Steady-state Number Research Articles

Probing the site of glutathione reduction by thioredoxin/glutathione reductase from Schistosoma mansoni under anaerobic conditions

Thioredoxin/glutathione reductase from Schistosoma mansoni (SmTGR) is a multifunctional enzyme that catalyzes the reduction of glutathione (GSSG) and thioredoxin, as well as the deglutathionylation of peptide and non-peptide substrates. SmTGR structurally resembles known glutathione reductases (GR) and thioredoxin reductases (TrxR) but with an appended N-terminal domain that has a typical glutaredoxin (Grx) fold. Despite structural homology with known GRs, the site of GSSG reduction has frequently been reported as the Grx domain, based primarily on aerobic, steady-state kinetic measurements and x-ray crystallography. Here, we present an anaerobic characterization of a series of variant SmTGRs to establish the site of GSSG reduction as the cysteine pair most proximal to the FAD, Cys154/Cys159, equivalent to the site of GSSG reduction in GRs. Anaerobic steady-state analysis of U597C, U597S, U597C + C31S, and I592STOP SmTGR demonstrate that the Grx domain is not involved in the catalytic reduction of GSSG, as redox silencing of the C-terminus results in no modulation of the observed turnover number (∼0.025 s−1) and redox silencing of the Grx domain results in an increased observed turnover number (∼0.08 s−1). Transient-state single turnover analysis of these variants corroborates this, as the slowest rate observed titrates hyperbolically with GSSG concentration and approaches a limit that coincides with the respective steady-state turnover number for each variant. Numerical integration fitting of the transient state data can only account for the observed trends when competitive binding of the C-terminus is included, indicating that the partitioning of electrons to either substrate occurs at the Cys154/Cys159 disulfide rather than the previously proposed Cys596/Sec597 sulfide/selenide. Paradoxically, truncating the C-terminus at Ile592 results in a loss of GR activity, indicating a crucial non-redox role for the C-terminus.

A New Sampling Scheme for an Improved Monitoring of the Process Mean

ABSTRACT This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple random sampling-based counterpart. Moreover, a new EWMA chart based on the mean estimator within the MS scheme is proposed. The performance of the EWMA charts, derived from both simple random sampling (SRS) and MS schemes, is evaluated using the metrics of steady-state average run-length and average number of items-to-signal. The findings underscore the superiority of the EWMA-MS chart over the EWMA-SRS chart. Additionally, as the magnitude of ranking errors escalates, the behavior of the EWMA-MS chart converges toward that of the EWMA-SRS chart. The practical implementation of the newly introduced EWMA chart is demonstrated through an illustrative example.

What can we learn when fitting a simple telegraph model to a complex gene expression model?

In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data for E. coli and mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.

Simple and Explicit Bounds for Multiserver Queues with 11−ρ Scaling

We consider the first-come-first-serve (FCFS) [Formula: see text] queue and prove the first simple and explicit bounds that scale as [Formula: see text] under only the assumption that interarrival times have finite second moment, and service times have finite [Formula: see text] moment for some [Formula: see text]. Here, ρ denotes the corresponding traffic intensity. Conceptually, our results can be viewed as a multiserver analogue of Kingman’s bound. Our main results are bounds for the tail of the steady-state queue length and the steady-state probability of delay. The strength of our bounds (e.g., in the form of tail decay rate) is a function of how many moments of the service distribution are assumed finite. Our bounds scale gracefully, even when the number of servers grows large and the traffic intensity converges to unity simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale better than [Formula: see text] in certain asymptotic regimes. In these same asymptotic regimes, we also prove bounds for the tail of the steady-state number in service. Our main proofs proceed by explicitly analyzing the bounding process that arises in the stochastic comparison bounds of Gamarnik and Goldberg for multiserver queues. Along the way, we derive several novel results for suprema of random walks and pooled renewal processes, which may be of independent interest. We also prove several additional bounds using drift arguments (which have much smaller prefactors) and point out a conjecture that would imply further related bounds and generalizations. We also show that when all moments of the service distribution are finite and satisfy a mild growth rate assumption, our bounds can be strengthened to yield explicit tail estimates decaying as [Formula: see text], with [Formula: see text], depending on the growth rate of these moments. Funding: Financial support from the National Science Foundation [Grant 1333457] is gratefully acknowledged. Supplemental Material: The supplemental appendix is available at https://doi.org/10.1287/moor.2022.0131 .

