Transition to turbulence in driven active matter.

A Lorenz-like model was set up recently to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain nonlinear terms. The additional nonlinear term comes from the active matter contribution to the stress tensor. In this work, we investigate the nonlinear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations.

Work fluctuations and work probability distributions are fundamentally different in systems with short-ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with short-ranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet, well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behavior of the work probability distribution and the associated fluctuations is presented.

Turing-Hopf instabilities through a combination of diffusion, advection, and finite size effects.

We show that in a reaction diffusion system on a two-dimensional substrate with advection in the confined direction, the drift (advection) induced instability occurs through a Hopf bifurcation, which can become a double Hopf bifurcation. The box size in the direction of the drift is a vital parameter. Our analysis involves reduction to a low dimensional dynamical system and constructing amplitude equations.

Periodic orbits in glycolytic oscillators: from elliptic orbits to relaxation oscillations.

We consider the Sel'kov model of glycolytic oscillator for a quantitative study of the limit cycle oscillations in the system. We identify a region of parameter space where perturbation theory holds and use both Linstedt Poincaré technique and harmonic balance to obtain the shape and frequency of the limit cycle. The agreement with the numerically obtained result is excellent. We also find a different extreme, where the limit cycle is of the relaxation oscillator variety, has a large time period and it is seen that, as a particular parameter in the model is varied, the time period increases indefinitely. We characterize this divergence numerically. A calculational method is devised to capture the divergence approximately.

Effects of nondenumerable fixed points in finite dynamical systems.

The motion of a spinning soccer ball brings forth the possible existence of a whole class of finite dynamical systems where there may be a nondenumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point that a point on the fixed point in the phase space should remain there forever, for, a fixed point can evolve as well! Under such considerations one can argue that a free-kicked soccer ball should be nonchaotic.

Global persistence exponent in critical dynamics: finite-size-induced crossover.

We extend the definition of a global order parameter to the case of a critical system confined between two infinite parallel plates separated by a distance L. For a quench to the critical point we study the persistence property of the global order parameter and show that there is a crossover behavior characterized by a nonuniversal exponent which depends on the ratio of the system size to a dynamic length scale.

Third-order structure function for rotating three-dimensional homogeneous turbulent flow.

A form for the two-point third-order structure function has been calculated for three-dimensional (3D) homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalization of the 3D incompressible turbulence owing to rotation.

Finite-size effect in persistence in random walks.

We have investigated the random walk problem in a finite system and studied the crossover induced in the persistence probability by the system size. Analytical and numerical work show that the scaling function is an exponentially decaying function. We consider two cases of trapping, one by a box of size L and the other by a harmonic trap. Our analytic calculations are supported by numerical works. We also present numerical results on the harmonically trapped randomly accelerated particle and the randomly accelerated particle with viscous drag.

Nonequilibrium statistical physics with fictitious time.

Problems in nonequilibrium statistical physics are characterized by the absence of a fluctuation dissipation theorem. The usual analytic route for treating these vast class of problems is to use response fields in addition to the real fields that are pertinent to a given problem. This line of argument was introduced by Martin, Siggia, and Rose. We show that instead of using the response field, one can, following the stochastic quantization of Parisi and Wu, introduce a fictitious time. In this extra dimension a fluctuation dissipation theorem is built in and provides a different outlook to problems in nonequilibrium statistical physics.

Novel lysine biosynthetic gene sequences (LYS1 and LYS5) used as PCR targets for the detection of the pathogenic Candida yeast.

We report here a sensitive and specific polymerase chain reaction (PCR) detection assay for the pathogenic Candida yeast based on the novel LYS1 [encoding saccharopine dehydrogenase (SDH)] and LYS5 [encoding phosphopantetheinyl transferase (PPTase)] gene sequences of the fungal unique lysine biosynthetic pathway. Both LYS1 and LYS5 DNA-specific PCR primers SG1, SG2 and SG3, SG4, respectively, amplified predicted 483 and 648-bp fragments from Candida albicans genomic DNA but not from other selected fungal, bacterial, or human DNA. The 18S rDNA control primers exhibited positive amplifications in all PCR assays. The LYS1-and LYS5-specific primers strongly amplified C. albicans and Candida tropicalis target sequences; however, the LYS1 primers also weakly amplified fragments from Candida kefyr and Candida lusitaniae DNA. Both sets of primers amplified target sequences from less than 10 pg of serially diluted C. albicans DNA, and the LYS1 specific primers also detected DNA isolated from serially diluted 50 C. albicans cells. The PCR primers reported here are sufficiently sensitive and specific for the potential early detection of Candida infections with no possibility of false positive results from cross-contamination with bacterial or human DNA.

Functional analysis through site-directed mutations and phylogeny of the Candida albicans LYS1-encoded saccharopine dehydrogenase.

