electrostatic potentials and free energies were calculated 
  with a modified version of the delphi program , adapted to solve the nonlinear 
  poisson - boltzmann equation for protein - membrane systems .
delphi yields 
  finite - difference solutions to the poisson - boltzmann equation ( the fdpb 
  method ) for a system where the solvent is described in terms of a bulk 
  dielectric constant and concentrations of mobile ions , whereas the solutes 
  ( here , the proteins and membrane ) are described in atomic detail by the 
  coordinates of the individual atoms , their atomic radii , and their partial 
  charges .
the fdpb methodology has been applied to numerous peptide - membrane 
  and protein - membrane systems , producing results that predict successfully and 
  with high accuracy the following : 1 ) macroscopic properties , such as 
  quantitative differences between the membrane interactions of homologous 
  proteins and effects of lipid composition or ionic strength ; and 2 ) 
  microscopic properties , such as the effect of point mutations or binding of 
  metal ions on membrane interactions ( for examples see refs . 
  30 , 
  33 , 
  35 - 40 ) .
atomic structural models of proteins and membranes  the 
  atomic model we used for the gt heterotrimer was based on the 
  gt / i111 crystal structure 
  ( pdb code 1got ) solved by lambright et al . 
 
because the g 
  subunit in this structure is a chimera of gt and 
  gi1 ( residues 216 - 294 of bovine gt were 
  replaced with residues 220 - 298 of rat gi1 to improve protein 
  expression ) , a composite model was built for heterotrimeric 
  gt by manually copying the backbone and side chains of these 
  residues from the corresponding region of native gt , taken 
  from the gt-gdp structure ( 1tag ) 
  ( 41 ) .
the structure of these 
  two corresponding regions is highly similar 
  ( 16 ) , and their backbone root 
  mean square deviation is 0.5  .
the structure of bovine 
  g11 ( pdb code 2trc ) 
  ( 42 ) was used in calculations 
  for dissociated g11 , as in a previous study 
  ( 30 ) . both 
  g1 termini in the heterotrimeric model , which are slightly 
  shorter than in the structure of dissociated 
  g11 ,
were extended by manually copying the 
  extra residues from the structure of dissociated 
  g11 .
the n terminus of 
  gt , in its heterotrimeric form , is in an extended helical 
  conformation and is stabilized by interactions with 
  g11 ( see supplemental fig .
after dissociation from 
  g11 , this subdomain does not have any 
  significant stabilizing interactions with the membrane ( supplemental fig .
available structures of monomeric gt are not applicable to 
  our calculations because they lack the entire n terminus , which was cleaved 
  prior to crystallization .
however , we note that the 
  n terminus in the crystal structure of the homologous 
  gi1-gdp ( 68% sequence identity to gt ) 
  refolds onto the bulk of the protein to form a compact subdomain that is 
  stabilized by a network of interacting residues that are conserved between 
  gi1 and its homologs go and 
  gt ( 43 ) . a 
  folded and highly ordered gi1 n terminus was also shown for 
  the myristoylated form of gi1 in solution , and it was 
  suggested that this feature is conserved in homologous g subunits 
  ( 44 ) .
we therefore assumed 
  that soluble gdp - bound gt adopts a similar conformation , and 
  we modeled it on the structure of monomeric gi1-gdp ( pdb 
  code 1gdd ) using the program nest 
  ( 45 ) and remodeled unconserved 
  side chains using scap 
  ( 46 ) .
hydrogen atoms were added to the protein structures with the program 
  charmm , and the structures were subjected to conjugate gradient minimization 
  with a harmonic restraint force of 50 kcal / mol /  applied to the heavy 
  atoms located at the original crystallographic coordinates .
hydrogens were 
  added to the guanine nucleotides bound to the g subunits using the 
  builder module in insight ii ( accelrys ) .
phospholipid bilayers of lateral dimensions 165  172  
  and ratios of 0:1 , 1:8 , 1:5 , 1:3 , 1:2 , and 1:1 acidic lipid 
  ( phosphatidylserine ) to neutral lipids ( phosphatidylcholine ) were built as 
  described in previous work 
  ( 30 , 
  33 - 37 , 
  39 , 
  47 ) . in vivo
, the 
  distribution of acidic lipids is known to be asymmetric across the bilayer , 
  and following previous studies 
  ( 30 , 
  33 , 
  35 - 40 , 
  48 , 
  49 ) , we assume that all of the 
  phosphatidylserine is located on the cytosolic leaflet of the rod outer 
  segment membranes . except where specified otherwise , in our calculations we 
  used bilayers with a ratio of 1:2 phosphatidylserine / phosphatidylcholine ; this 
  ratio has been assumed to be a reasonable approximation for the lipid 
  composition facing the transducin under physiological conditions 
  ( 30 ) , and indeed , as shown in 
  fig . 4 and discussed below , 
  this membrane composition is representative of the wider range of possible 
  compositions . as in previous work , we assume that the bilayer does not change 
  structure or position when it interacts with the protein ( see ref . 
 
the protein / membrane model was mapped onto a fine 
  three - dimensional grid , where each small cube represents a small region of the 
  peptide , membrane , or solvent . as in previous studies of comparable 
  protein - membrane systems ( 30 , 
  33 - 37 , 
  39 )
, we took the charges and 
  radii used for the amino acids from the charmm22 parameter set and for the 
  lipids from ref .
regions 
  inside the molecular surfaces of the protein and membrane were assigned a 
  dielectric constant of 2 , and those outside were assigned a dielectric 
  constant of 80 , combined with an ion exclusion layer of 2  around the 
  solute . unless stated otherwise , the salt concentration was set to 100 
  mm , as in previous studies 
  ( 30 , 
  33 , 
  35 - 40 ) . 
 
