A New Theory about Interfacial Proton Diffusion Revisited: The Commonly Accepted Laws of Electrostatics and Diffusion Prevail

The high propensity of protons to stay at interfaces has attracted much attention over the decades. It enables long-range interfacial proton diffusion without relying on titratable residues or electrostatic attraction. As a result, various phenomena manifest themselves, ranging from spillover in material sciences to local proton circuits between proton pumps and ATP synthases in bioenergetics. In an attempt to replace all existing theoretical and experimental insight into the origin of protons' preference for interfaces, TELP, the "Transmembrane Electrostatically-Localized Protons" hypothesis, has been proposed. The TELP hypothesis envisions static H+ and OH- layers on opposite sides of interfaces that are up to 75 µm thick. Yet, the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy is more than two orders of magnitude smaller and, as a result, the H+ and OH- layers cannot mutually stabilize each other, rendering proton accumulation at the interface energetically unfavorable. We show that (i) the law of electroneutrality, (ii) Fick's law of diffusion, and (iii) Coulomb's law prevail. Using them does not hinder but helps to interpret previously published experimental results, and also helps us understand the high entropy release barrier enabling long-range proton diffusion along the membrane surface.

Lee's transient protonic capacitor cannot explain the surface proton current observed in bacteriorhodopsin purple membranes

Recently in this Journal, James Lee employed his transmembrane electrostatically localized proton (TELP) hypothesis and the notion of a transient protonic capacitor to explain the force holding protons at the surface of bacteriorhodopsin purple membrane fragments. Here we show that purple membrane fragments cannot maintain the requisite transient non-zero transmembrane potential, and even if they could, it would not support the surface proton current moving from the P side to the N side that was reported by Heberle et al. (Nature, 1994). Currently accepted models explain the force keeping protons at the membrane surface by invoking the unusual structure of water at the interface which serves to stabilize the proton (energy well) and/or raise the activation ∆G‡ (energy barrier) for release to the bulk phase. Any future invocations of TELP should be required to include experimental measurements carried out at the surfaces of lipid bilayer membranes and/or biological membranes.

The real reason why ATP hydrolysis is spontaneous at pH > 7: It's (mostly) the proton concentration!

Common wisdom holds that ATP hydrolysis is spontaneous because of the weakness of its phosphoanhydride bonds, electrostatic repulsion within the polyanionic ATP4- molecule, and resonance stabilization of the inorganic phosphate and ADP products. By examining the pH-dependence of the hydrolysis Gibbs free energy, we show that in fact, above pH 7, ATP hydrolysis is spontaneous due mainly to the low concentration of the H+ that is released as product. Hence, ATP is essentially just an electrophilic target whose attack by H2 O causes the acidity of the water nucleophile to increase dramatically; the spontaneity of the resulting acid ionization supplies much of the released Gibbs free energy. We also find that fermentation lowers pH not due to its organic acid products (e.g., lactic, acetic, formic, or succinic acids), but again, due to the H+ product of ATP hydrolysis.

Lee's "Transmembrane Electrostatically-Localized Proton" model does NOT offer a better understanding of neuronal transmembrane potentials

Recently, in a paper entitled "Protonic conductor: Better understanding [sic] neural resting and action potential," Lee applied his Transmembrane Electrostatically-Localized Protons (TELP) hypothesis to neuronal signaling. He stated that Hodgkin's cable theory "could not fully explain the different conductive patterns in unmyelinated and myelinated nerves," whereas his TELP hypothesis "enables much better understanding of neural resting/action potential and [the biological significance of] axon myelination..." However, Lee's TELP hypothesis predicts that under resting conditions, the neuron "accumulat[es] excess negative charge (anions) inside," whereas resting chloride gradients actually feature excess Cl^- outside of the cell. Experiments on the neuron have shown that raising external [K⁺] and decreasing external [Cl^-] cause membrane potential depolarization, which is predicted by the Goldman equation, but opposite to TELP hypothesis predictions. Finally, based on his TELP hypothesis, Lee predicted that the main purpose of myelin is to insulate the axonal plasma membrane specifically against proton permeability. However, he cited literature showing that myelin contains proteins that may "serve as a proton conductor with the localized protons." Thus, we show here that Lee's TELP hypothesis is highly problematic, and does NOT offer a "better understanding" of neuronal transmembrane potentials.

Correction to "H2O(aq) Does Not Exist: Critique of a Proof-of-Concept Derivation"

[This corrects the article DOI: 10.1021/acs.jchemed.3c00099.].

