The proclivity of a quinone to accept an electron, or be reduced, is dependent upon its reduction potential, Eo’, as discussed in 1.1.2. This method of assessing
susceptibility via its reduction potential is applicable to all other chemical compounds, most importantly perhaps, it can be applied to reactive oxygen species (ROS). Furthermore, the ability for a quinone, in this case a semiquinone (SQ.-), to
donate the electron to generate the ROS may also be quantified via the thermodynamic linking of both reduction potentials.
Thermodynamic favourability of the reaction between the SQ.- and molecular oxygen
can be gauged by considering Eo’ for the (Q/ SQ.-) and (O
2/ O2.-), where the Eo’ for (O2/
O2.-) is -180 mV 49. The reaction equilibrium constant can also be calculated using
Equation (2-1). 𝐸0′(𝑂 2/𝑂2.−) − 𝐸0 ′ (𝑄/𝑆𝑄.−) = (𝑅𝑇 𝐹) ln 𝐾𝑒𝑞 . (2-1)
Where R is the universal gas constant (8.314 J/mol K); T is the temperature in Kelvin and Keq is the reaction equilibrium constant.
In essence, according to Equation (2-1), if the Eo’ (Q/ SQ.-) is lower than the Eo’ (O
2/O2.)
then the equilibrium will lie to the right-hand-side favouring O2. Formation. Similarly,
if the Eo’ (Q/ SQ.-) is higher than the Eo’ (O
2/O2.) then the opposite is true, favouring
the reverse reaction, and thereby leaving superoxide formation ultimately thermodynamically unfavourable. However, it is important to recognize that, regardless of which side of equilibrium is favoured, these reactions are reversible and therefore superoxide formation can occur even if the reverse rate constant is higher than the forward. The production of superoxide is then a function of other biological or chemical factors that influence the position of equilibrium, such as detoxification by superoxide dismutase enzymes (SOD) 7.
Reduction potentials for a myriad of quinone compounds have been published, along with their relative forward and reverse rate constants for the formation of superoxide from molecular oxygen, calculated using Equation (2-1) 7. Furthermore, these
reduction potentials are also inextricably linked to the quinone pKa values, as hydroquinones are weak diacids with pKa values typically in the range of 9-11. pKa values are extremely useful and well utilized for describing the electron density on an atom with which a hydrogen bond is formed. This gives the optimum opportunity to consolidate these crucial physicochemical thermodynamic properties into a mathematical framework from which rate constants may be obtained given any reduction potential or pKa value for a quinone containing compound. This model will be denoted the physicochemical thermodynamic quinone model (PTQM) henceforth.
The PTQM accounts for multiple quinone reduction potentials, rate constants for formation and pKa values for different quinone compounds. 12 structurally different quinone compounds were used to construct the PTQM, covering a large reduction potentials (-500 – 100 mV) and rate constants (log 4 – log 10 M s-1). The model
facilitates generation of a rate constant for the formation of superoxide from a semiquinone radical given a reduction potential or pKa, or vice versa by relating the reduction potential of these compounds to their pKa values, and then to the forward and reverse rate constants for superoxide formation. Values for reduction potentials
and pKa values for a group of quinone motif-based compounds, as well as the corresponding rate constants for formation of superoxide from the semiquinone radicals were taken from 7, and used to generate the PTQM. From these values,
activity relationships were established between pKa, reduction potential, superoxide formation and glutathione conjugate formation.
Figure 2-1: Reduction potential – pKa model. Corresponding pKa and reduction potential
values for para-hydroquinone compounds were consolidated into a mathematical framework, allowing computational estimation of a reduction potential from a pKa value should the reduction potential be unavailable. Compounds: a. ubiquionol-1, coenzyme Q- 1; b, tetramethyl-1,4-hydroquinone; c, 2,3,5-trimethyl-1,4-hydroquinone; d, plastoquinol- 1; e, 2,6-dimethyl-1,4-hydroquinone; f, 2-methyl-5-isopropyl-1,4-hydroquinone; g, 2,3- dimethyl-1,4-hydroquinone; h, 2,5- dimethyl-1,4-hydroquinone; i, 2-ethyl-1,4- hydroquinone; j, 1,4-hydroquinone; k, 2-chloro-1,4-hydroquinone; l, 2,6-dichloro-1,4- hydroquinone; m, 2,5-dichloro-1,4-hydroquinone 7.