the numerical calculation of the potential was iterated to convergence , 
  defined as the point at which the potential changes less than 10 
  kt / e between successive iterations .
a sequence of focusing runs of 
  increasing resolution was employed to calculate the electrostatic potentials 
  ( e.g. 0.3 , 0.6 , 1.2 , and 2.4 grid /  ) .
electrostatic energies 
  were obtained using the calculated potentials , and the electrostatic energy of 
  a protein - membrane interaction was determined as the difference between the 
  following : 1 ) the electrostatic free energy of the protein in a specific 
  orientation and distance relative to the membrane surface ; and 2 ) the 
  electrostatic free energies of the protein and membrane infinitely far apart 
  ( i.e. calculated separately ) .
the numerical error of the free energy 
  calculations , estimated by the difference between the calculations of the two 
  highest resolution scales , was < 0.1 kcal / mol in all calculations .
the nonspecific electrostatic interactions calculated here are relatively 
  insensitive to local changes in conformation .
different combinations of 
  composite models from two separate pdb structures or different minimization 
  protocols , which produced global root mean square deviations of up to 2 
   between models , changed the calculated electrostatic energies of 
  interactions by less than the numerical error for a given protein - membrane 
  complex
. global sampling of transducin orientations to calculate 
  transducin - membrane interactions  previous studies used visual 
  inspection to find an approximate minimum free energy orientation of a protein 
  relative to the membrane and then sampled extensively close to this 
  orientation to find the minimum free energy orientation 
  ( 30 , 
  33 - 37 ) . 
  here
, however , visual inspection could not reliably determine the approximate 
  minimum - energy orientation of the gt heterotrimer and 
  gt with respect to the membrane , because these proteins do 
  not have prominent positively charged patches that clearly determine the 
  orientation of minimum energy .
we therefore implemented a global sampling of 
  all nonredundant euler rotations , rotating the protein around the point in the 
  structure closest to the lipid attachment point .
this point corresponds to the 
  n terminus in gt calculations , the c terminus of 
  g1 in g11 calculations , 
  and the midpoint between them for the heterotrimer structure ( where the two 
  termini are 15  apart ) .
for each orientation , the membrane was 
  moved so as to place the molecular surfaces of the protein and membrane 3 
   apart ( r = 3  ) , and the electrostatic energy was 
  calculated as above .
r = 3  was chosen because at orientations 
  where the electrostatic interaction is attractive , the energy value at this 
  distance is minimal ( see supplemental material and refs . 
 
30 , 
  33 , 
  35 , 
  40 ) . combining lipid anchor constraints with global orientation 
  sampling
 the transducin structures used here do not have 
  coordinates for the lipid anchors nor for the termini to which the anchors are 
  covalently attached as follows : the myristoyl - gaga- at the n terminus of 
  gt and the -ggc - farnesyl at the c terminus of 
  g1 . for each orientation we assumed that a lipid anchor can 
  reach the membrane if the measured distance between each relevant terminus and 
  the membrane was equal to or less than 13  for gt and 
  10  for g1 , thresholds corresponding to the length of 
  the fully extended linkers .
16 , based on their amino acid 
  sequence ) and able to adopt fully extended conformations . when we determined 
  that a lipid anchor can reach the membrane in a specific orientation , we 
  assigned to this orientation an energetic contribution of -6 kcal / mol , which 
  corresponds to the estimated energetic contribution of an individual lipid 
  modification ( see under  discussion  for more details on these 
  estimates ) .
when both lipid anchors could reach the membrane , we assigned to 
  such an orientation an energetic contribution of -12 kcal / mol .
calculation of average energy and entropy  previous work 
  established that when the peripheral association between a protein and a 
  membrane is of substantial attractive nature , the relative binding energies 
  and the electrostatic contribution to binding are well approximated by the 
  energy value at the minimum free energy orientation 
  ( 30 , 
  33 - 37 , 
  39 ) .
in addition to finding 
  the minimal free energy value , we also calculated the boltzmann - weighted 
  average energy , as in ref .
37 , 
  and see equation 1 , where k is the boltzmann constant , and t is the absolute 
  temperature .
the calculations were repeated twice , with and without the 
  constraints of the lipid anchor .
the latter can show whether specific 
  orientations provide sufficient attraction to the membrane to compensate for 
  the energetic penalty associated with removing the lipid anchor out of the 
  bilayer ( see above ) , and represent the effect of electrostatics on the soluble 
  forms of the proteins ( i.e. before the lipid anchors attach to the 
  membrane ) .
we used the  bootstrapping  re - sampling method to check 
  the statistical significance of our results ( as in ref . 
 
. the free energy cost because of the entropic penalty associated with 
  limiting gt rotations was approximated by equation 
  2 , where s2 is the entropy of gt with the 
  additional constraints ( lipid anchor and/or electrostatics ) , and 
  s1 is the reference state ( having the same number of 
  microstates but with an equal probability of being in each state and with all 
  of these probabilities summing to unity ) .
we estimated the error in the 
  entropy calculation by adding a random value ( in the range of the numerical 
  error , 0.1 kcal / mol ) to the calculated free energies and repeated the entropy 
  calculations 100 times , reaching an estimated error of 0.02 kcal / mol .
figure 1.interactions of the gt heterotrimer with the membrane . 
 a , global orientation sampling of the gt heterotrimer .
the 
  x (  ) and y axes (  ) mark euler angles of rotation 
  from the initial orientation ( supplemental fig .
the z axis and 
  the color code both mark the calculated electrostatic free energy of 
  interaction with the membrane ; positive ( red ) energies will result in 
  repulsion , whereas negative ( blue ) energies will result in 
  attraction .
the magenta and cyan lines enclose lipid - allowed 
  orientations , which enable the g1 ( magenta ) and the 
  gt ( cyan ) lipid anchors to reach the membrane . 
 
representative gt orientations are marked on the plot of global 
  orientation sampling for gt , with letters corresponding to 
  subsequent panel captions .
b , gt orientation of minimum 
  free energy , which is representative of tilted orientations ; 
  gel = -0.8 kcal / mol .
c , electrostatic 
  potential map of the gt heterotrimer in the orientation of minimum 
  free energy ( the same orientation as in b ) .
electrostatic potential 
  maps were visualized by drawing equi - potential contour meshes for the values 
  + 1 kt / e ( 25mv , blue mesh ) and -1 kt / e ( -25 mv , 
  red mesh ) .
gt subunits are shown in connolly surface 
  representation and colored pink (  ) , light green 
  (  ) , and light blue (  ) , and the functionally relevant 
  termini are annotated .
two large negatively charged patches on 
  gt and g11 are marked 
  with orange and red arrows , respectively ; these patches 
  cause the repulsion observed in the lipid - allowed orientations at   
  0 and  > 60. d , representative parallel orientation ; 
  gel = 1.1 kcal / mol .
e , lipid - allowed 
  orientation with moderate repulsive electrostatics ; 
  gel = 1.8 kcal / mol .
f , lipid - disallowed 
  orientation , where the g1 lipid anchor can not reach the 
  membrane ; gel = 4 kcal / mol .
g , 
  lipid - disallowed orientation , where both lipid anchors can not reach the 
  membrane ; gel = 3.5 kcal / mol . b and 
  d - g , gt subunits are shown in worm representation 
  and are colored red (  ) , green (  ) , and 
  blue (  ) .
the n - terminal helix of gt is 
  colored magenta , and the c terminus of gt is 
  colored orange .
interactions of the gt heterotrimer with the membrane . 
 a , global orientation sampling of the gt heterotrimer . the 
  x (  ) and y axes (  ) mark euler angles of rotation 
  from the initial orientation ( supplemental fig .
the z axis and 
  the color code both mark the calculated electrostatic free energy of 
  interaction with the membrane ; positive ( red ) energies will result in 
  repulsion , whereas negative ( blue ) energies will result in 
  attraction .
the magenta and cyan lines enclose lipid - allowed 
  orientations , which enable the g1 ( magenta ) and the 
  gt ( cyan ) lipid anchors to reach the membrane . 
 
