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[(re)17.5(qu)15.5(ir)16.5(e)-252.9(t)0(h)18.5(e)-258.6(sy)20(nc)13.8(hr)19.3(on)21.2(iz)16.7(at)16.7(io)18.5(n)-256.8(o)0(f)-242.5(g)0(l)12.8(o)0(b)21.2(a)0(l)-245.1(s)0(t)17.3(a)0(t)16.7(e)0(s)-249.2(t)0(o)-243.3(g)0(u)15.5(i)0(d)18.5(e)-252.9(th)18.5(e)-258.6(s)0(e)18.3(a)0(r)17.5(c)0(h)-248(p)0(r)19.3(o)0(c)13.8(e)0(s)18.3(s)0(,)-247(f)14.3(or)-248.2(ex)19.4(am)15.9(pl)18.5(e,)-247.6(th)18.5(e)-258.6(g)0(l)18.5(o)0(b)21.2(a)0(l)-250.8(b)0(o)21.2(u)0(n)15.5(d)0(s)-247.4(i)13.5(n)-256.8(t)0(h)18.5(e)]TJ
T*
[(br)13.6(an)19.4(ch)19.4(-a)17.5(nd)15.5(-b)19.3(ou)15.5(nd)-348.7(\(B)14.5(nB)16.5(\))-355.6(a)0(l)16.7(g)0(o)15.5(r)0(i)16.5(t)13.5(hm)-352.2(an)13.8(d)-359.3(t)13.5(he)-356.1(pr)19.3(io)18.5(ri)16.5(t)13.5(y)-365(qu)21.2(eu)19.4(e)-361.1(i)0(n)-351.4(t)0(h)18.5(e)-361.1(A*)-352.6(al)16.7(go)15.5(ri)22.2(th)18.5(m.)-351.8(Th)15.7(e)-361.1(s)0(y)20(n)0(c)13.8(h)0(r)19.3(o)0(n)21.2(o)0(u)15.5(s)-360.5(co)19.4(mm)14.2(u-)]TJ
T*
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T*
[(in)18.5(ef)11.8()11.4(c)0(i)16.7(e)0(n)19.4(t)-498.6(on)-485.2(a)-491.9(c)0(l)16.7(o)0(u)15.5(d)-495.8(pl)18.5(at)16.7(fo)19.3(rm)15.7(.)-489.8(D)0(i)14.5(s)0(t)17.3(r)0(i)16.5(b)0(u)21.2(t)0(e)16.7(d)-495.8(co)19.4(mp)17.7(ut)18.5(at)16.7(io)18.5(na)13.8(l)-492.9(f)0(r)17.3(a)0(m)15.9(e)0(w)15.5(o)0(r)19.3(k)0(s)-486.4(s)0(u)20(c)0(h)-487(a)0(s)-488.2(M)0(a)17.5(p)0(R)16.5(e)0(d)13.8(u)0(c)19.4(e)-497.6(\(D)21(ea)12(n)-495.8(a)0(n)19.4(d)]TJ
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T*
[(bu)15.5(il)15.7(t)-390.5(d)0(i)18.5(s)0(t)17.3(r)0(i)22.2(b)0(u)15.5(t)0(e)16.7(d)-393.4(co)19.4(mb)17.7(in)18.5(at)16.7(or)19.3(ia)16.7(l)-390.5(s)0(e)18.3(a)0(r)17.5(c)0(h)-384.6(s)0(y)14.4(s)0(t)17.3(e)0(m)21.6(s)0(,)-383.6(s)0(u)14.4(c)0(h)-384.6(a)0(s)-380.1(D)0(r)15.3(y)0(a)19.4(d)0(O)17.3(p)0(t)-385.6(\()0(B)20.2(u)0(d)15.5(i)0(u)-379.9(e)0(t)-387.3(a)0(l)16.7(.)0(,)-382(2)0(0)21.2(1)0(1)15.5(\))-389.7(an)13.8(d)-387.7(B)0(r)14.5(a)0(n)19.4(c)0(h)13.8(R)11.6(ed)13.8(uc)19.4(e)]TJ
T*
[(\(B)14.5(ra)17.5(ch)19.4(re)17.5(du)15.5(ce)17.7(\))-406.8(b)0(u)21.2(t)-407.6(t)13.5(h)0(e)13.8(s)0(e)-397.2(f)0(r)17.3(a)0(m)21.6(w)0(o)11.6(r)14.3(ks)-395.4(ex)13.8(cl)16.7(ud)21.2(e)-406.6(i)0(m)14.9(p)0(o)21.2(r)0(t)16.5(a)0(n)19.4(t)-407.6(op)21.2(ti)15.7(m)12.8(i)0(z)16.7(a)0(t)16.7(i)0(o)18.5(n)0(s)14.4(,)-404.4(es)18.3(pe)19.4(ci)16.7(al)16.7(ly)-396.9(G)12.4(M)0(E)13.8(C)0(-)20.2(s)0(p)14.4(e)0(c)17.7(i)0()19.3(c)-406.6(he)19.4(ur)13.6(i)13.5(s)0(t)17.3(i)0(c)16.7(s)]TJ
T*
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T*
[(sear)-9.8(ch)-430.1(algorithms)-434.1(on)-434(the)-427.9(clou)-7.6(d)-427.6(platform)-9.5(s.)-423.4(With)-437.9(a)-423.7(com)-7.6(bination)-437.3(of)-424.6(algo)-7.6(rithm)-430.3(and)-430.9(syst)-8.2(em)-427.9(optim)-7.2(izations,)]TJ
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1.0015 -1.2007 TD
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-1.0015 -1.2007 TD
[(tra)-8.8(ditional)-280.7(BnB)-279.2(search)-286.3(for)-279.4(protein)-282.1(design.)-283.8(We)-279(embed)-278.4(a)-281.4(dead-end)-286.6(elimina)-9.3(tion)-276(\(DEE)-8.6(\)-based)-281.5(prunin)-9.3(g)-273.9(scheme)]TJ
T*
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T*
[(losing)-455.2(the)-456.4(global)-455.7(optimalit)-8.9(y)-450.3(guarantee.)-457.3(We)-455.4(also)-452.7(appl)-7.6(y)-444.6(sever)-10.6(al)-449.9(optim)-7.2(ization)-455.4(techniq)-8.7(ues)-449.1(to)-453.8(improv)-7.1(e)-452.1(the)]TJ
T*
[(tig)-7.8(htness)-347.2(of)-339.2(both)-347.2(lower)-344.3(and)-345.5(upper)-343.3(bounds)-347.2(in)-340(BnB)-347.5(search.)-349.2(On)-346.9(the)-342.6(system)-345.1(side)-8.8(,)-336.1(w)0(e)-348.7(design)-346.1(a)-344(low)-339(ov)-7.2(erhead)]TJ
T*
[(synchr)-9.5(onization)-343.1(scheme)-339(to)-340(keep)-336.7(track)-336.5(of)-339.2(the)-336.9(global)-336.2(states)-340.4(of)-333.6(the)-336.9(algo)-7.6(rithm.)]TJ
1.0015 -1.195 TD
[(We)-387.1(conduc)-8.1(t)-379.1(experiment)-12.6(s)-377.5(o)0(n)-382.8(a)-383.8(private)-386.3(64-serve)-9.1(r)-378.3(clou)-7.6(d)-382(infrastr)-9.1(ucture,)-383.2(as)-385.8(well)-384.2(as)-380.1(two)-384.6(virtua)-8.2(lized)-382.8(clou)-7.6(d)]TJ
-1.0015 -1.2007 TD
[(com)-7.6(puting)-197.9(system)-9.3(s)-195.4(including)-204.7(Amazons)-202.4(Elas)-8.6(tic)-197.4(Computi)-7.7(ng)-195(Cloud)-199.1(\(EC2\))-200.1(and)-197.6(an)-196.8(Ope)-8(nStack-ba)-10.5(sed)-198.7(cloud.)-196.5(We)]TJ
