Transient Transmembrane-Electrostatically Localized Protons and Transmembrane Potential in a Laser Flashed Bacteriorhodopsin Purple Membrane Open Flat Sheet
James Weifu Lee*
Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, VA 23529 USA
*Correspondence: jwlee@odu.edu
ORCID: 0000-0003-2525-5870
Keywords: Bacteriorhodopsin purple membrane, liquid water as protonic conductor, transmembrane potential, transmembrane-electrostatically localized protons/cations, bioenergetics
Submitted: September 16, 2024
Revised: July 20, 2025
Accepted: August 26, 2025
Published: September 26, 2025
Abstract
The transmembrane-electrostatically localized protons/cations charges (TELCs, also known as TELPs) model may serve as a unified framework to explain a wide range of bioenergetic phenomena. Transient transmembrane-electrostatically localized protons (TELPs) and transmembrane potential in a laser flash-energized bacteriorhodopsin (bR) purple membrane (PM) open flat sheet are now better analyzed. Under the Heberle et al. (1994) experimental conditions, the number of bR molecules is now calculated to be 8200 per PM open flat sheet with a diameter of 600 nm. With a single-turnover laser flash intensity of 3 mJ/cm2 to photoexcite 10% of the bR molecules, the laser flash-induced peak TELCs density is calculated to be 2900 per µm2 of PM, which translates to a peak transient transmembrane potential of 50 mV. The bR protonic outlet protrudes into the liquid phase outside the putative “potential well/barrier”. The observation is in line with the TELPs model, but does not support the “potential well/barrier” model. The author encourages research on more relevant protonic capacitor cell systems that have transmembrane potential with TELCs comprising excess positive charges at one side and excess anions at the other side of the membrane.
Introduction
The recently developed “transmembrane-electrostatically localized proton(s)/cation(s) charge(s) (TELC(s)) model” [1] [2] [3] provides a theoretical framework that can help explicate protonic cell energetics, including many experimental observations, and elucidate bioenergetic systems, including both delocalized and localized protonic couplings [4] [5] [6]. The term TELCs represents the “total transmembrane-electrostatically localized positive charges,” including the “charges of both the transmembrane-electrostatically localized proton(s) (TELP(s)) and the associated transmembrane-electrostatically localized non-proton cations after the proton-cation exchanging process reaching equilibrium” [5] [6]. TELCs are immediately related to transmembrane potential, which is now known as a function of TELCs population density within a TELCs-membrane-anions capacitor [1] [6]. Consequently, the excess positive charges of TELCs at one side of the membrane are balanced by the excess negative charges of transmembrane-electrostatically localized hydroxide anions (TELAs) at the other side of the membrane. The “formation of TELPs-membrane-TELAs capacitors has been experimentally demonstrated using a biomimetic anode water-Teflon membrane-water cathode system” [7] [8] [9] through two PhD thesis research projects [10] [11].
According to the TELCs model [2] [1] [12] [13], transmembrane potential (∆ψ) is a function of TELCs surface density, as shown in the following protonic membrane capacitor-based equation with a voltage unit (V in volts):
(1)
where C/S is the specific membrane capacitance per unit surface area; TELC is the number of positive charges per unit membrane surface area, which is the sum of TELPs and transmembrane-electrostatically localized non-proton cations after cation exchange with TELPs; and e is a proton (or cation) charge of 1.60 x 10−19 Coulomb.
Accordingly [2] [1] [12] [13], when a transmembrane protonic pumping process—which is an electrogenic (i.e., electrically non-compensated) charge transport across a bacteriorhodopsin purple membrane open flat sheet—is energized by a single-turnover pulsed laser flash [14] [15], a transient transmembrane potential (Δψ) will form and then decay as the pumped excess charges return to the other sides of the membrane. That is, the formation of a transient transmembrane potential (Δψ) will result from a protonic capacitor formation with TELPs on the positive (extracellular) side and with transmembrane-electrostatically localized hydroxide anions on the negative (cytoplasmic) side along a bacteriorhodopsin purple membrane open flat sheet, at least, transiently. Therefore, during its protonic capacitor formation, according to Eq. 1, there is at least a transient transmembrane potential (Δψ ≠ 0), in contrast to Silverstein’s claim of no “transient non-zero Δψ”: “where Δψ = 0” [16] [17].
In this article, we will first calculate the bacteriorhodopsin (bR) population density in a bacteriorhodopsin purple membrane open flat sheet that was tested in the experiment of Heberle et al. (1994) [15]. Then, the transient TELCs population and transmembrane potential in a laser flashed bacteriorhodopsin purple membrane open flat sheet will be calculated. The analyzed results will be discussed with commentary in the context of Silverstein’s recent argument [17] and the putative “potential well/barrier” model proposed by Junge and Mulkidjanian [18, 19] and advocated by Silverstein [17].
Calculation of Transient TELCs and Transmembrane Potential in a Laser Flashed Bacteriorhodopsin Purple Membrane Open Flat Sheet
The experiment of Heberle et al. (1994) [15] employed a piece of well-characterized purple membrane (PM) of H. salinarium, which is “a two-dimensional crystalline array of the integral membrane protein bacteriorhodopsin with lipids” that is also called a bacteriorhodopsin purple membrane open flat sheet. The natural PM is composed of 75% bR (w/w) and 25% lipid (w/w) [20]. As shown in Figure 1, each bacteriorhodopsin (bR) molecule consists of approximately seven helical segments transversing the membrane [21]. Upon photo-energization, a bR molecule can vectorially pump a proton across the membrane protein complex and thus can transiently result in a charge-separated pair of bRH+ and bROH‒.
The naturally-forming crystal structure of PM is a trimer of bR molecules within one hexagonal unit cell (a = 6.2 nm), as shown in the AFM images (Figure 2) [24]. That is, the bR trimers (encircled with the triangles) are arranged in a hexagonal lattice with a unit cell dimension of ~6.2 nm [24]. Using this information, as shown in Table 1, we have now calculated the number of bR molecules to be 8200 bR molecules per PM open flat sheet with a diameter of 600 nm that was tested in the experiment of Heberle et al. (1994) [15].
