voltage - gated cation 
 ( e.g. , na , k ) channels 
 are central to neurological signal transmission . x - ray 
 crystal structures of the open state of several voltage - gated potassium 
 ( kv ) channels and a sodium ( nav ) channel have 
 recently been determined . kv channels 
 are composed of four identical subunits , each containing a voltage - sensor 
 domain ( vsd ) and one - fourth of the pore domain ( pd ) , the latter forming 
 the complete pore in the homotetrameric channel . despite numerous 
 experimental and computational studies , the mechanism of voltage gating , 
 namely the coupling of specific conformational changes within the 
 vsd in response to depolarizing potentials with respect to the resting 
 transmembrane electric potential , to opening the pd resulting in transmembrane 
 ionic current , has not been fully resolved for two reasons . one arises 
 because the direct methods utilized for the investigation of the 3-d 
 structure of either the detergent solubilized vsd ( e.g. , x - ray crystallography and solution nmr ) 
 or the complete kv / nav channel ( e.g. , x - ray crystallography ) can not provide the structure as a function of the membrane potential 
 in the absence of the membrane , the closed form of the complete channel 
 occurring only at the resting potential . another arises because the 
 physical  chemical techniques utilized to investigate the structures 
 of the complete kv / nav channel in the membrane as a function of the 
 potential have been more indirect . because they generally utilize 
 site - directed mutation of one or two residues at a time within the 
 vsd to cysteine , followed by either their labeling with large chromophores 
 for the purpose of fluorescence or light - energy transfer measurements 
 [ e.g. , refs ( 8 and 9 ) ] or alternatively 
 for measuring their accessibility to lipid soluble or insoluble reagents 
 [ e.g. , refs ( 10 and 11 ) ] , as a function of the transmembrane electric 
 potential , they are likely to involve some perturbation of the structure 
 and dynamics of the protein and/or its membrane environment . the vsd itself can be considered as a distinct module that , when 
 linked to an otherwise voltage - insensitive , ion - selective membrane 
 pore , imparts voltage sensitivity to the channel . furthermore , voltage - sensor proteins homologous with the 
 vsd have recently been found to function themselves as voltage - gated 
 proton channels involved in ph regulation during phagocytosis or to impart voltage sensitivity to enzymes 
 involved in signaling . as for the complete 
 kv / nav channels , emerging x - ray crystal structures for these proteins can not directly address their membrane potential - dependent 
 conformational states . thus , elucidating the conformational states 
 associated with voltage gating within the vsd itself , and these homologous 
 voltage - sensor proteins , gains broad biological significance , especially 
 utilizing approaches that minimize any perturbation of the structure 
 and dynamics of either the protein itself or its membrane environment . we have developed a single membrane system containing the vectorially 
 oriented vsd , or the complete kv / nav channel , at high in - plane density 
 tethered to the surface of a solid inorganic substrate , as illustrated in figure 1 . two different methods were utilized to fabricate the single membrane 
 on the surface of the substrate : one referred to as  self - assembly  
 and the other as  directed assembly  . although published 
 previously , the methods are briefly summarized in the experimental methods section and illustrated with figures 
 in the supporting information . when placed 
 in a suitable electrochemical cell , the so - called profile 
 structure  of the membrane can be investigated using the direct 
 methods of high energy x - ray reflectivity and neutron reflectivity , 
 each enhanced by utilizing an interferometric technique enabled by 
 the fabrication of an inorganic multilayer structure on the surface 
 of the substrate to which the membrane is tethered . refers to the projection of the membrane s 3-d structure dominated 
 by the vsd protein , parallel to the plane onto the axis normal to 
 the plane of the membrane , as also illustrated in figure 1 . for x - rays , this projected structure is the x - ray 
 scattering length ( or electron ) density profile ( denoted herein as 
 the xsld profile ) and for neutrons the neutron scattering length density 
 profile ( similarly denoted as the nsld profile ) . the significance 
 of the x - ray ( or neutron ) interferometric technique was clearly demonstrated 
 in an earlier publication via a direct 
 comparison of the x - ray reflectivity from a langmuir monolayer of 
 an amphiphilic 4-helix bundle protein at the water  air interface 
 in the absence and presence of the interferometric effect . the technique 
 is briefly summarized in the experimental methods and illustrated with figures in the supporting 
 information using this example . molecular graphics representation 
 of a small 3  3 ensemble 
 of the vectorially oriented vsd molecules ( -helices represented 
 as solid cylinders ) solvated by a popc bilayer ( turquoise ) tethered 
 to the surface of a solid inorganic substrate ( not shown ) below the 
 monolayer of tethering chain molecules ( yellow ) in the side view . the  profile structure  arises from the projection of 
 the 3-d structure of the membrane along rxy vectors parallel to the plane onto the z - axis normal to the plane of the membrane . the vsd molecules 
 have been rotated randomly with respect to one another about the z - axis in the top view . however , unlike in the top view 
 shown , experimentally , the vsd s exhibit only glass - like order 
 in the x  y plane , even at 
 this low average area / vsd of 1400  approximating 
 that of the experimental situation . the profile structure of this single membrane system has 
 been extensively 
 characterized by neutron interferometry . this characterization is in full agreement with the independent , 
 but more limited results from x - ray interferometry . importantly , it demonstrated several key elements essential 
 for the success of the approach utilized in this work . with reference 
 to figure s1 in the supporting information ( from ref ( 19 ) ) , 
 the vsd protein exhibits a unidirectional vectorial orientation in 
 the membrane , the in - plane density of the protein is sufficiently 
 high so that the protein dominates the profile structure with the 
 protein occupying 50% of the membrane area , the space between 
 adjacent protein molecules in the membrane plane is filled by an asymmetric 
 phospholipid bilayer occupying the remaining 50% of the membrane 
 area , the layer containing the chain molecules tethering the membrane 
 to the inorganic surface positions the membrane 20  
 away from the inorganic surface , and the surface of the membrane proximal 
 to the inorganic surface is highly hydrated to the level of 50% 
 that of bulk water , the distal surface being fully hydrated . in this work , we report the characterization of the electrical 
 properties of this single membrane system via electrical impedance 
 spectroscopy . these properties ( resistance and capacitance ) were found 
 sufficient to permit the direct measurement of changes in the sld 
 profiles of the vsd protein , vectorially oriented within the single 
 phospholipid bilayer membrane , as a function of the steady - state transmembrane 
 electric potential . a time - resolved version of the direct methods 
 of x - ray and neutron interferometry was utilized , analogous to the 
 classic  pump - probe  approach widely applied using spectroscopic 
 techniques . the transmembrane potential was varied in a stepwise , 
 cyclic fashion with data collection at each of three values of the 
 potential . for the x - ray case , only one cycle was sufficient to achieve 
 satisfactory standard errors at each value of the potential due to 
 the high photon flux density available with the synchrotron x - ray 
 source , although four cycles of data were collected and analyzed separately . 
