Introduction to Polymer Physics

Introduction to Polymer Physics Enrico Carlon, KU Leuven, Belgium February-May, 2016 Enrico Carlon, KU Leuven, Belgium Introduction to Polymer Physics February-May, 2016 1 / 28

Polymers in Chemistry and Biology Polyethylene: Synthetic polymer. It is the most known form of plastic. The degree of polymerization can be n = 10 7. E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 2 / 28

Polymers in Chemistry and Biology Polyethylene: Synthetic polymer. It is the most known form of plastic. The degree of polymerization can be n = 10 7. Cellulose: the most abundant natural polymer on Earth. Essential component of the cell wall in plants. The degree of polymerization n 10 3. E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 2 / 28

DNA (most common: B form, alternatives: A and Z forms) E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 3 / 28

B-DNA: some details E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 4 / 28

Some basics of DNA... Two intertwined strands forming a double helix Four bases: Adenine Thymine Guanine Cytosine A and G are purines while T and C are pyrimidines Complementary bases form hydrogen bonds (A=T, C G) The two strands are antiparallel (5-3 and 3-5 ) One full helix turn corresponds to 10 base pairs The double helix has a major groove and a minor groove E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 5 / 28

RNA Similar chemically to DNA but with ribose (less stable). The four bases A, U (Uracil replaces the Thymine), G and C Usually single stranded, but can bind to form RNA/RNA and DNA/RNA helices It can fold into itself to form a three dimensional structure Here: transfer RNA (trna) E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 6 / 28

RNA Base pairings: C G A=U G=U E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 7 / 28

Proteins Building blocks 20 Aminoacids Common chemical composition with a variable side chain R R can be polar (hydrophilic) or non-polar (hydrophobic) Black: α-carbon Examples Red: Side chain Ser and Thr polar Cys nonpolar E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 8 / 28

Polar and non-polar aminoacids There is an equal number of polar and non-polar aminoacids E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 9 / 28

Peptide bonds Aminoacids are held together by peptide bonds These are formed between C and N terminals with the release of a water molecule Typical protein 50 2000 aa Primary structure... - Ser - Glu - Gln - Ala - Val -... (sequence of aminoacids) E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 10 / 28

Non-covalent bonds help protein folding Many weak bonds (hydrogen bonds, ionic bonds and van der Waals attractions) act together to fold a protein. Add to these hydrophobic forces. E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 11 / 28

Secondary structure: α-helix Helix period 0.54 nm (DNA 3.4 nm) Side chains are not involved in the structure formation Pattern due to hydrogen bonds between N-H and C=O groups Bonds between group i and group i + 4 E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 12 / 28

Secondary structure: β-sheet As α-helices, β-sheets are held together by hydrogen bonds between N-H and C=O groups Can be parallel or (as here) antiparallel Side chains project alternately outside and inside the sheet E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 13 / 28

Tertiary structure: a protein is biologically active when folded A protein may be composed by different domains (units that fold independently from each others). Here Src protein kinase carrying an ATP molecule. E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 14 / 28

DNA melting Dissociation of the two strands of the double helix by an increase of temperature. It is a reversible phase transition! Dissociation can occur also through a change of ph... Melting experiments are rather easy to do! They were performed since the sixties to investigate the double helix stabilities under changes of external conditions (salt, ph... ) E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 15 / 28

UV absorption spectrum of DNA Single stranded DNA absorbs 30% more UV light (260 nm) than double stranded DNA UV absorbance is used to measure dsdna concentration c at room temperature A 260 = lε dsdna c Here ε dsdna is known and l is the thickness of the sample E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 16 / 28

DNA melting experiment Increase of absorbance as the temperature is increased indicates the dissociation of the two strands, ie DNA melting E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 17 / 28

Two state model of melting Short sequences melt approximately as a two state process [s 1 s 2 ] [s 1 ] [s 2 ] [s i ] concentration of strand i [s 1 s 2 ] concentration of duplex Equilibrium constant K eq = [s 1] [s 2 ] [s 1 s 2 ] = e β G Free energy difference G = H T S Melting occurs at (c t total single strand concentration) [s 1 ] = [s 2 ] = [s 1 s 2 ] = c t /4 E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 18 / 28

The melting temperature The melting temperature is 1 = S T M H R log(c t/4) H The melting temperature depends on the concentration! The figure shows a plot of 1/T M vs. log(c t /4) Precise determination of H and S from experiments. E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 19 / 28

