Effects of Mutations of Lys41 and Asp102 of Bacteriorhodopsin

Size: px
Start display at page:

Download "Effects of Mutations of Lys41 and Asp102 of Bacteriorhodopsin"

Transcription

1 Biosci. Biotechnol. Biochem., 75 (7), , 2011 Effects of Muttions of Lys41 nd Asp102 of Bcteriorhodopsin Yingchun ZHAO, 1;2 Yzhuo WANG, 1 Dewng MA, 1 Ji WU, 1 Weid HUANG, 2 nd Jindong DING 1;y 1 Key Lortory of Moleculr Engineering of Polymers of the Ministry of Eduction, Deprtment of Mcromoleculr Science, Lortory of Advnced Mterils, Fudn University, Shnghi , Chin 2 Deprtment of Biochemistry, School of Life Sciences, Fudn University, Shnghi , Chin Received Mrch 8, 2011; Accepted April 12, 2011; Online Puliction, July 7, 2011 [doi: / ] Bcteriorhodopsin (BR) is retinl protein tht functions s light-driven proton pump. In this study, six novel mutnts including K41E nd D102K, were otined to verify or rule out the possiility tht residues Lys41 nd Asp102 re determinnts of the time order of proton relese nd uptke, ecuse we found tht the order ws reversed in nother retinl protein rcherhodopsin 4 (AR4), which hd different 41th nd 102th residues. Our results rule out tht possiility nd confirm tht the pk of the proton relese complex (PRC) determines the time order. Nevertheless, muttions, especilly D102K, were found to ffect the kinetics of proton uptke sustntilly nd the pk of Asp96. Compred to the wild-type BR (BR-WT), the decy of the M intermedite nd proton uptke in the photocycle ws slowed out 3-fold in D102K. Hence those residues might e involved in proton uptke nd delivery to the internl proton donor. Key words: cteriorhodopsin; point mutnt; proton pump; M decy BR is retinl-contining protein cting s lightdriven proton pump. It ws found in the purple memrne of the extremely hlophilic rchecterium Hlocterium slinrum. 1) BR hs een investigted extensively over the pst four decdes. 2 18) Upon photon sorption, the retinl is isomerized from the ll-trns to the 13-cis configurtion. This initites photocycle in which series of photointermedites re formed. They re distinguished y their sorption mxim: BR 570! hv K 610 $ L 550 $ M412 I! MII 412 $ N 560 $ O 640! BR 570 The photocycle is coupled to the directionl trnsfer of proton cross the memrne. Illumintion induces proton trnsfer from the nitrogen of the Schiff se linking retinl nd Lys-216 to Asp-85 during the L-to-M trnsition, which leds, on sumillisecond timescle, to prompt proton relese from the proton relese complex (PRC or XH) to the extrcellulr surfce t neutrl ph ) After proton relese, nother proton is tken up from the cytoplsmic side in the N 560 -to-o 640 trnsition 22) or trnsition etween the two N-susttes, 23) nd lifetime constnt of few milliseconds is usul. Therefore, proton pumping y BR under physiologicl conditions involves proton relese on the extrcellulr side, followed y proton uptke on the cytoplsmic side. Site-specific mutgenesis is used extensively to illustrte the reltionship of function nd structure for vrious proteins. 7,24 26) It hs een found tht croxylic residues in the proton-conducting cytoplsmic nd extrcellulr hlf-chnnels, D96, D85, E194, nd E204 re involved in the photocycle nd proton trnsfer. Negtively chrged D85 is prt of the counterion to the protonted Schiff se nd proton cceptor. Buried in the cytoplsmic domin, neutrl D96 serves s n internl proton donor for the Schiff se in the M intermedite. Two glutmtes t the extrcellulr surfce, E194 nd E204, nd some intercting wter molecules re thought to comprise PRC. 6,27 29) While much progress hs een mde in finding key residues in BR, only out 58 residues hve een exmined to dte while the functionl significnce of mjority of the residues in BR remins undetermined. Especilly the key residues in the cytoplsmic side re less investigted thn the extrcellulr side, where proton relese tkes plce nd the PRC is locted. The mutnts locted on the cytoplsmic side including D36N, D38N, D102N, nd D104N, were expressed in E. coli. They presented slightly decresed time of M decy, 30) ut proton pumping rtes similr or higher thn the BR-WT. 31) Among the other mutnts expressed in Hlocterium slinrum L33, with D36, D38, D102, nd D104 replced y cysteine or rginine, D36 ws found to ct s proton ttrctor t the orifice of the proton-conducting chnnel, 32) D38 ws found to influence the lte steps in the functionl photocycle, such s the occurrence of intermedites N nd O, 33) nd D104C lowered the trnsient proton inding cpcity of the cluster tht consists of D104, E161, nd E ) Hints from comprison of the BR sequence to those of other rchel nd cteril retinl proteins is helpful in serching for residues involved in proton pumping. 7) In the present study we exmined effects of mutting Lys- 41 (K41) nd Asp-102 (D102), two chrged residues on the cytoplsmic side of the light-driven proton pump. These two mino cid residues were selected for comprison of BR nd AR4. AR4 ws found in strin of the hlocterium Hlorurum species xz515 isolted from slt lke in y To whom correspondence should e ddressed. Fx: ; E-mil: jdding1@fudn.edu.cn Arevitions: BR, cteriorhodopsin; AR4, rcherhodopsin 4; PRC, proton relese complex; BR-WT, wild-type BR expressed in L33

