Directional proton conductance in bacteriorhodopsin is driven by concentration gradient, not affinity gradient

doi:10.21203/rs.3.rs-944138/v2

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Directional proton conductance in bacteriorhodopsin is driven by concentration gradient, not affinity gradient

https://doi.org/10.21203/rs.3.rs-944138/v2

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It is widely spread that microorganisms can harvest energy from sun light to establish electrochemical potential across cell membrane by pumping protons outward. Light driven proton pumping against a transmembrane gradient entails exquisite electronic and conformational reconfiguration at fs to ms time scales. However, transient molecular events along the photocycle of bacteriorhodopsin are difficult to comprehend from noisy electron density maps obtained from multiple experiments when the intermediate populations coexist and evolve as a function of 13 decades of time. Here I report an in-depth meta-analysis of the recent time-resolved datasets collected by several consortiums. This analysis deconvolutes the observed mixtures, thus substantially improves the quality of the electron density maps, and provides a clear visualization of the isolated intermediates from I to M. The primary photoproducts revealed here suggest a proton transfer uphill against 15 pH units is accomplished by the same physics that governs the tablecloth trick. While the Schiff base is displaced at the beginning of the photoisomerization within ~30 fs, the proton stays due to its inertia. This affinity-independent early deprotonation builds up a steep proton concentration gradient that drives the directional proton conductance toward the extracellular medium. This mechanism fundamentally deviates from the widely adopted assumption based on equilibrium processes driven by light-induced changes of proton affinities. The method of a numerical resolution of concurrent events from mixed observations is also generally applicable.

General Biochemistry

proton pump

retinal

serial crystallography

singular value decomposition

X-ray free electron laser

Bacteriorhodopsin (bR) captures photon energy to pump protons outward from the cytoplasm (CP) against the concentration gradient, thus converts light into electrochemical energy. This integral membrane protein of 28 kDa singlehandedly achieves the exact same goal of photosynthesis and cellular respiration combined. This simplicity is widely exploited in optogenetics and bioelectronics (Fenno et al., 2011; Li et al., 2018). A trimeric form of bR on the native purple membrane shares the retinal chromophore and the same protein fold of seven transmembrane helices A-G (Fig. S1) with large families of microbial and animal rhodopsins (Ernst et al., 2014; Kandori, 2015). An all-trans retinal is covalently connected to Lys216 of helix G through a protonated Schiff base (SB) pointing toward the extracellular side (EC) in the resting state, of which the double bond C₁₅=N_z is also in trans (traditionally also noted as anti (McCarty, 1970)) Upon absorption of a visible photon, the retinal isomerizes efficiently and selectively to adopt the 13-cis configuration (Govindjee et al., 1990). Extensive structural events during the ultrafast isomerization sampling and stereochemical selection were recently revealed by the companion study of this work (Ren, 2021).

Photocycle

It has been shown that the species I or a collection of species prior to the photoisomerization arises before 30 fs and remains in 13-trans instead of a near 90° configuration about C₁₃=C₁₄ (Zhong et al., 1996). A red-shifted intermediate species J in 13-cis forms around 450-500 fs and decays at 3 ps to a less red-shifted species K (Applebury et al., 1978; van den Berg et al., 1990), which lasts longer than five decades of time therefore becomes the most “stable” intermediate throughout the entire photocycle on a log-time scale. The blue-shifted L state emerges from K at 1-2 ms and converts to strongly blue-shifted M states at ~50 ms (Lozier et al., 1975). The L à M transition has been considered as the step for the proton acceptor, the carboxylate group of Asp85, to become neutralized by receiving a proton (Fahmy et al., 1992). This established view has been largely based on peak assignments in resonance Raman and Fourier transform infrared spectroscopy (FTIR) on wildtype bR and various mutants (Braiman et al., 1988, 1991; Gerwert et al., 1990; Lewis et al., 1974). However, the event of SB deprotonation has been mistakenly inferred from the observed protonation of the carboxylate of Asp85. It has been widely quoted in the literature that the proton transfer from the SB to the proton accepter occurs as the M formation. This study finds that this proton transfer spans ten decades in time instead of a single event. The electron density maps of I to M are unscrambled from one another in this analysis. They clearly show extensive conformational changes leading to and developing from the isomerization of the chromophore (Fig. 1).

Structure

Although the first low resolution map of bR was revealed in 1975 (Henderson and Unwin, 1975), the majority of structural information awaited technology advances until the 1990s in cryo electron microscopy (Henderson et al., 1990), electron diffraction (Grigorieff et al., 1996), and X-ray crystallography (Pebay-Peyroula et al., 1997). Finally, the atomic resolution of a bR model was achieved (Luecke et al., 1999a). The main technique to study intermediates along the photocycle used to be cryo trapping, including both light illumination of crystals at room temperature followed by rapid freezing and illumination at elevated cryo temperatures. The 13-cis retinal and its associated H-bond network have been observed in M state with extensive conformational changes in the anchor helix G (Luecke et al., 1999b), FG loop, EC half of helix C (Takeda et al., 2004), and an enlarged CP pocket (Sass et al., 2000). Numerous attempts have been made to capture intermediates other than M with inconsistent results (Wickstrand et al., 2015).