representative gt orientations are marked on the plot of global 
  orientation sampling for gt , with letters corresponding to 
  subsequent panel captions .
b , gt orientation of minimum 
  free energy , which is representative of tilted orientations ; 
  gel = -0.8 kcal / mol .
c , electrostatic 
  potential map of the gt heterotrimer in the orientation of minimum 
  free energy ( the same orientation as in b ) .
electrostatic potential 
  maps were visualized by drawing equi - potential contour meshes for the values 
  + 1 kt / e ( 25mv , blue mesh ) and -1 kt / e ( -25 mv , 
  red mesh ) .
gt subunits are shown in connolly surface 
  representation and colored pink (  ) , light green 
  (  ) , and light blue (  ) , and the functionally relevant 
  termini are annotated .
two large negatively charged patches on 
  gt and g11 are marked 
  with orange and red arrows , respectively ; these patches 
  cause the repulsion observed in the lipid - allowed orientations at   
  0 and  > 60. d , representative parallel orientation ; 
  gel = 1.1 kcal / mol .
e , lipid - allowed 
  orientation with moderate repulsive electrostatics ; 
  gel = 1.8 kcal / mol .
f , lipid - disallowed 
  orientation , where the g1 lipid anchor can not reach the 
  membrane ; gel = 4 kcal / mol .
g , 
  lipid - disallowed orientation , where both lipid anchors can not reach the 
  membrane ; gel = 3.5 kcal / mol . b and 
  d
- g , gt subunits are shown in worm representation 
  and are colored red (  ) , green (  ) , and 
  blue (  ) . the n - terminal helix of gt is 
  colored magenta , and the c terminus of gt is 
  colored orange .
we translated differences in the free energy of interaction to changes in 
  association / dissociation rates ( k ) using equation 3 , 
  ( eq.3)\documentclass[10pt]{article } 
 \usepackage{amsmath } 
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 \usepackage{amssymb } 
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 \pagestyle{empty } 

 \oddsidemargin -1.0 in 

 \begin{document } 
 \begin{equation*}\;\;{\delta}k\hspace{1em}=\hspace{1em}e^{-{\delta}gi / k_{b}t}\end{equation*}\end{document } 
  visualizing three - dimensional potential 
  maps  three - dimensional potential maps were visualized by mapping 
  the values onto the molecular surface of the protein and by drawing 
  equi - potential contour meshes that connect all the points in space having a 
  specific potential value ( here 1 kt / e , which are equal to 
   25 mv ) .
characterizing the interaction of the gt heterotrimer with 
  the lipid bilayer  we analyzed the interaction of gt with 
  the membrane using global orientation sampling , using the fdpb method to 
  calculate the electrostatic free energy of interaction at each orientation 
  ( fig .
at each 
  orientation , we also measured whether each of the two lipid anchors can reach 
  the lipid bilayer ( marked as  lipid - allowed  orientations in 
  fig .
these measurements show that 
  11% of all possible gt orientations enable both lipid anchors 
  to reach the membrane . by calculating the effects of electrostatics and the 
  lipid anchors separately
, we can examine their individual contributions and 
  analyze cases in which only one of these factors is significant for membrane 
  interactions ( e.g. when soluble transducin targets back to the 
  membrane from the cytosol , or when transducin interacts in vitro with 
  neutral membranes ) .
when we determined that a lipid anchor can reach the 
  membrane in a specific orientation , we assigned to this orientation an 
  energetic contribution of -6or -12 kcal / mol , corresponding to the estimated 
  energetic contribution of one or two lipid modifications , respectively ( see 
   discussion  for more details on these estimates ) .
we assumed that 
  a lipid anchor can reach the membrane when the distance between the bilayer 
  and the relevant terminus in the structure was equal to or less than 
  predetermined distance thresholds ( see  experimental procedures  ) . 
 
this assumption considers the terminal 3 - 4 amino acids that connect to the 
  lipid anchors and are not present in the crystal structure as conformationally 
  flexible linkers that are able to fully extend , as was suggested previously 
  based on their amino acid sequence 
  ( 16 ) .
nevertheless , our 
  results are not dependent on the exact values of these distance thresholds ; 
  because of the large size of gt , its geometry , and the close 
  proximity of the two relevant termini , increasing or decreasing these distance 
  thresholds by up to 50% resulted in essentially the same ensemble of 
  lipid - allowed orientations .
only a 
  minor ensemble of orientations ( 6% ) exhibits either a small attraction 
  ( 3% of all orientations ) or a weak repulsion .
we label orientations with 
  an interaction energy ( gel ) within 2 kcal / mol of 
  the minimum electrostatic free energy ( -0.8 kcal / mol , see 
  table 1 ) , as 
   electrostatically favorable orientations .
 we chose this 
  threshold because it corresponds to a substantial ( 30-fold ) decrease in 
  the occupation probability with respect to the energy minimum .
( note that the 
  results are relatively insensitive to the precise value of the threshold 
  because the selected value is far enough from the minimum so that changing it 
  by 0.5 kcal / mol has a small effect on which orientations are labeled 
  as favorable . )
the electrostatically favorable orientations of gt 
  are clustered around the orientation of minimum electrostatic free energy 
  ( fig .
a small positively charged patch around the attachment points of 
  the two lipid anchors is proximal to the membrane , whereas the negative 
  potential around most of gt is positioned further away from the 
  membrane ( e.g. fig . 
 
this results in a weak attraction at the orientation 
  of minimum electrostatic free energy ( -0.8 kcal / mol ) and an even smaller 
  average energy of interaction ( -0.3 kcal / mol , see 
  table 1 ) .
table 1minimum and average electrostatic free energies of interaction of 
  heterotrimeric / dissociated transducin with the lipid bilayerthe electrostatic free energy values are in kcal / mol , and the numerical 
  error is < 0.1 kcal / mol.transducin stategel , min ( lipid anchor 's in membrane)gel , min ( all possible 
  orientations)a<gel > b(lipid anchor / s in membrane)<gel > b(all possible 
  orientations)a  
   0.8 
   0.8 
   0.3 
   ~0 
    
