1. What you are going to learn today… DNA  RNA  Proteins  E—Boltzmann’s Equipartion (Why climbing Mt. Everest is tough)  S –Entropy  G—Free Energy Proteins and Enzymes Equilibrium and Kinetics (Why Sugar gets you high) RNA & Splicing (Why you’re different than a 1mm long Worm) First let’s introduce ourselves and discuss practicalities Introduction to Molecular Biophysics

2. Quick Announcement The lectures are videotaped. You are not videotaped and therefore cannot be recognized, either verbally or in the video. If anyone has a problem with this, at the end of class, please just write it in the lecture evaluation and we will work it out.

3. Questions Many excellent questions about what I said in first lecture I just hate “giving answers to you, so… We’ll talk about more today… make up Homeworks! or later…

4. Geckos are popular! 4. Most species of geckos are nocturnal and have excellent night vision. They have a lens in each iris that widens in the dark in order to let in more light. Also, their eyes are 350 times more sensitive to light than the eye of a human We’ll study about vision —can you see a single photon Ans: maybe, definitely close! 5. Also, it has only been discovered in recent years that something called, phospholipids, a fatty substance that is naturally produced by the gecko helps with its ability to adhere its feet to surfaces, as well as something called van der Waals. The simplest explanation of van der Waals in this particular case is that geckos are able to stick to surfaces because they can exploit weak molecular attractive forces. Your Comments: <1” to 2 feet long furrypetsandmore.com/tag/gecko-diet/ 6. Nearly all geckos lack eyelids, with the exception of the Eublepharidae family, who actually have moveable eyelids. The rest are unable to blink and simply have a transparent membrane which they keep clean by licking with their tongues.

5. Questions Difference in A-T (2H’s) and G-C (3 H’s)? How DNA Major and Minor grooves of DNA. How DNA is separated. To break apart or to bend it, easier if A-T K B T as unit of energy? Relation to eV or ergs or calories… Questions about van der Waals and xenon vs. Neon More about Central Dogma…will do! (Can RNA replicate? What are proteins…) How 90% of “Junk” DNA is used. Confused about evolution (?) What bonds the phosphates and sugars together in DNA. Earliest life forms use RNA. How does that fit into the DNA  RNA  Protein HW! Later HW! Later HINT: To break apart or to bend it, easier if A-T

6. Review of van der Waals Interaction Temporary Dipole causes in neighboring atom and induced dipoles Dipole-dipole interaction– attraction Strength of interaction—depends on size of atoms. Why?

7. Quiz #1 (really!—learn!-next Tuesday!)  H and  S

8. Central Dogma: DNA  RNA  Proteins http://learn.genetics.utah.edu/units/basics/transcribe/ DNA: linear series of 4 nucleotides (bases): A,T,G,C RNA: linear series of 4 nucleotides (bases): A,U,G,C   Transcription [DNA & RNA similar] (in nucleus) Translation [RNA & Proteins different] (in cytoplasm) Proteins: linear series of 20 amino acids: Met-Ala-Val-… each coded by 3 bases  amino acid AUG  Methionine; GCU  Alanine; GUU  Valine Proteins are 3-D strings of linear amino acids Do everything: structure, enzymes…

9. DNA  RNA U U U Must uncoil the DNA, separate the strands, and use one of strands as a template to make a RNA strand. RNA: uses U instead of T, uses ribose instead of deoxyribose The RNA that codes for proteins are called pre-messenger RNA is an exact copy of DNA.

10. RNA  Proteins 3 nucleotides codes for 1 amino acid. Proteins are made up for a linear string of 20 (or 21) different amino acids. Also need to know where to start making the protein, and where to stop making the protein. U U U    Histidine Cysteine Glycine If you can sequence all your DNA, how can you tell how many genes are there? Gene = sequence of DNA (or RNA) that makes a protein (approximately) Why 3? 4 3 = 64 possible a.a.

11. Amino Acids Structure 20-21 different “R” groups attach together. R1R1 R1R1 R2R2 R2R2 H2OH2O+

12. 21 Amino Acids (“Ordinarily” 20 amino acids. The 21 st one, called Selenocysteine is present in all 3 kingdoms of life, but is not universal in all organisms. It is made in its own way. As of 2003, twenty- five human proteins are known to contain selenocysteine.) https://en.wikipedia.org/wiki/Selenocysteine Wikipedia R1R1 R1R1 R2R2 R2R2 H2OH2O+ https://en.wikipedia.org/wiki/Amino_acid Contains Se, normally toxic to organisms.

13. Linear sequence of ~ 20 amino acids Can get enormous diversity and function with Proteins

14. Probability of it coming unbound: if DNA is 10 base-pair long? if DNA is a million base-pair long? Want to understand DNA Stability To be active, DNA must unzip (so base-pairs get exposed: RNA formed). How/why does DNA come apart, from dsDNA  ssDNA? A lot of H bonds must be broken. Does this happen easily or with much effort? Boltzmann Factor —at temperature T, What’s the probability of being in some state or another, each at energy E i.

15. Boltzmann factor + Partition function (review of basic Stat. Mech. – see Kittel, Thermal Physics) E1E0E1E0 Temp, T If T = 0 ºK, what proportion of particles will be in E 1, E o ? If T > 0 ºK, what proportion of particles will be in E 1, E o ? Answer: E o = 1 E 1 = 0 At T = 0ºK, there is no energy hanging around in solvent to knock the molecule into an excited state.

