an -helix possesses a dipole moment by virtue of the alignment of its peptide bonds having half - positive and negative charges at their ends . for this fractional charge separation when these microdipoles align along the axis of the -helix , making hydrogen bonds with the neighboring peptide units , the -helix behaves like a macrodipole with positive c - terminal and negative n - terminal on either end . the length and the dipole moment ( ) of an -helix macrodipole is 1.5n  and 3.5n debye , respectively , where n is the number of residues of the alpha helix . several groups have suggested that the -helix macrodipole can stabilize certain conformations of the protein . the structure and function of different voltage - gated potassium ( k ) ion channels have been reviewed . the structure of voltage - gated k ion channel of aeropyrum pernix ( kvap ) obtained by different methods[68 ] shows that , in a single subunit , the -helices are not ideally antiparallel but organized in a pairwise fashion , i.e. , s1-s2 , s3-s4 , and s5-s6 . the first four helices ( s1 , s2 , s3 , and s4 ) collectively are called the voltage sensor domain ( vsd ) , the remaining ( s5 , s6 ) being pore domain ( pd ) . the s3 helix has a kink at proline p99 , dividing it into two distinct helices s3a and s3b . s3b pairs with s4 , forming a tightly bound  paddle  unit shuttling in and out of the membrane . s3b and s4 form a somewhat antiparallel macrodipole pair.[68 ] taking s3b and s4 -helices of the full - length k ion channel of kvap ( pdb 1orq ) , the 14-residue ( a100-l113 ) s3b -helix is 21  , while the 17-residue ( r117- r133 ) s4 -helix is 25.5   long . the terminal dipole charges of s3b and s4 macrodipoles are n3 ( positive ) , c3 ( negative ) and n4 ( positive ) , c4 ( negative ) , respectively . besides these charges , the -helices have a number of charged residues on their surfaces . the negative glutamic acid ( e-107 ) and positive histidine ( h-109 ) of s3b are apart by a translational distance of x = 3  along the helix axis and by rotational angle of  = 200 about the same axis . the s4 -helix has five positive arginine residues : r117 , r120 , r123 , and r126 ( designated as r1-r4 , respectively ) , which lie periodically in a helical path of pitch 4.5  and angular separation of 60 ; and r133 ( r5 ) , which is 10.5  below r4 and separated by 20 [ figure 1 ] . the r117 residue is near the n - terminal and r133 is near the c - terminal of the s4 macrodipole . interaction between -helical macrodipoles . ( a ) potential energy vs. angular separation (  ) of two macrodipoles . the mutual orientations at different  values are shown at the top ( arrow head , positive end ) . ( b ) lines of force following the shortest path from positive to negative pole . ( c ) the charge distribution on s3b - s4 helix pair of full length ion channel . ( d ) schematic diagram of the relative angular position of the charged residues on s3b - s4 pair of kvap from the extracellular end ( e - e107 , r1-r117 , r2-r120 , r3-r123 , r4-r126 , r5-r133 ) various experimental and theoretical studies have shown the importance of the positive arginine residues of s4 and their interactions with the negative charged residues of s1-s3a . however , there is no specific information on the role of the negatively charged acidic side chain of s3b and the dipolar charges ( n3 , c3 , n4 , and c4 ) on the stability of the s3b - s4 pair in kvap . since the gating process is an electrical activity , all charges in the system of the vsd , including the dipolar charges , are expected to have some role in the process . here , the electrostatic theory was used to understand ( i ) the effect of dipolar charges on the antiparallel arrangement of the two -helix macrodipoles and the proximity of the extracellular and intracellular terminals of the s3b - s4 pair ; ( ii ) the role of charged residues and the dipolar terminal charges affecting the stabilization of the s3b - s4 aggregation ; and ( iii ) the contribution of energy of e107 of s3b in the  paddle  structure . according to the electrostatic theory , two electric dipoles interact to give the mutual electrostatic potential energy , which depends on their dipole moments and 1 and 2 , and their angular separation (  ) . hence , the potential energy value ( u ) varies as where 1 , 2 are dipole moment vectors and   is the position vector of 2 with respect to 1 , while r is the center - to - center distance between the two dipoles