Effect of electron–phonon interactions on a three-level QD-based spaser: linear and quadratic potentials

Abstract In this article, we study the effect of electron–phonon interaction on a spaser (surface plasmon amplification by stimulated emission of radiation) system consisting of a metal nanoparticle surrounded by a large number of quantum dots (QDs). Usually, the effect of electron–phonon interaction is neglected in the spaser-related literature. However, gain media, in this case QDs, attributed by the large Raman scattering cross-section, exhibit stronger electron–phonon interaction. In the present work, we investigate the effects of electron–phonon interaction on a three-level QD-based spaser. We consider two types of interaction potentials, linear and quadratic, and analyse their effects individually. First, we focus on the linear electron–phonon interaction that perturbs the electrons present in the excited state. This yields a periodic steady-state number of localized surface plasmons (LSPs). The accompanying analytic solution reveals that the population inversion of the gain medium depends on the linear potential strength (Frohlich constant) but does not affect the threshold of spaser considerably for the given numerical parameters. In addition to the LSP, phonons are generated during this process, the temporal dynamics of which are also presented here. Initially, the number of phonons exhibit decaying periodic oscillations, whose amplitude depends on the strength of the electron–phonon interaction. Under continuous pumping, at later times, the number of phonons reaches a steady-state value, which may find potential applications in the realization of continuous phonon nanolasers. Furthermore, the effect of the quadratic potential is investigated phenomenologically by increasing the excited-state decay rate. This results in numerous LSPs and an intense spaser spectrum.

Significance of quantitative analyses of the impact of heterogeneity in mitochondrial content and shape on cell differentiation.

Mitochondria, classically known as the powerhouse of cells, are unique double membrane-bound multifaceted organelles carrying a genome. Mitochondrial content varies between cell types and precisely doubles within cells during each proliferating cycle. Mitochondrial content also increases to a variable degree during cell differentiation triggered after exit from the proliferating cycle. The mitochondrial content is primarily maintained by the regulation of mitochondrial biogenesis, while damaged mitochondria are eliminated from the cells by mitophagy. In any cell with a given mitochondrial content, the steady-state mitochondrial number and shape are determined by a balance between mitochondrial fission and fusion processes. The increase in mitochondrial content and alteration in mitochondrial fission and fusion are causatively linked with the process of differentiation. Here, we critically review the quantitative aspects in the detection methods of mitochondrial content and shape. Thereafter, we quantitatively link these mitochondrial properties in differentiating cells and highlight the implications of such quantitative link on stem cell functionality. Finally, we discuss an example of cell size regulation predicted from quantitative analysis of mitochondrial shape and content. To highlight the significance of quantitative analyses of these mitochondrial properties, we propose three independent rationale based hypotheses and the relevant experimental designs to test them.

‘Life’ of dust originating from the irregular satellites of Jupiter

ABSTRACT The irregular satellites of Jupiter produce dust particles through the impact of interplanetary micrometeoroids. In this paper, the dynamics of these particles is studied by both high-accuracy numerical simulation and analytical theory, in order to learn their transport, final fate, and spatial distribution. The perturbation forces that are considered in our dynamical model include the solar radiation pressure, solar gravity, Poynting–Robertson drag, Jovian oblateness, and the Galilean satellites’ gravity. The trajectories of different size particles are simulated until they hit Jupiter, the Galilean satellites, or escape from the Jovian system. The average dynamical lifetimes of dust with different grain sizes are calculated, and the final fate of dust particles is reported and analysed. The steady-state spatial number density of particles is estimated by integrating the trajectories of dust particles over their initial size distribution, and compared to the previous work. The impact sites of dust on Callisto’s surface are recorded and provide an important clue for the study of the hemisphere asymmetry of Callisto. Besides, the mass accretion rate, cross-sectional area influx, and mass influx density of dust on Callisto are calculated. A ring outside the orbit of Callisto dominated by dust between 2 and 25 µm from Jupiter’s irregular satellites is suggested, with the average normal geometric optical depth of the order of 10−8 and the configuration of the ring ansae similar to Jupiter’s gossamer rings.

Investigation on interphase mass transfer coefficient of a deformable bubble with density contrast using phase-field lattice Boltzmann method

The gas–liquid mass transfer process with density contrast is modeled in this paper using a phase-field Lattice Boltzmann (LB) method. In this method, the phase-field model used to calculate the flow field and the continuous species transfer model used to calculate the concentration distribution are coupled by introducing the divergence condition of the velocity in the presence of mass transfer into the Allen-Cahn equation. For a deformable bubble rising in stagnant liquid, a two-dimensional parameter dependence study is conducted and the results indicate that an increase in initial diameter, as well as a decrease in liquid diffusion coefficient or liquid viscosity, can improve the steady-state value for the Sherwood number, whereas the distribution coefficient has a little impact on this steady-state value. Furthermore, a correlation originally proposed by Takemura and Yabe (1998) modified with a shape factor can be used to predict the steady-state Sherwood number in the numerical results.