T*
[(show)-269.9(that)-260.7(by)-263.3(coupling)-263.8(ele)-8.6(gant)-263.7(algorithm)-267.1(optim)-7.2(izations)-269.5(with)-262.9(novel)-264.4(system)-265.4(desi)-8.8(gn)-257.6(strat)-8.6(egies,)-267.8(we)-263.3(can)-261.9(achieve)]TJ
T*
[(sign)-7(icant)-286(improv)-7.2(ement)-286.8(of)-282.3(p)-6.5(rotein)-287(design)-283.5(perf)-8.8(ormance)-289.3(over)-285.7(traditi)-8.8(onal)-280.7(sear)-9.8(ch)-282.2(algori)-8.2(thms.)-284.1(Our)-287(new)-286.8(design)]TJ
T*
[(appro)-7.6(ach)-438.3(can)-438.3(solv)-7(e)-435(protein)-441.4(design)-437.1(case)-9.6(s)-434.4(that)-437.1(have)-439.1(never)-441.8(been)-439.1(possibl)-7.6(e)-435(with)-439.3(previous)-8.1(ly)-436.8(reported)-443.2(exact)]TJ
T*
[(algo)-7.6(rithms.)-313.1(Also,)-307.2(cOSPREY)-319.5(is)-301.4(data)-9.4(-compati)-9.3(ble)-308.4(with)-308.4(OSPREY)-9.7(,)-302(and)-311.4(thus)-308.6(research)-12.7(ers)-303.2(can)-313.1(easily)-310.8(migra)-8.2(te)-302(to)]TJ
/F2 1 Tf
0 67.0005 TD
(2)Tj
37.5064 0 TD
[(PAN)-340(ET)-335.3(AL.)]TJ
ET
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/GS1 gs
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/F1 1 Tf
9.9626 0 0 9.9626 107.6031 715.4644 Tm
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[(cOSPREY)-200(and)-191.9(take)-197.2(advantage)-198.9(of)-191.3(the)-194.6(massi)-8.6(ve)-191.1(scalabilit)-10.9(y)-188.6(o)0(f)-191.3(the)-194.6(cloud.)-196.5(We)-193.6(demonst)-8.9(rate)-193.5(such)-193.8(a)-190.3(migra)-8.2(tion)-190.7(using)]TJ
0 -1.195 TD
[(a)-270(real)-278.8(design)-272.1(case)-277.1(from)-278(recent)-276.4(literatu)-11.3(re.)]TJ
1.0015 -1.2007 TD
[(We)-335.9(have)-336.7(mad)-7.6(e)-332.6(the)-336.9(followi)-8.1(ng)-331.6(cont)-7.6(ributions)-342.7(in)-334.3(this)-334.1(artic)-9.2(le:)]TJ
0 -2.3047 TD
[(1.)-501.9(A)-357.5(new)-360.8(exte)-9.4(nsion)-360.6(to)-357.1(the)-359.7(widely)-362.9(used)-364.5(OSPREY)-362.5(softw)-8(are,)-361(cOSPREY)-12.2(,)-358.9(that)-357.5(ful)-7(ly)-357.1(exploits)-364.5(the)-359.7(massive)]TJ
1.2519 -1.195 TD
[(para)-8.6(llelism)-335.9(in)-340(cloud)-338.4(computing)-342.1(while)-339.4(being)-338.4(data-co)-9.7(mpatible)-340.2(with)-336.9(the)-336.9(exis)-8.8(ting)-332.9(soft)-9(ware.)]TJ
-1.2519 -1.2007 TD
[(2.)-501.9(A)-420.1(numb)-6.6(er)-420.7(of)-418.9(algorithm)-426.5(and)-419.5(system)-424.8(optim)-7.2(izations)-428.9(targeting)-424.7(the)-422.3(protei)-8.2(n)-416.2(design)-425.7(problem,)-425.5(including)]TJ
1.2519 -1.2007 TD
[(DEE-)-8.6(based)-441.1(pruni)-8.6(ng,)-440.1(linear)-442.4(progr)-7.8(amming)-10.5(-based)-443.8(lower)-446.8(bound)-442(estimat)-10.5(ion,)-437.9(loca)-9.4(l)-436(search-)-10.1(based)-446.7(upper)]TJ
T*
[(bound)-339.6(computa)-9.5(tion,)-333.3(and)-339.8(low-ov)-7.6(erhead)-342(global)-336.2(sta)-8(te)-330.4(synchr)-9.5(onization.)]TJ
-1.2519 -1.2007 TD
[(3.)-501.9(A)-391.7(compreh)-8.7(ensive)-393.4(and)-391(prac)-8.6(tical)-391.2(eval)-9.4(uation)-393.2(of)-390.5(cOSPREY)-399.2(on)-388.5(three)-393.4(dif)-7(ferent)-390.4(clou)-7.6(d)-387.7(technol)-8.7(ogies)-390.8(and)]TJ
1.2519 -1.2007 TD
[(dem)-7.6(onstratio)-8.7(n)-330.8(o)0(f)-333.6(i)0(t)-7.1(s)-332(applica)-10.5(tions)-334.9(in)-334.3(solv)-7(ing)-335.1(large-)-9.2(scale)-337.5(protei)-8.2(n)-330.8(desi)-8.8(gn)-331.6(probl)-8.6(ems.)]TJ
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[(2.)-501.9(METHODS)]TJ
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-16.4559 -1.6347 TD
[(2.1.)-496.9(Background)]TJ
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9.9626 0 0 9.9626 117.5811 512.277 Tm
[(To)-359.8(nd)-360(the)-365.3(optim)-7.2(al)-358.9(solu)-7(tion)-361.4(to)-357.1(the)-365.3(structure)-9.7(-based)-364.1(com)-7.6(putation)-10.5(al)-358.9(protei)-8.2(n)-359.3(design)-363.1(\(SC)-8.2(PD\))-360.2(problem)-9.7(,)-358.9(w)0(e)]TJ
-1.0015 -1.2007 TD
[(often)-243.7(need)-239.9(to)-237.6(sear)-9.8(ch)-236.6(over)-245.8(a)-235.9(huge)-243.8(conform)-8.9(ational)-244.8(space.)-244.1(As)-240(in)-237.6(mos)-7(t)-236.8(popular)-245.2(provable)-242(methods)-8.9(,)-239.4(w)0(e)-240.6(rst)-241.5(apply)]TJ
T*
[(dead-end)-309.3(elim)-8.2(ination)-305.6(\(D)-7.4(EE\))-305.5(as)-300.4(a)-304.2(prelte)-9.9(ring)-303.7(algo)-7.6(rithm)-305.1(to)-300.2(prune)-309.2(the)-302.8(rot)-7(amers)-304.3(that)-306.3(are)-309.4(provab)-8.3(ly)-300.2(not)-306.7(part)-305.5(of)]TJ
T*
[(the)-325.5(GM)-7.4(EC,)-325.1(sign)-7(icantly)-330.2(reduc)-9.4(ing)-323.7(the)-325.5(confo)-7.6(rmationa)-9.3(l)-322.2(space)-10.4(.)-324.7(Then)-329(we)-325.9(expl)-7.6(oit)-326.5(the)-325.5(distribut)-9.7(ed)-322(com)-7.6(putation)]TJ
