Classical Simulations on Quantum Computers: Interface-Driven Peptide Folding on Simulated Membrane Surfaces

Con en s lis s a ailable a ScienceDi ec Compu e s in Biology and Medicine jou nal homepage: www.else ie .com/loca e/compbiomed Classical Simula ions on Quan um Compu e s: In e ace-D i en Pep ide Folding on Simula ed Memb ane Su aces Daniel Conde-To esa,b, Ma iamo Mussa-Juanec, Daniel Faíldec, And és Gómezc, Rebeca Ga cía-Fandiñob,∗, Ángel Piñei oa,∗∗ aDepa amen o de Física Aplicada, Facul ade de Física, Uni e sidade de San iago de Compos ela, Campus Vida, San iago de Compos ela, E-15782, A Co uña, Spain bO ganic Chemis y Depa men , Cen o Singula de In es igación en Química Biolóxica e Ma e iais Molecula es (CiQUS), Uni e sidade de San iago de Compos ela, Campus Vida, San iago de Compos ela, E-15782, A Co uña, Spain cGalicia Supe compu ing Cen e (CESGA), A enida de Vigo, s/n, San iago de Compos ela, E-15782, A Co uña, Spain ARTICLE INFO Keywo ds: An imic obial pep ides Quan um compu ing Lipid memb anes In e ace Pep ide olding ABSTRACT Backg ound: An imic obial pep ides (AMPs) a e c ucial in he igh agains in ec ions and play signi ican oles in a ious heal h con ex s, including cance , au oimmune diseases, and aging. A key aspec o AMP unc ionali y is hei selec i e in e ac ion wi h pa hogen memb anes, which o en exhibi al e ed lipid composi ions. These in e ac ions a e hough o induce a con o ma ional shi in AMPs om andom coil o alpha-helical s uc u es, essen ial o hei ly ic ac i i y. T adi ional compu a ional app oaches ha e aced challenges in accu a ely modeling hese s uc u al changes, especially in memb ane en i onmen s, he eby opening and oppo uni y o mo e ad anced app oaches. Me hod: This s udy ex ends an exis ing quan um compu ing algo i hm, ini ially designed o pep ide olding simula ions in homogeneous en i onmen s, o add ess he complexi ies o AMP in e ac ions a in e aces. Ou app oach enables he p edic ion o he op imal con o ma ion o pep ides loca ed in he ansi ion egion be ween hyd ophilic and hyd ophobic phases, esembling lipid memb anes. The new me hod was es ed on h ee 10-amino-acid-long pep ides, each cha ac e ized by dis inc hyd ophobic, hyd ophilic, o amphipa hic p ope ies, ac oss di e en media and a in e aces be ween sol en s o di e en pola i y. Resul s: The de eloped me hod success ully modeled he s uc u e o he pep ides wi hou inc easing he num- be o qubi s equi ed compa ed o simula ions in homogeneous media, making i mo e easible wi h cu en quan um compu ing esou ces. Despi e he cu en limi a ions in compu a ional powe and qubi a ailabili y, he indings demons a e he signi ican po en ial o quan um compu ing in accu a ely cha ac e izing complex biomolecula p ocesses, pa icula ly AMP olding a memb ane models. Conclusions: This esea ch highligh s he p omising applica ions o quan um compu ing in biomolecula simula ions, pa ing he way o u u e ad ancemen s in he de elopmen o no el he apeu ic agen s. We aim o o e a new pe spec i e on enhancing he accu acy and applicabili y o biomolecula simula ions in he con ex o AMP in e ac ions wi h memb ane models. 1. In oduc ion An imic obial pep ides (AMPs) a e c i ical componen s o he inna e immune sys em p esen in all li ing o ganisms [1]. These pep ides ha e been p ima ily associa ed wi h a de ensi e ole agains exoge- nous in ec ions caused by bac e ia, i uses, and ungi, and hey a e conside ed powe ul and e sa ile endogenous an ibio ics, capable o esis ing bac e ial adap a ion o millions o yea s. Howe e , ecen e- sea ch ad ances ha e poin ed o he link be ween AMPs and a b oade ∗Co esponding au ho . ∗∗ Co esponding au ho . E-mail add esses: [email p o ec ed] (R. Ga cía-Fandiño), [email p o ec ed] (Á. Piñei o). spec um o diseases, such as cance and a ious human in lamma o y and au oimmune diseases, including aging [2,3]. Al hough mo e han 3000 AMPs ha e been iden i ied so a in dis inc cells and issues o animals, insec s, plan s, and bac e ia, only a ew ha e eached he pha maceu ical ma ke [4]. Challenges o he clinical applica ion o AMPs include cy o oxic e ec s, p oduc ion cos s, and p oblems ela ed o sus ained, a ge ed, and e ec i e deli e y [5–7]. The ques o dis- co e and e ine new an imic obial pep ides (AMPs), including bo h h ps://doi.o g/10.1016/j.compbiomed.2024.109157 Recei ed 5 Ma ch 2024; Recei ed in e ised o m 14 Augus 2024; Accep ed 12 Sep embe 2024 Compu e s in Biology and Medicine 182 (2024) 109157 A ailable online 24 Sep embe 2024 0010-4825/© 2024 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ). D. Conde-To es e al. Fig. 1. Two scena ios o an imic obial pep ide (AMP) in e ac ions wi h cell memb anes. Panel A shows di e en AMP uni s in he p esence o heal hy mammalian cell memb anes ( he lipid head g oups ep esen ed by blue sphe es), whe e he pep ides main ain a andom coil con o ma ion. Panel B depic s he in e ac ion o AMPs wi h a pa hogenic o pa