SHIN ƘWAYAR HALITTA ZA TA IYA YIN ZAFI DA DIGIRI DA DAMA DA GASKE?

Auna zafi a cikin ƙwayar halitta guda mai rai ya yiwu ne kusan shekaru goma sha biyar kawai, a cewar takardar. Ya haifar da wani wasa-ƙwaƙwalwa. Ayyuka masu ƙaruwa suna ruwaito zafi a cikin ƙwayoyin halitta kusan kelvin 1 zuwa 10 sama da muhallinsu; wani bincike da aka ambata yana da taken “Mitochondria are physiologically maintained at close to 50 °C”. Amma ƙiyasin da ya dogara ga yawan zafin da ƙwayar halitta ke samarwa da gaske, da kuma yaɗuwar zafi ta yau da kullum, yana hasashen bambance-bambance ƙasa da kashi ɗaya cikin dubu na digiri.

Kurakuran awo da aka sani ba sa bayyana cikin sauƙi dalilin da ya sa ma’aunin zafi daban-daban da yawa, masu bambanci a zahiri da a sinadarai, ke ba da sakamako iri ɗaya. Gyare-gyaren yaɗuwar zafi a ƙananan sikeli har yanzu sun yi ƙanƙanta sosai da ba za su rufe gibi na matakai da dama na girma ba.

Kalli ma’aunin zafi, ba tushen ba

Yawancin ƙoƙarin warware wasa-ƙwaƙwalwar suna mai da hankali kan tushen zafin: girman mitochondrion, siffarsa, tsarinsa da nisansa daga na’urar ji, duk masu wuyar tantancewa. Taras Plakhotnik (Jami’ar Queensland) ya juya matsalar.

Tushen zafi na ɗigo (point source) cikakke zai, a ka’ida, kai wa zafi marar iyaka. Amma babu ma’aunin zafi na gaske da ke auna ɗigo: yana da girman auna zafi (thermometric volume) mai iyaka, kuma abin da yake ruwaito matsakaici ne a kan wannan girman. Na’urar ji, ya lura, yawanci an fi saninta sosai fiye da tushen halittar.

Don haka ya tambaya: idan aka sanya ta a ko’ina a cikin wani yanki da ke samar da sananniyar jimillar zafi, yaya na’urar ji mai wani girma za ta iya yin zafi, a mafi yawa, a yanayin tsayayye (steady state)?

Iyaka mai sinadarai uku

Ta amfani da dokar Fourier ta yaɗuwar zafi kaɗai da wasu rashin daidaito (inequalities) biyu na gargajiya na geometry da nazari (analysis), ya samo wani theorem na mafi girman zafi:

⟨T⟩ − T_ref ≤ 9 Q / (2 (36π)^(2/3) κ V^(1/3))

inda Q shi ne jimillar ƙarfin zafin da aka samar, κ ƙaramar iyaka ta ƙarfin gudanar da zafi kuma V girman na’urar ji. Babu wani abu kuma da ke shiga: ba daga ina zafin ya fito ba, ba yadda aka rarraba shi ba, ba nisan da na’urar ji take ba.

Ga ƙwayar halittar dabba mai shayarwa (mammalian) da aka noma a ɗakin bincike, takardar ta ɗauki fitar zafi mai tsabta ta picowatts 50, ƙarfin gudanar da zafi na watt 0.1 a kowace mita a kowane kelvin, a ƙasan ƙimomin da aka ruwaito ga ƙwayoyin halitta, da na’urar ji ta cubic mita 10⁻²², wato kusan sphere mai faɗin nanomita 60. Mafi girman ɗumamar da zai yiwu: kusan millikelvin 2.

Iyakar tana da kaifi: ana kai wa gare ta lokacin da aka naɗe tushen zafi mai siffar sphere a cikin na’urar ji mai siffar harsashi. Ko a cikin wannan tsari mafi dacewa, hawan kelvin 1 zai buƙaci aƙalla nanowatts 25, ninki ɗari biyar na abin da aka auna ƙwayar halittar na fitarwa. Idan maimakon haka zafin ya bazu daidai a cikin girman ƙwayar halitta, iyakar za ta faɗi zuwa kusan microkelvin 2.

Me game da halayen sinadarai masu samar da zafi da masu shanye zafi da ke soke juna? Calorimetry yana auna fitarwa mai tsabta ne kawai, alhali theorem ɗin yana ƙirga dukkan zafin da aka samar. Karatun kelvin 1 da picowatts 50 kawai ke fita daga ƙwayar halittar zai buƙaci aƙalla nanowatts 25 da aka saki a wurin, da kusan daidai haka da aka shanye a wani wuri a cikin ƙwayar halittar ɗaya.

Sakamakon yana aiki kai tsaye a kan na’urorin ji da ake amfani da su: nanodiamonds, upconversion nanoparticles, ƙwayoyin polymer masu haske (fluorescent) da quantum dots masu tsakiya da harsashi (core–shell).

Ma’aunin zafi da ke jinkiri a baya

Theorem ɗin yana ɗauka cewa na’urar ji da kanta tana cikin daidaito (equilibrium) a ciki. Don nuna dalilin da ya sa hakan zai iya gazawa, marubucin ya kwaikwayi rumbunan iskar gas biyu, ɗaya mai zafi ɗaya mai sanyi, da wani siririn bango mai roba (elastic membrane) ya raba su. Iskar gas ɗin sun kai wa zafi ɗaya da sauri alhali bangon ya natsu a hankali sosai, kuma gibin ya ƙara faɗi yayin da bangon ke ƙara tauri. Ƙaramin abu zai iya kasancewa ba a daidaito ba ko da muhallinsa ya natsu, kuma daidaitaccen gyaran ma’auni (calibration) da zafin daidaito ba zai bayyana hakan ba.

Inda kimiyyar lissafin da ta ɓace dole ta ɓoye

Takardar ba ta da’awar cewa wuraren zafin da aka ruwaito kurakuran awo ne. Ta bayyana cewa idan siginar sikelin kelvin zafi ne da gaske, aƙalla ɗaya daga cikin zato na theorem ɗin dole ya gaza. ’Yan takarar da ta lissafa: ƙarin ƙarfi da na’urar binciken da kanta ta saka, kuzarin da aka adana na ɗan lokaci a cikin yanayi masu daɗewa, na’urar ji da ba ta taɓa kai wa cikakken daidaito ba, ko wani canji da ba na zafi ba a cikin na’urar ji ko muhallinta da ke kwaikwayon canjin zafi. Bambance su, marubucin ya kammala, zai buƙaci gwaje-gwajen da ke bin yadda ma’aunin zafin da kansa ke natsuwa.