A new phase began with time-resolved serial crystallography conducted at X-ray free electron lasers (XFELs). The ultrashort X-ray laser pulses open the opportunity to capture transient structural species in the photocycle as short-lived as fs. It is equally important that serial crystallography enables photo triggering and data collection at room temperature. Authentic signals of conformational changes of greater amplitudes are expected at room temperature compared to cryo trapping. Several international consortiums carried out large operations and accumulated abundant time points along the photocycle that spans more than 13 decades of time. Judged only from the extensiveness of the reported signals, time-resolved XFEL data at room temperature unfortunately do not surpass those captured by cryo trapping, which hints at much needed improvements in experimental protocols and data analysis methods. Nogly et al. captured retinal isomerization to 13-cis at 10 ps (Nogly et al., 2018). More importantly, they observed that the SB water moves before the isomerization and the SB itself has already displaced at the earliest time point of 49-406 fs, which is the key contribution to this analysis. Kovacs et al. contributed datasets at many short time delays (Kovacs et al., 2019). Nango et al. found an ordered water in a newly established H-bond network involving the SB in the 13-cis retinal pointing to the CP on ns-ms time scale, which led to their conclusion of the proton path (Nango et al., 2016). These are three major sources of data analyzed in this study (Table S1). Several synchrotron datasets at ms delays also contribute to this analysis (Weinert et al., 2019).

Structural heterogeneity is the common difficulty to both cryo trapping and time-resolved serial crystallography at room temperature. To what extend a specific species can be enriched in crystals depends on the reaction kinetics under a condition of illumination, such as wavelength and temperature. A more stable species K or M can reach a higher fractional concentration at a specific time point due to a greater ratio between the rates going into and exiting from that species. Others will be populated poorly because of their transient nature. This structural heterogeneity causes the practical difficulties in the interpretation of electron density maps and the refinement of these intermediate structures (Ren et al., 2013). An assumption in nearly all previous studies has been that each dataset, at a cryo temperature or at a time delay, is derived from a mixture of a single photoinduced species and the ground state. Therefore, the difference map reveals a pure intermediate structure. This assumption leads to the more time points the more overinterpretation rather than the more overdetermination. Previous studies using cryo trapping and time-resolved crystallography could not evaluate clear electron density maps of pure intermediate species without a proper deconvolution of heterogeneous species. Because none of the experimental conditions at a cryo temperature or a time point can guarantee an experimental map that does not involve heterogeneous mixture (Ren et al., 2013; Yang et al., 2011). This work is yet another case study to test our general strategy of dynamic crystallography, that is, from the outset every observation at a time point or a temperature setting is treated as a mixture of unknown number of structural species with unknown populations (Methods). The structures of all intermediate species are also unknown except the ground state. The analytical protocol is responsible for a reliable structural interpretation by overdetermination of these unknowns from consistent observations (Ren, 2019; Ren et al., 2013; Yang et al., 2011). Inconsistent observations are identified and isolated.

Mechanism

Understanding the mechanism of proton pumping uphill against gradient has been centered on two entangled aspects: Where are the proton uptake and release pathways? How does the retinal photoisomerization adjust the chemical groups’ ability to hold proton along these pathways? The ability of a chemical group to hold a proton is measured by its value of pK_a, where p stands for ‑log₁₀ function and K_a is the acid dissociation constant, one form of the equilibrium constant of a chemical reaction. It is clear that a proton previously retained by the SB is accepted by the carboxylate group of Asp85 in helix C and eventually released to the EC medium. Each of Arg82, Asp85, 212, Glu194, 204, and some waters could play a role (Balashov et al., 1997; Govindjee et al., 1996; Richter et al., 1996). However, the sequence of events during this proton conductance is unclear thus often mistakenly inferred.