hological memb ane model ypical o bac e ial memb anes, some i uses, cance cells, o senescen cells. He e, he AMPs adop a helical con o ma ion upon in e ac ing wi h he memb ane. The o ange sphe es ep esen he head g oups o se e al anionic lipids commonly ound in hese al e ed memb anes, highligh ing he s uc u al adap a ions o AMPs in di e en cellula en i onmen s. na u al and enginee ed a ian s, ep esen s a dynamic and p omising ield o esea ch. The goal is o o e come hese challenges, op imizing hese pep ides o medical use and le e aging hei ull po en ial as he apeu ic agen s. Un a eling his ma e is c ucial when an ibio ic esis ance is a g owing global h ea bu also in he igh agains cance and aging, a eas whe e AMPs can s ill p o ide signi ican solu ions. Despi e a ying leng h, sequence, and con o ma ion, mos AMPs sha e c ucial s uc u al and physicochemical p ope ies: hey a e ypi- cally sho , ca ionic, and amphipa hic pep ides. This unique combina- ion o cha ac e is ics enables hem o selec i ely a ge and in e ac wi h pa hogenic o pa hological memb anes, such as hose ound in cance , bac e ia, and senescen cells. This selec i e a ge ing s ems om a common ea u e in hese memb anes: a high p opo ion o nega i ely cha ged lipids, in con as o wha happens in heal hy mammalian cells whose elec os a ic cha ge densi y is no mally negli- gible. AMPs a e known o unde go con o ma ional shi s, ansi ioning om andom s uc u es in solu ion o helical s uc u es upon encoun- e ing a memb ane, a change d i en by hei inhe en amphiphilic na u e (Fig. 1). This ans o ma ion enhances he alignmen o hei hyd ophobic dipole momen s ac oss he memb ane, acili a ing op imal in e ac ion wi h he lipid bilaye . The spa ial a angemen o he amino acid esidues in AMPs is indispensable o hei biological unc ion. Following memb ane binding, AMPs exe hei e ec h ough a i- ous mechanisms, including he ba el s a e, ca pe , and o oidal po e models, among o he con o ma ions [8,9]. A deepe unde s anding o hese ac ion mechanisms is essen ial o imp o e AMP design, mo - ing om cu en ial-and-e o me hods owa ds mo e p ecise and e ec i e s a egies. Fo example, uning he modeling is especially ele an when he e is an al e a ion in he lipid composi ion. While he e a e models desc ibing AMP in e ac ions wi h cell memb anes, comp ehensi e a omic-le el de ails a e sca ce, indica ing a need o mo e in-dep h esea ch in his a ea. The ans o ma ion o a polypep ide chain in o i s unc ional h ee- dimensional s uc u e ep esen s a cen al challenge in molecula biol- ogy, especially a in e aces such as he su ace o a cell memb ane o upon he in luence o some he e ogeneous en i onmen . Despi e hei undamen al ole in nume ous biological mechanisms, he speed and dynamics o hese olding p ocesses emain puzzling. The Le in hal pa adox illus a es his complexi y by highligh ing he seeming im- possibili y o amino acid chains in inding hei na i e, unc ional con o ma ion in a biologically ele an imescale i hey we e o explo e all possible con o ma ions [10]. To add ess his challenge, a a ie y o compu a ional and expe imen al app oaches ha e been employed. AlphaFold ini ia i e [11] is a signi ican ad ance capable o p edic ing he h ee-dimensional s uc u e o p o eins wi h unp eceden ed accu- acy. Ne e heless, his imp essi e echnology is s ill unable o eliably p edic ing he in e ac ion be ween he 3D s uc u e o sho pep ides and he memb ane models ha accoun o speci ic lipid composi ions. In pa allel, molecula dynamics (MD) simula ions ha e eme ged as a powe ul ool o in es iga ing pep ide and p o ein olding dynamics o a leas s uc u al s abili y unde di e en condi ions [12,13]. S anda d MD simula ions explo e he ene gy landscape o he polypep ide chain, p o iding insigh s in o he olding o s uc u al e olu ion pa hway. Howe e , limi a ions in compu a ional powe o en es ic he simu- la ion imescales, hinde ing he obse a ion o comple e olding e en s o ansi ions be ween di e en s a es sepa a ed by signi ican ene gy ba ie s, e en o ela i ely sho sequences. Biased MD echniques o e come hese limi a ions by nudging he simula ion o sample di e se s a es [14,15]. These me hods can signi ican ly accele a e he olding p ocess, allowing o s udy i wi h g ea e de ail, including he p esence o speci ic he e ogeneous en i onmen s. Despi e hese ad ancemen s, p edic ing pep ide and p o ein olding emains a complex ask, pa - icula ly in he p esence o memb ane models due o hei in ica e in e ac ions be ween he mac omolecule and he lipid bilaye . This coupling unde lines a c i ical need o enhanced me hodologies ha Compu e s in Biology and Medicine 182 (2024) 109157 2 D. Conde-To es e al. Fig. 2. Te ahed al la ice in which a ep esen a i e pep ide will mo e, wi h subla ices A ( ed) and B (g een) indica ed. can accu a ely p edic pep ide s uc u es as a unc ion o hei speci ic en i onmen , which would allow signi ican ad ances in he cha ac e - iza ion o known