2 Effects of Muttions of Bcteriorhodopsin 1365 difficulty hs lso een reported for other rcherhodopsins. 42,43) Fig. 1. Schemtic Presenttion of All the Amino Acids in BR-WT nd Its Structure of Seven Trnsmemrne Helixes. In the photocycle, proton is relesed to the extrcellulr side nd nother proton is tken up from the cytoplsmic side. Squres nd dimonds denote cidic nd lkline residues respectively. Two chrged residues on the cytoplsmic side, K41 nd D102, in BR re highlighted y lrge ellipses. In AR4 these residues re replced y E nd K respectively. Tiet in ) Its mino cid sequence hs een determined. 36,37) It exhiits 59% sequence similrity to BR. 37) Like BR, AR4 functions s light-driven proton pump. In contrst to BR, it exhiits reversed order of light-driven proton relese nd uptke t neutrl ph, 35) even though oth BR nd AR4 hve key residues E194 nd E204, cting s PRC. It lso exhiits severl other fetures (fster decy of the M intermedite nd higher pk of the counterion). We hve found tht the inversion of the order of proton relese nd uptke is cused y the elevted pk of the PRC in the M intermedite (from 5.6 in BR to 8.3 in AR4) ) The higher pk of the PRC in the M intermedite of AR4 might e cused y replcement of nery or distnt residues. Severl polr or chrged residues locted in the extrcellulr side re conserved in BR nd AR4, including R7, E9, nd K129. 7) A few polr or chrged residues t the cytoplsmic side re different in these pigments. Especilly, K41 in helix B nd D102 in loop-linking helixes C nd D (the CD loop) re interesting. Their loctions re schemticlly presented in Fig. 1. In AR4, these two residues re replced y E nd K respectively. In this study, we exmined the consequences of muttions of the two residues (K41 nd D102) on the cytoplsmic surfce of BR. A series of point mutnts of BR, including K41E, K41D, D102K, D102E, K41E/ D102K, K41D/D102E re designed nd reported for the first time. Our investigtion indictes tht muttions of these two mino cid residues in the cytoplsmic side sustntilly slow the kinetics of M decy nd proton uptke, ut do not determine the temporl order of proton relese nd uptke. The structurl nd mechnicl implictions of these results re discussed. Mterils nd Methods BR-R 1 M 1 nd AR4-xz515. Nturl Hlocterium slinrum strin R 1 M 1 nd xz515 nd gene engineering strin L33 stndrd procedures 40,41) following previous report. 35) Retinl proteins BR-R 1 M 1 nd AR4-xz515 nd the gene engineering proteins expressed in L33 BR-WT nd other mutnts were isolted. BR-R 1 M 1 ws the only protein in the purple memrne isolted from strin R 1 M 1, nd AR4- xz515 ws the only protein in the clret memrne isolted from strin xz515. The clret memrne contins some crotenoid cterioruerin, which ws hrd to seprte from AR4 y our purifiction method. This Point muttion vi gene engineering. The regents needed for gene engineering, including the restricted nuclese, T4 ligse nd Tq DNA polymerse were purchsed from BioRd (Hercules, CA). The oligonucleotide primers for the mutnts were synthesized nd purified with oligonucleotide purifiction crtridge (OPC) from Applied Biosystems (USA). Gene engineering BR-WT nd mutnt proteins were expressed in H. slinrium strin L33. This stin is negtive for the synthesis of cterio-opsin (op), ut positive for the synthesis of retinl. Expression of the BR mutnt proteins in strin L33 ws done y the method of Ni et l. 44) The expressing plsmid for the K41E mutnt, Lys41 replced y Glu, ws derivtive from plsmid pxlnov-r-op, gift from Dr. Richrd Needlemn. Primer 1: 5 0 -GGATCCGCGTGAA- GATGGGGC-3 0 (BmHI site, underlined); primer 2: 5 0 -AAGCTT- CTAGATCAGTCGCTGG-3 0 (HindIII site, underlined); Primer 3: 5 0 -GCAAAGGAGTTCTACGCCATCACGACGC-3 0 ; nd Primer 4: 5 0 -GTAGAACTCCTTTGCATCTGGGTCCGAG-3 0 were used in order to produce the op gene sequence with K41E. A new 1.2-k DNA sequence ws otined nd, ws nmed op-(k41e), with BmHI nd HindIII sites. After the sequence of the op-(k41e) frgment ws checked, frctions produced y PCR mplifiction were ligted to the psk plsmid nd nlyzed for identifiction. Other point mutnts of BR, including K41D, D102K, D102E, K41E/D102K, nd K41D/D102E, were constructed y the sme method. All of the primers used to construct the mutnts re shown s the primers 3 to 10 in Supplementl Tle S1 (see Biosci. Biotechnol. Biochem. We site) in supporting informtion. The pxlnov-r plsmid does not contin the gene frgment of cterio-opsin in contrst with the pxlnov-r-op plsmid. This plsmid nd the PCR mplified products of the op-(k41e) gene were digested with BmHI nd HindIII restriction enzymes nd ligted together. The trnsformnts grew on pltes contining 1 mg/ml of novoiocin for 2 weeks, nd then were inoculted into liquid culture medium for lrge-scle culture in the presence of 1 mg/ml of novoiocin. The resulting purple memrnes were isolted y the sme procedure s previously. 40,41) Mss spectr. Mss spectr of BR-WT nd the series of mutnts were mesured in mtrix-ssisted lser desorption/ioniztion timeof-flight mss spectrometer (Applied Biosystems Voyger System 4310). The ice-dried protein smples were dissolved with pure cetic cid t concentrtion of 10 mg/ml. Then the mtrix, 2,5-dihydroxyenzoic cid (DHB), ws dissolved with methnol nd chloroform (v/v 2:1) t concentrtion of 10 mg/ml. Finlly, 2 ml of smple solution nd 5 ml of mtrix solution were mixed thoroughly nd dropped on the smple plte for MALDI-TOF mesurement. Circulr dichroism spectr. Circulr dichroism (CD) spectr in the ultrviolent (UV) region were mesured with spectropolrimeter (J- 715; Jsco, Tokyo) t 20 C. The smples were dissolved in Milli-Q wter t concentrtion of 20 mg/ml. The pth length of the mesured cells ws 1 cm. The molr ellipticity (degcm 2 dmol 1 ) ws determined on men-residue sis. Asorption spectr. The sorption spectr of the smples were mesured on Shimdzu UV-3150 spectrophotometer (Shimdzu, Ohtsu, Jpn). For light dpttion, 200 W tungsten lmp with 500 nm cut-off filter ws employed. Drk dpttion of smples ws chieved when necessry t 25 C for 24 h. The rte constnt of drk dpttion ws determined y mesuring the sorption chnges in the light-dpted smples t 570 nm t intervls of 1 min in the drk environment. The curve ws fitted with one-component exponentil decy. Smples were prepred in 0.2 mol/l phosphte uffer sline (PBS) solution t ph 7.0. Flsh-induced photocycle intermedites nd proton pump ehviors. Trces of flsh-induced proton relese nd uptke were detected in spectrophotometer, which we mnufctured in our l. A photoflsh for light-dpted smples ws used for excittion. The M intermedite ws monitored t 412 nm. In order to monitor flshinduced proton relese nd uptke y BR, sorption chnges in the

3 1366 Y. ZHAO et l. ph-sensitive dye pyrnine were detected t 456 nm, t which pyrnine hs mximum sorption while no BR intermedites hve significnt sorption. The signl without pyrnine ws sutrcted from tht with dye. All the mesurements were done t 25 C. Results Identifiction of mutnts The results for gene sequences of the mutnt frgments (Figs. S1 S6 in supporting informtion) nd the mss spectr of the mutnt (Figs. S7 S8) confirmed tht the pre-designed mutnts were successfully otined. The CD spectr of the mutnts in the UV region (Fig. S9) were similr to tht of BR-WT, suggesting tht the secondry structure did not chnge significntly in those mutnts nd confirming tht the mutnts might lso hve seven trnsmemrne -helixes. As the visile sorption spectr in Figs. S10 S11 indicte, the chromophore ws not pertured significntly. The rtes of drk dpttion of the BR mutnts indicte tht the replcements of mino cids t the cytoplsmic side did not significntly ffect the isomeriztion of the retinl chromophore (Fig. S12). Flsh-induced proton pumping nd M formtion nd decy The proton pumping kinetics of the AR4 nd BR nlogs t ph 7.0 re presented in Fig. 2. The smples were suspended in slt solution with 0.1 mol/l of NCl nd 0.02 mol/l of KCl. Proton-pumping ws trced with the ph-sensitive dye pyrnine. An increse in dye sornce t 456 nm reflected proton uptke y the protein, nd decrese in sornce corresponded to proton relese into the medium. As Fig. 2 shows, the BR mutnts exhiited proton-pumping ctivity with proton relese preceding proton uptke, similrly to BR-WT. These results confirm not only tht the mutnt mitined the sic iologicl function s light-driven proton pump, ut lso tht the replcement muttions did not lter the temporl order of proton relese nd uptke. The decrese in the rte of proton uptke presented most prominent in the D102K mutnt, which suggest D102 is involved in this process, perhps cting s proton ntenn in the cytoplsmic side. Flsh-induced chnges in sorption t 412 nm shown in Fig. 2 were due mostly to the M intermedite. The lifetime of M decy of the pigment ws otined y exponentil fitting. The fitting results re summrized in Fig. 3, long with the dely times of proton uptke s clculted y fitting the dt in Fig. 2 sed on single exponentil eqution. The chrcteristic times of M decy nd proton uptke were consistent with ech other. Compred to the wide-type BR, expressed in strin L33, every BR mutnt exhiited slower M decy. Two mutnts, D102K nd K41E/D102K showed 3-fold increses in M lifetime. ph dependence of M decy The kinetics of the M decy of BR-WT nd ll the mutnts were monitored t ph rnge of 4 to 10. As shown in Fig. 4, the M decy of BR-WT ws monophsic t neutrl ph nd ecme iphsic t higher ph, s fitted with two components, fst nd slow. Biphsic Fig. 2. Photoresponse of BR nd Its Mutnts nd of AR4. () Flsh-induced chnges in sorption re indicted y pyrnine t 456 nm. The sorption chnge is due to the trnsient chnge in the medium ph, indicting the time order of proton relese nd uptke of the light-driven proton pumps. () Flsh-induced chnges in sorption t 412 nm representing the M intermedite. In oth () nd (), the mesurements were done t neutrl ph. The titrtion trces were shifted for etter viewing. decy ws lso oserved t ph levels elow 7. The K41E/D102K mutnt exhiited iphsic decy t ll ph levels. The frction of fst M decy in the mutnt ws smller thn in the WT, suggesting tht the muttion on the surfce of the protein hd n effect on the internl proton trnsfer from Asp96 to the Schiff se. Aout 3-fold elongtion of the slow component of M decy in the mutnt ws oserved from ph 4 to 8, ut t higher ph levels the difference with the BR-WT ws smller, indicting the possiility tht it ws cused y the

