Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Stability of a nonequilibrium steady-state interface

We study the interfacial modes of a driven diffusive model under suitable nonequilibrium conditions leading to possible instability. The external field parallel to the interface, which sets up a steady-state parallel flux, enhances the growth or decay rates of the interfacial modes. More dramatically, asymmetry in the model can introduce an oscillatory component into the interfacial dispersion relation. In certain circumstances, the applied field behaves as a singular perturbation.

Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seiferts integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.

Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Adaptive learning in models with lagged variables

In this work I study the stability of the dynamics generated by adaptivelearning processes in intertemporal economies with lagged variables. Iprove that determinacy of the steady state is a necessary condition for the convergence of the learning dynamics and I show that the reciprocal is not true characterizing the economies where convergence holds. In the case of existence of cycles I show that there is not, in general, a relationship between determinacy and convergence of the learning process to the cycle. I also analyze the expectational stability of these equilibria.

Immigration and the survival of the welfare state

This paper analyzes the political sustainability of the welfare state in a model where immigration policy is also endogenous. In the model, the skills of the native population are affected by immigration and skill accumulation. Moreover, immigrants affect future policies, once they gain the right to vote. The main finding is that the long-run survival of redistributive policies is linked to an immigration policy specifying both skill and quantity restrictions. In particular, in steady state the unskilled majority admits a limited inflow of unskilled immigrants in order to offset growth in the fraction of skilled voters and maintain a high degree of income redistribution.Interestingly, equilibrium immigration policy shifts from unrestricted skilled immigration,when the country is skill-scarce, to restricted unskilled immigration, as the fraction of native skilled workers increases. The analysis also suggests a new set of variables that may help explain international differences in immigration restrictions.

Clathrin Assembly Lymphoid Myeloid Leukemia (CALM) Protein: Localization in Endocytic-coated Pits, Interactions with Clathrin, and the Impact of Overexpression on Clathrin-mediated Traffic

The clathrin assembly lymphoid myeloid leukemia (CALM) gene encodes a putative homologue of the clathrin assembly synaptic protein AP180. Hence the biochemical properties, the subcellular localization, and the role in endocytosis of a CALM protein were studied. In vitro binding and coimmunoprecipitation demonstrated that the clathrin heavy chain is the major binding partner of CALM. The bulk of cellular CALM was associated with the membrane fractions of the cell and localized to clathrin-coated areas of the plasma membrane. In the membrane fraction, CALM was present at near stoichiometric amounts relative to clathrin. To perform structure-function analysis of CALM, we engineered chimeric fusion proteins of CALM and its fragments with the green fluorescent protein (GFP). GFP-CALM was targeted to the plasma membrane-coated pits and also found colocalized with clathrin in the Golgi area. High levels of expression of GFP-CALM or its fragments with clathrin-binding activity inhibited the endocytosis of transferrin and epidermal growth factor receptors and altered the steady-state distribution of the mannose-6-phosphate receptor in the cell. In addition, GFP-CALM overexpression caused the loss of clathrin accumulation in the trans-Golgi network area, whereas the localization of the clathrin adaptor protein complex 1 in the trans-Golgi network remained unaffected. The ability of the GFP-tagged fragments of CALM to affect clathrin-mediated processes correlated with the targeting of the fragments to clathrin-coated areas and their clathrin-binding capacities. Clathrin-CALM interaction seems to be regulated by multiple contact interfaces. The C-terminal part of CALM binds clathrin heavy chain, although the full-length protein exhibited maximal ability for interaction. Altogether, the data suggest that CALM is an important component of coated pit internalization machinery, possibly involved in the regulation of clathrin recruitment to the membrane and/or the formation of the coated pit.

Equilibrium and nonequilibrium gap-state distribution in amorphous silicon

A general and straightforward analytical expression for the defect-state-energy distribution of a-Si:H is obtained through a statistical-mechanical treatment of the hydrogen occupation for different sites. Broadening of available defect energy levels (defect pool) and their charge state, both in electronic equilibrium and nonequilibrium steady-state situations, are considered. The model gives quantitative results that reproduce different defect phenomena, such as the thermally activated spin density, the gap-state dependence on the Fermi level, and the intensity and temperature dependence of light-induced spin density. An interpretation of the Staebler-Wronski effect is proposed, based on the ''conversion'' of shallow charged centers to neutrals near the middle of the gap as a consequence of hydrogen redistribution.

