fundamental molecular 
 transactions responsible for the cell s 
 homeostasis ( such as in transcription , translation , and replication ) 
 involve dynamic interactions of multiple components and their regulations 
 via allostery , conformational changes , or translocation . as an example , 
 protein  dna interactions play a crucial role in many essential 
 biological processes in which three - dimensional multicomponent structures 
 and their dynamic changes are often directly related to their functions . 
 especially , the dynamic aspects of structural changes that occur upon 
 protein binding to dna are still difficult to capture with standard 
 biophysical techniques . a powerful technique for the study of 
 dynamic conformational changes 
 in biomolecules is frster - type resonance energy transfer ( fret ) , which is capable of probing distances comparable 
 to the size of small - to - midsized proteins , as well as short dsdnas 
 ( 310 nm ) . two - color fret is a one - dimensional ( one 
 distance ) ruler that can probe the inter- or intramolecular distance 
 between donor and acceptor fluorophores attached to a macromolecule 
 ( or to two different components of a macromolecular complex ) . if the fluorophores are suitably positioned on 
 the macromolecule / complex , fret can report on the conformational states 
 and on dynamic fluctuation in their structure . if three or four different 
 fluorophores are used simultaneously , up to 6 distances can be probed 
 simultaneously . at the single molecule level , single molecule fret ( smfret ) can 
 mostly report on nonequilibrium time trajectories of the distance 
 reaction coordinate ( when molecules / complexes are immobilized ) and 
 distinguish subpopulations of different conformational states under 
 various biochemical conditions ( when molecules diffuse in solution ) . 
 in protein  dna interactions , such as in the case of rna polymerization 
 and nuclease activity by restriction enzymes , better insights into 
 the structure and function of these complexes could be gained by simultaneously 
 measuring multiple distances in the presence or absence of multiple 
 components within a complex . however , measuring several distances with the same distance range 
 is not always sufficient . in fact , a combination of two molecular 
 rulers with different distance scales may be beneficial to simultaneously 
 identify  large  structural conformational changes ( e.g. , 
 of dna ) together with smaller scale structural changes ( e.g. , by changes 
 in binding mode ) . we recently demonstrated the combination 
 of microsecond alternating - laser excitation ( salex)-smfret with a shorter - range single - molecule distance 
 ruler based on protein - induced fluorescence enhancement ( pife ) . in this technique ( which we dubbed alex - based pife - fret ) , an environmentally 
 sensitive cyanine fluorophore ( cy3 ) is placed at a position on a double - stranded 
 dna that is close ( <3 nm ) to a protein binding site . upon binding , 
 or upon small distance translocations of the protein with respect 
 to the labeled position , the fluorescence intensity of the environmentally 
 sensitive fluorophore is altered . the cyanine fluorophore cy3 acted 
 both as fret donor and as pife proximity probe . a fret acceptor fluorophore 
 ( atto 647n ) was attached on the same dsdna further away from the cy3 
 attachment base . utilizing a microsecond alternating laser excitation 
 ( salex ) scheme , we demonstrated 
 that the ratiometric observable fret efficiency , e , and the ratiometric observable stoichiometry , s , could report on the interprobe distance and the protein proximity , 
 respectively . in this work , we 
 present the theoretical framework of alex - based 
 pife - fret and demonstrate its ability to quantitate experimental results . we show that the fold - increase in cy3 emission intensity , fluorescence 
 quantum yield or fluorescence lifetime ( in single molecule pife experiments ) , 
 and changes in stoichiometry ( as utilized in alex - based pife - fret 
 experiments ) are manifestations of the underlying steric hindrance 
 of the cy3 isomerization mobility . due to its structure , the presence 
 of a bound protein in close proximity to the dye sterically hinders 
 its mobility and may also specifically interact with it . our model 
 reveals the dependencies of fluorescence emission intensity and quantum 
 yield on the hindered isomerization rate constants . we demonstrate 
 how alex - based pife - fret measurements can be fitted by the proposed 
 model and provide best fit values for the relevant parameters . we 
 then apply alex - based pife - fret to study the restriction enzyme bamhi  dsdna interaction and quantify the dynamic 
 range of the ruler . in addition , we studied the interaction of the 
 t7 polymerase gp5/trx with dna . lastly , we show how to disentangle 
 fret efficiency values from stoichiometry values in alex - based pife - fret . the results analyzed 
 here , were obtained from two different dsdna systems as described 
 before . in short , the distance dependence of pife in te absence of 