   3.2 
   3.2 
   2.8 
   2.7 
 
   
 
  + 1.8 
 
  1.2 
 
  + 2.2 
 
  0.4 
 
acalculated by sampling of all possible orientations ( i.e. without 
  the constraints of the lipid anchor / s).bboltzmann - weighted averaged energies ( see  experimental 
  procedures  for details ) .
minimum and average electrostatic free energies of interaction of 
  heterotrimeric / dissociated transducin with the lipid bilayer the electrostatic free energy values are in kcal / mol , and the numerical 
  error is < 0.1 kcal / mol . calculated by sampling of all possible orientations ( i.e. without 
  the constraints of the lipid anchor / s )
. boltzmann - weighted averaged energies ( see  experimental 
  procedures  for details ) . fig .
the orientation of minimum free energy 
  ( fig . 1 , b and 
  c ) places the n - terminal helix of gt at 
  an angle of 30 to the membrane surface and is similar to the tilted 
  orientations suggested previously ( see above ) .
1d ) position negatively charged patches near the c 
  terminus of gt ( marked with an orange arrow in 
  fig .
1c ) close to the 
  membrane and therefore result in electrostatic repulsion . because of this 
  repulsion , parallel orientations are less favorable than the orientation of 
  minimum free energy ( a tilted orientation ) by 2 kcal / mol , which 
  corresponds to 30-fold difference in occupancy probability . furthermore , 
  large negatively charged patches on g11 
  ( marked with a red arrow in fig . 
 
1c ) oppose rotations of gt to orientations 
  that position the n - terminal -helix of gt at angles 
  > 60 to the membrane surface ( fig . 
  1 , a and e ) .
these electrostatic repulsions 
  limit gt rotation and constrain the gt c 
  terminus , which is essential for binding activated rhodopsin , to face the 
  membrane surface in all of the allowed orientations of gt .
to estimate at the ensemble level how rotational electrostatic and/or lipid 
  anchor constraints affect membrane - associated gt , we calculated the 
  difference in the entropic component of the rotational free energy that 
  results from these constraints .
the reference state was a membrane - attached 
  gt that can occupy all possible orientations with an equal 
  probability ( i.e. without any rotational constraints ) .
note that the 
  effect on the degrees of freedom of gt does not depend on the 
  strength of the gt - membrane interactions in specific orientations , 
  but rather is a result of the global shape and characteristics of the 
  energy - orientation landscape on gt ( as shown in 
  fig .
when we 
  applied the rotational constraints of both lipid anchors , the entropic 
   cost  was 1.1 kcal / mol . applying only the constraint of the 
  electrostatic interactions with the membrane results in an entropic cost of 
  1.3 kcal / mol ( with an estimated error of 0.02 kcal / mol ,
when these constraints 
  were applied together , the entropic energy cost was 1.8 kcal / mol , 
  i.e. electrostatics further enhance the effect of the lipid anchors 
  by a factor of 3.5 .
membrane interactions of dissociated 
  g11electrostatic 
  interactions of the dissociated gt and 
  g11 with the lipid bilayer are very 
  different from one another and from those of the transducin heterotrimer 
  ( figs . 2 and 
  3 versus 
 fig .
2a ) , we found a 
  similar orientation of minimum electrostatic free energy ( with a similar 
  gel = -3.2 kcal / mol ; 
  table 1 ) as reported in a 
  previous study ( 30 ) , which 
  sampled around an initial orientation chosen by visual inspection .
we also 
  observed that , unlike the gt heterotrimer , 
  g11 is attracted to the membrane in many 
  orientations ( 18% of all possible orientations ) , allowing 
  membrane - attached g11 to sample a wide 
  range of dissimilar orientations that are both lipid - allowed and 
  electrostatically favorable ( fig . 
  2 ) .
furthermore , most of the electrostatically favorable orientations of 
  g11 and particularly all orientations with 
  gel less than -2 kcal / mol enable the lipid anchor 
  to reach the membrane ( fig . 
 
the larger range of lipid - allowed orientations with 
  significant electrostatic attraction to the membrane is also reflected in a 
  stronger boltzmann - weighted average interactions energy ( -2.8 kcal / mol ; see 
  table 1 for a detailed 
  comparison ) .
increasing or decreasing the distance threshold for determining 
  whether the lipid anchor can reach the membrane by 50% had no effect on these 
  results . additionally ,
when we removed the constraints of the lipid anchor and 
  sampled all possible orientations of g11 , 
  the electrostatic free energies of interaction did not change 
  ( table 1 ) .
taken together , 
  these results suggest that the contributions of the lipid anchor and 
  electrostatics to the free energy of g11 
  interaction with the membrane are independent of one another and therefore 
  additive .
figure 2.interactions of g11 
  with the membrane . a , global orientation sampling of 
  g11 .
the magenta line encloses 
  lipid - allowed orientations , which enable the g1 c - terminal 
  farnesyl to reach the membrane .
representative lipid - allowed and 
  electrostatically favorable g11 
  orientations are marked with letters corresponding to subsequent 
  panel captions .
b , g11 orientation 
  of minimum free energy ; gel = -3.2 kcal / mol . 
 
c , electrostatic potential map of 
  g11 in the orientation of minimum free 
  energy ( the same orientation as in b ) , but rotated 90 around the 
  z axis to better visualize the segregation of charges .
g11 subunits and the lipid bilayer are 
  depicted as in fig . 1 . 
 
b and d - f , the c terminus of g1 is marked 
  with a black arrow , and the c terminus of g1 is 
  marked with a magenta arrow .
interactions of g11 
  with the membrane . a , global orientation sampling of 
  g11 .
the magenta line encloses 
  lipid - allowed orientations , which enable the g1 c - terminal 
  farnesyl to reach the membrane .
representative lipid - allowed and 
  electrostatically favorable g11 
  orientations are marked with letters corresponding to subsequent 
  panel captions .
b , g11 orientation 
  of minimum free energy ; gel = -3.2 kcal / mol . 
 
c , electrostatic potential map of 
  g11 in the orientation of minimum free 
  energy ( the same orientation as in b ) , but rotated 90 around the 
  z axis to better visualize the segregation of charges .
g11 subunits and the lipid bilayer are 
  depicted as in fig . 1 . 
 
