Effect of Electrostatic Immobilization on the Electrochemistry of Human and Horse Cytochrome c

Effect of electrostatic immobilization on the electrochemistry of human and horse cytochrome c Jos´ e Luis Olloqui-Sariego a,* , I. M´ arquez a , Alejandra Guerra-Castellano b , M. Molero a , Miguel A. De la Rosa b , Juan Jos´ e Calvente a , Irene Díaz-Moreno b , Rafael Andreu a,* a Departamento de Química Física, Universidad de Sevilla, Profesor García Gonz´ alez, 1, 41012, Sevilla, Spain b Instituto de Investigaciones Químicas, cicCartuja, Universidad de Sevilla – Consejo Superior de Investigaciones Científicas (CSIC), Am´ erico Vespucio 49, 41092, Sevilla, Spain ARTICLE INFO Keywords: Cytochrome c Immobilization strength Heterogeneous electron transfer Electron transfer kinetics Arrhenius parameters Matyushov’s theory ABSTRACT Protein film voltammetry is a sensitive tool to characterize the electron transfer properties of redox proteins in a variety of environments and conformational states. Here, a detailed voltammetric study aimed to explore the effect of electrostatic immobilization on the electron transfer thermodynamics and kinetics of adsorbed humanand horsecytochrome c was carried out. For this purpose, the two cytochromes were adsorbed on thiol monolayers (SAM) with different immobilization strengths and donor–acceptor distances. While thermodynamic redox parameters do not seem to be affected by the monolayer thickness and charge density, electron transfer kinetics are significantly modulated by the protein immobilization strength. Stronger protein–SAM electrostatic interactions result in lower electron transfer rates in both non-adiabatic and friction kinetic regimes. This behavior is further characterized by smaller pre-exponential factors and activation enthalpies in Arrhenius type plots. These kinetic results in the physiologically relevant non-adiabatic electron transfer regime are shown to be consistent with the recently developed Matyushov’s theoretical formulation of protein electron transfer. Moreover, a comparison between the kinetic parameters of the two cytochrome variants supports the hypothesis that differences between their electron transfer rates originate in their structural flexibility to accommodate the conformational changes required to form the precursor complex between cytochrome and a negatively charged redox partner. 1. Introduction Cytochrome c (Cc) is an electron transferring protein, which is mainly found in the intermembrane region of mitochondria. It is an essential component in a large variety of metabolic processes [1–3]. Under homeostatic conditions, this protein behaves as an electron shuttle from cytochrome bc 1 complex to cytochrome c oxidase complex. Additionally, Cc has a number of alternative proapoptotic functions such as a cell death inducer analogous to a cardiolipin oxygenase, activator of the caspase-dependent apoptotic route in the earliest events of apoptosis, as well as other signaling pathways. [4–11] This functional versatility of Cc is intimately related to its high structural flexibility, which modulates its redox properties in different biological scenarios [12–17]. In fact, it has been reported that the Cc environment, including molecular crowding, pH and temperature [18–21], is crucial to its functional activity and stability. Besides, an extensive literature devoted to the characterization of the redox activity of Cc reveals that its functionality is modulated by its interaction with mitochondrial partners [22–28]. Particularly, electrostatic interactions in protein–biomolecule binding events are essential for controlling the redox function of the protein, though the detailed molecular mechanism of this control is not fully understood. Within this context, investigating the electron transfer between immobilized Cc and electrode surfaces, that mimic some aspects of the protein complex environment during its physiological function, is expected to provide valuable information on the influence of protein docking conditions on thermodynamic and kinetic electron transfer parameters. From the pioneering study of Eddowes and Hill on the electrochemical behavior of Horse heart ferricytochrome c at a gold electrode modified with 4,4 ′ -bipyridyl [29], many works have addressed from a fundamental point of view the investigation of electron transfer of a variety of mammalian Cc immobilized onto functionalized electrodes [25,30–42]. However, in sharp contrast with the large number of * Corresponding authors. E-mail addresses: [email protected] (J.L. Olloqui-Sariego), [email protected] (R. Andreu). Contents lists available at ScienceDirect Journal of Electroanalytical Chemistry journal homepage: www.elsevier.com/locate/jelechem https://doi.org/10.1016/j.jelechem.2025.118975 Received 10 December 2024; Received in revised form 20 January 2025; Accepted 24 January 2025 Journal of