 fret was tested on a 40bp - long dsdna carrying 
 cy3(b ) and atto 647n at opposite 5-ends . all dsdnas contained 
 a palindromic sequence 5-ggatcc-3 for the restriction 
 enzyme bamhi placed at 1,2,3,5 or 7 bp away from 
 the donor . for experiments involving unspecific binding of t7 polymerase 
 gp5/trx and controls for bamhi , 45 bp - long dsdna 
 was used as described before labeled 
 with cy3(b ) at the 5-end of the top strand , and atto 647n 
 at 8,13,18,23,28 or 33bp of the bottom strand were employed . alex - experiments were carried out at 2550 pm of dsdna 
 at room temperature ( 22 c ) . the imaging buffer contained 50 
 mm tris - hcl , 100 mm sodium chloride , 10 mm calcium chloride , 0.1 mm 
 edta and 143 mm bme at ph 7.4 . the instrumentation , 
 data acquisition and data analysis for s - alex have been previously 
 described in detail . shortly , the alternation period was set to 50 s , and the 
 excitation intensity to 60 w at 532 nm and 25 w at 640 
 nm . a 60 objective with na = 1.35 ( olympus , uplsapo 60xo , germany ) 
 was used . laser excitation was focused to a diffraction limited spot 
 20 m into the solution . fluorescence emission was collected , 
 filtered against background ( using a 50-m pinhole and bandpass 
 filters ) and detected with two avalanche photodiode detectors ( -spad , 
 picoquant , germany ) . all data analysis was performed using a home - built 
 python - based software . as described previously , salex spectroscopy records four photon streams : donor - based 
 donor emission f(dd ) , donor - based acceptor emission f(da ) , acceptor - based acceptor emission f(aa ) and donor - based emission after acceptor excitation f(ad ) ( which can be neglected ) . bursts in the three channels were 
 identified applying a dual color burst search with parameters m = 15 , t = 500 
 s , and l = 25 ; additional filtering removed 
 slow - varying changes in fluorescence intensity and thresholding selected 
 for bright single - molecule bursts ( > 100 photons per burst unless 
 otherwise 
 mentioned ) . after burst identification , fluorophore stoichiometries s and apparent fret efficiencies e * were 
 calculated for each burst . uncorrected fret 
 efficiency e * monitors the proximity between the 
 two fluorophores and is calculated according to1 s is defined as the 
 ratio between the overall green fluorescence intensity over the total 
 green and red fluorescence intensity and describes the ratio of donor - to - acceptor 
 fluorophores in the sample s:2 by binning the detected bursts into a 2d e*/s histogram , subpopulations as free 
 and protein - bound dna 
 species can be separated according to their s - values . e*- and s - distributions were fitted using 
 a gaussian function , yielding the mean values i of the distribution and an associated standard deviations wi . to obtain accurate e and corrected s values , finally , a gamma 
 factor correction was applied , i.e. , use of cy3b of free cy3b - labeled oligos to all 
 data sets . applying 
 the theory in 
 either simulations respectively for experimental data fitting was 
 performed using scripts in matlab r2008b respectively r2013b ( mathworks 
 matlab , natick , ma , usa ) . the differential equations ( eqs 5 ) were numerically solved by use 
 of the ordinary differential equation solver function ode45 . for the numerical solution of systems of coupled ordinary differential 
 equations , the matlab built - in ode package allows 
 full control over fine - tuning the numerical solution process . nevertheless , 
 the matlab built - in matrix exponentiation function expm allows for a faster and efficient numerical solution and can be 
 used instead of ode45 . data fitting was performed 
 by comparison of experimental s(e ) values to the theoretical computed ones until the square sum of 
 the fitting residues was minimized . accessible volume calculations 
 of cy3 attached to the 5-end of dsdna , in the absence or presence 
 of bamhi , were performed using the software provided 
 by sindbert et al . the crystal structure 
 ( pdb code : 2bam ) the 
 photophysics of cy3 as a molecular rotor used in pife is explained following the jablonski diagram in figure 1 . although the pi - conjugated system restricts rotations about the one - dimensional 
 polymethine group , the trans and cis ground - state isomers typically interconvert in the s time 
 range , probably via vibrational weakening 
 of the double bond inducing double bond twisting . out of the two ground - state isomers , the trans isomer has a larger absorption cross - section at  = 532 nm , 
 owing to its absorption spectrum peak ( cis isomer 
 is red - shifted by 20 nm ) , higher 
 thermodynamic stability , its symmetry , 
 and its larger excitation dipole moment ( in comparison to the dipole 
 of the cis form ) . we denote the fraction 
 of molecules excited from the trans ground - state 
 isomer with  , and the fraction of molecules excited from the cis isomer with 1- ( see figure 1c ) . ( b ) excited - state cy3 undergoes 
 isomerization between a bright trans isomer and a 
 dim cis isomer via a 90 isomerization intermediate . 
