Illusion of Control in a Brownian Game

Both single-player Parrondo games (SPPG) and multi-player Parrondo games (MPPG) display the Parrondo Effect (PE) wherein two or more individually fair (or Llosing) games yield a net winning outcome if alternated periodically or randomly. (There is a more formal, less restrictive definition of the PE.) We illustrate that, when subject to an elementary optimization rule, the PG displays degraded rather than enhanced returns. Optimization provides only the illusion of control, when low-entropy strategies (i.e. which use more information) under-perform random strategies (with maximal entropy). This illusion is unfortuntately widespread in many human attempts to manage or predict complex systems. For the PG, the illusion is especially striking in that the optimization rule reverses an already paradoxical-seeming positive gain - the Parrondo effect proper - and turns it negative. While this phenomenon has been previously demonstrated using somewhat artificial conditions in the MPPG (L. Dinios and J.M.R. Parrondo. Europhysics Letters 63, 319 (2003); J.M.R. Parrondo et al. Advances in Condensed Matter and Statistical Mechanics, eds. E. Korutcheva and R. Cuerno, Nova Science Publishers, 2003), we demonstrate it in the natural setting of a history-dependent SPPG.Comment: 8 page with 1 tabl

Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For {\it arbitrary} self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism encoding the self-adjoint extension chosen. For particular examples, like the Friedrich's extension, the answer is easily extracted from the general result. In combination with \cite{BKD}, a closed expression for the determinant of an arbitrary self-adjoint extension of the full Laplace-type operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic

An altered heme environment in an engineered cytochrome P450 enzyme enables the switch from monooxygenase to peroxygenase activity

Cytochrome P450 heme-thiolate monooxygenases are exceptionally versatile enzymes which insert an oxygen atom into the unreactive C–H bonds of organic molecules. They source O2 from the atmosphere and usually derive electrons from nicotinamide cofactors via electron transfer proteins. The requirement for an expensive nicotinamide adenine dinucleotide (phosphate) cofactor and the redox protein partners can be bypassed by driving the catalysis using hydrogen peroxide (H₂O₂). We demonstrate that the mutation of a highly conserved threonine residue, involved in dioxygen activation, to a glutamate shuts down monooxygenase activity in a P450 enzyme and converts it into a peroxygenase. The reason for this switch in the threonine to glutamate (T252E) mutant of CYP199A4 from Rhodopseudomonas palustris HaA2 was linked to the lack of a spin state change upon the addition of the substrate. The crystal structure of the substrate-bound form of this mutant highlighted a modified oxygen-binding groove in the I-helix and the retention of the iron-bound aqua ligand. This ligand interacts with the glutamate residue, which favors its retention. Electron paramagnetic resonance confirmed that the ferric heme aqua ligand of the mutant substrate-bound complex had altered characteristics compared to a standard ferric heme aqua complex. Significant improvements in peroxygenase activity were demonstrated for the oxidative demethylation of 4-methoxybenzoic acid to 4-hydroxybenzoic acid and veratric acid to vanillic acid (up to 6-fold). The detailed characterization of this engineered heme peroxygenase will facilitate the development of new methods for driving the biocatalytic generation of oxygenated organic molecules via selective C–H bond activation using heme enzymes.Matthew N. Podgorski, Joshua S. Harbort, Joel H.Z. Lee, Giang T.H. Nguyen, John B. Bruning, William A. Donald, Paul V. Bernhardt, Jeffrey R. Harmer, and Stephen G. Bel

Biophysical techniques for distinguishing ligand binding modes in cytochrome P450 monooxygenases

Published: February 14, 2020The cytochrome P450 superfamily of heme monooxygenases catalyzes important chemical reactions across nature. The changes in the optical spectra of these enzymes, induced by the addition of substrates or inhibitors, are critical for assessing how these molecules bind to the P450, enhancing or inhibiting the catalytic cycle. Here we use the bacterial CYP199A4 enzyme (Uniprot entry Q2IUO2 ), from Rhodopseudomonas palustris HaA2, and a range of substituted benzoic acids to investigate different binding modes. 4-Methoxybenzoic acid elicits an archetypal type I spectral response due to a ≥95% switch from the low- to high-spin state with concomitant dissociation of the sixth aqua ligand. 4-(Pyridin-3-yl)- and 4-(pyridin-2-yl)benzoic acid induced different type II ultraviolet-visible (UV-vis) spectral responses in CYP199A4. The former induced a greater red shift in the Soret wavelength (424 nm vs 422 nm) along with a larger overall absorbance change and other differences in the α-, β-, and δ-bands. There were also variations in the ferrous UV-vis spectra of these two substrate-bound forms with a spectrum indicative of Fe-N bond formation with 4-(pyridin-3-yl)benzoic acid. The crystal structures of CYP199A4, with the pyridinyl compounds bound, revealed that while the nitrogen of 4-(pyridin-3-yl)benzoic acid is coordinated to the heme, with 4-(pyridin-2-yl)benzoic acid an aqua ligand remains. Continuous wave and pulse electron paramagnetic resonance data in frozen solution revealed that the substrates are bound in the active site in a form consistent with the crystal structures. The redox potential of each CYP199A4-substrate combination was measured, allowing correlation among binding modes, spectroscopic properties, and the observed biochemical activity.Matthew N. Podgorski, Joshua S. Harbort, Tom Coleman, Jeanette E. Stok, Jake A. Yorke, Luet-Lok Wong, John B. Bruning, Paul V. Bernhardt, James J. De Voss, Jeffrey R. Harmer, and Stephen G. Bel