User:Kinkreet/Protein Science/Redox Proteins


 * Bioenergetics and the evolution of life
 * Quantitative Bioenergetics
 * Reduction Potentials


 * Kinetics of electron transfer


 * How nature regulate the electron transfer rate

Bioenergetics
Bioenergetics looks at how organism is able to extract energy from the environment and convert it into a form that drives reactions required for life. Most organisms take high enthalpy, low entropy sources, and metabolize them into low enthalpy, high entropy products, and using the Gibbs free energy derived to drive reactions.

One of the features of living things is that they are never at equilibrium, as only non-equilibrium processes can perform useful work and be controlled. Some see life as the maintenance of non-equilibrium so there is a constant flow and control of things.

Living systems are characterized in a steady state, the state where the flow, or thermodynamic efficiency, is at its maximum. This is the stable state of an open system, which is analogous to the equilibrium state of a closed system. As living organisms are physical, they follow all the laws of thermodynamics. The first law of thermodynamics, that energy is conserved, can be proven quite easily; however, the second law of thermodynamics, that entropy must never decrease, is more difficult to demonstrate.

Oxidation and Reduction reactions
Energy is the capacity to do work, and work is the displacement of a body against an opposing force. Therefore, when you move an electron towards another electron, energy is required to perform this work. The work (the displacement) is then used to generate a different form of energy - potential energy - in the form of repulsion between the electrons, which, in turn, can be used to produce work. The movement of electrons is the basis of reduction and oxidation reactions. Oxidation is the loss of electrons and reduction is the gain of electrons. In a redox reaction, the oxidation state of the components are changed. A redox reaction consists of an oxidation reaction along with a reduction reaction; the reduction of the acceptor must be coupled to the oxidation of the donor. Therefore, a redox reaction can be written as two half-equations, each representing either the oxidation or reduction reaction.

Transfer occurs because different moeities have different affinity for electrons - it will be favourable for an already-electron-rich moiety (a strong reducing agent) to donate its electron to an electron-deficient moiety (a strong oxidizing agent).

These reactions are of significance because most of the free energy derived uses redox reactions to derive them. Redox cycles can be viewed on the molecular level, but it can also be viewed globally, in the carbon and nitrogen cycles.

Reduction potential
Electromotive force (emf), or reduction potential, is the potential energy derived from the difference in affinity for electrons between two species. This energy can be used to accomplish work.

There are similarities between an acid-base reaction and a reduction-oxidation (redox) reaction. A Brønsted base have a tendency to gain a proton; likewise, a reductant have a tendency to gain an electron. In acid-base, we use water at standard condition as the reference, where pKa water =7.0. In redox reactions, we use the standard hydrogen electrode in a electrochemical cell as reference, where E0 (standard reduction potential) = 0.

The standard reduction potential is defined as a relative measure of the affinity of the electron acceptor to accept electrons from the donor. Unlike acid-base reactions, where the proton can only travel in solution and so both the acid and the base must be in the same compartment, in redox reactions, the electron may move through a wire so the two species (donor and acceptor) can be separated into two compartments.

The electron donor (reducing agent, or oxidant) will give out electrons as the electron acceptor (oxidizing agent, or reductant) have a higher affinity for the electron than the donor. The electron will travel though a wire. The potential difference (in volts) is measured. If the reduced half cell is the standard hydrogen electrode, and the oxidized half cell is the species to be studied, and the experiment is carried out under standard conditions of 1M, 1 atmospheric pressure (atm), and at 25°C, then the voltage measured is the standard reduction potential, E0

A species with a positive emf will be reduced by H2 and species with a negative emf will be oxidized by H2. However, in biochemistry, a 1 molar concentration is almost never observed, and so the standard reduction potential becomes impractical; instead pH 7 (10-7M H+) is used as the standard instead. This gives the hydrogen electrode a E0, of -0.42 V, any species with a higher E0, will be reduced, and those with a lower E0, will be oxidized.