 in the presence of an acceptor fluorophore , the excited trans isomer dtrans * of cy3 is deactivated via one 
 of three possible pathways : ( i ) by frster - type resonance energy 
 transfer kfret to the acceptor , ( ii ) direct 
 deexcitation from excited- to ground - state trans isomer 
 through either fluorescence or internal conversion kd , and ( iii ) deactivation by excited - state isomerization 
 ( kt90 ) . the excited intermediate 
 state d90 * is tightly coupled to the ground state 90-transition 
 state and hence undergoes fast de - excitation ( kd,90 ) to the ground state of both isomers . ( c ) the steady state 
 population density between the cis and trans isomers of cy3 is shifted toward the trans isomer 
 due to changes in the microenvironment of cy3 caused by steric hindrance 
 from a nearby bound protein . after excitation , the electronic configuration of the excited 
 state 
 allows fast rotation around the central polymethine bond , due to a 
 reduction in bond order following electronic excitation . this , in 
 turn , allows cy3 to isomerize between trans and cis through a 90 isomerization intermediate . the excited - state isomerization rate constants from trans to 90 intermediate and back are denoted by kd , trans90 , kd,90trans , and from cis to 90 intermediate as kd , cis90 , kd,90cis . this intermediate has been reported to be tightly coupled 
 to the ground - state , allowing fast 
 nonradiative de - excitation with branching into both cis and trans isomers . therefore , the 90 intermediate serves as an efficient sink 
 for excited - state deactivation and competes with fluorescence . the 
 de - excitation rate from the 90 excited - state intermediate is 
 denoted as kd,90 . excitation energy can 
 be depleted radiatively or transferred only from planar forms of cy3 . altogether , the excited - state cis and trans isomers may yield fluorescence or fret , but the 90 
 excited - state isomerization intermediate can not . the de - excitation 
 rate constants from the trans and cis isomers represent sums of all radiative and nonradiative de - excitation 
 processes including fluorescence , internal conversion , or frster - type 
 resonance energy transfer ( fret ) and are denoted as kd , t , and kd , c respectively . the de - excitation from the cis isomer has been reported 
 to be mostly nonradiative . in addition , the transient 
 absorption in the cis ground - state isomer , hundreds 
 of ns after excitation , reports on population of the cis ground - state isomer . the isomer is reached via branching on the 
 potential energy surface at the 90 transition - state , rather 
 than directly from the cis isomer after de - excitation . therefore , out of the three excited - state isomers , 
 it is mostly the trans isomer for which de - excitation 
 yields fluorescence . hence the longer cy3 survives in the trans excited - state isomer after excitation , the higher 
 the probability it will yield a fluorescence photon upon relaxation 
 back to ground state . pife is the results of a modulation in isomerization 
 rate due to steric hindrance . this hindrance is responsible for enhancement 
 in the trans isomer survival ( and reduction in isomerization 
 into the 90 isomerization intermediate ) . in pife - fret , 
 an acceptor fluorophore is placed closely to the 
 cy3 and acts as yet another nonradiative sink for the excitation energy . since fret is effective for distances of 310 nm , no 
 direct steric hindrance is imposed on cy3 by the acceptor fluorophore . however , the fret process reduces the time cy3 spends in the excited - state 
 ( including in the trans isomer hence reducing the 
 fluorescence quantum yield of the donor ) , which in turn will lead 
 to a reduction in the magnitude of a possible pife effect . if pife probes the binding of a protein proximal to a cy3 
 placed on dsdna and if the dsdna undergoes a conformational change 
 upon binding , a pife effect could potentially be masked by an increase 
 in fret efficiency . energy transfer from the trans excited - state isomer 
 is described here as another de - excitation rate constant ( eq 3):3where r0,t is 
 the frster radius , the distance at which 50% of the excitation 
 energy is transferred via fret to the acceptor , r is the distance between the dipole moments of cy3 and the acceptor 
 fluorophore , and e is the fret efficiency from the trans donor . energy transfer may also occur from the cis cy3 excited - state isomer ( eq 4):4 this treatment 
 of fret is accurate as long as the dsdna structures 
 with either a protein bound or unbound can be considered static . other cases require an extension of the model ( given in the si ) . in the static case , since pife modulates 
 the frster radii r0,t and r0,c , the fret rate constant is a function of 
 the modulated frster radius r0 and dye distance . since the latter might also be influenced depending 
 on the chosen protein system , we treat the rates as functions of fret 
