Science, serendipity, coincidence, and the Oregonator at the University of Oregon, 1969-1974.

This historical review of the development of the Oregonator model of the Belousov-Zhabotinsky reaction is based on a lecture Dick Field presented during IrvFest2015-Celebrating a founding father of chaos!, a meeting in commemoration of Irving R. Epstein's 70 th birthday. For Dick's 80 th birthday festschrift, we focus here on the five papers in the series named "Oscillations in chemical systems," published in 1972 [Noyes et al., J. Am. Chem. Soc. 94, 1394-1395 (1972); Field et al., J. Am. Chem. Soc. 94, 8649-8664 (1972); Field and Noyes, Nature 237, 390-392 (1972)] and 1974 [Field and Noyes, J. Chem. Phys. 60, 1877-1884 (1974); Field and Noyes, J. Am. Chem. Soc. 96, 2001-2006 (1974)].

Caring for the Patient.

Is there a simple secret to truly great patient care? Medical science is able to alleviate more diseases and mitigate more suffering than ever before, but physicians are left feeling less respected, more criticized, more judged, and more burned out. Too many patients say we just do not care about them, regardless of the expertise we trained so hard to give to them.Generational truths and personal experiences from a rural, community-based surgical practice in Mississippi suggest that the art and the science of medicine are inseparable and interdependent. It is indeed possible for a highly trained, teaching surgeon to sit with his patients every Sunday in church, take care of the local football team, and speak at funerals of those he fought to save. This level of emotional agility is a requisite character trait in a rural setting, and one that can serve all surgeons well, no matter where they practice. Genuine compassion and a hand on the shoulder, supported by a foundation of scientific knowledge and clinical judgment, will almost guarantee a strong, trusting bond between doctor and patient. The secret of great patient care is simply caring for the patient.

Rozycki-Feliciano Lecture Rudolph Matas, the Father of Vascular Surgery.

Rudolph Matas (1860-1957) was one of the foremost figures in the history of vascular surgery. He is considered the father of vascular surgery for his operations for arteriovenous fistula and peripheral artery aneurysm, all devised before the isolation of heparin and the wide adoption of techniques for vascular anastomosis. A medical and surgical prodigy, Matas received his medical degree from Tulane University at age 19 (1880) and was named its chair of surgery at 35 (1895), a position he would hold until 1927. A contemporary and friend of Halsted, Matas throughout his career was known as a leader in the field, holding the presidencies of the American College of Surgeons (1925-1926) and the American Surgical Association (1909). He maintained loyal relationships to those who trained in surgery with him at Touro Hospital in New Orleans, including the author's grandfather, the first Richard J. Field. Matas was an honored guest at the dedication of the Centreville Clinic in 1928, the facility where three generations of Field surgeons have provided continuous service to its rural Mississippi community for nearly a century.

Quint points lattice in a driven Belousov-Zhabotinsky reaction model.

We report the discovery of a regular lattice of exceptional quint points in a periodically driven oscillator, namely, in the frequency-amplitude control parameter space of a photochemically periodically perturbed ruthenium-catalyzed Belousov-Zhabotinsky reaction model. Quint points are singular boundary points where five distinct stable oscillatory phases coalesce. While spikes of the activator show a smooth and continuous variation, the spikes of the inhibitor show an intricate but regular branching into a myriad of stable phases that have fivefold contact points. Such boundary points form a wide parameter lattice as a function of the frequency and amplitude of light absorption. These findings revise current knowledge about the topology of the control parameter space of a celebrated prototypical example of an oscillating chemical reaction.

Kinetics of conversion of dihydroxyacetone to methylglyoxal in New Zealand manuka honey: Part IV - Formation of HMF.

During a study of the conversion of dihydroxyacetone (DHA) to methylglyoxal (MGO) in maturing New Zealand manuka honey, the kinetics of formation of 5-(hydroxymethyl)furfural (HMF) was studied at temperatures from 4 to 37°C. Formation of HMF was first-order during an induction period and zero-order thereafter indicating that the mechanism includes the formation of certain critical intermediates and that these require time to build up; the duration of the induction period depended primarily upon temperature. The zero-order rate constant at 37°C was the same for manuka honey and clover honey doped with 2000 or 10,000mg/kg DHA and for artificial honey with 2000mg/kg of DHA and either alanine or proline and alanine added. Zero-order rate constants for artificial honey with added amino acids were less than for a control without amino acids. A simulation was created to predict the formation of HMF over time at 37°C in manuka honey.

Oregonator Scaling Motivated by the Showalter-Noyes Limit.