b and d - f , the c terminus of g1 is marked 
  with a black arrow , and the c terminus of g1 is 
  marked with a magenta arrow .
figure 3.interactions of gt with the membrane . 
 a , global orientation sampling of gt. the cyan 
  line encloses lipid - allowed orientations , which enable the 
  gt n - terminal lipid anchor to reach the membrane . the 
  lipid - allowed orientation with minimal free energy of interaction 
  ( gel = 1.8 kcal / mol ) is marked with a black 
  arrow .
the lipid - disallowed orientation with minimal global electrostatic 
  free energy ( -1.2 kcal / mol ) is marked with a yellow arrow .
b , 
  electrostatic potential map of gt in the lipid - allowed 
  orientation with the minimal free energy of interaction , depicted as in 
  fig .
1 . interactions of gt with the membrane . 
 a , global orientation sampling of gt. the cyan 
  line encloses lipid - allowed orientations , which enable the 
  gt n - terminal lipid anchor to reach the membrane . the 
  lipid - allowed orientation with minimal free energy of interaction 
  ( gel = 1.8 kcal / mol ) is marked with a black 
  arrow .
the lipid - disallowed orientation with minimal global electrostatic 
  free energy ( -1.2 kcal / mol ) is marked with a yellow arrow .
b , 
  electrostatic potential map of gt in the lipid - allowed 
  orientation with the minimal free energy of interaction , depicted as in 
  fig .
membrane interactions of dissociated 
  gtwithin the gt heterotrimer , the 
  lipidated n terminus of gt assumes an extended helical 
  conformation stabilized by interactions with 
  g11 ( e.g. 
 fig .
however , this n - terminal 
  helix is likely to refold into a compact conformation upon the dissociation of 
  gt from g11 .
although no 
  available crystal structure of monomeric gt contains this 
  part of the molecule , because of its proteolytic removal prior to 
  crystallization , the crystal structure of the homologous 
  gi1-gdp ( 43 ) 
  does contain the n terminus , which is folded onto the bulk of 
  gt and is stabilized by a network of interacting residues 
  conserved between gi1 and gt ( and also 
  go ) ( 43 ) . 
  furthermore , a folded and highly ordered gi1 n terminus was 
  shown for the myristoylated form of gi1-gdp in solution , and 
  it was suggested that this structural feature is conserved in homologous 
  g subunits ( 44 ) .
we 
  therefore proceeded with calculations for dissociated gt-gdp 
  modeled on the structure of gi1-gdp 
  ( 43 ) as a template 
  ( fig .
3 ) . global orientation sampling of this gt conformation 
  showed repulsion by the negatively charged membrane in most orientations 
  ( fig .
3a ) , because the 
  entire surface of gt is dominated by negative charges 
  ( fig .
3b ) . in 
  particular , all the lipid - allowed orientations of gt 
  ( 11% of all possible orientations ) were repulsive .
a few orientations 
  that exhibited a small attraction to the membrane ( up to -1.2 kcal / mol ; see 
  fig .
3a and 
  table 1 ) placed the lipid 
  attachment point on the distal face of gt relative to the 
  membrane , and because of the energetic cost of removing the lipid anchor from 
  the bilayer ( approximately -6 kcal / mol , see  discussion  ) , these 
  orientations are disallowed .
calculation of the electrostatic free energy of interaction 
  of different gt states with bilayers of different acidic lipid 
  composition .
the vertical dashed line marks the lipid composition 
  used in most calculations here ( 33% acidic lipids ) , whereas the two 
  vertical dotted lines mark the range of possible lipid compositions 
  facing transducin in rod outer segment disks ( see text for details ) .
calculation of the electrostatic free energy of interaction 
  of different gt states with bilayers of different acidic lipid 
  composition .
the vertical dashed line marks the lipid composition 
  used in most calculations here ( 33% acidic lipids ) , whereas the two 
  vertical dotted lines mark the range of possible lipid compositions 
  facing transducin in rod outer segment disks ( see text for details ) .
we quantified how the repulsive interactions , which characterize the 
  lipid - allowed orientations of gt , affect its membrane 
  affinity ( table 1 ) . for 
  significant membrane attraction
, the minimal free energy of interaction 
  provides a good estimate and an upper bound to the membrane affinity 
  of the protein ( 30 , 
  33 , 
  35 , 
  39 ) .
however , for repulsive 
  interactions , as in the case of monomeric gt , the magnitude 
  of the minimal electrostatic repulsion in the lipid - allowed ensemble ( 1.8 
  kcal / mol ) provides a lower bound to the overall repulsion .
because 
  all the other lipid - allowed orientations are more repulsive , the 
  boltzmann - weighted average of all gt lipid - allowed 
  orientations is higher ( 2.2 kcal / mol ) , reducing the membrane affinity of 
  gt in this conformation by 40-fold . a 50% increase in 
  the distance threshold for determining whether the lipid anchor can reach the 
  membrane had a small effect on these results ( < 0.2 kcal / mol ) .
conversely , 
  decreasing the distance threshold ( i.e. assuming the linker is not 
  fully flexible ) resulted in significantly increased repulsion .
dependence of the electrostatic interactions on distance and membrane 
  composition  we investigated whether the choice of protein - bilayer 
  distance ( 3  ) influenced our major conclusions .
calculation of the free 
  energy of interaction as a function of distance showed a weak dependence 
  ( supplemental fig .
s3 ) , as long as the surfaces of the gt subunits 
  and the membrane are 3  apart , a likely assumption given their 
  highly charged nature and the strong repulsion at distances <3  ( see 
  refs .
30 , 
  33 , 
  35 - 40 ) . as in previous work ( 30 )
, 
  we used a bilayer model containing 33% acidic lipids to reproduce the bulk 
  electrostatic properties of the cytosolic leaflet of disk membranes that faces 
  transducin .
previous investigations reported various proportions of acidic to 
  neutral lipids in rod outer segment membranes 
  ( 51 - 54 ) 
  with the percentage of acidic lipids ranging from 13 to 20% .
the distribution 
  of acidic lipids is known to be asymmetric across the bilayer , and previous 
  studies assumed that all of the phosphatidylserine is located on the cytosolic 
  leaflet of the membrane ( 30 , 
  33 , 
  35 - 40 , 
  48 , 
  49 ) .
accordingly , the 
  percentage of acidic lipids facing gt can range from 25 to 40% . 
 