 efficiency in this uniform approach . for further discussion regarding 
 heterogeneous and dynamic fret systems , see discussion in the si . following the jablonski diagram ( figure 1 ) and the above - mentioned 
 rationale , pife - fret 
 can be described by the following set of coupled rate equations ( eqs 5):5here , dt * , d90 * and dc * represent 
 the time - dependent occupancy of cy3 excited - state trans , cy3 excited - state cis , and the 90 isomerization 
 intermediate , respectively . since the 90 isomerization intermediate is not expected to be de - excited radiatively , the fluorescence signal 
 of cy3 and the corresponding acceptor in pife - fret can be calculated 
 from dt * , dc*. and a * which is the survival 
 probability of the excited acceptor . we have recently demonstrated 
 applications of the pife ruler using 
 alex - based pife - fret ( i.e. , using fluorescence intensity - based measurements 
 rather than fluorescence lifetimes measurements ) . we demonstrated 
 that our approach could simultaneously provide two dynamic molecular 
 rulers at different length scales as long as the acceptor is insensitive 
 to changes in its microenvironment . here , we compare experimental 
 results obtained before to our derived model ( eqs 5 ) . this attempt requires knowledge of fret 
 efficiency e and the stoichiometry s both of which we derive from cy3 ( donor ) intensity and the acceptor 
 intensity according to67 the intensities 
 in eqs 6 and 7 are calculated for the alternation period 
 during which the donor is excited . during the acceptor s excitation 
 period , only the acceptor is excited , and hence it yields fluorescence 
 after direct excitation , with a rate and total intensity of8respectively . a good practice for carrying cy3-based pife - fret 
 measurements is 
 the utilization of the cy3b fluorophore in control experiments . cy3b 
 is the chemical equivalent of the trans cy3 isomer 
 without isomerization possibility . the fret rate equations , for cy3b 
 acting as a donor , are therefore simplified to9 the fluorescence 
 intensity of cy3b is then calculated according 
 to10 the mean values of the fret efficiency e and 
 stoichiometry s distributions given in an e  s histogram are calculated according 
 to1112 the fret efficiency calculated for 
 either the cy3-donor or cy3b - donor 
 assumes both fret pairs have been normalized to the same frster 
 radius using the r0 of the cy3b - acceptor 
 pair . this is achieved following the corrections scheme given 
 in ploetz and lerner et al . following 
 this approach , we treat all data after gamma correction and convert 
 all fret efficiencies onto the common r0-axis of cy3b by 
 employing the gamma of cy3b . the absolute quantum yield changes and 
 absolute gamma values of complex protein system do not interfere anymore 
 with the fret efficiency , but are decoupled . rotational diffusion of 
 cy3 on dsdna might be hindered upon binding 
 of a protein close to the attachment site . the fluorescence quantum 
 yield ( qy ) of cy3 is directly proportional to the degree of isomerization 
 inhibition from the excited - state trans isomer . since 
 isomerization requires available space to accommodate the spatial 
 change in the structure of cy3 , its fluorescence spectrum is sensitive 
 to the microenvironment . the average fluorescence intensity , fluorescence 
 lifetime , or qy of cy3 are expected to be low when the fluorophore 
 is free to isomerize . this occurs partly due to loss of excitation 
 energy via nonradiative relaxation through the 90 isomerization 
 intermediate . an induced change in the microenvironment , such as in 
 the case of protein binding in close proximity , can sterically restrict 
 cy3 and hence impede its isomerization . steric restriction will decrease 
 the isomerization rate and thus increase radiative recombination from 
 the trans isomer , leading to increased fluorescence 
 intensity and an increased fluorescence qy . according to kramers 
 kinetic theory , the isomerization rate constants ( eqs 5 ) depend on the free energy of 
 the excited - state isomers , on the free energy barrier between isomers 
 ( in the exponential term ) , and on the isomerization mobility / diffusivity 
 ( in the pre - exponential term ) . steric interactions are the manifestation 
 of volume excluded by a near - by molecular system ( excluding all other 
 types of interactions ) . cy3 isomerization mobility could 
 be influenced by the viscosity of its microenvironment ( microviscosity ) and/or by steric hindrance . these will affect the pre - exponential 
 term of the kramers isomerization rate constant without changing the 
 activation barrier for isomerization . however , specific interactions 
 of the fluorophore with a nearby molecule may also induce a delay 
 in isomerization , which will lead to an increase in activation barrier 
 for isomerization . here we provide a model that accounts for pife 
 as the effect of steric hindrance on cis / trans isomerization . 
