ÌÎÄÅËÈÐÎÂÀÍÈÅ ÏÐÎÒÎÍÍÎÃÎ ÒÐÀÍÑÏÎÐÒÀ Â ÊÀÍÀËÅ ÃÐÀÌÈÖÈÄÈÍÀ À ÓÄÊ 541.124
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ÂÅÑÒÍ. ÌÎÑÊ. ÓÍ-ÒÀ. ÑÅÐ. 2. ÕÈÌÈß. 2008. Ò. 49. ¹ 5 291 ÓÄÊ 541.124 ÌÎÄÅËÈÐÎÂÀÍÈÅ ÏÐÎÒÎÍÍÎÃÎ ÒÐÀÍÑÏÎÐÒÀ  ÊÀÍÀËÅ ÃÐÀÌÈÖÈÄÈÍÀ À È.À. Êàëèìàí, À.À. Ìîñêîâñêèé, Ñ.Ñ. Êîíþõîâ, À.Â. Íåìóõèí (êàôåäðà ôèçè÷åñêîé õèìèè; e-mail: ilya.kaliman@gmail.com) Ïðåäñòàâëåíû ðåçóëüòàòû ðàñ÷åòîâ ïðîôèëåé ñâîáîäíîé ýíåðãèè äëÿ ïðîöåññà ïåðåíîñà ïðîòîíà âäîëü îðèåíòèðîâàííîé öåïî÷êè ìîëåêóë âîäû â êàíàëå ãðàìèöèäèíà À. Èñïîëüçîâàí îðèãèíàëüíûé âàðèàíò ìåòîäà ìîëåêóëÿðíîé äèíàìèêè ñ æåñòêèìè ôðàãìåíòàìè äëÿ îïèñàíèÿ äâèæåíèé ïåïòèäíûõ ãðóïï êàíàëà è âíåøíèõ ìîëåêóë âîäû. Ìîäåëèðîâàíèå âíóòðåííåé öåïè, ñîñòîÿùåé èç ìîëåêóë âîäû îñóùåñòâëÿëîñü ïðè ïîìîùè ïàðàìåòðîâ ñèëîâîãî ïîëÿ PM6, ïîçâîëÿþùåãî îïèñûâàòü ðàçðûâû è îáðàçîâàíèå õèìè÷åñêèõ è âîäîðîäíûõ ñâÿçåé â ìîëåêóëàõ âîäû. Ðàññìîòðåíû ðàçíûå ìåõàíèçìû ïåðåíîñà ïðîòîíà ÷åðåç êàíàë ãðàìèöèäèíà À: ñòàäèè ïåðåíîñà ïðîòîíà H+, àíèîííîãî äåôåêòà OH– è ïåðåîðèåíòàöèè ìîëåêóë âîäû â êàíàëå. Ïàðàëëåëüíàÿ ñõåìà ðàñ÷åòà òðàåêòîðèé ðåàëèçîâàíà ïóòåì ðàçäåëåíèÿ êîîðäèíàòû ðåàêöèè íà ñåãìåíòû, à îáúåäèíåíèå ðåçóëüòàòîâ ïðîâîäèëîñü ïî ìåòîäó âçâåøåííûõ ãèñòîãðàìì. Ïîêàçàíî, ÷òî ïðîöåññû ïåðåìåùåíèÿ è ïðîòîíà, è àíèîíà OH– ÿâëÿþòñÿ áåçáàðüåðíûìè. Ýíåðãåòè÷åñêèé áàðüåð õàðàêòåðåí ëèøü äëÿ ñòàäèè ïåðåîðèåíòàöèè âîäíîé öåïè âíóòðè êàíàëà. Ãðàìèöèäèí À ïðåäñòàâëÿåò ñîáîé ïåíòàäåêàïåïòèä, ñîñòîÿùèé èç L è D àìèíîêèñëîò (Formyl L– Val L–Gly L–Ala D–Leu L–Ala D–Val L–Val D–Val L–Trp D–Leu L–Trp D–Leu L–Trp D–Leu L–Trp Ethanolamine), îáðàçóþùèõ ñïèðàëüíóþ ñòðóêòóðó, çàêðó÷åííóþ â ïðàâóþ ñòîðîíó. Ðàçìåð ìîëåêóëû ãðàìèöèäèíà À íåäîñòàòî÷åí äëÿ îáðàçîâàíèÿ êàíàëà â ìåìáðàíå, ïîýòîìó òðàíñìåìáðàííûé èîííûé êàíàë ôîðìèðóåò äèìåð. Âñëåäñòâèå íåáîëüøèõ ðàçìåðîâ ãðàìèöèäèí ïðåäñòàâëÿåò óäîáíóþ ñèñòåìó äëÿ òåîðåòè÷åñêîãî ìîäåëèðîâàíèÿ ðåàêöèé ïåðåíîñà ïðîòîíà ïî îðèåíòèðîâàííûì öåïî÷êàì ìîëåêóë âîäû, êîòîðûå ÷àñòî íàçûâàþò ïðîâîäíèêàìè ïðîòîíîâ [1–4] (ðèñ. 1). Íåñìîòðÿ íà ïîïóëÿðíîñòü ýòîé ìîäåëè, ìåõàíèçì ïðîòîííîãî òðàíñïîðòà ïî âîäíûì ïðîâîäíèêàì îñòàåòñÿ òåìîé äëÿ äèñêóñ- Ðèñ. 1. Êëàññè÷åñêàÿ ñõåìà ïåðåíîñà ïðîòîíà ïî öåïè èç ìîëåêóë âîäû 2 ÂÌÓ, õèìèÿ, ¹ 5 292 ÂÅÑÒÍ. ÌÎÑÊ. ÓÍ-ÒÀ. ÑÅÐ. 2. ÕÈÌÈß. 