s uc u es and u he he de elopmen o new AMP candida es. Thus, s udying p o ein and pep ide olding is an in insically e y complex p oblem whose p ac ical solu ion is beyond he each o clas- sical algo i hms [11,16]. In his scena io, quan um compu e s eme ge as a p omising ool despi e he noisy in e media e scale quan um (NISQ) e a. Recen wo k has a emp ed o sol e his p oblem o ela i ely sho amino acid sequences wi hin homogeneous media [17– 19]. These s udies adop se e al simpli ying app oaches ha neglec speci ic chemical de ails, such as mapping amino acids on o single sphe es and modeling hei in e ac ion ene gy using a simpli ied pai - wise po en ial. Addi ionally, o a ions o hese sphe es a e limi ed o disc e e angles ela i e o hei nea es neighbo s, u he educing compu a ional complexi y. Mo eo e , unde es ima ing explici in e ac- ions wi h sol en molecules is ano he e en ual sou ce o imp ecision. While hese simpli ica ions signi ican ly imp o e compu a ional e i- ciency and educe he equi ed numbe o qubi s (𝑁𝑞), hey come a he cos o educed accu acy. Ne e heless, hese app oaches o e a aluable ool o gaining ini ial insigh s in o pep ide s uc u e, p ecisely in he quan um compu ing con ex , whe e compu a ional esou ces a e limi ed. While hese me hods emains e ineable, he e is oom o make hem mo e e sa ile. In pa icula , ou ocus on AMPs and hei in e ac ion wi h memb ane models necessi a es ex ending hese app oaches o inco po a e a smoo h in e ace be ween wo media o di e ing pola i ies, ying o mimic he in e ace be ween a lipid bilaye and he aqueous phase in con ac wi h i . In his scena io, he olding p ocess becomes signi ican ly mo e complex, as he inhomogeneous and aniso opic en i onmen subs an ially in luences he s uc u e and unc ion o AMPs. This a emp highligh s he c i ical demand o in en- si ied e o s in de eloping quan um compu ing echniques, po en ially leading o b eak h oughs in s udying and designing no el AMPs. Ou wo k ex ends a quan um-compu ing ou ine o pep ide olding in homogeneous media o p edic he op imal s uc u e o amino acid sequences a he ansi ion egion be ween hyd ophilic and hyd opho- bic en i onmen s, used as memb ane models. The o iginal p oposal o Robe e al. [18] demons a ed he e ec i e use o quan um algo i hms in op imizing he con o ma ion o small pep ides, employing a Hamil- onian () model o olding polyme chains on a la ice. This app oach b idged he gap be ween simpli ied models and mo e de ailed pep ide ep esen a ions. Th ee amino acid sequences, chosen o hei dis inc cha ac e - is ics: pola , non-pola , and ha ing a high ans e sal hyd ophobic dipola momen when o ming an alpha helix, we e employed o es he new me hod in a ious homogeneous and non-homogeneous en- i onmen s. Ou p oposal in oduces a aluable new dimension o exis ing compu a ional models wi hou adding subs an ial compu a- ional esou ce demands o unnecessa y complexi y. This ep esen s a signi ican s ep owa ds e ining mo e sophis ica ed and p ecise pep ide modeling echniques, enhances ou unde s anding o p o ein chemis y in complex en i onmen s and lays he ounda ion o u u e ad ance- men s in he ield. We ha e con idence ha his wo k will inspi e u he esea ch, ul ima ely leading o he c ea ion o obus pep ide s uc u es ha e ec i ely conside di e en en i onmen al condi ions. This expansion o scien i ic knowledge holds p omise o he apeu ic applica ions, ha nessing he unique capabili ies o quan um compu ing o explo e he in ica e de ails o p o ein s uc u es. 2. Ma e ials and me hods 2.1. In e ace implemen a ion 2.1.1. Backg ound The p edic ion o pep ide s uc u e in homogeneous media wi hin he p o ein_ olding module o he qiski _ esea ch [20] lib a y u ilizes a quan um compu a ional app oach [18] ha employs a model Hamil onian and a a ia ional quan um algo i hm o old a polyme chain on a e ahed al la ice. The Hamil onian is based on he pai wise Miyazawa–Je nigan (MJ) po en ial [21,22], whe e each amino acid is ep esen ed by a single sphe e. The MJ coa se-g ained ep esen a ion igno es chemical de ails bu i is expec ed o desc ibe easonably well he in amolecula in e ac ions be ween he amino acid esidues. The la ice model simpli ies he ep esen a ion o he pep ide o make i compu a ionally easible o quan um simula ions. Speci ically, wo se s o non-equi alen la ice poin s (Aand B) a e de ined as subla ices. A si es A, he polyme can only g ow in he di ec ions 𝑡𝑖∈ {0,1,2,3} while a si e B, he possible di ec ions a e 𝑡𝑖∈ { 0, 1, 2, 3} (Fig. 2). Th oughou he sequence, he Aand Bsi es al e na e, allowing us o adop he con en ion ha Aand Bsi es co espond o e en and odd alues o i, espec i ely. Wi hou loss o gene ali y, he i s wo u ns can be se o 𝑡1= 1and 𝑡2= 0 due o symme ic degene acy. The u ns a e encoded by assigning a combina ion o wo qubi s pe axis. Each pai o qubi s can be in one o ou possible s a es: 00, 01, 10 and 11, hus allowing o a p ecise and e icien encoding o