Supporting information for: Hydrodynamic properties of wormlike
Supporting information for: Hydrodynamic properties of wormlike macromolecules: Monte Carlo simulation and global analysis of experimental data D. Amorós, A. Ortega, and J. García de la Torre ∗ Departamento de Química Física, Facultad de Química, Universidad de Murcia, 30071 Murcia, Spain E-mail: [email protected]
∗ To
whom correspondence should be addressed
S1
Table S-1: Numerical results from the Monte Carlo simulation, for the GT , GI and Rg /Rg,BD of wormlike chains without excluded volume, as functions of N and Z. Some columns (for Z=0.075, Z=0.33 and Z=0.60) have been suppresed for the sake of brevity. Values of GT (NO-EXCVOL) N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.000 1.225 1.397 1.680 1.889 2.124 2.401 2.603 3.243 3.512 3.695 4.072 4.306 4.357 4.304 4.042 3.562
1.000 1.225 1.397 1.679 1.887 2.120 2.395 2.594 3.212 3.460 3.626 3.936 4.055 4.035 3.893 3.569 3.120
1.000 1.225 1.397 1.678 1.885 2.117 2.389 2.584 3.182 3.411 3.560 3.815 3.853 3.789 3.620 3.290 2.886
1.000 1.225 1.396 1.676 1.882 2.112 2.380 2.571 3.139 3.343 3.473 3.659 3.622 3.515 3.324 3.001 2.680
1.000 1.225 1.396 1.673 1.875 2.100 2.359 2.541 3.048 3.206 3.298 3.382 3.245 3.110 2.935 2.662 2.410
1.000 1.225 1.395 1.668 1.868 2.087 2.336 2.507 2.958 3.075 3.139 3.152 2.980 2.838 2.686 2.446 2.191
1.000 1.225 1.394 1.664 1.860 2.075 2.314 2.476 2.878 2.967 3.009 2.982 2.792 2.665 2.524 2.312 2.089
1.000 1.225 1.391 1.656 1.845 2.049 2.270 2.415 2.737 2.782 2.800 2.724 2.544 2.432 2.322 2.147 2.001
1.000 1.225 1.385 1.632 1.803 1.980 2.158 2.266 2.455 2.449 2.440 2.338 2.200 2.135 2.066 1.943 1.846
1.000 1.225 1.379 1.609 1.764 1.920 2.067 2.152 2.277 2.257 2.245 2.157 2.044 2.001 1.925 1.875 1.783
1.000 1.000 1.000 1.225 1.225 1.225 1.368 1.352 1.342 1.568 1.517 1.488 1.698 1.618 1.576 1.822 1.711 1.655 1.929 1.787 1.717 1.986 1.825 1.748 2.056 1.872 1.790 2.033 1.854 1.779 2.027 1.852 1.778 1.968 1.823 1.761 1.894 1.777 1.727 1.861 1.762 1.716 1.812 1.754 1.710 1.777 1.709 1.673 1.745 1.641 1.662
N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
0.400
0.500
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.000 1.175 1.340 1.542 1.678 1.817 1.961 2.055 2.305 2.395 2.453 2.567 2.637 2.655 2.645 2.558 2.443
1.000 1.175 1.340 1.542 1.677 1.815 1.959 2.052 2.296 2.382 2.436 2.534 2.575 2.573 2.534 2.418 2.268
1.000 1.175 1.339 1.541 1.676 1.813 1.956 2.048 2.288 2.369 2.419 2.503 2.521 2.504 2.451 2.330 2.203
1.000 1.175 1.339 1.540 1.674 1.811 1.953 2.044 2.275 2.350 2.395 2.460 2.453 2.421 2.354 2.224 2.121
1.000 1.175 1.338 1.537 1.671 1.806 1.944 2.033 2.248 2.309 2.343 2.377 2.331 2.282 2.211 2.092 1.989
1.000 1.175 1.336 1.534 1.666 1.799 1.935 2.020 2.218 2.267 2.292 2.300 2.233 2.176 2.109 1.990 1.856
1.000 1.175 1.335 1.531 1.662 1.793 1.926 2.008 2.191 2.230 2.247 2.238 2.158 2.103 2.037 1.926 1.794
1.000 1.175 1.333 1.525 1.653 1.781 1.907 1.984 2.139 2.160 2.168 2.135 2.051 1.995 1.940 1.839 1.746
1.000 1.175 1.325 1.508 1.627 1.744 1.854 1.917 2.018 2.014 2.009 1.957 1.879 1.841 1.798 1.720 1.665
1.000 1.175 1.318 1.491 1.603 1.711 1.807 1.860 1.930 1.917 1.910 1.859 1.791 1.762 1.716 1.684 1.616
1.000 1.175 1.305 1.460 1.558 1.649 1.724 1.763 1.804 1.787 1.784 1.745 1.697 1.675 1.643 1.617 1.603
1.000 1.175 1.287 1.417 1.497 1.569 1.625 1.653 1.684 1.670 1.669 1.649 1.619 1.607 1.601 1.568 1.522
1.000 1.175 1.277 1.391 1.461 1.524 1.571 1.595 1.625 1.616 1.617 1.605 1.583 1.576 1.570 1.547 1.540
0.400
0.500
Values of GI (NO-EXCVOL)
Values of RR (NO-EXCVOL) N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
0.400
0.500
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.342 1.096 1.044 1.016 1.008 1.004 1.002 1.007 1.000 1.000 1.000 1.001 1.000 1.000 0.998 0.996 1.007
1.342 1.097 1.044 1.016 1.009 0.953 0.997 1.000 1.000 1.000 1.001 1.003 1.000 1.001 0.997 0.996 1.010
1.343 1.097 1.045 1.017 1.009 1.017 1.001 1.001 1.000 0.999 1.001 1.004 0.999 1.000 0.999 1.000 1.010
1.343 1.098 1.045 0.965 0.995 1.003 1.001 1.001 1.000 0.999 1.001 1.005 1.000 0.999 0.997 0.996 1.014
1.344 1.099 1.099 1.016 1.009 1.004 1.002 1.002 1.000 0.998 1.001 1.007 0.998 0.997 1.002 1.001 1.010
1.345 1.045 1.043 1.019 1.010 1.004 1.003 1.002 1.000 0.998 1.002 1.009 0.999 0.995 1.004 0.998 0.994
1.346 1.089 1.050 1.019 1.011 1.004 1.003 1.002 1.000 0.997 1.002 1.010 0.997 0.995 1.003 0.994 0.985
1.279 1.105 1.052 1.021 1.012 1.005 1.003 1.002 1.000 0.996 1.002 1.009 0.997 0.992 1.003 0.995 0.989
1.353 1.117 1.061 1.026 1.015 1.005 1.003 1.003 1.000 0.992 1.001 1.002 0.988 0.993 0.996 0.989 0.985
1.361 1.128 1.070 1.031 1.018 1.006 1.003 1.001 0.998 0.989 1.000 0.998 0.983 0.989 0.975 0.991 0.983
1.375 1.150 1.087 1.040 1.023 1.006 1.001 0.998 0.994 0.980 0.993 0.991 0.980 0.981 0.970 0.980 0.978
1.395 1.182 1.111 1.053 1.030 1.006 0.998 0.992 0.985 0.972 0.980 0.979 0.970 0.971 0.982 0.968 0.951
1.408 1.203 1.127 1.061 1.034 1.007 0.995 0.988 0.978 0.967 0.972 0.972 0.963 0.965 0.972 0.960 0.959
S2