when the distance between two dipoles is less than the length of individual dipoles , the interaction of the individual charges predominates . hence , the electrostatic coulombic potential energy of the system of charges of macrodipoles is calculated as where , ij is the distance between the charges qi and qj , 0 is the permittivity of the vacuum , and p is dielectric constant of the medium ( protein ) in which the macrodipoles are embedded . the force or potential energy is negative or positive depending upon whether the interaction is attractive or repulsive . the potential energy ( pe ) profile of any two dipoles ( equation 1 ) at different angular separation (  ) shows that when a pair of dipoles are in parallel position (  = 0 ) , the energy is maximum ; when perpendicular (  = 90 ) , energy is zero ; and when in antiparallel orientation (  = 180 ) , the energy is minimum [ figure 1a ] and is maximally stabilized . a pair of -helix macrodipoles tend to stabilize in an antiparallel position also because the lines of force always travel through the shortest path ( 14 ) from positive to negative terminals , bringing the opposite poles of two adjacent macrodipoles as close as possible [ figure 1b ] . in keeping with this theory , the structure of the kvap channel shows the helix pairs s1-s2 , s3b - s4 , and s5-s6 with the c - termini of s1 , s2 , s3 , s4 , and s5 being close to the n - termini of s2 , s3 , s4 , s5 , and s6 , respectively this can be explained by the help of the local force between the two terminals of the s3b - s4 macrodipole pair as an example . according to the different structures ( full - length and isolated vsd ) of kvap ion channel , the 17 residue s4 helix ( r117-r133 ) in the full - length ion channel is shorter than the 31-residue s4 helix ( r117-l148 ) in the isolated vsd . the pdb structure ( 1orq ) of the full - length ion channel [ figure 1c ] shows that at the intracellular end of the s3b - s4 pair , the dipolar charge n3 ( + 0.5e ) of s3b helix is at the vicinity of the dipolar charge c4 ( -0.5e ) and r133 ( + 1.0e ) of s4 helix , while at the extracellular end , the dipolar charge c3 ( -0.5e ) of s3b is near the dipolar charge n4 ( + 0.5e ) and r117 ( + 1.0e ) of s4 . in isolated vsd , the s4 helix is longer , with c4 terminal 15 residues farther away from r133 ; hence , in the vicinity of n3 of s3b only the r133 of s4 remains . in the full - length ion channel , the charges at the intracellular end of s3b ( + n3 ) and s4 ( -c4 and + r133 ) helix pair experience a net positive ( repulsive ) local force ( figure 2a , solid symbol ) due to the interaction between n3-c4 and n3-r133 , keeping the n3 terminal of s3b away from s4 . the charges at the extracellular termini of s3b ( -c3 ) and s4 ( + n4 and + r117 ) experience a net negative ( attractive ) local force [ figure 2b ] , pulling the c3 pole of s3b closer to s4 . the other , more remote charged residues add to the repulsive or attractive force towards n3 or c3 pole , respectively , but the magnitude of these forces are weaker due to greater interatomic distances . this unequal spacing between two poles [ figure 1c ] of the s3b - s4 pair at two cellular ends is quite evident from the pdb 1orq structure , of kvap ion channel protein . the force varies between the two termini with the rotation of s4 about its own axis . as the angle of rotation (  ) increases , the attractive force at the extracellular end decreases , but the repulsive force at the intracellular end increases , thus maintaining the unequal spacing between the two termini at two cellular ends . the s4 helix is assumed to be more mobile than s3b ; hence , in all orientations , the intracellular termini will always remain separated due to repulsive force and the extracellular termini will remain closer . local interaction force between the adjacent termini of s3b - s4 -helix pair vs. the distance (  ) between the two helices at different angle of rotation (  ) of s4 . ( a ) at the intracellular side , distance (  ) is between n3 of s3b and r133 of s4 for full length ion channel ( solid symbol ) and for isolated vsd ( open symbol ) . ( b ) at the extracellular side , distance (  ) is between the dipolar ends c3 of s3b and n4 of s4 . with s4 rotated by  = 120 , the local force in presence of all charges and in absence of charged residues / dipolar charges ( c ) at ntracellular end and ( d ) at extracellular end in comparison with the full - length ion channel , in