Study of electron transfer process between fullerenes and membrane cells of Escherichia coli in the presence of dinitrophenol and dicyclohexylcarbodiimide

1 Introduction

Microorganisms are the basis of all known biological activities, ecosystems and an understanding of the antimicrobial mechanisms handled by nano-materials may enable prevention, regulation or manipulation of associated environmental impacts (Damper and Epstein, 1981; Lyon and Alvarez, 2002). There are basically two forms of metabolic energy in microorganisms. These two types were classified as: energy-rich phosphate bonds such as ATP and electrochemical energy provided by ion (such as proton) gradients. The bacterial cell has a well organized cytoplasm. The correct localization of proteins is essential for the function and particularly for the bacterial cell involved in morphogenetic processes. Maintenance of this order requires energy, and it is not surprising that proteins that form cytoskeleton structures, or the cell division machinery, consume ATP or GTP (Damper and Epstein, 1981; Lyon and Alvarez, 2002; Kanner and Gutnick, 1972; Rryan et al., 1979; Rryan and Van Den Elzen, 1976; Campbell and Kadner, 1980; Taber and Halfenger, 1976; Damper et al., 1980; Mitchell, 1966; Padan et al., 1976; Medeiros et al., 1971; Youmans and Fischer, 1949). The proton motive force (PMF) generated is composed of the trans-membrane chemical proton gradient (ΔpH) and the trans-membrane electric potential (ΔΨ) (Damper and Epstein, 1981; Damper et al., 1980). ATP is made indirectly using the PMF as a source of energy (Damper and Epstein, 1981). Each pair of protons yields one ATP. Proton gradients are also made by bacteria by running ATP syntheses in reverse, and are used to drive flagella (Damper and Epstein, 1981). The proton gradient can be used as intermediate energy storage for heat production and flagella rotation. In addition, it is an inter-convertible form of energy in active transport, electron potential generation, NADPH synthesis, and ATP synthesis/hydrolysis (Damper and Epstein, 1981). Two protons are expelled at each coupling site, generating the proton motive force (PMF) (Damper and Epstein, 1981; Mitchell, 1966; Padan et al., 1976). The trans-membrane electric potential (ΔΨ) in cells can be determined by the distribution of lipophilic ionic molecules between the cells and the suspending medium. The PMF consists of the ΔΨ (in V) and the chemical proton potential (Damper and Epstein, 1981). The electrical potential difference across the membrane of Escherichia coli was measured by the distribution of lipid-soluble cations and correlated with resistance to dihydrostreptomycin as an aminoglycoside, 2,4-DNP and DCC where resistance was presumed due to reduced uptake of the medicine by Damper and Epstein (1981). The reported results were interpreted as support for a model in which the uptake of the polycationic aminoglycosides was electrogenic and therefore driven by ΔΨ (Damper and Epstein, 1981; Damper et al., 1980). The factor common to mutations and conditions which increase resistance was a reduction in ΔΨ (Damper and Epstein, 1981). They have developed a simple model which relates the minimal inhibitory concentration to the rate of aminoglycoside, 2,4-DNP and DCC uptake and the rate of growth (Damper and Epstein, 1981). Damper and Epstein examined a number of conditions that alter ΔΨ in E. coli and found a correlation between ΔΨ and susceptibility to 2,4-dinitrophenol (2,4-DNP) and dicyclohexylcarbodiimide (DCC). Their results indicate that the magnitude of ΔΨ is an important determinant of resistance to 2,4-DNP and DCC (Damper and Epstein, 1981; Damper et al., 1980; Padan et al., 1976; Medeiros et al., 1971; Youmans and Fischer, 1949). Some of the selected strains of E. coli were FRAG-5, TK-1207 and TK-1208 by Damper and Epstein (Damper and Epstein, 1981). The membrane potential (ΔΨ) in E. coli bacteria is generated by extrusion of protons coupled to oxidative reactions in the membrane of cell (Damper and Epstein, 1981). This process generates a potential for protons, or PMF, the term introduced by Mitchell (Damper and Epstein, 1981; Mitchell, 1966). The PMF consists of an electrical component, represented by ΔΨ, and a proton concentration component given by the difference in pH. The interior of bacteria is maintained near pH 7.5, so, there is little difference in pH across the membranes of cells in medium at this pH. Because of that almost all of the PMF is expressed as membrane potential (Damper and Epstein, 1981; Padan et al., 1976).