4 Effects of Muttions of Bcteriorhodopsin 1367 Fig. 5. pk Vlues of D96 in Proteins Expressed in Gene-Engineering Strin L33 s Well s Wild-Type Proteins from Strins R1M1 nd xz515. Vlues were otined y fitting the ph dependence of the mximum light-induced sorption chnge t 660 nm (O intermedite) divided y mximum sorption chnge t 410 nm (M stte) t the corresponding ph y the eqution y ¼ A 1 þða 2 A 1 Þ=½1 þ 10 nðx pkþ Š in the lkline regime, s shown in Fig. S13 in supporting informtion. chrge on Lys-102, which ws deprotonted t higher ph levels. Similr results were found for D102K (Fig. S13). Fig. 3. Histogrm of the Chrcteristic Times of () Proton Uptke nd () M Decy of the BR, BR Mutnts nd AR4 t Neutrl ph. Fig. 4. ph Dependence of M Decy of BR-WT nd Mutnts. () The kinetics of M decy of BR-WT nd its mutnt K41E/ D102K t ph 7.0 nd 10.0; () The lifetime of the M intermedite of BR-WT nd K41E/D102K fitted with i-exponentil eqution. The decy of BR-WT is monophsic, with similr fst nd slow t neutrl ph, while it is iphsic t the other indicted ph levels. K41E/D102K presented iphsic t ll ph levels exmined. ph dependence of the formtion nd decy of the O intermedite (pk of Asp-96) The kinetics of the O formtion nd decy of the BR- WT nd mutnt proteins t neutrl ph mesured t 660 nm re shown in Fig. S14. The ph dependence of the O intermedite ws used to estimte the pk of D96, the internl proton donor to the Schiff se in the photocycle. Figure S15 descries the chnge in mximum sorption t 660 nm reltive to the chnge mximum sorption t 412 nm during the N-to-O process in the photocycle. The trnsition in the cidic ph region corresponded to the lrger ccumultion of the O intermedite long with the decrese in the rte of its decy, nd reflects pk of the PRC in the O intermedite, nd the trnsition in the lkline region ws cused y slowing of proton uptke nd reflected the pk of D96 in the N intermedite. 45) All of the pk vlues in the lkline region of D96 of the AR4, BR- R 1 M 1, BR-WT nd BR mutnts re summrized in Fig. 5. These dt illustrte tht the mount of the O intermedite nd its pk strongly decresed in the K41E/D102K mutnt, consistently with slowing of M decy nd proton uptke in tht mutnt. The pk of PRC in the M intermedite Our group recently developed n efficient photoelectrochemicl pproch 14) to study the ph dependence of proton relese nd uptke of retinl proteins nd to determine the pk of PRC in the photocycles. In this study, we employed this pproch to investigte the BR mutnts. Figure 6 showed photo-response profiles from K41E/D102K film deposited on n ITO electrode in n electrolyte solution of 100 mmol/l NCl nd 20 mmol/l KCl t vrious ph. The mplitude nd polrity of the oserved signls chnged with the medium ph. The signls were negtive t ph levels ove 6, ut ecme positive t ph levels elow 5. A trnsition thus took plce etween 5 nd 6. The ph

5 1368 Y. ZHAO et l. Fig. 7. pk Vlues of PRC in the Indicted Proteins Expressed in Gene-Engineering Strin L33 s Well s Wild-Type Proteins from Strins R1M1 nd xz515. Vlues were otined y fitting the titrtion of the frction of fst proton relese versus medium ph in the photoelectrochemicl pproch with typicl trce, shown in Fig. 6, nd other trces, shown in Fig. S14. All pk vlues in the BR pigments were elow ph 7 (dotted line), while AR4 ws ove tht. Discussion c Fig. 6. Kinetics of Light-Induced Trnsient Potentil Chnges from K41E/D102K Film Deposited on n ITO Electrode nd Mesured in 100 mmol NCl nd 20 mmol KCl nd Estimtion of the pk of the PRC. () Flsh-induced photovoltge under the indicted ph vlues. Just one dt point for every 10 dt points collected is shown, for clrity, in () for ech ph; only five sets of dt re plotted, lthough nine ph conditions were exmined. () The time constnts of proton relese nd uptke t different ph levels otined from the fit. When ph ws elow 6, only proton uptke nd slow relese were oserved. (c) The frction of fst proton relese over ll protons relesed, f, s function of ph to determine the pk of PRC during the photocycle (in the M stte). The dt were fitted with the Henderson- Hssellch eqution, y ¼ A 1 þða 2 A 1 Þ=½1 þ 10 nðx pkþ Š, resulting in pk of 5:2 0:1 (n ¼ 1:3). dependence of the time constnts of proton relese nd uptke re presented in Fig. 6. Bsed on the frction of fst relese t series of ph levels, we determined the pk of PRC of K41E/D102K (Fig. 6c). The photo-response profiles nd the pk of PRC of the other mutnts re presented in Fig. S16 in supporting informtion. Figure 7 summrizes ll the pk vlues of the mutnts of BR nd AR4. The resulting pk vlues of PRC of ll the BR mutnts fter illumintion were lower thn 7, like tht of BR-WT (pk 6.3) nd tht of BR- R 1 M 1 (pk 5.7). Thus the temporl order of proton relese nd uptke of mutnts t neutrl ph were the sme s tht of BR-WT. Our mutgenesis of K41 nd D102 in BR ws initilly done to interpret the reversed time order of proton relese nd uptke of AR4. Govindjee et l. found tht muttion of surfce residue, Lys-129 of BR, on the extrcellulr side reversed the temporl sequence of proton relese nd uptke, 46) nd thus the replcement of one chrged residue might lter the time order. Hence, we devoted ttention to chrged residues on the cytoplsmic side where proton is tken up in the photocycle. Two chrged residues, K41 nd D102, which re different etween BR nd AR4, ecme cndidtes. The present study rules out the possiility tht mino cids Lys41 nd Asp102 re determinnts of the time order of proton relese nd uptke. The residues determining the different time orders of proton relese nd uptke ( much higher pk for PRC in rcherhodopsin 14) ) remin to e identified, nd further exmintion is clled for. Although mutgenesis did not reverse the order of proton relese nd uptke, the replcements resulted in significnt chnges in certin photo-response properties of BR, including the decy time of the M intermedite, the time constnt of proton uptke, nd the proton ffinity of D96 in the photocycle. As shown in Fig. 3, M-intermedite decy ws out 3-fold slowed down in D102K nd the corresponding doule mutnt K41E/ D102K, s compred to BR-WT. Thus, the replcement of Asp t site 102 with Lys ffected the efficiency of proton collection from the cytoplsmic surfce. This is especilly interesting considering tht D102 is locted in the CD loop. Our results gree with those of Riesle et l., 33) who proposed tht polr or chrged residues on the cytoplsmic side of BR might prticipte in or ffect re-protontion of the Schiff se nd proton uptke. In their studies, M decy ws prolonged strongly y the mutnt of D 2 102,104R 2, in which two sprttes were replced y rginines. 33,47) However, nother group found tht replcement of D102 with neutrl Asn did not cuse sustntil chnges, nd hence questioned the role of this Asp residue in proton collection. 48) Due to