the isolated vsd , according to the structure ( pdb 2kyh and 1ors ) , the extracellular termini experience a net attractive force but at the intracellular end , the net repulsive force ( between n3 and r133 ) ( figure 2a , open symbol ) is stronger in nature . this is because the s4 helix in isolated vsd is longer ( r117-l148 ) with c4 terminal 15 residues below r133 and farther away from n3 ; hence , the attractive force between n3 and c4 becomes weaker and the repulsive force between n3 and r133 predominates , making the bifurcation larger . in keeping with this finding , the observed distance between the n3 of s3b and r133 of s4 is approximately 26% and 63% greater in the structures of pdb 1ors and 2kyh , respectively , than in pdb 1orq , hence justifying the bifurcation at the intracellular side between the two antiparallel s3b - s4 helices , which is explained by the electrostatic theory . at the termini of s3b - s4 pair of the full - length ion channel , the effect of the primary charges ( n3 , c4 , r133 , c3 , n4 , and r117 ) involved in these local forces was studied by virtual mutagenesis . ( 1 ) on neutralizing all the dipolar charges ( n3 , c3 , n4 , and c4 ) , the local force was found to be almost negligible between the termini of the -helix pair at both the intracellular end [ figure 2c ] and extracellular end [ figure 2d ] . ( 2 ) when the charged residues ( r117 and r133 ) were mutated , both terminals experienced a comparable local attractive force similar to a typical antiparallel macrodipole pair . thus , in both cases , the intracellular bifurcation collapsed in absence of the repulsive force . therefore , the coordinated role of the charged residues and the dipolar charges at the two termini of s3b - s4 pair has a significant effect on the unequal spacing of the mutual spatial position of s3b - s4 , i.e. , holding the extracellular poles ( c3 and n4 ) closer and the intracellular n3 end far apart from the s4 helix . the total potential energy ( equation 2 ) , of the system of charges of the s3b - s4 pair was computed as a function of the translational motion of s4 along its helical axis and at different angles of rotation (  = 0 , 60 , 120 , 180 , 200 ) [ figure 1d ] about its axis . the energy profiles [ figure 3a ] showed minimum energy when the positive residues r117 , r120 , r123 , r126 , and r133 face the negative e107 at the translational positions of x = 0 , 4.5 , 9.0 , 13.5 , and 24  and rotational positions of  = 0 , 60 , 120 , 180 , and 200 , respectively . when s4 was rotated by  = 120 and translated by x = 9.0  , i.e. , with the positive r123 residue in close proximity to negative e107 , the system attained the minimum energy of 19.25 kcal / mol . this can be one of the possible conformations of the s3b - s4 pair when there is no transmembrane potential ( the zero - potential state ) . indeed , the crystal structures show the presence of e107 of s3b facing s4 at the vicinity of r123 and h109 is diametrically on the other side.[68 ] role of dipolar and side chain charges in the stability of the s3b - s4 pairs . ( a ) potential energy profile of the system of charges on s3b - s4 vs. the relative translational distance between s3b and s4 along the helix axis , in presence ( solid symbol ) and absence ( open symbol ) of e107 on s3b at different angles of rotation (  ) of s4 . ( b ) with s4 rotated by 120 potential energy in the presence of all charges and in the absence of each charge . ( c ) proportional potential energy contribution of the individual charges in stabilization of the macrodipole pair on neutralizing e107 of s3b for all possible rotational positions of s4 , the total energy becomes positive and the profile almost flattens out [ figure 3a ] , i.e. , the net energy of aggregation of s3b - s4 changes from attractive to repulsive , while [ figure 3b ] on neutralizing the other charges , the negative ( attractive ) energy varied . hence , e107 is the prime candidate in keeping s3b - s4 -helices together behaving like a single  paddle  unit . considering the minimum energy profile position at x = 9.0   and  = 120 , the effect of different charges on the stabilization of s3b - s4 pair was studied . through virtual mutagenesis , on neutralizing each charge one at a time , the energy profile changed [ figure 3b ] , implying that each charge ( dipolar charge or charged residue ) has a significant role in stabilization of the s3b - s4 pair . in the absence of the charged