Candida albicans LYS1-encoded saccharopine dehydrogenase (CaLys1p, SDH) catalyzes the final biosynthetic step (saccharopine to lysine + alpha-ketoglutarate) of the novel alpha-aminoadipate pathway for lysine synthesis in fungi. The reverse reaction catalyzed by lysine-alpha-ketoglutarate reductase (LKR) is used exclusively in animals and plants for the catabolism of excess lysine. The 1,146 bp C. albicans LYS1 ORF encodes a 382 amino acid SDH. In the present investigation, we have used E. coli-expressed recombinant C. albicans Lys1p for the determination of both forward and reverse SDH activities in vitro, compared the sequence identity of C. albicans Lys1p with other known SDHs and LKRs, performed extensive site-directed mutational analyses of conserved amino acid residues and analyzed the phylogenetic relationship of C. albicans Lys1p to other known SDHs and LKRs. We have identified 14 of the 68 amino acid substitutions as essential for C. albicans Lys1p SDH activity, including two highly conserved functional motifs, H93XXF96XH98 and G138XXXG142XXG145. These results provided new insight into the functional and phylogenetic characteristics of the distinct biosynthetic SDH in fungi and catabolic LKR in higher eukaryotes.

Posttranslational activation, site-directed mutation and phylogenetic analyses of the lysine biosynthesis enzymes alpha-aminoadipate reductase Lys1p (AAR) and the phosphopantetheinyl transferase Lys7p (PPTase) from Schizosaccharomyces pombe.

Alpha-aminoadipate reductase (AAR), the signature enzyme for lysine biosynthesis in fungi, catalyses the conversion of alpha-aminoadipate to alpha-aminoadipate-semiadehyde in the presence of ATP and NADPH. In Saccharomyces cerevisiae and Candida albicans, the LYS2-encoded AAR is posttranslationally activated by CoA and the LYS5-encoded PPTase. The fission yeast Schizosaccharomyces pombe is evolutionarily highly diverged from S. cerevisiae and C. albicans. We report here several unusual activation characteristics of Sz. pombe Lys1p and Lys7p, isofunctional to Lys2p (AAR) and Lys5p (PPTase), respectively. Unlike the Lys2p from S. cerevisiae and C. albicans, the Sz. pombe Lys1p was active when expressed in E. coli and exhibited significant AAR activity without the addition of CoA or the Sz. pombe Lys7p intron free PPTase. Somewhat higher AAR activity was obtained with the addition of CoA and the Sz. pombe Lys7p PPTase. Substitution of G910A, S913T or S913A in the Sz. pombe Lys1p activation domain (IGGHSI) resulted in no AAR activity. Similarly, substitutions of several amino acid residues in the Sz. pombe Lys7p PPTase domain (G79A, R80K and P81A in Core 1; F93W, D94E, F95W and N96D in Core 1a; G124A, V125I and D126E in Core 2; K172R, E173D and K177R in Core 3) also resulted in no activation of Lys1p and no AAR activity. The Sz. pombe Lys1p amino acid sequence showed a high degree of similarity to other fungal Lys2p proteins; however, the Lys7p amino acid sequence showed much less similarity to other bacterial, fungal and animal PPTases representing several phylogenetic groups.

Time-dependent perturbation theory with a classical limit.

We construct a quantum mechanical perturbation theory which uses the multiple time scale technique. Working with the time translation operator, we use a variant on the method of Bender and Bettencourt. Our perturbation theory smoothly crosses over to the classical result as Planck's -->0. It is seen that this technique has a nonperturbative element built into it.

Approach to equilibrium in adiabatically evolving potentials.

For a potential function (in one dimension) which evolves from a specified initial form V(i)(x) to a different V(f)(x) asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibrium. There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form V(x,t) = V(f)(x) + (V(i) - V(f)) e(-lambda t). For a V(f)(x), which is double welled and a V(i)(x) which is simple harmonic, we show that, in particular, if the evolution is adiabatic, this results in a decrease in the Kramers time characteristic of V(f)(x). Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when V(i)(x) and V(f)(x) are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterizing the potential variation and the Kramers time. Both these features are illustrated through representative examples.

Site-directed mutational analysis of the novel catalytic domains of alpha-aminoadipate reductase (Lys2p) from Candida albicans.