Table S-2: Numerical results from the Monte Carlo simulation, for the GT , GI, αg2 and Q∞ (N = ∞), of wormlike chains with excluded volume, as functions of N and Z. Some columns (for Z=0.075, Z=0.33 and Z=0.60) have been suppresed for the sake of brevity. Values of GT (EXCVOL) N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.000 1.225 1.397 1.680 1.889 2.124 2.401 2.603 3.242 3.512 3.695 4.074 4.306 4.357 4.307 3.972 3.540
1.000 1.225 1.397 1.679 1.887 2.120 2.395 2.594 3.211 3.460 3.626 3.935 4.053 4.036 3.909 3.617 3.103
1.000 1.225 1.397 1.678 1.885 2.117 2.389 2.584 3.180 3.411 3.560 3.814 3.854 3.789 3.647 3.303 2.855
1.000 1.225 1.396 1.676 1.882 2.112 2.380 2.571 3.137 3.343 3.473 3.660 3.618 3.519 3.329 3.039 2.627
1.000 1.225 1.396 1.673 1.875 2.101 2.359 2.540 3.044 3.205 3.298 3.382 3.234 3.118 2.932 2.683 2.394
1.000 1.225 1.395 1.668 1.868 2.088 2.336 2.508 2.952 3.076 3.139 3.123 2.981 2.852 2.692 2.449 2.215
1.000 1.225 1.394 1.664 1.860 2.075 2.314 2.476 2.871 2.968 3.009 2.957 2.785 2.696 2.526 2.337 2.144
1.000 1.225 1.391 1.656 1.845 2.050 2.270 2.415 2.728 2.786 2.789 2.695 2.568 2.453 2.330 2.182 2.062
1.000 1.225 1.385 1.632 1.803 1.983 2.159 2.266 2.453 2.458 2.443 2.342 2.237 2.160 2.100 2.006 1.914
1.000 1.225 1.379 1.609 1.764 1.925 2.069 2.151 2.281 2.276 2.265 2.171 2.088 2.054 2.013 1.946 1.918
1.000 1.000 1.000 1.225 1.225 1.225 1.368 1.352 1.341 1.567 1.520 1.492 1.703 1.622 1.586 1.845 1.714 1.665 1.933 1.800 1.753 1.993 1.844 1.778 2.069 1.922 1.860 2.061 1.930 1.873 2.039 1.919 1.877 2.012 1.907 1.881 1.973 1.896 1.872 1.951 1.892 1.872 1.920 1.887 1.872 1.905 1.882 1.871 1.892 1.878 1.871
N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
0.400
0.500
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.000 1.175 1.340 1.542 1.678 1.817 1.961 2.055 2.305 2.395 2.453 2.567 2.637 2.655 2.646 2.578 2.426
1.000 1.175 1.340 1.542 1.677 1.815 1.959 2.052 2.296 2.382 2.436 2.534 2.575 2.573 2.538 2.452 2.267
1.000 1.175 1.339 1.541 1.676 1.814 1.957 2.048 2.287 2.369 2.419 2.503 2.521 2.504 2.459 2.346 2.171
1.000 1.175 1.339 1.540 1.674 1.811 1.953 2.044 2.275 2.350 2.395 2.460 2.452 2.422 2.356 2.260 2.075
1.000 1.175 1.338 1.537 1.671 1.806 1.945 2.032 2.247 2.309 2.343 2.377 2.327 2.283 2.211 2.108 1.978
1.000 1.175 1.336 1.534 1.666 1.800 1.935 2.020 2.217 2.267 2.292 2.290 2.234 2.181 2.111 1.989 1.870
1.000 1.175 1.335 1.531 1.662 1.794 1.926 2.008 2.189 2.230 2.247 2.229 2.156 2.117 2.039 1.941 1.840
1.000 1.175 1.333 1.525 1.653 1.781 1.907 1.983 2.136 2.162 2.165 2.123 2.062 2.010 1.944 1.860 1.818
1.000 1.175 1.325 1.508 1.627 1.746 1.855 1.917 2.018 2.021 2.015 1.960 1.902 1.861 1.827 1.771 1.707
1.000 1.175 1.318 1.491 1.603 1.713 1.808 1.859 1.935 1.930 1.922 1.872 1.824 1.803 1.781 1.743 1.723
1.000 1.175 1.305 1.459 1.561 1.663 1.728 1.769 1.818 1.812 1.802 1.783 1.759 1.745 1.727 1.716 1.706
1.000 1.175 1.287 1.420 1.501 1.574 1.639 1.672 1.727 1.733 1.728 1.718 1.714 1.713 1.708 1.703 1.698
1.000 1.175 1.275 1.396 1.473 1.536 1.604 1.626 1.686 1.696 1.700 1.704 1.699 1.698 1.696 1.694 1.693
0.400
0.500
Values of GI (EXCVOL)
Values of αg2 (EXCVOL) N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
0.400
0.500
5 100 1000 5000
0.447 0.100 0.032 0.014
1.000 1.000 0.998 1.004
1.000 1.000 1.009 0.973
1.000 1.000 1.016 0.973
1.000 1.000 1.015 0.972
1.000 1.000 1.021 1.001
1.000 1.000 1.022 1.058
1.000 1.000 1.032 1.074
1.000 1.000 1.029 1.127
0.999 1.014 1.124 1.301
0.999 1.036 1.245 1.492
0.997 1.111 1.429 -
0.997 1.300 -
1.009 1.587 -
Values of Q∞ (EXCVOL) Z= 0.010
0.017
0.025
0.033
0.050
0.750
0.100
0.150
0.250
0.333
0.400
0.500
0.600
0.095
0.126
0.147
0.169
0.194
0.253
0.284
0.334
0.419
0.479
0.524
0.598
0.682
S3
Table S-3: Experimental sedimentation coefficient data obtained from different authors for DNA fragments of various lengths Source PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment Linear ColE1 T7 phage T5 phage T4 phage T7 phage Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment T2 phage T7 phage 1/2 T7, fragment phiX 174RF Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Mononucleosome, fragment Synthetic Synthetic Synthetic Synthetic Synthetic T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 phage Half T2 phage Quarter T2 phage
Ref 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2,3 4 4 4 5 6 6 6 6 6 6 6 7,8 7,8 9,10 9,10 11 11 11 11 11 11 11 12 13 13 13 13 13 8 8 8 8 8 8 8 8 8 8 14 14 14
S4
M 1.15E+06 1.06E+06 8.65E+05 5.64E+05 5.24E+05 4.24E+05 3.91E+05 3.29E+05 2.13E+05 1.90E+05 1.74E+05 1.06E+05 9.57E+04 7.72E+04 6.20E+04 3.30E+04 4.34E+06 2.60E+07 7.90E+07 1.13E+08 2.60E+07 2.43E+05 1.91E+05 1.14E+05 9.00E+04 8.80E+04 7.30E+04 4.50E+04 1.17E+08 2.60E+07 1.24E+07 3.58E+06 2.81E+05 3.62E+05 4.67E+05 5.40E+05 6.57E+05 8.46E+05 1.27E+06 1.10E+05 6.60E+03 7.92E+03 7.92E+03 9.24E+03 1.06E+04 2.00E+05 4.00E+05 8.00E+05 1.60E+06 3.20E+06 6.40E+06 1.28E+07 2.56E+07 5.12E+07 1.02E+08 1.17E+08 7.02E+07 2.69E+07
