In silico measurements of twist and bend. moduli for beta solenoid protein self-

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Joseph Maxwell
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1 In silico measurements of twist and bend moduli for beta solenoid protein self- assembly units Leonard P. Heinz, Krishnakumar M. Ravikumar, and Daniel L. Cox Department of Physics and Institute for Complex Adaptive Matter, University of California, Davis, California, USA SUPPORTING INFORMATION

2 Nano Letters Page of Supporting Information (a) (b) (c) (d) normalized persistence length Figure S: Persistence lengths, normalized by the number of hydrogen bonds per turn. The arrows indicate respective direction.

3 Page of Nano Letters Table S: Sequence of BSP. ASP LEU SER ILE VAL ASP LEU ARG GLY ALA VAL LEU GLU ASN ILE ASN LEU SER GLY ALA ILE LEU HIS GLY ALA MET LEU ASP GLU ALA ASN LEU GLN GLN ALA ASN LEU SER ARG ALA ASP LEU SER GLY ALA THR LEU ASN GLY ALA ASP LEU ARG GLY ALA ASN LEU SER LYS ALA ASP LEU SER ASP ALA ILE LEU ASP ASN ALA ILE LEU GLU GLY ALA ILE LEU ASP GLU ALA VAL LEU ASN GLN ALA ASN LEU LYS ALA ALA ASN LEU GLU GLN ALA ILE LEU SER HIS ALA ASN LEU ARG GLU ALA ASP LEU SER GLU ALA ASN LEU GLU ALA ALA ASP LEU SER GLY ALA ASP LEU ALA ILE ALA ASP LEU HIS GLN ALA ASN LEU HIS GLN ALA ALA LEU GLU ARG ALA

4 Nano Letters Page 0 of Table S: Sequence of BSP. ALA SER ARG ILE THR ASN SER GLN ILE VAL LYS SER GLU ALA THR ASN SER ASP ILE ASN ASN SER GLN LEU VAL ASP SER ILE SER THR ARG SER GLN TYR SER ASP ALA ASN VAL LYS LYS SER VAL THR THR ASP SER ASN ILE ASP LYS SER GLN VAL TYR LEU THR THR SER THR GLY SER GLN TYR ASN GLY ILE TYR ILE ARG SER SER ASP THR THR GLY SER GLU ILE SER GLY SER SER ILE SER THR SER ARG ILE THR ASN SER ARG ILE THR ASN SER GLN ILE VAL LYS SER GLU ALA THR ASN SER ASP ILE ASN ASN SER GLN LEU VAL ASP SER ILE SER THR ARG SER GLN TYR SER ASP ALA ASN VAL LYS LYS SER VAL THR THR ASP SER ASN ILE ASP LYS SER GLN VAL TYR LEU THR THR SER THR GLY SER GLN TYR ASN GLY ILE TYR ILE ARG SER SER ASP THR THR GLY SER GLU ILE SER GLY SER SER ILE SER THR SER ARG ILE THR 0

5 Page of Nano Letters Table S: Sequence of BSP. ASN ASP ILE ASP GLY THR ASN ASN GLU VAL ASP GLY SER GLU ASN VAL LEU ALA GLY ASN ASP ASN THR VAL SER GLY ASP ASN ASN SER VAL SER GLY SER ASN ASN THR VAL SER GLY ASN ASP ASN THR VAL THR GLY SER ASN HIS VAL VAL SER GLY THR ASN HIS ILE VAL THR ASP ASN ASN ASN ASN VAL SER GLY ASN ASP ASN ASN VAL SER GLY SER PHE HIS THR VAL SER GLY GLY HIS ASN THR VAL SER GLY SER ASN ASN THR VAL SER GLY LYS ARG HIS ARG VAL GLN GLY THR ASN ASN ARG VAL THR ASP