The alpha-aminoadipate reductase, a novel enzyme in the alpha-aminoadipic acid pathway for the biosynthesis of lysine in fungi, catalyzes the conversion of alpha-aminoadipic acid to alpha-aminoadipic-delta-semialdehyde in the presence of ATP, NADPH and MgCl(2). This reaction requires two distinct gene products, Lys2p and Lys5p. In the presence of CoA, Lys5p posttranslationally activates Lys2p for the alpha-aminoadipate reductase activity. Sequence alignments indicate the presence of all functional domains required for the activation, adenylation, dehydrogenation and alpha-aminoadipic acid binding in the Lys2p. In this report we present the results of site-directed mutational analysis of the conserved amino acid residues in the catalytic domains of Lys2p from the pathogenic yeast Candida albicans. Mutants were generated in the LYS2 sequence of pCaLYS2SEI by PCR mutagenesis and expressed in E. coli BL21 cells. Recombinant mutants and the wild-type Lys2p were analyzed for their alpha-aminoadipate reductase activity. Substitution of threonine 416, glycine 418, serine 419, and lysine 424 of the adenylation domain (TXGSXXXXK, residues 416-424) resulted in a significant reduction in alpha-aminoadipate reductase activity compared to the unmutagenized Lys2p control. Similarly replacement of glycine 978, threonine 980, glycine 981, phenylalanine 982, leucine 983 and glycine 984 of the NADPH binding domain (GXTGFLG, residues 978-984) caused a drastic decrease in alpha-aminoadipate reductase activity. Finally, substitution of histidine 460, aspartic acid 461, proline 462, isoleucine 463, glutamine 464, arginine 465, and aspartic acid 466 of the putative alpha-aminoadipic acid binding domain (HDPIQRD, residues 460-466) resulted in a highly reduced alpha-aminoadipate reductase activity. These results confirm the hypothesis that specific amino acid residues in highly conserved catalytic domains of Lys2p are essential for the alpha-aminoadipate reductase activity.

Realizability of stationary spherically symmetric transonic accretion.

The spherically symmetric stationary transonic (Bondi) flow is considered a classic example of an accretion flow. This flow, however, is along a separatrix, which is usually not physically realizable. We demonstrate, using a pedagogical example, that it is the dynamics which selects the transonic flow.

Novel posttranslational activation of the LYS2-encoded alpha-aminoadipate reductase for biosynthesis of lysine and site-directed mutational analysis of conserved amino acid residues in the activation domain of Candida albicans.

The alpha-aminoadipate pathway for lysine biosynthesis is present only in fungi. The alpha-aminoadipate reductase (AAR) of this pathway catalyzes the conversion of alpha-aminoadipic acid to alpha-aminoadipic-delta-semialdehyde by a complex mechanism involving two gene products, Lys2p and Lys5p. The LYS2 and LYS5 genes encode, respectively, a 155-kDa inactive AAR and a 30-kDa phosphopantetheinyl transferase (PPTase) which transfers a phosphopantetheinyl group from coenzyme A (CoA) to Lys2p for the activation of Lys2p and AAR activity. In the present investigation, we have confirmed the posttranslational activation of the 150-kDa Lys2p of Candida albicans, a pathogenic yeast, in the presence of CoA and C. albicans lys2 mutant (CLD2) extract as a source of PPTase (Lys5p). The recombinant Lys2p or CLD2 mutant extract exhibited no AAR activity with or without CoA. However, the recombinant 150-kDa Lys2p, when incubated with CLD2 extract and CoA, exhibited significant AAR activity compared to that of wild-type C. albicans CAI4 extract. The PPTase in the CLD2 extract was required only for the activation of Lys2p and not for AAR reaction. Site-directed mutational analysis of G882 and S884 of the Lys2p activation domain (LGGHSI) revealed no AAR activity, indicating that these two amino acids are essential for the activation. Replacement of other amino acid residues in the domain resulted in partial or full AAR activity. These results demonstrate the posttranslational activation and the requirement of specific amino acid residues in the activation domain of the AAR of C. albicans.

Zero-frequency critical bulk viscosity: is the amplitude ratio truly universal?

It was shown by Onuki that the zero-frequency bulk viscosity is associated with a universal amplitude ratio that was calculated to be around 0.10. We show that the sound attenuation data can be used to extract a value for this universal number and we find this number to be around 0.18, reasonably close to Onuki's estimate. However, we argue that a reconsideration of this amplitude ratio shows that this ratio is not truly universal. It has a logarithmic correction instead.

Rayleigh-Marangoni convection in a critical fluid: a tale of two crossovers.

We show that if we take a thin layer of fluid where surface tension effects are supposed to dominate and gradually bring the mean temperature of the layer closer and closer to the liquid vapor critical point, then first there is a crossover from Marangoni to Rayleigh-Benard convection and thence to a convection whose onset is determined by the Schwarzchild criterion.

Frequency-dependent viscosity near the critical point: the scale to two-loop order.

The recent accurate measurements of Berg, Moldover, and Zimmerli [Phys. Rev. Lett. 82, 920 (1999); Phys. Rev. E 60, 4079 (1999)] of the viscoelastic effect near the critical point of xenon has shown that the scale factor involved in the frequency scaling is about twice the scale factor obtained theoretically. We show that this discrepancy is a consequence of using first order perturbation theory. Including two-loop contribution goes a long way towards removing the discrepancy.