Various empty carbon fullerenes with different numbers “n” such as C₆₀, C₇₀, C₇₆, C₈₂ and C₈₆, with different chemical, physical and mechanical properties have been obtained (Kroto et al., 1985; Kroto, 1987; Shen, 2007; Kimura et al., 2003; Kavan et al., 2004; Sherigara et al., 2003; Haufler et al., 1990; Xie et al., 1992; Jehoulet et al., 1992; Janda et al., 1998; Touzik et al., 2002; Tsuchiya et al., 2001; Suzuki et al., 1996; Anderson et al., 2000; Cooper, 1998; Taherpour, 2007, 2008a,b, 2009, 2010; Taherpour and Asadi, 2011; Taherpour and Maleki, 2010; Taherpour and Keyvan, 2010; Taherpour and Lajevardi, 2011). The compressive mechanical properties of fullerene molecules C_n (n = 20, 60, 80, and 180) were investigated and discussed in detail using a quantum molecular dynamics (QMD) technique by Shen (Shen, 2007; Taherpour, 2008a). The unique stability of molecular allotropes such as C₆₀ and C₇₀, was demonstrated in 1985 (Kroto et al., 1985; Kroto, 1987; Shen, 2007). After the discovery of C₆₀ peapods by Luzzi and co-workers (Kimura et al., 2003; Smith et al., 1998; Miyake and Saito, 2003; Zhang et al., 2003; Kavan et al., 2004; Sherigara et al., 2003; Haufler et al., 1990; Xie et al., 1992; Jehoulet et al., 1992), the aligned structure of encapsulated molecules, due to the molecule–molecule and/or molecule–SWNT interactions, has been studied as a new type of hybrid material (Sherigara et al., 2003; Haufler et al., 1990). Zhang et al. (Kimura et al., 2003; Smith et al., 1998; Miyake and Saito, 2003; Zhang et al., 2003) reported evidence for the latter interaction measuring the thermal stability of C₆₀ peapods (Kimura et al., 2003; Smith et al., 1998; Miyake and Saito, 2003; Zhang et al., 2003; Kavan et al., 2004; Sherigara et al., 2003; Haufler et al., 1990; Xie et al., 1992). The electrochemical properties of the C₆₀ fullerene have been studied since the early 1990s, when these materials first became available in macroscopic quantities (for a review, see Sherigara et al., 2003; Kavan et al., 2004). In 1990, Haufler et al. (1990) showed that CH₂Cl₂ electrochemically reduces C₆₀ to ${\text{C}}_{60}^{1-}$ and ${\text{C}}_{60}^{2-}$ . In 1992, Echegoyen and co-workers cathodically reduced C₆₀ in six reversible one-electron steps for −0.97 V vs. Fc/Fc⁺ (Fc = ferrocene) (Xie et al., 1992). This fact, along with the inability to perform anodic electrochemistry on fullerenes, matches the electronic structure of fullerenes: the LUMO of C₆₀ can accept up to six electrons to form ${\text{C}}_{60}^{6-}$ , but the position of the HOMO does not allow for hole-doping under the usual reported electrochemical conditions. In 1991, Bard and co-workers first reported on the irreversible electrochemical and structural reorganization of solid fullerenes in acetonitrile (Jehoulet et al., 1992). Dunsch and co-workers (Janda et al., 1998) improved upon the experimental conditions by investigating highly organized C₆₀ films on HOPG, in an aqueous medium. The reduction of these films induces a morphological change; they re-structure into conductive nano-clusters ∼100 nm in diameter (Janda et al., 1998; Touzik et al., 2002).

