Evidence of Robustness in a Two-Component System Using a Synthetic Circuit.

Variation in the concentration of biological components is inescapable for any cell. Robustness in any biological circuit acts as a cushion against such variation and enables the cells to produce homogeneous output despite the fluctuation. The two-component system (TCS) with a bifunctional sensor kinase (that possesses both kinase and phosphatase activities) is proposed to be a robust circuit. Few theoretical models explain the robustness of a TCS, although the criteria and extent of robustness by these models differ. Here, we provide experimental evidence to validate the extent of the robustness of a TCS signaling pathway. We have designed a synthetic circuit in Escherichia coli using a representative TCS of Mycobacterium tuberculosis, MprAB, and monitored the in vivo output signal by systematically varying the concentration of either of the components or both. We observed that the output of the TCS is robust if the concentration of MprA is above a threshold value. This observation is further substantiated by two in vitro assays, in which we estimated the phosphorylated MprA pool or MprA-dependent transcription yield by varying either of the components of the TCS. This synthetic circuit could be used as a model system to analyze the relationship among different components of gene regulatory networks.IMPORTANCE Robustness in essential biological circuits is an important feature of the living organism. A few pieces of evidence support the existence of robustness in vivo in the two-component system (TCS) with a bifunctional sensor kinase (SK). The assays were done under physiological conditions in which the SK was much lower than the response regulator (RR). Here, using a synthetic circuit, we varied the concentrations of the SK and RR of a representative TCS to monitor output robustness in vivo. In vitro assays were also performed under conditions where the concentration of the SK was greater than that of the RR. Our results demonstrate the extent of output robustness in the TCS signaling pathway with respect to the concentrations of the two components.

Enhanced carbon-sulfur cycling in the sediments of Arabian Sea oxygen minimum zone center.

Biogeochemistry of oxygen minimum zone (OMZ) sediments, which are characterized by high input of labile organic matter, have crucial bearings on the benthic biota, gas and metal fluxes across the sediment-water interface, and carbon-sulfur cycling. Here we couple pore-fluid chemistry and comprehensive microbial diversity data to reveal the sedimentary carbon-sulfur cycle across a water-depth transect covering the entire thickness of eastern Arabian Sea OMZ, off the west coast of India. Geochemical data show remarkable increase in average total organic carbon content and aerial sulfate reduction rate (JSO42-) in the sediments of the OMZ center coupled with shallowing of sulfate methane transition zone and hydrogen sulfide and ammonium build-up. Total bacterial diversity, including those of complex organic matter degraders, fermentative and exoelectrogenic bacteria, and sulfate-reducers (that utilize only simple carbon compounds) were also found to be highest in the same region. The above findings indicate that higher organic carbon sequestration from the water-columns (apparently due to lower benthic consumption, biodegradation and biotransformation) and greater bioavailability of simple organic carbon compounds (apparently produced by fermetative microflora of the sediments) are instrumental in intensifying the carbon-sulfur cycle in the sediments of the OMZ center.

Idiopathic Calcinosis Cutis over Elbow in a 12-Year Old Child.

Calcinosis cutis is an uncommon disorder caused by an abnormal deposit of calcium phosphate in the skin in various parts of the body. Four main types of calcinosis cutis have been recognized according to etiology: associated with localized or widespread tissue changes or damage (dystrophic calcification), that associated with an abnormal calcium and phosphorus metabolism (metastatic calcification), not associated with any tissue damage or demonstrable metabolic disorder (idiopathic calcification), and Iatrogenic. Very few cases of idiopathic calcinosis cutis are reported in early childhood in the literature. We report one such case of idiopathic calcinosis cutis over elbow in a 12-year-old female child. Histological examinations of the lesions resected in this case reveal calcium deposits in the dermis, surrounded by foreign body giant cells. Idiopathic calcinosis cutis is a rare phenomenon and occurs in the absence of known tissue injury or systemic metabolic defect. It is important to delineate it from other calcification disorders for further plan of management. Medical therapy in calcinosis cutis is of limited benefit in pediatric age group and poses a challenging problem of postsurgical management.

Microscopic realization of cross-correlated noise processes.

We present a microscopic theory of cross-correlated noise processes, starting from a Hamiltonian system-reservoir description. In the proposed model, the system is nonlinearly coupled to a reservoir composed of harmonic oscillators, which in turn is driven by an external fluctuating force. We show that the resultant Langevin equation derived from the composite system (system+reservoir+external modulation) contains the essential features of cross-correlated noise processes.

Generalized Einstein relation in tilted periodic potential: a semiclassical approach.