Electroanalytical Chemistry 981 (2025) 118975 Available online 30 January 2025 1572-6657/© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/bync-nd/4.0/ ). reports dealing with the electrochemical properties of commercially available horseand bovine-Cc, only a few papers have been devoted to the study of the interfacial electron transfer of human-Cc [23,42–44]. A comparison of horseand human-Cc reveals that 90 % of the amino acid sequence is conserved and, specifically, the solvent accessibility and electrostatic charge distribution around the active site are nearly identical, so that only small differences are to be expected in relation to their redox functionality (see Fig. 1). Despite their structural similarities, a recent work has reported significant differences in the dissociation equilibrium constant of their respective Cc: Cytochrome c oxidase (CcO) complexes [46]. In addition, Rodríguez–Rold´ an et al. [47] showed that the complex between humanCc and CcO exhibits a remarkably lower intracomplex electron transfer rate than the analogous complex formed by horse-Cc and CcO. Since both cytochromes display similar kinetics when they are reduced by a series of flavin semiquinones, these authors suggested that the observed differences in electron transfer rate were originated in their interactions with their natural redox partners to form the precursor electron transfer complex. Likewise, Wegerich et al. reported a faster self–exchange electron rate for horse-Cc that they attributed to a more adequate protein–protein interaction in the vicinity of the heme crevice [48]. In addition, a higher value of the interfacial electron transfer rate constant was obtained again for horse-Cc as compared to the human variant (40 s −1 vs. 4 s −1 at 25 ◦C) when they were electrostatically immobilized onto silver electrodes coated with an 11–mercaptoundecanoic acid monolayer [44]. Considering these previous results, we intend to carry out in this work a detailed electrochemical comparison of both cytochromes, by determining their thermodynamic and kinetic electron transfer parameters when they are adsorbed onto negatively charged thiol self- –assembled monolayers (SAMs) of different lengths and charge densities. The interfacial electron transfer rate constants were initially analyzed in terms of the transition between non-adiabatic and frictional kinetic regimes as the electrode-protein distance is decreased. Then, a further dissection into pre-exponential and activation enthalpy terms for each kinetic limit was performed by considering the temperature dependence of the two limiting rate constants. For the two cytochromes, transition from strong to weak immobilization strength is accompanied by an increase of both pre-exponential and activation enthalpy values. In the non-adiabatic regime, this result agrees with the expected contributions of protein-electrode distance oscillations to the electron transfer rate constant in Matyushov’s model [49]. Qualitatively similar results were obtained in the frictional regime, in broad agreement with the expected higher activation energies and slower molecular motions in the presence of a strong immobilization field. Comparison between kinetic parameter values for the two proteins shows that differences tend to disappear as the immobilization strength decreases, therefore suggesting that they originate in the protein-monolayer interaction. 2. Experimental section 2.1. Proteins and chemicals Commercial horse heart Cc was purchased from Sigma Aldrich. Escherichia coli (E. coli) BL21 (DE3) cells were transformed with pBTR1WT plasmid to recombinantly express human Cyt c. Protein expression and purification was carried out as previously described [50]. Briefly, cells were cultured at 30 ◦C and 150 rpm for 20 h in LB medium supplemented with 100 μ g_mL −1 ampicillin. Cells were harvested by centrifugation (10 min at 9 000 g) and suspended in lysis buffer (10 mM Tricine-NaOH, pH 8.5, 0.02 mg mL −1 DNase, 1 mM phenylmethylsulfonyl fluoride and complete protease inhibitor). The resuspended cells were physically ruptured by sonication and were then centrifugated (30 min at 14 000 g and 4 ◦C) for cellular debris discard. The supernatant was loaded in a Nuvia-S (Bio-Rad, Hercules, CA, USA) column for protein purification using a FPLC system (Bio-Rad). The purity of protein samples was tested by UV–Vis spectrophotometry in a Jasco® V-650 spectrophotometer. The A 280 /A 550 ratio of the resulting Cc preparations in the reduced state was about 1.1, as previously reported [50]. Protein concentration was measured by visible spectrophotometry, using a value of 28.92 mM −1 cm −1 for the extinction coefficient of the reduced species at 550 nm. 3–mercaptopropionic acid (MPA), 8–mercaptooctanoic acid (MOA), 11–mercaptoundecanoic (MUA), acid, 3–mercaptopropanol (MPOL), 8–mercaptooctanol (MOOL) and 11–mercaptoundecanol (MUOL) were from Sigma Aldrich, and were used without further purification. Buffer solutions were prepared from anhydrous sodium dihydrogen phosphate, di–sodium hydrogen phosphate, both purchased from Fluka, and Millipore water. 