In the Heberle et al. (1994) experiment, the bR PM open flat sheet was transiently energized by use of a single-turnover pulsed laser flash. The laser wavelength was 532 nm and the pulse width was 8 ns. A pulsed laser flash (8 ns) energy density of 3 mJ/cm2 was used to photoexcite only about 10% of the bR molecules to ensure single-turnover conditions [14]. Therefore, a single-turnover laser flash energization at the intensity of 3 mJ/cm2 will transiently generate 820 charge-separated pairs of bRH+ and bROH‒ across the bacteriorhodopsin PM disk (diameter 600 nm). This constitutes 820 TELCs per PM disk, which is equivalent to a peak TELC density of 2900 per µm2 of PM. From the peak TELC density of 2900 per µm2 of PM, we employed Eq. 1 to calculate its peak transient transmembrane potential. Based on experimentally-measured cell membrane capacitance data [11], we used a specific membrane capacitance C/S of 9 mF/m2 and calculated the peak transient transmembrane potential to be about 50 mV (Table 1).
If the laser flash intensity is doubled to 6 mJ/cm2, then the peak TELCs density may double to 1640 TELCs per PM disk—equivalent to a peak TELCs density of 5800 per µm2—which will give rise to a peak transient transmembrane potential of about 100 mV, as shown in Table 1.
As listed in Table 1, the lifetime of the transient transmembrane potential is expected to be the same as the associated transient TELCs lifetime (152 µs) that was calculated from the experimental data of Heberle et al. (1994).
Transient TELC Activity Along a Laser Flash-Energized Bacteriorhodopsin Purple Membrane Open Flat Sheet
As previously discussed [12], the bR PM open flat sheet in liquid water can be regarded as a special protonic capacitor disk with its edge (rim) connected through a protonic conductor (liquid water), as shown in Figure 3a. Thus, when protons are actively pumped across the membrane through the membrane-embedded bR photochemistry mechanism from the cytoplasmic side to the extracellular side, it will create excess protons (bRH+) on the extracellular surface while leaving an equal number of excess hydroxide anions (bROH−) on the cytoplasmic surface.
The charge-separated pairs of excess protons (bRH+) and excess hydroxide anions (bROH−) created by the pulsed laser energized bR photophysical chemistry across the PM represent the initial (peak) population of the laser pulse-induced TELPs (TELCs), which can translate to a peak transient transmembrane potential through Eq. 1 as shown in Table 1.
Therefore, according to the protonic capacitor model [2] [1] [12], the excess protons in this case will be held, at least transiently, at the liquid-membrane interface along the extracellular surface by the transmembrane-electrostatic attractive force from the excess hydroxide anions at the liquid-membrane interface along the cytoplasmic surface, as illustrated in Figure 3a. Subsequently, the excess protons will rapidly move along the liquid-membrane interface on the extracellular surface and through the PM rim to return to the cytoplasmic side; meanwhile, the excess hydroxide anions can also quickly translocate on the cytoplasmic surface towards the rim of the bR PM flat sheet.
The formation of an “excess hydroxide anions-membrane-excess protons” [12] capacitor due to the photochemically-driven transmembrane proton pumping (Figure 3a) is immediately relevant to the formation of transmembrane potential. Other anions and cations such as carbonate and phosphate existing before photochemical energization likely have little relevance to protonic capacitor bioenergetics. Here, the “excess hydroxide anions” may be regarded as “protonic holes”, which are somewhat analogous to the concept of “electron-hole pairs” arising when an electron is excited from a lower energy level to a higher energy level, leaving behind a “hole”. That is, the concept of protonic holes is rooted in protonic translocations (through the “hops and turns” protonic conduction mechanism in liquid water) rather than hydroxide ions, in a way analogous to the electronic conduction through a metallic conductor. Therefore, from the negative charge point of view, hydroxide anions (protonic holes) are transferred in the opposite direction of proton conduction. Consequently, the translocation of the excess hydroxide anions on the cytoplasmic surface towards the rim of the bR PM open flat sheet is equivalent to the translocation of excess protons from the rim towards the center of the cytoplasmic surface in filling the “protonic holes” there. When the excess protons finally recombine with the excess hydroxides in forming water molecules, the transient transmembrane potential (Δψ) decays to zero.
Therefore, to observers who monitor the translocated protons using both localized protonic sensors (such as pH-indicating dye fluorescein) along two sides of the bR PM open flat sheet and a delocalized pH probe (pyranine) in the bulk liquid phase, they would observe that the excess protons pumped through bR appear to be moving along the extracellular membrane surface and then passing through the liquid around the rim to the cytoplasmic surface, but without getting into the bulk liquid phase, as shown in Figure 3a. These predicted features were exactly demonstrated in the bR PM open flat sheet experiment performed by Heberle et al. (1994) [15], where they employed a pulsed laser flash to suddenly energize bacteriorhodopsin-driven H+ pumping and monitored the flash-induced transient absorption changes of the protonic molecular probes. Therefore, as recently reported [12], the prediction from the TELPs model can now well explain the experimental results of Heberle et al. [15] that suggest “protons can efficiently diffuse along the membrane surface between a source and a sink (for example H+-ATP synthase) without dissipation losses into the aqueous bulk.”
Discussion and Commentary in Response to Silverstein (2023) Argument
Recently, Silverstein (2023) [17] tried again to defend his notion that “Δψ = 0” (9) using a bR membrane “particle-like” drawing (less than 10 nm in size, as judged by the size of liquid molecules with a single bR molecule) as shown in Figure 3b to represent the 600 nm diameter flat PM disk (Figure 3a) of Heberle et al. 1994 [15]. Note, the 600 nm diameter (geometric size) of a flat PM disk and the number of 8200 bR molecules per disk (see Table 1) are relevant parameters that may affect the TELC-associated transport activities and thus the lifetime and amplitude of transient transmembrane potential. Probably trying to favor his argument, Silverstein’s “particle-like” drawing (Figure 3b) shows only a single bacteriorhodopsin molecule with a few lipid molecules. According to the length of a lipid molecule—which is known to be about 2 nm—and a typical biomembrane thickness of 4 nm, his drawing (Figure 3b) appears to inappropriately portray the 600-nm diameter PM disk (containing 8200 bacteriorhodopsin molecules) as a single bR membrane particle with a size of 10 nm. Since his article [17] does not mention anything about the 600 nm diameter of the flat purple membrane disk, his 10-nm “particle-like” drawing with a single bR molecule (Figure 3b) could misrepresent the Heberle et al. (1994) experiment [15] and cause confusion in the scientific community.
Silverstein’s recent argument [17] centers on the claim that “the circuit is ‘shorted out’ by the free flow of ions between the two sides of the membrane, around the rims of the membrane fragments.” However, his own statement “Once a proton is released on the P side and a transient Δψ is generated, ions in solution will respond: K+ will move from the P side toward the N side, and Cl− will move in the opposite direction” professes that “a transient Δψ is generated” [17].