6 our novel muttions, the pk of D96 of BR-WT decresed from 7.9 to D102K (6.5) nd K41E/D102K (6.9) (Fig. 5). The lowered pk of D96 pprently wekens the ssocition of proton with sprtic cid, especilly t ph levels higher thn tht of pk. Proton trnsfer from the cytoplsmic surfce to D96 ws 3-fold slowed t ph levels elow 9, which is consistent with the slowing of the decy of M intermedite, since it is in equilirium with the N intermedite. The decy of the ltter is strightforwrdly relted to proton uptke. 6) Thus, the present study suggests tht the cidic 102 site of BR is involved in the process of proton uptke from the cytoplsmic side nd dontion of it to Asp96, since replcement of Asp102 with Lys interfered with de-protontion nd re-protontion of Asp96, nd even with re-protontion of the Schiff se. Using the photoelectrochemicl pproch recently developed y us, 14) the pk vlues of the PRC of BR mutnts fter illumintion were mesured. While the muttion t the cytoplsmic side might hve distured the chrge distriution of the cytoplsmic surfce of BR nd hve influenced the pk of PRC, the vlues were still fr lower thn tht of AR4. Hence those muttions of BR do not led to the reversed time order of proton relese nd uptke. In summry, we performed gene engineering on BR nd exmined the effects of the K41 nd D102 muttions on the functions of the light-driven proton pump. These replcements did not lter the sic sptil structure of the protein, nd the chrged mino cids ffected proton uptke on the cytoplsmic side. Hence the two residues re not key to the temporl order of proton relese nd uptke of BR nd AR4. Nevertheless, these replcements influenced the photocycle y ffecting the proton ffinity of D96 nd the rte of proton delivery to it through the proton chnnel. The mutnts contining D102K prolonged the lifetime of the M intermedite out 3-fold. They were intended to mke the cytoplsmic surfce of BR more similr to tht of AR, ut the results did not show erlier M decy or proton uptke, which re chrcteristic of AR. On the contrry, the rtes of these processes were slowed in the muttions. Acknowledgments This study ws supported in prt y the Chinese Ministry of Science nd Technology (973 Progrm no. 2009CB930000), Nturl Science Foundtion of Chin (Grnt no ). We thnk Professor Richrd Needlemn of Wyne Stte University for providing plsmid pnov-r-mi-ni nd Hlocterium slinrum strin L33. A criticl reding of the mnuscript y Dr. Sergei Blshov (University of Cliforni, Irvine) is sincerely pprecited. References 1) Oesterhelt D nd Stoeckenius W, Nt. New Biol., 233, (1971). 2) Lozier RH, Bogomolni RA, nd Stoeckenius W, Biophys. J., 15, (1975). 3) Erey TG, Light Energy Trnsduction in Bcteriorhodopsin, ed. Jcksson MB, CRC Press, Boc Rton, pp (1993). 4) Luecke H, Schoert B, Richter HT, Crtiller JP, nd Lnyi JK, Science, 286, (1999). Effects of Muttions of Bcteriorhodopsin ) Luecke H, Schoert B, Richter HT, Crtiller JP, nd Lnyi JK, J. Mol. Biol., 291, (1999). 6) Blshov SP, Biochim. Biophys. Act Bioenerg., 1460, (2000). 7) Brown LS, Biochemistry (Mosc), 66, (2001). 8) Lnyi JK, Annu. Rev. Physiol., 66, (2004). 9) Ghimire GD, Sugiym H, Sonoym M, nd Mitku S, Biosci. Biotechnol. Biochem., 69, (2005). 10) Sugiym H, Sonoym M, Ghimire GD, nd Mitku S, Biosci. Biotechnol. Biochem., 70, (2006). 11) Ritter E, Elgeti M, nd Brtl FJ, Photochem. Photoiol., 84, (2008). 12) Morgn JE, Gennis RB, nd Med A, Photochem. Photoiol., 84, (2008). 13) Shikmi M, Tsuihiji H, Miyoshi S, Nkmur M, Goto R, Mitku S, nd Sonoym M, Biosci. Biotechnol. Biochem., 72, (2008). 14) Wu J, M DW, Wng YZ, Ming M, Blshov SP, nd Ding JD, J. Phys. Chem. B, 113, (2009). 15) M DW, Zho YC, Wu J, Cui T, nd Ding JD, Soft Mtter, 5, (2009). 16) M DW, Wng YZ, Wu J, Zho YC, Ming M, nd Ding JD, Soft Mtter, 6, (2010). 17) Chu LK nd El-Syed MA, Photochem. Photoiol., 86, (2010). 18) Morgn JE, Vkksoglu AS, Lnyi JK, Gennis RB, nd Med A, Biochemistry, 49, (2010). 19) Liu SY, Biophys. J., 57, (1990). 20) Heerle J nd Dencher NA, Proc. Ntl. Acd. Sci. USA, 89, (1992). 21) Co Y, Brown LS, Sski J, Med A, Needlemn R, nd Lnyi JK, Biophys. J., 68, (1995). 22) Co Y, Brown LS, Needlemn R, nd Lnyi JK, Biochemistry, 32, (1993). 23) Dioumev AK, Brown LS, Needlemn R, nd Lnyi JK, Biochemistry, 40, (2001). 24) Kunkel TA, Roerts JD, nd Zkour RA, Methods Enzymol., 154, (1987). 25) Seki T, Mizushim S, Ued K, Iwmi K, nd Knmoto R, Biosci. Biotechnol. Biochem., 73, (2009). 26) Mench E, Ysukw K, nd Inouye K, Biosci. Biotechnol. Biochem., 74, (2010). 27) Lu M, Blshov SP, Erey TG, Chen N, Chen YM, Menick DR, nd Crouch RK, Biochemistry, 39, (2000). 28) Dioumev AK, Richter HT, Brown LS, Tnio M, Tuzi S, Sito H, Kimur Y, Needlemn R, nd Lnyi JK, Biochemistry, 37, (1998). 29) Wolf S, Freier E, Potschies M, Hofmnn E, nd Gerwert K, Angew. Chem. Int. Ed., 49, (2010). 30) Stern LJ, Ahl PL, Mrti T, Mogi T, Dunch M, Berkowitz S, Rothschild KJ, nd Khorn HG, Biochemistry, 28, (1989). 31) Mogi T, Stern LJ, Mrti T, Cho BH, nd Khorn HG, Proc. Ntl. Acd. Sci. USA, 85, (1988). 32) Checover S, Nchliel E, Dencher NA, nd Gutmn M, Biochemistry, 36, (1997). 33) Riesle J, Oesterhelt D, Dencher NA, nd Heerle J, Biochemistry, 35, (1996). 34) Checover S, Mrntz Y, Nchliel E, Gutmn M, Pfeiffer M, Tittor J, Oesterhelt D, nd Dencher NA, Biochemistry, 40, (2001). 35) Li QG, Sun QG, Zho W, Wng H, nd Xu DQ, Biochim. Biophys. Act Biomemr., 1466, (2000). 36) Wng H, Zhn SX, Sun QG, Xu DQ, Zho W, Hung WD, nd Li QG, Chin. Sci. Bull., 45, (2000). 37) Ming M, Lu M, Blshov SP, Erey TG, Li QG, nd Ding JD, Biophys. J., 90, (2006). 38) Ming M, Wng YZ, Wu J, M DW, Li QG, nd Ding JD, FEBS Lett., 580, (2006). 39) Wu J, Hung L, Liu J, Ming M, Li QG, nd Ding JD, Chin. J. Chem., 23, (2005). 40) Oesterhelt D nd Stoeckenius W, Methods Enzymol., 31, (1974).

