A twist on folding: Predicting optimal sequences and optimal folds of simple protein models with the hidden-force algorithm István Kolossváry, Kevin J. Bowers (Submitted on 21 May 2012) Abstract: We propose a new way of looking at global optimization of off-lattice protein models. We present a dual optimization concept of predicting optimal sequences as well as optimal folds. We validate the utility of the recently introduced hidden-force Monte Carlo optimization algorithm by finding significantly lower energy folds for minimalist protein models than previously reported. Further, we also find the protein sequence that yields the lowest energy fold amongst all sequences for a given chain length and residue mixture. In particular, for protein models with a binary sequence, we show that the sequence-optimized folds form more compact cores than the lowest energy folds of the historically fixed, Fibonacci-series sequences of chain lengths of 13, 21, 34, 55, and 89. We emphasize that while the protein model we used is minimalist, the methodology is applicable to detailed protein models, and sequence optimization may yield novel folds and aid de novo protein design. Cite as: arXiv:1205.4705v1 [physics.comp-ph] Description: List of coordinates, sequences, and energies of putative global minimum folds of PAB models. The coordinates are Cartesian coordinates. The sequence is identified by the residue type A or B in the first column. Energies are absolute energies in epsilon units. The first 5 models were computed with the potential in Eq. 1. The other 5 models were computed with the simplified potential including the pseudo Lennard-Jones potential, the bond length restraint and the flat-bottom angle bending constraint to keep the Calpha-Calpha-Calpha bond angles within the 85-145 degree range. S_13 Fibonacci sequence global minimum energy computed by Eq. 1 = -27.171382 A -2.210729 -0.766557 0.859473 B -1.468936 -0.515469 1.481321 B -1.125457 0.413991 1.346684 A -2.015611 0.307761 0.903583 B -2.875024 0.042923 0.466239 B -2.923165 -0.824726 -0.028602 A -2.104003 -1.398285 -0.026841 B -1.292453 -1.270099 0.543208 A -1.100612 -0.289674 0.498904 B -1.256479 0.656395 0.214902 B -2.203998 0.733500 -0.095357 A -1.998733 -0.244823 -0.122725 B -1.256899 -0.823838 -0.460991 S_21 Fibonacci sequence global minimum energy computed by Eq. 1 = -56.408990 B -3.502088 -2.347106 -2.580986 A -3.633583 -3.070794 -1.903502 B -3.182330 -2.964804 -1.017422 A -2.558379 -2.207111 -0.826145 B -1.942815 -1.419028 -0.828706 B -1.631517 -1.022569 -1.692370 A -1.917468 -1.469613 -2.539947 B -2.396659 -2.287089 -2.859494 A -2.809866 -3.188090 -2.727356 B -2.658749 -3.616882 -1.836679 B -2.088394 -3.137323 -1.169805 A -1.497975 -2.495615 -0.680298 B -0.926488 -1.760655 -1.045314 B -0.814412 -1.662030 -2.034107 A -1.235498 -2.340732 -2.635811 B -1.870827 -3.002000 -2.236963 A -2.685908 -2.555420 -1.867897 B -3.446519 -2.008019 -1.518868 B -2.589028 -1.522775 -1.689879 A -1.763180 -2.085958 -1.661572 B -0.995117 -2.724986 -1.620079 S_34 Fibonacci sequence global minimum energy computed by Eq. 1 = -106.115214 A -0.054962 2.229487 -0.900343 B -0.853011 2.143012 -1.496697 B -0.951238 1.732429 -0.590181 A -0.524775 1.446744 0.268022 B 0.330605 1.385370 0.782374 B 1.265892 1.429216 1.133538 A 1.199972 1.905059 0.256483 B 0.995707 2.354906 -0.612946 A 0.707322 2.800658 -1.460375 B -0.237086 3.129292 -1.450697 B -0.878686 2.917563 -0.713459 A -0.848802 2.520503 0.203846 B -0.411806 2.204694 1.046045 B 0.565968 2.364524 1.181737 A 1.553768 2.506594 1.117971 B 2.284360 2.032034 0.627028 A 2.006677 1.145438 0.257113 B 1.079417 0.771783 0.233288 B 0.127003 0.470460 0.187356 A -0.495836 0.717894 -0.554834 B -0.200073 1.245807 -1.350967 A 0.708342 1.655607 -1.433690 B 1.614781 2.075060 -1.482927 B 1.824123 2.954070 -1.054539 A 1.063933 3.448186 -0.632687 B 0.147975 3.147931 -0.366482 B 0.176094 2.278401 0.126597 A 0.388799 1.417582 -0.335729 B 0.682145 0.618698 -0.860826 A 1.419258 1.273341 -0.693175 B 2.059386 2.006824 -0.464622 B 1.809237 2.833024 0.040171 A 0.893430 3.031008 0.389595 B -0.039220 3.183399 0.716612 S_55 Fibonacci sequence global minimum energy computed by Eq. 1 = -190.579174 B -1.048644 -1.434770 -2.612892 A -0.857230 -1.125885 -1.681255 B -0.596707 -0.675295 -0.827388 A -0.290393 -0.155407 -0.029967 B 0.110010 0.484079 0.626335 B 0.162770 0.776914 -0.328370 A 0.162639 0.678281 -1.323493 B 0.219978 0.432508 -2.291121 A 0.444364 0.055716 -3.189829 B 1.268189 -0.503306 -3.283678 B 1.459310 -1.259428 -2.657776 A 0.965495 -1.656927 -1.884379 B 0.255341 -1.879653 -1.216491 B -0.653161 -1.783533 -0.809818 A -1.504582 -1.262869 -0.746650 B -1.578376 -0.369291 -1.189448 A -1.557596 0.523631 -1.639172 B -0.739898 1.066675 -1.830141 B 0.113194 1.559915 -2.000266 A 1.027615 1.166839 -1.903716 B 1.928092 0.747291 -1.789189 A 2.048504 0.042246 -1.090328 B 1.410687 -0.255968 -0.380218 B 0.694872 -0.476615 0.282294 A -0.074711 -0.632197 0.901598 B -0.858279 -0.013484 0.844884 B -0.934677 0.677467 0.126029 A -0.778999 0.418222 -0.827153 B -0.560743 -0.043843 -1.686720 A -0.310408 -0.533405 -2.521979 B 0.337372 -1.040818 -3.090234 B 0.770256 -0.531522 -2.346440 A 1.031028 0.081018 -1.600259 B 1.181685 0.761207 -0.882872 B 0.607766 1.578979 -0.926071 A -0.391078 1.531446 -0.918889 B -1.367073 1.318376 -0.873801 A -1.829006 0.501407 -0.528579 B -1.397912 -0.309658 -0.133193 B -0.837781 -1.075151 0.183464 A 0.074510 -1.212677 -0.202294 B 0.924085 -1.176072 -0.728487 A 1.540988 -0.860680 -1.449567 B 1.854634 -0.317133 -2.228143 B 1.320831 0.424115 -2.635087 A 0.699667 1.130165 -2.975156 B -0.300051 1.108245 -2.966151 B -0.904839 0.382850 -2.637471 A -1.426102 -0.387277 -2.269794 B -1.917393 -1.171891 -1.891624 A -1.532661 -2.027320 -1.544895 B -0.607225 -2.241704 -1.857312 B -0.015642 -1.517680 -2.212015 A 0.222705 -0.833229 -1.523018 B 0.419780 -0.197002 -0.777114 S_89 Fibonacci sequence global minimum energy computed by Eq. 1 = -325.578412 A -0.890676 5.222297 11.293380 B -1.668704 4.931778 10.736363 B -2.158498 5.528157 10.100414 A -1.668164 6.004270 9.370424 B -1.051123 6.389643 8.684315 B -0.152088 6.170183 8.305408 A 0.750047 5.925282 7.950197 B 1.538695 5.358181 8.187744 A 0.826827 4.723130 7.887825 B 0.036563 4.606234 7.286312 B -0.894691 4.884079 7.050588 A -1.682813 4.670039 7.627694 B -2.347825 4.340134 8.297708 B -2.648735 3.820308 9.097229 A -2.285703 3.421407 9.939301 B -1.657824 3.205639 10.687106 A -1.047698 2.438666 10.488372 B -0.448592 1.679773 10.233127 B -0.073118 1.635437 9.307356 A 0.175184 2.320731 8.622727 B 0.429502 3.028740 7.963908 A 0.961370 3.773140 8.367617 B 1.461699 4.496864 8.842896 B 1.060899 4.700943 9.736040 A 0.580722 4.800837 10.607502 B 0.051615 4.760676 11.455104 B -0.206286 3.937065 11.960229 A 0.307527 3.094937 11.796475 B 0.935780 2.921734 11.037992 A 1.503541 2.870146 10.216418 B 2.004594 2.923607 9.352655 B 1.989546 3.553174 8.575855 A 1.817329 4.208172 7.840111 B 1.556098 4.869972 7.137416 B 0.721844 5.407230 7.013423 A -0.183812 5.670363 7.345912 B -0.999588 5.548707 7.911342 A -1.748901 5.296576 8.523683 B -2.477520 5.020295 9.150407 B -2.337992 4.467211 9.971765 A -1.423481 4.092965 10.125423 B -0.656610 4.211696 9.494699 A 0.233414 4.007857 9.902503 B 1.076682 3.845623 10.414925 B 1.784226 4.498139 10.686219 A 1.493482 5.421480 10.435407 B 0.703605 5.818557 9.968050 B -0.134302 6.070308 9.483763 A -0.743820 5.424754 9.023605 B -0.914901 4.602955 8.480119 A -0.076806 5.105053 8.266837 B 0.622976 5.476910 8.876777 B 1.522606 5.563877 9.304680 A 2.156608 4.894567 9.692060 B 1.890921 3.930661 9.709134 A 1.058479 3.482964 9.382628 B 0.138880 3.359732 9.009600 B -0.812989 3.507476 8.741054 A -1.610013 4.038142 9.029405 B -1.492645 4.909885 9.505099 B -0.979113 5.537814 10.089894 A -0.136436 5.670471 10.611711 B 0.713138 5.769108 11.129872 A 1.235614 4.994903 11.487115 B 0.879173 4.060589 11.489658 B 0.131152 3.711345 10.925309 A -0.587034 3.420047 10.293368 B -1.290857 3.148875 9.636790 B -1.913205 2.998510 8.868630 A -1.660815 3.509169 8.046727 B -0.894610 3.973606 7.602627 A -0.054379 4.003275 8.144040 B 0.339086 4.438247 8.953967 B 0.011977 5.023939 9.695563 A -0.501837 4.623321 10.454180 B -0.959711 4.067838 11.148288 A -0.714692 3.117182 11.338593 B -0.066216 2.493851 10.901628 B 0.583538 2.018076 10.308790 A 0.927769 2.356424 9.432990 B 1.249645 