There is no evidence for Silverstein’s proposed vectorial ion flow: “K+ will move from the P side toward the N side, and Cl− will move in the opposite direction” at the PM flat sheet rim as he tried to portray with his 10-nm particle-like drawing with a single bR (Figure 3b) [17]. Even if the proposed vectorial ions flow were true, that would still have to be driven by an electrical field from the transient transmembrane potential Δψ, in accordance with the Fick’s laws of diffusion; this again indicates the presence of transient membrane potential (transient peak Δψ = 50 mV, as calculated in Table 1) in contrast to his notion [16] that “Δψ = 0”.
Silverstein [17] repeatedly argued that the photo-driven bR proton pump “is 56,000 times slower than proton diffusion in bulk aqueous solution”. This argument seems to be irrelevant, since the pulsed laser-induced formation of transient membrane potential (transient peak Δψ = 50 mV) is the first and primary step (1) because of the photo-driven bR proton pump, which is an active transport process. All the other steps are passive processes, including (2) proton translocation along the liquid-membrane interface (and around the PM flat sheet rim) and (3) slow (1.29 ms) partial (17%) proton release into the bulk liquid phase, likely as a result of cation-proton exchange associated with ion and proton diffusion in bulk aqueous solution [12]. Processes (2) and (3) happen later than the primary active transport step (1) since the passive transport processes (2 and 3) must be driven, at least transiently, by the pulsed laser-induced bR photophysical proton-pumping charge separation process (1) that creates a transient membrane potential (transient Δψ ≠ 0) as the driving force.
By now, readers can probably identify the mistakes in Silverstein’s arguments “Given D = 2 nm2/ns for K+ and Cl− in bulk water [26], it would take only 0.002 μs (= (5 nm)2/(6 × 2 nm2/ns) = 2 ns) for one of these ions to cross the 5 nm around the rim of the membrane fragment from the P and N side … So, light-driven H+ pumping via bacteriorhodopsin across the purple membrane fragment is not electrogenic; in the 76 μs it takes to pump a proton across the membrane, it is easily electrically compensated by K+ and Cl− diffusion around the fragment rim. Thus, one would not expect to find even a transient non-zero Δψ in this system.”
As mentioned previously, the pulsed laser-induced 76-μs photo-driven bacteriorhodopsin active proton pump and transient transmembrane potential formation is the primary (active) transport step (1) that drives the sequence of the subsequent transport events (2 and 3). The passive transport processes—including (2) proton translocation along the liquid-membrane interface and around the rim plus (3) slow (1.29 ms) partial (17%) proton release, likely through cation-proton exchange associated with ions and proton diffusion in bulk aqueous solution [12]—all happen later, after the laser pulse-induced primary (active) transport step (1). In his arguments above, Silverstein seems to assume that the passive transports (2 and 3) could occur simultaneously or before the laser pulse-induced primary (active) transport step (1), which seems to be a fundamental mistake. Therefore, readers may now be able to see four mistakes in Silverstein’s arguments [7]:
1) Improperly mixed up the sequence of events from the primary event of the 76-μs photo-driven bR active proton pump and transient transmembrane potential formation (1) to the passive transport processes including: (2) proton translocation along the liquid-membrane interface and around the rim plus (3) slow (1.29 ms) partial (17%) proton releasing associated with ions and proton diffusion in bulk aqueous solution [12];
2) Wrongly assumed a passive vectorial “flow of K+ and Cl− cross the 5 nm around the rim” to occur simultaneously or before the laser pulse-induced 76-μs bR proton-pump event that resulted in the formation of a transient membrane potential (peak transient Δψ = 50 mV, as calculated in Table 1);
3) Inaccurately assumed a passive vectorial “flow of K+ and Cl− cross the 5 nm around the rim” could instantaneously (τ =0) reduce transmembrane potential to zero;
4) Improperly claimed “2 ns” for a passive vectorial ion flow to cross the 5 nm around the rim as a decay lifetime for the transient transmembrane potential; even if the claimed “2 ns” decay time were true, it would still have to admit the transient transmembrane potential (transient Δψ ≠ 0) during its lifetime.
Note, the decay lifetime (τ) for a transient transmembrane potential (transient peak Δψ = 50 mV) is expected to be correlated with the amount of time that the excess protons at the extracellular side take to translocate from the center area of the 600-nm diameter bR PM open flat sheet through the rim to the center area of the cytoplasmic side to recombine with the excess hydroxides to form water molecules. According to the Heberle et al. (1994) experimental data [15] that employed a mean distance for the two-dimensional diffusion of 240 nm, we estimated the decay lifetime (τ) for the transient membrane potential (transient Δψ ≠ 0) to be about 152 μs (τ = 228 μs – 76 μs), as listed in Table 1.
Silverstein [17] recently also tried to argue for the presence of “porins and ion channels” in the 600-nm diameter bR PM open flat sheet (Figure 2a) employed in the Heberle et al. (1994) [15] experiment. This argument also seems to be moot since the PM open flat sheet is composed of 75% bR (w/w) and 25% lipid (w/w) [20]; there is no evidence for his claimed “porins and ion channels” in the 600-nm diameter bR PM open flat sheet that was used in the Heberle et al. (1994) experiment [15].
As recently reported [12], it can be shown through Ohm’s law that the voltage V = I·R ≠ 0, where I is the total current of protonic and ionic conduction through the bR PM rim plus through “the porins and ion channels” (if present) and R is the protonic and ionic resistance of the liquid medium which has a non-zero resistance. Therefore, Silverstein’s argument [17] and notion [16] that “Δψ = 0” for a laser-energized flat bacteriorhodopsin membrane sheet was apparently misconceived and it could not withstand even a quick test by Ohm’s law. Under the experimental conditions of Heberle et al. (1994) [15], the peak transient transmembrane potential (Δψ) has now been numerically calculated to be 50 mV (Table 1) based on the numbers of the charge-separated pairs of excess protons (bRH+) and excess hydroxide anions (bROH−) created by the laser-energized bR photophysical chemistry across the PM sheet.
Protonic Outlet of bR Structure Rejecting the “Potential Well/Barrier” Model
Silverstein [17] presented a quite interesting plot for the putative “potential well/barrier” model’s Gibbs free energy profile for moving protons from the water/decane interface to the bulk aqueous phase (Figure 4a). He wrote “ΔG for the depth of the potential well near the water/decane interface (4–8 RT at 1–2 Å) was calculated by ab initio free energy molecular dynamics [27]. The activation barrier, ΔG◦‡ ≈ 20–30 RT is calculated from Arrhenius/Eyring plots [27] [28].”