u ns. The e o e, a bi s ing ep esen s he h ee-dimensional s uc u e o he pep ide, which codi ies he sequen ial u ns o he coa se-g ain beads. A ela i ely low numbe o con o ma ion and in e ac ion qubi s is equi ed unde his app oach, including penal y e ms o p e en Compu e s in Biology and Medicine 182 (2024) 109157 3 D. Conde-To es e al. Fig. 3. Schema ic ep esen a ion o how he VQE algo i hm wo ks. Fig. 4. Compa ison be ween he sign unc ion (black line) and i s 7 h-deg ee polynomial app oxima ion (blue line). The e ical g een line indica es he loca ion o a i ual plane sepa a ing bo h sol en s and he dashed ed lines indica e he dis ances beyond which he di e ence be ween he sign unc ion and i s polynomial app oxima ion di e ges. meaningless con o ma ions o he pep ide, such as esidue o e laps and chi al iola ions. The numbe o qubi s equi ed o his model scales quad a ically wi h he numbe o amino acid esidues in he pep ide sequence (𝑁)while he numbe o e ms in he Hamil onian scales in 𝑂(𝑁4). Adding sidechains and inco po a ing s a e-o - he-a classical o ce ields based on Lenna d-Jones and Coulomb in e ac ions is also possible by keeping he s uc u e o he employed Hamil onian, albei his would equi e a highe numbe o pa icles and so a highe numbe o qubi s. Since he p o ein_ olding module akes ad an age o a Va i- a ional Quan um Eigensol e (VQE) [23] (Fig. 3), he Hamil onian is minimized o each i e a ion o he pa ame ized quan um ci cui . This means ha he Hamil onian should be sel -consis en o be execu ed in he quan um p ocesso uni wi hou depending on he s a e o he qubi s. 2.1.2. Amino acids loca ion conce ning he in e ace The posi ional displacemen o each bead along a speci ic e ahe- d al axis 𝑎is quan i ied as: 𝛥𝑛𝑎(𝑗) = 𝑗−1 ∑ 𝑘=1 (−1)𝑘𝑓𝑎(𝑘) + 𝛥𝑎(1) whe e he sum is pe o med om he i s o he cu en bead (𝑗), 𝛥𝑎 ep esen s he dis ance along axis 𝑎 om he i s bead o he pep ide (which is always ixed in ou app oach) o he phase-sepa a ing plane. The unc ion 𝑓𝑎(𝑘) e u ns 1i he e is a displacemen along axis 𝑎 o he u n o amino acid 𝑘, and 0o he wise. The e m (−1)𝑘indica es he di ec ionali y o he u n ela i e o subla ices Ao B, e ec i ely show- ing whe he he mo emen b ings he bead close o o u he om he phase-sepa a ing plane. 𝛥𝑛𝑎(𝑗)inhe en ly de e mines he phase loca ion o amino acid 𝑗, as well as he dis ance o he phase-sepa a ing plane. I is impo an o no e ha he con ibu ion o he in e ac ion be ween he amino acids and i s co esponding phase canno be p opo ional o 𝛥𝑛𝑎(𝑗)since, in ha case, such in e ac ion would linea ly inc ease he a ini y o epulsion (depending on he sign o he in e ac ion) o each amino acid o each phase as a unc ion o he dis ance o i . On he o he hand, ex ac ing di ec ly he sign o his unc ion is no a i ial ask wi hou eading he s a e o he qubi s. While auxilia y qubi s could acili a e his, hey would also inc ease he compu a ional demands, which is incon enien . Addi ionally, di ec ly using a s ep unc ion o iden i y he loca ion o he bead a each medium would be an unsui - able app oach since ac ual in e aces, such as ha be ween an aqueous media and a lipid memb ane, a e smoo h. The oughness o such in e aces is compa able o he diame e o a wa e molecule (3–6 Å), as Compu e s in Biology and Medicine 182 (2024) 109157 4 D. Conde-To es e al. es ima ed om neu on e lec ome y analysis [24], so a g adual an- si ion be ween bo h phases is o eseeable. To add ess all hese issues, we decided o use a polynomial app oxima ion o he sign unc ion (see Fig. 4) as a scaling ac o o he Hamil onian con ibu ion o he in e ac ion be ween each amino acid and he co esponding medium: 𝑓(𝑥)=0.48175𝑥− 0.0182𝑥3+ (2.95 ⋅10−4)𝑥5− (1.56 ⋅10−6)𝑥7(2) This app oach p o ides a smoo h ansi ion be ween he wo phases, wi h an in e ace hickness o app oxima ely 5 a bi a y uni s, co e- sponding o he dis ance be ween wo beads in he pep ide’s la ice. F om his egion and a dis ances lowe han 9 uni s, he polynomial unc ion exhibi s ela i ely small oscilla ions. A longe dis ances his polynomial di e ges om he sign unc ion. Since he s udied pep ides a e qui e sho (maximum 10 amino acids) and unlikely o ex end u - he om he in e ace cen e , his app oxima ion conside ably ailo s ou pu poses. 