 in diffusion activated reactions , restricted rotational mobility due 
 to steric hindrance . the modified isomerization rate of a cy3 in 
 the presence of a nearby protein could therefore be written as13where kiso represents 
 all isomerization rates ( kt90,k90t , kc90,k90c ) , kiso represents all modified isomerization rates due to steric hindrance , vt and vf are the 
 accessible volumes to cy3 ( see figure 2a ) in the absence and presence of steric hindrance , 
 respectively , and b is a proportionality constant 
 that accounts for solvent properties , tethering of the dye to the 
 dna , other specific interactions , etc . vf is the excluded volume , 
 and  = vt/(vt  vf ) is cy3s 
 normalized accessible volume in the presence of steric hindrance ( eq 13 ) . importantly , this 
 allows to define a universal pife parameter ,  , which is the 
 ratio of the isomerization rate constants in the absence and presence 
 of steric hindrance . ( a ) illustrations of dsdna with donor ( cy3 ) and acceptor ( atto 647n ) , 
 separated by 40 bp . the restriction enzyme bamhi 
 binds specifically to the dna containing its palindromic dna sequence 
 ( purple ) . binding of bamhi restricts the available 
 volume of cy3 at a separation of 1 bp away from the protein - binding 
 sequence , leading to an increased brightness . at a separation of 7 bp away from the binding site , the available volume of cy3 is maximized , 
 and the brightness of cy3 is low . ( b ) alex - based pife - fret experimental 
 results ( circles ) and a global fit using the pife model ( solid lines ) 
 for dsdna labeled with cy3(b ) at the 5-end and atto 647n as 
 acceptor on the complementary strand . control experiments with fret 
 distances of 33 , 23 , 18 , and 13 bp ( absence of bamhi ) are shown in black . pife - fret results at 33 bp separation in 
 the presence of bamhi are shown for 1 ( red ) , 2 ( orange ) , 
 3 ( green ) , 5 ( blue ) , and 7 ( purple ) bp separation between the donor 
 and bamhi . the obtained pife factors for the 5 dna 
 constructs are shown in the legend and in figure 3 . in order to calculate the pife effect for a particular case , one 
 needs to replace all isomerization rate constants in eq 5 with the modified isomerization 
 rate constants of eq 13 . for this , however , the volume explored by the fluorophore in the 
 absence and presence of the bound protein needs to be evaluated . if 
 a protein  dna crystal structure exists for a particular interaction 
 of interest , the volume explored by the mobile fluorophore could be 
 estimated via published procedures . in alex - based pife - fret , 
 a given cy3-acceptor pair will yield a particular s value . in the presence of a nearby bound protein ( or any other steric 
 hindrance ) , if contact quenching does not occur , this s value will increase ( assuming that there are no changes in e ) . following directly from the increase in cy3 fluorescence 
 intensity ( assuming there is no change in the acceptor s fluorescence ) . such a simple case was reported for the interaction of the restriction 
 enzyme bamhi with dsdna . since the nonradiative de - excitation of cy3 through isomerization 
 ( modulated by pife ) and through fret to the acceptor , the molecular 
 target and its binding position have to be carefully chosen so that 
 pife and fret are sensitive to binding and conformation , respectively . 
 to maximize the pife effect , it is advisible to position the acceptor 
 away from cy3 at a distance which is close - to or larger than the corresponding 
 frster radius r0 . in many 
 cases , protein  dna interactions trigger a conformational change 
 not only to the dna , but both to the protein and the dna . upon protein 
 binding , dna can exhibit bending ( e.g. , introduced by the restriction 
 enzyme ecorv ) , bubble - formation ( triggered by rna 
 polymerases ) and other types of dna conformational changes . such conformational 
 changes may alter the fret efficiency , which in turn will introduce 
 an increase in stoichiometry due to the decreased survival time in 
 the excited cy3 , regardless of pife effects . e and s values in alex - based pife - fret experiments are not independent 
 and require careful calibration . in the absence of pife and 
 depending on the intrinsic rate constants 
 and the relevant parameters ( eqs 5 ) , one could plot s values as a function 
 of e values , i.e. , s(e ) . this s(e ) curve will dictate 
 a lower bound on pife related change in s ( see figure 2b , black solid line ) . 