residues ( r117 , r120 , r123 , r126 , and r133 ) , the total energy has increased , and hence the system lost stability , while in the absence of h109 , the energy stability was increased . on neutralization of the c3 and n4 terminal charges , the potential energy profile was raised , while the absence of n3 and c4 charges lowered the minimum energy value . therefore , the dipolar end charges , in spite of being weaker , have a substantial role in the stability of s3b - s4 helix pair , which is still unexplored experimentally . figure 3c shows a comparative study of the potential energy contribution of individual charges in stabilizing the s3b - s4 -helix pair . of all the charges , the contribution of the potential energy of glutamic acid e107 of s3b is maximum , but all other charges also contribute to the stability . in particular , contribution of the dipolar terminal charges c3 is much greater than that of any of the positive arginine residues of s4 , while contribution of n4 is comparable to some of the arginine residues of s4 -helix . experimental evidences favor a significant role played by the arginine residues of s4 in the gating process , but the role of the dipolar charges and the glutamic acid of s3b in kvap , so far have not been taken into consideration . our calculations show , however , that in reference to the stability of the s3b - s4 pair , the dipolar charges and the negative glutamic acid can not be ignored . the alignment of the s3b - s4 sequence of different members of the k ion channel sub - family showed a previously unreported positional conservation of negatively charged glutamic acid / aspartic acid residues in the s3b -helical region [ table 1 ] . the extracellular half of the s3b helix in 11 out of 15 members contain at least one negative residue between the ninth and fourteenth positions from the proline , that bends the s3 helix into two parts  s3a and s3b . this conservation indicates a biological function of the negative charge in the s3b helix and the existence of the  paddle  unit of the s3b - s4 -helix pair . four members have an additional negative residue while the shaker channel , exceptionally , contains four contiguous negative residues that would form a negatively charged spiral in three dimensions . it is expected that the negative charge distribution on the s3b helix would significantly impact its interaction with the s4 helix in the absence or presence of an electric field . alignment of the sequence of s3b helix of k+ ion channel subfamilies of different species . negatively charged residues ( red ) and positively charged residues ( green ) the shaker ion channel contains this cluster of four acidic residues at its n - terminal end of s3b . deletion of either one or three of these residues ( as triplet ) in s3b have been found not to affect the voltage gating . however , in both the cases , there is at least one remaining acidic residue , which may be sufficient for maintaining stability as shown in our work with kvap [ figures 3a and c ] . moreover , by virtue of deletion , no matter how small the -helices s3b and s4 are , the terminal dipolar charges are always present to take part in the stability and will also have substantial role in the gating process . the potential energy ( pe ) profile of any two dipoles ( equation 1 ) at different angular separation (  ) shows that when a pair of dipoles are in parallel position (  = 0 ) , the energy is maximum ; when perpendicular (  = 90 ) , energy is zero ; and when in antiparallel orientation (  = 180 ) , the energy is minimum [ figure 1a ] and is maximally stabilized . a pair of -helix macrodipoles tend to stabilize in an antiparallel position also because the lines of force always travel through the shortest path ( 14 ) from positive to negative terminals , bringing the opposite poles of two adjacent macrodipoles as close as possible [ figure 1b ] . in keeping with this theory , the structure of the kvap channel shows the helix pairs s1-s2 , s3b - s4 , and s5-s6 with the c - termini of s1 , s2 , s3 , s4 , and s5 being close to the n - termini of s2 , s3 , s4 , s5 , and s6 , respectively this can be explained by the help of the local force between the two terminals of the s3b - s4 macrodipole pair as an example . according to the different structures ( full - length and isolated vsd ) of kvap ion channel , the 17 residue s4 helix ( r117-r133 ) in the full - length ion channel is shorter than the 31-residue s4 