At the experimental temperature of 20 oC (293 K) [15], Silverstein’s claimed “ΔG◦‡ ≈ 20–30 RT ” (+ 25 RT ?) in the liquid water phase at a location of 0.4 nm away from the decane surface would be equivalent to an activation barrier of about 60.9 kJ/mol; that is likely to be questionable since he has never explained how it could be possible for water molecules to form an activation barrier that is so much higher than their hydrogen bond energy. According to an independent study [29], the water hydrogen bond Gibbs energy ∆G0 is 2.7 kJ/mol (with ∆H0 = 7.9 kJ/mol and T∆S0 = 5.2 kJ/mol). For the mechanism of proton mobility, the activation energy EA is known to be 11.3 kJ/mol [29] [30], in contrast to Silverstein’s claimed “ΔG◦‡ ≈ 20–30 RT ” (around 60.9 kJ/mol).
Furthermore, even assuming the putative “potential well/barrier” model were true, it still could not explain the relevant bioenergetics. As shown in Figure 4a, the bottom of its putative Gibbs free energy potential well (−6 RT, if true) would be located about 0.15 nm away from the decane surface and the peak of the activation barrier (+25 RT, if true) would be located 0.4 nm away from the decane surface. Consequently, if the “potential well/barrier” model (Figure 4a) were correct, it would imply that the protonic outlet of the bR molecular structure would have been located precisely inside the “potential well” that would be within 0.4 nm from the alkane surface of the membrane. Otherwise, the bR protonic outlet (which protrudes into the liquid phase at least about 1 nm away from the hydrophobic core membrane surface) will be outside the putative “potential well/barrier.” If the protonic pump outlet protrudes more than 0.6 nm away from the hydrophobic core membrane surface (so that it is outside the putative potential well/barrier), the “potential well/barrier” model (even if it exists) would not work.
The proton (H+) transfer processes from the active center of bR to the extracellular side (Figure 4a, reaction 1) and from there along the membrane-water interface to the cytoplasmic side of bR (reaction 2) are kinetically and spatially resolved [20]. The pH indicator fluorescein (F) that was bound to K129 at the extracellular surface of bR demonstrated the bR protonic outlet activity at a position well above the lipid head groups, which is at least 1 nm away from the alkane surface of the membrane. As shown in Figure 4b, bR protonic outlet (K129) apparently protrudes into the liquid phase at least 1 nm away from the lipid bilayer’s alkane membrane surface. That is, the bR protonic outlet is located at the liquid phase outside the “potential well/barrier” (Figure 4a).
This observation (Figure 4), which is consistent with the known bR structure and function [23] [21] [22], is well in line with the TELPs model, but it does not support the putative “potential well/barrier” model. As more clearly shown in the X-ray crystallographic structure of bacteriorhodopsin (Figure 1a), its protonic outlet protrudes and injects protons (H+) into the bulk liquid phase of the extracellular space at least 1 nm away from the membrane surface [22]. Another independent study [21] (Figure 1b) also showed that the membrane-embedded bacteriorhodopsins translocate protons (H+) into the bulk liquid phase of the extracellular space at least about 1 nm away from the membrane surface. Note, the Heberle et al. (1994) experiment [15] demonstrated the laser-induced bR proton release (τ = 76 µs) at its K129, which apparently protrudes into the bulk liquid phase (bottom left, Figure 1b). Therefore, the structure and function of bacteriorhodopsin (Figure 1) quite clearly reject the putative “potential well/barrier” model (Figure 4a).
In addition to the bR structure with regard to its protonic outlet position that apparently rejects the “potential well/barrier” model, many other known protonic pump outlets such as those of complexes I, III and IV in mitochondria also apparently protrude into the liquid phase at least 1-3 nm away from the membrane surface [4] [3] [31] [32]; they thus do not support the “potential well/barrier” model either. Therefore, it is now again quite clear that the putative “potential well/barrier” (Figure 4a) as proposed by Junge and Mulkidjanian [18, 19] and advocated by Silverstein [17] does not really exist, or the putative potential well/barrier (even if it exists) is irrelevant to explaining the results of the Heberle et al. (1994) experiment [15].
Note, recently, Silverstein repeated similar types of misconceived arguments [33] [34] [35]. An independent researcher has now also pointed out that “Silverstein’s critiques are untenable” [36]. It is important for us to present clarification for the scientific community while welcoming constructive scientific discussions and feedback.
Present TELCs Research Progresses and Directions for Future Research
The TELCs (TELPs) model [1] [2] [3], which may represent “a complementary development to Mitchell’s chemiosmotic theory,”, is highly useful in helping to elucidate “real-world bioenergetic systems with both delocalized and localized protonic coupling” [3]. For instance, the TELPs model has been successfully employed in “elucidating the decades-longstanding energetic conundrum [37-39] of ATP synthesis in alkalophilic bacteria” [5, 40-44] and in “bettering the understanding of energetics in mitochondria” [2, 3]. Its application has recently led to the discovery of the TELPs-associated “thermotrophic function” as the “Type-B energetic process” [45, 46] [47] [48] [31] which can isothermally utilize environmental heat energy to do useful work in helping drive the synthesis of ATP [3, 49]. As discussed in a recent review article [9], protonic (TELPs) membrane capacitors have been experimentally demonstrated well beyond any reasonable doubt, and certain scientists—such as Prof. Lan Guan, “a special Collection editor for the Nature research journal Scientific Reports”—can well understand and appreciate the TELPs theory. In the journal editorial [50], Prof. Guan clearly acknowledged that the progresses of TELPs research “refined and improved our knowledge of transport bioenergetics”, including the discovery of the TELPs thermotrophic feature. More independent researchers have started to recognize the value of the TELPs theory in their publications [50-54]. For example, the TELPs model has now been successfully employed in an excellent elucidation of their independent experimental observations [55], including the “unexpected result” in a “cellular membrane ion transport protein complex (melibiose transporter MelB) [56] that could not be explained by any other existing models and/or theories.”