 if cy3 is replaced with cy3b , and all corrections are applied , the 
 corresponding s should , by definition , always be 
 0.5 . so any result that points to a pife effect 
 in an alex - based pife - fret measurement should fall above the s(e ) curve for cy3 and below that for cy3b 
 ( see figure 2b , black 
 dashed line ) . the experimental ( best fit extracted ; see figure 2 ) pife parameter 
 (  ) and the theoretical normalized ( b = 1 ) 
 accessible volume (  ) are plotted as a function of bp distance 
 ( black and red filled circles ) respectively . the theoretical ruler 
 based on the estimation of the accessible volume of cy3 serves as 
 a lower boundary for the experimental ruler , where specific interactions 
 of the dye with the bound - protein can delay the isomerization from trans isomer even longer . in previous published work , we 
 performed 
 salex measurement for the restriction enzyme bamhi bound to dsdna , having cy3 or cy3b as a donor , and atto 647n as 
 an acceptor , at different donor  acceptor separations . the results 
 of these experiments were fitted to the pife - fret model ( eqs 512 ) and are shown in figure 2 as a family of s(e ) curves . the extracted best fit values are 1/kd , c = 0.39 ( 0.150.55 ) ns , 1/kd,90 = 0.02 ( 0.010.03 ) ns , 1/kt90 = 1.00 ( 0.901.10 ) ns , 1/k90t = 0.89 ( 0.601.50 ) ns , 1/kc90 = 0.35 ( 0.200.55 ) ns , 1/k90c = 0.09 ( 0.080.30 ) ns , and  = 0.95 ( 0.940.99 ) 
 using lifetimes measured by ploetz and lerner et al . for cy3b - atto 647n , we also derive : 1/ka = 4.3  0.2 ns and 1/kd , t = 2.2  0.1 ns . a striking observation is the fast de - excitation 
 of cy3 via the 90 intermediate isomer in comparison to the isomerization 
 rate constants . this observation is not only consistent with the currently 
 accepted models for cy3 photoisomerization , but also supports the 
 hypothesis that this intermediate does indeed serve as a sink to the 
 excitation energy . pife is therefore dominated by a decrease in isomerization 
 yield from the trans isomer . also note that the fraction 
 of the excited - trans isomer is very high , as expected . when stepping the bamhi binding site 7 , 5 , 3 , 
 2 , and 1 bp toward cy3 , the stoichiometry s is increased 
 ( figure 2b , purple , 
 blue , green , orange , and red , in that order ) . this data were globally 
 fit to the pife - fret model ( eqs 513 ) , while keeping the pife 
 parameter (  - the fold decrease in isomerization rate ) free , 
 and fixing the photophysical rate constants of cy3 . the best fit results 
 ( figure 2 , colored 
 lines ) report on the dependence of the pife effect on the distance 
 of cy3 from the nearby bound bamhi , which is then 
 explicitly plotted in figure 3 . figure 3 shows that 
 the experimentally derived  linearly depends on the separation 
 between the cy3 fluorophore and the interaction interface ( leading 
 edge ) of the bamhi on dsdna . the theoretically derived normalized accessible volume  ( eq 13 ) is also plotted on 
 the same graph , showing a linear dependence on distance ( until a pife 
 separation of 5 bp ) when setting the proportionality factor to be b = 1 . the experimentally derived pife parameter values 
 ( figure 3 , black ) fit 
 with the theoretical evaluations of the ratio of cy3 available volumes 
 for pife distances 1 , 2 , and 7 bp away from the binding sequence ( figure 3 , red ) . however , 
 for pife distances 3 and 5 bp , the experimentally derived pife parameter 
 values are higher than the theoretical estimates of cy3 ratio of available 
 volumes . since the theoretical estimation of the pife effect shown 
 by eq 13 are derived 
 following the sole effect of steric hindrance and does not provide 
 information on possible specific interactions , the results for pife 
 separations 3 and 5 bp may report on specific interactions of cy3 
 at these positions with the bound bamhi . the resemblance 
 between the theoretical estimates driven solely by steric hindrance 
 effects and some of the experimentally derived pife values supports 
 the notion that pife of cy3 is caused by steric hindrance from the 
 nearby bound protein , which leads to a decrease in isomerization rate . the steric hindrance can be estimated directly from ratios of fluorophore 
 accessible volume calculations performed on dna in the absence and 
 presence of a protein , given that the crystal structure of the complex 
 is available . this theoretical estimation can act as a lower boundary 
 for the experimental - derived pife parameters and allows assessing 