At the resting state of bR, the SB holds a proton tightly with a pK_a of 13.3 pointing toward the EC channel (Druckmann et al., 1982; Sheves et al., 1986). The nearby proton acceptor Asp85 bridged to the SB by a water stays quite acidic with its pK_a spanning 2-3 range (Balashov et al., 1996). That water, often numbered as 402, has been identified as the centerpiece of the mechanism (Wickstrand et al., 2015). Therefore, the SB proton is associated with both N and O simultaneously in N_z:H⁺:OH₂ with both interactions much weaker than an ordinary single bond (Fig. 2c). One of the competing hypotheses is willing to consider that the proton is first brought to the CP side by the SB isomerization to 13-cis, and then conducted through Thr89 and a newly found water other than Wat402 on the CP side, and finally reaches Asp85 (Nango et al., 2016). The difficulty encountered by this hypothesis is the rollercoasting pK_a values that the proton has to go through. The other competing hypothesis relies on a H-bond network long after photoisomerization but largely similar to that in the resting state to translocate the proton on the SB. The H-bond from the SB to Wat402 has to be reconciled with two double bonds C₁₃=C₁₄ and C₁₅=N_z, both highly twisted away from trans and cis configurations to near 90°, until a successful proton translocation to Asp85 (Lanyi and Schobert, 2007). This interpretation of these highly twisted double bonds is a direct consequence of the inability to unscramble a mixed observation of multiple conformations.

Despite intense studies, fundamental questions on the operating mechanism of this proton pump remain puzzling and some unanswered. Q1) How does the protonated SB with a pK_a of 13.3 transfer its proton to the acidic acceptors and when? Q2) Which molecular event, the isomerization, or another event, switches the accessibility of the SB from EC to CP and how does the SB avoid reprotonation on the wrong side? Q3) How are protons conducted > 15 Å through the rollercoasting pK_a values and released into the EC medium from the SB of a high pK_a through aspartic acids of low pK_a, arginine (strictly speaking, its guanidinium ion) and tyrosines of high pK_a, and glutamic acids of low pK_a again? Q4) How is a gradient-driven proton backflow prevented in the resting state and during the pumping motions? No convincing evidence can directly demonstrate a photoinduced reversal of the drastically different proton holding abilities along the EC half channel to facilitate a spontaneous proton conductance that would require an ascending order of pK_a’s. The fundamental flaw in the previous line of thinking is multiple equilibrium steps driven by proton affinities as the values of pK_a describe. A proton is spontaneously transferred from one chemical group with a less proton affinity, that is, smaller pK_a, to another with a greater affinity, that is, larger pK_a (Jardetzky, 1966; Stoeckenius et al., 1979). Such proton conductance was presumed to be accomplished by the means of abundant thermal events of protonation and deprotonation, that is, equilibrium. If a slope of affinity does not satisfy the directional flow of protons, it has been commonly assumed that a photoinduced reversal of proton affinity must have occurred during the photocycle (Stoeckenius, 1999). This study shows that equilibrium is not how the light-driven proton pump bR works, and the directional proton conductance is not driven by increasing affinities but by a concentration gradient of protons.

Here the ultrafast molecular events revealed from the serial crystallographic datasets demonstrate that the photochemical reaction of bR transfers a proton held by the SB to form a strong acid that barely has any ability to hold a proton. However, this proton transfer is not achieved by equilibrium therefore not governed by pK_a’s. Instead, before the isomerization occurs, this proton transfer takes place due to the SB displacement within ~30 fs in a single molecular event. The proton’s inertia prevents it from accelerating as fast as the SB under the same physics of the tablecloth trick (Q1). Rapid photoisomerization flips the already deprotonated SB at 500 fs, thus protects the SB from being reprotonated on the wrong side (Q2). Proton conductance follows a descending order of the proton concentration gradient established in the EC half channel (Q3). A built-in seal constructed by an irregular helix reacts to the isomerization and ensures no proton leakage back to the CP channel during the motions of proton pumping (Q4). The inner EC channel is strictly surrounded by chemical groups of high pK_a’s so that protons can only flow out but cannot flow back in even during dark (Q4). See Supplementary Information (SI) for coherent answers to these questions.

A total of 42 datasets and 36 time points analyzed in this study are divided into two groups: 18 short delays up to 10 ps and 18 long delays ranging from ns to ms, which unfortunately leaves a gap longer than three decades not surveyed (Fig. 1 and Table S1). Difference Fourier maps among these time points and with respect to their corresponding dark datasets are calculated according to protocols previously described (Methods). Singular value decomposition (SVD) of difference maps and the subsequent Ren rotation in a multi-dimensional Euclidean space established by SVD (Ren, 2016, 2019, 2021) are performed separately to 126 difference maps of the short delays and 101 maps of the long delays (Methods). This method of “decomposition and deconvolution” results in a clean separation of electron density changes due to coexisting photoexcited species mixed in the observed datasets. The main findings are summarized in a Gantt chart (Fig. 1). Eight intermediate structures along the photocycle, now isolated from one another, are refined against reconstituted structure factor amplitudes (Methods; Table S2) (Ren, 2021). The assignments of the previously identified intermediates I to M to these refined structures are largely based on the time stamps of the observed signals. No absorption signatures are directly associated with the X-ray data.