Graph theory has been a useful tool in assessing the QSAR (quantitative structure–activity relationship) and QSPR (quantitative structure–property relationship). Numerous studies in different areas have used topological indices (TI) (Du et al., 2002; Randic, 1975; Bolboaca and Jantschi, 2007; Slanina et al., 2001; Taherpour and Shafiei, 2005; Taherpour, 2009b–d; Taherpour and Mohammadinasab, 2010). Any extrapolation of results from one compound to other compounds must take into account considerations based on a QSAR study, which mostly depends on how close physical and chemical properties are of the compounds in question. It is important to use effective mathematical methods to make good correlations between several properties of chemicals. In 1993 and 1997, several complex applications of the indices were reported (Taherpour, 2007, 2008a,b, 2009–d, 2010; Taherpour and Asadi, 2011; Taherpour and Maleki, 2010; Taherpour and Keyvan, 2010; Taherpour and Lajevardi, 2011; Du et al., 2002; Randic, 1975; Bolboaca and Jantschi, 2007; Slanina et al., 2001; Taherpour and Shafiei, 2005; Taherpour and Mohammadinasab, 2010; Slanina et al., 1997; Plavsic et al., 1993). The number of carbon atoms in the structures of the fullerenes was utilized here.

This study elaborates upon the electron transfer process between the selected fullerenes C_n (n = 60, 70, 76, 82 and 86) and the membrane cells of E. coli with strains FRAG-5, TK-1207 and TK-1208 in the presence of 2,4-dinitrophenol (2,4-DNP) and dicyclohexylcarbodiimide (DCC). The relationship between the number of carbon atoms and the calculated values of ΔG_et of the fullerenes C_n (n = 60, 70, 76, 82 and 86) with strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-dinitrophenol (2,4-DNP) and dicyclohexylcarbodiimide (DCC) was investigated. The investigation was on the basis of the oxidation potentials (^Ox.E₁) of the fullerenes, as assessed by applying the Rehm–Weller equation (Rehm and Weller, 1970). The results could extend to calculate the free energies of electron transfer (ΔG_et) of the other fullerenes and the selected conditions and strains of E. coli bacteria (see Eqs. (1)–(12), Tables 1–6 and Figs. 1–3).

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Figure 1

The schematic electron transfer process between the strains FRAG-5, TK-1207, TK-1208 and TK-1235 of Escherichia coli bacteria at the predicted experimental conditions and the fullerenes to construct the dipolar complexes.

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Figure 2

The second order polynomial relationship between the number of carbon atoms in the fullerenes (C_n) and the data values on the electron transfer (ΔG_et) between the strain FRAG-5 of Escherichia coli bacteria in the presence of 2,4-DNP (A) and DCC (B) with the fullerenes. The data of ΔG_et were predicted by the Rehm–Weller equation (Eq. (1)).

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Figure 3

The surfaces of the free energies of electron transfer ΔG_et and $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ between the strains of Escherichia coli bacteria in the presence of 2,4-DNP and DCC and the fullerenes.

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In this study, we also calculated the activated free energies $(\mathrm{\Delta }{G}_{\text{et}}^{\#})$ of electron transfer and the maximum wave length of the electron transfers (λ_et), as assessed using the Marcus theory and the equations on the basis of the oxidation potentials of fullerenes C_n (n = 60, 70, 76, 82 and 86) to the predicted data of the electron transfer process between the membranes of the strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-DNP and DCC and the fullerenes (see the equations, tables and figures).

The Marcus theory is based on the traditional Arrhenius equation for the rates of chemical reactions in two ways. First, it provides a formula for the pre-exponential factor in the Arrhenius equation, based on the electronic coupling between the initial and final state of the electron-transfer reaction (i.e., the overlap of the electronic wave functions of the two states). Second, it provides a formula for the activation energy, based on a parameter called the reorganization energy, as well as the Gibbs free energy. The reorganization energy is defined as the energy required reorganizing the structure of the system from initial to final coordinates without changing the electronic state (Marcus, 1965, 1993, 2008; Barbara, 1996; Newton, 1991; Jortner and Freed, 1970; Marcus and Sutin, 1985; Kuzmin, 2000).