s (S) 10.78 10.67 9.99 8.72 8.59 8.03 7.89 7.62 6.7 6.37 6.24 5.41 5.2 4.92 4.58 3.51 16.6 31.8 51.78 62.06 31.3 7.2 6.3 5.7 5.4 5.4 4.7 3.9 64.5 33.7 22.8 14.3 7.79 8.34 8.89 9.36 9.8 10.38 11.73 5.33 1.5 1.77 1.65 1.85 2.1 6.15 7.40 9.10 11.41 14.55 18.83 24.66 32.60 43.40 58.11 64.5 44 31.3
Table S-4: Experimental diffusion coefficient data obtained from different authors for DNA fragments of various lengths Source Ref M Dt (cm2 /s) 15,16 pLH fragments 1.53E+06 4.56E-08 2,3 Linear ColE1 4.34E+06 2.03E-08 17 pLH fragments 1.50E+06 4.56E-08 17 pLH fragments 6.70E+05 7.15E-08 17 pLH fragments 5.00E+05 9.05E-08 17 pLH fragments 2.40E+05 1.58E-07 15 pLH fragments 1.53E+06 4.42E-08 15,18 ColE1 4.32E+06 2.07E-08 19 phi29 1.15E+07 1.00E-08 12 Mononucleosome, fragment 1.10E+05 3.00E-07 20,21 Synthetic 5.28E+03 1.53E-06 20,21 Synthetic 7.92E+03 1.34E-06 20,21 Synthetic 1.32E+04 1.09E-06 13 Synthetic 6.60E+03 1.40E-06 13 Synthetic 7.92E+03 1.45E-06 13 Synthetic 7.92E+03 1.22E-06 13 Synthetic 9.24E+03 1.17E-06 13 Synthetic 1.06E+04 1.11E-06 13 Synthetic 7.92E+03 1.23E-06 13 Synthetic 9.24E+03 1.19E-06 13 Synthetic 1.58E+04 9.50E-07 22 Synthetic 1.32E+04 1.07E-06 22 Synthetic 1.32E+04 1.02E-06 22 Synthetic 1.32E+04 1.00E-06 23 1.79E+06 3.50E-08
S5
Table S-5: Experimental intrinsic viscosity data obtained from different authors for DNA fragments of various lengths Source Ref M (Da) [η ] (cm3/g) 24 T7 phage 2.60E+07 1.06E+04 24 T7 phage 2.60E+07 1.10E+04 25,26 T2 phage 1.17E+08 3.10E+04 26 T5 phage 7.90E+07 2.40E+04 26 T7 phage 2.60E+07 1.28E+04 26 CT 7.00E+06 4.60E+03 5 T7 phage 2.60E+07 1.25E+04 7,8 T2 phage 1.17E+08 3.16E+04 4,7 T4 phage 1.13E+08 3.13E+04 4,7 T5 phage 7.90E+07 2.40E+04 4,7 T5 sto 6.23E+07 2.26E+04 7,8 T7 phage 2.60E+07 1.11E+04 10,27 T4 phage 6x 3.95E+07 1.39E+04 10,27 T4 phage 11x 2.24E+07 9.60E+03 11 Calf thymus, fragment 2.81E+05 1.52E+02 11 Calf thymus, fragment 3.62E+05 2.32E+02 11 Calf thymus, fragment 4.67E+05 2.92E+02 11 Calf thymus, fragment 5.40E+05 3.66E+02 11 Calf thymus, fragment 6.57E+05 4.69E+02 11,28 Calf thymus, fragment 8.46E+05 5.82E+02 11,28 Calf thymus, fragment 1.27E+06 8.91E+02 29 T2 phage 1.17E+08 3.51E+04 8 T2 and T7 phages, fragment 4.00E+05 2.28E+02 8 T2 and T7 phages, fragment 8.00E+05 6.54E+02 T2 and T7 phages, fragment 8 1.60E+06 1.33E+03 8 T2 and T7 phages, fragment 3.20E+06 2.40E+03 8 T2 and T7 phages, fragment 6.40E+06 4.10E+03 T2 and T7 phages, fragment 8 1.28E+07 6.79E+03 8 T2 and T7 phages, fragment 2.56E+07 1.11E+04 8 T2 and T7 phages, fragment 5.12E+07 1.78E+04 8 T2 and T7 phages, fragment 1.02E+08 2.86E+04 30 Calf thymus 7.80E+06 4.73E+03 30 Calf thymus, fragment 2.06E+05 1.39E+02 30 Calf thymus, fragment 3.99E+05 2.34E+02 30 Calf thymus, fragment 3.62E+05 2.22E+02 30 Calf thymus, fragment 2.55E+05 1.57E+02 30 Calf thymus, fragment 1.65E+05 8.90E+01 30 Calf thymus, fragment 7.61E+04 3.00E+01 14 T2 phage 1.17E+08 2.77E+04 14 Half T2 phage 7.02E+07 1.82E+04 14 Quarter T2 phage 2.69E+07 1.13E+04
S6
Table S-6: Experimental radius of gyration data obtained from different authors for DNA fragments of various lengths Source Ref. M (Da) Rg (cm) 15,16 pLH fragment 1.53E+06 1.04E-05 24 T7 phage 2.60E+07 7.10E-05 24 T7 phage 2.60E+07 5.80E-05 31 ColE1 4.35E+06 1.95E-05 2,3 ColE1 4.34E+06 1.86E-05 32 T7 phage 2.60E+07 5.87E-05 11 Calf thymus, fragment 2.81E+05 3.46E-06 11 Calf thymus, fragment 3.62E+05 4.09E-06 11 Calf thymus, fragment 4.67E+05 4.87E-06 11 Calf thymus, fragment 5.40E+05 5.82E-06 11 Calf thymus, fragment 6.57E+05 6.43E-06 11 Calf thymus, fragment 8.46E+05 7.84E-06 11 Calf thymus, fragment 1.27E+06 1.05E-05 33 T7 phage 2.60E+07 7.10E-05 9 T7 phage 2.60E+07 5.20E-05 34 T7 phage 2.60E+07 6.10E-05 35 Calf thymus, fragments 2.00E+07 3.61E-05 36 T7 phage 2.60E+07 7.20E-05 37 Calf-thymus, fragment 3.05E+05 4.59E-06 36,38–41 T7 and Calf-thymus, fragment 1.97E+07 5.12E-05 T7 and Calf-thymus, fragment 36,38–41 1.56E+07 4.05E-05 T7 and Calf-thymus, fragment 36,38–41 1.17E+07 3.26E-05 T7 and Calf-thymus, fragment 36,38–41 5.82E+06 2.40E-05 T7 and Calf-thymus, fragment 36,38–41 4.35E+06 2.35E-05 T7 and Calf-thymus, fragment 36,38–41 3.45E+06 1.86E-05 T7 and Calf-thymus, fragment 36,38–41 1.88E+06 1.32E-05 T7 and Calf-thymus, fragment 36,38–41 6.22E+05 7.01E-06 14 T2 phage 1.17E+08 1.35E-04 14 Half T2 phage 7.02E+07 1.02E-04 14 Quarter T2 phage 2.69E+07 6.20E-05
S7
Table S-7: Multi-HYDFIT global analysis of DNA properties. Set of parameters having 100∆ < 7% −1 d / nm 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6
a / nm 52 54 54 56 56 58 58 60 52 52 54 54 54 56 56 58 58 58 60 60 62 62 64 52 54 54 56 56 56 58 58 58 60 60 60 62 62 62 64 64 54 54 56 56 56 58 58 58 60 60 60 62 62 62 64 64 64 56 56 58 58 58 60 60 60 62 62 62 64 64 64 56 58 58 60 60 60 62 62 62 64 64 64
ML / Da nm 1850 1850 1900 1900 1950 1900 1950 1950 1850 1900 1850 1900 1950 1900 1950 1900 1950 2000 1950 2000 1950 2000 2000 1900 1900 1950 1900 1950 2000 1900 1950 2000 1950 2000 2050 1950 2000 2050 2000 2050 1900 1950 1900 1950 2000 1950 2000 2050 1950 2000 2050 2000 2050 2100 2000 2050 2100 1950 2000 1950 2000 2050 1950 2000 2050 2000 2050 2100 2000 2050 2100 2000 2000 2050 2000 2050 2100 2000 2050 2100 2050 2100 2150