7 1370 Y. ZHAO et l. 41) Becher BM nd Cssim JY, Prep. Biochem., 5, (1975). 42) Mukoht Y, Sugiym Y, Ihr K, nd Yoshid M, Biochem. Biophys. Res. Commun., 151, (1988). 43) Lukshev EP, Govindjee R, Kono M, Erey TG, Sugiym Y, nd Mukoht Y, Photochem. Photoiol., 60, (1994). 44) Ni B, Chng M, Duschl A, Lnyi J, nd Needlemn R, Gene, 90, (1990). 45) Blshov SP, Lu M, Imshev ES, Govindjee R, Erey TG, Othersen B, Chen YM, Crouch RK, nd Menick DR, Biochemistry, 38, (1999). 46) Govindjee R, Imshev ES, Misr S, Blshov SP, Erey TG, Chen N, Menick DR, nd Crouch RK, Biophys. J., 72, (1997). 47) Riesle J, Heerle J, Oesterhelt D, nd Dencher NA, Biophys. J., 70, 545 (1996). 48) Brown LS, Needlemn R, nd Lnyi JK, Biochemistry, 38, (1999).

The influence of the halide ions on the photochemical reaction cycle of pharaonis halorhodopsin

The influence of the halide ions on the photochemical reaction cycle of pharaonis halorhodopsin Journl of Photochemistry nd Photoiology B: Biology 82 (26) 16 2 www.elsevier.com/locte/jphotoiol The influence of the hlide ions on the photochemicl rection cycle of phronis hlorhodopsin Klár Mgyri, Vioric

More information

6. Photoionization of acridine through singlet and triplet channels

6. Photoionization of acridine through singlet and triplet channels Chpter 6: Photoioniztion of cridine through singlet nd triplet chnnels 59 6. Photoioniztion of cridine through singlet nd triplet chnnels Photoioinztion of cridine (Ac) in queous micelles hs not yet een

More information

Rates of chemical reactions

Rates of chemical reactions Rtes of chemicl rections Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) 2 5 2 2 n(1 α) 2αn

More information

Fundamentals of Analytical Chemistry

Fundamentals of Analytical Chemistry Homework Fundmentls of nlyticl hemistry hpter 9 0, 1, 5, 7, 9 cids, Bses, nd hpter 9(b) Definitions cid Releses H ions in wter (rrhenius) Proton donor (Bronsted( Lowry) Electron-pir cceptor (Lewis) hrcteristic

More information

Interpreting Integrals and the Fundamental Theorem

Interpreting Integrals and the Fundamental Theorem Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of

More information

Supplementary Information

Supplementary Information Supplementry Informtion Spontneously mplified homochirl orgnic-inorgnic nno-helix complex vi self-prolifertion Hlei Zhi, Yn Qun, Li Li, Xing-Yng Liu, Xurong Xu c nd Ruikng Tng*,c Centre for Biomterils

More information

Charge Motion during the Photocycle of Bacteriorhodopsin

Charge Motion during the Photocycle of Bacteriorhodopsin Biochemistry (Moscow), Vol. 66, No. 11, 21, pp. 1234-1248. Trnslted from Biokhimiy, Vol. 66, No. 11, 21, pp. 1527-1545. Originl Russin Text Copyright 21 y Dér, Keszthelyi. REVIEW Chrge Motion during the

More information

2.4 Linear Inequalities and Interval Notation

2.4 Linear Inequalities and Interval Notation .4 Liner Inequlities nd Intervl Nottion We wnt to solve equtions tht hve n inequlity symol insted of n equl sign. There re four inequlity symols tht we will look t: Less thn , Less thn or

More information

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA Hrris: Quntittive Chemicl Anlysis, Eight Edition CHAPTER 08: MONOPROTIC ACIDBASE EQUILIBRIA CHAPTER 08: Opener A CHAPTER 08: Opener B CHAPTER 08: Opener C CHAPTER 08: Opener D CHAPTER 08: Opener E Chpter

More information

Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION

Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Purpose: Prt I: The cid ioniztion constnt of wek cid is to be determined, nd the cid is identified ccordingly.

More information

Physics 1402: Lecture 7 Today s Agenda

Physics 1402: Lecture 7 Today s Agenda 1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls:

More information

Section 4: Integration ECO4112F 2011

Section 4: Integration ECO4112F 2011 Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic

More information

Supplementary Material (ESI) for Soft Matter This journal is The Royal Society of Chemistry Supplementary data

Supplementary Material (ESI) for Soft Matter This journal is The Royal Society of Chemistry Supplementary data Supplementry Mteril (ESI) for Soft Mtter This journl is The Royl Society of hemistry 009 Supplementry dt Quntifying Hydrogel Response using Lser Light Scttering. Joshu M. G. Swnn, Wim Brs b, Jonthn R.

More information

u( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.

u( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph. nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $

More information

An Overview of Integration

An Overview of Integration An Overview of Integrtion S. F. Ellermeyer July 26, 2 The Definite Integrl of Function f Over n Intervl, Suppose tht f is continuous function defined on n intervl,. The definite integrl of f from to is

More information

Section 6.1 INTRO to LAPLACE TRANSFORMS

Section 6.1 INTRO to LAPLACE TRANSFORMS Section 6. INTRO to LAPLACE TRANSFORMS Key terms: Improper Integrl; diverge, converge A A f(t)dt lim f(t)dt Piecewise Continuous Function; jump discontinuity Function of Exponentil Order Lplce Trnsform

More information

Supplementary Information

Supplementary Information Supplementry Informtion Lignd exchnge triggered controlled-relese trgeted drug delivery system sed on core shell superprmgnetic mesoporous microspheres cpped with nnoprticles Zhogng Teng, Xingng Zhu, Gengfeng

More information

Organic Acids - Carboxylic Acids

Organic Acids - Carboxylic Acids Orgnic Acids - rboxylic Acids Orgnic cids - crboxylic cid functionl group rboxylic cids re redily deprotonted by bses such s NO eg 3 O O - + O - + O 3 O O Acid Bse onjugte Bse onjugte Acid This rection

More information

The development of nanoscale morphology in polymer:fullerene. photovoltaic blends during solvent casting

The development of nanoscale morphology in polymer:fullerene. photovoltaic blends during solvent casting Supplementry informtion Supplementry Mteril (ES) for Soft Mtter The development of nnoscle morphology in polymer:fullerene photovoltic lends during solvent csting To Wng, * Aln D. F. Dunr, Pul A. Stniec,

More information

Math 42 Chapter 7 Practice Problems Set B

Math 42 Chapter 7 Practice Problems Set B Mth 42 Chpter 7 Prctice Problems Set B 1. Which of the following functions is solution of the differentil eqution dy dx = 4xy? () y = e 4x (c) y = e 2x2 (e) y = e 2x (g) y = 4e2x2 (b) y = 4x (d) y = 4x

More information

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:

More information

The Influence of Interface and Semiconductor Bulk Traps Generated Under HEFS on MOSFET`s Electrical Characteristics

The Influence of Interface and Semiconductor Bulk Traps Generated Under HEFS on MOSFET`s Electrical Characteristics Proceedings of the 5th Smll Systems Simultion Symposium 2014, Niš, Seri, 12th-14th Ferury 2014 The Influence of Interfce nd Semiconductor Bulk Trps Generted Under HEFS on MOSFET`s Electricl Chrcteristics

More information

High-Resolution Spectrum of the 3n 1 Band of Cyanoacetylene Obtained via Infrared/Infrared Double Resonance

