5 The 2nd Law Unsustainable “All natural and technological processes proceed in such a way that the availability of the remaining energy decreases. In all energy exchanges, if no energy enters or leaves an isolated system, the entropy of that system increases. Energy continuously flows from being concentrated, to becoming dispersed, spread out, wasted, and useless. New energy cannot be created and high-grade energy is being destroyed. An economy based on endless growth is unsustainable.”
6 OverviewWhat is the relationship between the free energy change (G) of a reaction and its equilibrium constant?How can compounds like ATP be used to drive metabolic reactions that are unfavorable?What is it about the structure of ATP and related compounds that make them so “full of energy”?
8 Simple Thermodynamics aA + bB cC + dDIf a process is spontaneous then the reaction moving to the right (products) is favored and Keq > or Greactants > Gproducts
9 Example: an important reaction in biology is the inter-conversion of various sugars. The equilibrium shown below is the inter-conversion of glucose-6-phosphate (G6P) and fructose-6-phosphate (F6P):Glucose-6-phosphateG6PFructose-6-phosphateF6P
10 Suppose you dissolve 1 mole of G6P and 0 Suppose you dissolve 1 mole of G6P and 0.3 moles of F6P into a liter of water. What is the concentration of each at equilibrium?The sum is 1.3 moles in a liter or 1.3 M, so[F6P]+[G6P] = 1.3 M, thus [G6P] = 1.3 M – [F6P]Solve for [F6P] = 0.44 M.And the concentration of G6P = [G6P] = M = 0.86 M.
11 Free EnergyA measure of the spontaneity of a reaction is called the Gibbs free energy (G).The reactants and products have a free energy. We can only observe the change (D) in free energy as we go from reactants to products:DGºreaction = Gproducts - GreactantsFor a spontaneous process Greactants > Gproducts, soDGºreaction < 0
12 SPEnzyme-catalyzed reaction:EG (free energy)Reaction coordinateE+PES‡E+SG‡GS‡1. Enzymes do not alter the equilibrium or G.2. They accelerate reaction rates by decreasing G‡.3. They accomplish this by stabilizing the transition state(s).
13 Free EnergyDG° is called the standard Gibbs free energy change for a given reaction under standard conditions of pressure (1 atm), temperature (25 °C or 298 K) and [H+] (pH 7.0 or 0.1 mM). Under standard conditions the concentration of every reactant and product is 1 M (and water is 55 M!).It basically tells us whether, at equilibrium, a reaction lies to the right or left. However, inside living systems reactions are seldom at equilibrium, so a more useful quantity is DG under non-equilibrium conditions.
14 G = ∆G° + RT ln –––––––– = ∆G° + RT ln Q [A]a[B]b 1. Gibbs free energy (G) - free energy needed to convert reactants to products under a defined set of non-equilibrium conditions.aA + bB cC + dDWhich direction is favored?[C]c[D]dG = ∆G° + RT ln –––––––– = ∆G° + RT ln Q[A]a[B]bln(x) is the logarithm base e not base 10!∆G°: Standard free energy of a reaction. Depends on free energies inherent in the structures of the chemicals.RT ln Q: accounts for differences in the concentrations of reactants and products (law of mass action); R is the gas constant (8.31 J K-1 mol-1), T is the temperature in Kelvin.
15 ∆G = ∆G° + RT ln –––––––– = ∆G° + RT ln Q [A]a[B]b aA + bB cC + dDWhich direction is favored?[C]c[D]d∆G = ∆G° + RT ln –––––––– = ∆G° + RT ln Q[A]a[B]bConsider special cases to “test” this equation(1) [A], [B], [C], [D] = 1 MThen ∆G = ∆G° (by definition!)(2) Q is a very small number (eg. 1x10-6): [reactants] >> [products]Will make ∆G more negative/favorable with respect to ∆G°.Follows law of mass action, ie. low [products] will pull balance to right.(3) Q is a very large number (eg. 1x106): [products] >> [reactants] Will make ∆G more positive/unfavorable with respect to ∆G°.Follows law of mass action, ie. high [products] will push balance to left.
16 The Equilibrium State ∆G = ∆G° + RT ln Keq With ∆G° + RT ln Keq = 0 At equilibrium, neither direction of the reaction is favored, therefore ∆G = 0 (by definition).With ∆G° + RT ln Keq = 0ln Keq = -∆G°/RTKeq = e-∆G°/RT
17 Keq = e[-∆G°/RT] = e(-14,000 J/mol)/(8.314 J/K/mol x 298 K) ExampleGlucose + HPO Glu-6-phosphate ∆G° =(Glu) (Pi) (G6P) kJ/molKeq = e[-∆G°/RT] = e(-14,000 J/mol)/(8.314 J/K/mol x 298 K)= e = 3.5 x = ––––––––––[G6P][Glu][HPO4--]The equilibrium lies far to the left; thus the reaction is not favored. G6P has a higher inherent free energy than do glucose and Pi together.