 with the much lower flux density of neutrons from the spallation neutron 
 source , the data were necessarily averaged over many cycles for each 
 value of the potential to reduce the standard errors prior to further 
 data reduction and analysis . this approach for each case was employed 
 to ensure that the changes in the sld profiles detected were fully 
 reversible and to avoid the possibility of trapping the vsd in an 
 inactive state by exposing the protein to a particular potential for 
 an extended time . the changes in the experimental sld profiles so 
 observed were found to be qualitatively consistent with the results 
 from molecular dynamics simulations of a related membrane system , 
 thus suggesting an initial interpretation of these changes in terms 
 of the vsd s atomic - level 3-d structure . two different methods , designated as  self - assembly  
 and  directed assembly  and described previously , were used for the preparation of single membranes 
 tethered to the surface of an inorganic sigesi or sinisi multilayer 
 substrate , the membrane composed of a phospholipid bilayer ( popc ; 
 1-palmitoyl-2-oleoyl - sn - glycero-3-phosphocholine ) 
 containing the voltage sensing domain ( vsd ) of the voltage - gated potassium 
 channel from arepyrum pernix kvap , vectorially oriented 
 with respect to the normal to the membrane plane at high in - plane 
 surface density . importantly , 
 vsd : popc membranes formed by both the sa and da methods were investigated 
 in this work . the hybrid 
 bilayer was formed via the chemisorption of ots ( octadecyltrichlorosilane ) 
 onto the silicon oxide surface of a sigesi multilayer substrate . a 
 monolayer of popc ( 1-palmitoyl-2-oleoyl - sn - glycero-3-phosphocholine ) 
 was physisorbed onto the hydrophobic surface of the substrate alkylated 
 with the ots via the rapid solvent - exchange technique . the electrochemical cells 
 employed in the x - ray and neutron interferometry experiments are substantially 
 different for each of the two scattering techniques employed . as a 
 result electrical impedance spectroscopy ( eis ) measurements , 
 using a chi660d electrochemical workstation from ch instruments , were 
 performed in situ on the membrane specimens utilized 
 in the x - ray and neutron interferometry experiments , as well as on 
 many additional , entirely analogous specimens performed ex 
 situ . these data were usually successfully modeled with simple 
 equivalent circuits , composed of a resistance , 
 representing that of the silicon oxide surface of the si ge  si 
 or si  ni  si multilayer substrates , in series with an 
 rc component , representing the bio - organic overlayer on its surface , 
 e.g. , the reconstituted vsd : popc membrane or the hybrid ots : popc bilayer . interferometry is 
 a form of the specular x - ray or neutron reflectivity technique that 
 enhances the sensitivity to a bio - organic layer adjacent the surface 
 of a solid inorganic multilayer substrate and allows the direct determination 
 of the sld profile for the bioinorganic layer . the method for the collection of specular x - ray 
 reflectivity data , enhanced by interferometry and corrected for the 
 beam footprint on the specimen and off - specular reflectivity , from 
 single membranes tethered to the surface of an inorganic multilayer 
 substrate fully hydrated with an aqueous medium , utilizing synchrotron 
 radiation from an undulator source at sufficiently high x - ray energy 
 to penetrate the aqueous medium , has been described previously . with x - rays , the inorganic substrate was a sigesi 
 multilayer fabricated by magnetron sputtering onto heavily doped silicon . the electrochemical cell was formed by pressing the end of 1 cm diameter 
 kapton tubing against the surface of the substrate possessing the 
 membrane ; the area of the membrane exposed to the x - ray beam in front - side 
 reflection geometry was less than 0.1 
  1.0 cm at grazing angles of incidence . the electrolyte 
 was 100 mm kcl in 1 mm tris buffer at ph 7.8 . the substrate served 
 as the working electrode held at ground potential and a platinum electrode 
 in the electrolyte served as the counter electrode to which the potential 
 was applied via a commercially available potentiostat , also allowing 
 for in situ measurement of the electrical properties 
 of the membrane via impedance spectroscopy . specular x - ray reflectivity 
 from the substrate : bio - organic overlayer system was collected in front - side 
 geometry , utilizing a flat substrate and monochromatic radiation , 
 performing a 2 scan to collect data over a range 
 of momentum transfer perpendicular to the substrate surface , qz , where  is the angle 
 of x - ray incidence with respect to the plane of the substrate s 
 surface possessing the overlayer and 2 the angle of reflection 
 with respect to the incident beam . unlike highly penetrating neutrons , 
 high - energy x - rays ( e.g. , > 20 kev ) are required to penetrate the 
 aqueous 
 medium hydrating the membrane within an electrochemical cell . herein , 
  time resolution  is utilized only to denote the investigation 
 of the profile structure of the vsd protein at selected values of 
 the  steady - state  transmembrane potential as the potential 
 is varied cyclically in a stepwise manner over multiple cycles during 
 reflectivity data collection . an ensemble of vsds is capable of responding 
 to such a step in the potential on the time scale of a few milliseconds . the cyclic variation provides a key check on 
 reversibility while avoiding trapping the protein in an inactive conformational 
 state . with the vastly greater x - ray flux from an undulator - based 
 synchrotron x - ray source , only very short collection times of 520 s were required for the majority of the large number of angles of 
 incidence employed with monochromatic radiation , the incident beam 
 appropriately attenuated to satisfy the count - rate limitations of 
