10 pa. 10 pa. (0) = 2100 ± 200 s -1, z = 0.03 ± The flicker rates fit to: k f

Size: px

Start display at page:

Download "10 pa. 10 pa. (0) = 2100 ± 200 s -1, z = 0.03 ± The flicker rates fit to: k f"

Priscilla Bryan
5 years ago
Views:

1 Opening r clsing rate (s - ) Opening r flicker rate (s - ) clsing ing ing flicker Vltage (mv) Vltage (mv) C C 0 pa 0 pa, P = mv, P = mv, P = 00 ms 5 mv, P = mv, P = ms I F -0.6 FV/RT 00 e 0.85 FV/RT.84 e FV/RT 00 e 0.49 FV/RT e O O Supplementary Figure MthK inactivatin and flicker gating kinetics. (a) At psitive vltages, inactivatin gating in MthK displays vltage-dependent ing and clsing rates. Example MthK recrdings frm 75 5 mv with increasing inactivatin are shwn (right). Cntrl recrdings fr 50 5 mv were individually fit t the I O scheme in QuB. The plt shws the ing (lack squares) and clsing (red circles) rates as a functin f vltage with fits t k(v) = k(0) exp(zfv/rt). RT/F = 5.69 mv at 5 C. Symls are mean f eight measurements with S.. errr ars (ften smaller than symls). The ing rates fit t: k (0) = 00 ± 5 s -, z = -0.6 ± 06. The inactivatin rates fit t: k i (0) =.84 ± 4 s -, z = 0.85 ± 0. () At negative vltages, flicker gating in MthK is vltage dependent. The ing rate is essentially vltage-independent and the flicker rate decreases with increasing vltage. Example MthK recrdings at 5 mv and 50 mv are shwn (right). The recrdings were individually fit t the F O scheme in QuB. The plt shws the ing (lack squares) and flicker (red circles) rates as a functin f vltage with fits t k(v) = k(0) exp(zfv/rt). Symls are mean f fur measurements with S.. errr ars (ften smaller than the symls). The ing rates fit t: k (0) = 00 ± 00 s -, z = ±. The flicker rates fit t: k f (0) = ± s -, z = ±. Extraplated flicker rates at 50 mv and 5 mv are 5 s - and. s -, respectively, indicating that the F state will e rare and therefre nt needed fr the analysis f channel inactivatin at psitive vltages. Nature Structural & Mlecular Bilgy: di:08/nsm.47

2 0.98 C 0.79 C 0.48 C -50 mv Cntrl.5 μm TBA 0 μm TBA 0 pa 400 ms Open praility TBA TBA TBA Rates, s - c C 5 μm TBA TBA TBA TBA [TBA], μm lck-rate ff-rate Rates, s - [TBA], μm lck-rate ff-rate Rates, s [Blcker], μm lck-rate [TBA], μm ff-rate Supplementary Figure Blcker cncentratin dependencies are cnsistent with imlecular kinetics. (a) Example recrdings at 50 mv including cntrl and three cncentratins f TBA lcker. The praility is shwn t the left f each trace. () Blcker dse respnse data at 50 mv fr TBA (lack squares), TBA (red circles), and TBA (lue triangles). ata are fit t the equatin (lines), = max / ( + [B]/K ½ ), with max = 0.98, TBA: K ½ = 44 ± 6 μm, TBA: K ½ = 7.5 ± μm, TBA: K ½ = 0.9 ± 4 μm. (c) Blck-rates and ff-rates were determined as in Figure fr each recrding summarized in. The lcker ff-rates (lack squares) were cncentratin independent and the lck-rates (red circles) were linearly dependent n lcker cncentratin. Symls in and c are the mean f three t seven measurements with S.. errr ars. Nature Structural & Mlecular Bilgy: di:08/nsm.47

3 Scheme IA: c F F FB k i ff k k f k k f k k f O OB Scheme IB: k n [B] k n [B] O k n [B] OB *Scheme IC (tw affinities): I k i n [B] k k f O k n [B], μm, TBA * * TBA TBA Vltage (mv) Blcker n rates (μm - s - ) r Blcker ff rates (s - ), Vltage (mv) * * * * IB OB Supplementary Figure Analysis f state lck is nt significantly affected y channel flickers. (a) At negative vltages the P is very high. Hwever, the channel des spend a small time (~-5 %) clsed (flicker, F). T verify that the flickers d nt significantly affect the lck analysis, we fit lck data t a scheme where the lcker des nt ind t the clsed F state (Scheme IA) and cmpared the results with a scheme where the lcker inding is stateindependent (Scheme IB). Fr TBA lck at 5 and 50 mv, the significant increase in TBA affinity t the inactivated state resulted in a small numer f lnger clsings that culd nt e accunted fr y Schemes IA and IB. Scheme IC, called the state-independent access scheme in the main text, accunts fr the high-affinity lck events. () Cmparisn f state dissciatin cnstants,, tained frm an analysis using Scheme IA (filled symls) and Scheme IB (empty symls, highly verlapping filled symls) fr TBA (lack squares), TBA (red circles), and TBA (lue triangles). The stars ver the TBA data at 5 and 50 mv indicate thse data were analyzed with Scheme IC. (c) A cmparisn f lcker (TBA squares, TBA circles, TBA triangles) n-rates (lack fr Scheme IA, grey fr Scheme IB) and ff-rates (red fr Scheme IA, green fr Scheme IB) indicates that the n-rates are essentially vltage independent and the ff-rates are sustantially vltage dependent. The values did nt dependent significantly n hw flicker gating was included in the fit, Scheme IA vs. Scheme IB. Lines have n theretical meaning. Symls in and c are the mean f three t six measurements with S.. errr ars. Nature Structural & Mlecular Bilgy: di:08/nsm.47