Cascaded optically injection-locked semiconductor laser, rate equations analysis, frequency response, and its application for complex optical signal generation.

In this paper, we introduce the concept of the cascaded optically injection-locked (OIL) semiconductor laser and present its novel rate equations. Then, the new locking range for this configuration has been obtained by mathematical demonstration. Subsequently, we modified a new adjustment for the detuning frequencies (Δ f i n j ) of the cascaded OIL system as well as the linewidth enhancement factors (α) values. Utilizing these tunings, improvements in the steady-state photon number and the phase modulation (PM) range become possible. Afterward, we define the generation of the complex optical signal area and extract the transfer function for investigating the frequency response of the cascaded system. The simulations have been performed once with identical α values and once with the various α values in the slave laser (SL) stages. We conclude that these novel proposed adjustments, combined with a strong injection ratio (Rinj) of 15 dB and a high bias current, can significantly broaden the bandwidth near 700 GHz while maintaining the fair gain available up to 180 GHz. Further, the generation of complex optical signal areas has been boosted for high-quality complex modulation applications. Eventually, we exhibit a novel approach for generating different α values in the SL stages by applying managed temperature variations in the experimental setup of the cascaded system, regardless of employing similar SLs.

Steady-state redox status in circulating extracellular vesicles: A proof-of-principle study on the role of fitness level and short-term aerobic training in healthy young males.

Considering the role of redox homeostasis in exercise-induced signaling and adaptation, this study focuses on the exercise training-related intercellular communication of redox status mediated by circulating extracellular vesicles (EVs). 19 healthy young males were divided into trained (TG, 7) and untrained (UG, 12) subjects based on their VO2MAX. The UG subjects were further randomly distributed in experimental (UGEX, N = 7) and control (UGCTRL, N = 5) groups. The steady state of plasma EVs in TG and UGEX have been characterized for total number and size, as well as cargo redox status (antioxidants, transcription factors, HSPs) before, 3 and 24 h after a single bout of aerobic exercise (30', 70% HRM). Plasma EVs from UGEX and UGCTRL have been further characterized after 24 h from the last session of a 5-day consecutive aerobic training or no training, respectively. No differences were detected in the EVs' size and distribution at baseline in TG and UGEX (p>0.05), while the EVs cargo of UGEX showed a significantly higher concentration of protein carbonyl, Catalase, SOD2, and HSF1 compared to TG (p<0.05). 5 days of consecutive aerobic training in UGEX did not determine major changes in the steady-state number and size of EVs. The post-training levels of protein carbonyl, HSF1, Catalase, and SOD2 in EVs cargo of UGEX resulted significantly lower compared with UGEX before training and UGCTRL, resembling the steady-state levels in circulating EVs of TG subjects. Altogether, these preliminary data indicate that individual aerobic capacity influences the redox status of circulating EVs, and that short-term aerobic training impacts the steady-state redox status of EVs. Taking this pilot study as a paradigm for physio-pathological stimuli impacting redox homeostasis, our results offer new insights into the utilization of circulating EVs as biomarkers of exercise efficacy and of early impairment of oxidative-stress related diseases.

Strong single-photon to two-photon bundles emission in spin-1 Jaynes–Cummings model

High-quality special nonclassical states beyond the strong single atom-cavity coupling regime are fundamental elements in quantum information science. Here, we study strong single-photon blockade to two-photon bundles emission in a single spin-1 atom coupled to an optical cavity by constructing a spin-1 Jaynes–Cummings model (JCM). By tuning the quadratic Zeeman shift, the energy-spectrum anharmonicity can be significantly enhanced, leading to a remarkable increase in the dressed-state splitting of the well-resolved n-photon resonance. The mechanism, which benefits from the internal degrees of freedom in high-spin systems, compensates for the strong coupling condition required by the multi-photon blockade, thereby facilitating the experimental feasibility of engineering special nonclassical states beyond the strong-coupling limit. It is shown that the photon emission from the spin-1 JCM demonstrates high-quality single photon and two-photon bundles with large steady-state photon numbers in the cavity-driven and atom-pump cases, respectively. In particular, compared to the two-level two-photon JCM, the antibunching amplitude of the three-order correlation function for two-photon bundles in the spin-1 JCM is enhanced by 3 orders of magnitude. More interestingly, a multimode transducer, enabling a transition from strong single-photon blockade to two-photon bundles and super-Poissonian photon emission, is achieved and highly controllable by the light-cavity detuning in the presence of both atom and cavity driven fields. This study based on the high-spin JCM broadens the scope of engineering special nonclassical quantum states beyond the standard two-level JCM. Our proposal not only opens up a new avenue for generating high-quality n-photon sources but also provides versatile applications in quantum networks and metrology.