2.2. Electrochemical measurements Linear cyclic voltammograms were recorded with an AUTOLAB PGSTAT-30, from Eco Chemie B.V, in a three-electrode undivided glass cell. The cell was equipped with a Pt bar counter electrode, an Ag/AgCl/ NaCl saturated reference electrode and a gas flow system. The reference electrode was connected to the cell solution via a salt bridge and kept at room temperature (298 ±2 K) in a non-isothermal configuration. Reported potential values were corrected to the normal hydrogen electrode (NHE) potential scale by adding +192 mV to the experimental values. The working electrode was a polycrystalline gold disc with a 0.0314 cm 2 geometric area. All measurements were carried out under argon atmosphere. Working solutions were 20 mM sodium phosphate buffer solutions at pH 7.0. Prior to measurements, the gold surface was successively polished with 0.3 and 0.05 µm alumina and rinsed with Millipore water. Then, the electrode was sonicated in ethanol for 5 min to remove any residual alumina, dried with pure nitrogen, and chemically cleaned with Fig. 1. Ribbon representation of horse-Cc (blue, PDBid 1AAK) [45] and human-Cc (red, PDBid 2N9J [17]). Variations in amino acid composition are highlighted. J.L. Olloqui-Sariego et al. Journal of Electroanalytical Chemistry 981 (2025) 118975 2 a “piranha” solution. Then, the gold surface was functionalized by immersing the electrode into an ethanolic solution of either 1 mM ω -mercaptocarboxylic acid or of a mixture of 1 mM ω -mercaptocarboxylic acid plus 2.5 mM ω –hydroxy–n–alkanethiol, for 1 h at 277 K. Then, protein immobilization was carried out for 90 min at 277 K, by deposition of a 15 µL drop of a 12 µM Cc and 10 mM sodium phosphate buffer pH 7.0 solution onto the modified electrode. Thermodynamic and kinetic aspects of the electron exchange between protein and electrode were assessed from the variation of the voltammetric response with temperature and potential scan rate, respectively. The measuring temperature range was set between 0 ◦C and an upper temperature limit that was dictated by protein thermal desorption. Cyclic voltammograms were recorded at scan rates between 0.02 and 200 V s −1 , and positive feedback for ohmic drop compensation was applied whenever the potential scan rate was higher than 1 V s −1 . Though both double layer capacitance (C dl ) and solution resistance (R s ) vary with experimental conditions, such as nature of the thiol monolayer or temperature, typical values of C dl (for the shorter thiol monolayers) are ~1 μ F and of the uncompensated solution resistance R us ~ 100 Ω, so that the time constant τ =R us C dl to charge the double layer with positive feedback compensation is ~0.1 ms. 3. Results and Discussion 3.1. Electron transfer thermodynamics of immobilized Cc Temperature–variable cyclic voltammetry was employed to determine the entropic and enthalpic changes accompanying the electron exchange of human-Cc and horse-Cc with the electrode. Additionally, we have also assessed the effect of the electrostatic immobilization strength on the redox behavior of both proteins, by comparing their voltammetric response when they are adsorbed on either a highly charged monolayer of ω -mercaptocarboxylic acid, or on a weakly charged monolayer, which includes a mixture of a ω -mercaptocarboxylic acid and a ω –hydroxy–n–alkanethiol. This type of immobilization brings into play the electrostatic interactions that Cc experiences when it comes into contact with some of its physiological partners, such as Cytochrome c 1 , CcO, or the anionic phospholipid cardiolipin [26,27]. Fig. 2 illustrates some typical voltammograms recorded at low scan rate of humanand horse-Cc. They are associated with the heme Fe 3+ / Fe 2+ redox conversion and display a gaussian shape, typical of surfaceconfined redox species. We didn’t observe any additional voltammetric peaks at more negative potentials (see Fig. S1), which suggests the absence of proteins with non-native conformations. At low scan rates, voltammograms are characterized by a small separation of their cathodic and anodic peak potentials (~8 mV) and by full widths at half height of ~92 mV (FWMH) at 25 ◦C, close to the theoretical value (90.6 mV) for a monoelectronic transfer of a population of identical and noninteracting redox centers. By integrating the voltammetric peaks, we obtained protein coverages of ~10 ±4 pmol cm −2 , i. e. somewhat below a protein monolayer [51]. While the FWMH values remain almost constant within the entire range of temperatures, the amount of electroactive protein decreases upon increasing temperature, as expected for a thermally induced protein desorption. The midpoint