4 5 μm TBA cncentratin: 0 μm 5 μm 50 μm 00 μm 50 mv 00 mv 5 mv Clsed dwell times (lg 0 50 mv 00 mv 5 mv Open dwell times (lg 0 Supplementary Figure 4 Glal analysis f TBA lck and inactivatin fr a single MthK channel. (a, ) Cmplete set f dwell-time distriutins fr all recrded cnditins (TBA Channel in Supplementary Tales) including clsed dwell-times (a) and dwell-times (). A suset f these are shwn in Figure 4 f the main text. Best fits t three mdels are the same as in Figure 4, the channel lck mdel (Scheme IIA, Figure 4a, red dashed lines), the lcker trapping mdel (Scheme IIB, Figure 4a, green dtted lines), and the state-independent access mdel (Scheme III, Figure 4a, lack lines). Tw additinal datasets fr TBA gave similar results (nt shwn). Nature Structural & Mlecular Bilgy: di:08/nsm.47

5 TBA cncentratin: 0.5 μm μm.5 μm 5 μm 0 μm 5 μm 50 mv 00 mv 5 mv Clsed dwell times (lg 0 μm 0 μm 5 mv 0 0 Open dwell times (lg 0 Supplementary Figure 5 Glal analysis f TBA lck and inactivatin fr a single MthK channel. (a, ) well-time distriutins fr recrded cnditins (TBA Channel in Supplementary Tales) including cmplete clsed dwell-times (a) and fur representative dwell-time distriutins (). A suset f these are shwn in Figure 5a f the main text. Best fits t tw mdels are the same as in Figure 5a, the channel lck mdel (Scheme IIA, red dashed lines) and the stateindependent access mdel (Scheme III, lack lines). Tw additinal datasets fr TBA gave similar results (nt shwn). Nature Structural & Mlecular Bilgy: di:08/nsm.47

6 TBA cncentratin: μm 5 μm 0.5 μm μm.5 μm 5 μm 0 μm 50 mv 00 mv 0 5 mv Clsed dwell times (lg 0 5 mv 5 μm.5 μm 0 0 Open dwell times (lg 0 Supplementary Figure 6 Glal analysis f TBA lck and inactivatin fr a single MthK channel. (a, ) well-time distriutins fr recrded cnditins (TBA Channel in Supplementary Tales) including cmplete clsed dwell-times (a) and fur representative dwell-time distriutins (). A suset f these are shwn in Figure 5a f the main text. Best fits t tw mdels are the same as in Figure 5a, the channel lck mdel (Scheme IIA, red dashed lines) and the state-independent access mdel (Scheme III, lack lines). Tw additinal datasets fr TBA gave similar results (nt shwn). Nature Structural & Mlecular Bilgy: di:08/nsm.47

7 Vltage: 50 mv 00 mv 5 mv Clsed (tp) and Open (ttm) dwell times (lg 0 Supplementary Figure 7 Glal analysis f μm TPeA lck and inactivatin fr a single MthK channel. Only a single cncentratin f lcker was recrded ( μm) acrss the vltage range f inactivatin gating fr TPeA (mlecular mdel shwn). Shwn are the clsed (fit with lack line) and (fit with red line) dwell-time distriutins fr a single MthK channel fit t the state-independent access mdel (Scheme III). Tw additinal datasets gave similar results (nt shwn). Nature Structural & Mlecular Bilgy: di:08/nsm.47

8 Supplementary Tales Supplementary Tale. Scheme IIA, Best fit parameters f single channel data with Open channel lck mdel. Channel (events) (95) (658) (7995) (75) (656) (8958) (440596) (8478) (75969) TBA k k z z k n K Lg- (s - ) (s - ) (µm - s - ) (s - ) (µm) likelihd/event TBA TBA Supplementary Tale. Best fit parameters f single channel data with Scheme IIB, Blcker trapping mdel. Channel (events) (95) (658) (7995) TBA k k z z k k 4 z z 4 k n K Lg- (s - ) (s - ) (s - ) (s - ) (µm - s - ) (s - ) (µm) likelihd/event Nature Structural & Mlecular Bilgy: di:08/nsm.47