Reshape of the Bistable and Multistable Properties of Conical Structures Through Integrated Modification of Local Cross Section

Abstract Multistable structures can maintain multiple steady states without additional loads. However, the presence of geometric and material nonlinearities in multistable structures adds complexity and difficulty to their optimal design. In this paper, a novel method is proposed to achieve multistability in conical structures by local cross-section modification. A conical multistable structure with varying cross section is designed based on this method. The finite element model considering the nonlinear large deformation mechanics and rubber material’s hyperelasticity was established for analyzing the multistable properties and meanwhile verified by experiments. The influence of geometric parameters of the cross section (thickness, width, and position) on the multistabilities (number, distribution, and snapping threshold) was analyzed. The steady-state number can be effectively used to redesign the multistable properties by local reinforcement. It is also observed that the quasi-zero stiffness region of the force–displacement curve can be extended by 61.7% compared to the original conical structure. Moreover, the optimized QZS structure allows for an actively designable stepped dynamic response under forced vibration.

Two-dimensional interfacial diffusion model of inhibitory synaptic receptor dynamics

The diffusion-trapping of protein receptors in post-synaptic regions of a neuron’s plasma membrane plays a key role in determining the strength of synaptic connections and their regulation during learning and memory. In this paper, we construct and analyse a two-dimensional interfacial diffusion model of inhibitory synaptic receptor dynamics. The model involves three major components. First, the boundary of each synapse is treated as a semi-permeable interface due to the effects of cytoskeletal structures. Second, the effective diffusivity within a synapse is taken to be smaller than the extrasynaptic diffusivity due to the temporary binding to scaffold protein buffers within the synapse. Third, receptors from intracellular pools are inserted into the membrane extrasynaptically and internalized extrasynaptically and synaptically. We first solve the model equations for a single synapse in an unbounded domain and explore how the non-equilibrium steady-state number of synaptic receptors depends on model parameters including synaptic radius and the permeability of the synaptic interface. We then use matched asymptotic analysis to solve the corresponding problem of multiple synapses in a large, bounded domain. In particular, we show how diffusion mediates pairwise synaptic interactions that could provide a substrate for heterosynaptic plasticity. Finally, we indicate how to apply the model to the stochastic dynamics of single receptors.

Gutzwiller approximation for indistinguishable interacting Brownian particles on a lattice.

Nonequilibrium Brownian systems can be described using a creation and annihilation operator formalism for classical indistinguishable particles. This formalism has recently been used to derive a many-body master equationfor Brownian particles on a lattice with interactions of arbitrary strength and range. One advantage of this formalism is the possibility of using solution methods for analogous many-body quantum systems. In this paper, we adapt the Gutzwiller approximation for the quantum Bose-Hubbard model to the many-body master equationfor interacting Brownian particles in a lattice in the large-particle limit. Using the adapted Gutzwiller approximation, we numerically explore the complex behavior of nonequilibrium steady-state drift and number fluctuations throughout the full range of interaction strengths and densities for on-site and nearest-neighbor interactions.

Optical bistability and four-wave mixing response of a quantum dot coupled to an optomechanical photonic crystal nanocavity

We theoretically explore the nonlinear optical response including optical bistability and four-wave mixing (FWM) process in a hybrid cavity quantum electrodynamic (C-QED) system. The hybrid C-QED system consists of a quantum dot (QD) which is coherently driven by two-tone laser fields and embedded in an optomechanical photonic crystal (PhC) nanocavity. Our theoretical analysis demonstrates optical bistability, where the steady-state photon number follows a constant rise in the gain of the switch by controlling a strong pump field driving the QD. A strong coupling between quantised fields and matter (e.g. in optical cavities) is a successful approach for conventionally modifying the dressed state and by altering the field parameters, the modulation of QD dressed state is accomplished. In addition, we list the influence of off-resonant detuning, exciton-nanocavity coupling strength and Rabi coupling strength in our proposed system which generates a controllable four-wave mixing (FWM) signal in the output probe field of the system. The intensity of the FWM is significantly changed when strong coupling and high pump power are present simultaneously and results in the formation of an optomechanically induced transparency (OMIT) window and slow light. The investigation of the proposed system have potential application towards on-chip QD-based nanophotonic devices.

Spatial heterogeneity for APRIL production by eosinophils in the small intestine.

