Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.

Detecting KaiC Phosphorylation Rhythms of the Cyanobacterial Circadian Oscillator In Vitro and In Vivo

The central oscillator of the cyanobacterial circadian clock is unique in the biochemical simplicity of its components and the robustness of the oscillation. The oscillator is composed of three cyanobacterial proteins: KaiA, KaiB, and KaiC. If very pure preparations of these three proteins are mixed in a test tube in the right proportions and with ATP and MgCl2, the phosphorylation states of KaiC will oscillate with a circadian period, and these states can be analyzed simply by SDS-PAGE. The purity of the proteins is critical for obtaining robust oscillation. Contaminating proteases will destroy oscillation by degradation of Kai proteins, and ATPases will attenuate robustness by consumption of ATP. Here, we provide a detailed protocol to obtain pure recombinant proteins from Escherichia coli to construct a robust cyanobacterial circadian oscillator in vitro. In addition, we present a protocol that facilitates analysis of phosphorylation states of KaiC and other phosphorylated proteins from in vivo samples.

Temperature (over) compensation in an oscillatory surface reaction

Biological rhythms are regulated by homeostatic mechanisms that assure that physiological clocks function reliably independent of temperature changes in the environment. Temperature compensation, the independence of the oscillatory period on temperature, is known to play a central role in many biological rhythms, but it is rather rare in chemical oscillators. We study the influence of temperature on the oscillatory dynamics during the catalytic oxidation of formic acid on a polycrystalline platinum electrode. The experiments are performed at five temperatures from 5 to 25 degrees C, and the oscillations are studied under galvanostatic control. Under oscillatory conditions, only non-Arrhenius behavior is observed. Overcompensation with temperature coefficient (q(10), defined as the ratio between the rate constants at temperature T + 10 degrees C and at T) < I is found in most cases, except that temperature compensation with q(10) approximate to I predominates at high applied currents. The behavior of the period and the amplitude result from a complex interplay between temperature and applied current or, equivalently, the distance from thermodynamic equilibrium. High, positive apparent activation energies were obtained under voltammetric, nonoscillatory conditions, which implies that the non-Arrhenius behavior observed under oscillatory conditions results from the interplay among reaction steps rather than, from a weak temperature dependence of the individual steps.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

Programming chemical kinetics: engineering dynamic reaction networks with DNA strand displacement

Over the last century, the silicon revolution has enabled us to build faster, smaller and more sophisticated computers. Today, these computers control phones, cars, satellites, assembly lines, and other electromechanical devices. Just as electrical wiring controls electromechanical devices, living organisms employ "chemical wiring" to make decisions about their environment and control physical processes. Currently, the big difference between these two substrates is that while we have the abstractions, design principles, verification and fabrication techniques in place for programming with silicon, we have no comparable understanding or expertise for programming chemistry.

In this thesis we take a small step towards the goal of learning how to systematically engineer prescribed non-equilibrium dynamical behaviors in chemical systems. We use the formalism of chemical reaction networks (CRNs), combined with mass-action kinetics, as our programming language for specifying dynamical behaviors. Leveraging the tools of nucleic acid nanotechnology (introduced in Chapter 1), we employ synthetic DNA molecules as our molecular architecture and toehold-mediated DNA strand displacement as our reaction primitive.

Abstraction, modular design and systematic fabrication can work only with well-understood and quantitatively characterized tools. Therefore, we embark on a detailed study of the "device physics" of DNA strand displacement (Chapter 2). We present a unified view of strand displacement biophysics and kinetics by studying the process at multiple levels of detail, using an intuitive model of a random walk on a 1-dimensional energy landscape, a secondary structure kinetics model with single base-pair steps, and a coarse-grained molecular model that incorporates three-dimensional geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Our findings are consistent with previously measured or inferred rates for hybridization, fraying, and branch migration, and provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.

In Chapters 3 and 4, we identify and overcome the crucial experimental challenges involved in using our general DNA-based technology for engineering dynamical behaviors in the test tube. In this process, we identify important design rules that inform our choice of molecular motifs and our algorithms for designing and verifying DNA sequences for our molecular implementation. We also develop flexible molecular strategies for "tuning" our reaction rates and stoichiometries in order to compensate for unavoidable non-idealities in the molecular implementation, such as imperfectly synthesized molecules and spurious "leak" pathways that compete with desired pathways.

We successfully implement three distinct autocatalytic reactions, which we then combine into a de novo chemical oscillator. Unlike biological networks, which use sophisticated evolved molecules (like proteins) to realize such behavior, our test tube realization is the first to demonstrate that Watson-Crick base pairing interactions alone suffice for oscillatory dynamics. Since our design pipeline is general and applicable to any CRN, our experimental demonstration of a de novo chemical oscillator could enable the systematic construction of CRNs with other dynamic behaviors.