Dewaterability of sewage sludge by ultrasonic, thermal and chemical treatments

Sludges resulting from wastewater treatment processes have a characteristically high water content, which complicates handling operations such as pumping, transport and disposal. To enhance the dewatering of secondary sludge, the effect of ultrasound waves, thermal treatment and chemical conditioning with NaOH have been studied. Two features of treated sludges were examined: their rheological behavior and their dewaterability. The rheological tests consisted of recording shear stress when the shear rate increases and decreases continuously and linearly with time, and when it increases and decreases in steps. Steady-state viscosity and thixotropy were obtained from the rheological tests, and both decreased significantly in all cases with increased treatment intensity. Centrifugation of ultrasonicated and thermally treated sludges allowed the total solid content to be increased by approximately 16.2% and 17.6%, respectively. These dewatered sludges had a lower viscosity and thixotropy than the untreated sludge. In contrast, alkali conditioning barely allowed the sludge to be dewatered by centrifugation, despite decreasing its viscosity and thixotropy.

Shear thinning and thixotropy of HMHEC and HEC water solutions

Steady state viscosity and thixotropy of hydrophobically modified hydroxyethyl cellulose HMHEC and nonassociative cellulose water solutions are studied. Although all the samples are shear thinning, only the HMHEC is thixotropic, since the migration of hydrophobes to micelles is controlled by diffusion. The Cross model fits steady state curves. The Mewis model, a phenomenological model that proposes that the rate of change of viscosity when the shear rate is suddenly changed is related to the difference between the steady state and current values of viscosity raised to an exponent, fits structure construction experiments when the exponent, n, is estimated to be around 2. The Newtonian assumption used by Mewis cannot be used here, however. This seems to be related to the fact that the thickening is due to bridged micelle formation, which is a slow process, and also to topological constraints and entanglements, which are rapid processes. The kinetic parameter was redefined to kn in order to make it independent of initial conditions. So, kn depends only on how the shear affects the structure. kn reaches a plateau at shear rates too low to produce structure destruction and decreases at higher shear rates.

Mitochondrial dysfunction increases oxidative stress and decreases chronological life span in fission yeast

Background: Oxidative stress is a probable cause of aging and associated diseases. Reactive oxygen species (ROS) originate mainly from endogenous sources, namely the mitochondria. Methodology/Principal Findings: We analyzed the effect of aerobic metabolism on oxidative damage in Schizosaccharomyces pombe by global mapping of those genes that are required for growth on both respiratory-proficient media and hydrogen-peroxide-containing fermentable media. Out of a collection of approximately 2700 haploid yeast deletion mutants, 51 were sensitive to both conditions and 19 of these were related to mitochondrial function. Twelve deletion mutants lacked components of the electron transport chain. The growth defects of these mutants can be alleviated by the addition of antioxidants, which points to intrinsic oxidative stress as the origin of the phenotypes observed. These respiration-deficient mutants display elevated steady-state levels of ROS, probably due to enhanced electron leakage from their defective transport chains, which compromises the viability of chronologically-aged cells. Conclusion/Significance: Individual mitochondrial dysfunctions have often been described as the cause of diseases or aging, and our global characterization emphasizes the primacy of oxidative stress in the etiology of such processes.

Comission 49: Interplanetary plasma and heliosphere. TRIENNIAL REPORT 2006 - 2009

Commission 49 covers research on the solar wind, shocks and particle acceleration, both transient and steady-state, e.g., corotating, structures within the heliosphere, and the termination shock and boundary of the heliosphere. The present triennal report is particularly rich in important results and events. The crossing of the solar wind termination shock by Voyager 2 in 2007 is a highlight and a milestone that will certainly have important consequences for astrophysical processes in general (Section 7). The fiftieth anniversary of the International Geophysical Year (19571958), which is also the fiftieth anniversary of the birth of the Space Age, was marked not only by celebrations and a strong Education and Public Outreach Program, but also by efforts in coordinating present observations and in starting new scientific programs, particularly implying developing countries (Section 8). Studies of solar energetic particles (Section 3) and the related radio bursts (Section 4) benefited from new data from a number of spacecraft. The STEREO mission was launched in October 2006 and has obtained new results on 3-D aspects of the inner heliosphere. Meanwhile, solar cycle 24 is expected to become active soon, following what is already the deepest solar minimum of the space age...

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.