Chaotic Dynamics in an Electronic Model of a Genetic Network

We consider dynamics in a class of piecewise-linear ordinary differential equations and in an electronic circuit that model genetic networks. In these models, gene activity varies continuously in time. However, as in Boolean or discrete-time switching networks, gene activity is driven high or low based only on whether the activities of the regulating genes are high or low (i.e., above or below certain thresholds). Depending on the “regulatory logic”, these models can exhibit simple dynamics, like stable fixed points or oscillation, or chaotic dynamics. The observed qualitative and quantitative differences between the dynamics in the idealized equations and the dynamics in the electronic circuit lead us to focus attention on the analysis of the dynamics as a function of parameter values. We propose new techniques for solving the inverse problem – the problem of inferring the regulatory logic and parameters from time series data. We also give new symbolic and statistical methods for characterizing dynamics in these networks.     

Increased Water Reduction Efficiency of Polyelectrolyte‐Bound Trimetallic [Ru,Rh,Ru] Photocatalysts in Air‐Saturated Aqueous Solutions

The groundbreaking use of polyelectrolytes to increase the efficiency of supramolecular photocatalysts in solar H₂ production schemes under aqueous aerobic conditions is reported. Supramolecular photocatalysts of the architecture [{(TL)₂Ru(BL)}₂RhX₂]⁵⁺ (BL=bridging ligand, TL=terminal ligand, X=halide) demonstrate high efficiencies in deoxygenated organic solvents but do not function in air‐saturated aqueous solution because of the quenching of the metal‐to‐ligand charge‐transfer (MLCT) excited state under these conditions. The new photocatalytic system incorporates poly(4‐styrenesulfonate) (PSS) into aqueous solutions containing [{(bpy)₂Ru(dpp)}₂RhCl₂]⁵⁺ (bpy=2,2′‐bipyridine, dpp=2,3‐bis(2‐pyridyl)pyrazine). PSS has a profound impact on the photocatalyst efficiency, increasing H₂ production over three times that of deoxygenated aqueous solutions alone. H₂ photocatalysis proceeds even under aerobic conditions for PSS‐containing solutions, an exciting consequence for solar hydrogen‐production research.     

Equilibrium for a combinatorial Ricci flow with generalized weights on a tetrahedron

Chow and Lou [2] showed in 2003 that under certain conditions the combinatorial analogue of the Hamilton Ricci flow on surfaces converges to Thruston’s circle packing metric of constant curvature. The combinatorial setting includes weights defined for edges of a triangulation. A crucial assumption in [2] was that the weights are nonnegative. We have recently shown that the same statement on convergence can be proved under weaker conditions: some weights can be negative and should satisfy certain inequalities. In this note we show that there are some restrictions for weakening the conditions. Namely, we show that in some situations the combinatorial Ricci flow has no equilibrium or has several points of equilibrium and, in particular, the convergence theorem is no longer valid.     

A Districtwide Study of Automaticity When Included in Concept‐Based Elementary School Mathematics Instruction

While conceptual understanding of properties, operations, and the base‐ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three elementary schools in a school district implements mandatory automaticity drills for 10 minutes each day while the remaining two elementary schools, with the same curriculum and very similar demographics, do not. This study looks at (a) the impact that schoolwide implementation of automaticity drills has on schoolwide computational math skills as measured by the ITBS and (b) the relationship between automaticity and conceptual understanding as measured by statewide standardized testing. The results suggest that while there may be an association between automaticity and higher performance on standardized tests, caution should be taken before assuming there are benefits to promoting automaticity drills. These results are consistent with those that support a process‐driven approach to automaticity based on familiarity with properties and strategies associated with the base‐ten number system; they are not consistent with those that support an answer‐driven approach to automaticity based on memorization of answers.     

