Three Major Electronic States of Dioxygen (O2); Relevance to Differences in the Reactivities of Iron(IV)-Hemes

These diagrams show the three major electronic states of dioxygen (O2) [note: I can't change pictures, in the blogger software, after I upload them, without dismantling the whole posting, basically, but the final diagram should show either no single-electron-transfer arrow or a two-electron-transfer arrow on zwitterion II (showing transfer to zwitterion I), not a single-electron-transfer arrow]. I'll put up sketches of the molecular orbitals soon, here, but one of the main points of this article [see Yamaguchi et al., 2009: (http://linkinghub.elsevier.com/retrieve/pii/S0277538709000515)] and of many other articles is that triplet dioxygen exists in a robustly-diradical state, with regard to the 2pi*x and 2pi*y antibonding molecular orbitals that are singly-occupied by electrons of the same spin, and that, in all of the three major electronic states of dioxygen, the 2pz(sigma) (a.k.a. 2sigma(2pz) a.k.a. 3sigma(gerade)) bonding molecular orbital exhibits a less-robust, 2pz-2pz diradical character with "singlet coupling" between the two "partially unpaired" electrons [the 2pz atomic orbitals are oriented along the z-axis, which is the internuclear axis that intersects both oxygen nuclei, and form a "partial" 2sigma(2pz) (a.k.a. 3sigma(gerade)) sigma bond]. That's shown in one of the diagrams below. Also, the highest-energy singlet excited state (singlet sigma) exists as a pair of zwitterionic "resonance" forms (still within the same electronic state), and the first excited state (singlet delta) exists as four resonance forms (two zwitterions and two (2pi*x and 2pi*y) diradicals in which there is "sigma coupling" between the two orbitals that are singly-occupied by electrons of opposite spin). The other articles cited are these [Lyne et al., 1993: (http://pubs.acs.org/doi/abs/10.1021/ic00074a022); Bytautas and Ruedenberg, 2010: (http://link.aip.org/link/?JCPSA6/132/074109/1)]. The other point is that the FeO moieties of some of the electronic states of perferryl and ferryl heme (and other oxidation states of heme) exist as "singlet delta"-like diradicals or zwitterions, "singlet sigma"-like zwitterions alone, or triplet-O2-like diradicals [Yamaguchi et al., 2009; Filatov et al., 1999: (http://www.rsc.org/delivery/_ArticleLinking/DisplayArticleForFree.cfm?doi=a809385g&JournalCode=P2)(http://cat.inist.fr/?aModele=afficheN&cpsidt=10072829)].