 the scintillation detector and achieve the desired standard error 
 in the reflectivity data with increasing angle . the potential was 
 then cycled over the sequence of 0 mv , 100 mv , + 100 mv , 0 
 mv for each angle of incidence , utilizing 520 s / potential 
 with increasing angle . the entire 2 scan for 
 one cycle over all four values of the potential required a total of 
 82 min . although as many as four cycles were collected for a particular 
 specimen , the data were recorded separately for each cycle without 
 any averaging over multiple cycles because the standard errors achieved 
 for each value of the potential within a cycle were sufficient . the 
 values of the potentials indicated here and subsequently refer to 
 the potentials applied to the electrodes . impedance spectroscopy suggests 
 that the actual transmembrane potentials are at least 5070% 
 of these values , the reduction due to the silicon oxide surface of 
 the substrates as described in the results section . the method for the collection of specular 
 neutron reflectivity data , enhanced by interferometry and corrected 
 for the beam footprint on the specimen and off - specular reflectivity , 
 from single membranes tethered to the surface of an inorganic multilayer 
 substrate fully hydrated with an aqueous medium , utilizing a polychromatic , 
 pulsed spallation neutron source , has been described previously . for neutrons , the inorganic substrate was a sinisi multilayer fabricated 
 by magnetron sputtering onto undoped silicon . the electrochemical 
 cell was formed between the surface of the substrate possessing the 
 membrane and a silicon wafer separated by a nitrile gasket ; the area 
 of the membrane exposed to the incident neutron beam in backside geometry was 1.0  4.0 cm at grazing 
 angles of incidence . the electrolyte was also 100 mm kcl in 1 mm tris 
 buffer at ph 7.8 . again , the substrate served as the working electrode 
 held at ground potential , and a platinum electrode in the electrolyte 
 served as the counter electrode to which the potential was applied . 
 with the much lesser neutron flux from the spallation source , much 
 longer collection times of 3150 min were required for each 
 of the few angles of incidence employing polychromatic radiation to 
 achieve the desired standard error in the reflectivity data with increasing 
 angle . hence , the potential was cycled over the sequence of 0 mv , 
 + 100 mv , 100 mv , 0 mv for many cycles at each angle of incidence , 
 utilizing 20 s / potential , and the data for each potential were summed 
 prior to any further data reduction and analysis . the values of the 
 potentials indicated here and subsequently again refer to the potentials 
 applied to the electrodes . impedance spectroscopy suggests that the 
 actual transmembrane potentials are also at least 5070% of 
 these values , the reduction due to the silicon oxide surface of the 
 substrates , as described in the results section . we analyzed 
 the x - ray and neutron interferometry data in the first born approximation , 
 which employs the fresnel - normalized specular x - ray / neutron reflectivity , r(qz)/rf(qz ) , where r(qz ) is the experimental specular reflectivity and rf(qz ) is 
 the fresnel function . the fresnel - normalized reflectivity is proportional 
 to the modulus square of the fourier transform f(qz ) of the gradient of the scattering - length 
 density ( sld ) profile d(z)/dz , where the profile z - axis is normal to the plane 
 of the interfaces(s ) comprising the system of interest . the standard errors in these data are expressed in terms of the counting 
 statistics . these errors were propagated through the data reduction 
 procedure , including the footprint correction , the correction for 
 off - specular reflectivity , and division by the fresnel function for 
 an ideal interface . it is essential to note that this procedure was precisely the same employing the same parameters , irrespective 
 of the specimen or the applied potential for each reflectivity technique . the gradient xsld or nsld profile , [ d(z)/dz]0  mv or [ db(z)/dz]0  mv , respectively , 
 for a particular specimen was calculated from its respective modulus 
 data , |f(qz)| , at 0 mv potential utilizing a constrained refinement method 
 to solve the phase problem , the integral of the gradient profile providing 
 the xsld or nsld profile itself , (z , e /  ) or b(z , 10/  ) , as fully described in prior publications . two key constraints are utilized , namely the sld profile of the 
 inorganic multilayer substrate determined independently and the extent 
 of the sld profile of the multilayer with the adsorbed bio - organic 
 overlayer determined independently from the autocorrelation of its 
 gradient profile { d(z)/dz  d(z)/dz}. we then determined the difference between 
 the 
 xsld or nsld profile for a particular potential of 100 mv versus 
 that at 0 mv , [ (z , e / )]100  mv or [ b(z , 10/]100  mv , by analyzing the difference modulus data , |f(qz)| = { |f100  mv ( qz)|  |f0  mv(qz)| } , as fully described in the supporting information . the analysis constrained any potential differences within the region 
 of the difference sld profiles occupied by the inorganic 
 multilayer substrate to be negligible , compared to those within the 
 membrane tethered to its surface . the dependence of the experimental 
 xsld and nsld profiles on the transmembrane potential was compared 
 with those calculated from molecular dynamics simulations of a system 
 of one vsd embedded in an extended symmetric bilayer composed of 232 
 popc molecules in a symmetric water environment . in order to make this comparison with the experimental 
 system , only the vsd s nearest - neighbor lipids were utilized 
 in order to reduce the lipid / protein mole ratio to that comparable 
 to the experiments , and the profiles for this truncated membrane were 
 then calculated from the trajectories at the same potentials of 0 