Intermediates I’, I, and Schiff base deprotonation

Three decomposed map components U₁₀, U₁₄, and U₁₇ of the short delays contain extraordinary structural signals in terms of their extensiveness and quality (Ren, 2021). These signals originate exclusively from a few time points of Nogly et al., too few to fit the time dependency with exponentials. Instead, a spline fitting through these time points estimates the coefficients c₁₀, c₁₄, and c₁₇ in the linear combination of c₁₀U₁₀ + c₁₄U₁₄ + c₁₇U₁₇ for the early states I, J, and their respective precursors I’, J’ (Ren, 2021). The precursor prior to I state is located on the spline trajectory from the origin, that is, the ground state bR at the time point of 0- before the photon absorption, to the first time point of 49-406 fs (PDB entry 6g7i). It would be appropriate to name this location on the trajectory I’ as a precursor leading to I state judged only by the time point at ~30 fs.

The all-trans retinal in bR is largely flat except C₁₅ (Fig. 2b 2^nd panel). However, two single bonds of Lys216 are highly twisted to near 90° (Fig. 2b 4^th panel), which forms a corner at C_e that deviates from the flat plane of the all-trans retinal, protrudes inboard, and makes a van der Waals contact at 3.4 Å with Thr89 in helix C (Fig. 2b 2^nd panel). This contact is identified in this study as a seal between the extracellular (EC) and cytoplasmic (CP) half channels. The retinal in I’ remains in near perfect all-trans configuration, including the Schiff base (SB) double bond C₁₅=N_z (Fig. S2), while it is creased into an S-shape in an expanded retinal binding pocket together with other features revealing the isomerization sampling (Ren, 2021). The slit between Thr89 and the SB increases to 4.3 Å that may break the seal between two half channels, which is inconsequential as argued below. The C₂₀ methyl group swings 1.1 Å to the outboard direction, a motion previously known but at much later time. These motions are rotations around the long axis of the polyene chain instead of translations (Fig. 2b bottom panel). It is important that the displaced Wat402, now a hydronium ion H₃O⁺ (see below), remains H-bonded to both Asp residues in I’. However, its association with the SB increases to 3.3 Å that barely qualifies as a H-bond.

Due to the availability of the time stamp, a conformational change captured in a time-resolved experiment can be converted to the velocity of an atomic displacement that would further hint the acceleration and force required to achieve the observed conformation changes at the time of the measurement. It can be shown that a force > 500 pN is required to keep the proton accelerating as fast as N_z that has been displaced by 0.7 Å within 30 fs. A force of this magnitude could unfold a-helices or even an entire protein (Su and Purohit, 2009; Takahashi et al., 2018). Accelerating the proton with the SB is not achievable given the charge on the proton and its H-bond association with Wat402. Compared to the regular single bond N-H in an amine group at a pK_a of 40, the coordination bond N_z:H⁺ in the protonated SB at its pK_a of 13.3 is much weaker. In addition, a proton acceleration with the SB would have to break its interaction with Wat402, nearly as costly as to break the coordination bond N_z:H⁺ (Fig. 2c). Therefore, which of the two weak interactions N_z:H⁺:O402 survives the abrupt tare before the photoisomerization is determined by the inertia of the proton. I’ captures the starting moment of a reliable deprotonation from the SB that does not depend on thermal equilibrium. Here the 0.6 Å increase from the SB to Wat402 is attributed to the separation of the proton from the SB rather than from Wat402. Instead of accelerating with the SB, the proton stays with Wat402 to form a hydronium H₃O⁺ due to its inertia (Q1; Figs. 1 inset and 2c). Since several water molecules have been observed in the inner EC channel, possibilities of other proton complexes also exist, such as H₅O₂⁺ (Marx et al., 1999; Mathias and Marx, 2007). The hydronium 402 has been shown possible by magic angle spinning NMR (Friedrich et al., 2020).

This conjecture here, however, is not based on an observation of the scattered X-rays by the proton as the proton does not scatter X-ray. Direct evidence supporting this water cluster with excess protons reside in FTIR observations. Complex kinetic behaviors of several broad band continua at the frequencies > 1700 cm^-1 were recorded in FTIR experiments and interpreted as protonated water clusters (Garczarek et al., 2004, 2005; Lorenz-Fonfria et al., 2017; Wang and El-Sayed, 2001). However, detailed assignments of these continua remain debatable. For example, the removal of one terminal carboxylate near the exit of the EC channel (Fig. S1) in the mutant E204Q certainly could affect proton release. But the observed change in some FTIR continua cannot be easily pinpointed to a water cluster in the outer EC channel (Garczarek et al., 2004), since shutting down one proton release pathway could affect the kinetics of the upstream water cluster in the inner EC channel. Furthermore, the FTIR continua most likely originate from a super-acidic water cluster in the inner EC channel because a well-known proton barrier surrounds the inner EC channel but no proton barrier for the outer EC channel (see below).