Some of the Molecular Orbitals and Electronic States of Heme Species

I'm going to paste these diagrams for some of the major molecular orbitals of heme species and then for four "major" electronic states of perferryl heme species (in this case, the states are of compound I or another, very similar perferryl heme species that contains a proximal cysteinate ligand). In the doublet and quartet states that contain a sulfur ligand radical, there is still a pi-type bonding interaction (constructive overlap or "mixing") between a pi type lone-pair molecular orbital of cysteine. Iit's not clear to me if the 3pz or 3px nonbonding ("lone-pair") molecular orbital of the free, non-heme-bound cysteine residue forms a sigma-sigma type charge-transfer complex with the sigma*(z^2) antibonding molecular orbital of free heme, prior to its overlap with the a2u molecular orbital of heme, but the point is that some of the spin density of even the sulfur/thiolate ligand radical is in the porphyrin a2u molecular orbital (and not the a1u molecular orbital). It's not entirely clear to me what the nature of the "single" bond between the sulfur and the iron atoms is, but I've gotten a much more clear picture of the specific orbital occupations in the FeO (ferryl) moiety in different electronic states. I don't have time, at the moment, to put up diagrams that show the similarities between the different electronic states of the Fe=O moiety and the three major electronic states of dioxygen (O=O), but a lot of the articles have made the comparisons between various electronic states of ferryl and perferryl heme and the ground-state triplet, first excited singlet state ("delta singlet"), or second excited singlet state (sigma singlet) of dioxygen. In those different electronics states of dioxygen [the electronic state is more specific than the electronic configuration and specifies the relative energy levels of the molecular orbitals and the "spins" (the m(subscript)s quantum number) of the electrons in the various singly- and doubly-occupied molecular orbitals; within a given electronic configuration, any number of electronic states may exist (up to 25 or more, in some cases)] or of the Fe=O moiety, the key difference is that there is either a robust diradical (as in the states of heme species that are similar to ground-state triplet dioxygen, in which the spins of the electrons in the singly-occupied pi*(xz) and pi*(yz) molecular orbitals of O2 are both +1/2--this is the situation shown below, although other electronic states of heme species are more similar to triplet dioxygen, in terms of their orbital symmetries, than the electronic states shown below) or, I think, more of a partial diradical [in a manner analogous to the two major excited, singlet states of dioxygen, in which there is either a doubly-occupied pi*(xz) or pi*(yz) molecular orbital (singlet delta) or two singly-occupied pi*(xz) and pi*(yz) molecular orbitals containing electrons of opposite "spin" (sigma singlet)] character to the singly-occupied pi*(xz) and pi*(yz) antibonding molecular orbitals, such that the spin density is primarily localized to the Fe and the O, individually, and not shared to a significant extent. The triplet, singlet, and quartet terms in the diagrams are the spin multiplicities of the individual spin centers. The spin multiplicity is this: (the absolute value of 2S) + 1. S is the total spin for a given spin center and is this: [(# of alpha electrons ("positive spin")) x (+1/2)] + [(# of beta electrons ("negative spin")) x (-1/2)]. So S is (+1/2)(2) = 1 for the FeO moiety shown below, and 2(1)+1 = the spin multiplicity = 3 = triplet, for the FeO moiety. The FeO, porphyrin, and thiolate [as well as the iron atom itself, which can exist in more than one spin state (or, as it is sometimes referred to as being, configuration, such as d(superscript)5, d4, or d6 (or 5D or 5S or whatever the other terminology is--I'll put up diagrams on those aspects), within a given oxidation state, such as Fe(IV) or Fe(III), etc.] moieties are treated as being separate spin centers that may or may not participate in various types of "spin coupling" interactions with another spin center. Usually, the total spin for two "spin centers" can be "calculated" by just doing the calculation on the alpha and beta electrons, in the same manner as described above. In some cases, however, such as when the a1u and a2u orbitals are each singly-occupied by electrons of opposite spin, the singly-occupied porphyrin orbitals undergo "configuration interaction" and form a new orbital, basically or literally, that, effectively, contains two paired electrons that don't affect the total spin, when the new orbital(s) (I'm fairly certain that it can be a single orbital or pair of orbitals in A1g symmetry in the D4h point-group symmetry of the isolated, nonsubstituted, planar porphyrin moiety) are formed, of the would-be coupling between the porphyrin and FeO moieties. For example, in that situation, the overall singlet state [two singly-occupied molecular orbitals containing electrons of opposite spin (or referred to as alpha or beta orbitals, etc.)] of the a2u and a1u orbitals, taken together, does not figure in to the "calculation" of the total spin for the particular electronic state (it's still an overall triplet state, with the triplet designation being dictated entirely by the spins of the diradical electrons in the pi* xz and yz antibonding molecular orbitals of the FeO moiety (as shown below). I think it's either that it's like a new orbital an "A1g orbital" in a singlet state (a porphyrin molecular orbital of A1g symmetry in the D4h point group, which is different from "A1g state symmetry," referring to two doubly-occupied molecular orbitals, as shown in the diagrams below) or its symmetry is such that an interaction with the FeO moiety is symmetry-forbidden or spin-forbidden or something. I don't understand how to assign point-group symmetries to specific molecules, yet, but I can sort of work backwards and assign axes and planes of symmetry. The business of assigning molecules to point groups of symmetry and assigning orbital symmetry designations is very complex, and I need a lot more practice on that. Anyway, I don't have time to put up anything else right now.

