The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems

Many oscillatory biological systems show periodic travelling waves. These are often modelled using coupled reaction-diffusion equations. However, the effects of different movement rates (diffusion coefficients) of the interacting components on the predictions of these equations are largely unknown. Here we investigate the ways in which varying the diffusion coefficients in such equations alters the wave speed, time period, wavelength, amplitude and stability of periodic wave solutions. We focus on two sets of kinetics that are commonly used in ecological applications: lambda-omega equations, which are the normal form of an oscillatory coupled reaction-diffusion system close to a supercritical Hopf bifurcation, and a standard predator-prey model. Our results show that changing the ratio of the diffusion coefficients can significantly alter the shape of the one-parameter family of periodic travelling wave solutions. The position of the boundary between stable and unstable waves also depends on the ratio of the diffusion coefficients: in all cases, stability changes through an Eckhaus (‘sideband’) instability. These effects are always symmetrical in the two diffusion coefficients for the lambda-omega equations, but are asymmetric in the predator-prey equations, especially when the limit cycle of the kinetics is of large amplitude. In particular, there are two separate regions of stable waves in the travelling wave family for some parameter values in the predator-prey scenario. Our results also show the existence of a one-parameter family of travelling waves, but not necessarily a Hopf bifurcation, for all values of the diffusion coefficients. Simulations of the full partial differential equations reveals that varying the ratio of the diffusion coefficients can significantly change the properties of periodic travelling waves that arise from particular wave generation mechanisms, and our analysis of the travelling wave families assists in the understanding of these effects.     

Towards the stable chelation of radium for biomedical applications with an 18-membered macrocyclic ligand

Targeted alpha therapy is an emerging strategy for the treatment of disseminated cancer. [²²³Ra]RaCl₂ is the only clinically approved alpha particle-emitting drug, and it is used to treat castrate-resistant prostate cancer bone metastases, to which [²²³Ra]Ra²⁺ localizes. To specifically direct [²²³Ra]Ra²⁺ to non-osseous disease sites, chelation and conjugation to a cancer-targeting moiety is necessary. Although previous efforts to stably chelate [²²³Ra]Ra²⁺ for this purpose have had limited success, here we report a biologically stable radiocomplex with the 18-membered macrocyclic chelator macropa. Quantitative labeling of macropa with [²²³Ra]Ra²⁺ was accomplished within 5 min at room temperature with a radiolabeling efficiency of >95%, representing a significant advancement over conventional chelators such as DOTA and EDTA, which were unable to completely complex [²²³Ra]Ra²⁺ under these conditions. [²²³Ra][Ra(macropa)] was highly stable in human serum and exhibited dramatically reduced bone and spleen uptake in mice in comparison to bone-targeted [²²³Ra]RaCl₂, signifying that [²²³Ra][Ra(macropa)] remains intact in vivo. Upon conjugation of macropa to a single amino acid β-alanine as well as to the prostate-specific membrane antigen-targeting peptide DUPA, both constructs retained high affinity for ²²³Ra, complexing >95% of Ra²⁺ in solution. Furthermore, [²²³Ra][Ra(macropa-β-alanine)] was rapidly cleared from mice and showed low ²²³Ra bone absorption, indicating that this conjugate is stable under biological conditions. Unexpectedly, this stability was lost upon conjugation of macropa to DUPA, which suggests a role of targeting vectors in complex stability in vivo for this system. Nonetheless, our successful demonstration of efficient radiolabeling of the β-alanine conjugate with ²²³Ra and its subsequent stability in vivo establishes for the first time the possibility of delivering [²²³Ra]Ra²⁺ to metastases outside of the bone using functionalized chelators, marking a significant expansion of the therapeutic utility of this radiometal in the clinic.

The therapeutic alpha-emitter ²²³Ra can be stably complexed in vivo, creating opportunities for the development of targeted radiopharmaceutical agents with this radionuclide.     

Convenient synthesis of Cu3(BTC)2 encapsulated Keggin heteropolyacid nanomaterial for application in catalysis

Nanomaterial of Cu(3)(BTC)(2) (BTC = benzene tricarboxylic acid) incorporating Keggin heteropolyacid conveniently prepared at room temperature and recovered by freeze drying outperforms ultrastable Y zeolite in acid catalysed esterification reaction.     

Irregular wakes in reaction-diffusion waves

Reaction-diffusion equations have proved to be highly successful models for a wide range of biological and chemical systems, but chaotic solutions have been very rarely documented. We present a new mechanism for generating apparently chaotic spatiotemporal irregularity in such systems, by analysing in detail the bifurcation structure of a particular set of reaction-diffusion equations on an infinite one-dimensional domain, with particular initial conditions. We show that possible solutions include travelling fronts which leave behind either regular or irregular spatiotemporal oscillations. Using a combination of analytical and numerical analysis, we show that the irregular behaviour arises from the instability of oscillations induced by the passage of the front. Finally, we discuss the generality of this mechanism as a way in which spatiotemporal irregularities can arise naturally in reaction-diffusion systems.     

Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations

A variety of numerical methods are available for determining the stability of a given solution of a partial differential equation. However for a family of solutions, calculation of boundaries in parameter space between stable and unstable solutions remains a major challenge. This paper describes an algorithm for the calculation of such stability boundaries, for the case of periodic travelling wave solutions of spatially extended local dynamical systems. The algorithm is based on numerical continuation of the spectrum. It is implemented in a fully automated way by the software package wavetrain, and two examples of its use are presented. One example is the Klausmeier model for banded vegetation in semi-arid environments, for which the change in stability is of Eckhaus (sideband) type; the other is the two-component Oregonator model for the photosensitive Belousov–Zhabotinskii reaction, for which the change in stability is of Hopf type.     

Quantitative Prediction of Rate Constants for Aqueous Racemization To Avoid Pointless Stereoselective Syntheses

Racemization has a large impact upon the biological properties of molecules but the chemical scope of compounds with known rate constants for racemization in aqueous conditions was hitherto limited. To address this remarkable blind spot, we have measured the kinetics for racemization of 28 compounds using circular dichroism and ¹H NMR spectroscopy. We show that rate constants for racemization (measured by ourselves and others) correlate well with deprotonation energies from quantum mechanical (QM) and group contribution calculations. Such calculations thus provide predictions of the second‐order rate constants for general‐base‐catalyzed racemization that are usefully accurate. When applied to recent publications describing the stereoselective synthesis of compounds of purported biological value, the calculations reveal that racemization would be sufficiently fast to render these expensive syntheses pointless.     

Anti-Markovnikov hydroamination and hydrothiolation of electron-deficient vinylarenes catalyzed by well-defined monomeric copper(I) amido and thiolate complexes

Monomeric Cu(I) amido and thiolate complexes that are supported by the N-heterocyclic carbene ligand 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene (IPr) catalyze the hydroamination and hydrothiolation of electron-deficient vinylarenes with reactivity patterns that are consistent with an intermolecular nucleophilic addition of the amido/thiolate ligand of (IPr)Cu(XR) (X = NH or S; R = Ph, CH2Ph) to free vinylarene.     

Spin-forbidden ligand binding to the ferrous-heme group: ab initio and DFT studies

The potential energy surfaces (PESs) and associated energy barriers that characterize the spin-forbidden recombination reactions of the gas-phase ferrous deoxy-heme group with CO, NO, and H2O ligands have been calculated using density functional theory (DFT). The bond energy for binding of O2 has also been calculated. Extensive large basis set CCSD(T) calculations on two small models of the heme group have been used to calibrate the accuracy of different DFT functionals for treating these systems. Pure functionals are shown to overestimate the stability of the low-spin forms of the deoxy-heme model, and to overestimate the binding energy of H2O and CO, whereas hybrid functionals such as B3PW91 and B3LYP yield accurate results. Accordingly, the latter functionals have been used to explore the PESs for binding. CO binding is found to involve a significant barrier of ca. 3 kcal mol-1 due to the need to change from the deoxy-heme quintet ground state to the bound singlet state. Binding of water does not involve a barrier, but the resulting bond is weak and may be further weakened in the protein environment, which should explain why water binding is not usually observed in heme proteins such as myoglobin. NO binding involves a low barrier, which is consistent with observed rapid geminate recombination. The calculated bond energies are in good agreement with previous reported values and in fair agreement with experiment for CO and O2. The value for NO is significantly lower than the experimentally derived bond energy, suggesting that B3LYP is less accurate in this case.     

Combined experimental and computational study of W(II), Ru(II), Pt(IV) and Cu(I) amine and amido complexes using 15N NMR spectroscopy

Using 2D proton-coupled gHSQC pulse sequences in addition to 1D ¹⁵N NMR experiments of ¹⁵N labeled systems, ¹⁵N NMR chemical shifts of a range of transition metal amido and amine complexes were determined. Tungsten(II), ruthenium(II), platinum(IV) and copper(I) complexes with aniline and their anilido variants were studied and compared to free aniline, lithium anilido and anilinium tetrafluoroborate. Upon coordination of aniline to transition metals, upfield chemical shifts of 20–60 ppm were observed. Deprotonation of the amine complexes to form amido complexes resulted in downfield chemical shifts of 40–60 ppm for all of the complexes except for the tungsten d⁴ system. For the tungsten(II) complexes, the cationic aniline complex displayed a downfield shift of approximately 56 ppm relative to the neutral anilido complex. The change in chemical shift for amine to amido conversion is proposed to depend on the ability of the amido ligand to π-bond with the metal center, which influences the magnitude of the paramagnetic screening term.