There are more research opportunities with the TELCs theory in both bioenergetics and neurosciences. Recently, through studies [6-13] based on the TELCs model, the physical origin of neural resting and action potential has been better elucidated as the voltage contributed by TELCs in a neuron “localized protons/cations-membrane-anions capacitor” system. Consequently, it is now understood that neural transmembrane potential has an inverse relationship with TELCs surface density, which may represent a transformative progress in bettering the fundamental understanding of neuroscience [6] [13]. Application of the TELCs model enables calculation of TELCs surface density as a function of transmembrane potential [13], which may represent a complementary development to both the Hodgkin-Huxley classic cable theory and the Goldman-Hodgkin-Katz equation. Using the TELCs model, the neural touch signal transduction responding time required to fire an action potential spike has now, for the first time, been calculated to be as fast as 0.3 ms [57], which led to a better understanding on the question of “how the transient ion transport activity of touch receptors (PIEZO) could change the graded potential to stimulate an action potential firing” [57]. Many more research efforts with the TELCs model are needed in neurosciences to better elucidate how action potentials propagate along a remarkably long axon (such as from head to hand) and to better understand how the human brain and memory works. Future research with the TELCs-membrane-TELAs capacitor model may also help to better understand how the brain recognizes and processes neural “pain or joy” signals.
Notably, in protonic bioenergetics, Wolf et al. (2019) [58] discovered that “cristae within the same mitochondrion behave as independent bioenergetic units.” Further studies revealed that cristae undergo continuous cycles of membrane remodeling [59]. Quantification of cristae architecture revealed time-dependent characteristics of individual mitochondria [60]. All these exciting new experimental observations could be better explained with the TELCs-membrane-TELAs capacitor model [1] [2] [3] as well. For instance, future research with the TELCs-membrane-TELAs capacitor model may be able to better elucidate how the transmembrane potential in mitochondria is localized in the cristae, with each crista exhibiting different transmembrane potentials based on the mitochondria’s energy demands. Therefore, “the model of a protonic capacitor would represent a more local event on demand” [58] [59] [60].
The remarkable computer simulations recently published by Mallick and Agmon (2025) [61] further support the potential role of multi-proton interactions in forming a “protonic front” effect [62] [63] [64]. However, Mallick and Agmon (2025) [61] employed a quite small membrane system that consisted of only “8 lipids in each leaflet, along with 458 water molecules, resulting in a total of 3518 atoms”. The system was in “a rectangular box with edge lengths of 22.4 × 22.4 × 65.2 Å.” Mallick and Agmon (2025) [61] put as many as 3 excess protons into such a small system (2.24 × 2.24 × 6.52 nm), far exceeding the expected TELC density range from 5.62 x10+2 to 1.12 x10+4 excess charges per µm2 of membrane surface area that has recently been calculated [64]. According to the mean membrane surface area of 178 nm2 per TELC that has now been calculated at a moderate transmembrane potential of 100 mV [64], to properly simulate the collective activity of 3 excess protons, a much larger membrane system (ideally 3 x 178 nm2) may be needed, also requiring much larger computational powers. Furthermore, the simulation system that Mallick and Agmon (2019) [58] employed comprises a single water body without any consideration of transmembrane potential, which thus may not represent a good mimic of any living cell systems that typically have transmembrane potential; this problem is similar to that of the single water-droplet experimental system of Pohl’s group, [27] which, strictly speaking, does not qualify to be considered as any reasonable biomimetic system, as pointed out in my recent publications [63] [64]. The identified needs for improvements here also indicate new opportunities for future research.
Therefore, I hereby again encourage further research efforts in more relevant protonic cell systems that should have a transmembrane potential associated with a TELCs-membrane-TELAs capacitor comprising excess positive charges at one side and excess anions at the other side of the membrane.
Acknowledgement
The author thanks Dr. Joachim Heberle and Dr. Norbert Dencher for providing more detailed information about their 1994 experimental conditions—including the information about the bacteriorhodopsin molecular population density in the bacteriorhodopsin purple membrane open flat sheet, their pulsed laser property, and their operating conditions—that made some of the analyses reported in this article possible. The author also thanks the anonymous peer reviewers for their highly valuable and constructive review comments that made this article better.
Author Information
Corresponding author
*James Weifu Lee. Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, VA 23529 United States, Email: jwlee@odu.edu, Tel: 757-683-4260
Author Contributions
Lee designed and performed research, analyzed data, and authored the paper.
Funding Declaration
The protonic bioenergetics aspect of this research was supported in part by a Multidisciplinary Biomedical Research Seed Funding Grant from the Graduate School, the College of Sciences, and the Center for Bioelectrics at Old Dominion University, Norfolk, Virginia, USA.
Competing Interests
The author has declared that no competing interests exist.
Data Availability
All data generated or analyzed during this study are included in this article and in the cited references.
References
1. Lee JW. Electrostatically localized proton bioenergetics: better understanding membrane potential. Heliyon. 2019;5(7):e01961. https://doi.org/10.1016/j.heliyon.2019.e01961
2. Lee JW. Protonic capacitor: elucidating the biological significance of mitochondrial cristae formation. Sci Rep. 2020;10:10304. https://doi.org/10.1038/s41598-020-66203-6
3. Lee JW. Mitochondrial energetics with transmembrane electrostatically localized protons: do we have a thermotrophic feature? Sci Rep. 2021;11(1):93853. https://doi.org/10.1038/s41598-021-93853-x
4. Lee JW. TELP theory: elucidating the major observations of Rieger et al. 2021 in mitochondria. Mitochondr Commun. 2023;1:62–72. https://doi.org/10.1016/j.mitoco.2023.09.001
5. Lee JW. Isothermal environmental heat energy utilization by transmembrane electrostatically localized protons at the liquid-membrane interface. ACS Omega. 2020;5(28):17385–95. https://doi.org/10.1021/acsomega.0c01768
6. Lee JW. Protonic conductor: better understanding neural resting and action potential. J Neurophysiol. 2020;124(4):1029–44. https://doi.org/10.1152/jn.00281.2020
7. Saeed HA, Lee JW. Experimental demonstration of localized excess protons at a water-membrane interface. Bioenergetics. 2015;4(127):1–7. https://doi.org/10.4172/2167-7662.1000127
8. Saeed H, Lee J. Experimental determination of proton-cation exchange equilibrium constants at water-membrane interface fundamental to bioenergetics. Water. 2018;9:116–40. https://doi.org/10.14294/WATER.2018.2
9. Lee JW. Experimental demonstration and study of transmembrane-electrostatically localized protons prevail. Water. 2025;14:35–58. https://doi.org/10.14294/WATER.2024.2
10. Saeed H. Bioenergetics: experimental demonstration of excess protons and related features [dissertation]. Norfolk (VA): Old Dominion University; 2016.
11. Kharel G. Chapter 4: Investigation of calcium and magnesium cation-proton exchange with transmembrane electrostatically localized protons (TELP) at a liquid-membrane interface. In: Exploring cation exchange: unveiling its significance in biochar and bioenergetics applications [dissertation]. Norfolk (VA): Old Dominion University; 2024.