2008. Ò. 49. ¹ 5 Ðèñ. 2. Ñõåìà ïåðåíîñà àíèîííîãî äåôåêòà ñèé.  ÷àñòíîñòè, â ðàáîòå [5] ïðåäëîæåíà îðèãèíàëüíàÿ ñõåìà ïðîâîäèìîñòè ïðîòîíîâ ïî èîííîìó êàíàëó, â êîòîðîé ïðåäïîëàãàåòñÿ, ÷òî ïðîöåññ ìîæåò áûòü îïèñàí òðàíñïîðòîì àíèîííîãî äåôåêòà OH– (ðèñ. 2). Êîíå÷íûì ðåçóëüòàòîì â îáîèõ ñëó÷àÿõ ÿâëÿåòñÿ ôèçè÷åñêîå ïåðåìåùåíèå ïðîòîíà ñ îäíîãî êîíöà êàíàëà ê äðóãîìó, à ïîñëå êàæäîãî àêòà ïåðåíîñà ïðîòîíà íåîáõîäèìà ïåðåîðèåíòàöèÿ öåïî÷êè âîäíîãî ïðîâîäíèêà äëÿ ïîäãîòîâêè ñëåäóþùåãî àêòà.  äàííîé ðàáîòå ìû ñîïîñòàâèëè ðåçóëüòàòû ðàñ÷åòîâ ïðîôèëåé ñâîáîäíîé ýíåðãèè äëÿ ïåðåíîñà ïðîòîíîâ âäîëü îðèåíòèðîâàííîé öåïî÷êè ìîëåêóë âîäû â êàíàëå ãðàìèöèäèíà À, ïðåäïîëàãàÿ ñóùåñòâîâàíèå êàê ïðîòîííîãî, òàê è àíèîííîãî ìåõàíèçìîâ ïåðåíîñà. Ðàññìîòðåíà òàêæå ñòàäèÿ ïåðåîðèåíòàöèè ìîëåêóë âîäû âíóòðè êàíàëà. Íà ðèñ. 3 èçîáðàæåíà ìîëåêóëÿðíàÿ ìîäåëü, èñïîëüçîâàííàÿ äëÿ ðàñ÷åòîâ òðàåêòîðèé. Öåïü ìîëåêóë âîäû âíóòðè êàíàëà îáðàçîâàíà 9 ìîëåêóëàìè âîäû. Íà îáîèõ êîíöàõ êàíàëà íàõîäÿòñÿ êëàñòåðû èç 20 ìîëåêóë âîäû (âíåøíèå ìîëåêóëû âîäû), ñòåíêè êàíàëà îáðàçîâàíû ïåïòèäíûìè ãðóïïàìè (àòîìû âîäîðîäà íå ïîêàçàíû). Èñõîäíûå êîîðäèíàòû òÿæåëûõ àòîìîâ ïîñòðîåíû íà îñíîâå ñòðóêòóðû 1JNO [6] èç áàíêà äàííûõ áåëêîâûõ ñòðóêòóð. Äëÿ ðàñ÷åòîâ èñïîëüçîâàí íîâûé âàðèàíò ìåòîäà ìîëåêóëÿðíîé äèíàìèêè ñ æåñòêèìè ôðàãìåíòàìè [7, 8], êîòîðûé ïðèìåíÿåòñÿ äëÿ îïèñàíèÿ äâèæåíèé ïåïòèäíûõ ãðóïï êàíàëà è âíåøíèõ ìîëåêóë âîäû, ðàñïîëîæåííûõ âíå êàíàëà. Ïåïòèäíûå ãðóïïû ïîäðàçäåëÿþòñÿ íà äîñòàòî÷íî ìàëûå æåñòêèå ôðàãìåíòû, ïåðåìåùåíèå êîòîðûõ â ñîñòàâå ïåïòèäíûõ öåïåé îïèñûâàåòñÿ äèíàìèêîé òâåðäûõ òåë.  äàííîì ñëó÷àå ñòåíêè êàíàëà îáðàçîâàíû 144 æåñòêèìè ôðàãìåíòàìè. Âíåøíèå ìîëåêóëû âîäû òàêæå ïðåäñòàâëÿþò ñîáîé òâåðäûå òåëà. Ñèëû, äåéñòâóþùèå íà ýòè æåñòêèå ôðàãìåíòû, âû÷èñëÿþòñÿ ñ ïàðàìåòðàìè ñèëîâîãî ïîëÿ CHARMM27 [9]. Äëÿ ìîäåëèðîâàíèÿ âíóòðåííåé öåïè âîäíîãî ïðîâîäíèêà ñ ïðîòîíîì èëè ãèäðîêñèë àíèîíîì èñïîëüçîâàíû ïàðàìåòðû ñèëîâîãî ïîëÿ PM6 [10], ïîçâîëÿþùåãî îïèñûâàòü ðàçðûâû è îáðàçîâàíèå õèìè÷åñêèõ è âîäîðîäíûõ ñâÿçåé â ìîëåêóëàõ âîäû. Ïðè èíòåãðèðîâàíèè óðàâíåíèé ìîëåêóëÿðíîé äèíàìèêè