According to the bridged annulene model, macrocyclic aromaticity of a porphyrinoid species can be attributed to the annulene-like main macrocyclic conjugation pathway (MMCP). Macrocyclic aromaticity, however, is given theoretically as a sum of contributions from all macrocyclic circuits. We found that the aromaticity due to each macrocyclic circuit is determined formally but broadly by Hückel's [4n + 2] rule of aromaticity. Nitrogen atoms in the pyrrolic rings effectively suppress the variation in the number of π electrons staying along each macrocyclic circuit. As a result, all or most macrocyclic circuits in oligopyrrolic macrocycles are made aromatic (or antiaromaitc) in phase with the MMCP. Thus, the MMCP is not a determinant of macrocyclic aromaticity but can be regarded as a good indicator of this quantity. This is why the bridged annulene model appears to hold for many porphyrins.

The sequential line plot of topological resonance energy (TRE) against the number of π electrons (N(π)) for any polycyclic aromatic hydrocarbon (PAH) is very similar with the same number of extrema to that for benzene. Thus, global aromaticity of a PAH molecular ion strongly reflects that of a benzene molecular ion. Likewise, the N(π) dependence of TRE for any polycyclic π system formed by fusion of two or more rings of the same size reflects that for a monocyclic species of the same ring size. In general, TREs for such polycyclic π systems and their molecular ions can be interpreted consistently by reference to those for neutral and charged monocyclic species of the same ring size.

The global and macrocyclic aromaticity of porphyrinoids was characterized using our graph theory of aromaticity. The sequential line plots of topological resonance energy (TRE) against the number of π-electrons (N(π)) for different porphyrinoids are similar with four major extrema to those for five-membered heterocycles. This supports the view that five-membered rings are the main origin of global aromaticity in porphyrinoids. Macrocyclic circuits contribute significantly to macrocyclic π-circulation but modestly to global aromaticity. Macrocyclic aromaticity/antiaromaticity in oligopyrrolic macrocycles can be predicted by formally applying Hückel's [4n + 2] rule to an annulene-like main macrocyclic conjugation pathway (MMCP). This bridged annulene model can be justified by examining the contribution of individual macrocyclic circuits to macrocyclic aromaticity. A Hückel-like rule of macrocyclic aromaticity was found for porphyrinoid species.

The Kekulé structure count (K) for some types of polycyclic aromatic hydrocarbons (PAHs), such as fluoranthene and perylene, can be factorized into the product of those for two or more aromatic subunits. The ring-current map for these PAHs placed in a perpendicular magnetic field exhibits a substantial localization on aromatic subunits. We found that such localization of π circulation is a characteristic of fairly small K-factorizable species in the neutral electronic state. Even in such a case, no single π molecular orbital (πMO) is associated with localized π circulation. Apparent localization of π circulation is caused by the superposition of currents induced by all occupied πMOs. π circulation is less localized in larger K-factorizable species.

Preclinical studies have revealed that the elevation of nicotinamide adenine dinucleotide (NAD + ) upon the administration of nicotinamide mononucleotide (NMN), an NAD + precursor, can mitigate aging-related disorders; however, human data on this are limited. We investigated whether the chronic oral supplementation of NMN can elevate blood NAD + levels and alter physiological dysfunctions in healthy older participants. We administered 250 mg NMN per day to aged men for 6 or 12 weeks in a placebo-controlled, randomized, double-blind, parallel-group trial. Chronic NMN supplementation was well tolerated and caused no significant deleterious effect. Metabolomic analysis of whole blood samples demonstrated that oral NMN supplementation significantly increased the NAD + and NAD + metabolite concentrations. There were nominally significant improvements in gait speed and performance in the left grip test, which should be validated in larger studies; however, NMN exerted no significant effect on body composition. Therefore, chronic oral NMN supplementation can be an efficient NAD + booster for preventing aging-related muscle dysfunctions in humans.