Eosinophils may reside in the lower intestine to play several homeostatic functions. Regulation of IgA+ plasma-cell (PC) homeostasis is one of these functions. Here, we assessed regulation of expression for a proliferation-inducing ligand (APRIL), a key factor from the TNF superfamily for PC homeostasis, in eosinophils from the lower intestine. We observed a strong heterogeneity, since duodenum eosinophils did not produce APRIL at all, whereas a large majority of eosinophils from the ileum and right colon produced it. This was evidenced both in the human and mouse adult systems. At these places, the human data showed that eosinophils were the only cellular sources of APRIL. The number of IgA+ PCs did not vary along the lower intestine, but ileum and right colon IgA+ PC steady-state numbers significantly diminished in APRIL-deficient mice. Use of blood cells from healthy donors demonstrated that APRIL expression in eosinophils is inducible by bacterial products. Use of germ-free and antibiotics-treated mice confirmed the dependency on bacteria for APRIL production by eosinophils from the lower intestine. Taken together, our study shows that APRIL expression by eosinophils is spatially regulated in the lower intestine with a consequence on the APRIL dependency for IgA+ PC homeostasis.

Nonclassical correlated optical multistability at low photon level for cavity electromagnetically induced transparency

We study the nonequilibrium dynamic behaviors in a driven-dissipative single-atom cavity electromagnetically induced transparency. The optical bistability and multistability beyond a Kerr nonlinearity are observed utilizing the optical Stark shift induced strong nonlinearity. We show that the nonequilibrium dynamical phase transition between bistability and multistability is highly tunable by the system parameters in a large parameter region. The first-order dissipative optical bistability (multistability) always corresponds to the photon-bunching quantum statistics, which indicates that the quantum fluctuations and correlations play important roles in nonequilibrium dynamics. Interestingly, bistability and multistability with photon-bunching quantum statistics occurring at extremely low steady-state cavity photon number are observed, even under a very strong cavity driven field. Furthermore, we demonstrate that the unique cavity steady-state solution of the full quantum calculation is excellently consistent with the lowest solution based on the semiclassical mean-field approach in bistability and multistability regimes when the cavity photon number is much less than unity, albeit these nonclassical quantum states should possess strong quantum fluctuations in this parameter regime. Our results pave the way to exploring nonclassical correlated optical multistability in quantum regime, which may bring exciting opportunities for potential applications from quantum information processing to quantum metrology.

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a subvolume of a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady-state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. A formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

Visualizing the breakdown of quantum multimodality in coherently driven light-matter interaction

We show that the saturation of a multiphoton transition is accompanied by a gradual collapse of quantum multimodality in the strong-coupling limit of the weakly driven Jaynes-Cummings (JC) model. By means of a perturbative method, we illustrate the prominent role of quantum fluctuations by focusing on the two and three-photon resonance operation in a regime where the steady-state average photon number is below or marginally above unity. We also reveal two coexistent quantum beats in the intensity correlation function of the forwards scattered photons. These beats, originating from the states mediating the cascaded decay, arise as a direct consequence of the distinct JC spectrum. Their interference coordinates with the alternation of positive and negative values of the Wigner function around the phase-space origin in the transient conditioned on a photodetection.

Direct numerical simulation of film boiling on a horizontal periodic surface in three dimensions using front tracking

This study investigates film boiling on a horizontal periodic surface in three dimensions through direct numerical simulations. To solve the momentum and energy equations in both phases, a finite difference/front tracking method is used that accounts for inertia, viscosity, and interface deformation. The mathematical formulation and numerical method are presented. One of the challenging aspects of the front tracking method is breakup and coalescence of bubbles. Previous works continued the simulations up to the breakup and release of the bubble. We use an innovative topology changing algorithm to overcome this challenge. So, simulations are carried out over sufficiently long times to capture several bubble release cycles and to evaluate the quasi steady-state Nusselt number Nu¯. Effect of the Grashof and Jacob numbers on the interface dynamics, heat transfer, and fluid flow is studied. By increasing the Grashof number, buoyancy suppresses the viscous effect, so the average size of departing bubbles decreases, and the average Nusselt number increases. Wall superheat has direct influence on the Jacob number. At relatively low superheats, the bubbles are released periodically from the vapor film, but as the wall superheat increases, permanent vapor jets are formed and become thicker. However, the bubble size and the average Nusselt number decrease. The effect of unit cell size is investigated. It is observed that Nu¯ does not change much with unit cell size. To examine the effect of initial perturbation, single mode and multimode cases were simulated. The initial perturbation has no significant effect on the Nu¯. The density ratio was studied, and it is observed that the stationary steady state condition is reached at a shorter time.