T*
[(over)-399.5(a)-395.2(large-)-9.2(scale)-400.1(clou)-7.6(d)-393.4(platfo)-8.2(rm)-399.7(to)-396.9(search)-400.1(ov)-7.2(er)-397.9(the)-393.8(rem)-9.6(aining)-398.8(rotam)-8.2(er)-397.9(combina)-9.5(torial)-397.9(space)-403(to)-396.9(nd)-399.8(the)]TJ
T*
[(GME)-8(C)-329.8(solu)-7(tion.)]TJ
/F5 1 Tf
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[(Problem)-407.5(formulat)-8.1(ion.)]TJ
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9.2415 0 TD
[(Let)-405(us)-401.1(consider)-408.2(an)-401.7(SCPD)-408.5(problem)-408(with)]TJ
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17.0091 0 TD
(n)Tj
/F1 1 Tf
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[(mutable)-404.9(residue)-9.1(s,)-400.7(in)-402.6(which)-404.9(the)-405.2(total)]TJ
-28.1568 -1.2007 TD
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7.4718 0 0 6.641 144.2834 426.8975 Tm
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9.9626 0 0 9.9626 161.4047 428.5416 Tm
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(2)Tj
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(r)Tj
6.9738 0 0 6.9738 321.6188 394.9794 Tm
(i)Tj
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(\))Tj
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/F9 1 Tf
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(X)Tj
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6.9738 0 0 6.9738 343.2188 407.9054 Tm
(n)Tj
-.5853 -3.1867 TD
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(X)Tj
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6.9738 0 0 6.9738 361.9274 407.9054 Tm
(n)Tj
-1.1706 -3.1867 TD
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(E)Tj
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(\()Tj
/F5 1 Tf
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6.9738 0 0 6.9738 392.8251 394.9794 Tm
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()Tj
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6.9738 0 0 6.9738 404.1637 394.9794 Tm
(j)Tj
/F7 1 Tf
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(\))Tj
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-30.3363 -3.8184 TD
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6.9738 0 0 6.9738 140.8251 356.8818 Tm
(c)Tj
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[(is)-272.9(the)-268.6(const)-9.6(ant)-268.6(energ)-9.4(y)-268.2(o)0(f)-265.3(the)-274.3(backbo)-8.1(ne,)]TJ
/F5 1 Tf
16.0303 0 TD
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6.9738 0 0 6.9738 312.9448 356.8818 Tm
(i)Tj
/F7 1 Tf
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(\()Tj
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(r)Tj
6.9738 0 0 6.9738 322.4692 356.8818 Tm
(i)Tj
/F7 1 Tf
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(\))Tj
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[(is)-267.2(the)-274.3(self-ener)-10.7(gy)-269(of)-271(rotamer)]TJ
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7.4718 0 0 6.641 451.5022 356.7117 Tm
(i)Tj
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9.9626 0 0 9.9626 456.2644 358.4125 Tm
[(at)-267.8(residue)-276.6(posi)-7(tion)]TJ
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7.6709 0 TD
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/F1 1 Tf
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(,)Tj
-42.9466 -1.2007 TD
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6.9738 0 0 6.9738 131.5275 344.9196 Tm
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(\()Tj
/F5 1 Tf
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(r)Tj
6.9738 0 0 6.9738 142.9795 344.9196 Tm
(i)Tj
/F1 1 Tf
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()Tj
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(r)Tj
6.9738 0 0 6.9738 154.3181 344.9196 Tm
(j)Tj
/F7 1 Tf
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(\))Tj
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[(is)-335.5(the)-336.9(pairw)-8.6(ise)-338.1(interact)-10.3(ion)-335.1(energy)-340.2(between)-341.7(rotam)-8.2(ers)]TJ
/F5 1 Tf
21.5501 0 TD
(r)Tj
6.9738 0 0 6.9738 381.77 344.9196 Tm
(i)Tj
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(and)Tj
/F5 1 Tf
1.7868 0 TD
(r)Tj
6.9738 0 0 6.9738 409.2094 344.9196 Tm
(j)Tj
/F1 1 Tf
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(.)Tj
-29.5169 -1.2405 TD