Thermodynamics of base pairing A=T and G C base pairs have two and three hydrogen bonds! Is for instance the enthalpy simply H AT = 2ε and H CG = 3ε? base stacking hydrogen bonds No! There is also base stacking Bases prefere to pile up over other specific bases Stacking-unstacking is observed in single-stranded nucleic acids E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 20 / 28

The nearest neighbor model The model assumes that the stability of a given base pair depends on the identity of the adjacent base pair. For instance 5 3 GC C G 3 5 5 3 CG GC 3 5 5 3 GG C C 3 5 have all different stabilities! However, there are some symmetries 5 3 G A C T 3 5 5 3 T C AG 3 5 E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 21 / 28

The nearest neighbor model Experiments on melting of short RNA duplexes: Evidence against simple model T A = 26.5 C, T B = 34.4 C (c = 10 4 M, 1M NaCl) 5 3 GC GC C GCG 3 A 5 5 3 GGCC C C GG 3 B 5 Evidence for the nn model T A = 67.2 C, T B = 65.2 C (c = 10 4 M, 1M NaCl) 5 3 GCCGG C C GGC C G 3 A 5 5 3 GGCGC C C C GC G G 3 B 5 From experimental data on melting of short duplexes the nn parameters H ij, S ij are derived H = ij H ij + H init S = ij S ij + S init E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 22 / 28

Nearest neighbor parameters G 37 C (DNA/DNA) Table of nearest neighbor parameters for the hybridization free energies G 37 C in 1M NaCl expressed in kcal/mol. The orientation is 5-3 for the upper strand and 3-5 for the lower strand. Only 10 of the 16 parameters are independent. AA T T -1.00 AT T A -0.88 AC T G -1.44 AG T C -1.28 T A AT -0.58 T T AA -1.00 T C AG -1.30 T G AC -1.45 CA GT -1.45 GA CT -1.30 CT GA -1.28 GT CA -1.44 CC GG -1.84 CG GC -2.17 GC CG -2.24 GG CC -1.84 E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 23 / 28

Calculating free energies from the nn model Calculation of G 37 for a DNA/DNA duplex 5 A T G G C A T C 3 3 T A C C G T A G 5 0.88 1.84 1.45 1.30= 11.4 kcal/mole 1.45 2.24 0.88... plus boundary terms! The precise knowledge of DNA melting temperatures is very useful in many biotechnological applications! Note: the free energy parameters also depend on salt concentration! E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 24 / 28

Comparison with experiments The DNA base pairing thermodynamics is well-reproduced by the nn model T exp M T th. M 3 C Thermodynamic parameters have also been determined for RNA/RNA and RNA/DNA duplexes E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 25 / 28

Mismatches Base pairings can occurr also for non-complementary bases. Here: possible structure of a mismatch between G (left) and A (right) G A forms two hydrogen bonds! G A, G T and G G are the most stable DNA/DNA mismatches! Table of G 37 C at 1M NaCl for G A mismatches expressed in kcal/mol. The orientation is 5-3 for the upper strand and 3-5 for the lower strand. AA T G 0.14 AG T A 0.02 GA CG -0.25 GG CA -0.52 CA GG 0.03 CG GA T A AG 0.42 T G AA E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 26 / 28

DNA supercoiling in cells DNA in cells is mostly in a supercoiled form Here an electron microscope image of circular supercoiled bacterial DNA E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 27 / 28

DNA supercoiling in cells DNA in cells is mostly in a supercoiled form Here an electron microscope image of circular supercoiled bacterial DNA Supercoiling reduces the space occupied by DNA. Supercoiling is induced/reduced by specific enzymes the topoisomerases II, which cut, turn and resealed DNA. See: https://www.youtube.com/watch?v=t06lo8t8pmw E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 27 / 28

DNA supercoiling in MT experiments Supercoiling can be induced in a Magnetic Tweezer experiment If we apply a large number of turns (n > n c) the DNA is expected to buckle and form plectonemes The extension z decreases with the number of turns n and the torque on the bead increases with n. E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 28 / 28

DNA supercoiling in MT experiments Supercoiling can be induced in a Magnetic Tweezer experiment If we apply a large number of turns (n > n c) the DNA is expected to buckle and form plectonemes The extension z decreases with the number of turns n and the torque on the bead increases with n. z(n) stretched f 1 f 2 supercoil Here we show a typical experimental curves (called hat curves ) of extension vs. number of turns for two different forces. At zero turns (n = 0) this is the DNA force-extension curve, which is well-reproduced by the WLC model. n (#turns) E. Carlon (ITF, KU Leuven) Introduction to Polymer Physics February-May, 2016 28 / 28