Bidirectional soliton street

The bidirectional long-wave model introduced by Wu (1994)^[1] and Yih & Wu (1995)^[2] is applied to evaluate interactions between multiple solitary waves progressing in both directions in a uniform channel of rectangular cross-section and undergoing collisions of two classes, one being head-on and the other overtaking collisions between these solitons. For a binary head-on collision, the two interacting solitary waves are shown to merge during a phase-locking period from which they reemerge separated, each asymptotically recovering its own initial identity while both being retarded in phase from their original pathlines. For a binary overtaking collision between a soliton of height α₁ overtaking a weaker one of height α₁, the two solition peaks are shown to either pass through each other or remain separated throughout the encounter according as α₁/α₂ or <3, respectively. With no phase locking during the overtaking, the two solitary waves re-emerge afterwards with their initial forms recovered and with the stronger wave being advanced whereas the weaker one retarded in phase from their original pathlines. By extension, the theory is generalized to apply to uniform channels of arbitrary cross-sectional shape. The Inaugural Pei-Yuan Chou Memorial Lecture, presented at The Sixth Asian Congress of Fluid Mechanics. Singapore, 21–26 May 1995     

Catalytic C-H bond amination from high-spin iron imido complexes

Dipyrromethene ligand scaffolds were synthesized bearing large aryl (2,4,6-Ph(3)C(6)H(2), abbreviated Ar) or alkyl ((t)Bu, adamantyl) flanking groups to afford three new disubstituted ligands ((R)L, 1,9-R(2)-5-mesityldipyrromethene, R=aryl, alkyl). While high-spin (S=2), four-coordinate iron complexes of the type ((R)L)FeCl(solv) were obtained with the alkyl-substituted ligand varieties (for R=(t)Bu, Ad and solv=THF, OEt(2)), use of the sterically encumbered aryl-substituted ligand precluded binding of solvent and cleanly afforded a high-spin (S=2), three-coordinate complex of the type ((Ar)L)FeCl. Reaction of ((Ad)L)FeCl(OEt(2)) with alkyl azides resulted in the catalytic amination of C-H bonds or olefin aziridination at room temperature. Using a 5% catalyst loading, 12 turnovers were obtained for the amination of toluene as a substrate, while greater than 85% of alkyl azide was converted to the corresponding aziridine employing styrene as a substrate. A primary kinetic isotope effect of 12.8(5) was obtained for the reaction of ((Ad)L)FeCl(OEt(2)) with adamantyl azide in an equimolar toluene/toluene-d(8) mixture, consistent with the amination proceeding through a hydrogen atom abstraction, radical rebound type mechanism. Reaction of p-(t)BuC(6)H(4)N(3) with ((Ar)L)FeCl permitted isolation of a high-spin (S=2) iron complex featuring a terminal imido ligand, ((Ar)L)FeCl(N(p-(t)BuC(6)H(4))), as determined by (1)H NMR, X-ray crystallography, and (57)Fe Mo?ssbauer spectroscopy. The measured Fe-N(imide) bond distance (1.768(2) ?) is the longest reported for Fe(imido) complexes in any geometry or spin state, and the disruption of the bond metrics within the imido aryl substituent suggests delocalization of a radical throughout the aryl ring. Zero-field (57)Fe Mo?ssbauer parameters obtained for ((Ar)L)FeCl(N(p-(t)BuC(6)H(4))) suggest a Fe(III) formulation and are nearly identical with those observed for a structurally similar, high-spin Fe(III) complex bearing the same dipyrromethene framework. Theoretical analyses of ((Ar)L)FeCl(N(p-(t)BuC(6)H(4))) suggest a formulation for this reactive species to be a high-spin Fe(III) center antiferromagnetically coupled to an imido-based radical (J = -673 cm(-1)). The terminal imido complex was effective for delivering the nitrene moiety to both C-H bond substrates (42% yield) as well as styrene (76% yield). Furthermore, a primary kinetic isotope effect of 24(3) was obtained for the reaction of ((Ar)L)FeCl(N(p-(t)BuC(6)H(4))) with an equimolar toluene/toluene-d(8) mixture, consistent with the values obtained in the catalytic reaction. This commonality suggests the isolated high-spin Fe(III) imido radical is a viable intermediate in the catalytic reaction pathway. Given the breadth of iron imido complexes spanning several oxidation states (Fe(II)-Fe(V)) and several spin states (S=0→(3)/(2)), we propose the unusual electronic structure of the described high-spin iron imido complexes contributes to the observed catalytic reactivity.     