The hydronium 402 is likely short-lived. Either Asp85 or 212 “quickly” accepts another proton from the hydronium and returns it back to Wat402 (Fig. 1 inset). The lifetime of hydronium 402 is unclear from X-ray diffraction. Nevertheless, this lifetime does not have to contradict the commonly adopted view that these aspartic acids are protonated later in tens of ms to ms during M formation (Braiman et al., 1988, 1991; Gerwert et al., 1990), given that the pK_a difference between the aspartic acid and hydronium is < 4 pH units. As argued below, a super-acidic water cluster harboring excess protons in the inner EC channel must be established before proton release. Reliable deprotonations from the SB in consecutive photocycles continuously overcharge the inner EC channel. The deprotonation event cannot be directly inferred from the vibrational signatures due to the protonation of the carboxylic proton acceptors in the Asp residues. In other words, the “proton transfer” from the SB to the proton acceptor, as commonly stated in the literature, is not a single event. Instead, it spans ten decades in time.

The retinal in I state remains in near perfect all-trans, including the SB. However, the major difference from the precursor is that the single bond N_z-C_e is now in a perfect syn conformation, and the anchor Lys216 has largely returned to its resting conformation (Figs. 2b 4^th panel and S3). The SB makes a sharp U-turn toward inboard before 500 fs (Fig. S2) and closes the slit with Thr89 to 3.8 Å and ends the breakage in the seal that is too brief to result in a proton leakage (Q3). After the U-turn, the deprotonated SB is pointing toward inboard while Wat402, currently a hydronium, is displaced outboard but remains H-bonded to both Asp85 and 212. The SB and Wat402 are not only beyond a H-bond distance, but also in a bad geometry for proton exchange (Fig. S3d). The accessibility of the SB in I state is already very limited while the SB is reoriented toward inboard despite that the isomerization is yet to occur (Q2). This ultrafast U-turn is how the SB gets rid of the proton by a mechanism of the same physics that governs the tablecloth trick (Q1; Fig. S2). Holding Wat402 in place by Asp85 and 212 symmetrically from inboard and outboard, respectively, is as important as the ultrafast shaking of the SB to its successful deprotonation. See SI for mutant functions when the symmetric holding of Wat402 is disrupted. Here the tablecloth trick is not an analogy to the SB deprotonation. Both are governed by the exact same Newton mechanics: A certain mass, such as a planetary body, a dinning set, or a proton, does not accelerate fast enough unless a sufficient force is exerted on it. The U-turn of the SB marks the peak power, or the maximum rate of enthalpy change dH/dt, of the entire photochemical reaction (see Discussion). The spectrogram derived from the transient absorption or transmittance clearly supports that the photocycle reaches its peak power within the first tens of fs (Kahan et al., 2007; Kobayashi et al., 2001). If a deprotonation is unsuccessful at the peak power of the photocycle, there will be no further opportunity to translocate a proton from a fair base to a decent acid uphill against 11 pH units under equilibrium. The same is true that a proton transfer is energetically impossible from the protonated SB at a pK_a of 13.3 to form a hydronium, a strong acid of a pK_a of ‑1.7, under equilibrium. The deprotonated SB is extremely vulnerable at this moment in I state despite its limited accessibility, as it will be quickly reprotonated if it lingers on in the EC channel to allow an equilibrium. As shown below, the isomerization to a 13-cis retinal prevents such an equilibrium in a futile photocycle. However, some of the photocycles are indeed unsuccessful as its quantum yield indicates if a reprotonation event does occur before the isomerization.

Incidentally, all previous hypotheses on the mechanism of SB deprotonation imply a formation of hydronium at one point or another (Lanyi and Schobert, 2007; Nango et al., 2016). It would require a donor group with a pK_a more negative than ‑1.7 to reliably form a hydronium by the means of equilibrium. None of the previous hypotheses have successfully explained how this is possible.

Intermediates J’, J and traveling water or hydronium 402

Near perfect 13-cis is successfully refined in both structures of J’ at ~700 fs and J at ~20 ps with a contracted retinal binding pocket (Fig. 2b 4^th panel) (Ren, 2021). However, the SB double bond C₁₅=N_z is momentarily distorted from the trans configuration in J’ with a torsion angle of 133°. The trans double bond C₁₅=N_z is promptly restored in J (Fig. 2b 4^th panel). The SB N_z is rotating clockwise looking from the proximal to distal direction in the entire process of the isomerization I’ à I à J’ à J (Fig. 2a). If the deprotonated SB isomerizes to 13-cis at ~500 fs, this photocycle is productive. Otherwise, a photocycle could be wasted if reprotonation occurs prior to the isomerization as it could happen sometimes even in wildtype. The isomerization completes the accessibility switch for the SB from the EC half channel to the CP (Q2).