4 shows that within this 
  range , the membrane composition has almost no effect on the electrostatic 
  interaction of the charged bilayer with 
  gt / g11/gt in 
  their minimal free - energy orientation ; these different membrane compositions 
  change the calculated electrostatic interaction by less than 0.1 kcal / mol for 
  gt and less than 0.3 kcal / mol for gt and 
  g11 .
dependence of the electrostatic interactions on ionic strength and 
  implications for transducin purification protocols  the membrane 
  interactions of the transducin heterotrimer and its dissociated subunits 
  depend on the ionic strength , with each of the three molecules exhibiting a 
  unique salt dependence ( fig . 
  5 ) .
increasing the salt concentration from 100 mm , at 
  which our calculations were performed , to the physiological conditions of 
  150 mm , changes the membrane interaction energies of 
  transducin and its subunits by < 10% ( < 0.03 kcal / mol for the 
  heterotrimer , < 0.2 kcal / mol for gt , and < 0.3 kcal / mol 
  for g11 ) and therefore does not 
  significantly affect our major conclusions .
in contrast , hypotonic conditions 
  change the interaction energies for all three species dramatically .
the small 
  attraction of the gt heterotrimer to the membrane at physiological 
  ionic strength changes to a strong repulsion under hypotonic conditions . as 
  shown previously ( 30 ) ,
the 
  electrostatic interaction of dissociated 
  g11 exhibits a parabolic dependence on the 
  ionic strength , with a maximal attraction at 50 mm salt and a 
  reduction in affinity under more extreme hypotonic conditions . unlike 
  g11 , gt is 
  electrostatically repelled by the membrane at physiological ionic strength , 
  and this repulsion increases considerably when the ionic strength is reduced ; 
  a 10-fold reduction increases the repulsion to 8 kcal / mol , more than the 
  membrane affinity conferred by the lipid anchor ( -6 kcal / mol , see below ) .
in this study , we quantified how the interplay between lipid anchorage and 
  electrostatics determines both membrane affinity and the range of allowed 
  transducin orientations on the membrane surface .
these properties change 
  dramatically upon the activation - dependent dissociation of transducin into 
  gt and g11 and are likely 
  to significantly affect the protein - protein interactions and the subcellular 
  localization of the transducin heterotrimer and its individual subunits .
interactions of gt with the membrane and their implication 
  for transducin activation  it is well established that the membrane 
  affinity of gt is determined predominantly by its lipid anchors 
  ( 4 ) : the heterogeneous 
  n - terminal acylation of gt 
  ( 13 , 
  55 - 58 ) 
  and the c - terminal farnesylation of g1 
  ( 59 , 
  60 ) .
the majority of 
  gt subunits are acylated by c12 or c14:2 lipids , which 
  contribute approximately -6 kcal / mol to membrane binding 
  ( 61 ) .
farnesylation was shown 
  to confer a membrane affinity comparable with that of a lauryl ( c12 ) anchor 
  ( 62 ) and therefore can also 
  add approximately -6 kcal / mol to membrane binding . in a maximal estimate ,
the 
  contributions of both anchors are additive and sum to approximately -12 
  kcal / mol .
our results show that under physiological conditions the 
  electrostatic contribution to the membrane affinity of the heterotrimer is 
  insignificant ( -0.3 kcal / mol ) , and therefore its membrane attachment is likely 
  to be set exclusively by the lipid anchors . under hypotonic conditions
, 
  however , strong electrostatic repulsion counteracts the lipid anchors of 
  gt ( fig .
5 ) and 
  facilitates its release from membranes , as has been successfully utilized in 
  several transducin purification protocols 
  ( 26 - 29 ) .
global orientation sampling enabled us to compare the probabilities of all 
  previously proposed gt orientations on the membrane surface .
the 
  tilted orientations suggested by hessel et al . and chabre and le 
  maire ( 24 , 
  25 ) are similar to the 
  gt orientation identified by our analysis as the most favorable . on 
  the other hand , parallel orientations 
  ( 16 - 23 ) 
  place the negatively charged patches around the c terminus of 
  gt close to the negatively charged bilayer , making these 
  orientations less favorable by 2 kcal / mol ( 30-fold difference in 
  occupancy probability ) .
although the magnitude of these energetic differences 
  is relatively small , they are consistent with the dramatic charge distribution 
  on gt , where most of the surface of the heterotrimer is negatively 
  charged except for the small area around the lipid anchor attachment points 
  ( fig .
furthermore , we observe that in the electrostatically favorable orientations 
  of gt , the gt - bilayer interface is relatively small 
  ( e.g. fig . 
 
this small , positively charged 
  gtfootprint  on the membrane is consistent with the 
  results of hessel et al . 
 
( 24 ) , who showed that only a 
  small number of negatively charged lipids directly interact with 
  membrane - bound gt .
they speculated that such a small interface 
  might contribute to the fast diffusion of gt along the crowded 
  membrane surface of rod outer segment disks , which is necessary for the rapid 
  activation of many gt molecules by each rhodopsin ( see discussion 
  in ref . 2 and see below ) . 
 
notably , these results may appear to contradict the cryo - em structure of 
  membrane - bound gt 
  ( 63 ) , which suggested a 
  parallel gt orientation with a larger membrane interface and a 
  close contact between the c terminus of gt and the membrane 
  surface .
however , the membranes used in that study contained 20% cationic 
  lipids , which presumably attracted the negatively charged patches around the c 
  terminus of gt. our calculations predict that these very 
  patches are repelled by negatively charged biological membranes .
our analysis also shows that electrostatic repulsion by the membrane is one 
  of the factors limiting the rotational degrees of freedom of the heterotrimer . 
 
interestingly , all gt orientations that are lipid - allowed and 
  electrostatically favorable are sterically predisposed to interact with 
  rhodopsin ( supplemental fig .
this suggests that the orientational 
  confinement of transducin by lipid anchorage and electrostatics may contribute 
  to its extremely rapid activation rate .
indeed , the rate of transducin 
  activation on the surface of photoreceptor membranes can reach several hundred 
  gt molecules per photoexcited rhodopsin / s 
  ( 2 , 
  6 , 
  7 ) , whereas in detergent 
  solution the maximal speed of gt activation is only 30 - 50 
  gt molecules per second 
  ( 9 , 
  64 ) .
the faster gt 
  activation rate in native membranes was attributed by ernst et al . 
 