12. Lee JW. Transient protonic capacitor: explaining the bacteriorhodopsin membrane experiment of Heberle et al. 1994. Biophys Chem. 2023:107072. https://doi.org/10.1016/j.bpc.2023.107072
13. Lee JW. Application of TELC model to neurology: review and commentary responding to Silverstein’s critique. Curr Trends Neurol. 2023;17:83–9.
14. Thiedemann G, Heberle J, Dencher NA. Bacteriorhodopsin pump activity at reduced humidity. In: Rigaud JL, editor. Structures and functions of retinal proteins. Montrouge (France): John Libbey Eurotext Ltd; 1992. p. 217–20.
15. Heberle J, Riesle J, Thiedemann G, Oesterhelt D, Dencher NA. Proton migration along the membrane-surface and retarded surface to bulk transfer. Nature. 1994;370(6488):379–82. https://doi.org/10.1038/370379a0
16. Silverstein TP. A critique of the capacitor-based “transmembrane electrostatically localized proton” hypothesis. J Bioenerg Biomembr. 2022;54(2):59–65. https://doi.org/10.1007/s10863-022-09931-w
17. Silverstein TP. Lee’s transient protonic capacitor cannot explain the surface proton current observed in bacteriorhodopsin purple membranes. Biophys Chem. 2023;301:107096. https://doi.org/10.1016/j.bpc.2023.107096
18. Cherepanov DA, Feniouk BA, Junge W, Mulkidjanian AY. Low dielectric permittivity of water at the membrane interface: effect on the energy coupling mechanism in biological membranes. Biophys J. 2003;85(2):1307–16. https://doi.org/10.1016/S0006-3495(03)74565-2
19. Mulkidjanian AY, Heberle J, Cherepanov DA. Protons @ interfaces: implications for biological energy conversion. Biochim Biophys Acta Bioenerg. 2006;1757(8):913–30. https://doi.org/10.1016/j.bbabio.2006.02.015
20. Dencher NA, Sass HJ, Büldt G. Water and bacteriorhodopsin: structure, dynamics, and function. Biochim Biophys Acta. 2000;1460(1):192–203. https://doi.org/10.1016/S0005-2728(00)00139-0
21. Heberle J. Proton transfer reactions across bacteriorhodopsin and along the membrane. Biochim Biophys Acta Bioenerg. 2000;1458(1):135–47. https://doi.org/10.1016/S0005-2728(00)00064-5
22. Kawanabe A, Furutani Y, Jung KH, Kandori H. An inward proton transport using Anabaena sensory rhodopsin. J Microbiol. 2011;49(1):1–6. https://doi.org/10.1007/s12275-011-0547-x
23. Luecke H, Richter HT, Lanyi JK. Proton transfer pathways in bacteriorhodopsin at 2.3 angstrom resolution. Science. 1998;280(5371):1934–7. https://doi.org/10.1126/science.280.5371.1934
24. Yamashita H, Voïtchovsky K, Uchihashi T, Contera SA, Ryan JF, Ando T. Dynamics of bacteriorhodopsin 2D crystal observed by high-speed atomic force microscopy. J Struct Biol. 2009;167(2):153–8. https://doi.org/10.1016/j.jsb.2009.04.011
25. Gentet LJ, Stuart GJ, Clements JD. Direct measurement of specific membrane capacitance in neurons. Biophys J. 2000;79(1):314–20. https://doi.org/10.1016/S0006-3495(00)76293-X
26. Aqion. Table of diffusion coefficients. 2020. https://www.aqion.de/site/diffusion-coefficients
27. Zhang C, Knyazev DG, Vereshaga YA, Ippoliti E, Nguyen TH, Carloni P, et al. Water at hydrophobic interfaces delays proton surface-to-bulk transfer and provides a pathway for lateral proton diffusion. Proc Natl Acad Sci USA. 2012;109(25):9744–9. https://doi.org/10.1073/pnas.1121227109
28. Weichselbaum E, Österbauer M, Knyazev DG, Batishchev OV, Akimov SA, Nguyen TH, et al. Origin of proton affinity to membrane/water interfaces. Sci Rep. 2017;7(1):4553. https://doi.org/10.1038/s41598-017-04675-9
29. Markovitch O, Agmon N. Structure and energetics of the hydronium hydration shells. J Phys Chem A. 2007;111(12):2253–6. https://doi.org/10.1021/jp068960g
30. Lapid H, Agmon N, Petersen MK, Voth GA. A bond-order analysis of the mechanism for hydrated proton mobility in liquid water. J Chem Phys. 2004;122(1):014506. https://doi.org/10.1063/1.1814973
31. Lee JW. Type-B energetic processes: their identification and implications. Symmetry. 2024;16(7):808. https://doi.org/10.3390/sym16070808
32. Dudkina NV, Kouril R, Peters K, Braun HP, Boekema EJ. Structure and function of mitochondrial supercomplexes. Biochim Biophys Acta Bioenerg. 2010;1797(6–7):664–70. https://doi.org/10.1016/j.bbabio.2009.12.013
33. Silverstein TP. Explaining neuronal membrane potentials: the Goldman equation vs. Lee’s TELC hypothesis. Neuroscience. 2025;567:1–8. https://doi.org/10.1016/j.neuroscience.2024.12.065
34. Silverstein TP. Is localized chemiosmosis necessary in mitochondria? Is Lee’s TELP protonic capacitor hypothesis a reasonable model? Mitochondr Commun. 2024;2:48–57. https://doi.org/10.1016/j.mitoco.2024.06.001
35. Silverstein TP. Oxidative phosphorylation does not violate the second law of thermodynamics. J Phys Chem B. 2024;128(35):8448–58. https://doi.org/10.1021/acs.jpcb.4c03047
36. Tamagawa H. Comment on the Silverstein’s critiques of Lee’s TELC theory as a membrane potential generation mechanism. Neuroscience. 2025;573:381. https://doi.org/10.1016/j.neuroscience.2025.03.049
37. Guffanti A, Krulwich T. Bioenergetic problems of alkalophilic bacteria. Biochem Soc Trans. 1984;12(3):411. https://doi.org/10.1042/bst0120411
38. Krulwich TA, Gilmour R, Hicks DB, Guffanti AA, Ito M. Energetics of alkaliphilic Bacillus species: physiology and molecules. Adv Microb Physiol. 1998;40:401–38. https://doi.org/10.1016/s0065-2911(08)60136-8
39. Krulwich TA, Liu J, Morino M, Fujisawa M, Ito M, Hicks DB. Adaptive mechanisms of extreme alkaliphiles. Extremophiles Handbook. 2011:119–39.