 and 100 mv averaged over several microseconds , prior to calculating 
 the difference time - averaged xsld and nsld profiles 
 used in the comparison , as fully described in the supporting information . as described in the experimental methods , the electrochemical cells 
 were somewhat different for the x - ray interferometry and neutron interferometry 
 experiments , particularly with regard to the manner by which the electrolyte 
 was contained . for the cell used in the x - ray experiments , the resistance 
 of the silicon oxide surface was typically 200 k/cm for the si si multilayer reference structures 
 fabricated on silicon . for the reconstituted vsd : popc membranes , the 
 resistance typically varied from 200 to 400 k/cm with a capacitance of typically 23 f / cm . for the hybrid ots : popc bilayer membranes , the resistance typically 
 varied from 250 to 350 k/cm with a capacitance 
 of typically 12 f / cm . for the more tightly 
 sealed cell used in the neutron experiments , the resistance of the 
 silicon oxide surface increased to 300400 k/cm for the si si multilayer reference structures 
 fabricated on silicon . for the reconstituted vsd : popc membranes , the 
 resistance increased to 600700 k/cm with 
 the capacitance decreasing to 12 f / cm . for the hybrid bilayer membranes , the resistance increased to 12 
 m/cm and the capacitance decreased to 0.40.6 
 f / cm . examples of the fit of the equivalent circuit 
 model to the eis data from the cell used in the neutron experiments 
 for the vsd : popc membrane , the hybrid ots : popc bilayer , and the sam 
 used to tether the vsd : popc membrane to the surface of the sinisi 
 substrate are shown in figure s8 of the supporting 
 information . in view of these eis results , we estimate that 
 the potentials across the vsd : popc membrane are likely to be only 
 5070% of the potentials applied to the electrodes for either 
 the x - ray or neutron interferometry experiments , and similarly for 
 the hybrid ots : popc bilayer for the x - ray interferometry experiments , 
 reported herein . typical modulus 
 data |f(qz)| from a vsd : popc membrane tethered to the surface of a sigesi 
 multilayer substrate , prepared via  directed assembly ( da )  , for the first two cycles of variation of the 
 transmembrane potential are shown in figure 2 . the potential dependence of the modulus data was used for subsequent 
 analysis . since the difference in the modulus data 
 between p100 mv or m100 mv (  p/m  denote 
 + / , respectively ) and 0 mv were similar using the data for 
 either the first or last 0 mv potential in each cycle , the data for 
 the two 0 mv values were averaged . the difference modulus data for { p100mv-0mvave } , { m100mv-0mvave } , and { p100mv - m100mv } 
 are also shown in figure 3 . such difference 
 modulus data were similar for the first two cycles of the transmembrane 
 potential and are significant because the difference data exceed the 
 standard errors and they depend on the particular pair of potentials 
 utilized . comparable difference modulus data were 
 also obtained from a vsd : popc membrane , prepared via  self 
 assembly ( sa )  , for the first 
 two cycles of variation of the transmembrane potential , thereby providing 
 additional support for the reproducibility of these data specimen - to - specimen . 
 by the third and fourth cycles , some evolution of the modulus data 
 became evident , possibly arising from radiation damage ; the analyses 
 of these data will therefore not be presented here . a hybrid bilayer 
 membrane , composed of a chemisorbed layer of ots with an overlayer 
 of popc lacking the vsd protein , was employed in this work primarily 
 only as a control . typical modulus data for f(qz ) from 
 the ots : popc hybrid bilayer for the first two cycles of variation 
 of the transmembrane potential are shown in figure 2 . the difference modulus data for { p100mv-0mvave } 
 and { m100mv-0mvave } are also shown in figure 2 . these difference modulus data were also similar for the first two 
 cycles of the transmembrane potential and are significant because 
 the difference data exceed the standard errors and they depend on 
 the particular pair of potentials utilized . the difference modulus 
 data for the ots : popc hybrid bilayer differ dramatically from those 
 for the vsd : popc membrane , thereby providing an important control 
 in momentum transfer space . left side : typical modulus |f(qz)| data ( top ) , calculated 
 from the specular 
 x - ray reflectivity r(qz)/rf(qz ) , where |f(qz)| = r(qz)/rf(qz ) , for 
 the vsd : popc membrane tethered to the surface of a sigesi multilayer 
 substrate at a transmembrane potential of 0 mv for the first two cycles 
 of the series of potentials applied . the difference modulus data |f(qz)| for the second cycle are shown in the panels below 
 for the pairs of potentials indicated . right side : typical modulus 
 |f(qz)| data ( top ) for the ots : popc hybrid bilayer tethered to the surface 
 of a sigesi multilayer substrate at a transmembrane potential of 0 
 mv for the first two cycles of the series of potentials applied . the difference modulus data |f(qz)| for the first cycle are 
 shown in the panels below for the pairs of potentials indicated . the 
 standard errors in the data are indicated for each case . reduced x - ray scattering - length density ( xsld ) profiles , 
 (z)/si , calculated for the 
 vsd : popc membrane 
 tethered to the surface of a sigesi multilayer substrate ( upper left ) 
 and the ots : popc hybrid bilayer tethered to the surface of a sigesi 
 multilayer substrate ( upper right ) , each at a transmembrane potential 
 of 0 mv . the profile of the multilayer substrate occurs for z < 0  ( see figure s2 of the supporting information , for example ) . the respective difference reduced xsld profiles , (z)/si for each case are shown in the panels 
 below for the pairs of potentials indicated . the xsld profiles and their dependence on the applied potentials , 