( 9 ) to the orientation of 
  gt at the membrane surface before it encounters rhodopsin . in 
  agreement with this hypothesis and , assuming that our calculated reduction in 
  rotational entropy ( 1.8 kcal / mol ) lowers the activation energy for 
  gt - rhodopsin complex formation by a similar value , this orientation 
  confinement would accelerate gt activation by 20-fold .
it should be noted that although our calculations were performed with a 
  membrane bilayer , a significant portion of the photoreceptor membrane surface 
  is occupied by rhodopsin .
therefore , any direct projection of our analysis to 
  transducin activation in vivo should be treated cautiously . 
 
quantification of the effect of gt orientation by the membrane on 
  activation kinetics in vivo would require a more detailed 
  understanding of the surface characteristics of native photoreceptor membranes 
  and remains beyond the scope of this study .
nevertheless , the ability of a 
  single photoexcited rhodopsin to activate hundreds of gt 
  molecules / s requires rapid diffusion of gt along the membrane 
  bilayer ( 2 , 
  6 , 
  7 , 
  65 ) .
therefore , any 
  interactions between gt and nonactivated rhodopsin are expected to 
  be weak enough not to impede this fast lateral diffusion .
the orientation of transducin in relation to the membrane was also debated 
  in the context of whether transducin binds to a monomeric or dimeric rhodopsin 
  form ( ref .
66 for the most recent review 
  on g protein - coupled receptor oligomerization ) .
it has been suggested that 
  monomeric rhodopsin can bind transducin in a tilted orientation 
  ( 25 ) , whereas dimeric 
  rhodopsin was modeled in a complex with transducin in a parallel orientation 
  ( 67 ) . the tilted orientation 
  we find would appear to be more consistent with monomeric rhodopsin .
however , 
  the energy differences we calculate are not large enough to preclude a 
  reorientation of transducin so as to optimize its interaction with a rhodopsin 
  dimer .
membrane interactions of dissociated 
  g11 and 
  gtour analysis indicates that the electrostatic 
  properties of gt and g11 
  are different from one another and from those of gt . in the case of 
  g11 ,
( 30 ) , who described a 
  significant electrostatic attraction of g11 
  to the membrane , despite its negative net charge of -12 . because the averaged 
  electrostatic affinity of gb11 to the membrane is 
  the same with or without the constraints imposed by the farnesyl anchor , we 
  consider these two energetic contributions as independent and additive .
we 
  estimate that electrostatics increase the membrane affinity of 
  g11 from approximately -6 kcal / mol ( because 
  of the farnesyl anchor alone ) to approximately -9 kcal / mol . in comparison with 
  gt
, g11 can occupy a wider range 
  of orientations that are both lipid - allowed and electrostatically favorable 
  ( fig .
interestingly , the 
  sites on g subunits that interact with different effectors are 
  distributed over much of the g surface 
  ( 68 ) , and therefore this wide 
  range of allowed g orientations relative to the membrane can 
  facilitate productive interaction with various effectors .
calculations of gt interactions with the membrane are not 
  as straightforward as those of g11 because 
  the lipidated n terminus was proteolytically removed in all available 
  gt structures . although we can not rule out the possibility 
  that the n terminus of monomeric gt is intrinsically 
  unstructured , previous studies of its close homolog gi1 
  showed that although its n terminus is present as an extended helix in the 
  heterotrimer , in the monomer it packs against the rest of the subunit in a 
  compact conformation ( 43 ) .
a 
  highly ordered and compact conformation of the myristoylated n terminus of 
  gi1 was also shown in solution , and it was suggested that 
  this property is conserved in homologous g subunits 
  ( 44 ) .
on the basis of this 
  evidence , we assumed in our calculations that , following dissociation from 
  g11 , the extended n - terminal helix of 
  gt undergoes a similar conformational rearrangement . although gt and g11 
  have nearly identical net charges ( -13 and -12 , respectively ) , the 
  distributions of negative charges on their surfaces are different .
3b ) , and our 
  calculations predict that , unlike g11 , 
  gt is repelled by the membrane in all lipid - allowed 
  orientations .
this reduces the membrane affinity of the compact 
  gt conformation from the -6 kcal / mol provided by c12 or 
  c14:2 lipid anchors to less than -4 kcal / mol .
similarly , the membrane affinity 
  of the minority of gt subunits that are modified by c14:1 or 
  c14 lipids ( providing -7or -8 kcal / mol membrane affinity , respectively ) is 
  reduced to less than -5or -6 kcal / mol .
the membrane repulsion of 
  gt could be lower if its n terminus is unstructured , or 
  higher if the n - terminal linker of gt to its lipid anchor is 
  not fully extended and flexible as we assumed .
unlike gt and 
  g11 , the linker length does matter for 
  gt. a shorter or less flexible linker will increase 
  gt repulsion by the membrane because the least repulsive 
  orientation of gt falls right at the edge of the 
  lipid - allowed region , where the electrostatic repulsion increases steeply 
  ( fig .
3a ) . the 
  repulsive gt-membrane interactions that we predict are 
  consistent with the following experimental evidence .
1 ) gt 
  binding to negatively charged membranes is significantly weaker than the 
  binding of g11 
  ( 4 , 
  5 , 
  31 ) , despite the similar 
  hydrophobicity of their lipid anchors .
2 ) 
  g11 binding to nonmyristoylated 
  gt lowers g11 affinity to 
  negatively charged membranes 
  ( 4 ) .
3 ) acidic ph facilitates 
  the binding of gt to negatively charged membranes , which is 
  non - detectable at neutral ph 
  ( 5 ) .
 one of 
  the properties of transducin that has attracted much attention in the past 5 
  years is its ability to undergo reversible , light - induced translocation from 
  the rod outer segment to other subcellular compartments 
  ( 10 , 
  69 - 72 ) . 
 
this massive translocation is thought to contribute to photoreceptor light 
  adaptation and survival ( reviewed in refs . 
 
gt and 
  g11 translocate apart from one another , and 
  up to 90% of gt and 80% 
  g11 move out of the rod outer segment 
  within minutes ( 10 ) .
the 
  consensus is that transducin translocation in the light - induced direction 
  requires subunit dissociation and is accomplished by diffusion 
  ( 14 , 
  15 , 
  72 , 
  75 ) .
surprisingly , the rate of 
  this diffusion is comparable with that of soluble green fluorescent protein 
  through the same compartment 
  ( 75 ) , despite the fact that 
  lipidated gt and g11 have 
  to pass through narrow cytosolic spaces between hundreds of tightly packed 
  membranous disks .
our results suggest that the efficient translocation of monomeric 
  gt may be facilitated by electrostatic repulsion , which is 
  expected to reduce the affinity of gt to membranes .
this may 
  both accelerate the detachment of gt from the membrane and 
  enable faster gt diffusion through the rod outer segment 
  with minimal retardation by the disks . as would be expected , the translocation 
  of the majority of gt subunits , which are modified by c12 or 
  c14:2 lipids , is more pronounced than the translocation of the minority of 
  gt subunits modified by slightly more hydrophobic lipids 
  c14:1 and c14 ( 13 ) . in the 
  case of g11 ,
its electrostatic properties 
  enhance membrane binding , which is expected to impede translocation . 
 
accordingly , it has been shown that the efficient translocation of 
  g11 requires phosducin 
  ( 76 ) , a protein that 
  stabilizes the binding of the farnesyl moiety inside a cleft within 
  g1 ( 77 ) and 
  neutralizes the electrostatic attraction of 
  g11 to the membrane 
  ( 30 ) .
our results also reflect on how soluble transducin could reattach to the 
  membrane from the cytosol , as occurs in rods recovering from illumination . 
 