2.721486 8.559421 B 1.494238 3.149799 7.689523 A 0.878466 3.814968 7.267178 B -0.065908 3.506738 7.152503 A -0.606076 2.976902 7.806334 B -0.954466 2.474637 8.597758 B -1.161863 2.043503 9.475885 A -0.346425 2.607860 9.604576 B 0.415302 3.024958 10.100354 S_13 Fibonacci sequence global minimum energy computed by LJ term = -18.264451 A -1.872515 -0.893300 1.154829 B -2.731132 -0.568108 0.758563 B -2.520868 0.363275 1.055738 A -1.590969 0.182426 1.376019 B -1.309534 0.775524 0.621679 B -0.785642 0.122565 0.074705 A -0.850686 -0.469205 0.878182 B -1.174009 -1.161829 0.233409 A -2.165186 -1.224768 0.116772 B -2.796179 -0.659337 -0.414391 B -2.608159 0.249817 -0.042793 A -1.790042 -0.174069 0.345796 B -1.637280 -0.521693 -0.579308 S_21 Fibonacci sequence global minimum energy computed by LJ term = -38.280724 B -2.598970 -1.071744 -0.989501 A -2.555464 -1.832540 -1.637030 B -3.179306 -2.381891 -1.081124 A -3.006899 -3.100627 -1.754692 B -2.258990 -3.762954 -1.710463 B -1.448311 -3.577823 -1.155012 A -1.257632 -2.619644 -0.941625 B -0.956978 -2.301922 -1.840880 A -1.693473 -1.901240 -2.385884 B -1.498008 -2.638748 -3.032317 B -2.233398 -3.230214 -2.701607 A -2.734630 -2.377477 -2.554629 B -3.551075 -2.074591 -2.063023 B -3.307601 -1.117647 -1.904976 A -2.600028 -1.274972 -2.593879 B -1.969334 -0.931424 -1.898036 A -1.564488 -1.608399 -1.283378 B -2.179463 -2.041624 -0.624500 B -2.319442 -3.001169 -0.868793 A -1.967465 -2.733347 -1.765666 B -1.265945 -3.308704 -2.186183 S_34 Fibonacci sequence global minimum energy computed by LJ term = -75.170999 A 0.472359 2.418285 -0.638095 B -0.322102 2.299673 -1.233713 B -0.047300 1.650925 -1.943368 A 0.691744 1.410112 -1.314225 B 0.478766 0.496016 -0.969161 B -0.167306 0.439314 -0.207994 A -0.553580 1.238591 0.252382 B 0.290259 1.228340 0.788878 A 0.371417 2.187270 0.517094 B 0.329232 2.937186 1.177280 B 1.087189 3.424014 0.743116 A 1.236341 2.671553 0.101590 B 2.127574 2.239059 0.238152 B 2.271682 2.431017 -0.732612 A 1.412721 2.888905 -0.961792 B 0.950592 3.588052 -0.416237 A 0.206155 3.177982 0.110693 B -0.407799 3.236765 -0.676456 B 0.371919 3.267500 -1.301832 A 0.730286 2.427743 -1.709729 B 1.608837 1.981712 -1.538835 A 1.389475 1.818740 -0.576900 B 1.491686 0.851222 -0.808113 B 0.968414 0.654887 0.021127 A 0.390090 1.417616 -0.268326 B -0.318322 1.226465 -0.947748 B -1.130292 1.717089 -0.631537 A -0.481968 2.287088 -0.126787 B -0.645757 2.798181 0.716986 A -0.449328 1.931999 1.176489 B 0.464218 1.940154 1.583146 B 1.267028 2.344961 1.145395 A 1.267005 1.595162 0.483729 B 2.057765 1.152922 0.060503 S_55 Fibonacci sequence global minimum energy computed by LJ term = -137.241642 B 1.373813 0.169900 -0.003080 A 0.839574 0.156997 -0.848314 B 1.224370 0.867832 -1.437077 A 0.377357 0.770842 -1.959722 B -0.189950 