“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Twist grain boundaries in three-dimensional lamellar Turing structures

Steady spatial self-organization of three-dimensional chemical reaction-diffusion systems is discussed with the emphasis put on the possible defects that may alter the Turing patterns. It is shown that one of the stable defects of a three-dimensional lamellar Turing structure is a twist grain boundary embedding a Scherk minimal surface.

Neuropeptide release by efficient recruitment of diffusing cytoplasmic secretory vesicles

Neuropeptides are slowly released from a limited pool of secretory vesicles. Despite decades of research, the composition of this pool has remained unknown. Endocrine cell studies support the hypothesis that a population of docked vesicles supports the first minutes of hormone release. However, it has been proposed that mobile cytoplasmic vesicles dominate the releasable neuropeptide pool. Here, to determine the cellular basis of the releasable pool, single green fluorescent protein-labeled secretory vesicles were visualized in neuronal growth cones with the use of an inducible construct or total internal reflection fluorescence microscopy. We report that vesicle movement follows the diffusion equation. Furthermore, rapidly moving secretory vesicles are used more efficiently than stationary vesicles near the plasma membrane to support stimulated release. Thus, randomly moving cytoplasmic vesicles participate in the first minutes of neuropeptide release. Importantly, the preferential recruitment of diffusing cytoplasmic secretory vesicles contributes to the characteristic slow kinetics and limited extent of sustained neuropeptide release.

Microtubule self-organization is gravity-dependent

Although weightlessness is known to affect living cells, the manner by which this occurs is unknown. Some reaction-diffusion processes have been theoretically predicted as being gravity-dependent. Microtubules, a major constituent of the cellular cytoskeleton, self-organize in vitro by way of reaction-diffusion processes. To investigate how self-organization depends on gravity, microtubules were assembled under low gravity conditions produced during space flight. Contrary to the samples formed on an in-flight 1 × g centrifuge, the samples prepared in microgravity showed almost no self-organization and were locally disordered.

Theoretical prediction of a crystal structure.

The diffusion equation method of global minimization is applied to compute the crystal structure of S6, with no a priori knowledge about the system. The experimental lattice parameters and positions and orientations of the molecules in the unit cell are predicted correctly.

Ecological chaos in the wake of invasion.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is generated naturally in the wake of invasive waves of predators. We discuss in detail the mechanism by which the chaos is generated. By considering a mathematical caricature of the predator-prey models, we go on to explain the dynamical origin of the irregular behavior and to justify our assertion that the behavior we present is a genuine example of spatiotemporal chaos.

Proton transfer from the bulk to the bound ubiquinone QB of the reaction center in chromatophores of Rhodobacter sphaeroides: Retarded conveyance by neutral water

The mechanism of proton transfer from the bulk into the membrane protein interior was studied. The light-induced reduction of a bound ubiquinone molecule QB by the photosynthetic reaction center is accompanied by proton trapping. We used kinetic spectroscopy to measure (i) the electron transfer to QB (at 450 nm), (ii) the electrogenic proton delivery from the surface to the QB site (by electrochromic carotenoid response at 524 nm), and (iii) the disappearance of protons from the bulk solution (by pH indicators). The electron transfer to QB− and the proton-related electrogenesis proceeded with the same time constant of ≈100 μs (at pH 6.2), whereas the alkalinization in the bulk was distinctly delayed (τ ≈ 400 μs). We investigated the latter reaction as a function of the pH indicator concentration, the added pH buffers, and the temperature. The results led us to the following conclusions: (i) proton transfer from the surface-located acidic groups into the QB site followed the reduction of QB without measurable delay; (ii) the reprotonation of these surface groups by pH indicators and hydronium ions was impeded, supposedly, because of their slow diffusion in the surface water layer; and (iii) as a result, the protons were slowly donated by neutral water to refill the proton vacancies at the surface. It is conceivable that the same mechanism accounts for the delayed relaxation of the surface pH changes into the bulk observed previously with bacteriorhodopsin membranes and thylakoids. Concerning the coupling between proton pumps in bioenergetic membranes, our results imply a tendency for the transient confinement of protons at the membrane surface.