[(The)-254.3(goal)-258(of)-259.6(the)-257.2(SCPD)-260.5(problem)-260.1(is)-255.9(to)-254.7(n)-6.4(d)-251.2(the)-257.2(op)-7.2(timal)-256.4(rotam)-8.2(er)-255.7(seque)-8.6(nce)]TJ
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()Tj
/F1 1 Tf
9.9626 0 0 9.9626 413.5747 334.0912 Tm
[(that)-260.7(minimi)-8.5(zes)-257.4(the)-257.2(total)-258.6(energy)]TJ
-30.7119 -1.2007 TD
[(functi)-8.2(on,)-332(which)-342.3(is)]TJ
/F5 1 Tf
16.7359 -2.1169 TD
(E)Tj
6.9738 0 0 6.9738 280.4598 299.5086 Tm
(total)Tj
/F7 1 Tf
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(\()Tj
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()Tj
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(\))Tj
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(E)Tj
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(total)Tj
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(\()Tj
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(1)Tj
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(2)Tj
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()Tj
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(R)Tj
6.9738 0 0 6.9738 218.6078 271.7291 Tm
(n)Tj
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9.9626 0 0 9.9626 226.6582 273.2031 Tm
[(is)-403.8(the)-405.2(whole)-404.9(rotam)-8.2(er)-403.6(com)-7.6(binatoria)-9.3(l)-401.9(space,)-409.1(and)]TJ
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19.8202 0 TD
(R)Tj
6.9738 0 0 6.9738 430.2991 271.7291 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 436.7621 273.2031 Tm
[(is)-403.8(the)-405.2(set)-406.4(of)-401.8(all)-407.9(possible)]TJ
-33.0393 -1.2007 TD
[(rotam)-8.2(ers)-348.7(at)-347.5(residue)-356.3(position)]TJ
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(i)Tj
/F1 1 Tf
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[(.)-347.5(The)-351(optimal)-349(solu)-7(tion)]TJ
/F5 1 Tf
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(r)Tj
/F10 1 Tf
6.9738 0 0 6.9738 326.6078 264.8692 Tm
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 334.0345 261.2409 Tm
[(is)-352.6(also)-350.2(called)-351.2(the)-348.3(globa)-8.4(l)-345(minimu)-11.5(m)-345.7(energy)-351.6(confo)-7.6(r-)]TJ
-22.7281 -1.195 TD
[(mation)-339.8(\(GMEC)-10.5(\).)]TJ
/F5 1 Tf
1.0015 -1.2007 TD
[(Branch-and-)-9.4(bound.)]TJ
/F1 1 Tf
8.3879 0 TD
[(Th)-7(e)-514.7(branch-a)-9.7(nd-bou)-6.6(nd)-513.7(\(BnB\))-518(algori)-8.2(thm)-515(is)-511.9(a)-514.7(widel)-9.4(y)-512.9(used)-518.2(search)-519.6(algo)-7.6(rithm)-515.6(for)]TJ
-9.3894 -1.2007 TD
[(solving)-256.7(various)-257.7(com)-7.6(binatoria)-9.3(l)-248.2(optim)-7.2(ization)-256.2(probl)-8.5(ems.)-253.9(This)-257.2(algorithm)-255.8(const)-9.6(antly)-255.8(divides)-258.5(the)-251.5(confo)-7.6(rmationa)-9.3(l)]TJ
T*
[(space)-300.6(into)-304.5(several)-301.2(sma)-8.8(ller)-296.9(subspa)-8.7(ces)-303(\()]TJ
/F5 1 Tf
15.4328 0 TD
[(branch)-7.6(ing)]TJ
/F1 1 Tf
4.4216 0 TD
[(step\))-301.7(and)-300(then)-297.8(com)-7.6(putes)-299.8(the)-297.1(bou)-8(nds)-293.7(\(in)-7(cluding)-302.9(upper)-303.5(and)]TJ
-19.8543 -1.2007 TD
[(lower)-287.4(bo)-7.2(und\))-283.9(for)-290.8(each)-287.2(subspa)-8.7(ce)-283.9(\()]TJ
/F5 1 Tf
13.5151 0 TD
[(boundi)-7.3(ng)]TJ
/F1 1 Tf
4.0744 0 TD
[(step\).)-290.7(After)-289.4(that,)-289.6(those)-288.4(subspa)-8.7(ces)-285.9(that)-289.2(are)-286.7(impo)-9.3(ssible)-287.4(to)-288.8(contain)]TJ
-17.5895 -1.2007 TD
[(the)-416.6(optimal)-417.3(solution)-419.6(\(in)-411.1(which)-416.3(the)-416.6(lower)-418.3(bound)-413.5(is)-415.2(larger)-413.2(than)-417.3(the)-416.6(known)-417.5(best)-412.8(upper)-417.3(bound\))-416.3(are)-417.6(safely)]TJ
T*
[(prune)-7.6(d.)-422.2(To)-428.1(be)-430.1(more)-425.8(speci)-11.3(c,)-424(let)-430.7(us)-423.8(consi)-9.6(der)-427.2(the)-427.9(SCPD)-431.2(problem)-430.8(on)-428.3(confo)-7.6(rmationa)-9.3(l)-424.6(space)]TJ
/F5 1 Tf
38.195 0 TD
(S)Tj
/F1 1 Tf
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[(.)-427.2(The)-430.7(BnB)]TJ
-38.6957 -1.2007 TD
[(algori)-8.2(thm)-332.9(include)-8.7(s)-332(the)-336.9(fol)-7(lowing)-338.4(two)-333.3(main)-341.2(steps:)]TJ
/F2 1 Tf
1.0015 -1.195 TD
[(The)-247(branchin)-9.3(g)-239.8(step)]TJ
/F1 1 Tf
8.2684 0 TD
[(:)-242.5(The)-248.6(conformat)-9.3(ional)-244.4(space)]TJ
/F5 1 Tf
11.1933 0 TD
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[(is)-244.5(split)-246.6(into)-241.9(two)-248(or)-242.5(mor)-7.8(e)-241.6(subspa)-8.7(ces)]TJ
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14.0727 0 TD
(S)Tj
