Homework

1. Today Review quiz Homework Written HW #1 due Thursday Reading #2, Scientific American by Mattick, assigned today, due next Tuesday (a few question quiz next Tuesday) (Talks about what is the purpose of the “junk” DNA.)

2. Quiz Eukaryotes, Prokaryotes, Archea Central Dogma Biol: DNA RNA Proteins, or Nucleic Acids Proteins DG=DHsystem(enthalpy) –TDSsystem(entropy) DH < 0 ; DS > 0 DStotal must increase = DSsystem +DSsurrounding DHtotal = constant = DHsystem +DHsurrounding (Either one can go up or down) Water will H-bond with itself but also w amino acids. Therefore where H-bonding occurs within protein is often regions that water is excluded from.

3. Basic Biology • & some calculations • [Read Chpt 1 of Berg et al.: lots of important things about Molecular Binding, Central Dogma, Entropy, DG] • Size of Cells and King Kong • Entropy Matters, DG, ATP.

4. The Cell is the Fundamental Unit of Life from Latin cella, meaning "small room" Three types: A bacteria and archea, (w/o nucleus): 1 x 2 mm A eukaryotic cell, (w nucleus): 10-100 mm. What determines how small a cell can be? . Minimum size to have enough room for ~1000 reactions necessary for life. What determines how large a cell can be? Maximum size to make sure molecules find each other rapidly enough so metabolism can take place --will study more, but partly based on diffusion. Bacteria small enough that don’t need anything else beside diffusion. Eukaryotes also have molecular motors to cause molecules to get close together and react. (Bacteria has about 10x faster metabolism than eukaryotic cells.)

5. Mass? (density is the same): 10 x 10 x 10 = 103 Strength? a Cross-sectional area (rope): 10 x 10 = 102. 1/10… 1/dimension Strength/Mass ratio? King Kong is proportionally speaking is 10x weaker than regular gorilla! Regular gorilla with 10 gorilla’s on him—couldn’t walk.

6. Whales In water– held up by buoyant force. Bones do not need to support weight If have to, have super big bones– would sink. If whale stranded on the beach? Bones break; also overheat (because warm-blooded and water is going at conducting away heat, whereas air is not.)

7. Thermal energy matters a lot! Everything (which goes like x2 or v2 in PE or KE) has ½ kT of energy. If a barrier has on this order, you can jump over it and you will be a mixture of two states. Boltzman distribution = Z-1 exp (-DE/kBT) kf kb Keq = kf/kb DE

8. Entropy also matters(if lots of states can go into due to thermal motion)Probability of going into each state increases as # of states increases DE1 DE1 DE1 DE3 DE2 DE2 Add up the # of (micro-)states, and take logarithm: ln si= Si = Entropy

9. Boltzmann factor & Degeneracy In general, there can be a number of different states, Wi, that are degenerate—have the same energy, but can put a molecule into, with P(Ei) Usual Boltzmann Faxtor: P(Ei) = (1/Z) e-Ei/kT W=1 W=1 W= 1 W=1 W=3 W=2 W=3 W=2 3 3 2 2 1 1 With degeneracy 0 0 P(Ei, Wi) = (2/Z) e-0/kT + (3/Z) e-e/kT + (2/Z) e-2e/kT +… P(Ei, Wi) = (Wi/Z) e-Ei/kT

10. Generalize the definition of the free energy to include degeneracy. Like flipping a deck of cards twice. Each energy level may be populated with several molecules, i.e. have many accessible states. We define the multiplicity Wi as the number of accessible states with energy Ei. For example: Boltzmann factor & Degeneracy W=3 W=2 W=3 W=2 3  Assume that a more general formula for the probability P(Ei, Wi) = (Wi/Z) e-Ei/kT of finding a molecule with energy Ei, with the multiplicity factor Wi. Using Wi = exp[ln Wi] P(Ei, Wi) = (Wi/Z) exp(-Ei/kT) = 2 1 0 (1/Z) [exp(lnWi)] exp(-Ei/kT) = (1/Z) exp -(Ei – kTlnWi)/kT Define S= kln[Wi] P(Ei, Wi) = (1/Z) exp -(Ei – TS)/kT = = (1/Z) exp –[Fi /kT] where F = Helmholtz free energy which is same as Gibb’s Free Energy for liquids (non-gasses). Note: ∆G because always energy w.r.t. some zero (like E, ∆E); define E and S. Typically, 1M concentration.

11. DG vs DF Up till now we said change in energy = kinetic + potential energy. In some cases, there is a change in volume (e.g. explosives work) H (enthalpy) = E (energy) + pV. Takes into account changes in pressure and volume. In biochemical reactions, Dp and DV are ~ 0, so you can use either DF or DG. F = E – TS G = H – TS (F ~ G) Can use either. Bottom line: Whenever you usually use E, use G, and entropy is taken care of!

12. EquilibriumHow stable is one state over another? A  B Probability of being in B = Z-1exp(-GB/kT) Probability of being in A = Z-1(exp-GA/kT) Keq = B/A = exp (-GB/kT+ GA/kT) = exp –([GA- GA]/kT)= exp –(∆G/kT) Keq =exp –(∆G/kT) ∆G = -kTlnKeq What about A B + C Keq = [B][C]/[A]. But how to figure out in terms of ∆G?

13. This tells about equilibrium. Tells nothing about why two are stable

14. Stability and thermal activation Both systems are stable because they have activation energy to convert! All chemical reactions involve changes in energy. Some reactions release energy (exothermic) and others absorb it (endothermic). Keq= [B]/[A] [Says nothing about ∆G+rev/forward] ∆G+forward Keq = f(∆G)? Enzymes (Catalyst) ∆G+rev Keq = exp(-∆G/kT) ∆G ∆G = -kT ln (Keq) ∆G+rev ∆G+forward ∆G If Activation Energy < kT, then rxn goes forward. If not, need to couple it to external energy source (ATP).

15. ATP, Energy, Entropy ATP  ADP + Pi  Take energy from a couple of photons, and convert ADP + Pi into ATP You must add up not only the energy (two vs. three negative charges forced together), but the free energy arising from loss or gain in Entropy.

16. Energetics of ATP 1 ATP= 80-100 pN-nm of energy at 37 ºC = 20-25 kT of energy (much more than kT = 4 pN-nm) A lot of energy Why do I say 80 to 100 pN-nm? Why not an exact amount? Let’s say that you let reaction in a (small) box. Start out with no ADP and no Pi. Then there are a ton of places for each to go and so you have tons of places to go where negative charges are far from each other. Now if there is a lot of ADP and Pi around, not much energy from splitting ATP. ATP sometimes gives 20 kT, sometimes 25 kT You will have to calculate this. (Easiest to do in moles/liter, rather than by single molecules.)

17. How can use 90 lbs? Net weight = WATP-WADP

18. Class evaluation • What was the most interesting thing you learned in class today? • 2. What are you confused about? • 3. Related to today’s subject, what would you like to know more about? • 4. Any helpful comments. Answer, and turn in at the end of class.