Evidence for the Formation of a Two-Electron Oxidation Product of Deferoxamine That's Likely to be an Oxoammonium Cation

These authors [Sabourault et al., 1989: (http://www.ncbi.nlm.nih.gov/pubmed/2574220)] found evidence that a species can be formed through the two-electron oxidation of deferoxamine (two successive one-electron oxidations of deferoxamine, with the one-electron oxidation product, formed through the one-electron oxidation of deferoxamine by any of a number of different oxidants, being the deferoxamine nitroxide species (see below). In my view, this is the oxoammonium cation (a.k.a. nitrosonium) species of deferoxamine, and, although it's a short-lived species, in comparison to the nitroxide species that can be stable for 10-20 minutes or so, this species (the authors refer to it as R, in comparison to RH(rad) and RH2 for deferoxamine nitroxide and deferoxamine) can undergo a one-electron reduction by ferrous heme ("cyt c-Fe2+") to deferoxamine nitroxide and ferric heme. In addition, the authors found evidence that deferoxamine nitroxide can undergo a one-electron oxidation by ferric heme to form this species, R, and ferrous heme as products. I don't see what else it could be except the oxoammonium species. The authors also found evidence that two molecules of deferoxamine nitroxide can participate in a reaction that forms one molecule of R and one molecule of deferoxamine as products. So it basically has to be the oxoammonium cation species, in my view, and I've shown quick sketches of the reactions that the authors listed, in shorthand, in the article. Anyway, it's interesting to see it.

One-electron oxidation of deferoxamine to deferoxamine nitroxide by a hydroperoxyl radical (protonated form of the superoxide radical anion):

One-electron oxidation of deferoxamine nitroxide, by a hydroperoxyl radical, to the oxoammonium cation species and hydrogen peroxide (HOOH):



One-electron reduction of the oxoammonium cation species, by superoxide, to deferoxamine nitroxide and the one-electron oxidation product of superoxide--molecular oxygen. This, along with the other reactions, is essentially the same mechanism whereby cyclic nitroxide radicals can, via an oxoammonium intermediate, mediate their superoxide-dismutase-mimetic activity [Samuni et al., 2002: (http://pet.radiology.uiowa.edu/downloads/Xiang%20Wu%20Papers/Application/2002/NCI/Kinetics%20and%20mechanism%20%2321B.pdf)]:



Reaction of two molecules of deferoxamine nitroxide to form deferoxamine and the oxoammonium species. Other researchers have, incidentally, found experimental results that his reaction


One-electron reduction, by ferrous heme, of the oxoammonium cation species to the nitroxide and ferric heme:



One-electron oxidation of the nitroxide to the oxoammonium species by ferric heme, forming ferrous heme, also, as a product:

Magnesium Gluconate "Stuff" and Kinetics of Gluconic Acid and 1,5-Gluconolactone Interconversions; Silica Delights