Although electrons are commonly described as residing in electron bands in bulk materials and electrons of the orbitals in molecules, the following description will be described in molecular terms. When a photon excites a molecule, an electron in a ground state orbital can be excited to a higher energy orbital. This excited state leaves a vacancy in a ground state orbital that can be filled by an electron donor. An electron is produced in a high-energy orbital and can be donated to an electron acceptor. Photo-induced electron transfer is an electron transfer that occurs when certain photoactive materials interact with light, including semiconductors that can be photo-activated, such as many solar cells, biological systems like those used in photosynthesis, and small molecules with suitable absorptions and redox states (Rehm and Weller, 1970; Marcus, 1965, 1993, 2008; Barbara, 1996; Newton, 1991; Jortner and Freed, 1970; Marcus and Sutin, 1985; Kuzmin, 2000; Atkins, 1998).

It is supposed that the ET-process between the strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-dinitrophenol (2,4-DNP) and dicyclohexylcarbodiimide (DCC) and the fullerenes construct some of the dipolar complexes (between the cell walls of the bacteria and the fullerenes) to perform suitable conditions for bacterial (E. coli) damage. It seems that the discussed electron transfer has also stopped some phenomena related to restriction in bacterial (E. coli) growth by perturbation on the membrane charge of E. coli.

2 Graphing and mathematical method

All mathematical and graphing operations were performed using MATLAB-7.4.0(R2007a) and Microsoft Office Excel-2003 programs. Using the number of carbon atoms contained within the C_n fullerenes, several valuable properties of the fullerenes can be calculated. The values were used to calculate the values ΔG_et, according to the Rehm–Weller equation for the electron transfer process between the strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-dinitrophenol (2,4-DNP) and dicyclohexylcarbodiimide (DCC) and the fullerenes.

Eqs. (1) and (5)–(12) were utilized to calculate the remaining values of ΔG_et for complexes that have yet to be reported in the literature. Some of the other indices were examined, and the best results and equations for extending the physicochemical data were chosen (Taherpour and Shafiei, 2005; Taherpour, 2009b–d; Taherpour and Mohammadinasab, 2010; Plavsic et al., 1993).

The Rehm–Weller equation estimates the free energy change between an electron donor (D) and an acceptor (A) as (Rehm and Weller 1970):

Marcus theory of electron transfer implies rather weak (<0.05 eV) electronic coupling between the initial (locally excited, LE) and final (electron transfer, CT) states and presumes that the transition state is close to the crossing point of the LE and CT terms. The value of the electron transfer rate constant k_et is controlled by $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ , which is a function of the reorganization energy (l/4) and electron transfer driving force ΔG_et:

To calculate the maximum wavelengths (λ_(n); n = 1–2) of the electromagnetic photon for the electron transfer process in the nanostructure complexes, we used Planck’s formula:

3 Results and discussion

Damper and Epstein had reported the membrane potential ΔΨ (in V) of the strains FRAG-5, TK-1207 and TK-1208 and of E. coli bacteria in the presence of 2,4-dinitrophenol (2,4-DNP) and dicyclohexylcarbodiimide (DCC) with its minimum inhibitory concentrations (MIC, μg/ml) (Damper and Epstein, 1981). Their experimental data to apply in this study were extracted directly from the reference (Damper and Epstein, 1981). It was known that the addition of salt increases the resistance of E. coli bacteria to aminoglycosides (dihydrostreptomycin) and inhibits gentamycin uptake (Damper and Epstein, 1981; Campbell and Kadner, 1980; Medeiros et al., 1971; Youmans and Fischer, 1949). Damper and Epstein had found that such resistance was associated with a reduction in ΔΨ in both wild-type and mutant strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria (Damper and Epstein, 1981). They found that in two of the strains (FRAG-5 and TK-1208) 1 M of 2,4-DNP allowed reasonable rates of growth and produced over a half-fold decrease in MIC (1 and 0.5 μg/ml, respectively) and reduction in ΔΨ of −0.129 to −0.133 V (Damper and Epstein, 1981; Lyon and Alvarez, 2002). They have also reported that in two of the strains (TK-1207 and TK-1208) 0.5 M of DCC allowed reasonable rates of growth and produced over a 10-fold increase in MIC (5 and 0.5 μg/ml, respectively) and reduction in ΔΨ of −0.150 to −0.155 V (Damper and Epstein, 1981).

