Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before

Scale-Free topologies and Activatory-Inhibitory interactions

A simple model of activatory-inhibitory interactions controlling the activity of agents (substrates) through a "saturated response" dynamical rule in a scale-free network is thoroughly studied. After discussing the most remarkable dynamical features of the model, namely fragmentation and multistability, we present a characterization of the temporal (periodic and chaotic) fluctuations of the quasi-stasis asymptotic states of network activity. The double (both structural and dynamical) source of entangled complexity of the system temporal fluctuations, as an important partial aspect of the Correlation Structure-Function problem, is further discussed to the light of the numerical results, with a view on potential applications of these general results.Comment: Revtex style, 12 pages and 12 figures. Enlarged manuscript with major revision and new results incorporated. To appear in Chaos (2006

Quasiparticle Chirality in Epitaxial Graphene Probed at the Nanometer Scale

Graphene exhibits unconventional two-dimensional electronic properties resulting from the symmetry of its quasiparticles, which leads to the concepts of pseudospin and electronic chirality. Here we report that scanning tunneling microscopy can be used to probe these unique symmetry properties at the nanometer scale. They are reflected in the quantum interference pattern resulting from elastic scattering off impurities, and they can be directly read from its fast Fourier transform. Our data, complemented by theoretical calculations, demonstrate that the pseudospin and the electronic chirality in epitaxial graphene on SiC(0001) correspond to the ones predicted for ideal graphene.Comment: 4 pages, 3 figures, minor change

Michaelis-Menten dynamics in protein subnetworks

To understand the behaviour of complex systems it is often necessary to use models that describe the dynamics of subnetworks. It has previously been established using projection methods that such subnetwork dynamics generically involves memory of the past, and that the memory functions can be calculated explicitly for biochemical reaction networks made up of unary and binary reactions. However, many established network models involve also Michaelis-Menten kinetics, to describe e.g. enzymatic reactions. We show that the projection approach to subnetwork dynamics can be extended to such networks, thus significantly broadening its range of applicability. To derive the extension we construct a larger network that represents enzymes and enzyme complexes explicitly, obtain the projected equations, and finally take the limit of fast enzyme reactions that gives back Michaelis-Menten kinetics. The crucial point is that this limit can be taken in closed form. The outcome is a simple procedure that allows one to obtain a description of subnetwork dynamics, including memory functions, starting directly from any given network of unary, binary and Michaelis-Menten reactions. Numerical tests show that this closed form enzyme elimination gives a much more accurate description of the subnetwork dynamics than the simpler method that represents enzymes explicitly, and is also more efficient computationally

Dynamics of gene expression and the regulatory inference problem

From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription factor molecules to regulatory DNA. Here, we construct stochastic models of gene expression dynamics and test them on experimental time-series data of messenger-RNA concentrations. The models are used to infer biophysical parameters of gene transcription, including the statistics of transcription factor-DNA binding and the target genes controlled by a given transcription factor.Comment: revised version to appear in Europhys. Lett., new titl

Stub model for dephasing in a quantum dot

As an alternative to Buttiker's dephasing lead model, we examine a dephasing stub. Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.Comment: 8 pages with 1 figure; contribution for the special issue of J.Phys.A on "Trends in Quantum Chaotic Scattering

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System

Multiannual Seafloor Dynamics around a Subtidal Rocky Reef Habitat in the North Sea

Rocky reefs provide complex structures in the otherwise largely sand-dominated coastal North Sea. Therefore, these reefs are highly important natural habitats for the functioning of coastal ecosystems, as they provide shelter, refuge and nursery grounds for various mobile and sessile species. In the North Sea, the spatial distribution of these habitats has been intensively investigated over recent years. However, these studies generally provide static accounts of the current state of these reef systems, but limited data exist on the temporal variations in sediment dynamics at and around natural rocky reefs. In this study, we provide observations from a multiannual time series of hydroacoustic seafloor surveys conducted at an isolated rocky reef in the North Sea. We use multibeam bathymetry and side-scan sonar backscatter data in combination with video observations, sediment sampling, and sub-bottom profiler data to assess the long-term variations of the rocky reef system. The reef is located in water depths between 11 and 17 m with an areal extent of ~0.5 km2 and is surrounded by mobile sands. The topography of the rocky reef appears to create a distinct hydrodynamic system that permits mobile sands to settle or move into bathymetrical deeper parts of the reef. Our results suggest a very dynamic system surrounding the reef with large scale scouring, sediment reworking and transport, while the shallower central part of the reef remains stable over time. We demonstrate the importance of hydrodynamics and current scouring around reefs for the local variability in seafloor properties over time. These small-scale dynamics are likewise reflected in the spatial distribution of sessile species, which are less abundant in proximity to mobile sands. The hydroacoustic mapping and monitoring of seafloor dynamics at higher spatial and temporal resolutions presents an important future direction in the study of valuable coastal habitats