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

Multiple Pathways for the Primary Step of the Spiropyran Photochromic Reaction: A CASPT2//CASSCF Study

CASSCF and CASPT2 studies on the reaction mechanism of the photochromic ring-opening process of a spiropyran (SP) (1′,3′,3′-trimethylspiro-[2<i>H</i>-1-benzopyran-2,2′-indoline], also known as BIPS) have been performed and possible excited-state C–O (and C–N) bond cleavage pathways and S₁-to-S₀ nonadiabatic transition channels have been explored. (1) The C–O bond dissociation in SP does not follow a conical-intersection mechanism that has been proposed in a model study with a simplified benzopyran. The CASSCF-optimized crossing points are actually avoided crossings with a large S₁–S₀ energy gap at the CASPT2 level; thus, they could not act as efficient S₁-to-S₀ funnels. (2) C–O bond cleavage paths on S₁ leading to both the CCC (cis–cis–cis with respect to the configuration around α, β, γ) and TCC (trans–cis–cis) intermediates of merocyanine (MC) are barrierless, in line with the experimentally observed ultrafast formation of MC. (3) An unexpected low-energy hydrogen-out-of-plane (HOOP) valley on the (π→σ*) surface was located not far from the C–O bond cleavage path and was suggested to be an efficient S₁-to-S₀ nonadiabatic decay channel. Triggered by the active HOOP mode, the molecule can easily access the S₁–HOOP valley and then make a transition to the S₀ surface through the narrow S₁–S₀ gap that exists in an extended region. Nonadiabatic decay through a conical intersection on C–N dissociation path as well as the HOOP funnel is responsible for high internal conversion yields of SP. These findings shedding light on the complex mechanism of SP–MC interconversion provide fundamental information for design spiropyran-based photochromic devices

Drawing the Retinal Out of Its Comfort Zone: An ONIOM(QM/MM) Study of Mutant Squid Rhodopsin

Engineering squid rhodopsin with modified retinal analogues is essential for understanding the conserved steric and electrostatic interaction networks that govern the architecture of the Schiff base binding site. Depriving the retinal of its steric and electrostatic contacts affects the positioning of the Schiff-base relative to the key residues Asn87, Tyr111, and Glu180. Displacement of the W1 and W2 positions and the impact on the structural rearrangements near the Schiff base binding region reiterates the need for the presence of internal water molecules and the accessibility of binding sites to them. Also, the dominant role of the Glu180 counterion in inducing the S₁/S₂ state reversal for SBR is shown for the first time in squid rhodopsin

Revisiting the Passerini Reaction Mechanism: Existence of the Nitrilium, Organocatalysis of Its Formation, and Solvent Effect

The Passerini reaction mechanism is revisited using high-level DFT calculations. Contrary to the common belief, the nitrilium intermediate is found to be stable in solution and its formation is rate-determining. The present results point out that this step is catalyzed by a second carboxylic acid molecule, as the subsequent Mumm rearrangement is. The solvent effect on the reaction rate was investigated. In a protic solvent like methanol, hydrogen bonds are responsible of the increasing barrier of the rate-determining step, compared to the commonly used solvent, the dichloromethane

Photochemical Ring Opening and Closing of Three Isomers of Diarylethene: Spin–Flip Time-Dependent Density Functional Study

The reaction mechanism of photochemical ring opening and closing transformation was investigated for diarylethene (DAE), which works as a molecular switch and photodevice. Spin–flip time-dependent density functional theory is employed to map the potential energy surfaces and to elucidate the photochemical mechanism of three isomers (normal, inverse, and mixed types) of 1,2-dithienylethene, a model DAE. The potential energy characteristics including the minimum-energy conical intersection reveals the origin of different product preferences of the three isomers. For the normal type, the excited state from either closed or open form reaches the same conical intersection that gives preferentially the closed product. The inverse type preferentially gives the closed product. The mixed type has two pathways that are easily convertible, and both open and closed reactants give both open and closed products

Computational Study on the Working Mechanism of a Stilbene Light-Driven Molecular Rotary Motor: Sloped Minimal Energy Path and Unidirectional Nonadiabatic Photoisomerization

The working mechanism of a geometrically overcrowded, chiral stilbene light-driven molecular rotary motor [(<i>2R,2R</i>)-2,2′,7,7′-tetramethyl-1,1′-bis­(indanylidene), <b>3</b>] has been investigated by a potential energy surface (PES) study. The reaction paths of the two photoinitiated <i>cis</i>–<i>trans</i> (or <i>E/Z</i>) isomerization processes, namely, (<i>P,P</i>)-<i>stable-cis</i>→(<i>M,M</i>)-<i>unstable-trans</i>-<b>3</b> and (<i>P,P</i>)-<i>stable-trans</i>→(<i>M,M</i>)-<i>unstable-cis</i>-<b>3</b>, have been explored at the CASPT2//CASSCF level of theory. The minimal energy reaction paths (MEPs) of these two processes are nearly parallel on the PESs, separated by a ridge of high inversion barrier. The MEPs have a remarkably steep slope, which drives CC bond rotation unidirectionally. The asymmetric bias on the excited-state MEPs is caused by the substituents on the “fjord” region as well as by the phenyl moieties. The overall photoisomerization reaction can be described as a three-state (1B→2A→1A) multimode mechanism: The molecule excited to the 1B state first crosses one of the sloped 1B/2A seams, and then follows two cooperative torsional reaction modes to cross preferentially one of the two 2A/1A conical intersections to reach the isomerized ground-state product