 as expressed in difference xsld profiles , were calculated 
 from the modulus and difference modulus data , respectively , 
 as described in the experimental methods . a typical xsld profile for the vsd : popc membrane at 0 mv is shown 
 in figure 3 , along with the difference xsld profiles for { p100mv-0mvave } and { m100mv-0mvave}. by comparison 
 with figure s1 in the supporting information , the vsd : popc membrane for these specimens is about 70  in 
 total thickness and occurs within 25  < z < 95  of the xsld profile . the difference profiles exhibit substantial changes throughout the extent of the 
 membrane profile and are distinctly different depending on the particular 
 potentials utilized . in particular , for the potential pair { m100mv-0mvave } , 
 the major changes involve a larger increase in electron density ( xsld ) 
 over the region 55  < z < 70  and 
 corresponding lesser decreases in electron density over the two adjacent 
 regions 30  < z < 55  and 70  
 < z < 85  of the membrane profile . for 
 the potential pair { p100mv-0mvave } , the major changes involve an increase 
 in electron density ( xsld ) over the region 15  < z < 50  and a corresponding decrease in electron 
 density of comparable magnitude over the adjacent region 50  
 < z < 85  of the membrane profile . a typical xsld profile for the ots : popc hybrid bilayer lacking 
 the vsd protein at 0 mv along with the difference xsld profiles for { p100mv-0mvave } and { m100mv-0mvave } are also shown 
 in figure 3 . the ots : popc hybrid bilayer for 
 these specimens occurs within 0  < z < 
 50  of the xsld profile . the hydrocarbon core of the bilayer 
 occurs within 5  < z < 35  and 
 the popc polar headgroups within 35  < z < 55  . we note that the layer of popc polar headgroups 
 is somewhat thicker than expected by 5  , given the spatial 
 resolution of these profiles ( 13  ) , which may arise 
 from the surface roughness of the sigesi multilayer substrates . the difference profiles exhibit substantial changes throughout 
 the extent of bilayer profile , and they are distinctly different depending 
 on the particular potentials utilized . in particular , for the potential 
 pair { m100mv-0mvave } , the major changes involve increases in electron 
 density ( xsld ) over the regions 10  < z < 
 25  and 40  < z < 50  and 
 a corresponding decrease in electron density of comparable magnitude 
 over the intervening region 25  < z < 
 40  of the bilayer profile . for the potential pair { p100mv-0mvave } , the major changes involve a large increase in electron density ( xsld ) 
 over the region 35  < z < 55  and 
 a corresponding decrease in electron density of comparable magnitude 
 over the adjacent region 25  < z < 35 
  of the bilayer profile . importantly , these changes are very 
 different from those for the vsd : popc membrane described above , the 
 comparison facilitated by their juxtaposition in figure 3 , thereby providing an essential control in real space . while the standard errors are readily apparent in the modulus data , 
 they are not so evident in the fourier analysis of these data . however , 
 the control experiments utilized herein provide an important measure 
 of these errors propagated through the analysis . in the x - ray case , 
 the low amplitude , short wavelength fluctuations arising from transform 
 truncation in the reduced xsld profile for the ots : popc hybrid bilayer 
 within the region 60  < z < 120  , 
 occupied only by the aqueous electrolyte where the profile should 
 be flat , indicate that the propagated errors remain below the 5% level 
 ( with reference to figure 3 ; right side , top 
 panel ) . the propagated errors are thereby seen to rise to the 10% 
 level within the same region of the difference xsld 
 profiles ( with reference to figure 3 ; right 
 side , middle and lower panels ) . unlike the case 
 with x - rays , the modulus 
 data for f(qz ) from the fresnel - normalized neutron reflectivity data from 
 a vsd : popc membrane , prepared via  self assembly ( sa )  , the control was composed of only the chemisorbed organic 
 chain molecules , or sam , used to tether the vsd protein to the inorganic 
 substrate surface , thus lacking the vsd protein . the difference modulus data for { p100mv-0mvave } , 
 { m100mv-0mvave } , and { p100mv - m100mv } are shown in figure 4 for both the membrane and the sam . the errors for 
 both the membrane and sam are larger than those for the x - ray case . 
 nevertheless , the difference data remain significant as they barely 
 exceed the standard errors , they depend on the particular pair of 
 potentials utilized , and they differ between the vsd : popc membrane 
 and the control sam lacking vsd protein . modulus |f(qz)| data calculated 
 from the specular neutron reflectivity r(qz)/rf(qz ) , where |f(qz)| = r(qz)/rf(qz ) , for the vsd : popc membrane 
 tethered to the surface of a sinisi multilayer substrate ( upper left ) 
 and for the sam chemisorbed onto the surface of a sinisi multilayer 
 substrate ( upper right ) , each at a transmembrane potential of 0 mv . the respective difference modulus data |f(qz)| for 
 each case are shown in the panels below for the pairs of potentials 
 indicated . the nsld profiles and their dependence 
 on the applied potentials , 
 as expressed in difference nsld profiles , were calculated 
 from the modulus and difference modulus data , respectively , 
 as described in the experimental methods . 
 in figure 5 , we compare the nsld profile at 
 0 mv and the difference nsld profiles for { p100mv-0mvave } 
 and { m100mv-0mvave } for the vsd : popc membrane with those from the 
 sam . by comparison with figure s1 in the supporting 
 information , the vsd : popc membrane for these specimens occurs 
 within 25  < z < 95  of the nsld 
 profile . the difference profiles exhibit substantial 
 changes throughout the extent of vsd : popc membrane profile and are 
 distinctly different depending on the particular potentials utilized . 
