Bioenergetics

1

• Bioenergetics
• ATP is the basic energy currency'' of the
  cell.
• - Produced by energy-transducing membrane
  proteins.
• Protons are first pumped across a cell membrane.
• ATP-synthase harvests the proton concentration
  gradient to generate ATP from ADP Pi.
• ATP pool able to perform work since its
  maintained away from
• equilibrium.

2

• Enthalpy
• The first law of thermodynamics says total
  energy conserved
• D U q - w
• ie. the change in energy of a system is the heat
  absorbed by the system from the surroundings, q,
  minus the work done by the system on the
  surroundings, w.
• Enthalpy defined as
• H U PV
• Convenient for biology since, under constant
  pressure (DP 0),
• D H is measured as the heat produced or
  absorbed
• D H D U P D V q - w P D V q
• since at constant pressure w P D V.

3

• Entropy
• Thermodynamics describes the bulk behavior of
  reversible systems.
• - Key concepts enthalphy Gibbs free energy
  entropy.
• Entropy
• S kB ln W
  (1)
• where kB is Boltzman's constant and W is the
  number of ways of arranging a system.
• Systems adopt their most probably arrangement.
• Corresponds to those with maximum entropy.
• Example Ten gas molecules in a bulb with a
  barrier
• One way of having all ten in left bulb.
• Ten ways of having nine in left and one in
  right.
• And n!/l!(n-l)! 10!/(5! 5!) 252 ways
  of having five in left and five in right.

4

• Gibbs Free Energy
• Gibbs free energy defined as
• G H - TS
• T is the temperature, and S the entropy.
• For constant temperature and pressure (D T 0,
  D P 0)
• D G D H T D S
• D H is the changes in enthalpy (ie. heat
  exchanged).
• Closed system implies constant temperature and
  pressure.
• Typical experimental conditions.
• Reactions are spontaneous if D G lt 0.

5
Reversible reactions The reaction ATP ? ADP
Pi can be considered as two simultaneous
reactions The consumption of ATP ATP ? ADP
Pi with a rate constant k1 - d/dt
ATP d/dt ADP k1 ATP
(2) in competition with the production of
ATP ADP Pi ? ATP with a rate constant k2
d/dt ATP k2
ADP Pi (3)
6

• When at equilibrium (from Eqs. (2) and (3))
• d/dt ATP k2 ADP Pi - k1 ATP 0
• ie. rate of ATP production rate of ATP
  consumption hence
• ADP Pi / ATP k1/k2 KATP
  hydrolysis (4)
• which defines the equilibrium constant for ATP
  hydrolysis.
• The experimentally measured value is
• KATP hydrolysis 105 M
• In the presence of 10-2 M Pi and 10 -3 M ADP
  (approximate values for the mitochondrial
  cytoplasm)
• ATP 1/K ATP hydrolysis ADP Pi
• 1/105 10-3 10-2 M 10-10 M
• only one molecule of ATP per ten million of ADP
  if allowed to run down to equilibrium.

7

• Gibbs free energy in solution
• For the reaction
• A ? B C
• define the mass-action ratio
• G B C / A
  (5)
• such that G Kequil at equilibrium.
• From thermodynamics (ie. without proof), the
  change in Gibbs free energy for a reaction in
  solution is
• D G - 2.3 R
  T log10 Kequil / G (6)
• D G0 2.3 R T log10 G
• R the gas constant (R 8.3 J/(mol K)).
• T temperature in Kelvin (K).
• G0' - 2.3 R T log10 Kequil and ' indicates pH 7
  (bio. convention).
• At equilibrium G Kequil so DG 0.
• A half-proof'' of how Eq. (6) is derived from
  Eq. (1) is given as an appendix to Chapter 3 of
  Biochemistry, Voet and Voet.

8

• Example ATP hydrolysis reaction
• Use Eq. (5) to determine D G as G is displaced
  from equilibrium.
• G ADP Pi / ATP
• and
• KATP hydrolysis 105 M
• Suppose in the cell Pi 10-2 M and is (more or
  less) constant.

9

• In healthy cells ATP 10-2 M and ADP 10-5
  M, such that
• G 10-5 10-2 / 10-2 10-5 10-10 KATP
  hydrolysis
• Hence
• D G -2.3 R T log10 KATP hydrolysis / G
• -2.3 8.3 J/(mol K) 298 K 10 - 57 kJ/mol
• The reaction is so displaced from equilibrium
  that in consuming one mol of ATP 57 kJ of work
  can be performed.

10

• The standard free energy (25oC pH 7) of
  phosphate hydrolysis of ATP to ADP is DG0 '
  -30.5 kJ/mol.
• Free energy of a pure elements in their standard
  state (25oC, 1 atm) and most stable form (eg. O2)
  is defined as zero.
• Free energy of formation of another substance is
  the change in free energy accompanying the
  formation of one mol of that substance under
  standard conditions.
• - DG 0 ' is the difference between the free
  energies of formation of ATP versus ATD and Pi
  under '' standard'' conditions.
• Since 57 kJ/mol gt 30.5 kJ/mol is there a
  contradiction?
• - It is the displacement of G from equilibrium
  which gives the cell its ability to do work!
• When ATP is displaced 10 orders of magnitude
  from equilibrium it can do more work than that
  associated with phosphate bond hydrolysis under
  standard conditions.
• Entropy the driving force for gas molecules to be
  in both bulbs
• An entropy advantage of having a mixture of ATP,
  ADP, AMP etc. ie. more disordered'' if not a
  pure species.

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• Compare with
• DG0 2.3 R T log10 Kequil
• 2.3 8.3 J/(mol K) 298 K 5
• 28 kJ/mol.
• Difference between 30.5 kJ/mol and 28 kJ/mol is
  round-off error (eg. Kequil accurate to only one
  decimal place).

12

• Measuring the Gibbs free energy across a membrane
• The Gibbs free energy across a membrane is given
  by
• D G - F Dy - 2.3 RT log10 (HP /
  HN) (7)
• - F is Faraday's constant 0.097 kJ/(mol mV).
• - Dy electric potential difference either side
  of the membrane.
• - HP proton concentration on the positive
  side.
• - HN proton concentration on the negative
  side.
• The first term is the energy of the stored
  electrostatic potential (ie. like a capacitor).
• The second term Gibbs free energy for the
  reaction HP ? HN
• ie. the pH gradient is a displacement from
  equilibrium (Eq. 5).

13

• Measuring D pH
• A weak acid obeys
• HA ? H A-
• with Equilibrium constant
• Ka H A- / HA (8)
• Since HA is neutral it will freely permeate the
  membrane.
• - Either side of the membrane HAN HAP
• We know HP ? HN due to D pH.
• - Therefore A-P ? A-N at equilibrium.

Note for a weak acid HA gtgt H, A-, so
picture is just illustrative, don't take
literally!
14

• Measuring DpH done by
• Growing organelle's with physiological pH
  gradient (A).
• Adding A- to the incubation medium (B).
• Stop respiration (eg. rapidly separate organelle
  from incubation medium).
• Monitoring the fall of A- outside the organelle
  (C to D) since HA will diffuse through the
  organelle's membrane.
• Alternatively use a spectral indicator for A-
  as it accumulates inside the organelle (D).
• Amount of HA found inside the organelle closely
  related to
• (almost matching) the excess of H outside the
  organelle when
• A- added.

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• Measuring D y
• Measure the electrostatic potential difference
  by having an ion (eg. X) which can freely
  permeate the membrane
• - Requires a rapid transporter of X.
• Allow X to equilibrate either side of the
  membrane as the organelle functions.
• - Dy will drive a concentration gradient for X.
• At equilibrium
• DG - F Dy - 2.3 RT log10
  (XP / XN) 0. (9)

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• Solving Eq. (8) for Dy gives
• Dy - 2.3 RT / F log10 (XP /
  XN) (10)
• Measuring the fall in X outside the
  organelle, or increase inside, gives Dy directly.
  
• Must know internal volume of organelle.
• Must have only one rapid transport mechanism of
  X.
• X should not disturb pH gradient (ie. X must
  be low).
• Need a good indicator for X.

18

• First measurements of transmembrane Gibbs free
  energy
• Mitchell and Moyle (1969) employed pH and K
  specific electrodes in anaerobic, low K
  incubation
• Valinomycin used to transport K.
• Dy determined by K uptake during an O2 pulse.
• Used mitochondrial respiratory chain.
• DpH estimated by simultaneous proton extrusion.
• A value of 228 mV for Dy.
• - Equates to 22 kJ/mol.
• In the mitochondria DpH only makes a small
  contribution to total Gibbs free energy.
• - Buffer effects protect enzymes from pH
  extremes.
• In chloroplasts DpH makes a larger contribution.
  
• - Have very pH robust enzymes in these
  organelles.

19

• Does it Add Up?
• First success of the theory was it explained why
  charge transporters
• (eg. valinomycin, which transports K) kill
  ATP-synthesis.
• Mitchell and Moyle found Dy 228 mV in
  mitochondria.
• - Equates to 22 kJ/mol.
• Know the mitochondria maintains the ATP ? ADP
  Pi reaction ten orders of magnitude from
  equilibrium.
• - Equates to 57 kJ/mol energy storage by ATP.
• Believed that 3 to 4 H are pumped in the
  mitochondria per ATP molecule synthesized.
• - Between 66 and 88 kJ/mol of energy available
  for each 57kJ/mol ATP molecule generated.
• - Surprisingly efficient!
• This finding crucial, since if DG did not add
  up the whole theory would need to be abandoned.

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• Proton pumping
• Established that energy transduction proceeds by
  proton pumping.
• Proton motive potential then harvested by
  ATPsynthase.
• How can it possibly work in detail?
• - Demands structural information.

21

• Classical proton pump
• A binding site for a proton.
• Resting state has very high proton affinity.
• A proton taken up.
• Upon the input of energy
• Conformational change.
• Switches accessibility to the other side of the
  membrane.
• Dramatically reduces proton affinity of binding
  site.
• A proton is released.
• Net translocation of a proton.
• - Basic model Jardetzky, Nature 211, 969-970
  (1966).

22

• Redox coupled proton pump
• Contain two redox chemistry sites.
• - One either side of the membrane.
• Oxidation of substrate S1
• Reduces the enzyme.
• Electrons flow to second redox site.
• Protons released to one side of membrane.
• Reduction of substrate S2
• - Protons taken up from other side of the
  membrane.
• Net translocation of a proton.
• - Basic model Mitchell, Nature 191, 144-148
  (1961).

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• Electron proton movements
• Electrons (or protons) sit within potential
  energy wells.
• Have specific quantum mechanical''
  wavefunctions.
• Energy of wavefunction hn (n oscillation
  frequency).
• Neighboring potential energy wells always
  present.
• eg. an electron may move to a neighboring
  cofactor.
• eg. a proton may move to a neighboring
  residue/water molecule.
• To be probable that the electron/proton moves
• For a given set of nuclear coordinates the total
  potential energy of reactants and products must
  match.
• Efficient quantum-mechanical wavefunction
  coupling If hnreactants hnproducts

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• Rate constants of transfer
• Rates for electron (proton) transfer depend on
• centre-to-centre distance of reactants and
  products.
• As distance increases energy barrier goes up!
• Probability of fluctuations providing this
  energy goes down.
• Transfer probability of crossing from one
  surface to another depends on extent of
  wavefunction overlap.
• - eg. Certain angles favored for H-bonds.
• - eg. Electron wavefunctions have structure and
  therefore
• overlap better at favored orientations.
• - Proteins carefully arranges cofactor positions
  and orientations.

25

• Tunneling
• May expect that proteins provide pathways
  between electron donors and acceptors.
• - In practice not so.
• Electrons pass from one centre to another by
  tunneling.
• There is a finite probability that the electron
  is already in the product's potential well.
• - Diagnostic for tunneling is insensitivity to
  temperature changes.

26

• Proton Exchange
• Have hydrogen bond partners.
• - If distance and angles favorable have very
  rapid exchange of a proton.
• - Imagine the forward and reverse reaction
  happening continuously.
• H-bond networks of charged side chains and water
  molecules serve as proton wires''.

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• What determines where protons lie?
• Define the pKa of a residue/cofactor/water HA
  as
• pKa - log10 (HA- / HA)
• where the reaction is HA ? H A-.
• Low pKa means relatively high H.
• High pKa means relatively low H (ie.
  relatively high OH-).
• A number of residues have a pKa in the region
  where their
• protonation states can change
• - Aspartate (pKa 3.9), Glutamate (pKa 4.1),
  Histidine (pKa 6.0), Lysine (pKa 10.5),
  Arginine (pKa 12.5), Tyrosine (pKa 10.5),
  Cysteine (pKa 10.7).
• If two residues in H-bond contact (or linked via
  water molecules) the proton will lie on that with
  highest pKa.
• Several factors perturb the pKa of residues
• Number of H-bonds.
• Distribution of charges (eg. nearby positively
  charges can stablilse a negative charge on a
  residue and vice versa).
• How hydrophobic/hydrophilic the local
  environment is.

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• Classical proton pump
• Resting state has a high affinity proton binding
  site.
• - H-bonds/local charges etc. stabilise its high
  pKa.
• Conformational change.
• Switches accessibility to the other side of the
  membrane (eg. opens and closes entry/exit
  channels).
• pKa of proton binding site drops significantly.
• - Loss of H-bonds, movements of charges etc.
• A proton is released.

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• Flow of electrons
• Similar structural/energy barrier considerations
  to proton transfer.
• Electron flow faster since e- 1000 times lighter
  than H.
• Can also have significant tunneling'' through
  barriers.
• - It is the Oxidation-Reduction (Redox) potential
  which is relevant.
• General reaction is
• Oxidised ne- m H ? Reduced
• An Oxidised/Reduced pair is called a redox
  couple.
• In the case of a metal and its salt
• Two half cells of metal electrode and its salt
  versus a standard.
• Link them by a salt bridge and measure the
  potential difference.

30

• The metal electrode which gives up electrons has
  the lower electro-potential.
• Standard electro potentials defined against a
  H2/Pt electrode _at_ 1Mol concentration H (ie. pH
  0) and 25oC.
• Normal biological convention defines
  electropotentials _at_ pH7.
• Mid-point potential is that when Oxidised
  Reduced
• The actual redox potential at pH x is
• Eh,pHx Em, pH x ((2.3 R T)/(n F))
  log10(ox / red)
• Where Em, pH x is the mid-point potential at pH
  x.
• Note the energy term arising as Oxidised and
  Reduced
• change, related to earlier expressions!

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Some mid-point potentials _at_ pH 7 Oxidised ne-
m H ? Reduced
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• Common redox groups in biology
• Most enzymes use relatively few redox cofactors.
  
• Cu centres.
• Single Cu dinuclear (two Cu) centres binuclear
  (one Cu, one Fe) centres.
• Fe/S complexes.
• - Two Fe2 and two S2-.
• Heme.
• - Normally Fe2 within a porphyrin ring.
• Chlorophyll.
• - Like heme but with Mg2 rather than Fe2.
• Pheophytin.
• - Like heme but with 2H rather than Fe2.
• Quinone/Quinol.
• Redox potentials modified by subtle structural
  effects.

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• Redox coupled proton pump
• Contain two redox chemistry sites.
• Oxidation of substrate S1
• - Has a relatively negative electro-potential.
• - Electrons flow to second redox site.
• Reduction of substrate S2
• - Has a relatively positive electro-potential.
• Net translocation of a proton.

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• Structural methods
• To understand these processes need structural
  information.
• Nuclear Magnetic Resonance
• - Has a relatively low upper size limit.
• Electron microscopy.
• - Quite successful for membrane proteins but low
  resolution.
• Electron microscopy structure of Ca2-ATPase.
• X-ray diffraction.
• - The most successful and high resolution.
• - Difficult to get crystals.

35

• The X-ray approach
• Grow crystals.
• Travel to synchrotrons.
• Collect X-ray diffraction data.
• Interpret electron density.

36

• Summary Lecture 2
• Thermodynamics determines Gibbs free energy of
  reactions.
• - A reaction spontaneous if DG is negative.
• Measurements of proton gradients consistent with
  the energy content of ATP within the cell.
• Two types of proton pump
• - For classical proton pumps must consider pKa
  values.
• - For redox coupled pumps electropotentials the
  central idea.
• X-ray diffraction the most promising method for
  elucidating structural details.