A few organizational items Topic for Biophysics research paper was due Feb. 1 Outline of research paper is due March 4 (before spring break) We are going to have a pizza & movie night, (watch two movies about discovery of DNA structure). Time/date to be announced. Graduate students: Please remember presentation.

Homework 3 (due Fr., Feb. 12): Reading: Van Holde, Chapter 1 (Biological macromolecules) Van Holde Chapter 3.1 to 3.3 (Molecular interactions, skim 3.4) Van Holde Chapter 2 (Brief Thermodynamics, Gibb’s free energy) Van Holde Chapter 4 (cursory reading) 1.Consider the isomerization reaction of Dihydroxyacetone phosphate (DHP) to Glyceraldehyde 3-phosphate (GP) which occurs in glycolysis. At equilibrium the ratio of GP to DHP is at 25  C and pH 7 (standard conditions). (a) What is the standard free energy change for this reaction? (b) If the initial concentration of DHP is 2 x M and that of GP is 3 x M, what is  G for that state? Is it higher or lower than the value in (a)? In which direction will the reaction proceed (toward DHP or GP)? 2.van Holde, Problem van Holde, Problem Van Holde, Problem 2.8 (Solutions to odd-numbered problems are in back of book. Careful, sometimes solutions are a bit off). Note: Careful about occasional switch in units (J, J/mole, kJ, kJ/mole, etc) Introduction-3 Thermodynamics

In this section, we are asking, in which direction (forward/backward) will a biochemical reaction proceed? This will depend on two quantities: 1.The enthalpy,  H, of the reaction. This corresponds roughly to the sum of all the potential energies we discussed in Introduction-2. 2.The entropy,  S of the reaction. This relates to the number of ways the system can adopt. In other words, it will depend on the Gibbs’ free energy,  G of the reaction: Equilibrium constant and Gibbs free energy Van’t Hoff plot Hydrophobic effect and Kyte-Doolittle scale Introduction-3 Thermodynamics

Enthalpy Why is it useful? –The enthalpy change between the initial and final states of a biochemical process,  H, is the easily measured heat that it generates or absorbs. (Biochemical process, usually const. pressure reaction) –H is a state function.  H of a reaction only depends on initial state and final state of reaction; it does not matter what goes on between states. Example: Measuring enthalpy of oxidation of glucose to CO 2 and H 2 O directly in muscles would be very difficult. But, since enthalpy is a state function, we can measure the enthalpy of this reaction in any apparatus (e.g. a constant pressure calorimeter) and get the same result. We don’t even need to know the reaction mechanism, as long as we know the initial and final state. Definition: H = E + PV (is a state function) Most biochemical processes occur in liquids or solids (rather than gases), so volume changes are small.  To a good approximation, we can often neglect the difference between  H and  E in biochemistry and simply talk about the change in ‘energy’ accompanying a reaction.  H is basically, the sum of all the potential energies we discussed in Introduction-2.

Entropy Still, the enthalpy alone cannot tell us if a reaction occurs spontaneously (by itself). Two examples: –When two blocks are brought in contact, heat flows from the hot one to the cold one, never vice versa (‘reaction’ occurs, but enthalpy of system stays the same). –Two bulbs of equal volume connected by a valve. All molecules are on one side first; when the valveis opened, molecules diffuse back and forth, until they are equally distributed (‘reaction’ occurs, but enthalpy of system stays the same). Total number of states: 2 N. The number of ways W of putting L of the N molecules into the left bulb is: Most probable state: highest value of W L Here: L = N/2.

k B … Boltzmann constant k B = 1.38* J/K S is state function For gas bulb example (previous slide): Entropy of the one molecule on left: S = k B ln3 = 1.1k B. Entropy of all molecules on one side: W N = 1  S=0. Entropy of having N/2 molecules in each bulb is largest. The laws of random change cause any system of reasonable size to spontaneously adopt its most probable arrangement, the one in which entropy is a maximum, simply because it is so overwhelmingly probable. Once the most probable state has been reached, the system stays there (macroscopically) and is said to have reached equlibrium. (Here: Assume all states have same energy) Boltzmann’s grave, Vienna Entropy In chemical systems, the number of ways, W, of arranging a system in a particular state is huge. Define entropy of a system:

Example: A certain 100 amino-acid long polypeptide chain has only one alpha-helical conformation but there are three possible orientations for each residue in the random-coil state. 1. Calculate  S for the conformational change Random coil  alpha helix. 2. Does the entropy increase or decrease for this transition? As nicely illustrative as this problem is, it ignores the entropy of a very important element of biological systems – which one?