èñïîëüçîâàëñÿ êàíîíè÷åñêèé (NVT) àíñàìáëü ñ òåðìîñòàòîì Íîçå–Ïóàíêàðå [11]. Èíòåãðèðîâàíèå óðàâíåíèé äâèæåíèÿ ïðîâîäèëîñü ïî îðèãèíàëüíûì êîìïüþòåðíûì ïðîãðàììàì. Ñëåäóÿ ðåêîìåíäàöèÿì ðàáîòû [2], â êà÷åñòâå êîîðäèíàòû ðåàêöèè ìû èñïîëüçîâàëè çíà÷åíèå ïðîåêöèè äèïîëüíîãî ìîìåíòà íà îñü êàíàëà, êîòîðûé â ñâîþ î÷å- ÂÅÑÒÍ. ÌÎÑÊ. ÓÍ-ÒÀ. ÑÅÐ. 2. ÕÈÌÈß. 2008. Ò. 49. ¹ 5 293 Ðèñ. 3. Ìîäåëüíàÿ ñèñòåìà, ñîñòîÿùàÿ èç äèìåðà ãðàìèöèäèíà (ñòåðæíÿìè ïîêàçàíû òîëüêî òÿæåëûå àòîìû) ñ öåïüþ ìîëåêóë âîäû âíóòðè êàíàëà è âíåøíèìè ìîëåêóëàìè âîäû ðåäü âû÷èñëÿëñÿ äëÿ àòîìîâ öåïè ìîëåêóë âîäû. Òðàåêòîðèè ðàññ÷èòûâàëè äëÿ òåìïåðàòóðû 300 Ê ñ øàãîì èíòåãðèðîâàíèÿ 0,5 ôñ. Äëÿ ðåàëèçàöèè ïàðàëëåëüíîé ñõåìû ðàñ÷åòà òðàåêòîðèé êîîðäèíàòà ðåàêöèè áûëà ïîäðàçäåëåíà íà 6 ñåãìåíòîâ (îêîí), ñîãëàñíî çîíòè÷íîé ñõåìå ñêàíèðîâàíèÿ êîíôèãóðàöèîííîãî ïðîñòðàíñòâà (umbrella sampling) [12].  êàæäîì îêíå àíàëèçèðîâàëîñü 60 000 êîíôèãóðàöèé ñ èíòåðâàëîì 2,5 ôñ. Îáúåäèíåíèå ðåçóëüòàòîâ ïðîâîäèëîñü ïî ìåòîäó âçâåøåííûõ ãèñòîãðàìì [13]. Ñâîáîäíóþ ýíåðãèþ ðàññ÷èòûâàëè ïî ôîðìóëàì ñòàòèñòè÷åñêîé òåðìîäèíàìèêè ÷åðåç ðàñïðåäåëå- Ðèñ. 4. Ïðîôèëü ñâîáîäíîé ýíåðãèè äëÿ ñòàäèè ïåðåíîñà ïðîòîíà 3 ÂÌÓ, õèìèÿ, ¹ 5 Ðèñ. 5. Ïðîôèëü ñâîáîäíîé ýíåðãèè äëÿ ñòàäèè ïåðåíîñà OH– íèå âåðîÿòíîñòåé âäîëü êîîðäèíàòû ðåàêöèè. Ðåçóëüòàòû ðàñ÷åòîâ ïðèâåäåíû íà ðèñ. 4–6. Ïî ðåçóëüòàòàì ïðîâåäåííûõ ðàñ÷åòîâ ìîæíî ñäåëàòü âûâîä, ÷òî ïåðåìåùåíèå êàê ïðîòîíà, òàê è OH– íå èìåþò ýíåðãåòè÷åñêèõ áàðüåðîâ. Ñëåäóåò îòìåòèòü, ÷òî ïîòåíöèàëüíàÿ ÿìà, îòâå÷àþùàÿ íàõîæäåíèþ çàðÿæåííîé ÷àñòèöû â öåíòðå êàíàëà, áîëåå ãëóáîêàÿ äëÿ OH – (~4 êêàë/ìîëü), ÷åì äëÿ ïðîòîíà (~2 êêàë/ìîëü). Ýíåðãåòè÷åñêèé áàðüåð õàðàêòåðåí äëÿ ñòàäèè ïåðåîðèåíòàöèè âîäíîé öåïè âíóòðè êàíàëà, è èìåííî ýòà ñòàäèÿ ÿâëÿåòñÿ ëèìèòèðóþùåé. 294 ÂÅÑÒÍ. ÌÎÑÊ. ÓÍ-ÒÀ. ÑÅÐ. 2. ÕÈÌÈß. 2008. Ò. 49. ¹ 5 Ðèñ. 6. Ïðîôèëü ñâîáîäíîé ýíåðãèè äëÿ ñòàäèè ïåðåîðèåíòàöèè öåïè èç ìîëåêóë âîäû Ðàáîòà âûïîëíåíà ïðè ïîääåðæêå ÐÔÔÈ (ïðîåêò 06-03-33009-à). ÑÏÈÑÎÊ ËÈÒÅÐÀÒÓÐÛ 1. Sagnella D. E., Laasonen K., Klein M. L. // Biophys. J. 1996. 71. P. 1172. 2. Pomes R., Roux B. // Biophys. J. 2002. 82. P. 2304. 3. Braun-Sand S., Burykin A., Chu Z. T., Warshel A. // J. Phys. Chem. B. 2005. 