helix ( r117-l148 ) in the isolated vsd . the pdb structure ( 1orq ) of the full - length ion channel [ figure 1c ] shows that at the intracellular end of the s3b - s4 pair , the dipolar charge n3 ( + 0.5e ) of s3b helix is at the vicinity of the dipolar charge c4 ( -0.5e ) and r133 ( + 1.0e ) of s4 helix , while at the extracellular end , the dipolar charge c3 ( -0.5e ) of s3b is near the dipolar charge n4 ( + 0.5e ) and r117 ( + 1.0e ) of s4 . in isolated vsd , the s4 helix is longer , with c4 terminal 15 residues farther away from r133 ; hence , in the vicinity of n3 of s3b only the r133 of s4 remains . in the full - length ion channel , the charges at the intracellular end of s3b ( + n3 ) and s4 ( -c4 and + r133 ) helix pair experience a net positive ( repulsive ) local force ( figure 2a , solid symbol ) due to the interaction between n3-c4 and n3-r133 , keeping the n3 terminal of s3b away from s4 . the charges at the extracellular termini of s3b ( -c3 ) and s4 ( + n4 and + r117 ) experience a net negative ( attractive ) local force [ figure 2b ] , pulling the c3 pole of s3b closer to s4 . the other , more remote charged residues add to the repulsive or attractive force towards n3 or c3 pole , respectively , but the magnitude of these forces are weaker due to greater interatomic distances . this unequal spacing between two poles [ figure 1c ] of the s3b - s4 pair at two cellular ends is quite evident from the pdb 1orq structure , of kvap ion channel protein . the force varies between the two termini with the rotation of s4 about its own axis . as the angle of rotation (  ) increases , the attractive force at the extracellular end decreases , but the repulsive force at the intracellular end increases , thus maintaining the unequal spacing between the two termini at two cellular ends . the s4 helix is assumed to be more mobile than s3b ; hence , in all orientations , the intracellular termini will always remain separated due to repulsive force and the extracellular termini will remain closer . local interaction force between the adjacent termini of s3b - s4 -helix pair vs. the distance (  ) between the two helices at different angle of rotation (  ) of s4 . ( a ) at the intracellular side , distance (  ) is between n3 of s3b and r133 of s4 for full length ion channel ( solid symbol ) and for isolated vsd ( open symbol ) . ( b ) at the extracellular side , distance (  ) is between the dipolar ends c3 of s3b and n4 of s4 . with s4 rotated by  = 120 , the local force in presence of all charges and in absence of charged residues / dipolar charges ( c ) at ntracellular end and ( d ) at extracellular end in comparison with the full - length ion channel , in the isolated vsd , according to the structure ( pdb 2kyh and 1ors ) , the extracellular termini experience a net attractive force but at the intracellular end , the net repulsive force ( between n3 and r133 ) ( figure 2a , open symbol ) is stronger in nature . this is because the s4 helix in isolated vsd is longer ( r117-l148 ) with c4 terminal 15 residues below r133 and farther away from n3 ; hence , the attractive force between n3 and c4 becomes weaker and the repulsive force between n3 and r133 predominates , making the bifurcation larger . in keeping with this finding , the observed distance between the n3 of s3b and r133 of s4 is approximately 26% and 63% greater in the structures of pdb 1ors and 2kyh , respectively , than in pdb 1orq , hence justifying the bifurcation at the intracellular side between the two antiparallel s3b - s4 helices , which is explained by the electrostatic theory . at the termini of s3b - s4 pair of the full - length ion channel , the effect of the primary charges ( n3 , c4 , r133 , c3 , n4 , and r117 ) involved in these local forces was studied by virtual mutagenesis . ( 1 ) on neutralizing all the dipolar charges ( n3 , c3 , n4 , and c4 ) , the local force was found to be almost negligible between the termini of the -helix pair at both the intracellular end [ figure 2c ] and extracellular end [ figure 2d ] . ( 2 ) when the charged residues ( r117 and r133 ) were mutated , both terminals experienced a comparable local attractive force similar to a typical antiparallel macrodipole pair . thus , in both cases , the intracellular bifurcation collapsed in absence of the repulsive force . therefore , the coordinated role of the charged residues and the dipolar charges at the two termini of s3b - s4 pair has a significant effect on the