potential values (E 1/2 ) of immobilized humanand horse-Cc at 25 ◦C and pH 7 (see Table 1) were significantly lower than the value of ~260 mV vs. NHE determined for both proteins in solution [42,52], which is consistent with a relative stabilization of the protein ferric form following its adsorption on a negatively charged thiol monolayer, and it has been observed before for other mammalian, yeast, and bacterial Cc [25,52–55]. Moreover, irrespective of the alkane chain Fig. 2. Cyclic Voltammograms of human-Cc (red and orange lines) and horse Cc (blue and cyan lines) immobilized onto a gold electrode modified with mixed (top panel) or pure (bottom panel) thiol monolayers, whose hydrocarbon chain-length increases from left to right. The supporting electrolyte was a 0.02 M sodium phosphate buffer solution of pH 7, and the voltammograms were recorded at 0.5 V s −1 and 25 ◦C. Table 1 Thermodynamic parameters of the Fe(III)/Fe(II) redox conversion of immobilized humanand horse-Cc. Monolayer Cc E1/2/ mV a ΔS0 rc/ J K −1 mol −1 ΔH0 rc/ kJ mol −1 MPA:MPOL Human 205 ±5–86 ±5–45 ±3 Horse 208 ±5–68 ±5–40 ±3 MPA Human 195 ±5–84 ±5–44 ±3 Horse 201 ±5–73 ±4–41 ±3 MOA:MOOL Human 187 ±5–94 ±7–46 ±6 Horse 195 ±5–83 ±6–44 ±4 MOA Human 180 ±5–88 ±5–44 ±3 Horse 194 ±5–74 ±5–41 ±3 MUA:MUOL Human 180 ±5–98 ±5−46 ±4 Horse 185 ±5–96 ±5−46 ±5 MUA Human 175 ±5–101 ±6−47 ±4 Horse 185 ±5–96 ±6−46 ±5 a Measured at 25 ◦C, pH 7. J.L. Olloqui-Sariego et al. Journal of Electroanalytical Chemistry 981 (2025) 118975 3 length and composition of the thiol monolayer, the E 1/2 values for human-Cc are somewhat lower than those of horse-Cc, indicating a higher sensitivity of human-Cc towards its electrostatic interaction with the monolayer. It is also interesting to note in Table 1 a systematic trend towards more negative E 1/2 values (by ~ 20 mV) as the molecular thickness of the SAM increases. The same observation was made before by Murgida et al. [22] for horse-Cc immobilized on pure mercaptocarboxylic acid SAMs deposited on silver electrodes, which they interpreted quantitatively in terms of the electrostatic model of Smith and White [56]. However, the fact that essentially the same E 1/2 variation (see Fig. S2 in the Supporting Information section) is obtained irrespective of the nature of the metal substrate, or of the ionized charge density in the SAM, suggests an alternative explanation in terms of intrinsic properties of the monolayers, such as a change in their dipolar contribution to the surface potential as the molecular chain-length of the thiol varies. In this regard, it should be noted that the potential of zero charge of a MUA monolayer deposited on Au(1 1 1) was shown to be 50 mV more negative than that of a MPA monolayer at pH 7 [57], and that the observed E 1/2 variation can reasonably be reproduced from the change of alkanethiol dipole moments with molecular chain-length reported previously [58], by assuming an effective permittivity value of 13 inside the monolayers (see the Suporting Information). To obtain the entropy (ΔS0 rc) and enthalpy (ΔH0 rc) reduction changes, the variation of E 1/2 with temperature was determined in a nonisothermal cell configuration, so that [59–61]: ΔS0 rc =nF( ∂ E1/2 ∂ T)P,xi (1) ΔH0 rc = − nF( ∂ (E1/2/T) ∂ (1/T))P,xi (2) where n =1 and F has its usual meaning. Fig. 3 shows the E 1/2 vs T plots for Humanand Horse-Cc, when they are immobilized on either mixed or pure thiol monolayers. In all cases, a linear decrease of E 1/2 with temperature was observed up to ca. 45 ◦C (Fig. 3), which translates into negative ΔS0 rc values (see Table 1). Analogously, the ΔH0 rc values derived from E 1/2 /T vs. T −1 plots (Fig. S3) are also markedly negative (see Table 1), in agreement with the expected stabilization of the ferrous form due to the strong Fe(II)-S(Met) binding and the hydrophobicity of the heme environment that favors its uncharged ferrous state [62–64]. These entropic and enthalpic changes are close to reported values for a variety of Cc in solution [64,65]. A straightforward comparison of the enthalpic and entropic contributions to the standard potential (see Fig. 4) shows the prevalence of the ΔH0 rc term for both cytochromes. It is interesting to note that similar values of ΔH0 rc and ΔS0 rc are obtained for both proteins, though their absolute value tends to be smaller for horse-Cc than for human-Cc as the thiol chain-length in the monolayer becomes shorter and the proteins are located closer to the electrode surface. This trend keeps the enthalpy- –entropy compensation upon varying the thickness of the thiol monolayer, which presumably reflects the solvation rearrangement contribution to the ΔH0 rc and ΔS0 rc values [66]. 