverse. Most of these enzymes contain a varied number of Zn2+ finger motifs in the CTD. The Zn2+ finger motifs were found to be essential in Escherichia coli topoI but dispensable in the Thermotoga maritima enzyme. Although, the CTD of mycobacterial topoI lacks Zn2+ fingers, it is indispensable for the DNA relaxation activity of the enzyme. The divergent CTD harbors three stretches of basic amino acids needed for the strand passage step of the reaction as demonstrated by a new assay. We also show that the basic amino acids constitute an independent DNA-binding site apart from the NTD and assist the simultaneous binding of two molecules of DNA to the enzyme, as required during the catalytic step. Although the NTD binds to DNA in a site-specific fashion to carry out DNA cleavage and religation, the basic residues in CTD bind to non-scissile DNA in a sequence-independent manner to promote the crucial strand passage step during DNA relaxation. The loss of Zn2+ fingers from the mycobacterial topoI could be associated with Zn2+ export and homeostasis.

Pattern-growth based frequent serial episode discovery

Frequent episode discovery is a popular framework for pattern discovery from sequential data. It has found many applications in domains like alarm management in telecommunication networks, fault analysis in the manufacturing plants, predicting user behavior in web click streams and so on. In this paper, we address the discovery of serial episodes. In the episodes context, there have been multiple ways to quantify the frequency of an episode. Most of the current algorithms for episode discovery under various frequencies are apriori-based level-wise methods. These methods essentially perform a breadth-first search of the pattern space. However currently there are no depth-first based methods of pattern discovery in the frequent episode framework under many of the frequency definitions. In this paper, we try to bridge this gap. We provide new depth-first based algorithms for serial episode discovery under non-overlapped and total frequencies. Under non-overlapped frequency, we present algorithms that can take care of span constraint and gap constraint on episode occurrences. Under total frequency we present an algorithm that can handle span constraint. We provide proofs of correctness for the proposed algorithms. We demonstrate the effectiveness of the proposed algorithms by extensive simulations. We also give detailed run-time comparisons with the existing apriori-based methods and illustrate scenarios under which the proposed pattern-growth algorithms perform better than their apriori counterparts. (C) 2013 Elsevier B.V. All rights reserved.