S8
100∆ 7.0 7.0 6.9 6.8 6.9 7.0 6.9 6.9 7.0 7.0 7.0 6.8 7.0 6.7 6.7 6.9 6.7 6.9 6.8 6.8 7.0 6.8 7.0 7.0 6.8 6.9 6.8 6.7 6.9 7.0 6.6 6.7 6.7 6.6 6.9 7.0 6.7 6.8 6.9 6.8 7.0 6.9 7.0 6.7 6.8 6.7 6.6 6.9 6.8 6.6 6.7 6.7 6.6 6.9 6.9 6.7 6.8 6.9 6.9 6.9 6.7 6.9 7.0 6.6 6.6 6.7 6.6 6.8 7.0 6.7 6.7 7.0 6.8 6.9 6.8 6.7 7.0 6.9 6.7 6.8 6.7 6.7 7.0
Figure captions Figure S-1. GT , GI and IT ratios plotted vs. N −1/2 , for wormlike chains without excluded volume with the indicated values of Z. Figure S-2. GT , GI and IT ratios plotted vs. N −1/2 , for wormlike chains with excluded volume with the indicated values of Z. Figure S-3. Values of Q = αg2 /N 0.17 vs. N −1/2 for the indicated values of Z. The straight lines indicate the extrapolation to infinite chain length. Figure S-4. Dependence of the Q∞ values on Z. The continuous line is a least-squares fitting to a power law, Q∞ = 0.84Z 0.48 . Figure S-5. Experimental radius of gyration (A), intrinsic viscosity (B), sedimentation coefficient (C), and diffusion coefficient (D) values obtained for double helix B-DNA from different sources. Figure S-6. Summary of experimental (points) and calculated (line) properties for Schizophyllan, and the contours plots of the fits for the same polymer. Figure S-7. Summary of experimental (points) and calculated (line) properties for PHIC, and the contours plots of the fits for the same polymer. Figure S-8. Summary of experimental (points) and calculated (line) properties for PIB, and the contours plots of the fits for the same polymer. Figure S-9. Ratios of the equivalent radii computed with other theories to those computed in own simulations, for the set of parameters d=2.3 nm, a=55 nm, ML =1950 Da nm−1. Figure S-10. Ratios of the equivalent radii computed with other theories to those computed in own simulations. The parameters in this case, d=0.7 nm, a=3.5 nm, ML =500 Da nm−1 , correspond to a very flexible polymer and are chosen within the range of validity (d/2a = 0.1) of the Yamakawa-Fujii theory. 39
S9
Figure S-1
S10
Figure S-2
S11
Figure S-3
S12
Figure S-4
S13
Figure S-5
S14
Figure S-6
S15
Figure S-7
S16
Figure S-8
S17
Figure S-9
S18
Figure S-10
S19
References (1) Kovacic, R. T.; Holde, K. E. V. Biochemistry 1977, 16, 1490–1498. (2) Jolly, D.; Eisemberg, H. Biopolymers 1976, 15, 61–95. (3) Kam, Z.; Borochov, N.; Eisemberg, H. Biopolymers 1981, 20, 2671–2690. (4) Jr., H. B. G.; Hearst, J. E. J. Mol. Biol. 1968, 35, 111–129. (5) Rosemberg, A. H.; Studier, F. W. Biopolymers 1969, 7, 765–774. (6) Jr., M. T. R.; Woodbury, C. P. Biopolymers 1975, 14, 393–408. (7) Hearst, J. E.; Schmid, C. W.; Rineheart, F. P. Macromolecules 1968, 1, 491–494. (8) Crothers, D.; Zimm, B. J. Mol. Biol. 1965, 12, 525–536. (9) Schmid, C. W.; Rineheart, F. P.; Hearst, J. B. Biopolymers 1971, 10, 883–893. (10) Noda, I. Biopolymers 1974, 13, 591–599. (11) Godfrey, J. E. Biophys. Chem. 1976, 5, 285–299. (12) Nicolai, T.; Mandel, M. Macromolecules 1989, 22, 2348–2356. (13) Bonifacio, G. F.; Brown, T.; Conn, G. L.; Lane, A. N. Biophys. J. 1997, 73, 1532–1538. (14) Harpst, J. A.; Dawson, J. R. Biophys. J. 1989, 55, 1237–1249. (15) Sorlie, S. S.; Pecora, R. Macromolecules 1988, 21, 1437–1449. (16) Allison, S. A.; Sorlie, S. S.; Pecora, R. Macromolecules 1990, 23, 1110–1118. (17) Sorlie, S. S.; Pecora, R. Macromolecules 1990, 23, 487–497. (18) Soda, K.; Wada, A. Biophys. Chem. 1984, 20, 185–200. (19) Wilcoxon, J.; Schurr, J. M. Biopolymers 1983, 22, 2273–2321. (20) Eimer, W.; Williamson, J. R.; Boxer, S. G.; Pecora, R. Biochemistry 1990, 29, 799–811. (21) Eimer, W.; Pecora, R. J. Chem. Phys. 1991, 94, 2324–2329. S20
(22) Stellwagen, N. C.; Magnusdottir, S.; Gelfi, C.; Righetti, P. G. Biopolymers 2001, 58, 390– 397. (23) Seils, J.; Dorfmuller, T. Biopolymers 1991, 31, 813–825. (24) Krasna, A. I. J. Colloid Interface Sci. 1972, 39, 632–646. (25) Harrington, R. E. Biopolymers 1970, 9, 159–193. (26) Reeg, C. F.; Harrington, R. E. Biopolymers 1982, 21, 1315–1332. (27) Ross, P. D.; Scruggs, R. L. Biopolymers 1968, 6, 1005–1018. (28) Godfrey, J. E.; Eisemberg, H. Biophys. Chem. 1976, 5, 301–318. (29) Bowen, B. C.; Zimm, B. H. Biophys. Chem. 1978, 7, 235–252. (30) Tanigawa, M.; Mukaiyama, N.; Shimokubo, S.; Wakabayashi, K.; Fujita, Y.; Fukudome, K.; Yamaoka, K. Polym. J. 1994, 26, 291–302. (31) Borochov, N.; Eisemberg, H.; Kam, Z. Biopolymers 1981, 20, 231–235. (32) Harpst, J. A. Biophys. Chem. 1980, 11, 295–302. (33) Krasna, A. I.; Dawson, J. R.; Harpst, J. A. Biopolymers 1970, 9, 1017–1028. (34) Llorente, M. A.; Horta, A. Biopolymers 1976, 15, 2287–2290. (35) Levine, H. I.; Fiel, R. J.; Jr., F. W. B. Biopolymers 1976, 15, 1267–1281. (36) Harpst, J. A.; Krasna, A. I.; Zimm, B. H. Biopolymers 1968, 6, 595–603. (37) Mandel, M.; Schouten, J. Macromolecules 1980, 13, 1247–1251. (38) Kirste, R. G. Discuss. Faraday Soc. 1970, 49, 51. (39) Yamakawa, H.; Fujii, M. Macromolecules 1974, 7, 649–654. (40) Doty, P. Proc. Natl. Acad. Sci. U.S.A. 1958, 44, 432–438. (41) Cohen, G.; Eisenberg, H. Biopolymers 1966, 4, 429–440.
