The graphene sheet versus the 2DEG: a relativistic Fano spin-filter via STM and AFM tips

We explore theoretically the density of states (LDOS) probed by an STM tip of 2D systems hosting an adatom and a subsurface impurity,both capacitively coupled to AFM tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: the Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin-degeneracy of the LDOS is lifted exclusively in the graphene system, in particular for the asymmetric regime of Fano interference. The aftermath of this limit is a counterintuitive phenomenon, which consists of a dominant Fano factor due to the subsurface impurity even with a stronger STM-adatom coupling. Thus we find a full polarized conductance, achievable just by displacing vertically the position of the STM tip. To the best knowledge, our work is the first to propose the Fano effect as the mechanism to filter spins in graphene. This feature arises from the massless Dirac electrons within the band structure and allows us to employ the graphene host as a relativistic Fano spin-filter

Large scale dynamic model reconstruction for the central carbon metabolism of escherichia coli

The major objective of metabolic engineering is the construction of industrially relevant microbial strains with desired properties. From an engineering perspective, dynamic mathematical modeling to quantitatively assess intracellular metabolism and predict the complex behavior of living cells is one of the most successful tools to achieve that goal. In this work, we present an expansion of the original E. coli dynamic model [1], which links the acetate metabolism and tricarboxylic acid cycle (TCA) with the phosphotransferase systems, the pentose-phosphate pathway and the glycolysis system based on mechanistic enzymatic rate equations. The kinetic information is collected from available database and literature, and is used as an initial guess for the global fitting. The results of the numeric simulations were in good agreement with the experimental results. Thus, the results are sufficiently good to prompt us to seek further experimental data for comparison with the simulations

Integration of proteomic data for predicting dynamic behaviour in an E. coli central carbon network after genetic perturbations

One of the great challenges in the post‐genomic era is to understand the dynamic behaviour of a living cell. For that purpose, quantitative models describing metabolic network dynamics are a powerful tool as “dry lab” platforms to simulate experiments before they are performed in vivo. Kinetic models and stoichiometric genome scale models of the microbial metabolism are usually the two large‐scale modelling approaches most used. So far, few large scale kinetic models have been successfully constructed. The main reasons for this are not only the associated mathematical complexity, but also the large number of unknown kinetic parameters required in the rate equations to define the system. In contrast to kinetic models, the genome scale modelling approach bypasses these difficulties by using basically only stoichiometric information with certain physicochemical constraints to limit the space of a network without large fitted parameters sets. Although these constraint‐based models are highly relevant to predict a feasible set of steady‐state fluxes under a diverse range of genetic conditions, the steady‐state assumption may oversimplify cellular behaviour and cannot offer information about time dependent changes. To overcome these problems, combining these two approaches appears a reasonable alternative to modelling large‐scale metabolic networks. In this work, we used a large‐scale central carbon metabolic network of E. coli [1] to investigate whether including high throughput enzyme concentrations data into a model allows an improved prediction of the response to different single‐knockouts perturbations. For this purpose, a model based on the flux balance analysis (FBA) approach and linlog kinetics was constructed. As a first validation, we applied it to predict steady‐state changes in fluxes and metabolite concentrations, as well as dynamic responses to perturbations in the central E. coli metabolism. Then, the approach was evaluated by comparison with various sets of published in vivo measurements [2]. Our results indicate that integration of the quantitative enzyme levels into the kinetic models, in general, can be used to predict dynamic behavior changes

Dynamic modeling of E. coli central carbon metabolism combining different kinetic rate laws

Detailed dynamic kinetic models at the network reaction level are traditionally constructed using mechanistic enzymatic rate equations and a large number of kinetic parameters have to be determined under nonphysiological conditions in vitro. However, the validity of these parameters under in vivo conditions is doubtful and the rates equations are usually highly complex. Therefore, one of the major obstacles in building accurate kinetic models is the lack of detailed knowledge of the rate laws that describe the reaction mechanism and the absence of their associated parameters. There is an urgent need for alternative modelling approaches to fill this gap. In this study, we analyze four alternative hybrid modeling strategies to the reference large scale mechanistic E. coli central carbon metabolic network model based on the Michaelis-Menten equation only for the bimolecular reactions and the other reactions with different formats of approximative rate kinetics (Generalized Mass-Action, convenience equation, lin-log and power-law). These rate equations help to reduce the number of parameters that have to be estimated. The kinetic parameters optimization was performed through the combination of a global search evolutionary programming method followed by a local optimization method (Hooke and Jeeves) to refine the fitting. Predictions and stability analyses to test the viability of the alternative models were also performed. The good dynamic behaviour and powerful predictive power obtained by the mixed modeling composed on Michaelis-Menten kinetics and the approximate lin-log kinetics indicate that this as a suitable approach to complex large scale models where the exact rate laws are unknown

Reconstruction of dynamic metabolic networks : challenges, limitations and alternative solutions