A critique of the capacitor-based "Transmembrane Electrostatically Localized Proton" hypothesis

In his Transmembrane Electrostatically Localized Proton hypothesis (TELP), James W. Lee has modeled the bioenergetic membrane as a simple capacitor. According to this model, the surface concentration of protons is completely independent of proton concentration in the bulk phase, and is linearly proportional to the transmembrane potential. Such a proportionality runs counter to the results of experimental measurements, molecular dynamics simulations, and electrostatics calculations. We show that the TELP model dramatically overestimates the surface concentration of protons, and we discuss the electrostatic reasons why a simple capacitor is not an appropriate model for the bioenergetic membrane.

The Proton in Biochemistry: Impacts on Bioenergetics, Biophysical Chemistry, and Bioorganic Chemistry

The proton is the smallest atomic particle, and in aqueous solution it is the smallest hydrated ion, having only two waters in its first hydration shell. In this article we survey key aspects of the proton in chemistry and biochemistry, starting with the definitions of pH and pK _a and their application inside biological cells. This includes an exploration of pH in nanoscale spaces, distinguishing between bulk and interfacial phases. We survey the Eigen and Zundel models of the structure of the hydrated proton, and how these can be used to explain: a) the behavior of protons at the water-hydrophobic interface, and b) the extraordinarily high mobility of protons in bulk water via Grotthuss hopping, and inside proteins via proton wires. Lastly, we survey key aspects of the effect of proton concentration and proton transfer on biochemical reactions including ligand binding and enzyme catalysis, as well as pH effects on biochemical thermodynamics, including the Chemiosmotic Theory. We find, for example, that the spontaneity of ATP hydrolysis at pH ≥ 7 is not due to any inherent property of ATP (or ADP or phosphate), but rather to the low concentration of H⁺. Additionally, we show that acidification due to fermentation does not derive from the organic acid waste products, but rather from the proton produced by ATP hydrolysis.

How enzymes harness highly unfavorable proton transfer reactions

Acid-base reactions that are exceedingly unfavorable under standard conditions can be catalytically important at enzyme active sites. For example, in triose phosphate isomerase, a glutamate side chain (nominal pK_a ≈ 4 in solution) can in fact deprotonate a CH group that is vicinal to a carbonyl (pK_a ≈ 18 in solution). This is true because of three distinct interactions: (a) ground state pK_a shifts due to environment polarity and electrostatics; (b) dramatic increases in effective molarity due to optimization of proximity and orientation; and (c) transition state pK_a shifts due to binding interactions and the formation of strong low barrier hydrogen bonds. In this report, we review the literature showing that the sum of these three effects supplies more than enough free energy to push forward proton transfer reactions that under standard conditions are exceedingly nonspontaneous and slow.

CoViD-19 epidemic follows the "kinetics" of enzymes with cooperative substrate binding

The Hill equation, which models the cooperative ligand-receptor binding equilibrium, turns out to be useful in modeling the progression of infectious disease outbreaks such as CoViD-19. The equation fits well the data for total and daily case numbers, allows tentative predictions for the half-point and end point of the epidemic, and presents a mathematical characterization of how social interventions "flatten the curve" of the disease progression.

When both Km and Vmax are altered, Is the enzyme inhibited or activated?

Enzyme activators lower K_m (the Michaelis constant) and/or raise V_max (the asymptotic reaction velocity at infinite substrate concentration); conversely, inhibitors raise K_m and/or lower V_max . But what if an effector moves both K_m and V_max in the same direction? Uncompetitive inhibitors, which decrease both K_m and V_max by the same factor, are the most common example of this. A less well-known example occurs often when crowding agents are added to the buffer in order to mimic the environment commonly encountered in vivo. Crowding agents tested on different enzymes have been shown to have every conceivable effect on K_m or V_max , causing them to rise, fall, or stay the same. In this article, a mathematical analysis is presented allowing biochemists to judge whether an effector that causes K_m and V_max to both move in the same direction serves as an inhibitor, an activator, or most surprising, as both. © 2019 International Union of Biochemistry and Molecular Biology, 47(4):446-449, 2019.

Liposome permeability probed by laser light scattering

We have developed a laboratory project in which students prepare liposomes, expose them to hyperosmotic and hypoosmotic solutions, and follow the resulting shrinking and swelling (respectively) with laser light scattering. Each light intensity transient can be fit to an exponential decline or rise, with the decay constant (k) and the amplitude (ΔV_max ) being indirectly related to the kinetics and thermodynamics (respectively) of transmembrane osmotic flux. Students vary the experimental system by changing the types and concentrations of osmolytes such as alcohols, amides, and salts. Students then compare how these changes alter the rate and extent of osmotic flux. This upper division biochemistry laboratory project is a challenging and rewarding one that exposes students to a biomolecule (lipid) and a spectroscopic technique (laser spectroscopy) that are not commonly used in the undergraduate laboratory setting. © 2019 International Union of Biochemistry and Molecular Biology, 47(3):239-246, 2019.