The reported oxidation potentials (^Ox.E) of fullerenes C_n (C₆₀, C₇₀, C₇₆, C₈₂ and C₈₆) are: 1.21, 1.19, 0.81, 0.72 and 0.73 V, respectively (Suzuki et al., 1996).

Table 2 contains the summarized data (ΔG_et, $\mathrm{\Delta }{G}_{\text{et}(n)}^{\#}$ and λ_et) of the electron transfer process between the membranes of the strains FRAG-5, TK-1207, TK-1208 and TK-1235 of E. coli bacteria in NaCl and sucrose medias and in the presence of dihydrostreptomycin and the fullerenes. These values were calculated using the Rehm–Weller equation, Marcus theory and Plank’s formula (Eqs. (1)–(4)). Fig. 1 depicts the schematic electron transfer process between the strains of E. coli bacteria and the fullerenes.

Fig. 2 (graphs A and B) demonstrate the relationships between the number of carbon atoms of fullerenes “n” and the first ΔG_et of the strain FRAG-5 of E. coli bacteria in ordinary conditions and in the presence of 2,4-DNP (with minimum inhibitory concentrations MIC, 0 and 0.5 μg/ml) and the selected fullerenes. Eqs. (5) and (6) correspond to Fig. 2 (graphs A and B). These data were regressed with a second-order polynomial. The R-squared values (R²) for these graphs are 0.9875 and 0.9874, respectively. By using Eqs. (5) and (6), it is possible to calculate the values of ΔG_et for this ET-process. Table 2 contains the calculated values of the free-energies of electron transfer (ΔG_et; in kcal mol^–1) between the strain FRAG-5 of E. coli bacteria in the presence of 2,4-DNP (with minimum inhibitory concentrations MIC, 0 and 0.5 μg/ml) and the fullerenes.

Eqs. (7) and (8) demonstrate the relationships between the number “n” of carbon atoms in the fullerenes and the ΔG_et of the strain TK-1207 of E. coli bacteria in the presence of DCC (with minimum inhibitory concentrations MIC, 0 and 0.5 μg/ml) and the fullerenes (C₆₀, C₇₀, C₇₆, C₈₂ and C₈₆).

Eqs. (9) and (10), and Eqs. (11) and (12), were related to the relationships between the number “n” of carbon atoms in the fullerenes and the first ΔG_et of the strain TK-1208 of E. coli bacteria with the mentioned conditions of Table 1 in the presence of 2,4-DNP and DCC, respectively, and the fullerenes (C₆₀, C₇₀, C₇₆, C₈₂ and C₈₆). The R² values for the equations were good and shown in Table 2.

There was good agreement between the calculated and the predicted values. In lieu of increasing the number of carbons atoms in the fullerene structure, the values of ΔG_et were decreased. It seems that electron transfer increases as the electron population in the C_n (n = 60, 70, 76, 82 and 86) structures increases (see Tables 3–6). These results are related to the HOMO−LUMO gap of the fullerenes and ΔΨ of the strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-DNP and DCC. See the reported conditions in Table 1 by Damper and Epstein (1981). The HOMO−LUMO gap (ΔE_HOMO−LUMO) of the fullerenes decreases by increasing the number of the delocalized electrons in their structures. This phenomenon makes a good condition for the ET-process in bigger fullerenes with more delocalized electrons, because, the oxidation and reduction potentials of the fullerenes are related to the HOMO, LUMO orbitals energy levels as well as the values of the HOMO–LUMO gap. So, the values of ΔG_et and $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ were affected under the HOMO−LUMO gap (ΔE_HOMO−LUMO) of the fullerenes and the ET-process between fullerenes and the ΔΨ of the strains of E. coli bacteria in the presence of the mentioned experimental conditions.

The Marcus theory is currently the dominant theory of electron transfer in chemistry. Marcus theory is so widely accepted because it makes surprising predictions about electron transfer rates that have been nonetheless supported experimentally over the last several decades. The most significant prediction is that the rate of electron transfer will increase as the electron transfer reaction becomes more exergonic, but only to a point (Marcus, 1965, 1993, 2008; Barbara, 1996; Newton, 1991; Jortner and Freed, 1970; Marcus and Sutin, 1985; Kuzmin, 2000).