2.1.3. Tuning he in e ac ion be ween amino acids as a unc ion o he media The app oach al eady implemen ed in he qiski _ esea ch lib a y is well-designed o modeling pep ide olding in homogeneous media. De ails o he implemen a ion a e well documen ed in p e- ious publica ions [18] as well as in he o icial eposi o y o he p o ein_ olding module [20]. Howe e , i s applicabili y o unc- ional an imic obial pep ides is limi ed, as hese pep ides exe hei biological unc ion by in e ac ing wi h he su ace o pa hological mem- b anes, which could be oughly modeled as a hyd ophilic/hyd ophobic in e ace. Thus, se e al modi ica ions we e in oduced in o he o igi- nal model. Fi s , he Miyazawa–Je nigan (MJ) pa ame e s we e mod- i ied ollowing he wo k o Leonha d e al. [25,26] o accoun o in e ac ions be ween esidue beads in di e en phases: 𝑒𝐿𝑒𝑜𝑛ℎ𝑎𝑟𝑑 𝑖,𝑗 =𝑒𝑀𝐽 𝑖,𝑗 −𝑒𝑖,𝑝ℎ𝑎𝑠𝑒 −𝑒𝑗,𝑝ℎ𝑎𝑠𝑒 (3) whe e 𝑒𝑀𝐽 𝑖,𝑗 is he o iginal alue o he MJ in e ac ion e ms be ween amino acids 𝑖and 𝑗and 𝑒𝑘,𝑝ℎ𝑎𝑠𝑒 (wi h 𝑘=𝑖o 𝑗) ep esen s he in e ac ion o amino acid 𝑘wi h he phase i esides in. The alue o 𝑒𝑘,𝑝ℎ𝑎𝑠𝑒 o a homogeneous phase is calcula ed using he ollowing equa ion: 𝑒𝑘,𝑝ℎ𝑎𝑠𝑒 =1 2(1 − 𝐶𝑠)𝑒𝑀𝐽 𝑘𝑘 +𝜔 +𝐶𝑠 2𝑛 20 ∑ 𝑖=1 𝑒𝑀𝐽 𝑖𝑖 =1 2(1 − 𝐶𝑠)𝑒𝑀𝐽 𝑘𝑘 +𝜔′ (4) whe e 𝑖i e a es o e he o al numbe o amino acid ypes, and 𝐶𝑠 de e mines he con as be ween phases. A posi i e 𝐶𝑠 a o s con ac be ween sol en and hyd ophilic esidues, while a nega i e 𝐶𝑠 a o s con ac be ween sol en and hyd ophobic esidues. 𝜔 de e mines he a e age in e ac ion be ween amino acids and he sol en . Nega i e 𝜔 indica es a ac ion, while posi i e 𝜔 indica es epulsion. A he ansi ion egion be ween wo phases o di e en pola i y 𝑒𝑘,𝑝ℎ𝑎𝑠𝑒 will be eplaced by 𝑒𝑘,𝑝ℎ𝑎𝑠𝑒′: 𝑒𝑘,𝑝ℎ𝑎𝑠𝑒′=1 2[(1 −  𝑆)⋅𝑒𝑘,𝑝ℎ𝑎𝑠𝑒1+ (1 +  𝑆)⋅𝑒𝑘,𝑝ℎ𝑎𝑠𝑒2](5) whe e  𝑆can ake alues be ween 1and −1, depending on whe he he amino acid is in he pola o nonpola phase. In ou case,  𝑆will be eplaced by he unc ion p o ided by Eq. (2). Depending on he alue o  𝑆,𝑒𝑘,𝑝ℎ𝑎𝑠𝑒′can be close o he alue o 𝑒𝑘,𝑝ℎ𝑎𝑠𝑒1o 𝑒𝑘,𝑝ℎ𝑎𝑠𝑒2. This e m can be swi ched o in he Hamil onian, in case he s udy is pe o med in an homogeneous media and so he o iginal MJ po en ial is employed, as i is a boolean pa ame e . Table 1 Fauche e and Pliska [27] hyd ophobici y scale. Amino acid 𝛾Residue ype ASP −0.77 Cha ged (−) GLU −0.64 Cha ged (−) LYS −0.99 Cha ged (+) ARG −1.01 Cha ged (+) HIS 0.13 Cha ged (+) GLY 0.00 Nonpola ALA 0.31 Nonpola VAL 1.22 Nonpola LEU 1.70 Nonpola ILE 1.80 Nonpola PRO 0.72 Nonpola MET 1.23 Nonpola PHE 1.79 A oma ic TRP 2.25 A oma ic TYR 0.96 A oma ic THR −0.04 Pola SER 0.26 Pola CYS 1.54 Pola ASN −0.60 Pola GLN −0.22 Pola 2.1.4. In e acial con ibu ion o he Hamil onian The p e ious modi ica ions o he MJ po en ial accoun o he di e en occu ing in e ac ions be ween amino acids based on hei loca ion wi hin he aqueous o memb ane phases. Besides in e ac ing wi h each o he , amino acids also di ec ly in e ac wi h he sol en in bo h media. Thus, a new con ibu ion, 𝑠𝑜𝑙(𝑞𝑐𝑓 ), has been added o he o al Hamil onian: (𝑞) = 𝑔𝑐 (𝑞𝑐𝑓 ) + 𝑐ℎ(𝑞𝑐𝑓 ) + 𝑖𝑛(𝑞) + 𝑠𝑜𝑙(𝑞𝑐𝑓 )(6) whe e 𝑞=𝑞𝑐𝑓 , 𝑞𝑖𝑛 ep esen s he comple e se o qubi s used in he model, including bo h he con o ma ion qubi s (𝑞𝑐𝑓 ) and he in e ac ion qubi s (𝑞𝑖𝑛). The i s h ee- e ms desc ip ion is a ailable in [17,18]. B ie ly: •𝑔𝑐 (𝑞𝑐𝑓 )accoun s o he geome ical cons ain s imposed by he e ahed al la ice s uc u e o he amino acids. •𝑐ℎ(𝑞𝑐𝑓 )en o ces he co ec s e eochemis y o he sidechains (when p esen ), ensu ing he accu acy o he amino-acid-chi ali y ep esen a ion. •𝑖𝑛(𝑞)accoun s o he in e ac ions be ween neighbo ing beads using he Miyazawa–Je nigan (MJ) po en ial. The new e m 𝑠𝑜𝑙(𝑞𝑐𝑓 )accoun s o he in e ac ion be ween he amino acids and each sol en . This e m has been de ined he e as: 𝑠𝑜𝑙(𝑞𝑐𝑓 ) = ∑ 𝑖 𝛥𝑃 ⋅𝛾𝑖⋅ 𝑆(7) 𝛥𝑃 ep esen s he pola i y di e ence be ween he wo media and 𝛾𝑖 ep esen s a quan i a i e measu emen o he hyd ophobici y, o a ini y o each esidue o a hyd ophobic media. In he p esen wo k, he pa ame e s used we e p oposed by Fauche e and Pliska [27] (see Table 1), al hough he e a e di e en p oposals o his pa ame e in he li e a u e, ob ained om a a ie y o me hods [28–31]. No e ha cha ged esidues, wi h he s onges a ac ion o pola sol en s, ha e he lowes (mos nega i e) 𝛾 alues; pola esidues exhibi mode a e alues depending on hei speci ic side chains, ang- ing om sligh ly nega i e o sligh ly posi i e; nonpola esidues ha e consis en ly posi i e alues; while a oma ic esidues, wi h hei la ge hyd ophobic ings, possess he highes posi i e alues o 𝛾. The i- nal exp ession o 𝑠𝑜𝑙(𝑞𝑐𝑓 )p o ides a nega i e con ibu ion o he Hamil onian, a o s he in e ac ion o amino acids wi h 𝛾 < 1(mainly nonpola and a oma ic) a he posi i e side o he in e ace (phase I) and o amino acids wi h 𝛾 > 1(mainly cha ged) a he nega i e side o he in e ace (phase II) i 𝛥𝑃 > 1. The highe he alue o 𝛥𝑃 he s onge his con ibu ion. Compu e s in Biology and Medicine 182 (2024) 109157 5 D. Conde-To es e al. Fig. 5. Wheel ep esen a ion o P1,P2, and P3 wi h sequences WLWLWLWWLW, DRDRDRDRDR and WRDWGSGWDR, espec i ely. W, L, R, D, G and S deno e T yp ophan, Leucine, A ginine, Glu amic Acid, Glycine and Se ine, espec i ely. P1 and P2 a e expec ed o exhibi a high a ini y o a nonpola and o a pola media, espec i ely, while P3 is expec ed o acqui e a helical con o ma ion a he in e ace be ween wo media o di e en pola i y, wi h a high ans e sal componen o he hyd ophobic dipola momen . Posi i ely cha ged amino acids (A ginine) a e in blue, nega i ely cha ged amino acids (Glu amic Acid) a e in ed, pola amino acids (Se ine) a e in o ange, and neu al-nonpola (Glycine and Leucine) and a oma ic (T yp