Mapping behavioral specifications to model parameters in synthetic biology

With recent improvements of protocols for the assembly of transcriptional parts, synthetic biological devices can now more reliably be assembled according to a given design. The standardization of parts open up the way for in silico design tools that improve the construct and optimize devices with respect to given formal design specifications. The simplest such optimization is the selection of kinetic parameters and protein abundances such that the specified design constraints are robustly satisfied. In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model. We solve this inverse problem by linearizing the forward operator that maps parameter sets to specifications, and then inverting it locally. This approach has two advantages over brute-force random sampling. First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction. The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology

Corannulene: A Preference for <i>e</i><i>xo-</i>Metal Binding. X-ray Structural Characterization of [Ru₂(O₂CCF₃)₂(CO)₄·(<i>η</i>²-C₂₀H₁₀)₂]

X-ray crystallographic characterization of the title complex, having only one ruthenium(I) center bound to each bowl, shows exo η2-rim coordination of C20H10

X-ray and Density Functional Theory Structural Study of 1,3,5,7,9-Penta-<i>tert</i>-butylcorannulene, C₄₀H₅₀

The first X-ray structural characterization of an alkyl-substituted corannulene, namely, 1,3,5,7,9-penta-tert-butylcorannulene (C40H50), has been accomplished. The addition of bulky tert-butyl groups to the corannulene core flattens the bowl and affects the solid-state packing. The presence of two enantiomers, in addition to positional disorder of the C40H50 bowls in the solid-state structure, has prevented the acquisition of accurate geometric parameters of this open geodesic polyarene. Therefore, DFT calculations have been used to describe its molecular geometry and to access bond lengths, bond angles, and a bowl depth

Corannulene: A Preference for <i>e</i><i>xo-</i>Metal Binding. X-ray Structural Characterization of [Ru₂(O₂CCF₃)₂(CO)₄·(<i>η</i>²-C₂₀H₁₀)₂]

X-ray crystallographic characterization of the title complex, having only one ruthenium(I) center bound to each bowl, shows exo η2-rim coordination of C20H10

X-ray and Density Functional Theory Structural Study of 1,3,5,7,9-Penta-<i>tert</i>-butylcorannulene, C₄₀H₅₀

The first X-ray structural characterization of an alkyl-substituted corannulene, namely, 1,3,5,7,9-penta-tert-butylcorannulene (C40H50), has been accomplished. The addition of bulky tert-butyl groups to the corannulene core flattens the bowl and affects the solid-state packing. The presence of two enantiomers, in addition to positional disorder of the C40H50 bowls in the solid-state structure, has prevented the acquisition of accurate geometric parameters of this open geodesic polyarene. Therefore, DFT calculations have been used to describe its molecular geometry and to access bond lengths, bond angles, and a bowl depth

Corannulene: A Preference for <i>e</i><i>xo-</i>Metal Binding. X-ray Structural Characterization of [Ru₂(O₂CCF₃)₂(CO)₄·(<i>η</i>²-C₂₀H₁₀)₂]

X-ray crystallographic characterization of the title complex, having only one ruthenium(I) center bound to each bowl, shows exo η2-rim coordination of C20H10

Pentaindenocorannulene and Tetraindenocorannulene: New Aromatic Hydrocarbon π Systems with Curvatures Surpassing That of C₆₀

Short syntheses and X-ray crystal structures are reported for two new geodesic polyarenes, pentaindenocorannulene (1, C50H20) and tetraindenocorannulene (2, C44H18). These extended aromatic π systems constitute the largest curved subunits of C60 ever prepared. In agreement with theoretical predictions, the trigonal carbon atoms at the cores of these new hydrocarbons suffer even greater pyramidalization than that exhibited by the carbon atoms of C60 (average POAV angles = 12.6, 12.1, and 11.6° for 1, 2, and C60, respectively). These syntheses of such highly curved π systems by solution phase methods, starting from compounds that were derived from planar starting materials also by solution phase methods, demonstrate unequivocally that rational chemical syntheses of fullerenes, carbon nanotubes, and related carbon-rich molecules should all be possible using exclusively solution chemical methods! Recourse to high-temperature gas-phase pyrolysis should not be necessary. The synthesis of 1 begins with a 5-fold Suzuki−Miyaura coupling of 1,3,5,7,9-pentachlorocorannulene with 2-chlorophenylboronic acid, giving 1,3,5,7,9-pentakis(2-chlorophenyl)corannulene in 48% isolated yield (86% average yield per C−C coupling). Subsequent conversion to pentaindenocorannulene (1) was achieved in 35% isolated yield (81% average yield per C−C coupling) by a 5-fold, Pd(0)-catalyzed, intramolecular arylation reaction. The synthesis of tetraindenocorannulene (2) follows the same course but starts from 1,2,5,6-tetrabromocorannulene. Flash vacuum pyrolysis of the intermediate 1,2,5,6-tetrakis(2-chlorophenyl)corannulene also produces tetraindenocorannulene (2). The title compounds are both deep orange, thermally robust, air stable, crystalline solids (mp >400 °C) with rich UV−vis spectra that have long absorption tails in the visible region

Pentaindenocorannulene and Tetraindenocorannulene: New Aromatic Hydrocarbon π Systems with Curvatures Surpassing That of C₆₀