 specific interactions of cy3 with the bound protein or possible deviations 
 of the binding mode of the protein to the dna that may occur with 
 the labeled dna . the best fit of the model to pife data results in 
 a s(e ) curve with different e and s pair values ( figure 2 , colored lines ) . to provide a control experiment 
 in which no conformational changes 
 in the dna duplex are induced by protein binding ( observed in fret ) , 
 we also reanalyzed published data of unspecific binding of t7 dna 
 polymerase gp5/trx at different 
 fret distances . the unspecific sliding 
 of the polymerase is so fast that an average pife effect is observed 
 instead of multiple distinct pife state for different distances of 
 polymerase and cy3 . these pife - fret measurements of gp5/trx on dsdna 
 represent cases in which binding does induce conformational changes 
 in the dsdna , with data points that move on the s(e ) lines due to 
 the change in e ( figure 4 ) . the comparison between the achieved enhancement 
 factors for gp5/trx with bamhi ( figure 2 ,  = 2.47 ) clearly points 
 to the different nature of locally involved amino acids . this difference 
 of local environment renders it hence necessary in general , to calibrate 
 the ruler - characteristic of any protein and applied buffer system 
 separately in order to link the measured pife enhancement to an actual 
 spatial separation . alex - based pife - fret experimental results ( circles ) and 
 a global fit using the pife model ( solid lines ) . results for dsdna 
 labeled with cy3 and cy3b as the donor are denoted with filled and 
 open circles , respectively . the acceptor in both cases is atto 647n . 
 control experiments ( absence of gp5/trx ) are shown in black for 33 , 28 , 23 , 18 , 13 , and 8 bp . pife - fret 
 results in the presence of gp5/trx for dna constructs with 28 , 23 , and 18 bp separation are shown in 
 magenta . gp5/trx is known to slide 
 on dna , hence it does not have a known pife separation from 
 the bound protein . the best fit value of the pife parameter ,  , 
 to the data , is shown close to the best fit curve ( 4.14 ( 3.944.36 ) ) . in previous works , pife was quantified by the fold increase in cy3 fluorescence lifetime 
 or intensity ( or the related fluorescence qy ) . following the above 
 description the fluorescence 
 quantum yield of cy3 can be described as the ratio of radiative de - excitations 
 to all de - excitation processes:14 this expression assumes that the time 
 it takes to reach steady - state for all isomers is much shorter than 
 the excited - state lifetime . the probability of occupying the trans excited - state isomer is the highest immediately after 
 excitation , and it decreases thereafter . as the best fit results to 
 the model show ( figure 2 , black ) , the isomerization rates are not much different from the 
 excited - state lifetime . a temporal definition of the fluorescence qy can be given 
 by considering the weights on isomers state occupancy probability:15 at each moment after excitation , 
 the cy3 qy decreases as the population 
 of the excited - state trans isomer decreases , until 
 it reaches a steady - state . the mean qy should therefore be taken into 
 account ( figure 5a ) . the mean qy can be calculated accurately ( figure 5b , black ) , but can also be approximated by 
 the asymptote value of the qy curve at the long decay times ( figure 5b , gray ) . when referring 
 to the pife effect as the fold increase in fluorescence qy , we will 
 calculate the term in eq 15 in the absence and presence of steric hindrance and compare 
 the ratio between the two to the pife parameter  ( figure 5b ) . fold - decrease in cy3 
 mobility and fold - increase in mean fluorescence 
 quantum yield . ( a ) time dependence of cy3 and cy3b fluorescence quantum 
 yields ( following eq 15 in the absence (  = 1 ) and presence  = { 2,3,4,5,10 } ) 
 of pife . ( b ) time averaged ratio ( black ) and longtime asymptote ( gray ) 
 of cy3 qy in the presence and the absence of pife for different  
 values ,  = { 210}. the parameters used for this simulation 
 are the ones found in the analysis reported above ( figures 2 and 3 ) for a candidate fret efficiency of e = 0.4 . the fold increase in the fluorescence 
 qy of cy3 ( either using fluorescence 
 intensities or lifetimes ) is the measure that was used to quantify 
 pife in previous works.figure 5 shows that this measure does 
 not directly report on the fold decrease in isomerization mobility . the nonlinear dependence between the two measures holds even for large 