6 Nano Letters Page of Table S: Sequence of BSP. GLY VAL GLU ILE GLY GLU GLY THR VAL LEU LYS SER GLY VAL VAL VAL ASN GLY GLY THR LYS ILE GLY ARG ASP ASN GLU ILE TYR GLN GLY ALA SER ILE GLY GLY GLY VAL GLU ILE GLY ASP ARG ASN ARG ILE ARG GLU SER VAL THR ILE GLY GLY GLY GLY VAL VAL GLY SER ASP ASN LEU LEU MET ILE ASN ALA GLY ILE ALA GLY ASP CYS THR VAL GLY ASN ARG CYS ILE LEU ALA ASN ASN ALA THR LEU ALA GLY GLY VAL GLU ILE GLY GLU GLY THR VAL LEU LYS SER GLY VAL VAL VAL ASN GLY GLY THR LYS ILE GLY ARG ASP ASN GLU ILE TYR GLN GLY ALA SER ILE GLY GLY GLY VAL GLU ILE GLY ASP ARG ASN ARG ILE ARG GLU SER VAL THR ILE GLY GLY GLY GLY VAL VAL GLY SER ASP ASN LEU LEU MET ILE ASN ALA GLY ILE ALA GLY ASP CYS THR VAL GLY ASN ARG CYS ILE LEU ALA ASN ASN ALA THR LEU ALA GLY

7 Page of Nano Letters Validation of the Beam Model To check the validity of the simple beam model for calculating persistence lengths, we subjected the proteins to bending and twisting at dierent helical turns along their length in addition to the last turn reported in the main text. We used the longest (BSP, turns) and the shortest (BSP, turns) β-solenoid proteins for these simulations. Both proteins were subjected to forced bending and twisting simulations (as described in the Methods section), where velocities of pm/ps a and 0.0 /ps respectively were used. Bending (k x ) and torsional (k θ ) stiness values were obtained by using a linear t to the force-displacement curves. The direction of bending (or twisting) and the measured stiness at dierent helical turns are shown in Fig. S (blue dots). Note that in the simple beam model used, k / x = C x L and k θ = C θ L, where C x = (EI) / and C θ = (GJ) are the proportionality constants related to the exural and torsional rigidity respectively, and L is the length of the center of the helical turn from the xed end where the bending force is applied. These stiness values at dierent lengths ( L) are shown in Fig. S. The solid line in Fig. S are the linear ts based on the last turn alone, while the dashed lines are ts based on the last three turns of the helix. It is clear from Fig. Sa,c (solid line), that for L < nm, the simple beam model does not hold in the bending simulations suggesting that for length scales greater than nm, the simple beam model might be practically sucient to describe the mechanical behavior of the proteins. In the case of twisting, (Fig. Sb,d) rather surprisingly, the beam model works for even shorter length scales. Further, to get an estimate of the expected error in these measurements, we calculated the exural and torsional rigidity values and compared them with those for the last turn alone (calculated using the solid lines in Fig. S). The relative errors for exural rigidity are % (BSP) and % (BSP), while those for the torsional rigidity are % (BSP) and % (BSP) respectively. This material is available free of charge via the Internet at

8 Nano Letters Page of k -/ aa[(kj/mol/nm²) -/ ] k -/ aa[(kj/mol/nm²) -/ ] - - (a) (b) (c) (d) Lengtha[nm] k - aa[(kj/mol/rad) - ] k - aa[(kj/mol/rad) - ] Lengtha[nm] Figure S: Spring constants for bending ((a), (c)) and for torsion ((b), (d)) measured at dierent lengths (L) along the molecules (BSP, BSP). The direction of bending and torsion are marked b the arrows marked in the cross section of the proteins. The helical turn number is marked beside each data point. Solid lines show the linear t expected according to beam theory, calculated with the spring constant of the last turn alone. Dashed lines are ts for the last turns of the molecules. (b) and (d) show the analogous plots for torsion.

Programme Good morning and summary of last week Levels of Protein Structure - I Levels of Protein Structure - II

Programme Good morning and summary of last week Levels of Protein Structure - I Levels of Protein Structure - II Programme 8.00-8.10 Good morning and summary of last week 8.10-8.30 Levels of Protein Structure - I 8.30-9.00 Levels of Protein Structure - II 9.00-9.15 Break 9.15-11.15 Exercise: Building a protein model