18 Energy Coupling - an important role for enzymes and for high-energy compounds like ATP. (1) A B ∆G° = +14 kJ/mol (unfavorable)(2) C D ∆G° = -30 kJ/mol (favorable)A + C B + D ∆G° = -16 kJ/mol (favorable)EnzBy coupling (1) and and (2), an enzyme can “tap” the energy of a highly favorable reaction to drive an otherwise unfavorable reaction!
19 ADP vs. ATPADP, net charge: -3ATP, net charge: -4
20 Movie: Powering the Cell Mitochondria and ATPMovie: Powering the Cell
21 Example of energy coupling: hexokinase reaction Reaction ∆G° (kJ/mol)Glu + Pi G6P (unfavored)ATP ADP + Pi (favored)hexokinaseGlu + ATP G6P + ADP (favored)Using Keq = e[-∆G°/RT] with R = J/K/mol and T = 298 Kwe obtain Keq = 955
22 2. ATP hydrolysis is highly exergonic O O OAd-Rib-O-P-O-P-O-P-O + H2OATPO O OAd-Rib-O-P-O-P-O O-P-O + H+O O OHADP (Pi)∆G° = -31 kJ/mol
23 Why is ATP hydrolysis so highly exergonic? 1. Electrostatic repulsion - less with products2. Resonance forms - more with products3. Proton release[H+] is kept very low in the cell (~10-7 M or 0.1 mM)This favors reactions that release protons(mass action effect)4. Hydration stabilization - more with productsSimilar considerations explain why other phosphate ester compounds also store energy; for example phosphoenolpyruvate, phosphocreatine, etc.
24 Why is ATP hydrolysis so highly exergonic? 1. Electrostatic repulsion - less with products-2. Resonance forms - more with products
25 ATP turnoverEach of the approximately one hundred trillion human cells contains about one billion ATP molecules, or about 1023 ATP molecules in the body. For each of these ATP “the terminal phosphate is added and removed 3 times each minute” (Kornberg, 1989). This amount is sufficient for only a few minutes and must be rapidly recycled.The total human body content of ATP is only about 50 grams. The ultimate source of energy for generating ATP is food; ATP is simply the carrier or storage unit of energy. The average daily intake of 2,500 food calories translates into a turnover of a whopping 180 kg (400 lbs) of ATP (Kornberg, 1989).
26 Phosphocreatine is an “ATP buffer” in skeletal muscleADPATPMg++creatine kinaseG° = kJ/molphosphocreatinecreatine
27 Enthalpy and Entropy DG = DH - TDS DH or enthalpy is the heat given off in a reaction.DH is defined as Hproducts – Hreactants. When heat is given off then DH < 0. This means a given reaction is enthalpically favorable.Suppose we have a reaction going on in a beaker. If the beaker heats up then the reaction is giving off heat so DH < 0.
28 Enthalpy and Entropy DG = DH - TDS DS or entropy is a measure of disorder in a system.Similar to DH, DS is defined as Sproducts - Sreactants.A spontaneous or favorable process tends toward higherdisorder so DS > 0 is favorable.
29 Enthalpy and Entropy DG = DH - TDS In this container the same number of gas molecules have more space. Each molecule has more “freedom” and the system is more disordered. Here the entropy, S, is larger.In this container the gas molecules are confined to a small space. The order in the system is relatively high, so the entropy, S, is small.
30 Enthalpy and Entropy DG = DH - TDS Consider what happens to the thermodynamic quantities in a reaction between 2 molecules to form 1 molecule:A + B ABThe formation of a chemical bond is usually a heat-generating process so DH < 0. However, in going from 2 molecules to 1 molecule, the system will become more ordered. Therefore, DS < 0 (decrease in entropy). Whether or not a reaction is favorable depends on the balance between enthalpy and entropy. It is typical for enthalpy and entropy to balance or compensate for one another.
31 A classic example is the reaction between oxygen and hydrogen to form waterO2 + 2 H H2OTake a balloon filled with hydrogen gas. Touch a lit match to the balloon. What happens? A big boom and lots of heat given off. Is DH favorable or unfavorable??Add solid urea to a beaker of water. The beaker gets very cold. Is DH favorable or unfavorable???
32 ANOTHER EXAMPLE DG = DH - TDS N2O5 (solid) 2 NO2 (gas) + ½ O2 (gas) DG0 = -9.5 kcal/molDH0 = kcal/molTDS0 = kcal/mol at room temperature (293 K)So this reaction is entropically favorable even though the change in enthalpy is unfavorable.
33 The 2nd Bio98C/F $10 Challenge First one to send an with all correct answers with “98challenge“ in the subject line to wins $10! Double-or-nothing: You can double your winnings by playing me (and winning) best-of-3 in racquetball at the ARC!The 2nd Bio98C/F $10 Challenge
35 THE END Good luck with the midterm THE END Good luck with the midterm! My lab is looking for Bio199 students (GPA of 3.5 or better, A- or better in 97, 90% or better in 98 midterm, hours per week / 3-4 units per quarter, 2 year commitment and participation in Excellence in Research. Please after the midterm with “199” in the subject line if you’re interested.)
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