Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

Modelling allosteric regulation for prediction of flux control in the central carbon metabolism of E. coli

Rational strain design is a fundamental step in the development of microbial cell factories. Multiple genetic manipulations are often required in order to redirect the metabolic flux towards a product of industrial interest. Most manipulation targets are focused on central carbon metabolism, which provides the molecular precursors and the energy required for other biochemical pathways. However, the complex regulation of those pathways is still not completely unraveled. Recent studies have shown that central carbon metabolism is mostly regulated at post-transcriptional levels. In this work, we explore the role of allosteric regulation in the control of metabolic fluxes. We begin by expanding a metabolic network reconstruction of the central carbon metabolism of E. coli with allosteric interaction information from relevant databases. This model is used to integrate a multi-omic dataset for this organism. We analyze the coordinated changes in enzyme, metabolite and flux levels between multiple experimental conditions, and observe cases where allosteric regulators have a major contribution in the metabolic flux changes. We then develop a method for systematic prediction of potential cases of allosteric control for given metabolic perturbations. This is a valuable approach for predicting coordinated flux changes that would not be predicted with a purely stoichiometric model representation.BioInd - Biotechnology and Bioengineering for improved Industrial and Agro-Food processes, REF. NORTE-07-0124-FEDER-00002

Transcriptional vs post-transcriptional regulation of the central carbon metabolism of E. coli

Transcriptomics data are currently one of the most available types of large-scale biological data. A large number of methods have been developed to improve constraint-based simulations using these data. We recently performed a systematic comparison of these methods and observed that, at least for central carbon metabolism, there is no significant improvement in the prediction of flux distributions when gene expression data is used. These results are consistent with recent studies, in different organisms, showing that central carbon metabolism is predominantly regulated at post-transcriptional levels. Central carbon metabolism provides the precursors for the production of multiple compounds used in industrial biotechnology. Hence, it is the main target for intervention in most rational strain design strategies. However, its complexity is still not completely understood. In this work, we analyze the role of allosteric regulation, one of the main mechanisms of post-transcriptional regulation, for the control of central carbon metabolism. We extend a model of central carbon metabolism of E. coli with allosteric interactions, revealing a hidden topology in metabolic networks. We use this model to integrate a multi-omic dataset containing transcript, protein, flux and metabolite levels to further dissect the contribution of different types of regulation for metabolic flux control in these central pathways. Situations of predominant allosteric control could be identified, highlighting the importance of this kind of regulation in central carbon metabolism

Modeling the contribution of allosteric regulation for flux control in the central carbon metabolism of E. coli

Redesign of microbial metabolism is a critical step in biotechnology for the production of industrially relevant compounds. Central carbon metabolism provides the energy and building blocks required for cellular growth and synthesis of the desired byproducts and, consequently, it is the main target for intervention in most rational strain design approaches. However, the complexity of central carbon metabolism is still not completely understood. Recent studies in different organisms show that flux control in central carbon metabolism is predominantly regulated by non-transcriptional mechanisms, leaving post-translational modifications, allosteric regulation, and thermodynamics as main candidates. In this work, we extend a model of central carbon metabolism of E.coli with allosteric interactions in order to reveal a hidden topology in metabolic networks. We use this model to integrate a multi-omic dataset containing transcript, protein, flux and metabolite levels to further dissect and analyze the contribution of allosteric regulation for metabolic flux control

Fractional Hamiltonian analysis of higher order derivatives systems

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.Comment: 13 page

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

Design of a biosynthetic pathway for curcumin production in Escherichia coli

Curcumin is the yellow pigment from turmeric, a well known culinary spice produced from the herb Curcuma longa. Research over the last years has shown that curcumin presents a wide range of pharmacological effects, including anti-inflammatory, anti-oxidant and anticarcinogenic activity. Given its potential application in cancer treatment, there is an interest for industrial production of this natural compound. This work consists on a synthetic biology approach for the design of a heterologous pathway for curcumin synthesis in Escherichia coli, a widely used microbe in industrial biotechnology. Using pathway databases and literature research we have selected the best gene candidates for heterologous expression of a curcumin synthesis pathway in E. coli. The DNA sequences for these genes were retrieved from public databases and can be readily synthesized for insertion into the host using molecular biology techniques. The inclusion of this pathway in a recent genome-scale reconstruction of the metabolism of E. coli has enabled the in silico analysis of the production capabilities for this host. We have analysed the theoretical production yields and biomass growth under different experimental conditions. Using this model we have also searched for potential gene knockouts that partially redirect the metabolic flux to the heterologous pathway without compromising cellular growth. In overall, the methods used in this work allow the selection of the most suitable combination of experimental conditions and genetic manipulations for the design of an efficient biosynthetic pathway for curcumin production in E.coli

On the renormalization group flow of f(R)-gravity

We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \int d^dx \sqrt{g} f(R)$. Based on this equation we show that certain gravitational interactions monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The non-perturbative RG flow of non-local extensions of the Einstein-Hilbert truncation including $\int d^dx \sqrt{g} \ln(R)$ and $\int d^dx \sqrt{g} R^{-n}$ interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some $R^{-n}$-truncations all physical trajectories emanate from a Non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the $\ln(R)$-truncation contains an infrared attractor which drives a positive cosmological constant to zero dynamically.Comment: 55 pages, 7 figures, typos corrected, references added, version to appear in Phys. Rev.