High-Resolution Spectrum of the 3n 1 Band of Cyanoacetylene Obtained via Infrared/Infrared Double Resonance JOURNAL OF MOLECULAR SPECTROSCOPY 175, 198 202 (1996) ARTICLE NO. 0022 High-Resolution Spectrum of the 3n 1 Bnd of Cynocetylene Otined vi Infrred/Infrred Doule Resonnce Jon E. Gmogi, 1 Erik R. Th. Kerstel,

More information

BME 207 Introduction to Biomechanics Spring 2018

BME 207 Introduction to Biomechanics Spring 2018 April 6, 28 UNIVERSITY O RHODE ISAND Deprtment of Electricl, Computer nd Biomedicl Engineering BME 27 Introduction to Biomechnics Spring 28 Homework 8 Prolem 14.6 in the textook. In ddition to prts -e,

More information

CS12N: The Coming Revolution in Computer Architecture Laboratory 2 Preparation

CS12N: The Coming Revolution in Computer Architecture Laboratory 2 Preparation CS2N: The Coming Revolution in Computer Architecture Lortory 2 Preprtion Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes

More information

( ) as a fraction. Determine location of the highest

( ) as a fraction. Determine location of the highest AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if

More information

Energy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene

Energy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene Force (kcl mol -1 Å -1 ) Energy (kcl mol -1 ) 3 1-1 - -3 Mixed Mo-only S-only Grphene 6 5 3 1 Mixed Mo-only S-only Grphene - -1-1 1 Pore xis (Å) -1 1 Pore xis (Å) Supplementry Figure 1 Energy Brriers.

More information

Section 6.1 INTRO to LAPLACE TRANSFORMS

Section 6.1 INTRO to LAPLACE TRANSFORMS Section 6. INTRO to LAPLACE TRANSFORMS Key terms: Improper Integrl; diverge, converge A A f(t)dt lim f(t)dt Piecewise Continuous Function; jump discontinuity Function of Exponentil Order Lplce Trnsform

More information

AB Calculus Review Sheet

AB Calculus Review Sheet AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is

More information

Chapter 9 Definite Integrals

Chapter 9 Definite Integrals Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished

More information

Problem 22: Buffer solutions 1. The equilibrium, which governs the concentration of H + within the solution is HCOOH! HCOO + H + + Hence K

Problem 22: Buffer solutions 1. The equilibrium, which governs the concentration of H + within the solution is HCOOH! HCOO + H + + Hence K Problem : Buffer solutions. The equilibrium, hich governs the concentrtion of H ithin the solution is HCOOH! HCOO H [HCOO ] 4 Hence. [HCOOH] nd since [HCOOH] 0.00 M nd [HCOO ] 0.50 M -4 0.00 4..8 M 0.50

More information

west (mrw3223) HW 24 lyle (16001) 1

west (mrw3223) HW 24 lyle (16001) 1 west (mrw3223) HW 24 lyle (16001) 1 This print-out should hve 30 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Reding ssignment: Hecht, sections

More information

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x). AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f

More information

Examples Using both 2-D sections from Figure 3, data has been modeled for (acoustic) P and (elastic) S wave field

Examples Using both 2-D sections from Figure 3, data has been modeled for (acoustic) P and (elastic) S wave field Suslt illumintion studies through longitudinl nd trnsversl wve propgtion Riz Ali *, Jn Thorecke nd Eric Verschuur, Delft University of Technology, The Netherlnds Copyright 2007, SBGf - Sociedde Brsileir

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION doi:.38/nture8499 doi:.38/nture8499 5 6 5 4.5 Firing rte (Hz) -67-65 -66-6 -58 V m (mv) -7-67 -68-66 -64 c Thet power (mv ) -73-69 -7-7 -7.5.8 3....9.9.4.6.6. 9 8 9 8 9 8 9 8 9 8 Supplementry Figure Firing

More information

Method of Localisation and Controlled Ejection of Swarms of Likely Charged Particles

Method of Localisation and Controlled Ejection of Swarms of Likely Charged Particles Method of Loclistion nd Controlled Ejection of Swrms of Likely Chrged Prticles I. N. Tukev July 3, 17 Astrct This work considers Coulom forces cting on chrged point prticle locted etween the two coxil,

More information

4.4 Areas, Integrals and Antiderivatives

4.4 Areas, Integrals and Antiderivatives . res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order

More information

Homework Assignment 3 Solution Set

Homework Assignment 3 Solution Set Homework Assignment 3 Solution Set PHYCS 44 6 Ferury, 4 Prolem 1 (Griffiths.5(c The potentil due to ny continuous chrge distriution is the sum of the contriutions from ech infinitesiml chrge in the distriution.

More information

Acceptance Sampling by Attributes

Acceptance Sampling by Attributes Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire

More information

Section 6: Area, Volume, and Average Value

Section 6: Area, Volume, and Average Value Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find

More information

The Minimum Label Spanning Tree Problem: Illustrating the Utility of Genetic Algorithms

The Minimum Label Spanning Tree Problem: Illustrating the Utility of Genetic Algorithms The Minimum Lel Spnning Tree Prolem: Illustrting the Utility of Genetic Algorithms Yupei Xiong, Univ. of Mrylnd Bruce Golden, Univ. of Mrylnd Edwrd Wsil, Americn Univ. Presented t BAE Systems Distinguished

More information

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph?

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph? 95. Which of the following descries the net ionic rection for the hydrolysis of NH4Cl( s)? A. NH4 ( q) Cl & ( q) NH4Cl( s) B. NH Cl & 4 ( s) NH4 ( q) Cl ( q) C. Cl ( q) H O & 2 ( l) HCl( q) OH ( q) D.

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION DOI: 1.138/NMAT3984 Supplementry Informtion for Improved performnce nd stility in quntum dot solr cells through nd lignment engineering Chi- Ho M. Chung 1, Ptrick R. Brown 2, Vldimir Bulović 3 & Moungi

More information

Partial Derivatives. Limits. For a single variable function f (x), the limit lim

Partial Derivatives. Limits. For a single variable function f (x), the limit lim Limits Prtil Derivtives For single vrible function f (x), the limit lim x f (x) exists only if the right-hnd side limit equls to the left-hnd side limit, i.e., lim f (x) = lim f (x). x x + For two vribles

More information

Module 2: Rate Law & Stoichiomtery (Chapter 3, Fogler)

Module 2: Rate Law & Stoichiomtery (Chapter 3, Fogler) CHE 309: Chemicl Rection Engineering Lecture-8 Module 2: Rte Lw & Stoichiomtery (Chpter 3, Fogler) Topics to be covered in tody s lecture Thermodynmics nd Kinetics Rection rtes for reversible rections

More information

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 20: Second Law of Thermodynamics CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het

More information

10 Vector Integral Calculus

10 Vector Integral Calculus Vector Integrl lculus Vector integrl clculus extends integrls s known from clculus to integrls over curves ("line integrls"), surfces ("surfce integrls") nd solids ("volume integrls"). These integrls hve

More information

Linear Systems with Constant Coefficients

Linear Systems with Constant Coefficients Liner Systems with Constnt Coefficients 4-3-05 Here is system of n differentil equtions in n unknowns: x x + + n x n, x x + + n x n, x n n x + + nn x n This is constnt coefficient liner homogeneous system

More information

temperature is known as ionic product of water. It is designated as K w. Value of K w

temperature is known as ionic product of water. It is designated as K w. Value of K w Ionic product of ter The product of concentrtions of H nd OH ions in ter t prticulr temperture is knon s ionic product of ter. It is designted s K. H O H 1 OH ; H 57.3 kjm The vlue of [H ][OH ] K ; K[HO]

More information

Strong acids and bases. Strong acids and bases. Systematic Treatment of Equilibrium & Monoprotic Acid-base Equilibrium.