Short syntheses and X-ray crystal structures are reported for two new geodesic polyarenes, pentaindenocorannulene (1, C50H20) and tetraindenocorannulene (2, C44H18). These extended aromatic π systems constitute the largest curved subunits of C60 ever prepared. In agreement with theoretical predictions, the trigonal carbon atoms at the cores of these new hydrocarbons suffer even greater pyramidalization than that exhibited by the carbon atoms of C60 (average POAV angles = 12.6, 12.1, and 11.6° for 1, 2, and C60, respectively). These syntheses of such highly curved π systems by solution phase methods, starting from compounds that were derived from planar starting materials also by solution phase methods, demonstrate unequivocally that rational chemical syntheses of fullerenes, carbon nanotubes, and related carbon-rich molecules should all be possible using exclusively solution chemical methods! Recourse to high-temperature gas-phase pyrolysis should not be necessary. The synthesis of 1 begins with a 5-fold Suzuki−Miyaura coupling of 1,3,5,7,9-pentachlorocorannulene with 2-chlorophenylboronic acid, giving 1,3,5,7,9-pentakis(2-chlorophenyl)corannulene in 48% isolated yield (86% average yield per C−C coupling). Subsequent conversion to pentaindenocorannulene (1) was achieved in 35% isolated yield (81% average yield per C−C coupling) by a 5-fold, Pd(0)-catalyzed, intramolecular arylation reaction. The synthesis of tetraindenocorannulene (2) follows the same course but starts from 1,2,5,6-tetrabromocorannulene. Flash vacuum pyrolysis of the intermediate 1,2,5,6-tetrakis(2-chlorophenyl)corannulene also produces tetraindenocorannulene (2). The title compounds are both deep orange, thermally robust, air stable, crystalline solids (mp >400 °C) with rich UV−vis spectra that have long absorption tails in the visible region

Pentaindenocorannulene and Tetraindenocorannulene: New Aromatic Hydrocarbon π Systems with Curvatures Surpassing That of C₆₀

Short syntheses and X-ray crystal structures are reported for two new geodesic polyarenes, pentaindenocorannulene (1, C50H20) and tetraindenocorannulene (2, C44H18). These extended aromatic π systems constitute the largest curved subunits of C60 ever prepared. In agreement with theoretical predictions, the trigonal carbon atoms at the cores of these new hydrocarbons suffer even greater pyramidalization than that exhibited by the carbon atoms of C60 (average POAV angles = 12.6, 12.1, and 11.6° for 1, 2, and C60, respectively). These syntheses of such highly curved π systems by solution phase methods, starting from compounds that were derived from planar starting materials also by solution phase methods, demonstrate unequivocally that rational chemical syntheses of fullerenes, carbon nanotubes, and related carbon-rich molecules should all be possible using exclusively solution chemical methods! Recourse to high-temperature gas-phase pyrolysis should not be necessary. The synthesis of 1 begins with a 5-fold Suzuki−Miyaura coupling of 1,3,5,7,9-pentachlorocorannulene with 2-chlorophenylboronic acid, giving 1,3,5,7,9-pentakis(2-chlorophenyl)corannulene in 48% isolated yield (86% average yield per C−C coupling). Subsequent conversion to pentaindenocorannulene (1) was achieved in 35% isolated yield (81% average yield per C−C coupling) by a 5-fold, Pd(0)-catalyzed, intramolecular arylation reaction. The synthesis of tetraindenocorannulene (2) follows the same course but starts from 1,2,5,6-tetrabromocorannulene. Flash vacuum pyrolysis of the intermediate 1,2,5,6-tetrakis(2-chlorophenyl)corannulene also produces tetraindenocorannulene (2). The title compounds are both deep orange, thermally robust, air stable, crystalline solids (mp >400 °C) with rich UV−vis spectra that have long absorption tails in the visible region

Increasing the Curvature of a Bowl-Shaped Polyarene by Fullerene-like η²-Complexation of a Transition Metal at the Interior of the Convex Surface

The first transition metal complex of monoindenocorannulene, [{Rh2(O2CCF3)4}2·(C26H12)] (1), has been synthesized by gas-phase deposition and has been structurally characterized by X-ray crystallography. In the solid state, it forms a 2D organometallic network based on intermolecular Rh−C interactions and rare tetra-bridged coordination of a π-bowl. In addition to η2-rim binding, one Rh(II) center interacts exclusively with interior carbon atoms on the convex surface, exhibiting an η2-coordination type previously observed only in closed, all-carbon buckyballs. The latter unique coordination of Rh(II) accentuates the pyramidalization of the C atoms of monoindenocorannulene. Thus, in contrast to all other reported Rh(II) complexes with buckybowls, metal complexation leads to a curvature increase of the C26H12 core in 1. DFT calculations (PBE0) reveal the preferred coordination sites of C26H12 to be the rim of the corannulene core, followed by the interior spoke and then the rim CC bonds of the indeno site. This calculated trend is nicely followed by the average Rh−C bond distances in the solid-state structure of 1: 2.567 (rim) < 2.687 (spoke) < 2.715 Å (indeno site). The nature of Rh(II)−π interactions was quantitatively evaluated in terms of ligand-to-metal and metal-to-ligand contributions, showing the consistently greater role of the former in all computed complexes