A numerical approach to modeling the catalytic voltammetry of surface-confined redox enzymes

A finite difference method for simulating voltammograms of electrochemically driven enzyme catalysis is presented. The method enables any enzyme mechanism to be simulated. The finite difference equations can be represented as a matrix equation containing a nonlinear sparse matrix. This equation has been solved using the software package Mathematica. Our focus is on the use of cyclic voltammetry since this is the most commonly employed electrochemical method used to elucidate mechanisms. The use of cyclic voltammetry to obtain data from systems obeying Michaelis-Menten kinetics is discussed, and we then verify our observations on the Michaelis-Menten system using the finite difference simulation. Finally, we demonstrate how the method can be used to obtain mechanistic information on a real redox enzyme system, the complex bacterial molybdoenzyme xanthine dehydrogenase.

Bitwise bell-inequality violations for an entangled state involving 2N ions

Following on from previous work [J.-A. Larsson, Phys. Rev. A 67, 022108 (2003)], Bell inequalities based on correlations between binary digits are considered for a particular entangled state involving 2N trapped ions. These inequalities involve applying displacement operations to half of the ions and then measuring correlations between pairs of corresponding bits in the binary representations of the number of center-of-mass phonons of N particular ions. It is shown that the state violates the inequalities and thus displays nonclassical correlations. It is also demonstrated that it violates a Bell inequality when the displacements are replaced by squeezing operations.

Fock-state dynamics in Raman photoassociation of Bose-Einstein condensates

By stochastic modeling of the process of Raman photoassociation of Bose-Einstein condensates, we show that, the farther the initial quantum state is from a coherent state, the farther the one-dimensional predictions are from those of the commonly used zero-dimensional approach. We compare the dynamics of condensates, initially in different quantum states, finding that, even when the quantum prediction for an initial coherent state is relatively close to the Gross-Pitaevskii prediction, an initial Fock state gives qualitatively different predictions. We also show that this difference is not present in a single-mode type of model, but that the quantum statistics assume a more important role as the dimensionality of the model is increased. This contrasting behavior in different dimensions, well known with critical phenomena in statistical mechanics, makes itself plainly visible here in a mesoscopic system and is a strong demonstration of the need to consider physically realistic models of interacting condensates.

Effect of early marine diagenesis on coral reconstructions of surface-ocean 13C/12C and carbonate saturation state

Recent research suggests that future decreases in the carbonate saturation state of surface seawater associated with the projected build-up of atmospheric CO2 could cause a global decline in coral reef-building capacity. Whether significant reductions in coral calcification are underway is a matter of considerable debate. Multicentury records of skeletal calcification extracted from massive corals have the potential to reconstruct the progressive effect of anthropogenic changes in carbonate saturation on coral reefs. However, early marine aragonite cements are commonly precipitated from pore waters in the basal portions of massive coral skeletons and, if undetected, could result in apparent nonlinear reductions in coral calcification toward the present. To address this issue, we present records of coral skeletal density, extension rate, calcification rate, δ13C, and δ18O for well preserved and diagenetically altered coral cores spanning ∼1830-1994 A.D. at Ningaloo Reef Marine Park, Western Australia. The record for the pristine coral shows no significant decrease in skeletal density or δ13C indicative of anthropogenic changes in carbonate saturation state or δ13C of surface seawater (oceanic Suess effect). In contrast, progressive addition of early marine inorganic aragonite toward the base of the altered coral produces an apparent ∼25% decrease in skeletal density toward the present, which misleadingly matches the nonlinear twentieth century decrease in coral calcification predicted by recent modeling and experimental studies. In addition, the diagenetic aragonite is enriched in 13C, relative to coral aragonite, resulting in a nonlinear decrease in δ13C toward the present that mimics the decrease in δ13C expected from the oceanic Suess effect. Taken together, these diagenetic changes in skeletal density and δ13C could be misinterpreted to reflect changes in surface-ocean carbonate saturation state driven by the twentieth century build-up of atmospheric CO2. Copyright 2004 by the American Geophysical Union.

Modeling the development of acquired clinical immunity to Plasmodium falciparum malaria

Individuals living in regions where malaria is endemic develop an acquired immunity to malaria which enables them to remain asymptomatic while still carrying parasites. Field studies indicate that cumulative exposure to a variety of diverse Plasmodium parasites is required for the transition from symptomatic to asymptomatic malaria. This study used a simulation model of the within-host dynamics of P. falciparum to investigate the development of acquired clinical immunity under different transmission conditions and levels of parasite diversity. Antibodies developed to P. falciparum erythrocyte membrane protein 1 (PfEMP1), a clonally variant molecule, were assumed to be a key human immunological response to P. falciparum infection, along with responses to clonally conserved but polymorphic antigens. The time to the development of clinical immunity was found to be proportional to parasite diversity and inversely proportional to transmission intensity. The effect of early termination of symptomatic infections by chemotherapy was investigated and found not to inhibit the host's ability to develop acquired immunity. However, the time required to achieve this state was approximately double that compared to when no treatment was administered. This study demonstrates that an immune response primarily targeted against PfEMP1 has the ability to reduce clinical symptoms of infections irrespective of whether treatment is administered, supporting its role in the development of acquired clinical immunity. The results also illustrate a novel use for simulation models of P. falciparum infections, investigation of the influence of intervention strategies on the development of naturally acquired clinical immunity.

Quantum-gate characterization in an extended Hilbert space

We describe an approach for characterizing the process performed by a quantum gate using quantum process tomography, by first modeling the gate in an extended Hilbert space, which includes nonqubit degrees of freedom. To prevent unphysical processes from being predicted, present quantum process tomography procedures incorporate mathematical constraints, which make no assumptions as to the actual physical nature of the system being described. By contrast, the procedure presented here assumes a particular class of physical processes, and enforces physicality by fitting the data to this model. This allows quantum process tomography to be performed using a smaller experimental data set, and produces parameters with a direct physical interpretation. The approach is demonstrated by example of mode matching in an all-optical controlled-NOT gate. The techniques described are general and could be applied to other optical circuits or quantum computing architectures.

Modeling diffraction and imaging of laser beams by the mode-expansion method

We present a new method of modeling imaging of laser beams in the presence of diffraction. Our method is based on the concept of first orthogonally expanding the resultant diffraction field (that would have otherwise been obtained by the laborious application of the Huygens diffraction principle) and then representing it by an effective multimodal laser beam with different beam parameters. We show not only that the process of obtaining the new beam parameters is straightforward but also that it permits a different interpretation of the diffraction-caused focal shift in laser beams. All of the criteria that we have used to determine the minimum number of higher-order modes needed to accurately represent the diffraction field show that the mode-expansion method is numerically efficient. Finally, the characteristics of the mode-expansion method are such that it allows modeling of a vast array of diffraction problems, regardless of the characteristics of the incident laser beam, the diffracting element, or the observation plane. (C) 2005 Optical Society of America.

Tracking the states of a nonlinear system in the weight-space of a feed-forward neural network

Nonlinear, non-stationary signals are commonly found in a variety of disciplines such as biology, medicine, geology and financial modeling. The complexity (e.g. nonlinearity and non-stationarity) of such signals and their low signal to noise ratios often make it a challenging task to use them in critical applications. In this paper we propose a new neural network based technique to address those problems. We show that a feed forward, multi-layered neural network can conveniently capture the states of a nonlinear system in its connection weight-space, after a process of supervised training. The performance of the proposed method is investigated via computer simulations.