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How does cytochrome c carry electrons?

Answer
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Hint: Cytochromes are redox-active proteins containing a heme group with a central Fe atom at its core, as a cofactor. They are mainly involved in electron transport chain and redox catalysis and are classified according to the type of heme and its mode of binding. Four types are recognized by the International Union of Biochemistry and Molecular Biology (IUBMB): cytochromes a, cytochromes b, cytochromes c and cytochrome d.

Complete solution:
Cytochrome c is a water soluble protein which transports electrons; it is loosely associated with the mitochondrial inner membrane.
It contains a heme iron metal center that is essential to its function in the ETC. The ironmetal center in cytochrome c has an octahedral geometry and is coordinated by six ligands - 4 nitrogen atoms of the porphyrin ring, a nitrogen atom of a histidine imidazole ring and a Sulphur atom of a methionine residue.

All of the 6 electron-rich ligands stabilize the positively charged iron ion. The rigid, square planar porphyrin ring in cytochrome c is considered a tetradentate chelating ligand because the four nitrogen atoms of the porphyrin ring bind to the central iron and form a stable organometallic complex.

In the ETC an electron is transferred from Complex III to the heme $Fe^{3+}$ of oxidized cytochrome c which reduces it to $Fe^{2+}$. Now, Cytochrome c releases the electron to Complex IV. The iron center then returns to the $Fe^{3+}$ oxidized state. Even though the heme iron metal center changes oxidation state during the electron transport, cytochrome c always adopts the octahedral, low spin geometry irrespective of the oxidation state on the iron as this geometry is preferred based on
Ligand Field Stabilization Energy (LFSE). LFSE is the total energy of the d-electrons of a metal complex relative to the theoretical midpoint energy and a more negative LFSE value is indicative of a more stable complex.

When comparing the electron splitting diagrams and LFSE values for both low spin $Fe^{3+}$ and high spin $Fe^{3+}$, the more negative LFSE values for low spin iron compared to High spin iron indicates that this low spin conformation is more energetically favorable.

This is also the case when comparing low and high spin $Fe^{2+}$. Therefore, the heme iron metal center of cytochrome c will always adopt the low spin octahedral geometry, regardless of the oxidation state on the iron.

Note:
Cytochrome c is an essential part of the electron transport chain as without it the
ATP would not be produced and ATP works as fuel of life. Cytochrome c is only able to function in this capacity due to its heme iron metal center that undergoes redox reactions to transport electrons. Various researches have shown that this electron transfer will not only help to understand how cells function but also have applications in areas such as electrochemistry and biosensor technology.