This paper concerns the investigation of the quantum motion of a system in a dissipative Ohmic heat bath in the presence of an external field using the traditional system-reservoir model. Using physically motivated initial conditions, we then obtain the c-number of the generalized quantum Langevin equation by which we calculate the quantum correction terms using a perturbation technique. As a result of this, one can apply a classical differential equation-based approach to consider quantum diffusion in a tilted periodic potential, and thus our approach is easy to use. We use our expression to calculate the Einstein relation for the quantum Brownian particle in a ratchet-type potential in a very simple closed analytical form using a suitable and convenient approximation. It is found that the diffusion rate is independent of the detailed form of the potential both in quantum and classical regimes, which is the main essence of this work.

Multiplicative cross-correlated noise induced escape rate from a metastable state.

We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. By starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers theory for activated rate processes in a nonequilibrium open system (one dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary, and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same. By employing numerical simulation in the presence of external cross-correlated additive and multiplicative noises, we check the validity of our analytical formalism for constant dissipation, which shows a satisfactory agreement between both the approaches for the specific choice of noise processes. It is evident both from analytical development and the corresponding numerical simulation that the enhancement of rate is possible by increasing the degree of correlation of the external fluctuations.

Simple model for transport phenomena: microscopic construction of Maxwell demonlike engine.

We present a microscopic Hamiltonian framework to develop Maxwell demonlike engine. Our model consists of an equilibrium thermal bath and a nonequilibrium bath, latter generated by driving with an external stationary, Gaussian noise. The engine we develop can be considered as a device to extract work by modifying internal fluctuations. Our theoretical analysis focuses on finding the essential ingredients necessary for generating fluctuation induced transport under nonequilibrium condition. An important outcome of our model is that the net motion occurs when the nonlinear bath is modulated by the external noise, creating the nonzero effective temperature even when the temperature of both the baths are the same.

Generalization of the escape rate from a metastable state driven by external cross-correlated noise processes.

We propose generalization of the escape rate from a metastable state for externally driven correlated noise processes in one dimension. In addition to the internal non-Markovian thermal fluctuations, the external correlated noise processes we consider are Gaussian, stationary in nature and are of Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective noise processes with finite memory we derive the generalized escape rate from a metastable state in the moderate-to-large damping limit and investigate the effect of degree of correlation on the resulting rate. Comparison of the theoretical expression with numerical simulation gives a satisfactory agreement and shows that by increasing the degree of external noise correlation one can enhance the escape rate through the dressed effective noise strength.

Escape rate from a metastable state weakly interacting with a heat bath driven by external noise.

Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For the open system we derive the Fokker-Planck equation in the energy space and subsequently calculate the generalized non-Markovian escape rate from a metastable well in the energy diffusion domain. By considering the dynamics in a model cubic potential we show that the results obtained from numerical simulation are in good agreement with the theoretical prediction. It has been also shown numerically that the well-known turnover feature can be restored from our model.

Dynamics of a metastable state nonlinearly coupled to a heat bath driven by external noise.

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space-dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space-dependent diffusion coefficient to study the escape rate from a metastable state in the moderate- to large-damping regime. By considering the dynamics in a model cubic potential we analyze the results numerically which are in good agreement with theoretical predictions. It has been shown numerically that enhancement of the rate is possible by properly tuning the correlation time of the external noise.

Solution of quantum Langevin equation: approximations, theoretical and numerical aspects.

Based on a coherent state representation of noise operator and an ensemble averaging procedure using Wigner canonical thermal distribution for harmonic oscillators, a generalized quantum Langevin equation has been recently developed [Phys. Rev. E 65, 021109 (2002); 66, 051106 (2002)] to derive the equations of motion for probability distribution functions in c-number phase-space. We extend the treatment to explore several systematic approximation schemes for the solutions of the Langevin equation for nonlinear potentials for a wide range of noise correlation, strength and temperature down to the vacuum limit. The method is exemplified by an analytic application to harmonic oscillator for arbitrary memory kernel and with the help of a numerical calculation of barrier crossing, in a cubic potential to demonstrate the quantum Kramers' turnover and the quantum Arrhenius plot.

Class of self-limiting growth models in the presence of nonlinear diffusion.

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand, are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Approach to quantum Kramers' equation and barrier crossing dynamics.

We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum-mechanical mean values of their co-ordinates and momenta we have derived a c number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of the temperature and friction. While almost all the earlier theories rest on quasiprobability distribution functions (e.g., Wigner function) and path integral methods, the present work is based on true probability distribution functions and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermally activated processes and tunneling.

Quantum Kramers equation for energy diffusion and barrier crossing dynamics in the low-friction regime.

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value, which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.