40. Lee JW. Proton-electrostatic localization: explaining the bioenergetic conundrum in alkalophilic bacteria. Bioenergetics. 2015;4(121):1–8. https://doi.org/10.4172/2167-7662.1000121
41. Lee JW. Localized excess protons and methods of making and using the same, PCT International Patent Application Publication No. WO 2017/007762 A1. 2017:56 pages.
42. Lee JW. Physical chemistry of living systems: isothermal utilization of latent heat by electrostatically localized protons at liquid-membrane interface. Biophys J. 2019;116(3, Suppl 1):317a. https://doi.org/10.1016/j.bpj.2018.11.1719
43. Lee JW. Proton motive force computation revealing latent heat utilization by localized protons at a liquid-biomembrane interface. Abstr Pap Am Chem Soc. 2018;255. WOS:000435539905429
44. Lee JW. Elucidating the 30-year-longstanding bioenergetic mystery in alkalophilic bacteria. Biophys J. 2017;112(3, Suppl 1):278a–9a. https://doi.org/10.1016/j.bpj.2016.11.1509
45. Lee JW. Type-B energy process: asymmetric function-gated isothermal electricity production. Energies. 2022;15(19):7020. https://doi.org/10.3390/en15197020
46. Lee JW. Type-B energetic processes and their associated scientific implication. J Sci Explor. 2022;36(3):487–95. https://doi.org/10.31275/20222517
47. Lee JW. Thermotrophy exploratory study. J Sci Explor. 2023;37(1):5–16. https://doi.org/10.31275/20232655
48. Sheehan DP, Moddel G, Lee JW. More on the demons of thermodynamics. Phys Today. 2023;76(3):13–. https://doi.org/10.1063/Pt.3.5186
49. Lee JW. Energy renewal: isothermal utilization of environmental heat energy with asymmetric structures. Entropy (Basel). 2021;23(6):665. https://doi.org/10.3390/e23060665
50. Guan L. Structure and mechanism of membrane transporters. Sci Rep. 2022;12(1):13248. https://doi.org/10.1038/s41598-022-17524-1
51. Lee C, Wallace DC, Burke PJ. Super-resolution imaging of voltages in the interior of individual, vital mitochondria. ACS Nano. 2024;18(2):1345–56. https://doi.org/10.1021/acsnano.3c02768
52. Heine KB, Parry HA, Hood WR. How does density of the inner mitochondrial membrane influence mitochondrial performance? Am J Physiol Regul Integr Comp Physiol. 2023;324(2):R242–8. https://doi.org/10.1152/ajpregu.00254.2022
53. Teixeira P, Galland R, Chevrollier A. Super-resolution microscopies, technological breakthrough to decipher mitochondrial structure and dynamic. Semin Cell Dev Biol. 2024;159-160:38–51. https://doi.org/10.1016/j.semcdb.2024.01.006
54. Iovine JC, Claypool SM, Alder NN. Mitochondrial compartmentalization: emerging themes in structure and function. Trends Biochem Sci. 2021;46(11):902–17. https://doi.org/10.1016/j.tibs.2021.06.003
55. Hariharan P, Bakhtiiari A, Liang R, Guan L. Distinct roles of the major binding residues in the cation-binding pocket of the melibiose transporter MelB. J Biol Chem. 2024;300(7):107427. https://doi.org/10.1016/j.jbc.2024.107427
56. Hariharan P, Guan L. Thermodynamic cooperativity of cosubstrate binding and cation selectivity of Salmonella typhimurium MelB. J Gen Physiol. 2017;149(11):1029–39. https://doi.org/10.1085/jgp.201711788
57. Lee JW. Application of TELC model to better elucidate neural stimulation by touch. Explor Neurosci. 2025;4:100685. https://doi.org/10.37349/en.2025.100685
58. Wolf DM, Segawa M, Kondadi AK, Anand R, Bailey ST, Reichert AS, et al. Individual cristae within the same mitochondrion display different membrane potentials and are functionally independent. EMBO J. 2019;38(22):e101056. https://doi.org/10.15252/embj.2018101056
59. Kondadi AK, Anand R, Hänsch S, Urbach J, Zobel T, Wolf DM, et al. Cristae undergo continuous cycles of membrane remodelling in a MICOS-dependent manner. EMBO Rep. 2020;21(3). https://doi.org/10.15252/embr.201949776
60. Segawa M, Wolf DM, Hultgren NW, Williams DS, Van Der Bliek AM, Shackelford DB, et al. Quantification of cristae architecture reveals time-dependent characteristics of individual mitochondria. Life Sci Alliance. 2020;3(7):e201900620. https://doi.org/10.26508/lsa.201900620
61. Mallick S, Agmon N. Multi-proton dynamics near membrane-water interface. Nat Commun. 2025;16(1). https://doi.org/10.1038/s41467-025-58167-w
62. Agmon N, Gutman M. Proton fronts on membranes. Nat Chem. 2011;3(11):840–2. https://doi.org/10.1038/nchem.1184
63. Lee JW. Protonic conductor: Explaining the transient “excess protons” experiment of Pohl’s group 2012. Biophys Chem. 2023;106983. https://doi.org/10.1016/j.bpc.2023.106983
64. Lee JW. Calculation of proton transmembrane-electrostatic interaction force and elucidation of the water droplet experiment with a transient protonic front. RSC Adv. 2025;15(26):21108–20. https://doi.org/10.1039/D5RA03298A
Discussion with Reviewers
Reviewer 1: I have a few questions that would be good to point out in the manuscript. A photoexcited state would create a local charge distribution across the membrane, specifically at the boundaries of the bR region; however, it would be good to state that the excess of protons bRH+ and bROH- proposed is a simplified model that fits well with the experiments proposed by Heberle et al. Conceptually, “protonic holes” as hydroxide anions may be combining two different concepts, which is rather difficult for a chemist to grasp. However, in the field of physical chemistry, it makes more sense to read about holes and excitons. It would be good to explain the concept of protonic holes in more detail for an average reader.
Author: Thank you. To better explain the concept of protonic holes, we have now added the following statement in the revised manuscript:
“Here, the ‘excess hydroxide anions’ may be regarded as ‘protonic holes’, which are somewhat analogous to the concept of ‘electron-hole pairs’ arising when an electron is excited from a lower energy level to a higher energy level, leaving behind a ‘hole’.”