1.593290 -2.001428 B -0.752958 1.436535 -1.189978 A -0.408800 1.311824 -0.259385 B -1.308185 0.916183 -0.073446 A -0.858252 0.037826 -0.234832 B -1.284447 -0.789417 0.131262 B -0.695297 -1.273802 -0.515477 A -0.006945 -0.549511 -0.555161 B 0.858993 -0.783863 -0.113315 B 0.673085 -0.297359 0.740354 A -0.288062 -0.478856 0.532380 B 0.025050 -1.402222 0.310224 A 0.334731 -1.623659 -0.614471 B -0.271404 -2.223190 -1.137120 B -1.125174 -1.780380 -1.410972 A -1.487109 -1.038236 -1.975084 B -1.530026 -0.039385 -1.996363 A -0.665714 0.460180 -1.938074 B -1.205005 1.252159 -2.224309 B -1.998532 0.927871 -1.709381 A -1.323163 0.539623 -1.082374 B -1.904416 -0.024012 -0.495467 B -1.661492 -0.902707 -0.906419 A -0.844182 -0.435675 -1.243885 B -0.228644 -1.185260 -1.487269 A 0.415769 -0.978629 -2.223498 B 0.308049 -1.404688 -3.121756 B -0.235283 -0.595015 -3.343612 A 0.259806 0.006437 -2.716602 B 1.061168 -0.536598 -2.967464 B 1.955183 -0.345303 -2.562321 A 1.681263 -1.004307 -1.861835 B 1.202204 -1.648374 -2.458224 A 0.675894 -1.879328 -1.639899 B -0.125260 -1.963959 -2.232342 B -0.771985 -1.419525 -2.766510 A -0.580275 -0.552099 -2.307364 B -0.939675 0.136461 -2.937217 A -0.345111 0.937011 -2.862293 B 0.600021 1.261688 -2.898470 B 1.277340 0.561780 -2.671830 A 1.081183 -0.097319 -1.945809 B 1.974153 0.069299 -1.527669 B 1.666049 -0.570189 -0.823307 A 0.795558 -0.858027 -1.222548 B 0.130805 -0.203018 -1.581805 A -0.201357 0.515911 -0.971229 B 0.326022 1.360430 -1.064280 B 0.837993 1.095576 -0.247129 A 0.201303 0.373024 0.022210 B -0.534534 0.612033 0.655785 S_89 Fibonacci sequence global minimum energy computed by LJ term = -242.825509 A 0.262401 4.242779 8.095651 B 1.068432 4.121103 7.516420 B 0.659709 3.332733 7.056616 A -0.176719 3.349537 7.604434 B -1.092642 3.300990 7.206027 B -0.785156 4.044326 6.611969 A 0.099885 4.260447 7.024268 B 0.580675 5.096724 7.287862 A 1.005547 5.043997 8.191578 B 1.610226 4.300315 8.476709 B 1.707206 3.305931 8.519077 A 0.790503 3.287169 8.119952 B 0.917618 2.416369 7.645033 B -0.020586 2.336864 7.308208 A -0.820510 2.488857 7.888742 B -1.047035 3.375591 8.291715 A -0.135793 3.408852 8.702235 B 0.110602 2.490435 8.392721 B 0.127264 1.999318 9.263654 A -0.024691 2.898665 9.673627 B -0.906480 3.115770 10.092323 A -1.040584 3.705501 9.295941 B -1.951092 3.357325 9.072896 B -1.708706 2.545623 8.541497 A -0.829295 2.606496 9.013652 B -0.838998 2.075203 9.860784 B -0.099781 2.182613 10.525629 A -0.039922 3.167379 10.688878 B -0.649078 3.759855 11.216037 A -0.886562 4.157247 10.329651 B -1.805176 3.938417 10.000617 B -2.328988 4.370486 9.266494 A -1.628394 4.257806 8.561887 B -1.998209 3.625284 7.881336 B -1.661353 4.286907 7.211425 A -0.799669 4.226626 7.715275 B -0.551235 5.086298 7.268911 A -0.073144 5.290318 8.123196 B 0.571077 6.037373 