S21
∗ To
whom correspondence should be addressed
S1
Table S-1: Numerical results from the Monte Carlo simulation, for the GT , GI and Rg /Rg,BD of wormlike chains without excluded volume, as functions of N and Z. Some columns (for Z=0.075, Z=0.33 and Z=0.60) have been suppresed for the sake of brevity. Values of GT (NO-EXCVOL) N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.000 1.225 1.397 1.680 1.889 2.124 2.401 2.603 3.243 3.512 3.695 4.072 4.306 4.357 4.304 4.042 3.562
1.000 1.225 1.397 1.679 1.887 2.120 2.395 2.594 3.212 3.460 3.626 3.936 4.055 4.035 3.893 3.569 3.120
1.000 1.225 1.397 1.678 1.885 2.117 2.389 2.584 3.182 3.411 3.560 3.815 3.853 3.789 3.620 3.290 2.886
1.000 1.225 1.396 1.676 1.882 2.112 2.380 2.571 3.139 3.343 3.473 3.659 3.622 3.515 3.324 3.001 2.680
1.000 1.225 1.396 1.673 1.875 2.100 2.359 2.541 3.048 3.206 3.298 3.382 3.245 3.110 2.935 2.662 2.410
1.000 1.225 1.395 1.668 1.868 2.087 2.336 2.507 2.958 3.075 3.139 3.152 2.980 2.838 2.686 2.446 2.191
1.000 1.225 1.394 1.664 1.860 2.075 2.314 2.476 2.878 2.967 3.009 2.982 2.792 2.665 2.524 2.312 2.089
1.000 1.225 1.391 1.656 1.845 2.049 2.270 2.415 2.737 2.782 2.800 2.724 2.544 2.432 2.322 2.147 2.001
1.000 1.225 1.385 1.632 1.803 1.980 2.158 2.266 2.455 2.449 2.440 2.338 2.200 2.135 2.066 1.943 1.846
1.000 1.225 1.379 1.609 1.764 1.920 2.067 2.152 2.277 2.257 2.245 2.157 2.044 2.001 1.925 1.875 1.783
1.000 1.000 1.000 1.225 1.225 1.225 1.368 1.352 1.342 1.568 1.517 1.488 1.698 1.618 1.576 1.822 1.711 1.655 1.929 1.787 1.717 1.986 1.825 1.748 2.056 1.872 1.790 2.033 1.854 1.779 2.027 1.852 1.778 1.968 1.823 1.761 1.894 1.777 1.727 1.861 1.762 1.716 1.812 1.754 1.710 1.777 1.709 1.673 1.745 1.641 1.662
N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
0.400
0.500
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.000 1.175 1.340 1.542 1.678 1.817 1.961 2.055 2.305 2.395 2.453 2.567 2.637 2.655 2.645 2.558 2.443
1.000 1.175 1.340 1.542 1.677 1.815 1.959 2.052 2.296 2.382 2.436 2.534 2.575 2.573 2.534 2.418 2.268
1.000 1.175 1.339 1.541 1.676 1.813 1.956 2.048 2.288 2.369 2.419 2.503 2.521 2.504 2.451 2.330 2.203
1.000 1.175 1.339 1.540 1.674 1.811 1.953 2.044 2.275 2.350 2.395 2.460 2.453 2.421 2.354 2.224 2.121
1.000 1.175 1.338 1.537 1.671 1.806 1.944 2.033 2.248 2.309 2.343 2.377 2.331 2.282 2.211 2.092 1.989
1.000 1.175 1.336 1.534 1.666 1.799 1.935 2.020 2.218 2.267 2.292 2.300 2.233 2.176 2.109 1.990 1.856
1.000 1.175 1.335 1.531 1.662 1.793 1.926 2.008 2.191 2.230 2.247 2.238 2.158 2.103 2.037 1.926 1.794
1.000 1.175 1.333 1.525 1.653 1.781 1.907 1.984 2.139 2.160 2.168 2.135 2.051 1.995 1.940 1.839 1.746
1.000 1.175 1.325 1.508 1.627 1.744 1.854 1.917 2.018 2.014 2.009 1.957 1.879 1.841 1.798 1.720 1.665
1.000 1.175 1.318 1.491 1.603 1.711 1.807 1.860 1.930 1.917 1.910 1.859 1.791 1.762 1.716 1.684 1.616
1.000 1.175 1.305 1.460 1.558 1.649 1.724 1.763 1.804 1.787 1.784 1.745 1.697 1.675 1.643 1.617 1.603
1.000 1.175 1.287 1.417 1.497 1.569 1.625 1.653 1.684 1.670 1.669 1.649 1.619 1.607 1.601 1.568 1.522
1.000 1.175 1.277 1.391 1.461 1.524 1.571 1.595 1.625 1.616 1.617 1.605 1.583 1.576 1.570 1.547 1.540
0.400
0.500
Values of GI (NO-EXCVOL)
Values of RR (NO-EXCVOL) N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
0.400
0.500
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.342 1.096 1.044 1.016 1.008 1.004 1.002 1.007 1.000 1.000 1.000 1.001 1.000 1.000 0.998 0.996 1.007
1.342 1.097 1.044 1.016 1.009 0.953 0.997 1.000 1.000 1.000 1.001 1.003 1.000 1.001 0.997 0.996 1.010
1.343 1.097 1.045 1.017 1.009 1.017 1.001 1.001 1.000 0.999 1.001 1.004 0.999 1.000 0.999 1.000 1.010
1.343 1.098 1.045 0.965 0.995 1.003 1.001 1.001 1.000 0.999 1.001 1.005 1.000 0.999 0.997 0.996 1.014
1.344 1.099 1.099 1.016 1.009 1.004 1.002 1.002 1.000 0.998 1.001 1.007 0.998 0.997 1.002 1.001 1.010
1.345 1.045 1.043 1.019 1.010 1.004 1.003 1.002 1.000 0.998 1.002 1.009 0.999 0.995 1.004 0.998 0.994
1.346 1.089 1.050 1.019 1.011 1.004 1.003 1.002 1.000 0.997 1.002 1.010 0.997 0.995 1.003 0.994 0.985
1.279 1.105 1.052 1.021 1.012 1.005 1.003 1.002 1.000 0.996 1.002 1.009 0.997 0.992 1.003 0.995 0.989
1.353 1.117 1.061 1.026 1.015 1.005 1.003 1.003 1.000 0.992 1.001 1.002 0.988 0.993 0.996 0.989 0.985
1.361 1.128 1.070 1.031 1.018 1.006 1.003 1.001 0.998 0.989 1.000 0.998 0.983 0.989 0.975 0.991 0.983
1.375 1.150 1.087 1.040 1.023 1.006 1.001 0.998 0.994 0.980 0.993 0.991 0.980 0.981 0.970 0.980 0.978
1.395 1.182 1.111 1.053 1.030 1.006 0.998 0.992 0.985 0.972 0.980 0.979 0.970 0.971 0.982 0.968 0.951
1.408 1.203 1.127 1.061 1.034 1.007 0.995 0.988 0.978 0.967 0.972 0.972 0.963 0.965 0.972 0.960 0.959
S2
Table S-2: Numerical results from the Monte Carlo simulation, for the GT , GI, αg2 and Q∞ (N = ∞), of wormlike chains with excluded volume, as functions of N and Z. Some columns (for Z=0.075, Z=0.33 and Z=0.60) have been suppresed for the sake of brevity. Values of GT (EXCVOL) N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.000 1.225 1.397 1.680 1.889 2.124 2.401 2.603 3.242 3.512 3.695 4.074 4.306 4.357 4.307 3.972 3.540
