- Cytoplasm: Aqueous phase of cell containing DNA/most of materials used + transformed in biochemical reactions
- Mitochondria: 'fuel cells' carrying out respiration
- Chloroplasts: 'photocells' harnessing light energy in plants
- Membranes: Lipid bilary (4 nm thick) with hydrophobic interior, hydrophilic exterior and selective channels. Regulate pH, concentration gradient, etc.
Cell compartmentalization requires energy, ions often are pumped against a concentration gradient requiring energy provided through ATP hydrolysis. Electric potential generated across membrane.
- is high in cytoplasm and low outside cell, is low in cytoplasm and high outside cell
- Transport occurs throihg active ion pumps/passive ion channels (size selective)
- enzymes are extracellular (oxidizing environment) to avoid forming an inactive \text{Cu}^
- enzymes are intracellular (reducing environment) to avoid forming inactive \text{Fe}^
- Difference in potential across the membrane
- pool of metal containing species in living organisms. Techniques to study metallome include chromatography, elemental analysis, mass spectrometry, spectroscopy (NMR, EPR, Mössbauer, UV-vis, circular dichromism), X-ray diffraction, Cryo-EM
- Essential elements: C,H,N,O are main constituents of living matter. Most 3d elements are also used.
EPR spectroscopy led to the discovery of Fe-S clusters. EPR plots microwave absorption as a function of magnetic field intensity . In CW EPR, the resonance absorption is plotted as its first derivative. Key features of a CW EPR spectrum are
- Position - -value at a field value in
- Distance between lines - determined by the hyperfine coupling
- Number of lines in the hyperfine pattern - determined by nuclear spin
- Line width - determined by dynamic effects, unresolved superhyperfine, or hyperfine interactions
- Line intensity - determined by multiplicity of hyperfine lines or anisotropy of paramagnetic system
Anisotropic frozen EPR is typically used in bioinorganic chemistry as:
- Molecules are not typically isotropic (anisotropy as a result of powders/frozen solution)
- Intrinsic T1 and T2 relaxation times are too short for EPR signals to be observed at room temperature, so they are slowed by decreasing tempreature.
- Measurements are acquired at cryogenic temperatures
- Frozen solutions (single crystals are rare), asymmetric paramagnetics -> anisotropic EPR
Theory of Continuous Wave EPR
:
- Spin angular momentum: electrons can be regarded as magnetically 'charged' particles with spin angular momentum, whose magnitude is quantized.
- The spin precesses around the direction of the applied magnetic field at the larmor frequency (resonance frequency)
- When the applied microwave frequency matches , the electron comes into resonance/energy is absorbed to promote it to a high energy spin state - 'Electron-Zeeman interaction ' - splitting into non-degenerate states
- which is ~ 2.0023 for a free electron
- the value is quoted at the center of the EPR wave
- Increasing increases the separation of and ,
- Increasing the temperature decreases population difference in line with Botlzmann distribution, decreasing sensitivity
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- Deviation from free electron is due to spin-orbit coupling and mixing of excited and ground-states
- is a SOC constant, is the quantum mechanical coefficient
- For organic molecules is large,
- The EPR line in an axial powder spectrum from which the values are extracted is more intense than the line due to the higher probability of axes aligning with the external field to enact resonance
:
- The presence of a nucleus in a magnetic field results in further splitting of electronic energy levels
- The energy of a nuclear-spin state is given by
The total number of discrete states is given by the sum of electron zeeman and nuclear zeeman levels (number of peaks observed due to hyperfine coupling to nuclear spin)
- Interaction of electron-electron and electron-nuclear dipole moments results in pertrubations in the presence of a magnetic field to the nuclear-Zeeman levels
- This results in the same number of discrete states, but pertrubed
- :
- The energy of the perturbed levels are given by:
Where A is the hyperfine constant
The Nernst equation is given by
- High potentials are oxidizing potentials (reduction reaction dominates), low potentials are reducing potentials (oxidation reaction dominates)
- Reduction potentials can be tuned by alterting ligands coordinated to a metal center
- Donors stabilize high oxidation states (favoring low, reducing potentials)
- Weak donors and pi acceptors + hydrogen bonding stabilize low oxidation states (favoring high, oxidizing potentials)
pH dependence
- For the following redox equation
- The pH dependent Nernst equation can be written as:
- 0.059 (mV) is a factor to convert to , and at 298 K
- pH dependence is per increase in pH unit at 298 K
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Pourbaix diagrams
- pH plotted against reduction potential
- Horizontal line separates species related by electron transfer only
- Vertical line separates species related by hydrogen transfer only
- Sloped lines separate species represented by both (proton-coupled electron transfer)
- Every line can be plotted from the pH dependent Nernst equation
Cyclic voltammograms can be used to determine :
- The redox active analyte is dissolved in solution of electrochemical cell. The cyclic voltammogram is obtained from this system.
- Cyclic voltammogram for a reversible process:(Surface concentrations of and are maintained at the values required by the Nernst equation). Potential is sweeped over time, current is monitored.
- is the peak potential (minimum) at (the peak current) for the oxidized state, from the equilibrium current
- is the peak potential (maximum) at (the peak current) for the reduced state, from the equilibrium current
- A cyclic voltammogram gives 2 EPR signals. The signal drops after reaching the peak current for the reduced/oxidized state.
- Scan rate is given in . Larger scan rates give broader voltammograms
Film electrochemistry: Redox active analyte forms a film on the surface of the working electrode, eliminating the problem of diffusion encountered in solution electrochemistry/enabling study of buried redox centers in proteins
- Proteins diffuse slowly, and CV relies on fast diffusion of the redox-active species to and from the working electrode surface, which can't happen with large proteins in solution
- Blank CV is measured (CV due to non-faradaic background current)
- Potential is not constant with time, as electrons accumulate on film
- The non-turnover 'redox peak' (Faradaic current) is tiny compared to the capacitance (non-faradaic current).
- One- and two- electron transfer processes can be distinguished with film voltammetry
- The turnover rate of each species looks different for one- and two- electron species when plotting against . The first derivative spectrum is the cyclic voltammogram
- The ratio of species in the first graph is calculated as
- In a closed system (experimental) where [\text{Tot.}] = \text{[Ox]} + \text
Catalytic film voltammetry enables study of catalytic enzyme reactions. The working electrode rotates to eliminate limiting substrate/product diffusion.
- The Faradaic and Non-Faradaic current contributions add to give a total current response which is a cyclic voltammogram, with reducing potential occuring from right to left and oxidizing potential from left to right
Potentiomeric titrations
Film electrochemistry cannot always determine of a redox center in a protein for a few reasons:
- Difficulty of protein adsorption and distance of redox center to film surface (slow E.T. processes) are the most important
- of a redox couple can be determined by recording ratio of oxidized and reduced species after equilibriation with electrodes at different applied potentials (changing the potential, like changing the volume of titrant in a titration). The ratio is monitored spectroscopcally
- Protein is in solution with 2 electrodes (Working + Reference) (unlike CV which has Working, Reference and Counter electrode).