Homework 2 (due We, Feb. 1): Reading: Van Holde, Chapter 1 Van Holde Chapter 3.1 to 3.3 Van Holde Chapter 2 (we’ll go through Chapters 1 and 3 first. 1.Van Holde 3.1(Coulomb potential) 2.Van Holde 3.2(Dipole-diople interaction) 3.Van Holde 3.3(Lennard-Jones potential) 4.Van Holde 3.4(force is gradient of potential) 5.Van Holde 3.6(Manning theory of counterion condensation) 6.Van Holde 3.9(Hydrogen-bond potential) Paper list (for presentations) is posted on web site Introduction-2 Important molecular interactions in Biomolecules

The notion of potential energy The force, with which molecules attract or repel each other is: Force is negative of (gradient) slope of potential well  Molecules get “pushed” to the lowest point of potential  Molecules sit in minimum of potential function V x Molecular potentials: (We are ignoring entropy for the time being (  Gibbs free energy)

Bonding potential (covalent bonds) V bonding is big, but  V bonding between conformations is not so big  V nonbonding is what counts most for folding. The bond potentials are often approximated by harmonic potentials (good for small deflection): ( kJ/mole)

Charge-charge interaction A lot of biological molecules are charged. Amino acids: Asp -, Glu -, Lys + Arg +, His + ; DNA: phosphates - in backbone, salt ions, etc. Like charges repel, opposite charges attract. Z 1,2 … amount of charge e … charge of electron e = 1.6* C r … separation of charges D … Dielectric constant; D =  r  0  0 … permittivity constant  0 = 8.85* C 2 /Nm 2  …4  in SI units  r … relative permittivity (depends on material) The tricky part 1: D not constant) D water = 78.5·  0 (easy). D inside a protein varies (1·  0 to 20·  0, average ~3.5  0 ) and depends on the local environment Various approx. to deal with this Tricky part 2: (counterion screening) Really also related to D not being constant) Counterions (salt) condense/surround fixed charges on protein/DNA (~ 60 kJ/mole, long-range)

Counterion shielding (screening) N fixed charges in vacuum have the following potential: The ions in solution are then forming a “cloud” around those charges, which effectively screens the fixed charges from each other: Debye-Hückel screening parameter  : (“decay length of charge strength) D … dielectric constant k B … Boltzmann constant T … absolute temperature I … ionic strength; e … electron charge N A … Avogadro’s number c … ion concentration Z… valency Solution ions form a “cloud’ around the fixed charges on protein surfaces or DNA.  The electric potential of these fixed charges is weakened (damped). This damping is called Screening.

Counterion condensation (Manning theory) How large is the net charge of the phosphates then? Amount of charge neutralized: Thus, for B-DNA, 76% is compensated in aqueous Na+ environment and 24% is not compensated. Charges also condense (bind longer) onto fixed protein/DNA charges, and partly neutralize them. This effect does not depend on ion concentration (like screening). For condensation of counterions onto DNA: If a charge is actually “condensed”, depends on the parameter  For  > 1, condensation occurs. For an electrolyte in water,  = 0.71/b, with b in nm. At 25°C,  = 4.2 for B DNA.  So, counterions do condense on DNA. b … distance between charges. For DNA: b = h/Z = 0.34/2 = 0.17

Dipole-dipole Interactions Dipole moment (note: vectors) +- General dipole-dipole interaction: If  1 and  2 are side by side: If  1 and  2 are parallel: (~ -2 to 2 kJ/mole, shorter range, can act in series)

Induced dipole-induced dipole interactions (van der Waals interactions) Attractive London Dispersion potential: I … ionization energy of atoms  1,  2 polarizabilities of atoms Repulsive potential from electron cloud: Strong force when r is small, m = 5 to 12 Combining them we get the van der Waals potential: And for m = 12 the Lennard-Jones potential: A, B are constants that depend on the type of interacting atoms in table 3.4 (~ kJ/mole, very short range)

Hydrogen-bonds Important for protein/DNA stability Easy make-easy break, directional  requires very accurate alignment. 11 22 D-H …………. A This potential is added to the dipole-dipole interaction and only contributes ~ 2 KJ/mole of energy. H-bonds – it is still debated how to treat H-bond potential. Treat like dipole-dipole interaction (4-48 kJ/mole). Best alignment (diagram) gives: However, some aspects of H-bond are similar to covalent bonds – e.g. the optimal distance between donor and acceptor is very short (see next page)! So, model that by a van der Waals potential: C, D depend on the particular donor and acceptor In real life, we need to consider H-bonding to water too!! So unless solvent is accounted for, H-bonding affect is overestimated. Hydrogen bond are important in the inside of proteins and DNA (obviously). (0-48 kJ/mole, very short range, directional  provide specificity)

H-bond examples Watson-Crick base- pairing

 -helix (© by Irvine Geis) Biochemistry Voet & Voet Red – oxygen Black – carbon Blue – nitrogen Purple – R-group White – C  Hydrogen-bonds between C-O of n th and N-H group of n+4 th residue. Non-Watson-Crick base-pairing Watson-Crick base- pairing