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6.9738 0 0 6.9738 464.0881 152.1638 Tm
(1)Tj
9.9626 0 0 9.9626 468.0566 153.6945 Tm
()Tj
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6.9738 0 0 6.9738 478.0345 152.1638 Tm
(2)Tj
9.9626 0 0 9.9626 482.0597 153.6945 Tm
()Tj
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1.3145 0 TD
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6.9738 0 0 6.9738 511.7668 152.1638 Tm
(m)Tj
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9.9626 0 0 9.9626 519.7038 153.6945 Tm
(such)Tj
-41.3646 -1.2007 TD
(that)Tj
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6.9738 0 0 6.9738 130.9606 140.2016 Tm
(1)Tj
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9.9626 0 0 9.9626 135.5527 141.7323 Tm
([)Tj
/F5 1 Tf
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(S)Tj
/F1 1 Tf
6.9738 0 0 6.9738 147.6283 140.2016 Tm
(2)Tj
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9.9626 0 0 9.9626 152.1637 141.7323 Tm
([)Tj
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(...)Tj
/F10 1 Tf
1.3657 0 TD
0 Tc
([)Tj
/F5 1 Tf
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(S)Tj
6.9738 0 0 6.9738 186.6897 140.2016 Tm
(m)Tj
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9.9626 0 0 9.9626 193.833 141.7323 Tm
(=)Tj
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/F1 1 Tf
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(and)Tj
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1.7868 0 TD
(S)Tj
6.9738 0 0 6.9738 232.1007 140.2016 Tm
(i)Tj
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9.9626 0 0 9.9626 235.1054 141.7323 Tm
(\\)Tj
/F5 1 Tf
.7113 0 TD
(S)Tj
6.9738 0 0 6.9738 247.181 140.2016 Tm
(j)Tj
/F6 1 Tf
9.9626 0 0 9.9626 251.3196 141.7323 Tm
(=)Tj
/F10 1 Tf
.7227 0 TD
(;)Tj
/F1 1 Tf
.8308 0 TD
[(for)-336.3(all)]TJ
/F5 1 Tf
2.851 0 TD
(i)Tj
/F10 1 Tf
.5577 0 TD
(6)Tj
T*
()Tj
/F5 1 Tf
1.0471 0 TD
(j)Tj
/F1 1 Tf
.2845 0 TD
(.)Tj
/F2 1 Tf
-19.7178 -1.2007 TD
[(The)-269.8(bounding)-272.4(step)]TJ
/F1 1 Tf
7.9668 0 TD
[(:)-265.3(T)0(h)-7(e)-264.3(lower)-270.3(bound)-271.3(and)-265.8(the)-268.6(upper)-269.3(bou)-8(nd)-263.3(of)-265.3(each)-270.2(subspa)-8.7(ce)]TJ
/F5 1 Tf
23.3256 0 TD
(S)Tj
7.4718 0 0 6.641 434.3243 128.1259 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 439.0865 129.7701 Tm
[(are)-269.6(comp)-8.4(uted,)-264.1(whi)-9(ch)-265.1(are)]TJ
-33.2726 -1.2007 TD
[(denoted)-415.7(by)]TJ
/F5 1 Tf
4.9963 0 TD
(LB)Tj
/F1 1 Tf
1.1666 0 TD
(\()Tj
/F5 1 Tf
.3357 0 TD
(S)Tj
7.4718 0 0 6.641 177.3354 116.1638 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 179.433 117.8078 Tm
[(\))-406.8(and)]TJ
/F5 1 Tf
2.5949 0 TD
(UB)Tj
/F1 1 Tf
1.3373 0 TD
(\()Tj
/F5 1 Tf
.3357 0 TD
(S)Tj
7.4718 0 0 6.641 226.9417 116.1638 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 229.0393 117.8078 Tm
[(\),)-407.2(respect)-10.9(ively.)-409.8(Let)]TJ
/F5 1 Tf
8.2627 0 TD
(GUB)Tj
/F6 1 Tf
2.2193 0 TD
(=)Tj
/F1 1 Tf
.7227 0 TD
(min)Tj
7.4718 0 0 6.641 356.2582 116.1638 Tm
(1)Tj
/F6 1 Tf
.5008 0 TD
()Tj
/F5 1 Tf
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(i)Tj
/F6 1 Tf
.2807 0 TD
()Tj
/F5 1 Tf
.5539 0 TD
(m)Tj
9.9626 0 0 9.9626 379.7857 117.8078 Tm
(UB)Tj
/F1 1 Tf
1.3373 0 TD
(\()Tj
/F5 1 Tf
.3301 0 TD
(S)Tj
7.4718 0 0 6.641 401.3857 116.1638 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 403.4834 117.8078 Tm
[(\))-406.8(b)0(e)-413(the)-405.2(minimum)-414.1(upper)-411.6(bound.)]TJ
-29.699 -1.2007 TD
[(Then)-300.6(we)-297.5(can)-301.8(safely)-304.3(prune)-303.5(the)-297.1(subspa)-8.7(ce)]TJ
/F5 1 Tf
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(E)Tj
6.9738 0 0 6.9738 272.1826 405.8644 Tm
(ij)Tj
/F7 1 Tf
9.9626 0 0 9.9626 276.6046 407.3952 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 283.6913 405.8644 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 286.129 407.3952 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 294.9731 405.8644 Tm
(j)Tj
/F7 1 Tf
9.9626 0 0 9.9626 297.4677 407.3952 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
(-)Tj
/F5 1 Tf
.717 0 TD
(E)Tj
6.9738 0 0 6.9738 315.6661 405.8644 Tm
(ij)Tj
/F7 1 Tf
9.9626 0 0 9.9626 320.0881 407.3952 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
/F10 1 Tf
6.9738 0 0 6.9738 327.4582 411.4771 Tm
(0)Tj
/F5 1 Tf
-.0488 -.9837 TD
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 329.8393 407.3952 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 338.6833 405.8644 Tm
(j)Tj
/F7 1 Tf
9.9626 0 0 9.9626 341.1212 407.3952 Tm