Electron transfer (ET) is one of the most important chemical processes in nature, playing a central role in many biological, physical and chemical (both organic and inorganic) systems. Solid state electronics depends on the control of the ET in semiconductors, and the new area of molecular electronics depends critically on the understanding and the control of the transfer of electrons in and between molecules and nanostructures. The other reason to study electron transfer is that it is a very simple kind of chemical reaction and in understanding it, one can gain insight into other kinds of chemistry and biochemistry. After all, what is important is the chemistry of the transfer of electrons from one place to another (Marcus, 1965, 1993, 2008; Barbara, 1996; Newton, 1991; Jortner and Freed, 1970; Marcus and Sutin, 1985; Kuzmin, 2000).

ΔG_et is the difference between the reactants on the left and the products on the right, and $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ ; is the activation energy. The reorganization energy is the energy it would take to force the reactants to have the same nuclear configuration as the products without permitting the electron transfer. If the entropy changes are ignored, the free energy becomes energy or potential energy (Marcus, 1965, 1993; 2008; Barbara, 1996; Newton, 1991; Jortner and Freed, 1970; Marcus and Sutin, 1985; Kuzmin, 2000).

In Tables 2–6 we have shown the calculated values of $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ and λ_et by utilizing Eqs. (2) and (3). In accordance with the Marcus theory it is possible to calculate the first $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ and the maximum wave length for the electron transfers (λ_et) for the ET-process between the membranes of the strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-DNP and DCC and the fullerenes, by using Eqs. (2) and (3). Fig. 3 shows the levels of the ΔG_et and $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ in this ET-process. The values of the first $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ for this ET-process, increase with increasing the ΔG_et and the number of carbon atoms in the complexes, while the λ_et, decreases with increasing ΔG_et and $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ for the electron transfer process (see Tables 2–6 and Fig. 3).

By using Eq. (1) (Rehm–Weller equation), Eqs. (2) and (3) (Marcus theory) and Eqs. (5)–(12), the values of ΔG_et, $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ and λ_et were calculated for the electron transfer process between the membranes of the strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-DNP and DCC and the fullerenes. The values of the number of carbon atoms (n) show a good relationship with the values of the free energies of electron transfer ΔG_et, $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ and λ_et. With the appropriate equations, it is possible to calculate the values of ΔG_et (in kcal mol⁻¹), $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ and λ_et, respectively, for the electron transfer process between the membranes of the strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-DNP and DCC and the fullerenes, in close accordance with the results of the Marcus theory.

The results which were discussed here, and the calculated values of ΔG_et, $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ and λ_et corresponding to the ET-process were neither predicted nor reported before. It is supposed that the electron transfer process between the strains of E. coli bacteria with the fullerenes make conditions to restrict the bacterial (E. coli) growth by perturbation in the membrane charges of E. coli.

4 Conclusion

The electron transfer process between the selected strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-DNP and DCC and fullerenes has shown important effects to restrict the bacterial (E. coli) growth by perturbation in the membrane charges of E. coli. The electrochemical data of this electron transfer between the membranes of the selected strains of E. coli bacteria and fullerenes are reported here. These included the free-energies of electron transfer (ΔG_et), calculated using the Rehm–Weller equation and $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ as well as λ_et using equations of the Marcus theory and the Plank’s formula for the ET-process. Using the number of carbon atoms (n), along with the equations of the model, one can derive sound structural relationships between the aforementioned physicochemical data. These equations allow one to calculate ΔG_et, $\mathrm{\Delta }{G}_{\text{et}}^{\#}$ and λ_et for the ET-process between the selected strains FRAG-5, TK-1207 and TK-1208 of E. coli bacteria in the presence of 2,4-DNP and DCC and fullerenes (C₆₀, C₇₀, C₇₆, C₈₂ and C₈₆). It seems that the discussed electron transfer could stop some of the phenomena related to the bacterial (E. coli) growth by perturbation in the membrane charges of E. coli.