ophan) amino acids a e in g ay. Bo h he pai wise MJ po en ial and he hyd ophobici y 𝛾ha e a bi a y uni s and bo h a e o he same o de , so hey compe e wi h each o he o modula e he op imal s uc u e o he pep ide a he in- e ace. Impo an ly, his Hamil onian implemen a ion does no equi e addi ional qubi s, and he numbe o ex a ope a ions is modes . In pa icula , he calcula ion o a sequence o 10 amino acids he numbe o equi ed qubi s is 𝑁𝑞= 22. Hence, including he ex a dimension o he in e ace, he inal compu a ional cos is no ema kably highe compa ed o he o iginal model o homogeneous media. All he desc ibed modi ica ions o he model we e implemen ed in he p o ein_ olding module o he qiski _ esea ch lib a y. The whole code is w i en in Py hon [32], making special use o he Qiski [33], Numpy [34], Ma plo lib [35] and Maya i [36] lib a ies and i is publicly a ailable a h ps://gi hub.com/TeamMduse. 2.2. S udied sys ems and pa ame e s We ha e employed h ee amino acid sequences deno ed P1,P2, and P3 o alida e ou app oach. These sequences we e chosen o exhibi dis inc a ini ies o media o di e en pola i y, based on he 𝛾 alues p esen ed in Table 1. 1. P1 (WLWLWLWWLW) comp ises exclusi ely hyd ophobic amino acids (Leucine and T yp ophan), maximizing i s a ini y o non- pola en i onmen s (See Fig. 5). 2. P2 (DRDRDRDRDR) consis s solely o cha ged amino acids (Glu- amic Acid and A ginine), p omo ing i s in e ac ion wi h pola media (See Fig. 5). 3. P3 (WRDWGSGWDR) ep esen s a mo e in ica e sequence, con- aining cha ged amino acids o opposing cha ges (Glu amic Acid and A ginine), highly pola and neu al esidues (Se ine), highly pola (T yp ophan) and neu al-nonpola (Glycine) amino acids, dis ibu ed such ha gene a es a signi ican ans e sal compo- nen o he hyd ophobic dipole momen when adop ing a helical con o ma ion (See Fig. 5). This selec ion o sequences allows o a comp ehensi e e alua ion o he abili y o ou app oach o accu a ely cap u e and p edic he beha io o pep ides wi h a ange o physicochemical p ope ies in en i onmen s o di e ing pola i y. By analyzing hei pa i ioning be- ween phases o opposi e pola i y unde he in luence o ou model, we can assess i s e icacy in e lec ing he unde lying p inciples o amino acid–sol en in e ac ions. I is wo h eminding ha he model ou pu is a bi s ing wi h he sequen ial u ns o he amino acids ela i e o hei p e ious closes neighbo s. Subs an ially, he i s wo beads, ep esen ing he i s wo amino acids, ha e ixed posi ions. The loca ion o hese beads de ines hei dis ance and o ien a ion conce ning he plane sepa a ing he wo phases. Upon hese es ain s and hose p o ided by he model (chem- ical consis ency and e ahed al la ice), he u ns o he emaining beads es ablish he s uc u e o he pep ide. Axis 1 o he e ahed al la ice (see Fig. 2) was chosen o de ine he pola i y g adien . The i s bead o he pep ides, ep esen ing he i s amino acid, was placed a di e en posi ions along he same axis (−1,−0.5, 0, 0.5, and 1). This se o con igu a ions led o a ious dis ances be ween such a bead and he phase-sepa a ing plane owa ds bo h sol en s. In all cases, he second bead was aligned along he same axis in he di ec ion o he mo e pola sol en . Addi ionally, di e en alues o 𝛥𝑃 (0.1, 1 and 10) we e essayed in o de o balance he compe i ion be ween he weigh o he in e ac ion be ween amino acids and he weigh o hei in e ac ion wi h he sol en . Finally, he weigh s o he exis ing penal y e ms in he o iginal app oach we e inc eased om 10 o 1000. This was done o p e en hem om being o e shadowed by he new con ibu ion o he Hamil onian. The esul s ob ained om his combina ion o pa ame e s o he h ee s udied sequences a e p esen ed in he nex sec ion. 3. Resul s and discussion The op imal con o ma ions o he pep ide sequences desc ibed in he me hods sec ion we e ob ained h oughou he minimiza ion o he Hamil onian, using he VQE algo i hm, unde di e en condi ions: in pola and nonpola homogeneous phases as well as a pola /nonpola in e aces. The loca ion and o ien a ion o he i s wo amino acids o each sequence conce ning he phase-sepa a ing plane (when wo di e en media a e conside ed) we e es ained. 3.1. Homogeneous media The con o ma ion o each pep ide is highly sensi i e o he pola i y o he en i onmen in homogeneous media (Fig. 6). The pep ide con- sis ing jus o hyd ophobic amino acids (P1) and ha o med jus by cha ged amino acids (P2) exhibi an opposi e beha io , as expec ed. P1 is olded in pola en i onmen s and ully ex ended in nonpola media, while P2 is ully ex ended in pola en i onmen s and olded in nonpola media. We obse e ha he beha io o P3 is simila o ha o P1. The h ee pep ides acqui e di e en olded con o ma ions when using he o iginal MJ po en ial. The ex ended con o ma ions o P1 and P2 in nonpola and pola media, espec i ely, a e due o highly a o able in e ac ions be ween he amino acids consis ing o hose pep ides and he model sol en in hose scena ios. In hese cases he in e ac ion wi h he media la gely domina es he Hamil onian while he in amolecula in e ac ions a e less impo an . Con e sely, he olded con o ma ions o he same pep- ides in he opposi e media (P1 in pola sol en and P2 in nonpola sol en ) a ise om he a o able in e ac ions be ween he amino acids consis ing o hose pep ides combined wi h un a o able in e ac ions wi h he media. No clea seconda y s uc u e pa e ns a e obse ed in any o he olded con o ma ions. 3.2. Pola /nonpola in e aces Acco ding o he p esen ed calcula ions wi hin wo media, pep ide con o ma ion elies hea ily on se e al compe ing ene gy ac o s. These ac o s p ima ily include he in e ac ions among he amino acids, as well as hei in e ac ions wi h he wo model sol en s used in he s udy. Fo ins ance, i is possible o iden i y scena ios whe e wo di e en amino acids ha e a s ong mu ual a ac ion bu an e en s onge a ini y o opposi e phases. This disbalance can de ini ely in luence he pep ide con o ma ion, po en ially esul ing in he spa ial sepa a ion o hese amino acids despi e hei in insic a ac ion. The eme gence o dispa a e pep ide con igu a ions in he e ogeneous en i onmen s high- ligh s he complex in e play be ween in a-pep ide and pep ide-sol en in e ac ions and he ele ance o implemen ing an in e ace model. Compu e s in Biology and Medicine 182 (2024) 109157 6 D. Conde-To es e al. Fig. 6. Con o ma ions o pep ides P1,P2, and P3 in homogeneous media o di e en pola i y and also igno ing he pola i y o he media (i.e. using he o iginal MJ po en ial). Di e en colo s a e employed o each esidue: W in b own, L in g een, R in blue, D in ed, G in cyan, and S in yellow. The esul s obse ed o sequences P1,P2, and P3 clea ly show ha hyd ophobic esidues a e mo e s able in he nonpola en i onmen , e en i he pep ide sequence needs a u n o eo ien a e he co e- sponding coa se-g ained beads. No e ha he loca ion o he i s wo amino acids is ixed in ou app oach, so he pep ide canno a el as a whole om one media o he o he , and he o ien a ion o he i s wo amino acids conce ning he phase-sepa a ing plane is no op imized by minimizing he Hamil onian. The beha io o cha ged esidues (D and R) is opposi e o ha o hyd ophobic esidues (W and L). Thus, he con o ma ion o pep ides P1 and P2 a he in e acial model could be easily p edic ed (Fig. 7). Besides, P3 was designed o ideally old in o a helical s uc u e in his he e ogeneous en i onmen . This pep ide does no exhibi a clea end o s ay in one o o he phase, bu he amino acids a e dis ibu ed be ween he wo media, as expec ed. The ob ained con o ma ion is no an ideal helix. Mo eo e , some amino acids a e loca ed in he w ong phase, p obably due o he limi a ions o he employed e ahed al model. While he possibili y o con e gence o local minima in he VQE algo i hm canno be comple ely uled ou , we ook ho ough measu es o mi iga e his issue. The calcula ions we e epea ed mul iple imes o he mos con o e sial cases, employing a conse a i ely high numbe o i e a ions and a ying he seeds, ye hese adjus men s did no al e he inal s uc u e ob ained. Addi ional calcula ions using di e en ini ial coo dina es o he wo i s amino acids o he employed sequences p o ided di e en con o ma ions o he pep ides (as expec ed) bu hey ollowed he same quali a i e beha io as he esul s shown in Fig. 7. 4. Conclusions This s udy aims o con ibu e signi ican ly o he ield o pep ide olding simula ions using quan um compu ing by in oducing a new dimension o a p eexis ing model [18]. Ou esea ch ocuses on he olding o pep ides in di e en en i onmen s, pa icula ly a he in- e ace be ween hyd ophobic and hyd ophilic phases, which is c i ical o unde s anding he unc ion o an imic obial pep ides (AMPs) in biological sys ems. Based on a modi ied e sion o he Miyazawa– Je nigan po en ial, ou app oach employs a e ahed al la ice model o ep esen pep ide s uc u es, combined wi h he in oduc ion o a Hamil onian con ibu ion accoun ing o he in e ac ion be ween he amino acids and he sol en in each phase. The ansi ion egion om one o ano he media is modeled as an smoo h unc ion, ying o mimic he ac ual in e ace a he icini y o a cell memb ane. Fu he mo e, ou implemen a ion is compu a ionally e icien and does no equi e addi ional qubi s compa ed o he o iginal model ha only conside s an homogeneous phase. Ou indings demons a e ha pep ides exhibi dis inc olding pa e ns in esponse o he pola i y o hei su ounding en i onmen . Resul s poin ou he po en ial o quan um compu ing o simula e complex biological p ocesses, which classical compu ing app oaches s uggle o accomplish due o compu a ional limi a ions. While in eg a ing a pola /nonpola in e ace in pep ide olding ep esen s a signi ican achie emen , he ex ended model leans on app oxima ions o iginally p oposed o calcula ions in homogeneous media. In pa icula , he conside a ion o a e ahed al la ice ha es ains he u ns o he amino acids combined wi h he minimalis MJ pai wise po en ial in