9 Supplementary Tale. Best fit parameters f single channel data with Scheme III, State- independent access mdel. Channel (events) (95) (658) (7995) Mean ± S.. (75) (656) (8958) Mean ± S.. (440596) (8478) (75969) Mean ± S.. (906) (5875) (95) Mean ± S.. TBA k k z z k n K k i n k i ff K inact Lg- (s - ) (s - ) (µm - s - ) (s - ) (µm) (µm - s - ) (s - ) (µm) likelihd/event ± 0.8 ± ± ±.6 ± 0.5 TBA 0.7 ± ± ± ± 46.4 ± ± ± 08.9 ± 0.4 TBA 5.6 ±.6.9 ± ± ± ± 4. ±. TPeA.8 ± ± ± 56. ± ± 0.86 ± 4.4 ± 0.6. ± ±. ± 0.4. ± ± ± ± ± ± ±. 4.0 ± ± 5 Nature Structural & Mlecular Bilgy: di:08/nsm.47

10 Supplementary Nte Here we present fr cnvenience an utline derivatin f K ap fr Schemes IIA, IIB, and III. K ap fr Scheme III (Equatin 4, Methds) was presented in Figures 4 and 5. The text als gives K ap fr the channel lck mdel, Scheme IIA, as: ap = cntrl Scheme IIA, the channel lck mdel The equiliria etween states in Scheme IIA, are as fllws: [O] [I] = k k G (S) [OB] [O] = k [B] n = [B] The praility as a functin f vltage and lcker cncentratin is: [O] [O]+[I]+[OB] Rewriting this expressin in terms f the equiliria ave: + G + [B] Cntrl P in the asence f lcker is given y: (V, 0) = G + G P cntrl Therefre, rewriting (S4) in terms f P cntrl and rearranging: P cntrl + P = P cntrl cntrl [B] + [B] K ap Where, fr Scheme IIA, the channel lck mdel: K ap = (S7) P cntrl uring inactivatin gating, P cntrl <, making the value f K ap > K. This result is ppsite t the ehavir f TBA lck during inactivatin, ut may descrie the ehavir f TBA and TBA lck during inactivatin (see Figure 5). (S) (S) (S4) (S5) (S6) Scheme IIB, the lcker trapping mdel The equiliria etween states in Scheme IIB, are equatins (S), (S), and: [OB] [IB] = k k 4 G* The praility as a functin f vltage and lcker cncentratin is: [O] [O]+[I]+[OB]+[IB] Rewriting this expressin in terms f the equiliria ave: (S8) (S9) Nature Structural & Mlecular Bilgy: di:08/nsm.47

11 + G + [B] (S0) K + [B] G * efining the lcked P as the praility f ccupying OB relative t IB: P lcked [OB] = [OB]+[IB] = G* (S) + G * Using P cntrl (S5) and the definitin (S), equatin (S0) may e written as: P cntrl + P = P cntrl cntrl [B] + [B] (S) P lcked K ap Where, fr Scheme IIB, the lcker trapping mdel: K ap = P lcked (S) P cntrl uring inactivatin gating, if P cntrl < P lcked, meaning that inactivatin is less likely when lcker is und, then K ap > K. On the ther hand, if P cntrl > P lcked, meaning that inactivatin is mre likely when lcker is und, then K ap < K. Therefre, the lcker trapping mdel can fit either trend in apparent affinity in Figure. Scheme III, the state- independent access mdel The equiliria etween states in Scheme III, are equatins (S), (S), and: [IB] [I] = k i n[b] = [B] i inact (S4) Rewriting the expressin fr P (S9) in terms f the equiliria ave: + G + [B] (S5) K + [B] inact G Using P cntrl (S5), equatin (S0) may e written as: P cntrl + P cntrl + P = P cntrl " cntrl % $ inact '[B] + [B] (S6) # & K ap Where, fr Scheme III, the state- independent access mdel: K ap K inact = P cntrl K inact + ( P cntrl )K (S7) Therefre, when the channel is nt inactivating, P cntrl = and K ap = K. On the ther hand, when the channel is cmpletely inactivated, P cntrl = 0 and K ap = K inact. Equatin (S7) can e rewritten using the kinetic parameters f Scheme III (Equatin 4):!! + k $ $ # &e (z z )FV /RT # &K inact " k K ap " = % % (S8)! K inact k + K $ # &e (z z )FV /RT " % k Nature Structural & Mlecular Bilgy: di:08/nsm.47

NUMBERS, MATHEMATICS AND EQUATIONS

AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t