In my view, the use of magnesium gluconate (a.k.a. magnesium di-D-gluconate) would be advantageous, in comparison to the uses of magnesium salts of tricarboxylic acid cycle intermediates or magnesium aspartate or various other magnesium salts, for a number of reasons. A significant issue with the use of organic magnesium salts is that the counterion, such as aspartate or glycine or citrate or gluconate, etc., to magnesium needs to be both tolerable and "safe" when a person ingests the counterion in relatively large amounts. In each of the organic salts of magnesium, the percentage of magnesium is quite low. Anhydrous magnesium di-D-gluconate is about 5.9 percent magnesium, and the percents of magnesium in other organic salts are in the range of 10-20 percent or so. A tablet that supplies 30 mg of magnesium from anhydrous magnesium gluconate supplies 481 mg of gluconate, and this shows that the intake of magnesium from magnesium gluconate, in doses that are at all significant, will provide significant amounts of gluconate. I'm not impressed with the effects of magnesium salts of tricarboxylic acid (TCA) cycle intermediates, such as citrate or fumarate or alpha-ketoglutarate, given that the TCA cycle intermediates tend to produce intestinal osmoregulatory disturbances and can cause nausea or diarrhea in relatively low dosages, for whatever reason. I've seen researchers sort of explain this in terms of the fact that TCA cycle intermediates are trianions at physiological pH and are likely to also be partially ionized at gastric pH, and weak acids that are water-soluble would be expected to be very poorly absorbed through the gastric mucosal cells (compounds are absorbed through the stomach) [Milne et al., 1965: (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1898658/); (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1898658/pdf/procrsmed00189-0022.pdf)]. Another aspect might be differences in the lipophilicity of the protonated species of, for example, citrate and gluconate. The log P (octanol/water) coefficient for gluconic acid is -1.97 (http://www.chem.unep.ch/irptc/sids/OECDSIDS/gluconates.pdf), and I'll bet the log P values of the monoanion species (dihydrogen citrate is, I guess, the term for the species) of citrate would be even lower, at various ionic strengths, etc. [Avdeef, 1993: (http://www.ncbi.nlm.nih.gov/pubmed/8445533)]. One can do the calculations oneself, but, loathe as I am to link to it, wikipedia provides a decent graph of the percentages of citrate species present across the acidic pH range, and one sees that the monoanion would be expected to exist in significant amounts at gastric pH (http://en.wikipedia.org/wiki/Acid_dissociation_constant). I found this article that I can't get the full text of but that probably includes log P data on citrate species [Avdeef, 1992: (http://www3.interscience.wiley.com/journal/118640091/abstract?CRETRY=1&SRETRY=0)]. Citrate also disturbs systemic acid-base balance, in the sense that exogenous citrate can produce an elevation in serum bicarbonate, but gluconate does not elevate serum bicarbonate. I don't have time to put up the rest of the references now, but I will soon. An important point is that gluconate does not undergo lactonization [Shimahara et al., 1970: (http://www.ncbi.nlm.nih.gov/pubmed/5437655)], and negligible amounts of the 1,4-lactone are formed at or above pH 2.5. That's the basis for the calculation of the rate equation and concentration-vs.-time curves, as shown below. I used this physical chemistry textbook as a guide [Tinoco et al., 1995: (http://books.google.com/books?id=I34mAAAACAAJ&dq=tinoco+physical+chemistry+1995+%22principles+and+applications%22)], but the authors didn't do any of the derivations. The derivation I did shows the general rate equation for a single-step, reversible, first-order, spontaneous reaction, and the final, concentration-vs.-time equations are also general results. That textbook is actually really good, incidentally. This is a terrific article that just provides this trick of substitution that allows one to integrate various second-order rate equations and find concentration-vs.-time curves, assuming one has the kinetic constants and the equilibrium constant for the reaction [Lavabre, 1993: (http://pubs.acs.org/doi/abs/10.1021/j100122a024)]. It's just a factoring trick and tricks of substitution. I, incidentally, found that it's advisable to distinguish between the terms "[reactant or product]eq" and [r or p]. I mean that one can write something like this, for the reaction A <---> B, and end up making silly errors, subsequently: "At equilibrium, k1[A] = k-1[B], and [B]/[A] = K1 = k1/k-1." One can end up making an invalid substitution, based on something like that, by looking and thinking that [B] = (k1/k-1)[A], when this is not the case. In actuality, [B]eq = (k1/k-1)[A]eq. I didn't look at all of the cases presented by Lavabre et al. (1993), but it looks like they basically used something similar or identical to the x and x(sub)e substitutions that are commonly used. I think the R and R(sub)e terms presented by Lavabre et al. (1993) are the same quantities, along with more complexity for 2nd-order equations, that the terms x and x(sub)e encompass. They're similar, in any case. I did part of the calculation for the case of A + B <---> C, to estimate the actual kinetics of the Mg2+ + G- <---> (MgG)+ equilibrium, and the general equation is very complex but wouldn't seem complex if one substituted some of the experimental constants in at a relatively early stage in the calculation, etc. Anyway, it's useful to be able to use these.

