1. 3.052 Nanomechanics of Materials and Biomaterials Prof. Christine Ortiz DMSE, RM 13-4022 Phone : (617) 452-3084 Email : cortiz@mit.edu WWW : http://web.mit.edu/cortiz/www LECTURE #18 : ELASTICITY OF SINGLE MACROMOLECULES III Nanomechanics of Biopolymers

2. Review : Elasticity Models for Single Polymer Chains Freely-Jointed Chain (FJC) (Kuhn and Grün, 1942 James and Guth, 1943) Extensible Freely-Jointed Chain (Smith, et. al, 1996) Worm-Like Chain (WLC) (Kratky and Porod, 1943 Fixman and Kovac, 1973 Bustamante, et. al 1994) Extensible Worm-Like Chain (Odijk, 1995) Gaussian : F elastic = [3k B T /L contour a] r Non-Gaussian : F elastic = (k B T/a) L*(r/L contour ) low stretches : Gaussian, L*(x)= “inverse Langevin function”= 3x+(9/5)x 3 +(297/175)x 5 +(1539/875)x 7 +... high stretches : F elastic =(k B T/a)(1-r/L contour ) -1 Non-Gaussian : F elastic = (k B T/a) L*(r/L total ) where : L total = L contour + nF elastic /k segment Exact : Numerical solution Interpolation Formula : F elastic = (k B T/p)[1/4(1-r/L contour ) -2 -1/4+r/L contour ] low stretches : Gaussian, F elastic = [3k B T /2pL contour ] r high stretches : F elastic = (k B T/4p)(1-r/L contour ) -2 Interpolation Formula : F elastic = (k B T/p)[1/4(1-r/L total ) -2 -1/4 + r/L total ] low stretches : Gaussian high stretches : r = L contour [1-0.5(k B T /F elastic p) 1/2 + F elastic /k segment ] F F r F elastic  F F r  F F r  (a, n) (a, n, k segment ) (p, n) (p, n, k segment ) MODELSCHEMATICFORMULAS F r F elastic  F

3. Force Spectroscopy Experiment on Single Polymer Chains

4. Force (nN) Distance (nm) Typical Force Spectroscopy Experiment on Single Polystyrene Chain retracting approaching L chain  180 nm AFM probe tip substrate V IV II III VI I III CHCH 2 n

5. Force Spectroscopy Experiment on a Single Polystyrene Chain : APPROACH I. No Tip-Sample Interaction L o  2R F D (nm) F (nN) -0.1 0 0.1 0.2 0.3 -202060100140180220 RFRF I. LoLo end-anchored polymer brushes, L o  6R F (H. J. Taunton, et al. Nature 1988, 332, 713) adsorbed polymer layers, L o  3R F (J. Klein, et al. Nature 1984, 308, 836)

6. -0.1 0 0.1 0.2 0.3 -202060100140180220 Force Spectroscopy Experiment on a Single Polystyrene Chain : APPROACH II. Compression of Polymer Chain and Chain Segment Adsorption to Tip (VDW) D (nm) F (nN) L o  2R F II. LoLo

7. Force Spectroscopy Experiment on a Single Polystyrene Chain : APPROACH / RETRACT III. No Jump-To-Contact* Constant Compliance Regime -0.1 0 0.1 0.2 0.3 -202060100140180220 D (nm) F (nN) III. (* polymer screens tip-surface VDW interaction)

8. Force Spectroscopy Experiment on a Single Polystyrene Chain : RETRACT D (nm) F (nN) L o  2R F IV. -0.1 0 0.1 0.2 0.3 -202060100140180220 LoLo

9. Force Spectroscopy Experiment on a Single Polystyrene Chain : RETRACT L o  2R F L chain D (nm) F (nN) V. -0.1 0 0.1 0.2 0.3 -202060100140180220 L chain LoLo F chain

10. Force Spectroscopy Experiment on a Single Polystyrene Chain : RETRACT D (nm) F (nN) VI. -0.1 0 0.1 0.2 0.3 -202060100140180220 F chain F adsorption F bond Since F adsorption << F bond (AU-S) = 2-3 nN* chain always desorbs from tip (*based on Morse potential using E b(AU-S) =170 kJ/mol; Ulman, A. Chem. Rev. 1996, 96, 1553)

11. -0.15 -0.1 -0.05 0 0100200300400500 F chain (nN) Comparison of Experimental Data on Polystyrene with the Freely-Jointed Chain Model (a = 0.68 nm) Distance (nm) 68040029014676 n

12. Muscle Elasticity (*MARSZALEK, et. al Nature 402, 100 - 103 (1999)) (*Cell and Molecular Biology, G. Karp) SARCOMERE TITIN Actin TITIN Myosin Nebulin

13. PROTEIN STRUCTURE : TITIN secondary structure : local chain configuration  -helix primary structure : sequence of amino acids chemical structure : atomic order, chemical bonds (e.g. peptide) tertiary structure : additional chain folding over longer distances : globular domain “MODULAR” STRUCTURE linear array of folded domains in series  -sheet

14. Molecular Elasticity of Titin (*Rief, et al. Science 1997, 276, 1109)

15. Molecular Elasticity of Titin (*Rief, et al. Science 1997, 276, 1109)

16. Molecular Elasticity of Titin (*Rief, et al. Science 1997, 276, 1109)

17. Molecular Elasticity of Titin (* http://www.ks.uiuc.edu/Research/titinIg/ )