 in particular , for the potential pair { m100mv-0mvave } , the major changes 
 involve an increase in nsld over the region 80  < z < 100  and corresponding decrease in nsld over 
 the adjacent region 55  < z < 80  
 of the membrane profile . for the potential pair { p100mv-0mvave } , the 
 major changes involve a comparable increase in nsld over the two regions 
 30  < z < 50  and 70  < z < 90  , with smaller decreases in nsld for the 
 region z < 30  and the intervening region 
 50  < z < 70  of the membrane profile . 
 the corresponding difference profiles for the sam 
 are essentially featureless , again providing an essential control 
 in real space . neutron scattering - length density ( nsld ) profiles , b(z ) , calculated for the vsd : popc membrane 
 tethered to the surface of a sinisi multilayer substrate ( upper left ) 
 and for the sam chemisorbed onto the surface of a sinisi multilayer 
 substrate ( upper right ) , each at a transmembrane potential of 0 mv . the respective difference nsld profiles , 
 b(z ) , for each case are 
 shown in the panels below for the pairs of potentials indicated . again , while the standard errors 
 are readily apparent in the modulus 
 data , they are not so evident in the fourier analysis of these data . the control experiments utilized provide an important measure of these 
 errors propagated through the analysis . in the neutron case , the low 
 amplitude , short wavelength fluctuations arising from transform truncation 
 in the reduced nsld profile for the sam within the region 40  
 < z < 120  , occupied only by the aqueous 
 electrolyte where the profile should be flat , indicate that the propagated 
 errors are larger but remain below the 10% level ( with reference to 
 figure 5 ; right side , top panel ) . the propagated 
 errors are thereby seen to rise to the 20% level within the same region 
 of the difference nsld profiles ( with reference to 
 figure 5 ; right side , middle and lower panels ) . as described in the introduction , the structure 
 of the reconstituted vsd : popc membranes central to these studies has 
 been extensively characterized by both x - ray and neutron interferometry 
 in prior work . their electrical properties within 
 the electrochemical cells utilized in this work have been found sufficient 
 to support transmembrane electric potentials , although these are only 
 5070% of the potentials applied to the electrodes due to the 
 presence of a silicon oxide layer on the surface of the inorganic 
 substrates to which the membranes are tethered . the structure of the 
 ots : popc bilayer , utilized only as a control in these studies , has 
 also been characterized by x - ray interferometry . its electrical properties 
 within the electrochemical cells utilized in this work have been found 
 sufficient to support transbilayer electric potentials , although again 
 these are only 5070% of the potentials applied to the electrodes . the results from both the time - resolved x - ray and neutron interferometry 
 experiments described demonstrate directly that significant changes 
 occur throughout the profile structure of the vsd : popc membrane upon 
 application of a transmembrane electric potential , and the changes 
 depend on the sign of the applied potential with respect to zero potential . 
 with reference to the resting potential of the natural membrane , for the vectorial orientation of the vsd within the membrane in 
 our electrochemical cells , { p100mv-0mv } would refer to a polarizing  
 potential difference while { m100mv-0mv } would refer to a  depolarizing  
 potential difference . such potential - dependent changes are either 
 completely different for the ots : popc hybrid bilayer membrane or essentially 
 absent for the sam , both serving as important controls lacking the 
 vsd protein . since the physical origin of the atomic scattering factors 
 for x - rays and neutrons is entirely different , the latter being much 
 more sensitive to the distribution of exchangeable hydrogen including 
 water , we have therefore verified the existence of potential - dependent 
 changes within the profile structure of the vsd : popc membrane by two 
 independent scattering methods . in addition , the difference sld profiles 
 for the depolarizing potential 
 pair { m100mv-0mv } convincingly demonstrate that a potential of 0 mv 
 does not produce the depolarized state of the vsd , as has been commonly 
 assumed [ e.g. , refs ( 3) , etc . ] . it is important to note that these new experimental results stand 
 on their own , in the sense that any modeling of their structural significance 
 at the 3-d atomic - level must account for the changes in the profile 
 structure described . prior to addressing the structural significance 
 of the observed 
 potential - dependent changes in the sld profiles , it is important to 
 reiterate that the changes described were both reproducible and reversible . reproducibility for both the x - ray and neutron experiments is described 
 in some detail in the supporting information . the  inactivation  associated with the complete kvap 
 channel ( from which the vsd was derived ) in electrophysiological experiments , arising from multiple cycles of depolarization 
 and repolarization of the membrane potential on a time scale of 100200 
 ms per potential , could have undermined these experiments . in the 
 x - ray case , it was not necessary to average over multiple cycles , 
 and the experimental modulus data for the two 0 mv potentials employed 
 within each of the four cycles investigated superimposed to within 
 the noise level , demonstrating reversibility despite the longer time 
 scale of 520 s per potential . furthermore , the potential - dependent 
 changes in the xsld profiles were similar for the first and second 
 cycles , in terms of the positions and amplitudes of their major features 
 as evident from a comparison of figures 3 and 6 , although they do differ in detail . neither would 
 have occurred with any substantial level of inactivation comparable 
 to that for the complete kvap channel , for which the entire ensemble 
 becomes inactivated after only three cycles . for the neutron case , averaging over many cycles was required to 
 achieve a satisfactory noise level in the modulus data for each value 
 of the potential . again , if inactivation on a time scale of 20 s , 
 comparable to that for the complete kvap channel , had been a major 
 factor cycle - to - cycle , potential - dependent changes in the modulus 
 data would have vanished with averaging over many cycles . thus , the 
 inactivation associated with the complete channel does not appear 
 to play any significant role in these studies of the isolated vsd 
 protein . left side : comparison of the difference xsld profiles 
 determined from the x - ray interferometry experiments for vsd : popc 