Due to the 13-cis configuration, C₂₀ methyl group protrudes to a CP direction that is further tilted toward outboard from its original direction. No additional consequence is immediately obvious until the retinal flattens and returns to its original plane at later intermediates. At this moment, Trp182 and the retinal anchor Lys216 stay in their resting positions. Wat402, perhaps currently still a hydronium ion, is well defined in both Js (Ren, 2021). Contrary to the previous conclusion (Wickstrand et al., 2015), this traveling water is never disordered throughout the surveyed portion of the photocycle up to M₂ (see below) despite its large trajectory spanning greater than 3 Å (Fig. 2a). Wat402 is observed with both strong difference electron density and its refined electron density. Its association with Asp85 and 212 remains unwavering throughout the photocycle except one increase to 4.1 Å from Asp212 during J’, the first moment after isomerization. This observation demonstrates that Wat402, a hydronium through a large part of the photocycle, is an integral part of the moving cluster that accepts the proton from the SB. Most likely, this water will remain ordered throughout the rest of the photocycle not yet surveyed.

The main cause to this contradiction is that a light induced change at any given time point consists of a mixture of multiple conformations. As the most straightforward example, the dramatic motion of Wat402 appears to be a disorder in an experimental map prior to deconvolution. An experimental map is a spatial average over the diffracting crystals and a temporal average over the X-ray exposures. In case of serial crystallography, the range of this average is an extensive pool of crystals potentially with diverse individualities (Ren et al., 2018). The only common feature among multiple species of bR intermediates is the negative density on the original location of Wat402 due to its departure. Multiple positive features at various locations are of low occupancies without a proper deconvolution. In this analysis, a linear combination of several SVD components unscrambles the mixture so that each state along the photocycle presents a pure conformational species, a time-independent structure. Is there an experimental solution to this problem of structural heterogeneity? Would a better time resolution improve an experimental difference map so that a traveling water molecule would always be temporally resolved? The answer is both surprisingly and conclusively no, even if, for the sake of argument, an ultimate time resolution of truly zero is achievable by two zero-width impulses of pump and probe (Strictly speaking, each crystal must also be a spatial impulse, that is, zero size.). Because at no time throughout the entire photocycle, the traveling water is synchronized throughout the entire crystal, even if every retinal in the crystal absorbs a visible photon at the exact same time zero. There is no difference between crystal and solution in this aspect, which has been long recognized as Moffat laid the foundation of time-resolved crystallography (Moffat, 1989, 2001). In conclusion, a numerical resolution of structural heterogeneity, as exemplified here, is the last and the only resort (Ren et al., 2013).

Five-decade long-lived K and global change in L

This work continues with another joint analysis of the time-resolved datasets at long delays > 10 ns collected mainly by Nango et al. with contributions from Nogly et al., Kovacs et al., and Weinert et al. (Table S1). These datasets at the long delays are relatively noisier and contain systematic errors from one experiment to another. The analytical procedure of SVD and the subsequent Ren rotation (Ren, 2016, 2019, 2021) is capable of isolating time-resolved signals from these error and noise components. SVD of 101 difference Fourier maps identifies 19 major components (Fig. S4a). Four of them contain outstanding signals of structural changes (Fig. S5). Two others also carry structural signals but without a clear time dependency (Fig. S6). The number of datasets at long delays warrants an exponential fitting to the SVD coefficients (Fig. S7) (Schmidt et al., 2010), which models the reaction scheme of the photocycle better compared to the spline fitting applied to the limited number of short delays above. The time constants obtained from the exponential fitting agree well with the transition times between intermediates K, L, M₁, and M₂ known from spectroscopy. Coefficients for relatively pure states are estimated and the refinement protocol based on reconstituted difference maps again produce atomic coordinates of these states (Methods) (Ren, 2021).

The refined structures of K and L are discussed in SI (Figs. S8 and S9). A flattened 13-cis retinal is finally achieved in L with many global changes. The L state represents the end goal of the global conformational changes due to the retinal isomerization. Additional changes after L are no longer global (see below). C_d-C_e of the anchor moves outboard and could break the seal with Thr89 once again. Last time, a potential breakage occurs in I’ at tens of fs that is too brief for any proton leak (Fig. 2b 2^nd panel). This time, the ns-ms time scale allows the protein to react. It is clearly observed that Thr89 and helix C always follow C_d-C_e outboard in J, K, and L and maintain a distance no more than 3.6 Å because of its tendency to be straightened (Figs. 3f and S10a). This motion was also captured previously in cryo-trapped intermediates (Royant et al., 2000). Therefore, the seal between two half channels is kept intact (Q4). Here the mechanism of these motions of helices is attributed to several irregularities in these helices (Fig. S10), the kinked helix C (Grigorieff et al., 1996), the stretched helix F, and the p helical segment in G (Pebay-Peyroula et al., 1997). Contrary to the previous belief (Luecke et al., 1999a), it is our general conclusion also from studies of other protein mechanisms that irregularities in secondary structures not merely fulfill some structural requirements but offer a wide variety of mechanical properties to achieve the functions of protein nanodevices (Ren et al., 2016; Shin et al., 2019). These motions of the helical segments collectively result in a tighter EC channel and an open CP channel in L (Fig. S11).