E0 can be viewed as 'affinity for electrons'. ΔE0 is the energy derived and can be calculated by E0,acceptor - E0,donor. The Gibbs free energy is calculated using G0, = -nFΔE0,, where F is the Faraday constant (96.5 kJ/mol.V)

However, redox reactions in biochemistry rarely happens at standard conditions. For example, the concentration of the acceptor and donor might not be equal, temperature might not be 25°C, pH is not 7, etc. To calculate the actual reduction potential in non-standard conditions, a modified standard reduction potential is used. This is represented by the Nernst equation:

$$E^,={E_0}^,\frac{RT}{nF}ln{\frac{[e^- acceptor]}{[e^- donor]}}$$

Electron Transfer
Electron transfer is controlled thermodynamically, by regulating the donors and acceptors, as well as the environment, to ultimately control the free energy of transfer and thus determine the rate of transfer. But it is also controlled kinetically, as represented by the Marcus theory.

Electron transfer for chemicals occur as the donor and acceptor collide; this rarely happens in biology because the donor and acceptor are often large proteins or complexes whcih are retarded by the medium they are in. If biological electron transfer relies on these collisions, then reaction rates will be too slow to sustain life. Instead, redox centres are found confined to complexes, and these are transported to close proximity to aid transfer. But still, the electrons must travel through an insulating medium for a few Å.

There are two types of motions involved when electrons transfer, the motion of the electron and the movement of the nuclei. The movement of the electron is almost an instantaneous process, as the electron have virtually no mass. The nuclei move because charge have been redistributed, and it must now move to a new equilibrium where it experience the least repulsion; this might involve a breakage/formation of bonds, it can also make the protein as a whole more/less polar. The movement of the nuclei is much slower, this is due to its relatively enormous mass compared to the electron, and thus larger inertia. The nuclei effectively only moves after the electron have completed its movement, and this movement results in vibrations around its new equilibrium position.

The Frank-Condon principle assumes that electron transfer occurs within a stationary nuclear framework. At the lowest vibrational state of a molecule at its ground state, the nuclei are at their equilibrium locations and experience no net forces from the electrons and other nuclei in the molecule.

When an electron transfer, the charge distribution/density is changed, and there is now a net force on the nuclei from the electrostatic repulsion/attraction of electrons and neighbourning nuclei in this new distribution. Thus, the nuclei will start to vibrate around their new equilibrium position.

Because the original 'stationary' equilibrium position of the nuclei in the initial electronic state is where the nucleus must move from, it becomes a turning point in the vibrational movements in its new vibrational higher electronic state, this transition is known as a vertical transition, and assumes the nuclei do not move.

In quantum mechanics, particles are not viewed as particles in the classical sense, but rather a probability distribution. So instead of saying the nuclei stay at the same location, we say that the nuclei retain their initial dynamic state. In quantum mechanics, the dynamic state is represented by the wave function, and so it can also be said that the nuclear wave function does not change during electronic transition.

Initially, at the ground state, the nucleus have a bell-shaped wave function centred around the equilibrium position. When it is excited to its new electronic state, it will enter into a vibrational state which most resembles its initial state. This vibrational state will have its wave function centred around the new equilibrium position, but one of its peaks will superimpose relatively well with the wave function of the peak of the ground state wave function, because this transition corresponds to the nuclear dynamic state which is least changed.

However, there are many wavefunctions which peaks superimpose well, and so many transitions to different vibrational states are observed, each with different intensities (higher intensities with higher resemblance).

The Frank-Condon factor is a measure of this resemblance. In word, it basically states "the intensity of a vibronic transition is proportional to the square of the overlap integral between the vibrational wavefunctions of the two states that are involved in the transition".

Dynamics of Electron Transfer
Transition state theory Quantum theory

Electrons are transferred by tunnelling though a potential energy barrier.

The rate of electron transfer in a donor-acceptor complex depends on the distance between the electron donor and acceptor, the standard reaction Gibbs energy, and the reorganization energy.

Note
Electronic-Vibrational-Rotational