Fluorescence correlation analysis of probe diffusion simplifies quantitative pathogen detection by PCR

A sensitive, labor-saving, and easily automatable nonradioactive procedure named APEX-FCS (amplified probe extension detected by fluorescence correlation spectroscopy) has been established to detect specific in vitro amplification of pathogen genomic sequences. As an example, Mycobacterium tuberculosis genomic DNA was subjected to PCR amplification with the Stoffel fragment of Thermus aquaticus DNA polymerase in the presence of nanomolar concentrations of a rhodamine-labeled probe (third primer), binding to the target in between the micromolar amplification primers. The probe becomes extended only when specific amplification occurs. Its low concentration avoids false-positives due to unspecific hybridization under PCR conditions. With increasing portion of extended probe molecules, the probe’s average translational diffusion properties gradually change over the course of the reaction, reflecting amplification kinetics. Following PCR, this change from a stage of high to a stage of low mobility can directly be monitored during a 30-s measurement using a fluorescence correlation spectroscopy device. Quantitation down to 10 target molecules in a background of 2.5 μg unspecific DNA without post-PCR probe manipulations could be achieved with different primer/probe combinations. The assay holds the promise to concurrently perform amplification, probe hybridization, and specific detection without opening the reaction chamber, if sealable foils are used.

Single-molecule protein folding: Diffusion fluorescence resonance energy transfer studies of the denaturation of chymotrypsin inhibitor 2

We report single-molecule folding studies of a small, single-domain protein, chymotrypsin inhibitor 2 (CI2). CI2 is an excellent model system for protein folding studies and has been extensively studied, both experimentally (at the ensemble level) and theoretically. Conformationally assisted ligation methodology was used to synthesize the proteins and site-specifically label them with donor and acceptor dyes. Folded and denatured subpopulations were observed by fluorescence resonance energy transfer (FRET) measurements on freely diffusing single protein molecules. Properties of these subpopulations were directly monitored as a function of guanidinium chloride concentration. It is shown that new information about different aspects of the protein folding reaction can be extracted from such subpopulation properties. Shifts in the mean transfer efficiencies are discussed, FRET efficiency distributions are translated into potentials, and denaturation curves are directly plotted from the areas of the FRET peaks. Changes in stability caused by mutation also are measured by comparing pseudo wild-type CI2 with a destabilized mutant (K17G). Current limitations and future possibilities and prospects for single-pair FRET protein folding investigations are discussed.

Co-Permeability of 3H-Labeled Water and 14C-Labeled Organic Acids across Isolated Plant Cuticles1 : Investigating Cuticular Paths of Diffusion and Predicting Cuticular Transpiration

Penetration of 3H-labeled water (3H2O) and the 14C-labeled organic acids benzoic acid ([14C]BA), salicylic acid ([14C]SA), and 2,4-dichlorophenoxyacetic acid ([14C]2,4-D) were measured simultaneously in isolated cuticular membranes of Prunus laurocerasus L., Ginkgo biloba L., and Juglans regia L. For each of the three pairs of compounds (3H2O/[14C]BA, 3H2O/[14C]SA, and 3H2O/[14C]2,4-D) rates of cuticular water penetration were highly correlated with the rates of penetration of the organic acids. Therefore, water and organic acids penetrated the cuticles by the same routes. With the combination 3H2O/[14C]BA, co-permeability was measured with isolated cuticles of nine other plant species. Permeances of 3H2O of all 12 investigated species were highly correlated with the permeances of [14C]BA (r2 = 0.95). Thus, cuticular transpiration can be predicted from BA permeance. The application of this experimental method, together with the established prediction equation, offers the opportunity to answer several important questions about cuticular transport physiology in future investigations.