1.000 1.225 1.397 1.679 1.887 2.120 2.395 2.594 3.211 3.460 3.626 3.935 4.053 4.036 3.909 3.617 3.103
1.000 1.225 1.397 1.678 1.885 2.117 2.389 2.584 3.180 3.411 3.560 3.814 3.854 3.789 3.647 3.303 2.855
1.000 1.225 1.396 1.676 1.882 2.112 2.380 2.571 3.137 3.343 3.473 3.660 3.618 3.519 3.329 3.039 2.627
1.000 1.225 1.396 1.673 1.875 2.101 2.359 2.540 3.044 3.205 3.298 3.382 3.234 3.118 2.932 2.683 2.394
1.000 1.225 1.395 1.668 1.868 2.088 2.336 2.508 2.952 3.076 3.139 3.123 2.981 2.852 2.692 2.449 2.215
1.000 1.225 1.394 1.664 1.860 2.075 2.314 2.476 2.871 2.968 3.009 2.957 2.785 2.696 2.526 2.337 2.144
1.000 1.225 1.391 1.656 1.845 2.050 2.270 2.415 2.728 2.786 2.789 2.695 2.568 2.453 2.330 2.182 2.062
1.000 1.225 1.385 1.632 1.803 1.983 2.159 2.266 2.453 2.458 2.443 2.342 2.237 2.160 2.100 2.006 1.914
1.000 1.225 1.379 1.609 1.764 1.925 2.069 2.151 2.281 2.276 2.265 2.171 2.088 2.054 2.013 1.946 1.918
1.000 1.000 1.000 1.225 1.225 1.225 1.368 1.352 1.341 1.567 1.520 1.492 1.703 1.622 1.586 1.845 1.714 1.665 1.933 1.800 1.753 1.993 1.844 1.778 2.069 1.922 1.860 2.061 1.930 1.873 2.039 1.919 1.877 2.012 1.907 1.881 1.973 1.896 1.872 1.951 1.892 1.872 1.920 1.887 1.872 1.905 1.882 1.871 1.892 1.878 1.871
N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
0.400
0.500
1 2 3 5 7 10 15 20 50 75 100 200 400 600 1000 2000 5000
1.000 0.707 0.577 0.447 0.378 0.316 0.258 0.224 0.141 0.115 0.100 0.071 0.050 0.041 0.032 0.022 0.014
1.000 1.175 1.340 1.542 1.678 1.817 1.961 2.055 2.305 2.395 2.453 2.567 2.637 2.655 2.646 2.578 2.426
1.000 1.175 1.340 1.542 1.677 1.815 1.959 2.052 2.296 2.382 2.436 2.534 2.575 2.573 2.538 2.452 2.267
1.000 1.175 1.339 1.541 1.676 1.814 1.957 2.048 2.287 2.369 2.419 2.503 2.521 2.504 2.459 2.346 2.171
1.000 1.175 1.339 1.540 1.674 1.811 1.953 2.044 2.275 2.350 2.395 2.460 2.452 2.422 2.356 2.260 2.075
1.000 1.175 1.338 1.537 1.671 1.806 1.945 2.032 2.247 2.309 2.343 2.377 2.327 2.283 2.211 2.108 1.978
1.000 1.175 1.336 1.534 1.666 1.800 1.935 2.020 2.217 2.267 2.292 2.290 2.234 2.181 2.111 1.989 1.870
1.000 1.175 1.335 1.531 1.662 1.794 1.926 2.008 2.189 2.230 2.247 2.229 2.156 2.117 2.039 1.941 1.840
1.000 1.175 1.333 1.525 1.653 1.781 1.907 1.983 2.136 2.162 2.165 2.123 2.062 2.010 1.944 1.860 1.818
1.000 1.175 1.325 1.508 1.627 1.746 1.855 1.917 2.018 2.021 2.015 1.960 1.902 1.861 1.827 1.771 1.707
1.000 1.175 1.318 1.491 1.603 1.713 1.808 1.859 1.935 1.930 1.922 1.872 1.824 1.803 1.781 1.743 1.723
1.000 1.175 1.305 1.459 1.561 1.663 1.728 1.769 1.818 1.812 1.802 1.783 1.759 1.745 1.727 1.716 1.706
1.000 1.175 1.287 1.420 1.501 1.574 1.639 1.672 1.727 1.733 1.728 1.718 1.714 1.713 1.708 1.703 1.698
1.000 1.175 1.275 1.396 1.473 1.536 1.604 1.626 1.686 1.696 1.700 1.704 1.699 1.698 1.696 1.694 1.693
0.400
0.500
Values of GI (EXCVOL)
Values of αg2 (EXCVOL) N
N −1/2
Z= 0.003
0.005
0.007
0.010
0.017
0.025
0.033
0.050
0.100
0.150
0.250
0.400
0.500
5 100 1000 5000
0.447 0.100 0.032 0.014
1.000 1.000 0.998 1.004
1.000 1.000 1.009 0.973
1.000 1.000 1.016 0.973
1.000 1.000 1.015 0.972
1.000 1.000 1.021 1.001
1.000 1.000 1.022 1.058
1.000 1.000 1.032 1.074
1.000 1.000 1.029 1.127
0.999 1.014 1.124 1.301
0.999 1.036 1.245 1.492
0.997 1.111 1.429 -
0.997 1.300 -
1.009 1.587 -
Values of Q∞ (EXCVOL) Z= 0.010
0.017
0.025
0.033
0.050
0.750
0.100
0.150
0.250
0.333
0.400
0.500
0.600
0.095
0.126
0.147
0.169
0.194
0.253
0.284
0.334
0.419
0.479
0.524
0.598
0.682
S3
Table S-3: Experimental sedimentation coefficient data obtained from different authors for DNA fragments of various lengths Source PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment PM2 phage, fragment Linear ColE1 T7 phage T5 phage T4 phage T7 phage Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment T2 phage T7 phage 1/2 T7, fragment phiX 174RF Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Calf thymus, fragment Mononucleosome, fragment Synthetic Synthetic Synthetic Synthetic Synthetic T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 and T7 phages, fragment T2 phage Half T2 phage Quarter T2 phage
Ref 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2,3 4 4 4 5 6 6 6 6 6 6 6 7,8 7,8 9,10 9,10 11 11 11 11 11 11 11 12 13 13 13 13 13 8 8 8 8 8 8 8 8 8 8 14 14 14
S4
M 1.15E+06 1.06E+06 8.65E+05 5.64E+05 5.24E+05 4.24E+05 3.91E+05 3.29E+05 2.13E+05 1.90E+05 1.74E+05 1.06E+05 9.57E+04 7.72E+04 6.20E+04 3.30E+04 4.34E+06 2.60E+07 7.90E+07 1.13E+08 2.60E+07 2.43E+05 1.91E+05 1.14E+05 9.00E+04 8.80E+04 7.30E+04 4.50E+04 1.17E+08 2.60E+07 1.24E+07 3.58E+06 2.81E+05 3.62E+05 4.67E+05 5.40E+05 6.57E+05 8.46E+05 1.27E+06 1.10E+05 6.60E+03 7.92E+03 7.92E+03 9.24E+03 1.06E+04 2.00E+05 4.00E+05 8.00E+05 1.60E+06 3.20E+06 6.40E+06 1.28E+07 2.56E+07 5.12E+07 1.02E+08 1.17E+08 7.02E+07 2.69E+07
s (S) 10.78 10.67 9.99 8.72 8.59 8.03 7.89 7.62 6.7 6.37 6.24 5.41 5.2 4.92 4.58 3.51 16.6 31.8 51.78 62.06 31.3 7.2 6.3 5.7 5.4 5.4 4.7 3.9 64.5 33.7 22.8 14.3 7.79 8.34 8.89 9.36 9.8 10.38 11.73 5.33 1.5 1.77 1.65 1.85 2.1 6.15 7.40 9.10 11.41 14.55 18.83 24.66 32.60 43.40 58.11 64.5 44 31.3