Fundação para a Ciência e a Tecnologia (FCT)MIT-Portuga

Critical perspective on the consequences of the limited availability of kinetic data in metabolic dynamic modeling

Detailed kinetic models at the network reaction level are usually constructed using enzymatic mechanistic rate equations and the associated kinetic parameters. However, during the cellular life cycle thousands of different reactions occur, which makes it very difficult to build a detailed large-scale ldnetic model. In this work, we provide a critical overview of specific limitations found during the reconstruction of the central carbon metabolism dynamic model from E. coli (based on kinetic data available). In addition, we provide clues that will hopefully allow the systems biology community to more accurately construct metabolic dynamic models in the future. The difficulties faced during the construction of dynamic models are due not only to the lack of kinetic information but also to the fact that some data are still not curated. We hope that in the future, with the standardization of the in vitro enzyme protocols the approximation of in vitro conditions to the in vivo ones, it will be possible to integrate the available kinetic data into a complete large scale model. We also expect that collaborative projects between modellers and biologists will provide valuable kinetic data and permit the exchange of important information to solve most of these issues.Rafael S. Costa would like to thank Fundacao para a Ciencia e Tecnologia for providing the grant SFRH/BD/25506/2005. The authors also acknowledge the MIT-Portugal project 'Bridging Systems and Synthetic Biology for the development of improved microbial cell factories' MIT-Pt/BS-BB/0082/2008

An approach towards genome-scale kinetic modelling : application to the Escherichia coli metabolism

Understanding the dynamic behavior of living organisms is a great challenge in systems biology. To address this, computational dynamic modeling of metabolic networks is essential to guide experimentation and to explain properties of complex biological systems. Large-scale kinetic models at the reaction network level are usually constructed using mechanistic enzymatic rate equations and a large number of kinetic parameters. However, two of the biggest obstacles to construct accurate dynamic models are model complexity and limited in vivo kinetic information. In the present work, we test an alternative strategy with a relatively small number of kinetic parameters composed by the approximated lin-log kinetics, coupled with a constraint-based method and a priori model reduction based on time scale analysis and a conjunctive fusion approach (Machado et al., 2010).. This workflow was evaluated for the condensed version of a genome-scale kinetic model of Escherichia coli metabolism (Orth et al., 2010). The presented approach seems to be a promising mechanism for detailed kinetic modeling even at the genome-scale of the metabolism of other organisms

Towards a genome-scale kinetic modeling of Escherichia coli metabolism

Understanding the dynamic behavior of living organisms is a great challenge in systems biology. To address this, computational dynamic modeling of metabolic networks is essential to guide experimentation and to explain properties of complex biological systems. Large-scale kinetic models at the reaction network level are usually constructed using mechanistic enzymatic rate equations and a large number of kinetic parameters. However, two of the biggest obstacles to construct accurate dynamic models are model complexity and limited in vivo kinetic information. In the present work, we test an alternative strategy with a relatively small number of kinetic parameters composed by the approximated lin-log kinetics, coupled with a constraint-based method and a priori model reduction based on time scale analysis and a conjunctive fusion approach, for building a genome-scale kinetic model of Escherichia coli metabolism. This workflow was evaluated for the condensed version of a genome-scale network of E. coli (Orth et al., 2010). The presented approach appears to be a promising mechanism for detailed kinetic modeling at the genome-scale of the metabolism of other organisms

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

Quantum phase transition triggering magnetic BICs in graphene

Graphene hosting a pair of collinear adatoms in the phantom atom configuration has pseudogap with cubic scaling on energy, $\Delta\propto|\varepsilon|^{3}$ which leads to the appearance of spin-degenerate bound states in the continuum (BICs) [Phys. Rev. B 92, 045409 (2015)]. In the case when adatoms are locally coupled to a single carbon atom the pseudogap scales linearly with energy, which prevents the formation of BICs. In this Letter, we explore the effects of non-local coupling characterized by the Fano factor of interference $q_{0},$ tunable by changing the slope of the Dirac cones in the graphene band-structure. We demonstrate that three distinct regimes can be identified: i) for $q_{0}<q_{c1}$ (critical point) a mixed pseudogap $\Delta\propto|\varepsilon|,|\varepsilon|^{2}$ appears yielding a phase with spin-degenerate BICs; ii) near $q_{0}=q_{c1}$ when $\Delta\propto|\varepsilon|^{2}$ the system undergoes a quantum phase transition in which the new phase is characterized by magnetic BICs and iii) at a second critical value $q_{0}>q_{c2}$ the cubic scaling of the pseudogap with energy $\Delta\propto|\varepsilon|^{3}$ characteristic to the phantom atom configuration is restored and the phase with non-magnetic BICs is recovered. The phase with magnetic BICs can be described in terms of an effective intrinsic exchange field of ferromagnetic nature between the adatoms mediated by graphene monolayer. We thus propose a new type of quantum phase transition resulting from the competition between the states characterized by spin-degenerate and magnetic BICs