 membrane tethered to the surface of an inorganic multilayer substrate 
 ( dotted ) from the first cycle of the series of potentials applied , 
 with those calculated from molecular dynamics simulations for an untethered 
 vsd : popc membrane ( solid ) for the two pairs of potentials indicated , 
 each membrane fully hydrated . right side : the same comparison , but 
 with the abscissa scale for the difference profiles 
 calculated from the simulation expanded by 25% . the time - averaged 
 profiles calculated from the simulations have been smoothed via convolution 
 with a gaussian whose 1/e width was 2. the difference in the physical origin of the atomic scattering 
 factors for x - rays and neutrons noted above makes it difficult to 
 compare xsld and nsld profiles , and their respective potential - dependent 
 difference profiles employed in this work , in the absence of a detailed 
 atomic - level model for the vsd : popc membrane . furthermore , given the 
 complexity of the membrane , and the fact that the profile structure 
 is a 1-d projection of the 3-d structure , the observed changes in 
 the profile structure of the vsd : popc membrane , in terms of its xsld 
 and nsld profiles , have no simple interpretation . however , both the 
 vsd itself and in a full - length kv - channel within fully hydrated popc membranes have been 
 extensively investigated recently via molecular dynamics simulations as a function of the applied transmembrane electric potential . such simulations of only a single vsd or full - length kv - channel protein 
 within the hydrated bilayer membrane require very long trajectories 
 ( 10 and 100 s time scale , respectively ) as made possible by 
 anton , a special - purpose supercomputer for molecular dynamics simulations . since these simulations contain the full 3-d 
 atomic - level structure of the complex membrane system , it is straightforward 
 to calculate its projected profile structure , time - averaged over a 
 selected segment near the end of the trajectory over which the structure 
 exhibits stability . in figure 6 , we compare 
 the difference xsld profile structures from the experiments 
 reported here for the 
 first cycle in the variation of the transmembrane potential with those 
 calculated from the simulations of the vsd within a fully hydrated 
 popc membrane for both the polarizing and depolarizing 
 cases as defined above . it is essential to note here that although 
 the simulations were for an isolated vsd , they were set up based on 
 indirect experimental data on the complete kvap channel , thereby biasing the results toward those for the vsd within the 
 complete channel . the agreement from this comparison is only qualitative 
 because although the difference profiles exhibit very similar shapes 
 ( using  similar  in the geometric sense ) , the membrane 
 profile from the simulations appears 2025% thinner 
 than those for the tethered membrane in the experiments . for the purpose of demonstrating this geometric similarity , a 25% 
 expansion of the abscissa scale for the simulation can readily be 
 seen to improve the agreement between the experiments and the simulation , 
 as also shown in figure 6 . this agreement between 
 the experiment and the simulation is slightly better for the first 
 cycle in the variation of the potential , as shown , than for the second 
 cycle ( not shown ) . in figure 7 , we compare 
 the difference nsld profile structures from the experiments 
 reported here , in which the interferometric data for each value of 
 the potential was an average over many cycles in the variation of 
 the transmembrane potential , with those calculated from the simulations 
 for the vsd within a fully hydrated popc membrane for both the polarizing and depolarizing cases as defined above . 
 here , we show only the case for the 25% expansion of the abscissa 
 scale . like the x - ray case , the experimental difference nsld profiles have very similar geometric shapes compared to their 
 counterparts from these simulations . comparison of the difference nsld profiles determined 
 from the neutron interferometry experiments for vsd : popc membrane 
 tethered to the surface of an inorganic multilayer substrate ( dotted ) 
 with those calculated from molecular dynamics simulations for an untethered 
 vsd : popc membrane ( solid ) for the two pairs of potentials indicated , 
 each membrane fully hydrated . as with the comparison of the difference xsld profiles shown in figure 6 , we show here only the case where the abscissa scale for 
 the difference profiles calculated from the simulation 
 have been expanded by 25% . the time - averaged profiles calculated from 
 the simulations have been smoothed via convolution with a gaussian 
 whose 1/e width was 2 , the larger value used here to allow 
 for the lower spatial resolution of the nsld profiles . . there may be an explanation for the larger extent of the 
 vsd : popc 
 membrane profile in our experiments arising from differences in the 
 x - ray crystal and nmr solution structures of the isolated , detergent - solubilized 
 vsd compared to that within the x - ray crystal structure of the complete 
 kv channel utilized in the simulations . first , the vsd protein construct in the experiments includes 18 additional 
 residues on the n - terminus that were not explicitly modeled in the 
 simulations , since it only appears in the nmr solution structure of 
 the isolated vsd . ten residues in this sequence form an -helix 
 ( designated as the s0 helix ) that , while not expected to change configuration 
 under an applied potential , would occur on the proximal side of the 
 membrane ( with respect to the substrate surface ) . it could increase 
 the overall membrane thickness by as much as 15  , were its orientation 
 approximately parallel to the axis of the transmembrane 4-helix bundle 
 structure formed by helices s1s4 of the vsd , as in the nmr 
 structure , and thereby approximately perpendicular 
 to the membrane surface . second , in the simulations , the 12-residue 
 s4s5 linker helix was aligned nearly parallel to the membrane 
 surface as within the x - ray structure of the complete kv channel , unlike that for the isolated vsd in these experiments where the linker helix is an linear extension 
 of the s4 transmembrane helix , thereby extending the length of the 
 s4 helix in the transmembrane direction by as much as 18  , again 
 depending on its precise orientation approximately perpendicular to 
 the membrane surface . thus , favorable orientations of the s0 helix 
 and of the s4s5 linker helix on the proximal side of the membrane 
 approximately perpendicular to the membrane surface , associated with 
 the very low lipid content of the membrane of only 24 popc 
