t4 lysozyme , as a member 
 of the lysozyme family produced by bacteriophage , 
 breaks down the bacterial cell wall by catalyzing the hydrolysis of 
 poly saccharide chains during infection of the bacteria .
the enzyme specifically cleaves the glycosidic bonds connecting 
 the repeating subunits of cell walls between n - acetylglucosamine 
 and n - acetylmuramic acid that are substituted with 
 peptide side chains .
the three - dimensional 
 structure is clearly organized with two domains connected by a long 
 -helix ( figure 1 ) . the active site cleft , 
 where hydrolysis of the glycosidic linkage takes place , is located 
 at the interface between the two domains .
it has been widely accepted 
 that t4 lysozyme exhibit hinge - bending conformational motions , referring 
 to rotation of one domain relative to the other domain along an axis 
 running through the interface of the two domains . both 
 ensemble - level and
single - molecule measurements have revealed hinge - bending 
 motions in which the opening of the active site cleft is within a 
 nanometer .
as we have reported previously , the t4 lysozyme enzymatic reaction involves complex conformational 
 state changes in the enzymatic turnovers . a simplified michaelis 
menten 
 type of mechanism can be presented as1where e , s , es , es * , and ep represent enzyme , 
 substrate , nonspecific enzyme  substrate complex , specific or 
 active enzyme  substrate complex , and enzyme  product 
 complex , respectively .
the process of forming the active complex of 
 es * involves multiple conformational states .
the process of e + s 
  es  es * essentially involves the enzyme active site 
 opening up to take the substrate , forming a nonspecific es complex , 
 and binding down to form the active complex of es * ready to react 
 followed by turnover to ep .
the process of reaction and product releasing 
 es *  ep  e + p may not involve significant enzymatic 
 active site conformational changes . while t4 lysozyme hinge - bending 
 motions have been extensively probed 
 by single - molecule fret ( fluorescence resonance energy transfer ) spectroscopy , 

the domain motion of t4 lysozyme is rather complex and contains motions 
 besides hinge - bending .
it is reasonable to assume that the hinge - bending 
 motion in nature involves multiple coupled nuclear coordinates that 
 can be projected to a nuclear coordinate associated with the -helix . 
 in order to capture the complexity of t4 lysozyme conformational motions , 

single - molecule spectroscopy 
 is a powerful approach for mechanistic 
 understanding of complex and fluctuating biological processes by resolving 
 time - dependent dynamic process and allowing exploration of hidden 
 heterogeneity beyond nonsynchronized ensemble - averaged measurements .
single - molecule fret spectroscopy sensitive to single - molecule conformational 
 fluctuation dynamics has offered possible direct observations of biological 
 conformational dynamics by rendering spatial and temporal information 
 between donor and acceptor fluorophores placed within a certain proximity 
 on individual molecules of interest .
this approach 
 has made significant and extensive contributions to the understanding 
 of complex biological dynamics through the perspectives of heterogeneous 
 dynamics of protein molecules , nucleic acids , and their interactions 
 with other molecules .
for example , single - molecule fret has been used to 
 study rna folding pathways , hairpin ribozymes 
 intimidate states , dna bubbles kinetics , epidermal growth factor receptor ( egfr ) dimerization , and conformational dynamics of enzymes .
lu and co - workers have focused on conformational dynamics of t4 
 lysozymes and have observed conformational bunching effects in the 
 process of t4 lysozyme hinge - bending . for complex 
 biological systems , such as protein 
protein 
 interactions , ion channel receptor activations , protein folding and 
 aggregations , and protein conformational fluctuations under enzymatic 
 reactions , it is more than often that multiple conformational nuclear 
 coordinates simultaneously play critical roles in regulating and gating 
 biological functions .
under such complex multiple coordinate conformational 
 dynamic rate processes , one - dimensional fret may be insufficient to 
 characterize the intrinsic complexity of molecular dynamics .
hence , 
 it is desirable to have advanced fret techniques capable of probing 
 more than one - dimensional dynamic information .
for example , some efforts 
 have been made to develop three - color and four - color fret in which 
 more than one fret pair are used to probe multiple site - to - site distance 
 changes at a time .
nevertheless , multicolor fret requires fluorophores with high photostability 
 and clear spectral separation , which are much more difficult to achieve 
 than one fret pair , especially at single - molecule level .
in addition , 
 the fact that energy transfer between donor and acceptor obeys orientation 
 dependence (  ) as expected for a dipole 
dipole 
 interaction has seldom been took into account , instead , the assumption 
  = 2/3 ( the fluorephores undergo freely rotation 
 in a time much shorter than fluorescence lifetimes ) is widely used for approximate distance estimate .
it has 
 been experimentally proved that fluorescence energy transfer between 
 cy3 and cy5 depends on the orientation .
it has also been reported that the degree of position accuracy relies 
 on the rotational mobility of single molecules .
therefore , the understanding of orientation effect could 
 result in more accurate fret distance approximation and molecular 
 angular information for position determination .
for this purpose , 
 several groups have shed light on molecular orientations ( or rotations ) 
 via imaging and fluorescence anisotropy ( or polarization ) spectroscopy . 