3.2. Electron transfer kinetics of immobilized Cc Standard electron transfer rate constants (kS) for the Fe 3+ /Fe 2+ redox conversion were determined from the variation of the voltammetric peak potential separation with scan rate, by using a fitting procedure based on the Butler Volmer formalism with a transfer coefficient of 0.5 [67]. Symmetrical trumpet plots were obtained (see Fig. S4), as expected for a well behaved and quasi-reversible redox couple. The kS values determined at 25 ◦ C upon immobilization of humanand horse-Cc on six thiol monolayers are plotted in Fig. 5 as a function of the number of methylene groups in the molecular backbone of the thiol. Fig. 3. Variation of the midpoint potential E 1/2 with temperature for horse-Cc (blue and cyan symbols) and human-Cc (red and orange symbols) immobilized on gold electrodes modified with either mixed SAMs (right panels) or pure SAMs (left panels). Solid lines are linear least-square fits of the data. The electrolyte solution was 20 mM sodium phosphate at pH 7. Fig. 4. Enthalpic (solid circles) and entropic (open circles) contributions to the reduction of horse-Cc (blue symbols) and human-Cc (red symbols) immobilized onto gold electrodes modified with the indicated mixed SAMs (upper panel) or pure SAMs (lower panel), as a function of the number of methylene groups in the thiol hydrocarbon chain. The electrolyte solution was 20 mM sodium phosphate at pH 7. J.L. Olloqui-Sariego et al. Journal of Electroanalytical Chemistry 981 (2025) 118975 4 Two qualitative trends are easily noticeable. First, the rate constant values of both cytochromes are higher when they are adsorbed on mixed COOH:OH-SAMs rather than on pure COOH-SAMs of the same thickness, as it has been previously described in the case of horse-Cc [68,69]. Second, the electron exchange rate for human-Cc is lower than for horseCc when they are adsorbed on the same monolayer. It may also be observed how both proteins display a characteristic biphasic variation of k S with the monolayer thickness, which has been shown to arise from a transition from a frictional control of the electron transfer rate, at small electrode-protein distances, to a non-adiabatic control at long electrodeprotein distances. Therefore, the observed behavior of kS as a function of the monolayer thickness can be accounted for the following serial combination of frictional and non-adiabatic rate constants [70,71]: 1 kS=1 kFR +1 kNA =1 kFR +1 k0 NA⋅e−γ(d−d0)=1 kFR +1 k0 NA⋅e−1.12⋅nCH2(3) where kFR and kNA are the frictional and non-adiabatic standard rate constants, respectively, d is the electron transfer distance, d0 is a distance of reference, k0 NA is the non-adiabatic standard rate constant at the distance d0, γ is the exponential distance decay tunneling parameter, which takes a value of 1.12 per methylene unit [72,73], and nCH2 is the number of methylene groups in the hydrocarbon chain of the thiol monolayer. Separate values of kFR and k0 NAwere obtained by fitting ln kSvs nCH2 plots to Eq. (3). Keeping in mind that the kFR/k0 NA ratio typically takes small values (~10 −3 ), the nCH2=0 ordinate in Fig. 5 may be identified with the frictional term (ln kFR), while the nCH2=10 ordinate is close to its nonadiabatic counterpart (ln kNA). Then, a visual comparison of the four plots in Fig. 5 shows that (at 25 ◦C) both frictional and non–adiabatic rate constants are larger for horse–Cc than for human–Cc for any given monolayer, and that kinetic differences between the two cytochromes decrease significantly when they are adsorbed on the less charged mixed monolayers. To provide a physical interpretation of the observed kinetic trends, kFR and kNA should be expressed in terms of the microscopic parameters that characterize each kinetic regime. Then, following Matyushov formalism [49], we obtain: kNA =k0 NAe−γ(d−d0)=Δ0e−γ(d−d0) ℏ 4RT π λ √exp(−λ 4RT)(4) kFR =1 τ s 4RT π λ √exp(−λ 4RT)=1 τ 0 s 4RT π λ √exp(−(λ/4)+Es RT )(5) where Δ=Δ0e−γ(d−d0)is the electronic coupling strength between the heme group and the electrode, λ is the reorganization energy, τ s is the Stokes-shift relaxation time, whose dependence on temperature is expressed as a product of a pre-exponential factor ( τ 0 s) and an exponential activation term (exp(Es/RT)) [34], and all other symbols have their usual meaning. It should be noted that a direct assessment of our results in terms of Eqs. (4) and (5) doesn’t allow us to examine the individual behavior of Δ0, λ, τ 0 s and E s . Therefore, we have extended our k s measurements to ten temperatures within the 0–45 ◦C range, so that plots of either ln (k0 NA/ T √)or ln (kFR/ T √)vs.1/T in Fig. 6 lead now to separate estimates of the four kinetic parameters for each protein and immobilization strength, which are collected in Table 2. It may be seen in Table 2 how the values of the two kinetic parameters determined in the non-adiabatic limit, i. e. the reorganization energy (λ) and the electron hopping frequency at nCH2 =0 (Δ0ℏ−1), are higher for the mixed monolayers. Similar results have been reported for horse-Cc adsorbed on pure