although it remains to be determined experimentally whether transducin 
  reattaches to the membrane in a heterotrimeric or in a dissociated state 
  ( 14 ) , our results suggest the 
  following .
1 ) the electrostatically favorable orientations of gt 
  enable it to approach the membrane without experiencing an electrostatic 
  energy barrier ( fig .
2 ) soluble 
  g11 is actively attracted to the membrane 
  in many orientations ( fig .
3 ) electrostatic interactions orient the lipid anchors of soluble 
  gt or g11 toward the membrane , 
  thereby favoring lipid anchor insertion into the membrane for both 
  gt and g11.4)incontrast , 
  electrostatic interactions oppose the approach of soluble gt 
  to the membrane in orientations that enable membrane insertion of its lipid 
  anchor ( fig .
78 that 
  association with g11 is required to 
  efficiently reattach gt to membranes .
implications for membrane interactions of other g 
  proteins  our calculations were performed on bovine gt , 
  but they are also applicable to all mammalian gt orthologs 
  because they are > 98% identical in sequence .
gt orthologs 
  in more distantly related vertebrates also show > 90% sequence identity , 
  both globally and when considering only their charged residues . similarly , 
  murray et al .
( 30 ) 
  showed that the electrostatic properties of not just 
  g11 from different species , but all 
  mammalian g subunits ( which share > 80% sequence identity ) , are 
  generally conserved and resemble those of 
  g11 .
visualization of the 
  gi112 heterotrimer ( pdb 
  code 1gp2 ) in a similar orientation to that of gt in 
  fig .
the subunits 
  are shown in connolly surface representation and colored pink 
  (  ) , light green (  ) , and light blue (  ) . 
 
the 
  conserved negatively charged patches discussed in the text are marked with 
  red ( g12 ) and orange 
  ( gi1 ) arrows .
visualization of the 
  gi112 heterotrimer ( pdb 
  code 1gp2 ) in a similar orientation to that of gt in 
  fig .
the subunits 
  are shown in connolly surface representation and colored pink 
  (  ) , light green (  ) , and light blue (  ) . 
 
the 
  conserved negatively charged patches discussed in the text are marked with 
  red ( g12 ) and orange 
  ( gi1 ) arrows .
other members of the gi subunit subfamily 
  ( go1 , go2 , gi1 , gi2 , and 
  gi3 ) share a lower sequence identity with gt , 
  ranging between 60 and 70% .
nevertheless , the electrostatic potential maps of 
  these related g subunits are similar , and in particular the dominant 
  negative patches that produce gt-membrane repulsion are also 
  observed in these proteins 
  ( 32 ) .
these similarities 
  suggest that the electrostatic repulsion of dissociated g subunits by 
  the membrane is common among all members of the gi subfamily . 
  additionally , when we compared the electrostatic potential map of the 
  gi112 heterotrimer 
  ( 79 ) 
  ( fig .
in particular , the negatively charged patches that limit the rotation of 
  gt are also present in the 
  gi112 heterotrimer ( marked with 
  arrows in fig .
therefore , the characteristics of the dynamic interactions of the 
  gt heterotrimer with the membrane are expected to apply to the 
  entire gi subfamily .
unlike gi subfamily members , g subunits that are 
  palmitoylated only ( e.g. gq , gs , and 
  g12 ) contain prominent basic patches at their n termini 
  ( 32 ) .
a number of these 
  proteins have been shown to undergo cycles of reversible membrane association 
  and dissociation , mediated by the cleavage and re - attachment of their labile 
  palmitate anchors ( 11 , 
  80 , 
  81 ) . the basic electrostatic 
  motif in these
g subunits may initiate membrane binding 
  ( 32 ) , whereas their subsequent 
  palmitoylation would strengthen this attachment 
  ( 80 , 
  81 ) .
this interdependence , 
  which could be viewed as an example of the  two - signal model of membrane 
  binding 
( 80 , 
  81 ) , was recently observed in 
  experiments analyzing the roles of the basic n - terminal motif and 
  palmitoylation in membrane attachment of gq , gs , 
  g14 , and g16 
  ( 82 , 
  83 ) . these results support the 
  hypothesis that , unlike gt and its homologs , the  
  subunits of the gq , gs , and g12 subfamilies 
  are attracted to the membrane . in a broader context , it is well established that both membrane binding and 
  subcellular localization of numerous peripheral membrane proteins are 
  determined by various combinations of lipid anchorage and electrostatic 
  interactions ( 30 , 
  33 - 40 ) . 
  although g proteins follow this general theme , they also represent an example 
  of how the activity - dependent dissociation of a multisubunit protein complex 
  changes the interplay between lipid anchors and electrostatics .
the unique 
  electrostatic properties of the heterotrimer and its subunits thereby provide 
  different membrane binding affinities and contribute to the specificity of 
  their protein - protein interactions .
therefore , extending the computational 
  approaches used here to analyzing differences among a broad range of g 
  proteins is a promising direction of future work .
 the heterotrimeric g protein transducin is a key component of the 
  vertebrate phototransduction cascade . 
 transducin is peripherally attached to 
  membranes of the rod outer segment , where it interacts with other proteins at 
  the membrane - cytosol interface . however , upon sustained activation by light , 
  the dissociated gt and 
  g11 subunits of transducin translocate from 
  the outer segment to other parts of the rod cell . 
 here we used a computational 
  approach to analyze the interaction strength of transducin and its subunits 
  with acidic lipid bilayers , as well as the range of orientations that they are 
  allowed to occupy on the membrane surface . 
 our results suggest that the 
  combined constraints of electrostatics and lipid anchors substantially limit 
  the rotational degrees of freedom of the membrane - bound transducin 
  heterotrimer . 
 this may contribute to a faster transducin activation rate by 
  accelerating transducin - rhodopsin complex formation . 
 notably , the membrane 
  interactions of the dissociated transducin subunits are very different from 
  those of the heterotrimer . as shown previously , 
  g11 experiences significant attractive 
  interactions with negatively charged membranes , whereas our new results 
  suggest that gt is electrostatically repelled by such 
  membranes . 
 we suggest that this repulsion could facilitate the membrane 
  dissociation and intracellular translocation of gt. 
  moreover , based on similarities in sequence and electrostatic properties , we 
  propose that the properties described for transducin are common to its 
  homologs within the gi subfamily . in a broader view , this work 
  exemplifies how the activity - dependent association and dissociation of a g 
  protein can change both the affinity for membranes and the range of allowed 
  orientations , thereby modulating g protein function . 
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
Supplementary Material