Mercury(II) binds to both of chymotrypsin's histidines, causing inhibition followed by irreversible denaturation/aggregation

The toxicity of mercury is often attributed to its tight binding to cysteine thiolate anions in vital enzymes. To test our hypothesis that Hg(II) binding to histidine could be a significant factor in mercury's toxic effects, we studied the enzyme chymotrypsin, which lacks free cysteine thiols; we found that chymotrypsin is not only inhibited, but also denatured by Hg(II). We followed the aggregation of denatured enzyme by the increase in visible absorbance due to light scattering. Hg(II)-induced chymotrypsin precipitation increased dramatically above pH 6.5, and free imidazole inhibited this precipitation, implicating histidine-Hg(II) binding in the process of chymotrypsin denaturation/aggregation. Diethylpyrocarbonate (DEPC) blocked chymotrypsin's two histidines (his40 and his57 ) quickly and completely, with an IC50 of 35 ± 6 µM. DEPC at 350 µM reduced the hydrolytic activity of chymotrypsin by 90%, suggesting that low concentrations of DEPC react with his57 at the active site catalytic triad; furthermore, DEPC below 400 µM enhanced the Hg(II)-induced precipitation of chymotrypsin. We conclude that his57 reacts readily with DEPC, causing enzyme inhibition and enhancement of Hg(II)-induced aggregation. Above 500 µM, DEPC inhibited Hg(II)-induced precipitation, and [DEPC] >2.5 mM completely protected chymotrypsin against precipitation. This suggests that his40 reacts less readily with DEPC, and that chymotrypsin denaturation is caused by Hg(II) binding specifically to the his40 residue. Finally, we show that Hg(II)-histidine binding may trigger hemoglobin aggregation as well. Because of results with these two enzymes, we suggest that metal-histidine binding may be key to understanding all heavy metal-induced protein aggregation.

Myoglobin structure and function: A multiweek biochemistry laboratory project

We have developed a multiweek laboratory project in which students isolate myoglobin and characterize its structure, function, and redox state. The important laboratory techniques covered in this project include size-exclusion chromatography, electrophoresis, spectrophotometric titration, and FTIR spectroscopy. Regarding protein structure, students work with computer modeling and visualization of myoglobin and its homologues, after which they spectroscopically characterize its thermal denaturation. Students also study protein function (ligand binding equilibrium) and are instructed on topics in data analysis (calibration curves, nonlinear vs. linear regression). This upper division biochemistry laboratory project is a challenging and rewarding one that not only exposes students to a wide variety of important biochemical laboratory techniques but also ties those techniques together to work with a single readily available and easily characterized protein, myoglobin.

An exploration of how the thermodynamic efficiency of bioenergetic membrane systems varies with c-subunit stoichiometry of F₁F₀ ATP synthases

Recently the F0 portion of the bovine mitochondrial F1F0-ATP synthase was shown to contain eight 'c' subunits (n = 8). This surprised many in the field, as previously, the only other mitochondrial F0 (for yeast) was shown to have ten 'c' subunits. The metabolic implications of 'c' subunit copy number explored in this paper lead to several surprising conclusions: (1) Aerobically respiring E. coli (n = 10) and animal mitochondria (n = 8) both have very high F1F0 thermodynamic efficiencies of ≈90% under typical conditions, whereas efficiency is only ≈65% for chloroplasts (n = 14). Reasons for this difference, including the importance of transmembrane potential (∆Ψ) as a rotational catalyst, as opposed to an energy source, are discussed. (2) Maximum theoretical P/O ratios in animal mitochondria (n = 8) are calculated to be 2.73 ATP/NADH and 1.64 ATP/FADH2, yielding 34.5 ATP/glucose (assuming NADH import via the malate/aspartate shuttle). The experimentally measured values of 2.44 (±0.15), 1.47 (±0.13), and 31.3 (±1.5), respectively, are only about 10% lower, suggesting very little energy depletion via transmembrane proton leakage. (3) Finally, the thermodynamic efficiency of oxidative phosphorylation is not lower than that of substrate level phosphorylation, as previously believed. The overall thermodynamic efficiencies of oxidative phosphorylation, glycolysis, and the citric acid cycle are ≈80% in all three processes.