109. P. 583. 4. Nemukhin A. V., Grigorenko B. L., Topol I. A., Burt S. K. // J. Phys. Chem. B. 2003. 107. P. 2958. 5. Rokitskaya T. I., Kotova E. A., Antonenko Y. N. // Biophys. J. 2002. 82. P. 865. 6. Townsley L.E., Tucker W.A., Sham S., Hinton J.F. // Biochemistry. 2001. 40. P. 11676. 7. Moskovsky A. A., Vanovschi V. V., Konyukhov S. S., Nemukhin A. V. // Intern. J. Quant. Chem. 2006. 106. P. 2208. 8. Ìîñêîâñêèé À. À., Êàëèìàí È. À., Àêèìîâ À. Â., Êîíþõîâ Ñ. Ñ., Ãðèãîðåíêî Á. Ë., Íåìóõèí À. Â. // Âåñòí. Ìîñê. óí-òà. Ñåð. 2. Õèìèÿ. 2007. 48. C. 219. 9. MacKerell A. D., Bashford D., Bellot M. et al. // J. Phys. Chem. B. 1998. 102. P. 3586. 10. Weber T. A., Stillinger F. H. // J. Phys. Chem. 1982. 8. P. 1314. 11. Hisashi O., Itoh S. G., Okamoto Y. // J. Chem. Phys. 2007. 126. P. 84103. 12. Roux B. // Comput. Phys. Comm. 1995. 91. P. 275. 13. Kumar S., Bouzida D., Swendsen R. H., Kollman P. A., Rosenberg J. M. // J. Comput. Chem. 1992. 13. P. 1011. Ïîñòóïèëà â ðåäàêöèþ 15.02.08 MODELING PROTON TRANSPORT IN THE CHANNEL OF GRAMICIDIN A I.A. Kaliman, A.A. Moskovsky, S.S. Konyukhov, A.V. Nemukhin (Division of Physical Chemistry) The energy profiles for the proton transfer along the oriented water molecules inside the gramicidin A channel were computed. We use an original implementation of the rigid body molecular dynamics method for description of the peptide groups of the channel as well as of the outer water molecules. In order to simulate the inner water wire, the force field parameters PM6 allowing formation and cleavage of chemical and hydrogen bonds in water molecules are used. We + – studied the intrinsic stage of the proton H translocation, the transfer of the anionic defect OH , and the stage of re-orientation of the water file inside the channel. To facilitate parallel calculations of trajectories, the reaction coordinate is subdivided into segments, and the weighted histogram analysis method is applied. No energy barrier was found for the transfer of an anion defect from the center of the channel, as well as for the proton transfer. The re-orientation of water file inside the channel is the only stage, that has a barrier.