Table S-4: Experimental diffusion coefficient data obtained from different authors for DNA fragments of various lengths Source Ref M Dt (cm2 /s) 15,16 pLH fragments 1.53E+06 4.56E-08 2,3 Linear ColE1 4.34E+06 2.03E-08 17 pLH fragments 1.50E+06 4.56E-08 17 pLH fragments 6.70E+05 7.15E-08 17 pLH fragments 5.00E+05 9.05E-08 17 pLH fragments 2.40E+05 1.58E-07 15 pLH fragments 1.53E+06 4.42E-08 15,18 ColE1 4.32E+06 2.07E-08 19 phi29 1.15E+07 1.00E-08 12 Mononucleosome, fragment 1.10E+05 3.00E-07 20,21 Synthetic 5.28E+03 1.53E-06 20,21 Synthetic 7.92E+03 1.34E-06 20,21 Synthetic 1.32E+04 1.09E-06 13 Synthetic 6.60E+03 1.40E-06 13 Synthetic 7.92E+03 1.45E-06 13 Synthetic 7.92E+03 1.22E-06 13 Synthetic 9.24E+03 1.17E-06 13 Synthetic 1.06E+04 1.11E-06 13 Synthetic 7.92E+03 1.23E-06 13 Synthetic 9.24E+03 1.19E-06 13 Synthetic 1.58E+04 9.50E-07 22 Synthetic 1.32E+04 1.07E-06 22 Synthetic 1.32E+04 1.02E-06 22 Synthetic 1.32E+04 1.00E-06 23 1.79E+06 3.50E-08
S5
Table S-5: Experimental intrinsic viscosity data obtained from different authors for DNA fragments of various lengths Source Ref M (Da) [η ] (cm3/g) 24 T7 phage 2.60E+07 1.06E+04 24 T7 phage 2.60E+07 1.10E+04 25,26 T2 phage 1.17E+08 3.10E+04 26 T5 phage 7.90E+07 2.40E+04 26 T7 phage 2.60E+07 1.28E+04 26 CT 7.00E+06 4.60E+03 5 T7 phage 2.60E+07 1.25E+04 7,8 T2 phage 1.17E+08 3.16E+04 4,7 T4 phage 1.13E+08 3.13E+04 4,7 T5 phage 7.90E+07 2.40E+04 4,7 T5 sto 6.23E+07 2.26E+04 7,8 T7 phage 2.60E+07 1.11E+04 10,27 T4 phage 6x 3.95E+07 1.39E+04 10,27 T4 phage 11x 2.24E+07 9.60E+03 11 Calf thymus, fragment 2.81E+05 1.52E+02 11 Calf thymus, fragment 3.62E+05 2.32E+02 11 Calf thymus, fragment 4.67E+05 2.92E+02 11 Calf thymus, fragment 5.40E+05 3.66E+02 11 Calf thymus, fragment 6.57E+05 4.69E+02 11,28 Calf thymus, fragment 8.46E+05 5.82E+02 11,28 Calf thymus, fragment 1.27E+06 8.91E+02 29 T2 phage 1.17E+08 3.51E+04 8 T2 and T7 phages, fragment 4.00E+05 2.28E+02 8 T2 and T7 phages, fragment 8.00E+05 6.54E+02 T2 and T7 phages, fragment 8 1.60E+06 1.33E+03 8 T2 and T7 phages, fragment 3.20E+06 2.40E+03 8 T2 and T7 phages, fragment 6.40E+06 4.10E+03 T2 and T7 phages, fragment 8 1.28E+07 6.79E+03 8 T2 and T7 phages, fragment 2.56E+07 1.11E+04 8 T2 and T7 phages, fragment 5.12E+07 1.78E+04 8 T2 and T7 phages, fragment 1.02E+08 2.86E+04 30 Calf thymus 7.80E+06 4.73E+03 30 Calf thymus, fragment 2.06E+05 1.39E+02 30 Calf thymus, fragment 3.99E+05 2.34E+02 30 Calf thymus, fragment 3.62E+05 2.22E+02 30 Calf thymus, fragment 2.55E+05 1.57E+02 30 Calf thymus, fragment 1.65E+05 8.90E+01 30 Calf thymus, fragment 7.61E+04 3.00E+01 14 T2 phage 1.17E+08 2.77E+04 14 Half T2 phage 7.02E+07 1.82E+04 14 Quarter T2 phage 2.69E+07 1.13E+04
S6
Table S-6: Experimental radius of gyration data obtained from different authors for DNA fragments of various lengths Source Ref. M (Da) Rg (cm) 15,16 pLH fragment 1.53E+06 1.04E-05 24 T7 phage 2.60E+07 7.10E-05 24 T7 phage 2.60E+07 5.80E-05 31 ColE1 4.35E+06 1.95E-05 2,3 ColE1 4.34E+06 1.86E-05 32 T7 phage 2.60E+07 5.87E-05 11 Calf thymus, fragment 2.81E+05 3.46E-06 11 Calf thymus, fragment 3.62E+05 4.09E-06 11 Calf thymus, fragment 4.67E+05 4.87E-06 11 Calf thymus, fragment 5.40E+05 5.82E-06 11 Calf thymus, fragment 6.57E+05 6.43E-06 11 Calf thymus, fragment 8.46E+05 7.84E-06 11 Calf thymus, fragment 1.27E+06 1.05E-05 33 T7 phage 2.60E+07 7.10E-05 9 T7 phage 2.60E+07 5.20E-05 34 T7 phage 2.60E+07 6.10E-05 35 Calf thymus, fragments 2.00E+07 3.61E-05 36 T7 phage 2.60E+07 7.20E-05 37 Calf-thymus, fragment 3.05E+05 4.59E-06 36,38–41 T7 and Calf-thymus, fragment 1.97E+07 5.12E-05 T7 and Calf-thymus, fragment 36,38–41 1.56E+07 4.05E-05 T7 and Calf-thymus, fragment 36,38–41 1.17E+07 3.26E-05 T7 and Calf-thymus, fragment 36,38–41 5.82E+06 2.40E-05 T7 and Calf-thymus, fragment 36,38–41 4.35E+06 2.35E-05 T7 and Calf-thymus, fragment 36,38–41 3.45E+06 1.86E-05 T7 and Calf-thymus, fragment 36,38–41 1.88E+06 1.32E-05 T7 and Calf-thymus, fragment 36,38–41 6.22E+05 7.01E-06 14 T2 phage 1.17E+08 1.35E-04 14 Half T2 phage 7.02E+07 1.02E-04 14 Quarter T2 phage 2.69E+07 6.20E-05
S7
Table S-7: Multi-HYDFIT global analysis of DNA properties. Set of parameters having 100∆ < 7% −1 d / nm 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6
a / nm 52 54 54 56 56 58 58 60 52 52 54 54 54 56 56 58 58 58 60 60 62 62 64 52 54 54 56 56 56 58 58 58 60 60 60 62 62 62 64 64 54 54 56 56 56 58 58 58 60 60 60 62 62 62 64 64 64 56 56 58 58 58 60 60 60 62 62 62 64 64 64 56 58 58 60 60 60 62 62 62 64 64 64
ML / Da nm 1850 1850 1900 1900 1950 1900 1950 1950 1850 1900 1850 1900 1950 1900 1950 1900 1950 2000 1950 2000 1950 2000 2000 1900 1900 1950 1900 1950 2000 1900 1950 2000 1950 2000 2050 1950 2000 2050 2000 2050 1900 1950 1900 1950 2000 1950 2000 2050 1950 2000 2050 2000 2050 2100 2000 2050 2100 1950 2000 1950 2000 2050 1950 2000 2050 2000 2050 2100 2000 2050 2100 2000 2000 2050 2000 2050 2100 2000 2050 2100 2050 2100 2150
S8