I don't have time to post any more of this right now, but other issues to consider are the amounts of calcium or silica (or even stearic acid, as opposed to magnesium stearate) in magnesium gluconate supplements. The amounts of calcium that supplemental magnesium gluconate could provide, in the form of the dicalcium phosphate or tricalcium phosphate or calcium silicate used as excipients in the tablets, have the potential to be very large and to "ruin" the beneficial effects of magnesium supplementation. I've seen tablets, whose manufacturers actually choose to list the amounts of elemental calcium in a tablet, that are smaller than a US dime ("US currency") and that supply 85 mg of calcium from the excipient. That ends up supplying a lot of calcium, if one uses reasonable dosages of magnesium. Those forms of calcium are also going to be absorbed to just as great an extent as highly-soluble forms of calcium, despite the fact that they're "insoluble" or "sparingly-soluble" in water and aren't supposed to be absorbed, as shown in this article [Heaney et al., 1990: (http://www.ncbi.nlm.nih.gov/pubmed/2110852)]. I only found about three brands that contain no calcium as an excipient, and all but one also contain silica.

Incidentally, there's a large amount of research suggesting that colloidal silica can be absorbed, even in polymeric form (Sripanyakorn et al., 2009, cited below), that it's an indestructable antigen that can undergo phagocytosis by intestinal antigen-presenting cells (Powell et al., 1996, cited below), that it shows up in the Peyer's patch lymphoid tissue, that epithelial-cell-based granulomas in the GI tract contain silica and are associated with the development of ulcerative colitis or Crohn's disease [Powell et al., 1996: (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1383324/)], that absorbed silica can "concentrate" in the kidneys, etc. Sounds fantastic. In any case, if one wants to remove a meaningful percentage of the colloidal silica from suspension in water, the idea is that one would want a sub-micron pore-size mechanical filter that doesn't adsorb metals (as in magnesium). This means that one would not want activated carbon as a component of the filter mechanism, and there are a couple of cheap camping filters that satisfy those requirements and have pore sizes of 0.01 microns (10 nm) or 0.02 microns (20 nm) and that would be expected to filter much of the suspended, solid colloidal silica particles, although some of the particles can be as small as 5 nm. But the pore size isn't the only variable that determines the capacity of a filter medium to retain the suspended solid. And the silica particles tend to aggregate into larger "superstructures." Traditionally, ultrafiltration membranes have been thought to be required to remove colloidal silica from suspension, but the electrostatic forces that begin to occur in filter media with extremely small pore sizes could begin to produce adsorption of metals in solution (i.e. magnesium). Anyway, I really can't say if those camping filters would work, but I just put this information up for all the freaks like me who don't like the idea of ingesting quartz and feldspar and whatnot and who appreciate scientific and systematic approaches to solving problems. I'll put up references for this stuff, but some statements in the literature imply, in my opinion, that some of the silica used in supplements may, apparently, exist as particulate silica in network-covalent form (as in "rock" dust or extremely-finely-grained, particulate quartz). Apparently, some "polymeric" silica may "actually" be "particulate" silica (Sripanyakorn et al., 2009, cited below) and may, as implied here [Rowsell et al., 1958: (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1196625/)(http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1196625/pdf/biochemj00829-0067.pdf)], exist as suspended particles, in a solid phase, of network-covalent quartz or feldspar or another form. Here's a quote from an article showing the absorption of several different forms of silica: "what is referred to by the manufacturers as ‘colloidal silica’ is really particulate silica" [Sripanyakorn et al., 2009: (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2744664/)(http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2744664/pdf/ukmss-27619.pdf)] So some particulate "silicates" are soluble and may exist, at least partially, as quartz or feldspar [Rowsell et al., 1958: (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1196625/)(http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1196625/pdf/biochemj00829-0067.pdf)]? But particulate silica wouldn't even have to be soluble to be absorbed, given that small percentages (how small and how variable?) of colloidal silica, which consists of solid silica particles suspended in water, such that the particles are of, apparently, indeterminate size, can be absorbed from the GI tract into the lymphatic fluid and reach the systemic circulation [Sripanyakorn et al., 2009; references cited here: (http://hardcorephysiologyfun.blogspot.com/2009/11/quartz-silica-goodies.html)]. It's not clear to me that anyone can know what the hell silica in supplements actually is, and it's all just this big mess of nonsense, basically, with the experimental findings staring people in the face, in my opinion, in "technicolor horror." I'm joking with that, but I don't like this kind of haphazard "attention," or lack thereof, to detail in manufacturing. Yeah, here are several more reports of silica-containing kidney stones in humans, in addition to the recent one I linked to [Flythe et al., 2009: (http://linkinghub.elsevier.com/retrieve/pii/S0272638608016132), cited here: (http://hardcorephysiologyfun.blogspot.com/2009/11/quartz-silica-goodies.html)] [see related articles on pubmed, related to this article: Alpaugh et al., 1984: (http://www.ncbi.nlm.nih.gov/pubmed/6091262)]. So there was quartz (network-covalent SiO2) in their silica-containing kidney stones, and the crystal structure of the quartz was consistent with the crystal structure of glacial sand (Alpaugh et al., 1984). Polymeric and monomeric silica cannot be converted into a network-covalent structure in the absence of tremendous heat and pressure, as in the forces that occur in "geology," over "geological time." So the people had been ingesting network-covalent silica, meaning quartz or other rock dust. Had the people who developed quartz-containing kidney stones been eating rocks or sand? I seriously doubt it. It seems to me that the silica might have come from supplements or foods, but that's just my opinion. There are lots and lots of reports of silica-containing kidney stones (http://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed&cmd=link&linkname=pubmed_pubmed&uid=6091262). This article shows that some silica can be present in gallstones [Yamamoto et al., 1985: (http://www.ncbi.nlm.nih.gov/pubmed/3920818)], implying that silica can reach the liver, and these authors [Marinaccio et al., 2006: (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2077997/)(http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2077997/pdf/762.pdf)] found evidence of an increase in the incidence of liver cancer among people who had had silicosis in their lungs due to the inhalation of silica dust. Particulate silica is toxic to the Kupffer cells that constitute the major population of monocyte-macrophage-lineage cells of the liver [Kolb-Bachofen, 1992: (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC443241/)(http://www.ncbi.nlm.nih.gov/pmc/articles/PMC443241/pdf/jcinvest00053-0193.pdf)]. Anyway, these articles aren't great to see, but no one knows if silica actually contributes to any diseases. I'm not suggesting that I know if the ingestion of quartz particles does or does not produce meaningfully-harmful effects in any given disease state, but it doesn't sound great to me.

I wanted to find out if significant amounts of 1,5-gluconolactone (abbreviated GL), which can be formed from gluconic acid (but not the gluconate anion) spontaneously or in an acid-catalyzed reaction, could be formed in the gastric luminal fluid, following the ingestion and protonation of gluconate, from magnesium gluconate. GL is an inhibitor of glycogen phosphorylase, and the inhibition of glycogen phosphorylase would be undesirable. Significant amounts of GL are very unlikely to be formed in vivo, but I figured I'd use this problem as a way of practicing chemical kinetics problems. Only about 5 percent would be converted into GL within 30 minutes, and this is consistent with the data from the articles (it's precisely the percentage that Zhang et al. (2009) [Zhang et al., 2009: (http://www.ncbi.nlm.nih.gov/pubmed/19320439)] calculated for pH 4, although I did my "derivation" or "calculation" on data collected at pH 2.5). I'm going to paste the pictures and put up the citations later.

<--->

<--->

Conversion of 1,5-gluconolactone into 1,4-gluconolactone: