Lecture 12

Energy and ATP

  1. Introduction:

    1. Schröedinger: "The ability to decrease entropy is the MOST characteristic feature of living systems."

    2. Decrease in entropy means an increase in order (a state of low probability).

    3. Further, order may create information. Maximum entropy: scrambled letters of quote; ordered letters in quote = information.

  2. Energy flow through a system orders that system:

    1. Energy flow from the sun has ordered the earth.

    2. Energy flow through biological systems: The means for creating the order seen in living cells.

  3. Thermodynamics and Kinetics (do not confuse these terms)

    1. Thermodynamics relates to spontaneity or "will it happen?"

    2. Kinetics relates to reaction rate or "how fast will it happen?"

  4. Energy vs. Reaction coordinate plot for A ® B

    1. showing Eact; average energy of A and B; and the thermodynamic difference, G.

    2. Eact is the kinetic term; G is the thermodynamic term.

    3. Considering a Boltzmann energy distribution plot illustrates the differences between these values.

    4. Real example of a reaction:

      1. C6H12O6 + 6 O2 ® 6 CO2 + 6 H2O

      2. G° = -686,000 cal/mol

      3. G° = -2,870,000 Joules/mol (1 cal. = 4.284 Joules)

      4. But glucose is very stable in aqueous solution in the presence of air due to a high energy of activation.

  5. Consider:

    1. A ® B + energy

    2. G = GB - GA (Gproducts - Greactants)

    3. G is negative for spontaneous processes

    4. if GA > GB, G is negative

  6. What is G?

      It is the change in free energy in a reaction.

    1. In a chemical reaction, the change in free energy (G) is equal to the change in enthalpy (H) minus the absolute temperature (T) times the change in entropy (S):

      G = H - TS

    2. G = that part of the total energy change in a process that is available to do useful work

    3. H = heat of reaction, the change in enthalpy (heat content). In dilute aqueous solutions (which cells approximate), H = E, where E = the change in the internal energy of the molecules (EB - EA)

    4. TS = that part of the internal energy change that is dissipated in the form of increased random molecular motion and hence unavailable to do useful work. Simplistically, E = G + TS

    5. So, G = change in internal energy corrected for the change in entropy, where entropy changes are energy losses that cannot be used to do useful work.

    6. G tells us how much energy is available to do useful work.

    7. Now, the standard-state free energy change for a reaction (defined as the free energy change when both products and reactants are present at 1 Molar concentrations) is

      D G° = -RTlnKeq

      where Keq = [B]eq/[A]eq

      If Keq is small, D G is positive

      If Keq is large, D G is negative

    8. D G is just another way of writing an equilibrium constant for a reaction.

  7. A Cell Does 3 Kinds of Work

    1. Mechanical work: muscle contraction; axonal transport; cytoplasmic streaming

    2. Transport work: the pumping of substances against concentration gradients, e.g., the Na+,K+ pump (Na+,K+-ATPase)

    3. Chemical work: driving reactions that are not spontaneous (reactions that have a +D G, such as do all dehydration synthesis reactions)

  8. In most cases, ATP is the source of energy for cellular work.

    1. ATP hydrolysis releases lots of energy:

    2. ATP + H2O _ ADP + Pi + energy released

    3. DG° = -7,300 calories/mol = -7.3 kcal/mol = -30.5 kJ/mol

    4. D Gcellular » -12,000 calories/mol = -12 kcal/mol = -50 kJ/mol

    5. Of course, ATP synthesis "costs" a lot of energy (+50 kJ/mol in the cell).

  9. How ATP Works

    1. Consider a reaction, A ® B, where D G° = +4 kcal/mol

      1. DG° = +4,000 cal/mol = -RTlnKeq

      2. DG° = -(1.987 cal/° mol)(310K)lnKeq

      3. lnKeq = -6.49

      4. Keq = 0.0015 = [B]eq/[A]eq very little B at equilibrium!

    2. Now consider the coupled reaction,
      1. A + ATP + H2O ® B + ADP + Pi

      2. Since for A ® B, D G° = +4 kcal/mol,

      3. and for ATP + H2O ® ADP + Pi, D G° = -7.3 kcal/mol,

      4. D G° overall = -3.3 kcal/mol

      5. Therefore, -3,300 cal/mol = -RTlnKeq for the coupled reaction.

      6. lnKeq = 5.36 ;Keq = 212

      7. Note that

        Keq = ([B]eq[ADP][Pi])/([A]eq[ATP]

        (by convention, the concentration of the solvent, [H2O] º 1 in these thermodynamic calculations)

    3. We can substitute here a typical value for the ratio of [ATP]/[ADP][Pi] in a living cell.

      1. (ATP]/[ADP][Pi])in vivo » 500

      2. Keq = 212 = [B]eq/500[A]eq

      3. [B]eq/[A]eq = 106,000

      4. Now compare the ratio [B]eq/[A]eq in the presence versus in the absence of ATP:

        106,000/0.0015 = 7 x 107

    4. General Principle:

      Coupling of ATP hydrolysis to A ® B raises the equilibrium ratio of [B]/[A] by a factor of almost 108-fold (almost 100 million fold).

    5. Note that A ® B is generally defined: It could be

      1. a chemical reaction

      2. mechanical work

      3. transport of a substance against its concentration gradient

      4. Anything!

  10. Why is ATP "Energy-Rich"? Or, in other words, why is D G° a large negative number?

    1. In simple terms, ATP bears a lot of negative charge (ATP4- in solution). ATP is characterized by a lot of internal electrostatic repulsion; this repulsion is relieved upon hydrolysis. Or viewed another way, ATP hydrolysis creates 2 anions, HPO42- and ADP3-. To re-form ATP from ADP + Pi requires bringing 2 like-charged molecules together (electrostatic replusion between ADP3- and HPO42- must be overcome to form ATP).

    2. [ATP]in vivo » 10 mM » 5 g/liter

    3. A person needs about 2,000 Calories per day ( = 2,000 kcal/day). Note: a calorie is the heat necessary to raise 1 gram of water one degree Centrigrade. A kilocalorie or kcal is 1,000 calories. A kilocalorie is also equal to one Calorie (note the capital "C") which is the "calorie" unit used in nutrition.

    4. 12 kcal/mol of ATP ® 167 moles of ATP to get 2,000 kcal

    5. 167(495 g/mole) » 83 kg ATP per day (more than the weight of the average (70 kg) person).

    6. A person has » 250-300 grams of ATP total.

    7. Therefore, each molecule of ATP must turn over (be synthesized from ADP + Pi and hydrolyzed again) about 300 times a day. (If not resynthesized, all the body's ATP would be converted to ADP + Pi in about 5 minutes.)