unequal spacing of the mutual spatial position of s3b - s4 , i.e. , holding the extracellular poles ( c3 and n4 ) closer and the intracellular n3 end far apart from the s4 helix . the total potential energy ( equation 2 ) , of the system of charges of the s3b - s4 pair was computed as a function of the translational motion of s4 along its helical axis and at different angles of rotation (  = 0 , 60 , 120 , 180 , 200 ) [ figure 1d ] about its axis . the energy profiles [ figure 3a ] showed minimum energy when the positive residues r117 , r120 , r123 , r126 , and r133 face the negative e107 at the translational positions of x = 0 , 4.5 , 9.0 , 13.5 , and 24  and rotational positions of  = 0 , 60 , 120 , 180 , and 200 , respectively . when s4 was rotated by  = 120 and translated by x = 9.0  , i.e. , with the positive r123 residue in close proximity to negative e107 , the system attained the minimum energy of 19.25 kcal / mol . this can be one of the possible conformations of the s3b - s4 pair when there is no transmembrane potential ( the zero - potential state ) . indeed , the crystal structures show the presence of e107 of s3b facing s4 at the vicinity of r123 and h109 is diametrically on the other side.[68 ] role of dipolar and side chain charges in the stability of the s3b - s4 pairs . ( a ) potential energy profile of the system of charges on s3b - s4 vs. the relative translational distance between s3b and s4 along the helix axis , in presence ( solid symbol ) and absence ( open symbol ) of e107 on s3b at different angles of rotation (  ) of s4 . ( b ) with s4 rotated by 120 potential energy in the presence of all charges and in the absence of each charge . ( c ) proportional potential energy contribution of the individual charges in stabilization of the macrodipole pair on neutralizing e107 of s3b for all possible rotational positions of s4 , the total energy becomes positive and the profile almost flattens out [ figure 3a ] , i.e. , the net energy of aggregation of s3b - s4 changes from attractive to repulsive , while [ figure 3b ] on neutralizing the other charges , the negative ( attractive ) energy varied . hence , e107 is the prime candidate in keeping s3b - s4 -helices together behaving like a single  paddle  unit . considering the minimum energy profile position at x = 9.0   and  = 120 , the effect of different charges on the stabilization of s3b - s4 pair was studied . through virtual mutagenesis , on neutralizing each charge one at a time , the energy profile changed [ figure 3b ] , implying that each charge ( dipolar charge or charged residue ) has a significant role in stabilization of the s3b - s4 pair . in the absence of the charged residues ( r117 , r120 , r123 , r126 , and r133 ) , the total energy has increased , and hence the system lost stability , while in the absence of h109 , the energy stability was increased . on neutralization of the c3 and n4 terminal charges , the potential energy profile was raised , while the absence of n3 and c4 charges lowered the minimum energy value . therefore , the dipolar end charges , in spite of being weaker , have a substantial role in the stability of s3b - s4 helix pair , which is still unexplored experimentally . figure 3c shows a comparative study of the potential energy contribution of individual charges in stabilizing the s3b - s4 -helix pair . of all the charges , the contribution of the potential energy of glutamic acid e107 of s3b is maximum , but all other charges also contribute to the stability . in particular , contribution of the dipolar terminal charges c3 is much greater than that of any of the positive arginine residues of s4 , while contribution of n4 is comparable to some of the arginine residues of s4 -helix . experimental evidences favor a significant role played by the arginine residues of s4 in the gating process , but the role of the dipolar charges and the glutamic acid of s3b in kvap , so far have not been taken into consideration . our calculations show , however , that in reference to the stability of the s3b - s4 pair , the dipolar charges and the negative glutamic acid can not be ignored . the alignment of the s3b - s4 sequence of different members of the k ion channel sub - family showed a previously unreported positional conservation of negatively charged glutamic acid / aspartic acid residues in the s3b -helical region [ table 1 ] . the extracellular half of the s3b helix in 11 out of 15 members contain at least one