(\))Tj
/F9 1 Tf
-7.9838 .8137 TD
7.8612 Tc
()Tj
/F11 1 Tf
9.2016 -.8137 TD
0 Tc
(>)Tj
/F1 1 Tf
1.2178 0 TD
(0)Tj
/F11 1 Tf
.5008 0 TD
(:)Tj
/F7 1 Tf
12.3144 1.7811 TD
(\()Tj
/F1 1 Tf
.3244 0 TD
(3)Tj
/F7 1 Tf
.5008 0 TD
(\))Tj
/F1 1 Tf
-41.8768 -4.7573 TD
[(Through)-348.6(the)-342.6(above)-343.1(pruni)-8.6(ng)-337.3(cri)-8.8(terion,)-344.3(we)-343(can)-341.6(prune)-349(a)-338.3(large)-347.9(fraction)-349.2(of)-339.2(infeasib)-12.7(le)-341.8(conformat)-9.3(ional)-341.2(space)]TJ
-1.0015 -1.2007 TD
[(and)-254.5(thus)-251.7(greatly)-255.4(improv)-7.2(e)-247.2(the)-251.5(efcienc)-11.5(y)-245.5(o)0(f)-253.9(our)-249(branch-a)-9.7(nd-bou)-6.6(nd)-246.2(sear)-9.8(ch)-248(process.)-258.3(Our)-247.2(dead-)-9.4(end)-248.8(elim)-8.2(ination-)]TJ
T*
[(based)-247.6(branch)-237.7(p)-6.5(runing)-236.9(\(D)-7.4(EE-based)-245.8(pruning\))-240.4(differ)-9.4(s)-235.3(from)-238.2(othe)-7.6(r)-236.1(DEE)-239.2(algo)-7.6(rithms:)-242.2(the)-240.2(tradition)-10.3(al)-233.7(DEE)-244.8(or)-236.8(split-)]TJ
T*
[(DEE)-244.8(pruning)-243.4(algorithm)-244.4(\(Desm)-10.5(et)-233.7(et)-239.4(al.,)-240.1(1992;)-239.9(Geo)-8(rgiev)-238(et)-239.4(al.,)-240.2(2006;)-239.9(Gainza)-249.9(et)-233.7(al.,)-240.2(2013)-8.7(;)-236.8(Hallen)-239.5(et)-239.4(al.,)-240.2(2013\),)]TJ
T*
[(elim)-8.2(inates)-276.6(the)-274.3(infeasibl)-10.5(e)-270(rot)-7(amers,)-276.2(whe)-8(reas)-271.6(our)-277.4(DEE-base)-10.7(d)-273.9(pruning)-271.8(algo)-7.6(rithm)-276.6(prunes)-277(those)-277(conform)-8.9(ational)]TJ
T*
[(space)-10.4(s)-332(that)-340.4(do)-331.6(not)-335.1(cont)-7.6(ain)-336.9(the)-336.9(optimal)-337.6(solu)-7(tion.)]TJ
/F5 1 Tf
10.959 0 0 10.959 84.0755 294.066 Tm
[(2.2.2.)-497(Lower)-274.6(bound.)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 185.2157 294.066 Tm
[(Suppose)-275(that)-272.1(the)-274.3(rotamers)-277.2(of)-271(the)-274.3(rst)]TJ
/F5 1 Tf
15.1539 0 TD
(k)Tj
/F1 1 Tf
.717 0 TD
[(residue)-276.6(posi)-7(tions)-272.3(have)-274.1(been)-274.1(determ)-10.7(ined.)]TJ
-27.0244 -1.2007 TD
[(We)-364.4(can)-358.7(easily)-362(compute)-362.3(a)-355.4(simpl)-8.4(e)-355.4(admiss)-9.3(ible)-357.5(lower)-361.4(bound)-362.3(of)-356.3(the)-354(ener)-8.6(gy)-354.3(funct)-10.3(ion)-357.9(by)-354.3(consider)-9.9(ing)-357.9(the)-359.7(best)]TJ
T*
[(po)-7.2(ssible)-338.6(rotamer)-337.8(assi)-10(gnment)-337(in)-334.3(each)-338.5(of)-339.2(the)-331.2(u)-6.5(ndetermi)-9.3(ned)-334.1(residue)-9.2(s)-332(\()0(G)-7.4(ainza)-336.3(et)-336.1(al.,)-336.9(2013\),)-336.2(which)-342.3(is)]TJ
/F5 1 Tf
11.9046 -2.9136 TD
(D)Tj
/F7 1 Tf
.717 0 TD
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
/F7 1 Tf
.4154 0 TD
(\))Tj
/F6 1 Tf
.4894 0 TD
(+)Tj
/F9 1 Tf
1.2292 .9446 TD
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 229.7196 252.5102 Tm
(n)Tj
-1.2601 -3.1949 TD
(i)Tj
/F6 1 Tf
.4471 0 TD
(=)Tj
/F5 1 Tf
.7235 0 TD
(k)Tj
/F6 1 Tf
.6341 0 TD
(+)Tj
/F1 1 Tf
.7154 0 TD
(1)Tj
9.9626 0 0 9.9626 243.6661 241.1149 Tm
(min)Tj
/F5 1 Tf
6.9738 0 0 6.9738 249.1653 235.1054 Tm
(r)Tj
4.9813 0 0 4.9813 251.8865 234.085 Tm
(i)Tj
9.9626 0 0 9.9626 267.0802 241.1149 Tm
(E)Tj
/F10 1 Tf
6.9738 0 0 6.9738 273.4298 245.1968 Tm
(0)Tj
/F5 1 Tf
.1057 -.8048 TD
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 276.6046 241.1149 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 283.6913 239.5842 Tm
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 286.129 241.1149 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
(+)Tj
/F9 1 Tf
1.1609 .9446 TD
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 308.0125 252.5102 Tm
(n)Tj
-1.1706 -3.1786 TD
(j)Tj
/F6 1 Tf
.4471 0 TD
(=)Tj
/F5 1 Tf
.7235 0 TD
(i)Tj
/F6 1 Tf
.4471 0 TD
(+)Tj
/F1 1 Tf
.7154 0 TD
(1)Tj
9.9626 0 0 9.9626 321.2787 241.1149 Tm
(min)Tj
/F5 1 Tf
6.9738 0 0 6.9738 326.7779 235.1054 Tm
(r)Tj
4.9813 0 0 4.9813 329.4991 234.085 Tm
(j)Tj
9.9626 0 0 9.9626 338.57 241.1149 Tm
(E)Tj
6.9738 0 0 6.9738 344.6928 239.5842 Tm
(ij)Tj
/F7 1 Tf
9.9626 0 0 9.9626 349.1149 241.1149 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 356.2015 239.5842 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 358.6393 241.1149 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 367.4834 239.5842 Tm
(j)Tj
/F7 1 Tf
9.9626 0 0 9.9626 369.9211 241.1149 Tm
(\))Tj
/F9 1 Tf
-11.1079 1.7129 TD
10.6513 Tc
( !)Tj
/F1 1 Tf
12.2176 -1.7129 TD
0 Tc
()Tj
/F7 1 Tf
11.2502 0 TD
(\()Tj
/F1 1 Tf
.3244 0 TD
(4)Tj
/F7 1 Tf
.5008 0 TD
(\))Tj
/F1 1 Tf
-42.8783 -2.9705 TD
[(whe)-8(re)]TJ