HS-(CH 2 ) 15 -COOH and mixed HS-(CH 2 ) 15 - COOH/HS-(CH 2 ) 15 -CH 2 OH monolayers [30,32]. The Δ0ℏ−1pre-exponential term depends on the thickness and electronic conductivity of the intervening medium between the electrode and the protein’s redox center, which are not expected to differ significantly for pure and mixed monolayers. Analogously, the close similarity between their ΔH0 rc and ΔS0 rc values in Table 1 does not anticipate differences in solvation or bond energy redox related changes and, therefore, in the reorganization energy λ values for the two types of monolayers. In any case, a detailed assessment of these kinetic results would require a theoretical framework that accounts explicitly for the strength of the interaction between monolayer and protein. 3.3. Rationalization of electron transfer kinetics Recently, Matyushov [49] has developed a theoretical model that accounts for the influence of the oscillatory motion of proteins attached to thiol monolayers on the rate of their electron exchange with the electrode, encompassing both non-adiabatic and frictional kinetic limits. In this model, protein oscillations that take place perpendicularly to the electrode surface are assumed to obey an harmonic potential characterized by a force constant κ. These thermally driven oscillations modify continuously the length of the electron transfer path, leading to the following expression for the non-adiabatic rate constant: k0 NA =Δc 0 ℏ 4RT π λc √exp(γ2RT 2κ)exp(−λc 4RT)(6) Fig. 5. Logarithmic plots of the standard electron transfer rate constant of human-Cc (a) and horse-Cc (b) as a function of the number of methylene groups per thiol molecule in the adsorbed monolayers. Circles correspond to pure COOH SAMs, and triangles to mixed COOH:OH SAMs. Broken lines are least-square fits to Eq. (3), with kFR and k0 NA as fitting parameters. Experiments were carried out in 20 mM sodium phosphate buffer of pH 7 and at 25 ◦C. J.L. Olloqui-Sariego et al. Journal of Electroanalytical Chemistry 981 (2025) 118975 5 where Δc 0 is the electronic coupling at the equilibrium distance of the oscillating protein, corresponding to nCH2=0, and λc is the corrected reorganization energy. It should be noted that the Δ0ℏ−1 and λ values collected in Table 1 were derived according to Eq. (4) from the intercepts and slopes of Fig. 6b plots and, according to Eq. (6), they are expected now to vary with the strength of the protein-monolayer interaction (as measured by κ), since a comparison of Eqs. (4) and (6) shows that (see the Supporting Information section): Δ0 ℏ≈Δc 0 ℏ λ λc √exp(γ2RTav κ)(7a) and λ≈λc+2(γRTav)2 κ(7b) where Tav is the average temperature in the interval we have analyzed. Eqs. (7a) and (7b) predict a decrease of the Δ0/ℏ and λ values upon increasing the protein immobilization strength, until they eventually reach their Δc 0/ℏ and λ c limiting values when Tav/κ→0. These theoretical expectations agree well with the observed trends in the kinetic parameter values collected in Table 2 and in previous studies [30,32]. A quantitative assessment of the theoretical predictions can be performed by noting that, according to Eqs. (4), (6) and (7), changes in κ corresponding to mixed and pure thiol monolayers can be related to those in k0 NA, Δ0ℏ−1 and λ through the following expressions: (Δ0ℏ−1)mixed (Δ0ℏ−1)pure = λmixed λpure √exp(γ2RTav(κ−1 mixed −κ−1 pure)) = λmixed λpure √exp(λmixed −λpure 2RTav )(8a) (k0 NA)mixed (k0 NA)pure = λmixed λpure √exp(1 2γ2RTav(κ−1 mixed −κ−1 pure)) = λmixed λpure √exp((λmixed −λpure) 4RTav )(8b) which show clearly how a weaker interaction of the protein with the mixed monolayer (i. e.κ−1 mixed −κ−1 pure >0) results in higher values of k0 NA, Δ0ℏ−1 and λ. From a quantitative point of view, the observed Δ0ℏ−1 ratios for the two types of monolayers are 7.2 for human-Cc and 3.3 for horse Cc, and the observed k0 NA ratios at 25 ◦C are 2.4 for human-Cc and 1.3 for horse Cc, while the estimated values from the above relationships, with λ mixed −λ pure differences that are within the confidence intervals of the λ values collected in Table 2, lie in the following ranges: (4.3–9.9) for human-Cc and (2.8–6.5) for horse Cc in the case of the Δ0ℏ−1 ratios, and (2.2–3.4) for human-Cc and (1.7–2.7) for horse Cc in the case of the k0 NA ratios, showing a reasonable agreement between the related variations of hopping frequency and reorganization energy. Arrhenius-like plots in Fig. 6a correspond to the frictional kinetic regime and their slopes and intercepts were analyzed according to Eq. (4), after inserting our previous estimates of λ, to obtain the ( τ 0 S)−1 and E S values collected in Table 2. It may be seen that both the preexponential relaxation time and its associated activation energy increase with the strength of the protein/monolayer interaction, as expected in the presence of stronger electrostatic interactions between