Kushal Shah

On the origin of three base periodicity in genomes.

Genomes of almost all organisms have been found to exhibit several periodicities, the most prominent one is the three base periodicity. It is more pronounced in the gene coding regions and has been exploited to identify the segments of a genome that code for a protein. The reason for this three base periodicity in the gene-coding region has been attributed to inhomogeneous nucleotide compositions in the three codon positions. However, this reason cannot explain the three base periodicity present at the level of the whole genome where the codon concept is not applicable. Even though the distribution of each nucleotide is uniform at the positions 0(mod 3), 1(mod 3) and 2(mod 3) when the whole genome data is considered, our analysis reveals that the three base periodicity is arising because of higher correlations among the nucleotides separated by three bases.

Analytic, nonlinearly exact solutions for an rf confined plasma

RF confined electron plasmas are of importance in Paul traps [W. Paul, Rev. Mod. Phys. 62, 531 (1990)]. The stability of such plasmas is unclear and statistical heating arguments have been advanced to explain the observed heating in such plasmas [I. Siemers et al., Phys. Rev. A 38, 5121 (1988)]. This study investigates the nature of a one-dimensional collisionless electron plasma that is confined by an rf field of the form [−B+Acos(ωt)]x, where x is the space coordinate and ω is the rf frequency. Nonlinearly exact solutions are obtained. The distribution function and the plasma density are obtained in closed form and have constant shapes with time varying oscillations. These oscillations are at the rf frequency and its harmonics, modulated by a low frequency related to the electron bounce time. The linear limit of weak fields is recovered. Analytic expressions are obtained for the required external field to make it consistent with prescribed distribution functions. These solutions remain valid even in the...

Nucleotide correlation based measure for identifying origin of replication in genomic sequences

Computational prediction of the origin of replication is a challenging problem and of immense interest to biologists. Several methods have been proposed for identifying the replicon site for various classes of organisms. However, these methods have limited applicability since the replication mechanism is different in different organisms. We propose a correlation measure and show that it is correctly able to predict the origin of replication in most of the bacterial genomes. When applied to Methanocaldococcus jannaschii, Plasmodium falciparum apicoplast and Nicotiana tabacum plastid, this correlation based method is able to correctly predict the origin of replication whereas the generally used GC skew measure fails. Thus, this correlation based measure is a novel and promising tool for predicting the origin of replication in a wide class of organisms. This could have important implications in not only gaining a deeper understanding of the replication machinery in higher organisms, but also for drug discovery.

Space charge effects in rf traps: Ponderomotive concept and stroboscopic analysis

Exact solutions for one-dimensional (1D) plasma dynamics in an rf trap are known when space charge effects are neglected [K. Shah and H. S. Ramachandran, Phys. Plasmas 15, 062303 (2008)]. In this work, weak space charge effects in an rf trap are considered. An analytic expression for the time varying distribution function of the 1D plasma is obtained. It is shown that the plasma is a Maxwellian up to the lowest order in nonlinearity and that the spatially constant temperature periodically oscillates in time at the same rate as the rf frequency. It was shown by Krapchev [Phys. Rev. Lett. 42, 497 (1979)] that the time averaged distribution function is double humped with respect to velocity beyond a certain threshold in space. The time average of the complete time varying distribution function is obtained and some of the predictions of Krapchev are recovered, while also finding discrepancies. The relationship between stroboscopic orbits and the time averaged ponderomotive orbit are obtained for such traps.

Identification and characterization of ARS‐like sequences as putative origin(s) of replication in human malaria parasite Plasmodium falciparum

DNA replication is a fundamental process in genome maintenance, and initiates from several genomic sites (origins) in eukaryotes. In Saccharomyces cerevisiae, conserved sequences known as autonomously replicating sequences (ARSs) provide a landing pad for the origin recognition complex (ORC), leading to replication initiation. Although origins from higher eukaryotes share some common sequence features, the definitive genomic organization of these sites remains elusive. The human malaria parasite Plasmodium falciparum undergoes multiple rounds of DNA replication; therefore, control of initiation events is crucial to ensure proper replication. However, the sites of DNA replication initiation and the mechanism by which replication is initiated are poorly understood. Here, we have identified and characterized putative origins in P. falciparum by bioinformatics analyses and experimental approaches. An autocorrelation measure method was initially used to search for regions with marked fluctuation (dips) in the chromosome, which we hypothesized might contain potential origins. Indeed, S. cerevisiae ARS consensus sequences were found in dip regions. Several of these P. falciparum sequences were validated with chromatin immunoprecipitation‐quantitative PCR, nascent strand abundance and a plasmid stability assay. Subsequently, the same sequences were used in yeast to confirm their potential as origins in vivo. Our results identify the presence of functional ARSs in P. falciparum and provide meaningful insights into replication origins in these deadly parasites. These data could be useful in designing transgenic vectors with improved stability for transfection in P. falciparum.