Strong acids and bases. Strong acids and bases. Systematic Treatment of Equilibrium & Monoprotic Acid-base Equilibrium. Strong cids nd bses Systemtic Tretment of Equilibrium & Monoprotic cid-bse Equilibrium onc. (M) 0.0.00 -.00-5.00-8 p Strong cids nd bses onc. (M) p 0.0.0.00 -.0.00-5 5.0.00-8 8.0? We hve to consider utoprotolysis

More information

3.94 ± 0.50 (95% CI) Correlative inhibition index (slope)

3.94 ± 0.50 (95% CI) Correlative inhibition index (slope) Supplementl Tle S. Selected rchitecturl prmeters of phy nd phyphy grown under. Vlues re mens ± SE, except for predicted primry rosette rnches where the vlues re the men with the ssocited 9% confidence

More information

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0) 1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this

More information

Experiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION

Experiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Experiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Purpose: Prt I: The cid ioniztion constnt of wek cid is to be determined, nd the cid is identified ccordingly. Prt II: The

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION DOI: 10.1038/NCHEM.2398 Locl virtionl coherences drive the primry photochemistry of vision Philip J. M. Johnson 1, Alexei Hlpin 1, Tkefumi Morizumi 2, Vlentyn I. Prokhorenko 3, Oliver P. Ernst 2,4, & R.

More information

Silicon Nanowire Based Single-Molecule SERS Sensor

Silicon Nanowire Based Single-Molecule SERS Sensor Supporting informtion Silicon Nnowire Bsed Single-Molecule SERS Sensor Hui Wng, Xuemei Hn, Xuemei Ou, Chun-Sing Lee, Xiohong Zhng* nd Shuit-Tong Lee S1, A series of Si nnowires coted with compct ggregtes

More information

Strategy: Use the Gibbs phase rule (Equation 5.3). How many components are present?

Strategy: Use the Gibbs phase rule (Equation 5.3). How many components are present? University Chemistry Quiz 4 2014/12/11 1. (5%) Wht is the dimensionlity of the three-phse coexistence region in mixture of Al, Ni, nd Cu? Wht type of geometricl region dose this define? Strtegy: Use the

More information

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs MATHS NOTES The Institute of Eduction 06 SUBJECT: Mths LEVEL: Higher TEACHER: Aidn Rontree Topics Covered: Powers nd Logs About Aidn: Aidn is our senior Mths techer t the Institute, where he hs been teching

More information

XX-th ARS SEPARATORIA Szklarska Poręba, Poland 2005

XX-th ARS SEPARATORIA Szklarska Poręba, Poland 2005 XX-th ARS SEPARATORIA Szklrsk Porę, Polnd 25 DIALYSIS OF METAL IONS THROUGH ULTRAFILTRATION POLYSULFONE MEMBRANES ENHANCED BY POLY(ACRYLIC ACID) Gryzeld POŹNIAK Wroclw University of Technology, Deprtment

More information

Diverse modes of eco-evolutionary dynamics in communities of antibiotic-producing microorganisms

Diverse modes of eco-evolutionary dynamics in communities of antibiotic-producing microorganisms In the formt provided y the uthors nd unedited. ULEMENTAY INFOMATION VOLUME: 1 ATICLE NUMBE: 0189 iverse modes of eco-evolutionry dynmics in communities of ntiiotic-producing microorgnisms Klin Vetsigin

More information

0.1 THE REAL NUMBER LINE AND ORDER

0.1 THE REAL NUMBER LINE AND ORDER 6000_000.qd //0 :6 AM Pge 0-0- CHAPTER 0 A Preclculus Review 0. THE REAL NUMBER LINE AND ORDER Represent, clssify, nd order rel numers. Use inequlities to represent sets of rel numers. Solve inequlities.

More information

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?

How do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique? XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk out solving systems of liner equtions. These re prolems tht give couple of equtions with couple of unknowns, like: 6= x + x 7=

More information

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS MOLECULAR PHYSICS REPORTS 0 (00) 8-86 STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/ x Fe! x MULTILAYERS P. WANDZIUK, M. KOPCEWICZ, B. SZYMAŃSKI, AND T. LUCIŃSKI Institute of Moleculr Physics, Polish Acdemy

More information

Genetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary

Genetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary Outline Genetic Progrmming Evolutionry strtegies Genetic progrmming Summry Bsed on the mteril provided y Professor Michel Negnevitsky Evolutionry Strtegies An pproch simulting nturl evolution ws proposed

More information

LINEAR ALGEBRA APPLIED

LINEAR ALGEBRA APPLIED 5.5 Applictions of Inner Product Spces 5.5 Applictions of Inner Product Spces 7 Find the cross product of two vectors in R. Find the liner or qudrtic lest squres pproimtion of function. Find the nth-order

More information

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus

7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus 7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e

More information

10.2 The Ellipse and the Hyperbola

10.2 The Ellipse and the Hyperbola CHAPTER 0 Conic Sections Solve. 97. Two surveors need to find the distnce cross lke. The plce reference pole t point A in the digrm. Point B is meters est nd meter north of the reference point A. Point

More information

Chapter 6 Techniques of Integration

Chapter 6 Techniques of Integration MA Techniques of Integrtion Asst.Prof.Dr.Suprnee Liswdi Chpter 6 Techniques of Integrtion Recll: Some importnt integrls tht we hve lernt so fr. Tle of Integrls n+ n d = + C n + e d = e + C ( n ) d = ln

More information

Designing Information Devices and Systems I Spring 2018 Homework 8

Designing Information Devices and Systems I Spring 2018 Homework 8 EECS 16A Designing Informtion Devices nd Systems I Spring 2018 Homework 8 This homework is due Mrch 19, 2018, t 23:59. Self-grdes re due Mrch 22, 2018, t 23:59. Sumission Formt Your homework sumission

More information

Note 12. Introduction to Digital Control Systems

Note 12. Introduction to Digital Control Systems Note Introduction to Digitl Control Systems Deprtment of Mechnicl Engineering, University Of Ssktchewn, 57 Cmpus Drive, Ssktoon, SK S7N 5A9, Cnd . Introduction A digitl control system is one in which the

More information

Chapter 17: Additional Aspects of Aqueous Equilibria

Chapter 17: Additional Aspects of Aqueous Equilibria 1 Chpter 17: Additionl Aspects of Aqueous Equilibri Khoot! 1. Adding Br to sturted queous solution of decreses its solubility in wter. BSO 4, Li CO 3, PbS, AgBr. Which of the following mitures could be

More information

Role of Missing Carotenoid in Reducing the Fluorescence of Single Monomeric Photosystem II Core Complexes

Role of Missing Carotenoid in Reducing the Fluorescence of Single Monomeric Photosystem II Core Complexes Electronic Supplementry Mteril (ESI for Physicl Chemistry Chemicl Physics. This journl is the Owner Societies 017 Supporting Informtion Role of Missing Crotenoid in Reducing the Fluorescence of Single

More information

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses

More information

This chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2

This chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2 1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion

More information

SUMMER KNOWHOW STUDY AND LEARNING CENTRE

SUMMER KNOWHOW STUDY AND LEARNING CENTRE SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18

More information

Review of Probability Distributions. CS1538: Introduction to Simulations

Review of Probability Distributions. CS1538: Introduction to Simulations Review of Proility Distriutions CS1538: Introduction to Simultions Some Well-Known Proility Distriutions Bernoulli Binomil Geometric Negtive Binomil Poisson Uniform Exponentil Gmm Erlng Gussin/Norml Relevnce

More information

dx dt dy = G(t, x, y), dt where the functions are defined on I Ω, and are locally Lipschitz w.r.t. variable (x, y) Ω.

dx dt dy = G(t, x, y), dt where the functions are defined on I Ω, and are locally Lipschitz w.r.t. variable (x, y) Ω. Chpter 8 Stility theory We discuss properties of solutions of first order two dimensionl system, nd stility theory for specil clss of liner systems. We denote the independent vrile y t in plce of x, nd