Examples of entropy Quasi-reversible heat transfer (const Temp): Isothermal, reversible expansion of gas from V 1 to V 2 (p. 84): Isothermal dilution of a solute from concentration C 1 to C 2 (p. 85): Entropy of mixing (p. 86): X i mole fraction of species i n… number of moles of species i

Systems at constant temperature and pressure (most biochemical systems) Define Gibbs free energy: G = H – TS, then dG = VdP – SdT; for const. P & const. T systems (dP = dT = 0); dG = 0.  G must be an extremum (minimum) for such a system to be at equilibrium! Gibbs free energy is of enormous importance in deciding the direction processes & equilibrium positions in biochemical systems If  G for a particular process is negative, that process is spontaneous, because it leads in the direction of equilibrium.  H and  S are equally important  Energy minimization and entropy maximization play a part in determining the position of equilibrium.

Gibbs free energy

The native and denatured forms of a protein are generally in equilibrium. For a certain protein, (total conc 2.0 * M) the concentration of the denatured and native forms at 50°C and 100°C is given in the table. TempDenatured (M)Native (M) 505.1* * * * Determine  H and  S for the folding reaction (assuming they are independent of T) 2.Calculate  G for this protein at 25°C. Is the folding process spontaneous? 3.What is the denaturing temperature for this protein at standard conditions?

Van’t Hoff Plot K eq and G 0 are temperature dependent 1/T (1/K) ln K eq Slope: -  H 0 /R Enthalpy can be calculated from slope; Then get  S from van’t Hoff equation  H and  S are temp- independent over small temp ranges. Measure K eq as a function of T: Van’t Hoff equation

Gibbs free energy in real life For real biochemical reactions we need to consider  G for the object under study (e.g. protein, reaction, etc) AND  G for the solvent (usually water) Water molecules form Hydrogen bonds (enthalpy). “Fixing” water molecules will “cost” decrease entropy of system (entropy).

Application of Gibbs free energy to protein and DNA stability Need to consider enthalpy part of protein/DNA. These are the potential energies we discussed. Bonding potential, Hydrogen bonds, charge- charge interactions, dipole-dipole interactions, van-der-Waals, etc. Need to consider entropy part of protein/DNA. Folded protein has one conformation (low entropy) and unfolded protein has many conformations (high entropy). Need to consider enthalpy of water. Water forms many H-bonds. Need to consider entropy of water. Need to consider enthalpy of ions in solution (charge-charge interactions) Need to consider entropy of ions in solution (binding (fixing) will lower entropy).

Hydrophobic effect Perhaps most important contribution to protein folding. Hydrophobic (non-polar) substances don’t want to “touch” water. –  hydrophobic residues are on protein inside –  bases are on DNA inside (base-pairing (H- bonds), doesn’t contribute much)

Hydrophobic effect It is an entropy effect: Transfer of hydrophobic residues from water to non-polar solvent (e.g. benzene) Often a small  H, but a large, favorable  S component. Why?  Sticking a hydrophobic substance into water, makes the water form a fixed cavity around the substance  This “costs” (decreases) the entropy of the water.

Hydrophobicity determines placement of amino acid in protein (related to protein folding). In aqueous environment, hydrophobic residues hide inside; (this is reversed in the membrane). Hydropathy – feeling about water; hydrophilic – likes water; hydrophobic – does not like water. Kyte-Doolittle Scale: They used vapor to water, others have used ethanol to water. In this equation: If X aq > X nonaq then  G is negative – hydrophilic If X nonaq > X aq then  G is positive – hydrophobic e.g.  G transfer for val is 2.78,  G transfer for Glu is (in Kcal/mole) Kyte and Doolittle actually used combination of: *  G transfer *(fraction 100% buried) – *(fraction 95% buried) – 4.71 aa H2OH2O Non-polar They combined these three things to get a hydropathy index that ranges from +5 (very hydrophobic) to -5 (very hydrophilic).