peptide residues and monolayer. However, relaxation times τ S derived from the ( τ 0 S)−1 and E S values in Table 2 lie in the 0.5–10 μ s range at 298 K and, therefore, are much larger than usual estimates derived either from the longitudinal relaxation time of water (0.5 ps [75]) or from simulations of Cyt c in aqueous solution (800 ps [74]). The above discrepancy between theoretically expected and experimentally observed frictional time scales can be reconciled in Matyushov’s theory by considering the dynamical response of the protein in addition to that of the solvent. While the solvent contribution is characterized by the Stokes-shift relaxation time τ S, the dynamics of the protein motion are described by a characteristic time τ γ for translational diffusion over the tunneling decay length γ −1 . Then, under conditions applicable to the electron exchange between a thiol modified electrode and adsorbed Cyt c [49]: Fig. 6. Logarithmic plots of (a) kFRT−1/2 and (b) k0 NAT−1/2 vs. T−1 for human-Cc (red and orange symbols) and horse-Cc (blue and cyan symbols) adsorbed on pure COOH terminated SAMs (circles) and on mixed COOH:OH terminated SAMs. Broken lines are least-square fits to data. Experiments were carried out in 20 mM sodium phosphate buffer of pH 7. Table 2 Kinetic parameters describing the rate of electron exchange between a thiol modified gold electrode and humanand horse-Cc according to eqs. (4) and (5). Monolayer Cc Δ0ℏ−1/ μ s−1( τ 0 S)−1/ μ s−1λ/eV ES/eV Pure acid Human 150 ±3 7.2 ±0.3 0.29 ± 0.02 0.112 ± 0.007 Pure acid Horse 610 ±14 11.2 ±0.5 0.34 ± 0.02 0.094 ± 0.006 Mixed acid Human 1080 ±30 44 ±2 0.40 ± 0.03 0.097 ± 0.006 Mixed acid Horse 2040 ±50 56 ±3 0.43 ± 0.03 0.086 ± 0.005 J.L. Olloqui-Sariego et al. Journal of Electroanalytical Chemistry 981 (2025) 118975 6 kFR =1 τ 0 γ 4RT π λc √exp(−γ2RT κ)exp(−(λc/4)+Eγ RT )(9) where τ 0 γ is the pre-exponential factor of τ γ, Eγ its activation energy and all other symbols have their previous meaning. Now, an effective frictional time τ eff can be defined as: τ eff = τ γexp(γ2RT κ)=1 γ2Dcyt exp(γ2RT κ)(10) where Dcyt is the diffusion coefficient of Cyt c. Assuming that the diffusion coefficient takes its value in aqueous solution Dcyt ≈10−6 cm 2 s −1 [76], and since γ≈1 A −1 [72,73], the observed 0.5–10 μ s range of relaxation times at 298 K, corresponds to a 3.0 ⋅ 10 −3 –2.2 ⋅ 10 −3 eV Å −2 range of force constant values. Similar values (i.e. 2.5 ⋅ 10 −3 –2.4 ⋅ 10 −3 eV Å −2 ) have been reported for azurin and a Cu A subunit of cytochrome c oxidase physisorbed on pure and mixed alkanethiol monolayers [77], while a somewhat higher value of 3.7 ⋅ 10 −3 eV Å −2 can be derived for horse Cyt c immobilized on alkanethiol monolayers by a pyridine-Fe coordinative ligation [34]. These force constant values have been shown [49] to be consistent with reasonable average protein displacements of ~3 Å. It should be noted again that the ( τ 0 S)−1 and Es values collected in Table 2 were derived according to Eq. (5) from the intercepts and slopes of Fig. 6a plots and, according to Eq. (9), they are expected to vary with the strength of the protein-monolayer interaction, since (see the Supporting Information section): Es≈Eγ−3(γRTav)2 2κ(11a) and 1 τ 0 s≈1 τ 0 γ λ λc √exp(−2γ2RTav κ)≈1 τ 0 γ exp(−2γ2RTav κ)(11b) If τ 0 γ and Eγ are assumed to be independent of the monolayer/protein interaction strength, eq (11a) correctly predicts an increase of Es with κ, but eq (11b) leads to an analogous trend of ( τ 0 S)−1, which is contrary to the observed results in Table 2 and to simple physical expectations [78]. While Δc 0/ℏ and λ c can reasonably be assumed to be independent of κ in the non-adiabatic case, the kinetic parameters τ 0 γ and Eγ are inherently dependent on κ, which limits the usefulness of Eq. (9) to assess the role of the immobilization strength in the frictional limit. As it may be observed in Fig. 6, and in agreement with previous reports [44,48], the electrochemical electron exchange is faster for horse-Cc than for human-Cc under the same immobilization conditions. However, it is interesting to note that the ratio between the values of any given kinetic parameter P (where P stands for Δ0ℏ−1, λ, ( τ 0 S)−1 or Es) for the two proteins (i. e.: P horse / P human ) approaches unity when the molar fraction of carboxylic groups (x acid ) in the monolayer decreases, and the SAM-protein electrostatic interaction becomes negligible, as it is illustrated in Fig. 7. This quantitative trend suggests that the differences in kinetic behavior between the two proteins are originated in their distinct structural response to the electrostatic perturbation brought about by their interaction with the monolayer. A similar conclusion can be reached from the kinetic experiments performed in homogeneous solution by Rodríguez-Rold´ an et al. [47], where the second order rate constant for the electron transfer between a series of flavins and either horse-Cc or human-Cc remained the same (within ~ 30 %) for both proteins, though the first order rate constant for the electron transfer within the precursor complex with Cytochrome c oxidase was four times higher for horse-Cc than for human-Cc. Again, horse-Cc displays faster electron transfer kinetics only after interacting with a negatively charged anchoring site, while their electron transfer kinetics remain essentially the same in the absence of this type of electrostatic perturbation. 