Today’s lecture #2 Close the door (thanks anonymous person) Web cite: PRS.html (my web site…click on Physics 475 Sp13) xSP13.html Kind of rushed today cause want to get to protein structures for Klaus Schulten’s lecture Quick things 01/15/2013

Questions from last Lecture Liked King Kong Could he have existed? No Quantum Mechanics Not really relevant, Although Heisenberg Uncertainty Principle and theory of fluorescence/light is somewhat relevant. Topics of written/oral --you choice, although most likely should be from Science, Nature, Cell. See handout on Web page.

Today’s lecture Temperature of earth: Greenhouse Effect What is Life? ∆G and ∆E stability of molecules The 4 types of macromolecules Nucleic Acids, Proteins, Carbohydrates, Lipids Central Dogma of Molecular Biology DNA Protein Structure

Is there water-based life on other planets? Example of physical limits to life. Idea: For water-based life, 0º < T ave < 100ºC Answer: Heat (photons) from sun I e = 1.35 kW/m 2 # Floodlight ~ 30 (1 meter away) (Incandescent light 3% efficient) Can we calculate T ave of planets in our solar system? Earth What determines (surface) temp? 1 meter How much light? How many (flood)lights?

= (1-  e  R e 2  = reflectivity of object  earth ≈ 0.3 Too cold! Actual = 288 ° K = 15 ˚C =  σ T 4 x (surface area) σ = const (=5.7 x W/m 20 k 4 ) T = absolute Temp. (Stefan-Boltzmann Law) Kittel, Thermal Physics pg  I e  R e 2 = (  σT 4 )( 4  R e 2 ) [Note: R e 2 cancel] Why determines earth temperature? Why can life exist? = 253° K = -15 ˚C Heat In (Absorbed) = Heat Out If Earth had no atmosphere the global average surface temperature would be -15˚C. With an atmosphere, temp is actually would be ≈15˚C.    Heat out Heat in Temp of earth constant Heat in = Heat out 

Conclusions of calculations Temp of earth primarily determined by sun’s photons, not earth’s mantle. Sun Heat out Heat in Earth Calculation off because of Greenhouse effect: earth has an atmosphere. You calculate what temperature should be!

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 (1/Z) [exp(lnW i )] exp(-E i /kT) 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 ] ; and later define S= kln[W i ]; G= E-TS P(E i, W i ) = (W i /Z) exp(-E i /kT) = = (1/Z) exp -(E i – kTlnW i )/kT Define S= kln[W i ] P(E i, W i ) = (1/Z) exp -(E i – TS)/kT = = (1/Z) exp –(F i )/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.

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) ∆G = -kTlnK eq

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). 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 + forward ∆G + rev ∆G ∆G + forward ∆G + rev ∆G K eq = exp(-∆G/kT) K eq = f(∆G)? ∆G = -kT ln (K eq )

Breaking down a polymer How you get energy/ Why you eat. (b) Hydrolysis: breaking down a polymer Hydrolysis adds a water molecule, breaking a bond Gives (free) Energy (E final < E initial ; S final > S initial ) Both systems are stable cause they have activation energy to convert! High energy E initial Low(er) energy E finall Carbohydrate—polymer You eat food, break it down into smaller pieces and you gain energy

(a) Dehydration reaction: synthesizing a polymer Short polymer Unlinked monomer Dehydration removes a water molecule, forming a new bond. Longer polymer Forming/breaking down a polymer Takes (free) Energy (ATP) (E final > E initial ; S final < S initial ) You live by taking some energy (in the form of a small molecule ATP, Adenosine Tri- Phosphate, whose energy ultimately comes from food, which gets energy from the Sun) and building up polymers. E final = E initial + ATP + heat

Need to know Chemical Bonding – 100kT. Sharing of electrons. C-H –kT (weakest, but many of them together--significant). Two neutral atoms have instantaneous dipoles, and attract. 1.Hydrogen attached to a very electro- negative elements, (O, N) causing the hydrogen to acquire a significant amount of positive charge. 2.Lone pair– electrons in relatively small space, very negative. Result is H is (+) and O is (-). Will bind to other molecules Neon: -246°C; Xenon: -108°C Is light enough to break covalent bond? 1um =1eV; kT=1/20eV. 1um= 20kT: close (yup) - varies tremendously, 100kT to few kT. + and – attract, but depends on solvent. Na + Cl - = few kT (break up easily) – few kT, up to 5kT 4 types 1. Covalent 2. Ionic 3. Hydrogen 4. Van der Waals

Break time! Somebody wrote: “It’s very funny to meet random people in class” so do like last time… 4 minutes (2 min per person) With someone you don’t know, Find out their: 1.Name, Year, undergrad vs. grad. 2.Why you’re taking the course. 3.Tell one thing that’s surprising. A few people will have to report!

4 Large [Macro]Molecules (from small molecules) Biological polymers (Large molecule made from many smaller building block) DNA & RNA  Nucleotides Proteins  Amino Acids Carbohydrates  Sugars Fats (also called Lipids)  Fatty acids Each is used to: a.Make macromolecules/structural b.Energy Source c.Information– Storage/signaling DNA & RNA ; ATP; Genetic Information Proteins; break down yields energy; nerve impulses. :

The 4 types of macromolecules DNA (RNA) Proteins Lipids (Fat) Carbohydrates

Primary --20 different amino acids Secondary Tertiary (single polypeptide) Quaternary– multiple polypeptides Myoglobin- 1 Protein Structures

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

Figure 5.20b Secondary structure Tertiary structure Quaternary structure Hydrogen bond  helix  pleated sheet  strand Hydrogen bond Transthyretin polypeptide Transthyretin protein (  arrow toward carboxyl end) 4 Different layers of Protein Structure

Minimal knowledge about Nucleotides 4 nucleotides: A,T,G,C A=T ≈ 2kT two hydrogen bonds G=C ≈ 4kT three hydrogen bonds [More Next time]

Homework #1 Assigned! Due at beginning of class Jan. 23, 2013 [also read Chpt 1 of Phillips et al.

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.)