negative residue between the ninth and fourteenth positions from the proline , that bends the s3 helix into two parts  s3a and s3b . this conservation indicates a biological function of the negative charge in the s3b helix and the existence of the  paddle  unit of the s3b - s4 -helix pair . four members have an additional negative residue while the shaker channel , exceptionally , contains four contiguous negative residues that would form a negatively charged spiral in three dimensions . it is expected that the negative charge distribution on the s3b helix would significantly impact its interaction with the s4 helix in the absence or presence of an electric field . alignment of the sequence of s3b helix of k+ ion channel subfamilies of different species . negatively charged residues ( red ) and positively charged residues ( green ) the shaker ion channel contains this cluster of four acidic residues at its n - terminal end of s3b . deletion of either one or three of these residues ( as triplet ) in s3b have been found not to affect the voltage gating . however , in both the cases , there is at least one remaining acidic residue , which may be sufficient for maintaining stability as shown in our work with kvap [ figures 3a and c ] . moreover , by virtue of deletion , no matter how small the -helices s3b and s4 are , the terminal dipolar charges are always present to take part in the stability and will also have substantial role in the gating process . the electrostatic theory explains various aspects of the stability of the s3b - s4 -helix pair of the vsd of kvap ion channel at zero potential . ( i ) the -helix pair arrange themselves in a dipole pair - wise fashion like two macrodipoles obeying the electrostatic laws ; ( ii ) the unequal spacing of the extracellular and intracellular poles of s3b - s4 is due to the local attractive and repulsive forces , respectively , which makes the s3b - s4 pair not ideally antiparallel . the presence of the dipolar charges along with the terminal charged residues is the cause of this spacing ; ( iii ) in the absence of any transmembrane voltage ( zero potential ) , positive r123 of s4 is in the closest proximity of the negative glutamic acid e107 of s3b ; ( iv ) e107 of s3b has a dominant role in stabilizing the s3b - s4  paddle  ; and ( v ) the extracellular terminal dipolar charges c3 of s3b and n4 of s4 contribute substantially to the stability of s3b - s4 -helix pair . this report on the role of the dipolar charges in stabilization is important because in the ion channel , all -helices will behave like macrodipoles and their terminal charges will not only add impetus to the stabilization of other helix pairs , but also may have contribution in the gating process in presence of the transmembrane voltage . the glutamic acid , which is found to be playing a dominant role in holding the s3b and s4 together as a  paddle  , can give an insight to the paddle model as to why the s4 helix carry the s3b as a cargo during the gating process . our subsequent work will be to untangle some controversy that arose between different models with our dipole electrostatic theory .
background : it is well known that -helices of protein , possessing equal and opposite charged ends , behaves like a macrodipole , but the relative importance of such macrodipoles to the aggregation of a pair of helix in the voltage sensor domain ( vsd ) of k+ ion channel , has not been assessed . in the vsd , importance has been given primarily to the helically arranged arginine residues of helix , but the role of the charged residues of s3b is less focused.method and objective : applying electrostatic theory , we have studied the interaction between the charges of s3b - s4 -helix pair of kvap through virtual mutagenesis.result and conclusion : we have shown that the terminal charges arising from the inherent dipolar property of -helices play an important role in affecting the stability of the s3b - s4 pair , and in determining its spatial position at zero transmembrane potential . moreover , the negatively charged side chain of s3b was found to be the primary stabilizing factor in holding s3b - s4 pair together as a  paddle  . 
 comparison of sequences of s3b helix of k+ channels from different species showed a previously unreported positional conservation of negative residues , highlighting their functional importance . 
 these charges may contribute to the energetic of -helix movements in an electric field .