Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions

An inhomogeneous profile of chemostatted species generates a rich variety of patterns in glycolytic waves depicted in a Selkov reaction-diffusion framework here. A key role played by diffusion amplitude and symmetry in the chemostatted species profile in dictating the fate of local spatial dynamics involving periodic, quasiperiodic, and chaotic patterns and transitions among them are investigated systematically. More importantly, various dynamic transitions, including wave propagation direction changes, are illustrated in interesting situations. Besides numerical results, our analytical formulation of the amplitude equation connecting complex Ginzburg-Landau and Lambda-omega representation shed light on the phase dynamics of the system. This systematic study of the glycolytic reaction-diffusion wave is in line with previous experimental results in open spatial reactor and will provide a knowledge about the dynamics that shape and control biological information processing and related phenomena.     

Front waves in the NO + NH3 reaction on Pt{100}

In the present work, we spatially extended a brand new kinetic mechanism of the NO + NH3 reaction on Pt{100} to simulate the experimentally observed spatiotemporal traveling waves. The kinetic mechanism developed by Irurzun, Mola, and Imbihl (IMI model) improves the former model developed by Lombardo, Fink, and Imbihl (LFI model) by replacing several elementary steps to take into account experimental evidence published since the LFI model appeared. The IMI model achieves a better agreement with the experimentally observed dependence of the oscillation period on temperature. In the present work, the IMI model is extended by considering Fickean diffusion and coupling via the gas phase. Traveling waves propagating across the surface are obtained at realistic values of temperature and partial pressure. A transition from amplitude to phase waves is observed, induced either by temperature or by the gas global coupling strength. The traveling waves simulated in the present work are not associated with fixed defects, in agreement with experimental evidence of spiral centers capable of moving on the surface. Also, the IMI model adequately predicts the presence of macroscopic oscillations in the partial pressures of the reactants coexisting with front wave patterns on the surface.     

Discrete and heterogeneous rotational dynamics of single membrane probe dyes in gel phase supported lipid bilayer

In order to probe the local dynamics of lipid bilayers in the gel phase, we measured the rotational time trajectories of a membrane probe, diI(3), in supported bilayers of DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine) using single molecule fluorescence polarization imaging. diI(3) has two hydrocarbon tails that mimic phospholipid tails and has its transition dipole moment lying mostly on the plane of the membrane; hence it is an excellent probe for rotational dynamics in membranes. Above the transition temperature, the probes are laterally mobile and do not display polarized emission. In the gel phase below the transition temperature, lateral mobility is severely reduced and the emission becomes polarized with its polarization direction changing in the milliseconds time scale. Molecule by molecule analysis of the rotational time scales revealed significant heterogeneities among molecules, much larger than would be due to statistical noise. Control experiments using small unilamellar vesicles suggest that the heterogeneities are not caused by surface interactions and are intrinsic to the gel phase membrane. The rotational dynamics is strongly temperature dependent and the thermally activated state for the rotational motion has a large entropic barrier (> 30kB), indicating that relatively large local disorder is required for the rotational motion to occur. Rotational hopping between discrete angles has been observed at the lowest temperatures (approximately 10 degrees C). Our results suggest that the gel phase membrane is not uniform at the microscopic level but is highly dynamic with the rigidity of local environments constantly changing.     

Spatio-temporal dynamics in glycolysis

During the glycolytic degradation of sugar in a thin layer of yeast extract, travelling waves of NADH and protons can be generated that carry a state of high enzymatic activity through the system. The controlled initiation of such waves with an activator of the enzyme phosphofructokinase (PFK) and the influence of various salts and co-factors on the propagation dynamics are investigated. Furthermore a first study of the dispersion of waves is presented. The experimental characterisation of this in vitro system contributes to unravelling the possible role of glycolysis for biological information processing. In this context, the provision of chemically available energy in the absence of compartmentation by glycolysis is of primary importance.     

Bromide control, bifurcation and activation in the Belousov-Zhabotinsky reaction

The unstirred, ferroin (Fe(phen)3(2+)) catalyzed Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. Reaction media with added Br(-) appear red (reduced, low [Fe(phen)3(3+)]) during an induction period of several minutes, followed by the "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and the red, reduced state and generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Koros and Noyes (FKN), a robust, reduced model that captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here we develop a generalized Oregonator-like model with no explicit bifurcation parameter that yields the observed transition from a red initial state to oscillatory dynamics, and displays a new bifurcation mechanism not seen in the original Oregonator.     