16. Constant in Boltzman factor: Partition function E1E0E1E0 Temp, T Z = partition function What is constant = to? The molecule exists somewhere!

17. Partition Function for 2-state system State 0: Energy E 0 State 1: Energy E 1 What is P(E 1 )?

18. Example: Ball in gravitational field Thermal fluctuations, finite probability of being at height, h. E = ?? As ball gets bigger (more mass), probability of being at h gets smaller / larger ? Relative probability of being at height = 0? At height = h?

19. What if “ball” were the size of an oxygen atom? Why can you breathe standing up? Breathing 8,848 m (29,029 ft) What if h is very tall, like a mountain? Why is > 8,000called “the death zone”?

20. 2. Calculate Probability of unwinding for a DNA, where the average E i = 2k B T Prob(unwinding) = 1 base pair, 10 bp, million bp The conclusion is that for very short DNA, unwinds all the time; For DNA reasonably long, never unwinds. Homework: 1.Calculate how hard it is to breathe at (29k ft) 8,000 meters. (Why do they call “the death zone” anything over 24,000 ft?) Chances of you dying ~ 10% every time you try to climb Everest! How does DNA then unwind?

21. Problem with previous calculation using Boltzmann’s constant. Entropy.

22. Thermal energy matters a lot! Everything (which goes like x 2 or v 2 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 (-  E/k B T) EE kfkf kbkb K eq = k f /k b

23. 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 E1E1 E1E1 E1E1 Add up the # of (micro-)states, and take logarithm: ln  i  = S i = Entropy E2E2 E2E2 E3E3

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

25. 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 W i as the number of accessible states with energy E i. For example: Boltzmann factor & Degeneracy 22 11 0 33 W=3 W=2 W=3 W=2 Assume that a more general formula for the probability P(E i, W i ) = (W i /Z) e -E i /kT of finding a molecule with energy E i, with the multiplicity factor W i. Using W i = exp[ln W i ] P(E i, W i ) = (1/Z) [exp(lnW i )] exp(-E i /k B T) P(E i, W i ) = (1/Z) exp -(E i – k B TlnW i )/k B T

26. Boltzmann continued Define S= k B ln[W i ] Note: ∆G because always energy w.r.t. some zero (like E, ∆E); define E and S. Typically, 1M concentration. P(E i, W i ) = (1/Z) exp -(E i – k B TlnW i )/k B T P(E i, W i ) = (1/Z) exp -(E i – TS)/k B T = = (1/Z) exp –[F i /k B T] where F = Helmholtz free energy which is same as Gibb’s Free Energy for liquids (non-gasses).

27.  G vs  F 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,  p and  V are ~ 0, so you can use either  F or  G. 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!

28. If you have many weak bonds (e.g. each bond only few kT) you can get a biomolecule that will not fall apart, like DNA. Zipped vs. unzipped What if 10 weak bonds?Answer? What if just one bond? Bond/unbound? Answer? DNA double helix: Many weak (H-bonds), makes for very stable structure. Many base pairs, essentially completely stable. Still have end-fraying, but probability that whole thing comes apart– essentially zero. H bonded ~ 2 k B T (for the free energy,  G) Note: The 2 k B T is the free energy, not potential energy, E i, so it includes the entropy term. It is a rough estimate (sequence dependent, and varies with length because the entropic effects vary), but in the ballpark.* * Nowadays, the per-pair entropic and enthalpic effects can be accounted for so accurately that 10-50 mer DNA melting points can be calculated to 1-2 °C.

29. Equilibrium How stable is one state over another? A  B Probability of being in B = Z -1 exp(-G B /kT) Probability of being in A = Z -1 (exp-G A /kT) K eq = B/A = exp (-G B /kT+ G A /kT) = exp –([G A - G A ]/kT)= exp –(∆G/kT) What about A  B + C K eq = [B][C]/[A]. But how to figure out in terms of ∆G ? K eq = exp –(∆G/kT) ∆G = -kTlnK eq

30. This tells about equilibrium. Tells nothing about kinetics. Tells nothing about why two are stable.

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

32. Breaking down a polymer How you get energy/ Why you eat. (b) Hydrolysis: breaking down a polymer Hydrolysis is addition of a water molecule, breaking a bond. 1 23 4 1 23 Both initial and final systems are stable at equilibrium, cause they have activation energy to convert! E initial = High or Low energy ? E final = High or Low energy? S initial = High or Low entropy ? S final = High or Low entropy At your body T,  G =  H - T  S < 0 and at equilibrium, it will go. Notice that depending on T,  G can flip sign, from e.g. rt T to body T.  G can also depend on conditions —e.g. a lot of acid in your stomach, make peptide bonds unstable. Eat protein [poly-amino-acid], polysaccharides [sugars] into smaller pieces, get energy out. It is the change in energy or entropy that matters: is E initial (S initial ) higher or lower than E final (S final ) ?

33. Sugar—high energy use carbohydrates for energy Why is sugar stable? –run eractions forward vs backwards—it’s  G transition : not whether products are above or below reactants.

34. Evaluate class 1. 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. Put your name in upper right-corner. Then tear off your name before turning in. (That way you can be brutally honest!) Answer, and turn in at the end of class. (I’ll give you ~5 minutes.)