4. Conclusions In the present work we have explored the thermodynamics and kinetics of the interfacial electron transfer of human-Cc and horse-Cc adsorbed on a variety of single and binary thiol monolayers. Thermodynamic parameters do not seem to be affected by the monolayer charge density, though redox potentials and reduction entropies become somewhat more positive when the electroactive proteins are immobilized on thinner monolayers and, therefore, are located closer to the electrode surface. Kinetic parameters, on the other hand, offer a much richer behavior. Thus, electron transfer rate constants for both proteins are higher when they are adsorbed on the less charged monolayers, and display a characteristic biphasic behavior as a function of the monolayer thickness, which corresponds to the transition from the frictional to the non-adiabatic kinetic limits. Higher pre-exponential and activation factors are observed in both kinetic regimes upon decreasing the number of carboxylic groups in the monolayer. We have shown that, according to Matyushov’s theory in the non-adiabatic limit, the apparent hopping frequency and reorganization energy derived from Arrhenius-like plots are expected to increase as the protein/monolayer interaction becomes weaker, and that their respective variations are quantitatively related to each other, in good agreement with the experimental results. Analogous results in the frictional limit were interpreted qualitatively in terms of an increase of molecular friction with the strength of the electrostatic interaction between protein and monolayer. When human-Cc and horseCc electron transfer kinetics are compared, the horse variant always displays faster rates but, interestingly, the values of the kinetic parameters of the two proteins approach to each other as the number of carboxylic groups in the monolayer decreases. This result suggests that the origin of the different electron transfer rates observed lies in differences of their structural flexibility to accommodate the conformational changes required to form the precursor complex with a negatively charged redox partner. Fig. 7. Logarithm of the ratio between kinetic parameter values for horse-Cc (P horse ) and human-Cc (P human ) as a function of the mole fraction of carboxylic groups in the monolayer. Parameter values were taken from Table 2, and they correspond to: Δ0/ℏ (red circles), ( τ 0 S)−1 (blue triangles), λ (green squares) and Es (black diamonds). J.L. Olloqui-Sariego et al. Journal of Electroanalytical Chemistry 981 (2025) 118975 7 CRediT authorship contribution statement Jos´ e Luis Olloqui-Sariego: Writing – original draft, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization. I. M´ arquez: Investigation, Data curation, Conceptualization. Alejandra Guerra-Castellano: Investigation, Data curation, Conceptualization. M. Molero: Investigation, Methodology, Data curation. Miguel A. De la Rosa: Visualization, Conceptualization, Funding acquisition. Juan Jos´ e Calvente: Writing – review & editing, Visualization, Validation, Funding acquisition, Conceptualization. Irene Díaz-Moreno: Visualization, Validation, Conceptualization, Writing – review & editing, Funding acquisition. Rafael Andreu: Supervision, Formal analysis, Conceptualization, Visualization, Writing – review & editing. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments Authors thank the financial support by the grants PID2021–126799NB–I00, PID2021-126663NB-I00, funded by MICIU/ AEI/10.13039/501100011033 and by ERDF/EU, TED2021-130191BC42 and RED2022-134120-T funded by MCIU/AEI/10.13039/ 501100011033 and ERDF A way for making Europe, and European Union Next GenerationEU/PRTR, Andalusian Government (BIO-198, US/JUNTA/FEDER; to I.D.-M.) and Ram´ on Areces Foundation (20212024 to I.D.-M.). This publication is part of the grant POSTD.O. C_21_00395, financed by the Junta de Andalucía/CUII and by the ESF+” (for A.G.-C.). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi. org/10.1016/j.jelechem.2025.118975. References [1] G. P´ erez-Mejías, A. Díaz-Quintana, A. Guerra-Castellano, I. Díaz-Moreno, M.A. de la Rosa, Novel insights into the mechanism of electron transfer in mitochondrial cytochrome c, Coord. Chem. Rev. 450 (2022) 214233, https://doi.org/10.1016/j. ccr.2021.214233. [2] D. 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