/F5 1 Tf
2.777 0 TD
(D)Tj
/F7 1 Tf
.7227 0 TD
(\()Tj
/F5 1 Tf
.3187 0 TD
(r)Tj
/F7 1 Tf
.4211 0 TD
(\))Tj
/F6 1 Tf
.4894 0 TD
(=)Tj
/F9 1 Tf
.8877 .7511 TD
(P)Tj
/F5 1 Tf
6.9738 0 0 6.9738 140.485 216.2834 Tm
(k)Tj
0 -1.0893 TD
(i)Tj
/F6 1 Tf
.4552 0 TD
(=)Tj
/F1 1 Tf
.7154 0 TD
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 154.3181 211.5212 Tm
(E)Tj
6.9738 0 0 6.9738 160.4409 209.9905 Tm
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 162.8787 211.5212 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 169.9653 209.9905 Tm
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 172.4598 211.5212 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
(+)Tj
/F9 1 Tf
.8877 .7511 TD
(P)Tj
/F5 1 Tf
6.9738 0 0 6.9738 196.611 216.2834 Tm
(k)Tj
0 -1.0893 TD
(i)Tj
/F6 1 Tf
.4471 0 TD
(=)Tj
/F1 1 Tf
.7235 0 TD
(1)Tj
/F9 1 Tf
9.9626 0 0 9.9626 210.444 219.0046 Tm
(P)Tj
/F5 1 Tf
6.9738 0 0 6.9738 220.9322 216.2834 Tm
(k)Tj
0 -1.0893 TD
(j)Tj
/F6 1 Tf
.4471 0 TD
(=)Tj
/F5 1 Tf
.7154 0 TD
(i)Tj
/F6 1 Tf
.4471 0 TD
(+)Tj
/F1 1 Tf
.7235 0 TD
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 242.8724 211.5212 Tm
(E)Tj
6.9738 0 0 6.9738 248.9952 209.9905 Tm
(ij)Tj
/F7 1 Tf
9.9626 0 0 9.9626 253.4172 211.5212 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 260.5038 209.9905 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 262.9417 211.5212 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 271.7858 209.9905 Tm
(j)Tj
/F7 1 Tf
9.9626 0 0 9.9626 274.2235 211.5212 Tm
(\))Tj
/F1 1 Tf
.6487 0 TD
[(is)-324.2(the)-325.5(assigned)-333.5(energy)-328.8(term)-326.1(for)-324.9(the)-325.5(rotam)-8.2(er)-324(sequence)]TJ
/F5 1 Tf
22.0509 0 TD
(r)Tj
/F1 1 Tf
-42.7872 -1.2007 TD
[(aft)-8.8(er)-272.7(x)-6.4(ing)-272.5(the)-280(rotam)-8.2(ers)-274.7(of)-276.7(the)-280(rst)]TJ
/F5 1 Tf
14.4768 0 TD
(k)Tj
/F1 1 Tf
.7227 0 TD
[(posi)-7(tions,)-278.4(and)]TJ
/F5 1 Tf
5.8726 0 TD
(E)Tj
/F10 1 Tf
6.9738 0 0 6.9738 290.381 203.1874 Tm
(0)Tj
/F5 1 Tf
.1057 -.7317 TD
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 293.5558 199.559 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 300.6424 198.085 Tm
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 303.0802 199.559 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
(=)Tj
/F5 1 Tf
.7227 0 TD
(E)Tj
6.9738 0 0 6.9738 321.2787 198.085 Tm
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 323.7731 199.559 Tm
(\()Tj
/F5 1 Tf
.3187 0 TD
(r)Tj
6.9738 0 0 6.9738 330.8031 198.085 Tm
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 333.2975 199.559 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
(+)Tj
/F9 1 Tf
.8877 .7512 TD
(P)Tj
/F5 1 Tf
6.9738 0 0 6.9738 357.5054 204.3212 Tm
(k)Tj
0 -1.0893 TD
(j)Tj
/F6 1 Tf
.4471 0 TD
(=)Tj
/F1 1 Tf
.7154 0 TD
(1)Tj
/F5 1 Tf
9.9626 0 0 9.9626 371.2818 199.559 Tm
(E)Tj
6.9738 0 0 6.9738 377.4046 198.085 Tm
(ij)Tj
/F7 1 Tf
9.9626 0 0 9.9626 381.8267 199.559 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 388.9133 198.085 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 391.3511 199.559 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 400.1952 198.085 Tm
(j)Tj
/F7 1 Tf
9.9626 0 0 9.9626 402.6896 199.559 Tm
(\))Tj
/F1 1 Tf
.5975 0 TD
[(This)-280(lower)-276(bo)-7.2(und)-275.4(is)-272.9(not)]TJ
-33.5799 -1.2007 TD
[(tig)-7.8(ht)-334.3(enough)-336.4(thoug)-6.6(h,)-331.2(and)-339.8(we)-337.3(provide)-336.2(a)-338.3(much)-338.4(tighter)-341.7(one)-334.1(using)-337.8(linear)-340(progr)-7.8(amming)-340.5(techniques)-344.1(here.)]TJ
1.0015 -1.2007 TD
[(Obs)-7.4(erving)-267.2(the)-262.9(admissible)-270.1(lower)-264.7(boun)-8.7(d)-256.8(i)0(n)-266.1(Equation)-269.3(\(4\),)-262.7(if)-262.3(we)-263.3(split)]TJ
/F5 1 Tf
26.7114 0 TD
(E)Tj
6.9738 0 0 6.9738 356.3149 174.1606 Tm
(ij)Tj
/F1 1 Tf
9.9626 0 0 9.9626 363.3448 175.6346 Tm
[(into)-264.7(two)-265.1(terms)]TJ
/F13 1 Tf
6.0832 0 TD
(b)Tj
/F5 1 Tf
6.9738 0 0 6.9738 429.4487 173.3102 Tm
(ij)Tj
/F1 1 Tf
9.9626 0 0 9.9626 436.4786 175.6346 Tm
(and)Tj
/F13 1 Tf
1.7128 0 TD
(b)Tj
/F5 1 Tf
6.9738 0 0 6.9738 459.0424 173.3102 Tm
(ji)Tj
/F1 1 Tf
9.9626 0 0 9.9626 463.4644 175.6346 Tm
[(,)-262.2(such)-262.1(that)]TJ
/F13 1 Tf
-39.0827 -1.2007 TD
(b)Tj
/F5 1 Tf
6.9738 0 0 6.9738 79.6535 161.348 Tm
(ij)Tj
/F7 1 Tf
9.9626 0 0 9.9626 84.0755 163.6724 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 91.1055 162.1984 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 93.6 163.6724 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 102.4441 162.1984 Tm