e ac ion seems o be inaccu a e in success ully p edic ing pep ide seconda y s uc u e. The limi ed numbe o a ailable qubi s cu en ly makes i un easible o add mo e deg ees o eedom and a mo e eliable po en ial o amino acid in e ac ion. Al hough ou s udy was limi ed o pep ides wi h 10 amino acids, longe sequences can be s udied ollowing he same me hodology. Howe e , such calcula ions would equi e a la ge numbe o qubi s, inc easing he compu a ional cos and po en ially educing accu acy due o he app oxima ions inhe en in he model. Fu u e wo k migh explo e his ex ension as quan um compu ing esou ces and echniques e ol e, bu he cu en wo k in oduces a iable app oach, showing ha pep ide olding a pola -nonpola in e aces can be simula ed wi h a easonable use o compu a ional esou ces. The speci ic aim o his s udy is o in oduce, o he i s ime, an e icien me hod o le e age quan um compu ing o p edic ing easonable pep ide s uc u es a he in e ace be ween media o di e - en pola i y. This s a ing poin opens new a enues o unde s anding pep ide in e ac ions a he molecula le el, which could lead o sig- ni ican ad ances in de eloping new he apeu ic agen s, pa icula ly in he ealm o an imic obial pep ides. Fu u e esea ch should aim o e ine he quan um compu a ional app oach o enhance i s accu acy and applicabili y o a b oade ange o biomolecules. Fu he mo e, in eg a ing mo e de ailed chemical p ope ies and in e ac ions in o he model could yield e en mo e nuanced insigh s in o pep ide olding dynamics. The gene al goal is o de elop a quan um compu a ional amewo k capable o simula ing a ious biological p ocesses. Ad anc- ing ou unde s anding and capabili ies in molecula biology unde sco e he c i ical impo ance o ongoing esea ch and de elopmen in he ield o quan um compu ing, pa icula ly in i s applica ion o complex biological sys ems. Compu e s in Biology and Medicine 182 (2024) 109157 7 D. Conde-To es e al. Fig. 7. Con o ma ions o pep ides P1,P2, and P3 a he in e ace be ween wo media o di e en pola i y. Fo each pep ide a side iew (le ), a iew om he nonpola phase (middle) and ano he iew om he pola phase ( igh ), a e shown. In he side iew he in e ace is shown as an ho izon al line. Di e en colo s a e employed o each esidue: W in b own, L in g een, R in blue, D in ed, G in cyan, and S in yellow. CRediT au ho ship con ibu ion s a emen Daniel Conde-To es: W i ing – e iew & edi ing, W i ing – o igi- nal d a , Visualiza ion, Valida ion, So wa e, Me hodology, In es iga- ion, Fo mal analysis, Da a cu a ion. Ma iamo Mussa-Juane: W i ing – e iew & edi ing, Supe ision, Me hodology, In es iga ion, Concep- ualiza ion. Daniel Faílde: W i ing – e iew & edi ing, Supe ision, Me hodology, In es iga ion, Concep ualiza ion. And és Gómez: W i - ing – e iew & edi ing, Supe ision, P ojec adminis a ion, Funding acquisi ion, Concep ualiza ion. Rebeca Ga cía-Fandiño: W i ing – e- iew & edi ing, W i ing – o iginal d a , Supe ision, Resou ces, P ojec adminis a ion, Me hodology, In es iga ion, Funding acquisi ion, Con- cep ualiza ion. Ángel Piñei o: W i ing – e iew & edi ing, W i ing – o iginal d a , Supe ision, So wa e, Resou ces, P ojec adminis a ion, Me hodology, In es iga ion, Funding acquisi ion, Concep ualiza ion. Decla a ion o compe ing in e es The au ho s decla e ha hey ha e no known compe ing inan- cial in e es s o pe sonal ela ionships ha could ha e appea ed o in luence he wo k epo ed in his pape . Decla a ion o Gene a i e AI and AI-assis ed echnologies in he w i ing p ocess Du ing he p epa a ion o his wo k he au ho s used cha GPT4o om OpenAI and Claude 3.5 Sonne om An h opic in o de o imp o e language and eadabili y. A e using hese ools, he au ho s e iewed and edi ed he con en as needed and ake ull esponsibili y o he con en o he publica ion. Acknowledgmen s D.C.T hanks o he Minis e io de Uni e sidades o his p edoc o al con ac (FPU22/00636). This wo k was suppo ed by he In e eg Sudoe and he ERDF (S1/1.1/P0033), by he Spanish Agencia Es a al de In es igación (AEI) and he ERDF (PID2022-141534OB-I00, PDC2022- 133402-I00, CNS2023-144353 and PID2019111327GBI00), by MICINN h ough he Eu opean Union Nex Gene a ionEU eco e y plan (PRTR- C17.I1), by Xun a de Galicia h ough he “Planes Complemen a ios de I+D+I con las Comunidades Au onomas” in Quan um Communica ion, by Xun a de Galicia, Spain and he ERDF (ED431C 2021/21, ED431B 2022/36) and Cen o singula de in es igación de Galicia acc edi a ion 2016–2019, ED431G/09 and Axencia Galega de Inno ación, Spain h ough he G an Ag eemen ‘‘Desp egamen o dunha in aes u u a baseada en ecnoloxías cuán icas da in o mación que pe mi a impulsa a I+D+I en Galicia’’ wi hin he p og am FEDER Galicia 2014–2020. Simula ions on his wo k we e pe o med using he Finis e ae III Supe compu e , unded by he p ojec CESGA-01 FINISTERRAE III. Re e ences [1] S. Nayab, M.A. Aslam, S.u. Rahman, Z.u.D. Sindhu, S. 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