Molecular dynamics simulation of phase separating binary liquids in cylindrical Couette flow

We use molecular dynamics simulations to study phase separation of a 50:50 (by volume) fluid mixture in a confined and curved (Taylor-Couette) geometry, consisting of two concentric cylinders. The inner cylinder may be rotated to achieve a shear flow. In nonsheared systems we observe that, for all cases under consideration, the final equilibrium state has a stacked structure. Depending on the lowest free energy in the geometry the stack may be either flat, with its normal in the z direction, or curved, with its normal in the r or theta direction. In sheared systems we make several observations. First, when starting from a prearranged stacked structure, we find that sheared gradient and vorticity stacks retain their character for the durations of the simulation, even when another configuration is preferred (as found when starting from a randomly mixed configuration). This slow transition to another configuration is attributed to a large free energy barrier between the two states. In case of stacks with a normal in the gradient direction, we find interesting interfacial waves moving with a prescribed angular velocity in the flow direction. Because such a wave is not observed in simulations with a flat geometry at similar shear rates, the curvature of the wall is an essential ingredient of this phenomenon. Second, when starting from a randomly mixed configuration, stacks are also observed, with an orientation that depends on the applied shear rate. Such transitions to other orientations are similar to observations in microphase separated diblock copolymer melts. At higher shear rates complex patterns emerge, accompanied by deviations from a homogeneous flow profile. The transition from steady stacks to complex patterns takes place around a shear rate 1/tau(dv), where tau(dv) is the crossover time from diffusive to viscous dominated growth of phase-separated domains, as measured in equilibrium simulations.     

Slow dynamics of a colloidal lamellar phase

We used x-ray photon correlation spectroscopy to study the dynamics in the lamellar phase of a platelet suspension as a function of the particle concentration. We measured the collective diffusion coefficient along the director of the phase, over length scales down to the interparticle distance, and quantified the hydrodynamic interaction between the particles. This interaction sets in with increasing concentration and can be described qualitatively by a simplified model. No change in the microscopic structure or dynamics is observed at the transition between the fluid and the gel-like lamellar phases.     

Programmed Locomotion of an Active Gel Driven by Spiral Waves

Active media that host spiral waves can display complex modes of locomotion driven by the dynamics of those waves. We use a model of a photosensitive stimulus‐responsive gel that supports the propagation of spiral chemical waves to study locomotive transition and programmed locomotion. The mode transition between circular and toroidal locomotion results from the onset of spiral tip meandering that arises via a secondary Hopf bifurcation as the level of illumination is increased. This dynamic instability of the system introduces a second circular locomotion with a small diameter caused by tip meandering. The original circular locomotion with large diameter is driven by the push‐pull asymmetry of the wavefront and waveback of the simple spiral waves initiated at one corner of gel. By harnessing this mode transition of the gel locomotion via coded illumination, we design programmable pathways of nature‐inspired angular locomotion of the gel.     

Theoretical study of pattern formation during the catalytic oxidation of CO on Pt{100} at low pressures

Theoretical studies have thus far been unable to model pattern formation during the reaction in this system on physically feasible length and time scales. In this paper, we derive a computational reaction-diffusion model for this system in which most of the input parameters have been determined experimentally. We model the surface on a mesoscopic scale intermediate between the microscopic size of CO islands and the macroscopic length scale of pattern formation. In agreement with experimental investigations [M. Eiswirth et al., Z. Phys. Chem., Neue Folge 144, 59 (1985)], the results from our model divide the CO and O(2) partial pressure parameter space into three regions defined by the level of CO coverage or the presence of sustained oscillations. We see CO fronts moving into oxygen-covered regions, with the 1 x 1 to hex phase change occurring at the leading edge. There are also traveling waves consisting of successive oxygen and CO fronts that move into areas of relatively high CO coverage, and in this case, the phase change is more gradual and of lower amplitude. The propagation speed of these reaction waves is similar to those observed experimentally for CO and oxygen fronts [H. H. Rotermund et al., J. Chem. Phys. 91, 4942 (1989); H. H. Rotermund et al., Nature (London) 343, 355 (1990); J. Lauterbach and H. H. Rotermund, Surf. Sci. 311, 231 (1994)]. In the two-dimensional version of our model, the traveling waves take the form of target patterns emitted from surface inhomogeneities.     