100∆ 7.0 7.0 6.9 6.8 6.9 7.0 6.9 6.9 7.0 7.0 7.0 6.8 7.0 6.7 6.7 6.9 6.7 6.9 6.8 6.8 7.0 6.8 7.0 7.0 6.8 6.9 6.8 6.7 6.9 7.0 6.6 6.7 6.7 6.6 6.9 7.0 6.7 6.8 6.9 6.8 7.0 6.9 7.0 6.7 6.8 6.7 6.6 6.9 6.8 6.6 6.7 6.7 6.6 6.9 6.9 6.7 6.8 6.9 6.9 6.9 6.7 6.9 7.0 6.6 6.6 6.7 6.6 6.8 7.0 6.7 6.7 7.0 6.8 6.9 6.8 6.7 7.0 6.9 6.7 6.8 6.7 6.7 7.0
Figure captions Figure S-1. GT , GI and IT ratios plotted vs. N −1/2 , for wormlike chains without excluded volume with the indicated values of Z. Figure S-2. GT , GI and IT ratios plotted vs. N −1/2 , for wormlike chains with excluded volume with the indicated values of Z. Figure S-3. Values of Q = αg2 /N 0.17 vs. N −1/2 for the indicated values of Z. The straight lines indicate the extrapolation to infinite chain length. Figure S-4. Dependence of the Q∞ values on Z. The continuous line is a least-squares fitting to a power law, Q∞ = 0.84Z 0.48 . Figure S-5. Experimental radius of gyration (A), intrinsic viscosity (B), sedimentation coefficient (C), and diffusion coefficient (D) values obtained for double helix B-DNA from different sources. Figure S-6. Summary of experimental (points) and calculated (line) properties for Schizophyllan, and the contours plots of the fits for the same polymer. Figure S-7. Summary of experimental (points) and calculated (line) properties for PHIC, and the contours plots of the fits for the same polymer. Figure S-8. Summary of experimental (points) and calculated (line) properties for PIB, and the contours plots of the fits for the same polymer. Figure S-9. Ratios of the equivalent radii computed with other theories to those computed in own simulations, for the set of parameters d=2.3 nm, a=55 nm, ML =1950 Da nm−1. Figure S-10. Ratios of the equivalent radii computed with other theories to those computed in own simulations. The parameters in this case, d=0.7 nm, a=3.5 nm, ML =500 Da nm−1 , correspond to a very flexible polymer and are chosen within the range of validity (d/2a = 0.1) of the Yamakawa-Fujii theory. 39
S9
Figure S-1
S10
Figure S-2
S11
Figure S-3
S12
Figure S-4
S13
Figure S-5
S14
Figure S-6
S15
Figure S-7
S16
Figure S-8
S17
Figure S-9
S18
Figure S-10
S19
References (1) Kovacic, R. T.; Holde, K. E. V. Biochemistry 1977, 16, 1490–1498. (2) Jolly, D.; Eisemberg, H. Biopolymers 1976, 15, 61–95. (3) Kam, Z.; Borochov, N.; Eisemberg, H. Biopolymers 1981, 20, 2671–2690. (4) Jr., H. B. G.; Hearst, J. E. J. Mol. Biol. 1968, 35, 111–129. (5) Rosemberg, A. H.; Studier, F. W. Biopolymers 1969, 7, 765–774. (6) Jr., M. T. R.; Woodbury, C. P. Biopolymers 1975, 14, 393–408. (7) Hearst, J. E.; Schmid, C. W.; Rineheart, F. P. Macromolecules 1968, 1, 491–494. (8) Crothers, D.; Zimm, B. J. Mol. Biol. 1965, 12, 525–536. (9) Schmid, C. W.; Rineheart, F. P.; Hearst, J. B. Biopolymers 1971, 10, 883–893. (10) Noda, I. Biopolymers 1974, 13, 591–599. (11) Godfrey, J. E. Biophys. Chem. 1976, 5, 285–299. (12) Nicolai, T.; Mandel, M. Macromolecules 1989, 22, 2348–2356. (13) Bonifacio, G. F.; Brown, T.; Conn, G. L.; Lane, A. N. Biophys. J. 1997, 73, 1532–1538. (14) Harpst, J. A.; Dawson, J. R. Biophys. J. 1989, 55, 1237–1249. (15) Sorlie, S. S.; Pecora, R. Macromolecules 1988, 21, 1437–1449. (16) Allison, S. A.; Sorlie, S. S.; Pecora, R. Macromolecules 1990, 23, 1110–1118. (17) Sorlie, S. S.; Pecora, R. Macromolecules 1990, 23, 487–497. (18) Soda, K.; Wada, A. Biophys. Chem. 1984, 20, 185–200. (19) Wilcoxon, J.; Schurr, J. M. Biopolymers 1983, 22, 2273–2321. (20) Eimer, W.; Williamson, J. R.; Boxer, S. G.; Pecora, R. Biochemistry 1990, 29, 799–811. (21) Eimer, W.; Pecora, R. J. Chem. Phys. 1991, 94, 2324–2329. S20
(22) Stellwagen, N. C.; Magnusdottir, S.; Gelfi, C.; Righetti, P. G. Biopolymers 2001, 58, 390– 397. (23) Seils, J.; Dorfmuller, T. Biopolymers 1991, 31, 813–825. (24) Krasna, A. I. J. Colloid Interface Sci. 1972, 39, 632–646. (25) Harrington, R. E. Biopolymers 1970, 9, 159–193. (26) Reeg, C. F.; Harrington, R. E. Biopolymers 1982, 21, 1315–1332. (27) Ross, P. D.; Scruggs, R. L. Biopolymers 1968, 6, 1005–1018. (28) Godfrey, J. E.; Eisemberg, H. Biophys. Chem. 1976, 5, 301–318. (29) Bowen, B. C.; Zimm, B. H. Biophys. Chem. 1978, 7, 235–252. (30) Tanigawa, M.; Mukaiyama, N.; Shimokubo, S.; Wakabayashi, K.; Fujita, Y.; Fukudome, K.; Yamaoka, K. Polym. J. 1994, 26, 291–302. (31) Borochov, N.; Eisemberg, H.; Kam, Z. Biopolymers 1981, 20, 231–235. (32) Harpst, J. A. Biophys. Chem. 1980, 11, 295–302. (33) Krasna, A. I.; Dawson, J. R.; Harpst, J. A. Biopolymers 1970, 9, 1017–1028. (34) Llorente, M. A.; Horta, A. Biopolymers 1976, 15, 2287–2290. (35) Levine, H. I.; Fiel, R. J.; Jr., F. W. B. Biopolymers 1976, 15, 1267–1281. (36) Harpst, J. A.; Krasna, A. I.; Zimm, B. H. Biopolymers 1968, 6, 595–603. (37) Mandel, M.; Schouten, J. Macromolecules 1980, 13, 1247–1251. (38) Kirste, R. G. Discuss. Faraday Soc. 1970, 49, 51. (39) Yamakawa, H.; Fujii, M. Macromolecules 1974, 7, 649–654. (40) Doty, P. Proc. Natl. Acad. Sci. U.S.A. 1958, 44, 432–438. (41) Cohen, G.; Eisenberg, H. Biopolymers 1966, 4, 429–440.
S21
