PMC

Definition and demonstration of the concept of intrinsic barrier width. Marcus-type analysis of the barrier widths. Left-hand-side reactions (i), (iii), and (v) have the same intrinsic barrier width, whereas right-hand-side reactions (ii), (iv), and (vi) all have a different common intrinsic barrier width. (a) The two reactions have the same intrinsic barrier height but different intrinsic barrier widths. (b) The barrier widths of the two reactions respond to the same thermodynamic driving force change at different sensitivities. (c) Because of a large thermodynamic bias, reaction (vi) has a greater intrinsic barrier width but a smaller actual barrier width than reaction (v).

Considerations of potential energy hypersurfaces. Pictorial presentation of the formulation of a unified reactivity paradigm that dissects and combines, compares, and contrasts over-the-barrier thermal reactions and intrinsic and thermodynamic contributions to the overall reactivity. The intrinsic barrier height reflects the reorganization energy, whereas the intrinsic barrier width reflects the reorganization distance. As the barrier width is most significantly (though not exclusively) represented by QMT, we take the barrier width as the reorganization distance over which the wave functions of the reactant state extend into the classically forbidden region under the barrier.

Importance of the intrinsic barrier: (a) Given equal thermodynamic driving force, a higher intrinsic barrier slows both the forward reaction, heterolysis, and its microscopically reverse reaction, nucleophilic addition. (b) The principle of kinetic versus thermodynamic control is a general phenomenological consequence of Marcus dissection: due to its lower intrinsic barrier, the actual barrier of the kinetic path is lower despite its thermodynamic disadvantage.

A: The intrinsic barrier height versus . B: The intrinsic barrier height versus the population barrier height in for and . C: The escape time from the valley versus the intrinsic barrier height . D: The dissipation rate versus the decreasing parameter .

Left: Rate-driving force relationships in thermal and QMT reactions, with different slopes and intercepts, i.e., various intrinsic and thermodynamic contributions to the barrier height and the barrier width. The slopes and intercepts are arbitrarily assigned. Right: Multidimensional reaction energy contour.

The barrier heights of intrinsic potential landscape versus (A), (B), (C). The free energy versus (D), (E), (F).

Computational predictions. (a) BEP correlations for three series of different ortho-substituents manifesting three different intrinsic barrier widths. All computations were performed at MP2/cc-pVDZ. The vertical axis, the “barrier width”, shows the mass-weighted Cartesian coordinates in units of amu^1/2 Bohr along the path for R = H, X = CN, Cl, F, CH₂F, H, Me; for R = Me, X = NO₂, CN, AcNMe, Cl, F, CCH, H, Me; and for R = iPr, X = CN, NO₂, CF₃, Cl, F, H, Me, all in ascending order of the Gibbs energy change of isomerization (i.e., these are ordered as above left to right). (b) Qualitative IRCs of two reactions signifying different intrinsic barrier widths: with the same thermodynamic driving force, different barrier widths are the result of the different intrinsic barrier widths.

The barrier heights of intrinsic potential landscape versus (A), (B), (C). The free energy versus (D), (E), (F).

The barrier heights of intrinsic potential landscape versus parameters (A), (B), (C). The free energy versus (D), (E), (F).

1A - Free-energy profile for a reaction where the work term ω_r is zero, the observed barrier for the thermoneutral reaction is equal to the intrinsic reaction barrier, and a minimum shift in the position of the reaction transition state with changing reaction driving force is observed. 1B - Free-energy profile for a reaction where there is a large work term ω_r, the observed barrier for the thermoneutral reaction is much larger than the intrinsic reaction barrier, and a substantial shift in the position of the reaction transition state with changing reaction driving force is observed.

Illustration of a Hammond effect and its relationship to the intrinsic barrier. (A) For steep, narrow wells, the intrinsic barrier is high, and a perturbation does not have a large effect on the position of the transition state (narrow lines). (B) For broad, shallow wells, the intrinsic barrier is low, and the magnitude of the Hammond effect is large.

In atopic dermatitis, immune dysregulation, barrier dysfunction, hormonal fluctuations, and alterations in the skin microbiome are key intrinsic factors that can be influenced by both genomic, epigenomic, and environmental factors.

Intrinsic barriers to infection and transmission of arboviruses in mosquitoes. The midgut infection barrier (MIB), midgut escape barrier (MEB), dissemination barrier (DB), salivary gland infection barrier (SGIB), salivary gland escape barrier (SGEB), and transovarial transmission barrier (TOTB) are potentially interfering with infection, dissemination, and transmission of viruses after the ingestion of an infectious blood meal by a mosquito. Only virus release in the saliva and transmission by bite of a vertebrate host confirm the completion of the extrinsic incubation period (EIP) and vector competence of a mosquito (Adapted from Mellor et al. ; Hardy et al. )

Percentages of thermal contribution and intrinsic barrier in the activation barrier at the B3LYP level.

Definition of the Marcus intrinsic barrier.

The gut functions as a chemical and physical barrier to the environment and serves as an integration site to respond to diverse intrinsic as well as extrinsic stimuli. These stimuli display a wide range of metabolites, age‐related changes, microbiota as well as inflammation‐associated processes. The resulting functional consequences include adaption in stem cell and proliferation, immune responses, reinforcement of the barrier function, cellular senescence as well as stem cell exhaustion. Functional consequences constantly affect the epithelial homeostasis and subsequently the barrier function of the intestine, eventually leading to epithelial barrier defects.

Transcription proteins, including TTF-1, HNF, and GATA family members, mediate lung morphogenesis, epithelial cell differentiation, and gene expression, creating the diverse cells of the epithelial barrier and regulating intrinsic and innate host defense responses.

A Switching rate versus energy barrier for the stochastic system with intrinsic multiplicative noise. The lines represent the values obtained through theoretical MFPT calculations, Eq (16), and the circles represent the values obtained through simulation (Gillespie and Langevin are identical). In both panels, the energy barriers were calculated from Eq (3). Blue colour corresponds to switching from ON to OFF and green color corresponds to OFF to ON switching. B Switching rate versus energy barrier for the additive noise case. Notice how the rates for both states keep the same relation with the energy barriers. Colour code is as in previous panel. Symbols correspond to theoretical MFPT calculations. Simulations are in perfect agreement, but are not represented for clarity. In both panels, the nondimensional cell volume is .