Intermediates M₁, M₂ and proton release

The refined structures of M₁ and M₂ are described in SI (Figs. S12 and S13). Thr89 is kept 3.1 Å away from the SB in L, M₁, and M₂ constantly so that the seal is well maintained between two half channels (Q4). Compared to the slightly longer distance between Thr89 and the SB at 3.6 Å in J and K, it is obvious that Thr89 and helix C react to the retreating SB during J and K, but the SB is actively pushing Thr89 and helix C from L to M (Fig. 4c). As discussed below, during pumping activity, drastic proton concentration gradient is present across this seal that divides two half channels. A well-maintained seal is crucial to the efficiency of the pump. Various mutants with substitutions of Thr89 that could result in a proton leak retain ~2/3 of the pumping activity compared to the wildtype (Marti et al., 1991).

The motions over the EC half of the molecule from tens of ms to ms are directly related to the pathway of the proton release (Q3). Residues in the EC half channel are not arranged in a monotonic order of their pK_a’s. Quite the contrary, acidic residues Asp85 and 212 with the smallest pK_a’s are at the end of the half channel next to the SB with the greatest pK_a. Another layer of acidic residues Glu9, 194, and 204 are at the EC surface. It is puzzling that Arg82, Tyr57, and 83 are located between these two acidic layers (Figs. 5 and S1). It had been depicted multiple times by similar illustrations in the past that a high pK_a layer is sandwiched between two acidic layers with low pK_a’s in the EC half channel. Yet, the question remains: How are protons conducted through the proton barrier of the guanidinium group of Arg82 that is already protonated and the phenol hydroxyl groups of the Tyr residues that cannot be protonated anymore (Brown et al., 1993)? No evidence shows that such rollercoasting pK_a values would change in any meaningful way by the light-induced conformations. Therefore, the previous proposal on an affinity-driven proton conductance is fundamentally flawed.

Proton conductance after SB deprotonation through the EC half channel not necessarily operates on the basis of one event of proton release per photocycle. It was previously suggested that a proton pumped in one photocycle could be released in the next or subsequent photocycles (Braiman et al., 1991). However, a flawed common assumption persists that the pumping and releasing of each proton are somehow scheduled in different periods of a photocycle. Here a concentration-driven, instead of affinity-driven, proton conductance is hypothesized. Proton release becomes synchronized to the photocycle only when a super-acidic inner EC channel is established. The first a few photocycles build up a proton concentration at the end of the EC half channel. Multiple groups in the inner EC channel, including various waters, could be all protonated after consecutive photocycles, that is, a puddle of protons establishes a super-acidic inner EC channel as long as the seal of Thr89 is well maintained (Fig. 5c). This is possible because the proton pumping step is a physical process instead of a chemical equilibrium (see above). Although the first a few photocycles are productive, they are not capable of releasing any proton before an established proton concentration gradient. An established super-acidic inner EC channel triggers a concentration-driven proton conductance (Fig. 5d). Proton release from the wildtype bR was observed before proton uptake as if it is coupled with, if not faster than, the protonation of the proton acceptor Asp85 (Braiman et al., 1988, 1991; Gerwert et al., 1990; Zimanyi et al., 1992), which strongly suggests that the newly pumped proton is not the one released to the EC medium in the same photocycle. Here the concentration-driven proton conductance argues that the newly pumped proton causes a proton overflow from the already super-acidic inner EC channel. Therefore, the observed “early release” is actually a very late release during a subsequent photocycle, several cycles after the very proton has been pumped into the inner EC channel (Fig. 5e).