The Belousov-Zhabotinsky (BZ) reaction is the prototype oscillatory chemical system. We investigate here a new scaling of the Oregonator model of BZ chemical kinetics and use this scaling to elucidate fundamental properties of BZ dynamics. In particular, the Showalter-Noyes criterion for oscillation, that the product [BrO3-][H+] exceeds a critical value, arises naturally as a subcritical Hopf bifurcation in this setting, as does the reduction to a two-variable model. We thus provide chemical explanations of the role of time scales in the BZ reaction.

Kinetics of conversion of dihydroxyacetone to methylglyoxal in New Zealand manuka honey: Part I--Honey systems.

The kinetics of conversion of dihydroxyacetone (DHA) to methylglyoxal (MGO) were investigated in manuka honeys and DHA-doped clover honeys stored between 4 and 37°C. Both the disappearance of DHA and appearance of MGO were confirmed as overall, first order reactions, albeit probably composites of multiple reactions. Increasing the storage temperature accelerated the rate of DHA loss and the initial rate of formation of MGO, but better conversion efficiency was observed at lower temperature. At 37°C, more MGO was lost at later times in manuka honey compared to DHA-doped-clover honey. Thirty-seven New Zealand manuka honeys and four clover honeys were analysed for various chemical and physical properties; comparison of rate constants and these parameters identified some positive correlations.

Kinetics of the conversion of dihydroxyacetone to methylglyoxal in New Zealand manuka honey: Part II--Model systems.

The irreversible dehydration reaction of dihydroxyacetone (DHA) to methylglyoxal (MGO) in a honey model system has been examined to investigate the influence of added perturbant species on the reaction rate. The secondary amino acid proline, primary amino acids (alanine, lysine and serine), and iron, or combinations of these perturbants, were added to artificial honey with either DHA or MGO and stored at 20, 27 and 37°C. These systems were monitored over time. A 1:1 conversion of DHA to MGO was not observed in any system studied, including the control system with no added perturbants. Addition of proline to the matrix increased consumption of DHA but did not produce any more MGO than the control sample. Lysine and serine behaved similarly. Alanine enhanced the conversion of DHA to MGO and had the best efficiency of conversion of DHA to MGO for the amino acids studied. An iron II salt enhanced the conversion of DHA to MGO, even in the presence of proline.

Kinetics of conversion of dihydroxyacetone to methylglyoxal in New Zealand manuka honey: Part III--A model to simulate the conversion.

A kinetic model for the conversion of dihydroxyacetone (DHA) to methylglyoxal (MGO) in honey is proposed; a building block approach was used to create the model. Artificial honeys doped with DHA and individual perturbants were fitted first, then multiple perturbants (alanine, proline and iron, and combinations of these) were fitted before comparing the simulation to real honey samples (doped clover and manuka honey). The main responses in the prediction model were DHA, MGO, proline, primary amino acids, acidity, 3-phenyllactic acid and 4-methoxyphenyllactic acid. Three temperatures (20, 27 and 37°C) were studied and the conversion of DHA to MGO was monitored over at least 1year. Differences in the conversion between clover doped with DHA and manuka honey were observed. The simulation fitted well for the honeys tested.

Quantification of nitropropanoyl glucosides in karaka nuts before and after treatment.

A high performance liquid chromatography (HPLC) method was developed to assay nitropropanoyl glucosides in the nuts of karaka (Corynocarpus laevigatus) a traditional food of New Zealand Maori. Levels of glucosides, measured as 3-nitropropanoic acid, ranged from 50.25 to 138.62 g kg(-1) (5.0-13.9% w/w) and were highest in nuts from unripe drupes; these levels are higher than any previously reported. Other parts of the drupe also contained nitropropanoyl glucosides but at lower levels than the nut. Treatment procedures to remove the glucosides from the nuts varied in their efficacy with soxhlet extraction removing 98.7% and prolonged boiling and cold water extraction both removing 96%. These findings confirm the traditional methods for preparation of these nuts for consumption.

Social-support moderated stress: a nonlinear dynamical model and the stress-buffering hypothesis.

Health psychology has studied the cross-sectional, stationary relationships linking stress, social support, and health. Levels of stress-related illness are generally modeled by including a nonlinear multiplicative or 'buffering' effect, corresponding to the interaction of stressor levels with social support from family and friends. The motivation of the present research is to extend an iterative, dynamic model of this well-investigated psychological process using a dynamical systems model expressed as a set of continuous, nonlinear differential equations similar to those of the 'Oregonator,' a model of a nonlinear dynamic chemical system. This model of the behavior of an individual is amenable to numerical investigation of its stationary-state stability properties, temporal evolution, and cause-effect relationships. The continuous variables in this new approach refer to varying states of an individual; they are Perceived stress (X), Symptoms (Y), and Social support (Z). It is expected that poor health in this model, represented by Symptoms (Y), is directly related to Perceived stress, as well as being tied in more complicated ways to Social support. A number of such models may be envisioned, some including a multiplicative, 'buffering' (- X x Z) effect of social support dependent on stress levels. We explore the behavior of this model over ranges of parameter values and initial conditions and relate these results to how an individual reacts to environmental challenges at various levels of stressors and social-support recruitment. Data generated by the model are in turn analyzed with a traditional cross-sectional statistical technique. Similarities and differences between chemical and psychological systems are discussed.