What is the Real Nature of Ferrous Soybean Lipoxygenase-1? A New Two-Conformation Model Based on Combined ONIOM(DFT:MM) and Multireference Configuration Interaction Characterization

The geometric and spectral features of the ferrous resting state of soybean lipoxygenase-1 (SLO-1) have remained puzzling. We have theoretically characterized ferrous SLO-1 by means of the ONIOM(DFT:MM), TDDFT, and CASSCF/SORCI methods, taking explicitly into account the effect of the protein environment. Two conformations found theoretically in this study, Conf-A and Conf-B, have almost equal stability but have quite different geometries, with short and long Fe−O₆₉₄ distances, respectively. While neither of the geometries agreed well with the crystal structure of the enzyme, an averaged geometry showed excellent agreement. Therefore, we propose that the crystal structure reflects a mixture of these two conformations. The calculated circular dichroism (CD) spectra for Conf-A and Conf-B were found to agree well with the two experimental spectra obtained previously for “six-coordinate” and “five-coordinate” forms of ferrous SLO-1, respectively

Role of Water in Mukaiyama–Aldol Reaction Catalyzed by Lanthanide Lewis Acid: A Computational Study

Carbon–carbon bond formations, such as Kobayashi modification of the Mukaiyama–Aldol reaction, catalyzed by lanthanide (Ln) Lewis acid in aqueous solution comprise one of the most attractive types of reactions in terms of green chemistry. However, their detailed mechanisms and the role of water molecules remained unclear. In order to explore complex potential energy surfaces for the water and substrate coordination around Eu³⁺ as well as the detailed mechanism of the Mukaiyama–Aldol reaction between trimethylsilyl (TMS) cylcohexenolate and benzaldehyde (BA) catalyzed by Eu³⁺, the recently developed anharmonic downward distortion following (ADDF) and artificial force-induced reaction (AFIR) methods were used with the B3LYP-D3 theory. The most favorable water coordination structures are Eu³⁺(H₂O)₈ and Eu³⁺(H₂O)₉; they are comparable in free energy and are likely to coexist, with an effective coordination number of 8.3. Eu³⁺(H₂O)₈(BA) is the best aldehyde coordinated structure. Starting with this complex, the Mukaiyama–Aldol reaction proceeds via a stepwise mechanism, first C–C bond formation between the substrates, followed by proton transfer from water to BA and then TMS dissociation caused by nucleophilic attack by bulk water molecules. Why did the yield of the Mukaiyama–Aldol reaction catalyzed by Ln³⁺ in organic solvent dramatically increase upon addition of water? Without water, the reverse reaction (C–C cleavage) takes place easily. Why did this reaction show <i>syn</i>-preference in water? The <i>anti</i> transition state for C–C formation in water is entropically less favored relative to the <i>syn</i> transition state because of the existence of a rigid hydrogen bond between the TMS part and coordination water around Eu³⁺ in the former

How Can Fluctional Chiral Lanthanide (III) Complexes Achieve a High Stereoselectivity in Aqueous Mukaiyama-Aldol Reaction?

The aqueous Mukaiyama-Aldol reaction catalyzed by lanthanide (Ln) Lewis acid is one of the most attractive reactions for green chemistry. One of the chiral catalysts that achieved a high stereoselectivity is Ln³⁺ complexed with fluctional DODP, (2<i>R</i>,2′<i>R</i>)-dialkyl 2,2′-(1,7-dioxa-4,10-diazacyclododecane-4,10-diyl)­dipropanoates. In this study, we theoretically studied the structure of the Ln³⁺–DODP (Ln = Eu) complex and the transition states (TSs) for stereodetermining C–C bond formation step between benzaldehyde and silyl enol ether catalyzed by this complex to elucidate the origin of stereoselectivity of the reaction. To explore the local minima and TSs exhaustively, we used an automated exploration method, called the Global Reaction Root Mapping (GRRM) strategy. Unlike conventional rigid chiral catalysts, three conformers of the Eu³⁺–DODP (the lowest <b>A</b>, the second lowest <b>B</b>, and the third lowest <b>C</b>) coexisted in the reaction system. Considering all the TSs obtained from the three conformers, we reproduced the experimental enantio excess and diastereomeric ratio quantitatively. The most stable TS for the C–C bond formation producing the major stereoisomer (<i>R,R</i>) was obtained from the second lowest conformer <b>B</b>. The lowest TS producing the enantiomer (<i>S,S</i>) was obtained from the conformer <b>C</b>; the similar (<i>S,S</i>) TS obtained from the conformer <b>B</b> was 0.4 kcal/mol less stable. Thus, to improve the enantioselectivity, the existing probability of the conformer <b>C</b> had to be reduced. The easiest way to achieve this is replacing Eu³⁺ by other Ln³⁺ with larger ionic radii, which was consistent with the experimental facts

Toward Predicting Full Catalytic Cycle Using Automatic Reaction Path Search Method: A Case Study on HCo(CO)₃-Catalyzed Hydroformylation

Toward systematic prediction of reaction pathways in complex chemical reaction systems by quantum chemical calculations, a new automatic reaction path search approach has been proposed on the basis of the artificial force induced reaction (AFIR) method [<i>J. Chem. Theory Comput.</i> <b>2011</b>, <i>7</i>, 2335–2345.]. We demonstrate in this Letter that this approach enabled semiautomatic determination of the full catalytic cycle of the HCo(CO)₃-catalyzed hydroformylation. The search was fully systematic; no initial guess was required concerning the entire reaction mechanism as well as each transition-state structure. This approach opens the door to nonempirical prediction of complex reaction mechanisms involving multiple steps in multiple pathways, such as full cycles of catalytic reactions