(j)Tj
/F7 1 Tf
9.9626 0 0 9.9626 104.8819 163.6724 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
(+)Tj
/F13 1 Tf
.7227 0 TD
(b)Tj
/F5 1 Tf
6.9738 0 0 6.9738 122.4566 161.348 Tm
(ji)Tj
/F7 1 Tf
9.9626 0 0 9.9626 126.8787 163.6724 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 133.9653 162.1984 Tm
(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 136.4031 163.6724 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 145.2472 162.1984 Tm
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 147.7417 163.6724 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
(=)Tj
/F5 1 Tf
.717 0 TD
(E)Tj
6.9738 0 0 6.9738 165.8834 162.1984 Tm
(ij)Tj
/F7 1 Tf
9.9626 0 0 9.9626 170.3621 163.6724 Tm
(\()Tj
/F5 1 Tf
.3187 0 TD
(r)Tj
6.9738 0 0 6.9738 177.3921 162.1984 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 179.8866 163.6724 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 188.7307 162.1984 Tm
(j)Tj
/F7 1 Tf
9.9626 0 0 9.9626 191.1685 163.6724 Tm
(\))Tj
/F1 1 Tf
.6544 0 TD
[(for)-336.3(all)]TJ
/F5 1 Tf
2.851 0 TD
(r)Tj
6.9738 0 0 6.9738 229.9464 162.1984 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 232.3842 163.6724 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 241.2283 162.1984 Tm
(j)Tj
/F1 1 Tf
9.9626 0 0 9.9626 243.6661 163.6724 Tm
[(,)-336.1(the)-336.9(lower)-338.6(bound)-339.6(becomes)]TJ
/F9 1 Tf
-5.4629 -2.5323 TD
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 194.6267 140.4283 Tm
(n)Tj
-1.2601 -3.1949 TD
(i)Tj
/F6 1 Tf
.4471 0 TD
(=)Tj
/F5 1 Tf
.7235 0 TD
(k)Tj
/F6 1 Tf
.6341 0 TD
(+)Tj
/F1 1 Tf
.7235 0 TD
(1)Tj
9.9626 0 0 9.9626 208.5732 128.9763 Tm
[(mi)-7.8(n)]TJ
/F5 1 Tf
6.9738 0 0 6.9738 214.0724 123.0236 Tm
(r)Tj
4.9813 0 0 4.9813 216.7936 122.0031 Tm
(i)Tj
9.9626 0 0 9.9626 232.9511 128.9763 Tm
(E)Tj
/F10 1 Tf
6.9738 0 0 6.9738 239.244 133.1149 Tm
(0)Tj
/F5 1 Tf
-.1301 -.8048 TD
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 243.5527 128.9763 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 250.6393 127.5023 Tm
(i)Tj
/F7 1 Tf
9.9626 0 0 9.9626 253.0771 128.9763 Tm
(\))Tj
/F6 1 Tf
.4894 0 TD
(+)Tj
/F9 1 Tf
3.1469 .9503 TD
(X)Tj
/F5 1 Tf
6.9738 0 0 6.9738 294.7464 140.4283 Tm
(n)Tj
9.9626 0 0 9.9626 268.4409 115.4268 Tm
(j)Tj
/F6 1 Tf
.4496 0 TD
(=)Tj
/F5 1 Tf
.7227 0 TD
(k)Tj
/F6 1 Tf
.6316 0 TD
(+)Tj
/F1 1 Tf
.7227 0 TD
(1)Tj
/F8 1 Tf
6.9739 0 0 6.9739 298.6015 115.4268 Tm
(&)Tj
/F5 1 Tf
9.9626 0 0 9.9626 305.6314 115.4268 Tm
(j)Tj
/F10 1 Tf
.5634 0 TD
(6)Tj
T*
()Tj
/F5 1 Tf
1.0471 0 TD
(i)Tj
/F1 1 Tf
.6146 1.36 TD
(min)Tj
/F5 1 Tf
6.9738 0 0 6.9738 333.2975 123.0236 Tm
(r)Tj
4.9813 0 0 4.9813 336.0188 122.0031 Tm
(j)Tj
/F13 1 Tf
9.9626 0 0 9.9626 345.0897 128.9763 Tm
(b)Tj
/F5 1 Tf
6.9738 0 0 6.9738 350.5889 126.7086 Tm
(ij)Tj
/F7 1 Tf
9.9626 0 0 9.9626 355.0109 128.9763 Tm
(\()Tj
/F5 1 Tf
.3244 0 TD
(r)Tj
6.9738 0 0 6.9738 362.0975 127.5023 Tm
(i)Tj
/F1 1 Tf
9.9626 0 0 9.9626 364.5353 128.9763 Tm
()Tj
/F5 1 Tf
.5008 0 TD
(r)Tj
6.9738 0 0 6.9738 373.3794 127.5023 Tm
(j)Tj
/F7 1 Tf
9.9626 0 0 9.9626 375.8172 128.9763 Tm
(\))Tj
/F9 1 Tf
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[(3U)19.3(7Y)]TJ
/F1 1 Tf
2.7062 0 TD
[(\(R)18.9(o)13.1(n)]TJ
-20.6127 -1.2267 TD
[(et)-416.4(al)19.8(.,)-416.8(2)13.1(0)0(1)19.9(1)13.1(\)])14.7(.)-420.2(T)0(h)20.1(e)-425.6(p)13.1(r)0(o)17.3(t)0(e)19.8(i)0(n)-414(g)0(p)19.9(1)0(2)19.9(0)-423.1(is)-415.2(v)13.1(i)0(s)21.1(u)0(a)17.5(l)0(i)18.2(z)0(e)21.4(d)-423.1(as)-413.6(gr)17.3(ay)]TJ
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[(su)18.8(rf)14.7(ac)21.4(e,)-270.4(wh)16.6(il)18.2(e)-280.1(t)0(h)22.2(e)-286.5(h)13.1(e)0(a)15.1(v)13.1(y)-284(a)0(n)17.5(d)-277.7(li)18.2(gh)19.9(t)-281.7(c)0(h)17.5(a)0(i)19.8(n)13.1(s)-285.2(o)13.1(f)-286.6(t)0(h)22.2(e)-280.1(an)17.5(ti)18.2(b)13.1(o)0(d)19.9(y)]TJ
T*
[(NI)14(H4)23(5-)17.3(4)13.1(6)-410.5(ar)21.2(e)-412.9(s)0(h)18.8(o)13.1(wn)-400.7(wi)18.9(th)-395.1(ma)14(g)13.1(e)0(n)17.5(t)0(a)-397.5(l)0(i)18.2(n)13.1(es)16.3(.)-407.6(T)0(h)20.1(e)-412.9(mu)22.7(ta)19.8(bl)15.9(e)]TJ
T*
[(re)14.9(si)21.1(du)19.9(es)-242.9(o)13.1(n)-252.4(th)22.3(e)-254.8(g)13.1(p1)19.9(20)-239.3(su)18.8(rf)21.1(ac)15.1(e)-248.5(a)0(r)21.2(e)-254.8(sh)18.8(o)13.1(w)0(n)-242.6(i)0(n)-237(g)0(r)17.3(e)0(e)21.4(n)0(.)]TJ
/F2 1 Tf
9.9626 0 0 9.9626 74.0976 737.4045 Tm
(8)Tj
37.5064 0 TD
[(PAN)-340(ET)-335.3(AL.)]TJ
ET
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