Relative abundance and structure of chaotic behavior: the nonpolynomial Belousov-Zhabotinsky reaction kinetics.

We report a detailed numerical investigation of the relative abundance of periodic and chaotic oscillations in phase diagrams for the Belousov-Zhabotinsky (BZ) reaction as described by a nonpolynomial, autonomous, three-variable model suggested by Gyorgyi and Field [Nature (London) 355, 808 (1992)]. The model contains 14 parameters that may be tuned to produce rich dynamical scenarios. By computing the Lyapunov spectra, we find the structuring of periodic and chaotic phases of the BZ reaction to display unusual global patterns, very distinct from those recently found for gas and semiconductor lasers, for electric circuits, and for a few other familiar nonlinear oscillators. The unusual patterns found for the BZ reaction are surprisingly robust and independent of the parameter explored.

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.

Activation energy for the disproportionation of HBrO2 and estimated heats of formation of HBrO2 and BrO2.

The kinetics of the reaction HBrO(2) + HBrO(2) --> HOBr + BrO(3)(-) + H(+) is investigated in aqueous HClO(4) (0.04-0.9 M) and H(2)SO(4) (0.3-0.9 M) media and at temperatures in the range 15-38 degrees C. The reaction is found to be cleanly second order in [HBrO(2)], with the experimental rate constant having the form k(exp) = k + k'[H(+)]. The half-life of the reaction is on the order of a few tenths of a second in the range 0.01 M < [HBrO(2)](0) < 0.02 M. The detailed mechanism of this reaction is discussed. The activation parameters for kare found to be E(double dagger) = 19.0 +/- 0.9 kJ/mol and DeltaS(double dagger) = -132 +/- 3 J/(K mol) in HClO(4), and E(double dagger) = 23.0 +/- 0.5 kJ/mol and DeltaS(double dagger) = -119 +/- 1 J/(K mol) in H(2)SO(4). The activation parameters for k' are found to be E(double dagger) = 25.8 +/- 0.5 kJ/mol and DeltaS(double dagger) = -106 +/- 1 J/(K mol) in HClO(4), and E(double dagger) = 18 +/- 3 kJ/mol and DeltaS(double dagger) = -130 +/- 11 J/(K mol) in H(2)SO(4). The values Delta(f)H(29)(8)(0)[BrO(2)(aq)] = 157 kJ/mol and Delta(f)H(29)(8)(0)[HBrO(2)(aq)] = -33 kJ/mol are estimated using a trend analysis (bond strengths) based on the assumption Delta(f)H(29)(8)(0)[HBrO(2)(aq)] lies between Delta(f)H(29)(8)(0)[HOBr(aq)] and Delta(f)H(29)(8)(0)[HBrO(3)(aq)] as Delta(f)H(29)(8)(0)[HClO(2)(aq)] lies between Delta(f)H(29)(8)(0)[HOCl(aq)] and Delta(f)H(29)(8)(0)[HClO(3)(aq)]. The estimated value of Delta(f)H(29)(8)(0)[BrO(2)(aq)] agrees well with calculated gas-phase values, but the estimated value of Delta(f)H(29)(8)(0)[HBrO(2)(aq)], as well as the tabulated value of Delta(f)H(29)(8)(0)[HClO(2)(aq)], is in substantial disagreement with calculated gas-phase values. Values of Delta(r)H(0) are estimated for various reactions involving BrO(2) or HBrO(2).

Oxidation state of BZ reaction mixtures.

The unstirred, ferroin (Fe(phen)(3)2+)-catalyzed Belousov-Zhabotinsky (BZ) reaction1-4 is the prototype oscillatory chemical system. After an induction period of several minutes, one sees "spontaneous" formation of "pacemaker" sites, which oscillate between a blue, oxidized state (high [Fe(phen)3(3+)]) and a red, reduced state (low [Fe(phen)(3)3+]). The reaction medium appears red (reduced) during the induction phase, and the pacemaker sites generate target patterns of concentric, outwardly moving waves of oxidation (blue). Auto-oscillatory behavior is also seen in the Oregonator model of Field, Korös, and Noyes (FKN), a robust, reduced model which captures qualitative BZ kinetics in the auto-oscillatory regime. However, the Oregonator model predicts a blue (oxidized) induction phase. Here, we show that including reaction R8 of the FKN mechanism, not incorporated in the original Oregonator, accounts for bromide release during the induction phase, thus producing the observed red oxidation state.