Probing coherence in synthetic cyclic light-harvesting pigments

A series of π-extended cyclic thiophene oligomers of 12, 18, 24, and 30 repeat units have been studied using methods of ultrafast time-resolved absorption, fluorescence upconversion, and three-pulse photon echo. These measurements were conducted in order to examine the structure-function relationships that may affect the coherence between chromophores within the organic macrocycles. Our results indicate that an initial delocalized state can be seen upon excitation of the cyclic thiophenes. Anisotropy measurements show that this delocalized state decays on an ultrafast time scale and is followed by the presence of incoherent hopping. From the use of a phenomenological model, we conclude that our ultrafast anisotropy decay measurements suggest that the system does not reside in the Fo?rster regime and coherence within the system must be considered. Three-pulse photon echo peak shift experiments reveal a clear dependence of initial peak shift with ring size, indicating a weaker coupling to the bath (and stronger intramolecular interactions) as the ring size is increased. Our results suggest that the initial delocalized state increases with ring size to distances (and number of chromophores) comparable to the natural light-harvesting system.     

Conformational analysis of aliskiren, a potent renin inhibitor, using high-resolution nuclear magnetic resonance and molecular dynamics simulations

Aliskiren is a nonpeptide antihypertensive drug that potently inhibits the human enzyme renin in vitro and in vivo. Many clinical trials have shown the efficacy of aliskiren to lower blood pressure in correlation with other antihypertensive agents. In this report, the conformational behavior of aliskiren is studied in water, trifluoroethanol, and dimethylformamide solutions by means of 2D-NMR spectroscopy and molecular dynamics simulations. The stereochemical characteristics of aliskiren in different solutions, in combination with the previously published crystal structure of the renin-aliskiren complex have been investigated. The aim of this study was to explore the conformational behavior of this first successful renin inhibitor in relation to its environment. In aqueous solution, aliskiren adapts a U-shape conformation, whereas in DMF, the molecule is basically endowed with an "extended" conformation, which has more similarities to the one bound to the receptor.     

Sensitizing the Sensitizer: The Synthesis and Photophysical Study of Bodipy-Pt(II)(diimine)(dithiolate) Conjugates

The dyads 3, 4, and 6, combining the Bodipy chromophore with a Pt(bpy)(bdt) (bpy = 2,2'-bipyridine, bdt = 1,2-benzenedithiolate, 3 and 6) or a Pt(bpy)(mnt) (mnt = maleonitriledithiolate, 4) moiety, have been synthesized and studied by UV-vis steady-state absorption, transient absorption, and emission spectroscopies and cyclic voltammetry. Comparison of the absorption spectra and cyclic voltammograms of dyads 3, 4, and 6 and those of their model compounds 1a, 2, 5, and 7 shows that the spectroscopic and electrochemical properties of the dyads are essentially the sum of their constituent chromophores, indicating negligible interaction of the constituent chromophores in the ground state. However, emission studies on 3 and 6 show a complete absence of both Bodipy-based fluorescence and the characteristic luminescence of the Pt(bpy)(bdt) unit. Dyad 4 shows a weak Pt(mnt)-based emission. Transient absorption studies show that excitation of the dyads into the Bodipy-based (1)ππ* excited state is followed by singlet energy transfer (SEnT) to the Pt(dithiolate)-based (1)MMLL'CT (mixed metal-ligand to ligand charge transfer) excited state ([Formula: see text] = 0.6 ps, [Formula: see text] = 0.5 ps, and [Formula: see text] = 1.6 ps), which undergoes rapid intersystem crossing to the (3)MMLL'CT state due to the heavy Pt(II) ion. The (3)MMLL'CT state is then depopulated by triplet energy transfer (TEnT) to the low-lying Bodipy-based (3)ππ* excited state ([Formula: see text] = 8.2 ps, [Formula: see text] = 5 ps, and [Formula: see text] = 160 ps). The transition assignments are supported by TD-DFT calculations. Both energy-transfer processes are shown to proceed via a Dexter electron exchange mechanism. The much longer time constants for dyad 6 relative to 3 are attributed to the significantly poorer coupling and resonance of charge-separated species that are intermediates in the electron exchange process.