Collective and molecular dynamics in low molar mass and polymeric ferroelectric liquid crystals

By use of a novel sample preparation technique, it is possible to measure with one sample cell the collective and molecular dynamics (10^-1 Hz-10⁹ Hz) of macroscopically (in bookshelf geometry) oriented ferroelectric liquid crystals. Below 10⁶ Hz, two ferroelectric modes, Goldstone- and soft-mode, are observed, being assigned to fluctuations of the phase and amplitude of the helical superstructure respectively. Between 10⁶ and 10⁹ Hz, one dielectric loss process exists, the β-relaxation which originates from the librational motion (hindered rotation) of the mesogen around its molecular long axis. This process does not split or broaden at the non-ferroelectric-ferroelectric phase transition and it has an Arrhenius type temperature dependence. In comparing a racemic mixture with a chiral sample, it performs a similar frequency and temperature dependence. The experimental findings for the β-relaxation are in qualitative contrast to the predictions of the (generalized) Landau expansion of the free energy at the non-ferroelectric-ferroelectric phase transition. The experiment also leads to a modified understanding for the molecular origin of ferroelectricity in FLCs.     

Budding dynamics of multicomponent tubular vesicles

Real-time budding dynamics of multicomponent, tubular lipid vesicles was investigated. By using a fluorescence microscope, three typical growth modes of the buds were observed, corresponding, respectively, to bud growth through coalescence between flat patches, a bud and a patch, as well as that of two buds. The spatial and temporal scales measured in the observation were used to estimate the bending rigidity of the membrane. In the late stage, the continuing coalescence between the buds resulted in large shape deformation of the vesicles, from tubular to spherical vesicles, and the number of the buds decayed with time as N approximately t-2/3. This scaling relation was observed for the first time in experiment and confirmed early theoretical predictions. Our observation showed a difference between the diffusivity of the buds on the lipid membrane and that of the embedded membrane proteins.     

Analysis of the Raman intensities near the phase transitions in ammonium halides

This study concentrates on the temperature dependence of the Raman intensities for the lattice modes in ammonium halides (NH(4)Cl and NH(4)Br) close to phase transitions. We predict their intensities using the results of a shell model for the Raman polarizability within the framework of an Ising pseudospin-phonon coupled model. From our observed Raman intensities of those phonon modes studied here, we extract the values of the critical exponent for the order parameter in these crystalline systems. The exponent values indicate that the Raman intensities show a logarithmic divergence at higher pressures in NH(4)Cl, whereas they predict a lambda-type phase transition at zero pressure in NH(4)Br.     

Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed large-scale computer simulations, demonstrating that universality holds at long times in the immediate vicinity of the transition. The scaling function describing the crossover from anomalous transport to diffusive motion is found to vary extremely slowly and spans at least five decades in time. To extract the scaling function, one has to allow for the leading universal corrections to scaling. Our findings suggest that apparent power laws with varying exponents generically occur and dominate experimentally accessible time windows as soon as the heterogeneities cover a decade in length scale. We extract the divergent length scales, quantify the spatial heterogeneities in terms of the non-Gaussian parameter, and corroborate our results by a thorough finite-size analysis.     

Local polymer dynamics under strong connectivity constraints: the dendrimer case

The characteristics of local motion are explored by molecular dynamics simulations in a series of AB(2)-type dendrimer melts. Systems of generations 3-5 were simulated in a wide temperature range, allowing the assessment of effects associated with molecular size, proximity to the detected glasslike transitions, and the strong connectivity constraints imposed by the dendritic topology. Investigation of the mechanisms involved in local motion at short temporal and spatial scales revealed the connection between the non-Gaussian nature of monomer displacements to alpha-relaxation and the caging/decaging process under different degrees of confinement. In the latter mechanism, two characteristic localization lengths were identified: at the low temperature limit spatial localization was realized within approximately 10% of the nearest neighbor distance while at temperatures higher than the glass transition, the existence of an analogous length scale is ascribed to the geometric constraints due to the dense connectivity pattern. As the results from this study are discussed in comparison to the behavior observed in linear polymers and supercooled liquids, new insight is provided on the universal/specific mechanisms involved in local dynamics of different glass-forming systems.     

Phase Transitions in Solid Methanol

Neutron powder diffraction patterns were measured for the ordered α-phase and the disordered β-phase of deuterated methanol. The structure of the α-phase at 160 K is in agreement with that found earlier at 15 K. A complete refinement of the structure of the β-phase at 170 K was also carried out. The space groups are α-P2₁2₁2₁ and β-Cmcm. For the disordered phase, the thermal parameters indicate that the molecules are localized rather than being in free rotation. A transformation matrix was found that relates the unit cells of the two phases. The transition involves mainly the large-angle rotation of molecules in a plane. In a second experiment, the α- to β-phase transition in both deuterated and undeuterated solid methanol was examined using Raman spectroscopy and a metastable phase was produced, for the undeutered sample, by rapid quenching through the phase transition. Only two modes of the methyl groups in this metastable phase differ from the internal modes of the stable α-phase.     