 nearest - neighbor molecules per vsd in these experiments , 
 would be sufficient to explain the increase in the profile extent 
 of the membrane dominated by the vsd protein , namely from 55 
  in the simulations to 70  , or by 25% . furthermore , potential - dependent changes in the profile would also 
 be expected to occur over this increased extent given the likely origin 
 of the conformational changes expected in the vsd that involve translation 
 of the s4 helix in the transmembrane direction , as described below , 
 that would likely include the translation of its linear extension 
 through the s4s5 linker helix for the isolated vsd . the qualitative level of agreement between experiments and simulations , 
 as shown in figures 6 and 7 , suggests that the voltage - dependent changes observed in 
 the sld profiles arise from conformational changes in the isolated 
 vsd that include an effective displacement of the helical hairpin 
 formed by the s4 helix and the c - terminal half of the s3 helix ( termed 
 s3b ) , as depicted in figure 8 , similar to those 
 measured indirectly within the complete kv channel . the basic side chains in s4 contribute most of the charge that give 
 rise to the gating currents in electrophysiology experiments . the simulations used here predict a substantial translational motion 
 of the s4 helix along the transmembrane direction of 1012 
  between the depolarized and the polarized states . the indirect 
 experiments on the complete kv channel suggest that the magnitude 
 of this displacement may be slightly larger of 1215  
 ( see figure 2 in ref ( 26 ) for a direct comparison ) . importantly , these particular conformational 
 changes must result in the propagation of changes over the entire 
 60  extent of the profile structure of the isolated 
 vsd , as evident from the qualitative level of agreement between the 
 experiments and the simulations . a key structural feature of the membrane - embedded 
 vsd predicted by simulations and confirmed by neutron interferometry is that the interior of the vsd is hydrated 
 along the entire length of its profile . our simulations suggest that 
 measured gating charge displacements are the result of water - catalyzed 
 rearrangements of salt bridges between the s4 basic side chains and 
 the set of conserved acidic side chains on the s1s3 helical 
 segments in the hydrated interior of the vsd ( figure 8) , an observation that is consistent with more extensive simulations 
 of the kv full - length channel performed in the absence of any experimental 
 restraints . these specific structural 
 and mechanistic models gain definitive support from the direct measurements 
 of potential - dependent structural changes within the isolated vsd 
 protein reported here . top row : the vsd backbone is shown in ribbon representation with the 
 s1s3a segments colored orange , the s3b  s4 helix - turn - helix 
 in purple , and the s4s5 linker in green . conserved charged 
 side chains ( shown as filled spheres ) are colored by atom type ( carbon , 
 silver ; oxygen , red ; nitrogen , blue ) . upon a change in applied membrane 
 potential , the motion of the highly conserved basic side chains on 
 ( r1 through k7 ) on the s4 helix induces conformational changes in 
 the s3b s4 helical hairpin . as the basic side chains move within 
 the membrane electric field , they exchange salt - bridge interactions 
 with acidic side chains in conserved positions ( e1 , d2a , d2b , and 
 e3 ) as well as two additional acidic side chains in s3b and s1 ( unlabeled ) . bottom row : the solvation of the vsd by the membrane environment is 
 represented as a h bond network between the vsd basic and acidic side 
 chains ( blue and red , respectively ) , lipid phosphate groups ( yellow ) , 
 and waters ( colored by atom type ) . nevertheless , in order to obtain a more quantitative level 
 of agreement 
 with the experiments , the simulations would need to be modified to 
 better represent the application of transmembrane electric potentials 
 to a tethered vsd : popc membrane more closely approximating that of 
 the experiments , specifically with regard to the asymmetric profile 
 structure of the popc bilayer and the elongated profile extension 
 of the isolated vsd protein within the membrane , as well as the partial 
 hydration on the proximal side of the membrane in contrast to the 
 full hydration of its distal side . such simulations are a substantial 
 investigation on their own beyond the scope of this work . in addition , 
 we anticipate that the experimental structural results will be further 
 refined in the future to define the potential - dependent positions 
 of the key elements of helical secondary structure within the isolated 
 vsd , employing site - directed labeling with methyl - hg for time - resolved 
 resonance x - ray interferometry and site - specific deuterium labeling 
 ( enabled by protein semisynthesis ) for 
 time - resolved neutron interferometry . lastly , we note that the 
 time - resolved x - ray interferometry approach 
 can be also applied to the complete kvap channel , despite its inactivation associated with multiple cycles 
 of depolarization and repolarization , because satisfactory standard errors can be achieved within a single 
 cycle . this will allow a more definitive comparison of the conformational 
 changes within the vsd s profile structure associated with 
 voltage gating for the isolated vsd with those for the vsd within 
 the complete kv channel , due to the distinct advantage of utilizing 
 the same direct method on each of the two proteins under otherwise 
 identical experimental conditions . in 
 contrast with prior studies , this work describes the measurement 
 of changes in the structure of the isolated vsd protein , vectorially 
 oriented within a reconstituted phospholipid bilayer membrane , as 
 a function of the transmembrane electric potential using two direct 
 and independent scattering techniques . time - resolved x - ray interferometry 
 and time - resolved neutron interferometry have been employed to provide 
 the dependence of their respective scattering - length density ( xsld 
 and nsld ) profiles at three values of the potential spanning the physiological 
 range . the results convincingly demonstrate that a potential of 0 
 mv does not actually produce the depolarized state of the vsd , as 
 has been commonly assumed . the changes in the experimental xsld and 
 nsld profiles for both polarizing and depolarizing potentials with 
 respect to zero potential extend over the entire 60  
 length of the profile structure of the isolated vsd . these changes 
 are in qualitative agreement with molecular dynamics simulations of 
 a related membrane system , thus suggesting a possible origin of these 
 changes in terms of the isolated vsd s atomic - level 3-d structure .