Standing wave oscillations in an electrocatalytic reaction

Experimental standing wave oscillations of the interfacial potential across an electrode have been observed in the electrocatalytic oxidation of formic acid on a Pt ring working electrode. The instantaneous potential distribution was monitored by means of equispaced potential microprobes along the electrode. The oscillatory standing waves spontaneously arose from a homogeneous stationary state prior to a Hopf bifurcation if the reference electrode was placed close to the working electrode. Reduced electrolyte concentrations resulted in aperiodic potential patterns, while the presence of a sufficiently large ohmic resistance completely suppressed spatial inhomogeneities. The experimental findings confirm numerical predictions of a reaction-migration formalism: under the chosen geometry, a long-range negative potential coupling between distant points across the ring electrode can lead to oscillatory potential domains of distinct phase. It is further shown that the occurrence of oscillatory standing waves can be rationalized as the electrochemical equivalent of Turing's second bifurcation (wave bifurcation). In the presence of an external resistance, the coupling becomes positive throughout and leads to spatial synchronization.

Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations. (C) 2011 Elsevier Ltd. All rights reserved.

Carbon monoxide oxidation over platinum: Stable, oscillatory and quasi-chaotic regimes

We model the heterogeneously catalyzed oxidation of CO over a Pt surface. A phase diagram analysis is used to probe the several steady state regimes and their stability. We incorporate an experimentally observed 'slow' sub-oxide kinetic step, thereby generalizing a previously presented model. In agreement with experimental data, stable, oscillatory and quasi-chaotic regimes are obtained. Furthermore, the inclusion of the sub-oxide step yields a relaxation oscillation regime. © 1998 Elsevier Science B.V. All rights reserved.

OSCILLATORY DYNAMICS IN SYSTEMS CONTAINING BROMATE AND 1,4-CYCLOHEXANEDIONE IN ACIDIC MEDIA. I. THE EFFECT OF TEMPERATURE.

OSCILLATORY DYNAMICS IN SYSTEMS CONTAINING BROMATE AND 1,4-CYCLOHEXANEDIONE IN ACIDIC MEDIA. I. THE EFFECT OF TEMPERATURE. We present in this work the influence of temperature on the dynamics of homogeneous chemical systems containing bromate and 1,4-cyclohexanedione (1,4-CHD) in acidic media. In particular, the following systems were studied: bromate/1,4-CHD/acid, bromate/1,4-CHD/ferroin/acid and bromate/1,4-CHD/trisbipyridine ruthenium/acid. Investigations were carried out by means of an electrochemical probe, at five temperatures between 5 and 45 degrees C. Activation energies (E-a) were estimated in different ways for the pre-oscillatory and oscillatory regimes. In any case, the E-a was found to depend on the catalyst, composition and initial concentrations. In addition, it was observed that ferroin and trisbipyridine ruthenium act as catalysts only during the transition between the induction period and oscillatory regime.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

Oscillatory beta activity mediates neuroplastic effects of motor cortex stimulation in humans

Continuous theta burst stimulation (cTBS) is a repetitive transcranial magnetic stimulation protocol that can inhibithumanmotor cortex (M1) excitability and impair movement for ≤1 h. While offering valuable insights into brain function and potential therapeutic benefits, these neuroplastic effects are highly variable between individuals. The source of this variability, and the electrophysiological mechanisms underlying the inhibitory after-effects, are largely unknown. In this regard, oscillatory activity at beta frequency (15-35 Hz) is of particular interest as it is elevated in motor disorders such as Parkinson's disease and modulated during the generation of movements. Here, we used a source-level magnetoencephalography approach to investigate the hypothesis that the presence of neuroplastic effects following cTBS is associated with concurrent changes in oscillatory M1 beta activity. M1 cortices were localized with a synthetic aperture magnetometry beamforming analysis of visually cued index finger movements. Virtual electrode analysis was used to reconstruct the spontaneous and movement-related oscillatory activity in bilateral M1 cortices, before and from 10 to 45 min after cTBS. We demonstrate that 40 s of cTBS applied over left M1 reduced corticospinal excitability in the right index finger of 8/16 participants. In these responder participants only, cTBS increased the power of the spontaneous beta oscillations in stimulated M1 and delayed reaction times in the contralateral index finger. No further changes were observed in the latency or power of movement-related beta oscillations. These data provide insights into the electrophysiological mechanisms underlying cTBS-mediated impairment of motor function and demonstrate the association between spontaneous oscillatory beta activity in M1 and the inhibition of motor function. © 2013 the authors.

Heterogeneous catalysis in an oscillatory baffled flow reactor

The first demonstration of heterogeneous catalysis within an oscillatory baffled flow reactor (OBR) is reported, exemplified by the solid acid catalysed esterification of organic acids, an important prototypical reaction for fine chemicals and biofuel synthesis. Suspension of a PrSOH-SBA-15 catalyst powder is readily achieved within the OBR under an oscillatory flow, facilitating the continuous esterification of hexanoic acid. Excellent semi-quantitative agreement is obtained between OBR and conventional stirred batch reaction kinetics, demonstrating efficient mixing, and highlighting the potential of OBRs for continuous, heterogeneously catalysed liquid phase transformations. Kinetic analysis highlights acid chain length (i.e. steric factors) as a key predictor of activity. Continuous esterification offers improved ester yields compared with batch operation, due to the removal of water by-product from the catalyst, evidencing the versatility of the OBR for heterogeneous flow chemistry and potential role as a new clean catalytic technology. © The Royal Society of Chemistry 2013.