 values of qy ( as in the case of bamhi ) . however , note that as the pife effect is increasing , 
 one pife parameter , the fold - increase in qy , approaches an asymptote , 
 while another pife parameter , the fold - decrease in cy3 isomerization 
 mobility , still increases . the fold - decrease in cy3 isomerization mobility ,  , 
 however , has a linear dependence on the change in cy3 accessible volume , 
 and hence on steric hindrance . therefore , the  parameter is 
 a more direct measure of the pife effect . we compared our obtained 
 values ( figure 5b ) 
 with those reported by hwang et al . through 
 a direct calculation of the fold - increase in fluorescence intensity 
 or fluorescence lifetime , performed on the same dna constructs in 
 the absence and presence of bamhi ( figure s1 ) . this comparison 
 revealed that ( 1 ) the intensity - based data found with smpife is higher 
 than the alex - based pife - fret results using our model with bamhi ; ( 2 ) the lifetime - based data found with smpife is 
 mostly lower or equal to the alex - based pife - fret results using our 
 model for bamhi ( note the large error values ) ; however 
 ( 3 ) the intensity- and lifetime - derived smpife data found by hwang 
 et al . already differ from each other with statistical significance 
 ( no intersection of error ranges for both ) . most importantly the results 
 of our re - evaluation of the bamhi pife experiment 
 using alex - based pife - fret with the herein proposed model are in the 
 middle between the intensity- and lifetime - derived smpife results , 
 and hence reconcile the two . in alex - based 
 pife - fret , the mean values of e and s are 
 determined via 2d gaussian fittings of subpopulations in the e  s histogram . these subpopulations 
 tend to exhibit intrinsic width which depends on shot - noise and other 
 photophysical effects . alex - based pife - fret experiments involve measuring 
 separately the cy3-acceptor dsdna in order to characterize the system 
 parameters in the absence of pife . in a next step , if the protein binds in close 
 proximity to the cy3 fluorophore and induces an increase in its fluorescence 
 due to pife , the fraction of single dna molecules bound to the protein 
 will show up as a second s(e ) subpopulation . due to the widths of these subpopulations , it is always better to 
 have the mean e and s of the two 
 well separated . the best fit results shown in figure 2 represent the s(e ) curves for different values of the pife factor . they allow us to observe what will be the dynamic range of changes 
 in the stoichiometry for different nominal fret efficiency values : 
 the higher the fret efficiency value is , the smaller the changes in 
 stoichiometry will be . in addition , if a conformational change that 
 increases e is concurrent with protein binding ( and pife ) , one should 
 exercise great caution in correctly interpreting the increase in s , since it could be due to increase in e only and vice versa . the region in figure 2 that is bound by the black cy3 and cy3b 
 curves ( no protein bound ) is the region in which e and s values will report on pife either with or 
 without fret changes . pife is a powerful single 
 molecule spectroscopy technique that 
 provides a distance ruler shorter than fret but longer than contact - quenching - based 
 rulers , such as photoinduced electron transfer . the combination of 
 pife with fret allows us not only to probe both short and long distances 
 simultaneously , but also to study binding - induced conformational changes 
 in nucleic acids triggered by unlabeled proteins . in this work we 
 have provided a model that allows correct interpretation of pife experiments 
 in general and of alex - based pife - fret experiments in particular , 
 and elucidated the nonlinear dependence of s on e in a pife experiment . we identified steric hindrance ( aside 
 from other possible effects such as a specific interaction of the 
 fluorophore with the bound protein ) and slowing down of cy3 isomerization 
 mobility as the main mechanisms responsible for pife . the resulting 
 change in the fluorescence qy , the fluorescence lifetime and hence 
 cy3 s brightness can serve as a signal reporting on pife in 
 different implementations of confocal smfret experiments . given that this assay can be 
 applied for surface immobilized smfret , the presented work represents 
 a generalized and comprehensive framework for studying protein  nucleic 
 acid interactions in a quantitative manner .