Equilibration of energy in slow–fast systems

Significance Do partial energies in slow–fast Hamiltonian systems equilibrate? This is a long-standing problem related to the foundation of statistical mechanics. Altering the traditional ergodic assumption, we propose that nonergodicity in the fast subsystem leads to equilibration of the whole system. To show this principle, we introduce a set of mechanical toy models—the springy billiards—and describe stochastic processes corresponding to their adiabatic behavior. We expect that these models and this principle will play an important role in the quest to establish and study the underlying postulates of statistical mechanics, one of the long-standing scientific grails. Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. However, in systems with several characteristic timescales, the ergodicity of the fast subsystem impedes the equilibration of the whole system because of the presence of an adiabatic invariant. In this paper, we show that violation of ergodicity in the fast dynamics can drive the whole system to equilibrium. To show this principle, we investigate the dynamics of springy billiards, which are mechanical systems composed of a small particle bouncing elastically in a bounded domain, where one of the boundary walls has finite mass and is attached to a linear spring. Numerical simulations show that the springy billiard systems approach equilibrium at an exponential rate. However, in the limit of vanishing particle-to-wall mass ratio, the equilibration rates remain strictly positive only when the fast particle dynamics reveal two or more ergodic components for a range of wall positions. For this case, we show that the slow dynamics of the moving wall can be modeled by a random process. Numerical simulations of the corresponding springy billiards and their random models show equilibration with similar positive rates.

Asymptotic solution of Fokker-Planck equation for plasma in Paul traps

An exact analytic solution of the Vlasov equation for the plasma distribution in a Paul trap is known to be a Maxwellian and thus, immune to collisions under the assumption of infinitely fast relaxation [K. Shah and H. S. Ramachandran, Phys. Plasmas 15, 062303 (2008)]. In this paper, it is shown that even for a more realistic situation of finite time relaxation, solutions of the Fokker–Planck equation lead to an equilibrium solution of the form of a Maxwellian with oscillatory temperature. This shows that the rf heating observed in Paul traps cannot be caused due to collisional effects alone.

Time Evolution of Tsallis Distribution in Paul Trap

Motion of individual charged particles inside a Paul trap is very well understood, but the understanding of collective dynamics offers a challenge and opens up avenues for investigation. This problem has been addressed earlier by solving the 1-D Vlasov equation assuming the initial distribution to be Gaussian. In this paper, we generalize this solution by taking a Tsallis distribution, since in some Paul trap experiments, the plasma distribution has been reported to have power law tails. The time averaged distribution function is found to be doubled humped in velocity beyond a spatial threshold and the hump moves away from the bulk as the Tsallis parameter is increased from 1. The plasma temperature is found to vary quadratically with the spatial coordinate.

Leaky Fermi accelerators

A Fermi accelerator is a billiard with oscillating walls. A leaky accelerator interacts with an environment of an ideal gas at equilibrium by exchange of particles through a small hole on its boundary. Such interaction may heat the gas: we estimate the net energy flow through the hole under the assumption that the particles inside the billiard do not collide with each other and remain in the accelerator for a sufficiently long time. The heat production is found to depend strongly on the type of Fermi accelerator. An ergodic accelerator, i.e., one that has a single ergodic component, produces a weaker energy flow than a multicomponent accelerator. Specifically, in the ergodic case the energy gain is independent of the hole size, whereas in the multicomponent case the energy flow may be significantly increased by shrinking the hole size.

Plasma response to nonlinear time-periodic electric fields in one dimension

Plasma response to spatially nonuniform time-periodic electric fields is of importance in many applications. For the case of a spatially linear monochromatic electric field in Paul traps, exact analytic expressions for the time-dependent plasma distribution function have been recently obtained [K. Shah and H. S. Ramachandran, Phys. Plasmas 15, 062303 (2008)]. In this paper, the problem of plasma response to a one-dimensional time-periodic electric field with a general spatial dependence is considered and analytic expressions for the time-averaged plasma distribution function and density are derived by solving the Vlasov equation under two limiting cases of high and low frequencies. Under this approximation, it is shown that the time-averaged plasma density is a function of the square of the oscillatory electric potential.