Figure 2-1 shows the relationship between pKa and reduction potential, illustrating the general trend of decrease in reduction potential results in an increase in pKa. The electron density of a proton is reflected in its associated pKa value, with the greater
the electron density it shares with the atom it forms the hydrogen bond with, the greater the negative chare remaining once removed, i.e. the greater the negative charge, the higher the pKa value. This directly correlates to the ease of reduction of a quinone, as the more negative the reduction potential, the harder it is to reduce.
Figure 2-2: Reduction potential superoxide formation rate constant model. Quinone
reduction potential thermodynamic data was consolidated into a mathematical framework in order to facilitate superoxide rate constant determination for a range of reduction potentials. The models were fitted using data from 7, using the Matlab fitting
tool, allowing ameliorated curved fitting compared to source fit. The responsible parent quinone for the semiquinone radicals: a,1,4-benzoquinone; b, methyl-1,4-benzoquinone; c, 2,3-dimethyl-1,4-benzoquinone; d, 2,5-dimethyl-1,4-benzoquinone; e, 2,6-dimethyl-1,4- benzoquinone; f, duroquinone; g, 2-methyl-1,4-naphthoquinone; h, 2,3-dimethyl-1,4- naphthoquinone; i, anthraquinone; j, Mitomycin; k, Adriamycin; l, AZQ: 2,5-diaziridinyl- 3,6-bis(carbethoxyamino)-1,4-benzoquinone.
Figure 2-2 illustrates the relationship between reduction potential and the subsequent rate constants for superoxide formation, generating an activity relationship. The forward rate constant follows the likelihood of electron donation onto molecular oxygen from the relevant SQ.-, whereby the more negative the
reduction potential, the higher forward the rate constant (kf). A less readily reduced
SQ.- possesses a more negative reduction potential and as such, will seek to rapidly
donate its surplus electron to molecular oxygen if it itself reduced, hence the higher rate constant of formation (kf) of superoxide. The reverse rate (kr) constant follows
the opposite rational, with the more negative the reduction potential, the slower the rate.
The final set of data to consolidate into this framework is the relationship between the reduction potential and the rate constant for the formation of glutathione adducts (Q-GSH) via irreversible Michael addition. Figure 2-3 shows how increases in reduction potential correspond to a linear increase in the formation rate constant. An increase in reduction potential reflects a more readily reducible quinone, which in turn results in increased proclivity for radical species formation. As such, the rate at which GSH adducts form, is concentration dependent based upon mass action, and therefore will also increase. Figure 2-1,Figure 2-2 and Figure 2-3 form the primary construct of the PTQM model, from which, information regarding reduction potential, pKa, superoxide formation rate constants and glutathione reaction rate constants may be obtained.
Figure 2-3: Reduction potential GSH adduct rate constant model. Quinone reduction
potential thermodynamic data was consolidated into a mathematical framework in order to facilitate superoxide rate constant determination for a range of reduction potentials. The models was fitted using data from 7, using the Matlab fitting tool, allowing ameliorated
curved fitting compared to source fit. The responsible parent quinone for the semiquinone radicals: a, 1,4-benzoquinone; b, methyl-1,4-benzoquinone; c, 2,6-dimethyl-1,4- benzoquinone; d, 2,5-dimethyl-1,4-benzoquinone; e, 2,3,5-trimethyl-1,4-benzoquinone.
The three models relating reduction potential to superoxide and glutathione adduct formation were then housed in a single model fronted with a graphical user interface (GUI) (Figure 2.4). This facilitates open access for all users, particularly those who are unfamiliar with fitting algorithms or coding. The PTQM GUI works by entering a reduction potential followed by clicking “Generate”, which displays the corresponding forward and reverse rate constants (kf and kr) for semiquinone
induced superoxide formation and the rate constant for glutathione adduct formation. If the reduction potential for the quinone is unknown, then a pKa value may be entered followed by clicking “Generate” once to generate the reduction potential, then clicking “Generate” a second time to display the rate constants.
Figure 2-4: Physicochemical thermodynamic quinone model GUI. Users are able to input a
reduction potential or pKa value to obtain specific rate constants for quinone based redox cycling.