for example , out - of - focus and in - focus images have been combined to 
 refer three - dimensional single molecule orientations .
dual - color and dual - polarization images of single molecules 
 have been captured by ccd ( charge - coupled device ) camera .
a multiparameter single - molecule fluorescence 
 spectroscopy , photon distribution analysis , along with structural modeling have been developed to quantitatively describe single - molecule 
 fret in which several fret - related parameters such as distance , molecular 
 orientation , and dye quenching ( or bleaching ) are taken into account . 

lu and co - workers have demonstrated the use of single - molecule nanosecond 
 anisotropy to study spatially confined rotational diffusion dynamics 
 of individual tethered proteins and nanosecond 
 protein motion dynamics .
the possibility 
 of probing multidimensional conformational dynamics 
 of complex biological systems calls for fret - anisotropy correlated 
 measurements on demand .
fluorescence anisotropy not only allows for 
 estimating orientation effect on fret or position determination for 
 imaging mentioned above but also allows for acquiring information 
 about the motion of the fluorophore , the rotational dynamics of subdomains , 
 or the entire proteins .
the methods of measuring rotational or tilting 
 motions by fluorescence anisotropy in single molecules have been reviewed 
 and discussed .
lu and co - workers have successfully probed nanosecond 
 protein motions of calmodulin and t4 lysozyme by single - molecule fluorescence 
 anisotropy .
unfortunately , most of fluorescence 
 anisotropy research have been either limited to the study of orientation 
 effect for fret , or limited to the rotational dynamics of molecules ; 
 although the potential ability of fluorescence anisotropy in the identification 
 of multiple conformational states of biological molecules has been 
 mentioned .
nevertheless , the potential 
 abilities of correlated single - molecule fret and fluorescence anisotropy 
 for direct observing multidimensional conformational dynamics have 
 not been demonstrated yet , to our best knowledge . in this article
, 
 we report our new technical approach integrating single - molecule fret , 
 photo stamping spectroscopy and fluorescence anisotropy to study multicoordinate 
 conformational dynamics of t4 lysozyme under enzymatic reaction conditions . 
 from conformational dynamics perspectives ,
this approach enables us 
 to simultaneously probe multidimensional or multicoordinate conformational 
 dynamics of proteins , including fret coordinate motions probed by 
 fret pair and rotational motions monitored by fluorescence anisotropy . in this work
, we exploit the multidimensional aspect of t4 lysozyme 
 conformational dynamics and demonstrate the potential of our new correlated 
 single - molecule multidimensional photon stamping spectroscopy .
multidimensional 
 conformational motions of wild - type t4 lysozyme 
 ( pdb - code , 3lzm ) , including hinge - bending motions along -helix and rotational 
 motions of each domain .
cy3 and cy5 are covalently labeled to two 
 cysteines : cys 54 on n - domain and cys 97 on c - domain .
cy3-cy5 labeled 
 t4 lysozyme is tethered through an amine - to - sulfhydryl bifunctional 
 cross - linker molecule to thiol - functionalized glass coverslip surface . 