The inner EC channel has been called a proton cage at the active site of bR (Friedrich et al., 2020), which reflects the same fact of the proton barrier (Fig. 5). Here I argue that the super-acidic inner EC channel causes a second protonation of the guanidinium group because of three electron-rich nitrogens (Fig. 5d). The observation to corroborate this speculation is the motions of Arg82, Glu194, and 204 during K à L à M₁ à M₂. The monovalent guanidinium cation during the early photocycle has no salt bridge to Glu194 and 204 until M state. It appears that Asp85 and 212 are continuously protonated by proton pumping thus neutralized in the inner EC channel. Several hydronium ions make the inner EC channel positively charged. The observed kinetics of FTIR continua could explain excess protons harbored by the water cluster in the inner EC channel (Garczarek et al., 2004, 2005; Lorenz-Fonfria et al., 2017; Wang and El-Sayed, 2001). An extra positive charge on the short-lived divalent guanidinium drives itself away from the inner EC channel and toward the negative charged Glu residues in the outer EC channel (Fig. 5a). The EC segments of helices C and G move closer to each other in the refined M structures, where Arg82 is sandwiched in between (SI; Fig. 4). Molecular dynamics simulations found that the orientation of Arg82 is correlated with the charge difference between the inner and outer acids (Ge and Gunner, 2016). The contact between Glu194, 204, and the guanidinium discharges the second extra proton to the outer EC channel and the EC medium (Fig. 5e). A monovalent guanidinium cation is unable to discharge its proton to the carboxylates of the Glu residues due to their low proton affinity. Therefore, Arg82 is a unidirectional proton valve that conducts protons outward, but only under sufficient proton concentration in the inner EC channel. During dark, Arg82 prevents a concentration-driven proton leak back into the cell, because the EC medium cannot become super acidic as long as sufficient water is available. See SI for mutant functions when the proton barrier is breached by substitutes for Arg82.

Under the guidance of Jardetzky’s allostery model of transmembrane pump (Jardetzky, 1966) and the common line of thinking led by Stoeckenius (Stoeckenius et al., 1979), evidences were sought in the past half century to explain how the absorbed photon energy is used to alter the proton affinity landscape along its pathway so that protons can flow in one direction along an ascending order of pK_a values. Neither a hydraulic powered noria or an animal powered sakia in the old time, nor an electric powered fluid pump in the modern days, works under such an operating principle that requires energy for a reconstruction of the landscape. Quite the contrary, the landscape is a given constant and energy is absorbed by the to-be-pumped substance to gain its potential energy, such as water is lifted by a noria or pressurized by an electric pump. The energized substance will then flow freely along the largely constant landscape governed by thermodynamics. In the meanwhile, it is critical to prevent a backflow along a far steeper gradient than the forward-driving gradient. The molecular pump bacteriorhodopsin (bR) for protons works under the exact same principle that fundamentally differs from what Jardetzky and Stoeckenius once imagined. Other transmembrane molecular pumps and transporters likely work the same way at this philosophical level disregarding any molecular detail. Alteration of affinities to the pumped substance cannot be an effective strategy because it is against the chemical nature along the translocation pathway and therefore energetically difficult to achieve. For example, the pK_a values differ more than 11 pH units at the resting state between the protonated SB and the Asp acids, the proton acceptors. That is to say, a photoinduced reduction of one million times to the proton affinity of the SB must occur simultaneously with an increase of one million times to the proton affinity of the carboxylates. Even if these changes in proton affinity are achievable, there will be 10% failed attempts of proton transfers at a prolonged equilibrium. The proton levee, consisting of a few tyrosine residues, main chain carbonyls, and most importantly, Arg82, is strategically constructed around the inner EC channel to prevent proton backflow (Fig. 5). Their high pK_a values are not meant to be changed even though small changes could be detected. In this study, the assumption of an affinity-driven proton conductance is replaced by a mechanism of concentration-driven proton conductance that is not necessarily synchronous to the early photocycles.

All chemical reactions involve energy transfer or conversion, known as enthalpy change DH. This flow of energy in a unit time is the temporal rate of enthalpy change dH/dt or power as a function of time. This function is usually far from a constant. The peak power of a chemical reaction could be orders of magnitude greater than its average power. This is particularly true for each individual molecular event compared to a molecular ensemble. Consider the photochemical reaction of the retinal isomerization in bR. Its peak power is reached at the U-turn of the SB (Figs. 2a and S2), which accomplishes the initial deprotonation of each photocycle. The protein structure of bR prevents a photochemical reaction from reaching its equilibrium as the photoisomerization of the retinal switches the accessibility of the Schiff base to a different reaction space. This is usually unachievable in chemical reactions of small molecules.

Acknowledgements

This work is supported in part by the grant R01EY024363 from National Institutes of Health. The following database and software are used in this work: CCP4 (ccp4.ac.uk), Coot (www2.mrc-lmb.cam.ac.uk/Personal/pemsley/coot), dynamiXÔ (Renz Research, Inc.), gnuplot (gnuplot.info), PDB (rcsb.org), PHENIX (phenix-online.org), PyMOL (pymol.org), Python (python.org), and SciPy (scipy.org).

Competing interests

ZR is the founder of Renz Research, Inc. that currently holds the copyright of the computer software dynamiX^TM.

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Yes there is potential Competing Interest. ZR is the founder of Renz Research, Inc. that currently holds the copyright of the computer software dynamiX.

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Directional proton conductance in bacteriorhodopsin is driven by concentration gradient, not affinity gradient

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