7.959217 B 0.517272 6.824111 8.574157 A 0.401977 6.758480 9.565318 B 1.204549 6.162898 9.531305 A 0.617416 5.492169 9.984507 B 0.713704 6.080373 10.787467 B -0.234202 6.389185 10.865619 A -0.345923 5.994866 9.953464 B -0.724722 6.652212 9.302000 B -0.402554 6.266276 8.437558 A 0.307962 5.836758 8.994945 B 0.333013 4.837120 9.004377 A -0.571119 4.495350 8.747993 B -1.120092 5.123399 8.196463 B -1.849419 5.310010 8.854684 A -1.339882 4.756065 9.513103 B -2.071029 4.998725 10.150706 A -1.718019 4.498096 10.941120 B -0.872181 4.798858 11.381687 B 0.077675 4.558385 11.581548 A 0.182024 4.230095 10.642753 B 1.108881 3.982703 10.925125 B 1.911000 4.295324 10.416331 A 1.632244 5.247700 10.292738 B 0.902394 5.026502 10.939569 A -0.052887 5.286314 10.798382 B -0.303312 5.670244 11.687135 B -1.181011 5.874377 11.253575 A -1.080298 5.286839 10.450671 B -1.417309 5.856847 9.701329 B -0.703314 5.492788 9.103273 A -0.296294 4.909130 9.805896 B -0.038124 3.964528 9.603241 A 0.775288 3.919465 9.023301 B 1.664446 3.811010 9.467861 B 2.195119 4.657098 9.417666 A 1.314974 5.095290 9.235099 B 0.926354 4.483003 9.923632 A 0.806105 3.497458 10.042964 B 1.700779 3.211873 10.386473 B 1.777215 2.716025 9.521436 A 0.879318 2.857280 9.104515 B 1.042755 1.975180 8.662719 B 1.157882 1.628993 9.593793 A 0.871987 2.423081 10.130158 B 0.909424 2.861616 11.028093 A 0.419355 3.524880 11.593702 B -0.266002 2.803327 11.691918 B -0.983369 2.604411 11.024224 A -1.597429 3.379182 10.873698 B -1.932869 2.849475 10.094665 S_13 Optimized sequence global minimum energy computed by LJ term = -18.610603 A 1.038830 -0.765684 0.479799 A 1.015785 -0.076582 -0.244499 B 0.669287 -0.248282 -1.166702 B -0.056089 -0.909581 -0.975615 A 0.055459 -0.625012 -0.023471 B 0.255497 -1.586615 0.164427 B 1.221177 -1.841911 0.212231 B 1.814616 -1.696593 -0.579420 A 1.903484 -0.763329 -0.231396 B 1.786908 -0.246508 -1.079514 B 1.376632 -1.087295 -1.432712 A 0.902306 -1.121712 -0.553038 B 0.741207 -2.082997 -0.776590 S_21 Optimized sequence global minimum energy computed by LJ term = -39.650163 B -1.168606 -0.122705 -2.808934 A -1.862785 0.435824 -2.354887 A -2.028844 0.286177 -1.380195 B -2.208717 0.787195 -0.533660 B -2.321778 1.581406 -1.130690 A -2.688791 1.008135 -1.863261 B -3.071911 0.417466 -1.153099 A -2.710029 -0.513141 -1.098203 B -1.740871 -0.628266 -0.880305 B -1.228007 0.201424 -0.659886 B -1.321287 1.055575 -1.171476 B -1.642009 1.469229 -2.023548 B -2.236188 1.350234 -2.819030 A -2.846012 0.559679 -2.875036 A -2.806989 -0.083118 -2.109995 A -1.972821 -0.621171 -1.988909 B -1.118503 -0.184810 -1.706544 B -0.832964 0.693723 -2.089489 B -1.179475 1.016090 -2.970403 B -1.880494 0.483777 -3.444972 A -2.235819 -0.357323 -3.037179 S_34 Optimized sequence global minimum energy computed by LJ term = -77.919140 A -1.545522 1.177180 0.136790 B -1.852461 0.277788 -0.174471 B -2.305021 -0.428425 0.370003 B -3.101351 0.175172 0.330931 A -3.195326 0.957649 0.946476 B -4.038946 1.291080 1.367341 B -4.224617 1.700988 0.474313 A -3.255779 1.948018 0.456213 B -2.867313 2.642656 -0.149237 A -2.003360 2.160413 -0.004241 A -1.353174 2.093840 0.752612 B -0.702807 1.334230 0.756818 B -1.148185 0.439531 0.790805 A -2.144132 0.521769 0.827252 B -2.763715 0.018408 1.429532 B -3.745329 0.034185 1.239312 B -4.162410 0.586755 0.517710 B -3.599110 1.065813 -0.155487 A -2.615162 1.147361 0.003235 A -2.300719 1.565377 0.855517 A -1.531879 1.230223 1.400088 B -1.698313 0.324516 1.789952 B -2.423976 0.230089 2.471492 B -2.808893 1.058299 2.878807 B -2.591776 1.960076 2.505099 A -2.020424 2.161472 1.709489 A -2.436276 2.622496 0.925573 B -3.342021 3.018557 0.774705 B -3.946384 2.397500 1.273737 A -3.103517 1.925973 1.533034 B -3.622960 1.621311 2.331381 B -3.408948 0.689301 2.038883 A -2.513309 1.063787 1.798910 B -1.783385 1.210412 2.466526 S_55 Optimized sequence global minimum energy computed by LJ term = -146.316053 A -2.973835 0.271336 -0.744174 A -2.379573 -0.505505 -0.535926 B -2.754117 -1.430975 -0.592679 B -3.648686 -1.649556 -0.202848 B -3.695617 -1.228583 0.703010 A -3.529803 -0.268431 0.927986 B -3.858544 0.200964 1.747496 B -4.795079 0.534182 1.856442 B -5.226262 1.098880 1.152737 B -5.657353 0.725177 0.331451 B -5.332960 -0.127324 -0.078441 A -4.412782 -0.344033 0.247606 B -4.467569 -0.661575 1.194267 B -3.727868 -0.898194 1.824230 B -2.825390 -0.967957 1.399183 B -2.667484 -0.976216 0.411764 A -3.408784 -0.604395 -0.147004 A -3.362471 -0.704323 -1.140919 B -2.573241 -0.313214 -1.614362 B -1.827804 0.182300 -1.168505 A -2.052405 0.686429 -0.334595 B -1.634234 -0.087315 0.141275 B -1.988619 -0.352474 1.037991 B -2.719519 0.142977 1.507366 A -3.266001 0.829831 1.028211 A -2.887597 1.186242 0.173939 B -3.195715 2.069915 -0.178455 B -3.631644 2.059588 -1.078376 B -3.574188 1.270052 -1.689385 A -3.540737 0.270685 -1.677332 A -4.301702 -0.377270 -1.710315 A -5.072404 -0.159082 -1.111640 B -5.432354 0.717969 -0.793489 A -4.650887 0.712986 -0.169563 B -5.035067 1.568016 0.178760 B -4.598191 2.046878 0.940226 B -4.142720 1.313925 1.445523 A -4.369110 0.524691 0.874686 B -5.225473 0.021948 0.992555 B -5.377799 -0.910216 0.664122 B -4.656841 -1.377197 0.152117 A -4.358333 -0.925402 -0.688582 A -4.064674 0.028497 -0.750527 A -4.475313 0.734922 -1.327012 B -4.626157 1.593895 -0.837716 B -4.254866 2.224542 -0.156227 A -3.969040 1.409887 0.348391 B -3.388986 1.976633 0.933481 B -2.482623 1.596761 1.118423 B -2.082081 0.738179 0.798419 A -2.703822 0.106200 0.335778 A -3.627577 0.416598 0.111441 A -3.686799 1.075113 -0.638791 B -2.761678 1.354487 -0.895892 B -2.574822 0.783251 -1.695125 S_89 Optimized sequence global minimum energy computed by LJ term = -261.401077 A 5.335687 2.905267 -9.716160 A 5.832940 3.467213 -9.055139 A 6.573647 2.963723 -8.610340 A 6.588762 1.996723 -8.356021 B 5.847304 1.652888 -7.779812 B 5.450839 0.761876 -8.000976 B 5.614742 0.326729 -8.886291 B 6.455216 0.556758 -9.376892 A 6.901018 1.437602 -9.217604 A 7.452963 1.296742 -8.395709 A 8.130765 1.874034 -8.851024 A 7.343220 2.415189 -9.145851 A 7.573687 3.296985 -8.734368 B 8.399980 3.828942 -8.919462 B 7.784366 4.611600 -9.011471 B 6.863774 4.955809 -8.826990 B 5.981103 4.509978 -8.678237 B 6.107616 3.756833 -8.032664 B 5.201538 3.341739 -8.114643 B 4.914555 2.436884 -7.800192 B 4.961990 1.641023 -8.403811 A 5.822732 1.383511 -8.842915 B 6.484006 0.839015 -8.326934 B 6.836661 1.268568 -7.495599 B 6.784960 2.248266 -7.301905 B 6.008944 2.723401 -7.716685 A 5.606019 2.472408 -8.596829 A 6.184722 2.264265 -9.385352 A 6.065528 1.427481 -9.919749 B 5.418240 0.665944 -9.952566 B 4.790851 0.986499 -9.242901 A 5.132237 1.897241 -9.475287 B 4.599280 2.534158 -8.918247 B 4.710900 3.517102 -9.064396 B 5.232536 4.180442 -9.600936 A 5.942526 3.752122 -10.159911 A 6.116817 3.564621 -11.126589 B 5.343402 3.660016 -11.753270 B 5.037800 2.712679 -11.848961 A 5.925344 2.478301 -11.452313 B 6.425150 3.088922 -12.066588 B 6.376102 4.087309 -12.037999 B 5.764629 4.603617 -11.438394 B 6.511205 4.548973 -10.775344 A 6.987514 3.704822 -10.529306 B 7.819385 4.211375 -10.756005 B 8.393817 4.441852 -9.970570 B 8.697227 3.490507 -10.024274 A 8.324763 2.816763 -9.386044 B 8.431279 2.794482 -8.391982 A 7.559624 2.419576 -8.076287 B 7.090471 3.228031 -7.720905 B 7.129588 4.108302 -8.193762 A 6.794454 3.948602 -9.122298 A 6.713603 3.124316 -9.682663 A 6.139630 2.723901 -10.396961 A 5.267798 3.014540 -10.791219 B 4.503855 2.386220 -10.938199 B 4.323784 2.515777 -9.963116 B 4.521673 3.479175 -10.143959 B 5.075225 4.062989 -10.737880 B 5.536667 4.879314 -10.390486 B 6.245523 4.684382 -9.712604 B 7.218278 4.576227 -9.917663 A 7.676200 3.711366 -9.711939 A 7.613535 2.857795 -10.229128 A 6.959172 2.114544 -10.089911 A 6.478405 1.761216 -10.892414 B 6.988109 1.005053 -11.302800 B 7.362086 0.196718 -10.848117 B 7.433998 0.151774 -9.851718 A 7.851979 0.980870 -9.480380 A 7.972920 1.876910 -9.907562 B 8.564523 2.432906 -10.491407 B 8.228152 3.223417 -11.003215 B 7.833432 2.633804 -11.707879 A 7.642734 1.991391 -10.965627 B 7.933594 1.092223 -10.638680 A 7.025067 1.046270 -10.223394 B 6.376887 0.309481 -10.415756 B 5.815884 0.956523 -10.932099 B 4.839685 0.739740 -10.938399 B 4.591087 1.453429 -10.283537 A 5.409067 1.958511 -10.558853 B 5.186689 1.664048 -11.488282 B 6.093856 1.482577 -11.867911 B 6.892296 2.082913 -11.822188 A 6.928889 2.779607 -11.105753 B 7.273290 3.603558 -11.555743