More information

Acid-Base Equilibria

Acid-Base Equilibria Tdeusz Górecki Ionic Equiliri Acid-Bse Equiliri Brønsted-Lory: n cid is proton, se is. Acid Bse ( 3 PO 4, O), ( N 4 ) nd ( PO - 4 ) cn ll ehve s cids. Exmple: 4 N N3 Sustnces hich cn ehve oth s cids nd

More information

7/19/2011. Models of Solution Chemistry- III Acids and Bases

7/19/2011. Models of Solution Chemistry- III Acids and Bases Models of Solution Chemistry- III Acids nd Bses Ionic Atmosphere Model : Revisiting Ionic Strength Ionic strength - mesure of totl concentrtion of ions in the solution Chpter 8 1 2 i μ ( ) 2 c i z c concentrtion

More information

Exponentials & Logarithms Unit 8

Exponentials & Logarithms Unit 8 U n i t 8 AdvF Dte: Nme: Eponentils & Logrithms Unit 8 Tenttive TEST dte Big ide/lerning Gols This unit begins with the review of eponent lws, solving eponentil equtions (by mtching bses method nd tril

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

ANSWERS TO REVIEW PROBLEM SET CH F

ANSWERS TO REVIEW PROBLEM SET CH F ANSWERS T REVIEW PRBLEM SET C41-018F [1] () The chirl isomer is stilized y intrmoleculr hydrogen onding etween the two guche groups. Such n rrngement lso keeps the ulky tert-utyl groups frther prt s they

More information

Cu 3 (PO 4 ) 2 (s) 3 Cu 2+ (aq) + 2 PO 4 3- (aq) circle answer: pure water or Na 3 PO 4 solution This is the common-ion effect.

Cu 3 (PO 4 ) 2 (s) 3 Cu 2+ (aq) + 2 PO 4 3- (aq) circle answer: pure water or Na 3 PO 4 solution This is the common-ion effect. CHEM 1122011 NAME: ANSWER KEY Vining, Exm # SHORT ANSWER QUESTIONS ============= 4 points ech ============ All work must be shown. 1. Wht re [H O ] nd [OH ] for solution tht hs ph of 9.0? Choose one. ()

More information

Quantum Nonlocality Pt. 2: No-Signaling and Local Hidden Variables May 1, / 16

Quantum Nonlocality Pt. 2: No-Signaling and Local Hidden Variables May 1, / 16 Quntum Nonloclity Pt. 2: No-Signling nd Locl Hidden Vriles My 1, 2018 Quntum Nonloclity Pt. 2: No-Signling nd Locl Hidden Vriles My 1, 2018 1 / 16 Non-Signling Boxes The primry lesson from lst lecture

More information

Conservation Law. Chapter Goal. 5.2 Theory

Conservation Law. Chapter Goal. 5.2 Theory Chpter 5 Conservtion Lw 5.1 Gol Our long term gol is to understnd how mny mthemticl models re derived. We study how certin quntity chnges with time in given region (sptil domin). We first derive the very

More information

ANALYSIS OF FAST REACTORS SYSTEMS

ANALYSIS OF FAST REACTORS SYSTEMS ANALYSIS OF FAST REACTORS SYSTEMS M. Rghe 4/7/006 INTRODUCTION Fst rectors differ from therml rectors in severl spects nd require specil tretment. The prsitic cpture cross sections in the fuel, coolnt

More information

AN IMPROVED SMALL CLOSED DRIFT THRUSTER WITH BOTH CONDUCTING AND DIELECT RIC CHANNELS

AN IMPROVED SMALL CLOSED DRIFT THRUSTER WITH BOTH CONDUCTING AND DIELECT RIC CHANNELS AN IMPROVED SMALL CLOSED DRIFT THRUSTER WITH BOTH CONDUCTING AND DIELECT RIC CHANNELS A.I.Bugrov, A.D.Desitskov, H.R.Kufmn, V.K.Khrchevnikov, A.I.Morozov c, V.V.Zhurin d Moscow Institute of Rdioelectronics,

More information

Period #2 Notes: Electronic Structure of Atoms

Period #2 Notes: Electronic Structure of Atoms Period # Notes: Electronic Structure of Atoms The logicl plce (for civil engineers) to begin in describing mterils is t the tomic scle. The bsic elements of the tom re the proton, the neutron, nd the electron:

More information

p-adic Egyptian Fractions

p-adic Egyptian Fractions p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction

More information

MA 15910, Lessons 2a and 2b Introduction to Functions Algebra: Sections 3.5 and 7.4 Calculus: Sections 1.2 and 2.1

MA 15910, Lessons 2a and 2b Introduction to Functions Algebra: Sections 3.5 and 7.4 Calculus: Sections 1.2 and 2.1 MA 15910, Lessons nd Introduction to Functions Alger: Sections 3.5 nd 7.4 Clculus: Sections 1. nd.1 Representing n Intervl Set of Numers Inequlity Symol Numer Line Grph Intervl Nottion ) (, ) ( (, ) ]

More information

UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY. CH237 - Chemical Thermodynamics and Kinetics. Tutorial Sheet VIII

UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY. CH237 - Chemical Thermodynamics and Kinetics. Tutorial Sheet VIII UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY CH237 - Chemicl Thermodynmics nd Kinetics Tutoril Sheet VIII 1 () (i) The rte of the rection A + 2B 3C + D ws reported s 1.0 mol L -1 s -1. Stte the rtes of

More information

8.6 The Hyperbola. and F 2. is a constant. P F 2. P =k The two fixed points, F 1. , are called the foci of the hyperbola. The line segments F 1

8.6 The Hyperbola. and F 2. is a constant. P F 2. P =k The two fixed points, F 1. , are called the foci of the hyperbola. The line segments F 1 8. The Hperol Some ships nvigte using rdio nvigtion sstem clled LORAN, which is n cronm for LOng RAnge Nvigtion. A ship receives rdio signls from pirs of trnsmitting sttions tht send signls t the sme time.

More information

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive

More information

KINEMATICS OF RIGID BODIES

KINEMATICS OF RIGID BODIES KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description

More information

Math 1B, lecture 4: Error bounds for numerical methods

Math 1B, lecture 4: Error bounds for numerical methods Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the

More information

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3 2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is

More information

Advanced Functions Page 1 of 3 Investigating Exponential Functions y= b x

Advanced Functions Page 1 of 3 Investigating Exponential Functions y= b x Advnced Functions Pge of Investigting Eponentil Functions = b Emple : Write n Eqution to Fit Dt Write n eqution to fit the dt in the tble of vlues. 0 4 4 Properties of the Eponentil Function =b () The

More information

Tremor-rich shallow dyke formation followed by silent magma flow at Bárðarbunga in Iceland

Tremor-rich shallow dyke formation followed by silent magma flow at Bárðarbunga in Iceland In the formt provided y the uthors nd unedited. SUPPLEMENTARY INFORMATION DOI: 1.138/NGEO9 Tremor-rich shllow dyke formtion followed y silent mgm flow t Bárðrung in Icelnd 1,, 1, 3 1, 1 1, NATURE GEOSCIENCE

More information

CHEMICAL KINETICS

CHEMICAL KINETICS CHEMICAL KINETICS Long Answer Questions: 1. Explin the following terms with suitble exmples ) Averge rte of Rection b) Slow nd Fst Rections c) Order of Rection d) Moleculrity of Rection e) Activtion Energy

More information

Mathematics. Area under Curve.

Mathematics. Area under Curve. Mthemtics Are under Curve www.testprepkrt.com Tle of Content 1. Introduction.. Procedure of Curve Sketching. 3. Sketching of Some common Curves. 4. Are of Bounded Regions. 5. Sign convention for finding

More information

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn

More information