Reviewer 1: The negative charge of phospholipids facilitates the movement of protons across and along membranes. However, it is quite challenging to understand how hydroxide would translocate. I guess the concept of protonic holes is rooted in protonic translocations rather than hydroxide ions, as stated. Why hydroxide ions and not some deprotonated anion from the cytosol? Such as some buffering species e.g., carbonate, phosphate, etc.
Author: Thank you. Yes, as stated in the manuscript, the concept of protonic holes is rooted in protonic translocations (through the “hops and turns” protonic conduction mechanism in liquid water) rather than hydroxide ions, in a way somewhat analogous to the electric conduction through a metallic conductor. Excess hydroxide ions that are created as a result of the photochemically-driven transmembrane proton pumping are relevant to the formation of transmembrane potential. Other anions such as carbonate and phosphate existing before photochemical energization are likely to have little relevance to protonic bioenergetics. To better clarify this, we have now added the following statement in the revised manuscript:
“The formation of “excess hydroxide anions-membrane-excess protons” capacitor created as a result of the photochemically-driven transmembrane proton pumping is immediately relevant to the formation of transmembrane potential. Other anions and cations such as carbonate and phosphate existing before photochemical energization are likely to have little relevance to protonic bioenergetics”.
Reviewer 1: The model is appealing due to its simplicity, but further studies are necessary to develop a more robust model. For instance, it has recently been proposed that the transmembrane potential in mitochondria is localized in the crests, with each crest exhibiting different transmembrane potentials based on the mitochondria’s energy demands. Therefore, the model of a protonic capacitor would represent a more local event on demand.
Author: This is an excellent and highly valuable point. Therefore, in the revised manuscript, we have now added a section “Present TELCs research progresses and directions for future research” with the following paragraph:
“Notably, in protonic bioenergetics, Wolf et al. 2019 [54] discovered that ‘cristae within the same mitochondrion behave as independent bioenergetic units.’ Further studies revealed that cristae undergo continuous cycles of membrane remodeling [55]. Quantification of cristae architecture revealed time-dependent characteristics of individual mitochondria [56]. All these exciting new experimental observations could be better elucidated with the TELCs-membrane-TELAs capacitor model [1] [2] [3] as well. For instance, future research with the TELCs-membrane-TELAs capacitor model may be able to better elucidate how the transmembrane potential in mitochondria is localized in the cristae, with each crista exhibiting different transmembrane potentials based on the mitochondria’s energy demands. Therefore, ‘the model of a protonic capacitor would represent a more local event on demand’ [54] [55] [56].”
Reviewer 1: Lastly, I think the rebuttal to Silverstein’s statements comes across as a bit bold in my modest opinion. I would recommend the author to tone down that section and make it more neutral, as it is a scientific discussion, not a political debate.
Author: Thank you for this important comment. As the Reviewer recommended, we have now tried again “to tone down that section and make it more neutral” by the following changes in the revised manuscript:
1) Changed the word “is” to soft words “seems to be” where appropriate;
2) Removed the strong word “flawed”;
3) Minimized the use of words “Silverstein” and “his” where possible;
4) Defined the word “mistakes” with a softer term “misunderstandings or errors” where possible;
5) Removed the strong sentence “The argument shall now be over”.
Reviewer 2: The basic problem that Dr. Lee was addressing—how protons behave at an interface—was settled down by Noam Agmon “multi-proton dynamics near membrane-water interface”, as published in Nature Communications (April 2025).
The essence of the Agmon paper is that one should consider the system in terms of PROTONS rather than a proton. When a surface interacts with many protons, its properties are affected by the presence of nearby protons acquiring features not common for a “single proton at the interface”. This cross interaction was well accounted for in my mode of analysis, where the rate of proton exchange among sites was specifically addressed. But this was a micro model and was not expanded to macroscopic dimension.
In Phol’s analysis it appeared as an enhanced diffusion coefficient and an “undefined down-gradient” flow.
As Agmon presents it, the nature/properties of the lipid membrane vary with its state of protonation, a marvelous concept that calls for further sophistication. The model of Dr. Lee accounts for “gross properties” of the surface by electrostatic terms (but the expressions are very complex). In order to put an end to this long (and painful) discussion, it will be best for Dr. Lee to find the linkage between his electric model and the “proximity effect” aspects of Agmon. I am sure that Dr. Lee will be able to make the connection between the “Micro” of Agmon and his “Macro” system.
Author: Thank you very much for your review comments, which are very interesting (good). The interesting computer simulations recently published by Mallick and Agmon [57] nicely add to the body of knowledge supporting the potential role of multi-protons interactions in forming a “protonic front” effect. However, the simulation system that Mallick and Agmon [58] employed was quite small and comprised a single water body without any consideration of transmembrane potential, which thus may not represent a good mimic of any living cell systems which typically have transmembrane potential. That also indicates more opportunities for future research.
Therefore, in the revised manuscript, we have now added a section “Present TELCs research progresses and directions for future research” with the following paragraphs:
“The remarkable computer simulations recently published by Mallick and Agmon (2025) [61] further support the potential role of multi-proton interactions in forming a “protonic front” effect [62] [63] [64]. However, Mallick and Agmon (2025) [61] employed a quite small membrane system that consisted of only “8 lipids in each leaflet, along with 458 water molecules, resulting in a total of 3518 atoms”. The system was in “a rectangular box with edge lengths of 22.4 × 22.4 × 65.2 Å.” Mallick and Agmon (2025) [61] put as many as 3 excess protons into such a small system (2.24 × 2.24 × 6.52 nm), far exceeding the expected TELC density range from 5.62 x10+2 to 1.12 x10+4 excess charges per µm2 of membrane surface area that has recently been calculated [64]. According to the mean membrane surface area of 178 nm2 per TELC that has now been calculated at a moderate transmembrane potential of 100 mV [64], to properly simulate the collective activity of 3 excess protons, a much larger membrane system (ideally 3 x 178 nm2) may be needed, also requiring much larger computational powers. Furthermore, the simulation system that Mallick and Agmon (2019) [58] employed comprises a single water body without any consideration of transmembrane potential, which thus may not represent a good mimic of any living cell systems that typically have transmembrane potential; this problem is similar to that of the single water-droplet experimental system of Pohl’s group, [27] which, strictly speaking, does not qualify to be considered as any reasonable biomimetic system, as pointed out in my recent publications [63] [64]. The identified needs for improvements here also indicate new opportunities for future research.
Therefore, I hereby again encourage further research efforts in more relevant protonic cell systems that should have a transmembrane potential associated with a TELCs-membrane-TELAs capacitor comprising excess positive charges at one side and excess anions at the other side of the membrane.”