SAUYE-SAUYEN HALITTA NAWA AKE BUƘATA DON ƘIRƘIRAR SABON AIKI?

Ƙwayoyin halitta suna samar da sababbin ayyuka ta hanyar sauye-sauyen halitta (mutations), amma fagen da juyin halitta zai bincika yana da girma mai ban mamaki. Ƙwayar gado (gene) ta ƙwayar cuta (bacteria) ta yau da kullum mai haruffan DNA 1,000 za a iya rubuta ta ta hanyoyi daban-daban kimanin 10⁶⁰⁰, kuma kowace siga tana da nisan sauyin halitta guda ɗaya kawai daga wasu 3,000. Duk da haka gwaje-gwaje kan sami sababbin ayyuka cikin ’yan sauye-sauyen halitta kaɗan: tara sun canza abin da wani enzyme ke samarwa, biyar sun sa wani ya ƙara jure wa maganin ƙwayoyin cuta (antibiotic) sau 100,000. Shin babban fagen yiwuwa yana sa juyin halitta ya yi jinkiri, saboda sauyin da ya dace yana da wuyar samu — ko kuma yana sa ya yi sauri, saboda hanyoyi da yawa suna kaiwa wani wuri?

Da’irorin da ke rikiɗa

Nida Farheen da Jané Kondev na Jami’ar Brandeis, tare da Zachary Boroda da Ethan Levien, sun tunkari tambayar da wani samfuri da ake iya ƙirga komai a cikinsa. “Halittunsu” ƙananan da’irori ne (circuits): shigarwa biyu, adadin N na ƙofofin dabaru (logic gates) na NAND — kowacce tana fitar da 0 ne kawai idan shigarwarta biyu duka 1 ne, in ba haka ba 1 — da fitarwa ɗaya. Jonawar wayoyin ita ce tsarin gado (genotype). Aikin dabaru da da’irar ke lissafawa a kan shigarwarta biyu shi ne siffar zahiri (phenotype) — akwai guda 16 kawai masu yiwuwa.

Dacewa (fitness) mai sauƙi ce: kason nau’i-nau’i huɗu na shigarwa masu yiwuwa da da’irar ke ba da amsar da ake nema a kansu, wato 0, 0.25, 0.5, 0.75 ko 1. Sauyin halitta yana sake jona haɗi ɗaya ba da tsari ba, yana ajiye adadin ƙofofi a yadda yake; ba a yarda da sake jonawa da za ta haifar da zagaye (loop) ba. Ko wani mai sauyin halitta (mutant) zai mamaye al’umma (population) ta 10,000 yana bin wata dabarar lissafi da aka saba da ita a fannin ilimin gado na al’umma (population genetics), wadda ke fifita ingantawa, kuma ba ta barin sauye-sauye marasa tasiri su yaɗu sai da wuya.

Ƙara N yana faɗaɗa fagen da’irori masu yiwuwa kusan kamar N mai ƙarfi N (N to the power N), kuma yana ba kowace da’ira maƙwabta kimanin N² da ke da nisan sauyin halitta ɗaya. Da a ce ayyukan 16 sun rarrabu daidai-wa-daida, marubutan sun lura, sauye-sauyen halitta kimanin 16 za su isa koyaushe, ko yaya girman yake.

Kimanin sauye-sauyen halitta goma ga kowace ƙofa

Sun fara daga da’irar da ke lissafa NAND — kowace ƙofa a jone da shigarwar biyu, fitarwar a haɗe da ƙofa ta 1 — kuma suka bar ta ta rikiɗa zuwa AND, ainihin kishiyarta. Ga girma daga ƙofofi 5 zuwa 1,000, sun gudanar da kwaikwayo (simulations) 500 ga kowane.

Adadin sauye-sauyen halitta da ake buƙata ya ƙaru kusan daidai gwargwado da girman da’irar, yana bin kusan 9.8 × N^0.96: kimanin goma ga kowace ƙofa. Hasashen rarrabuwa daidai-wa-daida na 16 ya yi nisa sosai. Kusan dukkan waɗannan sauye-sauyen halitta marasa tasiri (neutral) ne — ba su canza dacewa ba — kuma ba su taɓa yaɗuwa ba. Ingantawa huɗu ne kawai ake buƙata a mafi yawa, tunda dacewa tana hawa ne mataki-mataki na kwata; sauran lokacin, juyin halitta yana jira ne.

Wayoyin da ke da muhimmanci

Me ya sa? Marubutan sun ware wayoyin lissafi (computing wires): waɗanda ke kan hanya daga shigarwa zuwa fitarwa. Sake jona kowace waya dabam ba zai iya canza fitarwar ba. A cikin waɗannan da’irori, wayoyi kimanin uku ne kawai ke lissafi, ko yaya girman yake, alhali jimillar adadin wayoyin shi ne 2N + 1. Don haka damar faɗawa kan wayar da ke da muhimmanci tana raguwa kamar 1/N. Da zarar an faɗa kan wayar lissafi, damar cewa sauyin zai taimaka ba ta dogara da girma ba. Idan aka haɗa su, ana buƙatar ƙoƙari kimanin N don samun sauyin halitta guda ɗaya mai amfani.

Idan aka kalla a matsayin taswirar dukkan da’irori, kowace tana da maƙwabta kimanin N², amma kimanin N kawai daga cikinsu ne ke bambanta ta hanyar sauyi a wayar lissafi.

Canza farawa, canza doka

Wannan bayani yana yin wani hasashe. Idan maimakon haka aka fara daga da’irar da kowace waya ke lissafi, damar faɗawa kan wayar da ke da muhimmanci ba za ta ƙara raguwa da girma ba. A lokacin, adadin sauye-sauyen halitta ya kamata ya daina ƙaruwa. Kwaikwayon sun yarda: kimanin 31 × N^0.07, kusan a kwance. Daga ainihin da’irar NAND, ko da da ƙaramar al’umma ta 10 kawai, inda sauye-sauye marasa tasiri ke yawan yaɗuwa, ƙaruwar ta kasance kusan madaidaiciya (linear).

Akwai wata karkata game da lokaci. Manyan da’irori suna da ƙarin wayoyi, don haka suna tara sauye-sauyen halitta da sauri. Idan adadin sauye-sauyen halitta ya ƙaru daidai gwargwado da N, lokacin rikiɗa zuwa AND yana nan daidai ga dukkan girma; idan bai ƙaru ba, manyan da’irori suna kaiwa can da wuri.

Abin da girma kaɗai ba ya faɗi

Marubutan sun kammala cewa yawan sauye-sauyen halitta masu yiwuwa kawai ba shi ne ke ƙayyade wahalar samar da wani sabon abu ta juyin halitta ba. Abin da ke da muhimmanci shi ne kason sauye-sauyen halitta da za su iya inganta dacewa — waɗanda ke taɓa sassan da ke yin lissafin, kuma a cikinsu, waɗanda ke taimakawa. Sun fito fili game da iyakoki: da’irorinsu suna da matakan dacewa biyar kawai da ayyuka 16 masu yiwuwa, sakamakon ya dogara da da’irar farawa, kuma har ina ya shafi ainihin jimillar ƙwayoyin gado (genomes) tambaya ce a buɗe. Amsar “sauye-sauyen halitta nawa?” za ta iya kasancewa ba sosai a girman jimillar ƙwayoyin gado ba, sai dai a yawan sashenta da ke aiki.