PEG-POSS Star Molecules Blended in Polyurethane with Flexible Hard Segments: Morphology and Dynamics

A star polymer with a polyhedral oligomeric silsesquioxanne (POSS) core and poly(ethylene glycol) (PEG) vertex groups is incorporated in a polyurethane with flexible hard segments in-situ during the polymerization process. The blends are studied in terms of morphology, molecular dynamics, and charge mobility. The methods utilized for this purpose are scanning electron and atomic force microscopies (SEM, AFM), X-ray diffraction (XRD), differential scanning calorimetry (DSC), and to a larger extent dielectric relaxation spectroscopy (DRS). It is found that POSS reduces the degree of crystallinity of the hard segments. Contrary to what was observed in a similar system with POSS pendent along the main chain, soft phase calorimetric glass transition temperature drops as a result of plasticization, and homogenization of the soft phase by the star molecules. The dynamic glass transition though, remains practically unaffected, and a hypothesis is formed to resolve the discrepancy, based on the assumption of different thermal and dielectric responses of slow and fast modes of the system. A relaxation α′, slower than the bulky segmental α and common in polyurethanes, appears here too. A detailed analysis of dielectric spectra provides some evidence that this relaxation has cooperative character. An additional relaxation g, which is not commonly observed, accompanies the Maxwell Wagner Sillars interfacial polarization process, and has dynamics similar to it. POSS is found to introduce conductivity and possibly alter its mechanism. The study points out that different architectures of incorporation of POSS in polyurethane affect its physical properties by different mechanisms.     

Fickian crossover and length scales from two point functions in supercooled liquids

Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self-scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The length scale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characteristic time scale is several times larger than the alpha relaxation time. A second crossover length scale is observed, which corresponds to the typical time and length of heterogeneities, in agreement with results from four point functions. The different regimes can be traced back to the behavior of the van Hove distribution of displacements, which shows a characteristic exponential regime in the heterogeneous region before the crossover to Gaussian diffusion and should be observable in experiments. Our results show that it is possible to obtain characteristic length scales of heterogeneities through the computation of two point functions at different times.     

Stimulated emission three-pulse photo-echo peakshift: a mixed pump-probe and photon-echo technique for studying excited-state dynamics

A novel four-pulse photon-echo technique for exploring condensed phase dynamics at different parts of the excited-state potential energy surface is presented. In contrast to traditional three-pulse photon-echo signals, the introduction of a fourth pump pulse allows the use of photon-echo techniques to probe excited-state phenomena. Here, a "proof of principle" experiment is presented where the excited-state solvent dynamics of the coumarin 153 chromophore dissolved in methanol is explored. The fluctuations of the stimulated emission transition is probed, in contrast to the ground-state absorption transition explored in traditional echo measurements. Distinctly different excited-state dynamics, in contrast to ground-state signals, is observed and discussed.     

The probe rules in single particle tracking

Single particle tracking (SPT) enables light microscopy at a sub-diffraction limited spatial resolution by a combination of imaging at low molecular labeling densities and computational image processing. SPT and related single molecule imaging techniques have found a rapidly expanded use within the life sciences. This expanded use is due to an increased demand and requisite for developing a comprehensive understanding of the spatial dynamics of bio-molecular interactions at a spatial scale that is equivalent to the size of the molecules themselves, as well as by the emergence of new imaging techniques and probes that have made historically very demanding and specialized bio-imaging techniques more easily accessible and achievable. SPT has in particular found extensive use for analyzing the molecular organization of biological membranes. From these and other studies using complementary techniques it has been determined that the organization of native plasma membranes is heterogeneous over a very large range of spatial and temporal scales. The observed heterogeneities in the organization have the practical consequence that the SPT results in investigations of native plasma membranes are time dependent. Furthermore, because the accessible time dynamics, and also the spatial resolution, in an SPT experiment is mainly dependent on the luminous brightness and photostability of the particular SPT probe that is used, available SPT results are ultimately dependent on the SPT probes. The focus of this review is on the impact that the SPT probe has on the experimental results in SPT.