the approximate 45 nm spacer allows free rotation 
 of single t4 lysozyme without perturbation or confinement from the 
 modified surface .
distance changes between the two labeling sites 
 involved in hinge - bending conformational motions can be monitored 
 by tracing the dynamic fluctuations of donor lifetime during the fret 
 process .
besides hinge - bending motions along -helix line , the 
 two domains of t4 lysozyme also exhibit other types of conformational 
 motions , for example , rotational motions .
wild - type 
 t4 lysozyme plasmid was bought 
 from addgene , which was authorized by prof .
two cysteines ( residue 54 on n - terminal domain 
 and residue 97 on c - terminal domain ) of the wild - type t4 lysozyme 
 are accessible to thiolation reactions .
a cy3-cy5 fret pair ( ge healthcare ) 
 was nonselectively labeled on these two cysteines .
the crystal structure 
 of wild - type cy3-cy5 labeled t4 lysozyme is shown in figure 1 .
the individual donor  acceptor labeled t4 
 lysozyme can be easily distinguished by four - channel optical images 
 as shown in figure 2 , because only donor 
acceptor 
 labeled molecules can simultaneously exhibit four emission spots ( dual 
 color and dual polarization for each color ) . the substrate for t4 
 lysozyme used in our experiments is peptidoglycan that is the major 
 component of the bacterial cell wall that t4 lysozyme breaks .
peptidoglycan 
 isolated from micrococcus luteus was purchased from 
 sigma - aldrich and was directly used without further purification . 

the substrate was suspended to a final concentration of 25 g / ml 
 in ph 7.3 pbs buffer during single - molecule experimental measurements . in our 
 single - molecule fret experiments ,
t4 lysozyme was tethered 
 through a bifunctional nhs - peg6-maleimide cross - linker 
 to a modified glass coverslip surface .
this cross - linker is functional 
 between primary amines ( nh2 ) and sulfhydryl ( sh ) groups 
 in which the n - hydroxysuccinimide ester ( nhs ) group 
 reacts specifically with primary amino groups of lysine to form stable 
 amide bonds , and the maleimide group reacts with sulfhydryl to form 
 stable thioether bonds .
the glass coverslip was first sonicated with 
 acetone for half an hour , followed by rinsing with alcohol solution 
 and distilled water several times .
the clean coverslip was treated 
 overnight with a 10% ( v / v ) mixture of 3-mercaptopropyl - trimethoxysilane 
 and isobutyl - trimethoxysilane ( 1/1000 ratio ) in 15.0 ml of dimethyl 
 sulfoxide ( dmso ) . after rinsing with ethanol and water ,
the coverslip 
 was put in the ph 7.3 pbs buffer solution for 1 h to remove unreacted 
 solvent .
the coverslip was then incubated with 40.0 l of 250 
 mm bifunctional cross - linker stock solution ( nhs - peg6-malemiade , 
 thermo scientific ) in 12.0 ml of pbs buffer solution for 2 h at 4 
 c .
the amine - to - sulfhydryl cross - linkers with hydrophilic polyethylene 
 glycol ( peg ) spacer arms can be attached to the glass coverslip surface . 

after additional washing , the coverslip was incubated with 0.66 nm 
 t4 lysozyme in the pbs buffer for 2 h at 4 c .
after the linkage 
 between amine - reactive group of nhs - peg6-malemiade and 
 primary amine group of t4 lysozyme s lysine , the tethered enzyme 
 sample was assembled on the glass coverslip surface . during our single - molecule 
 measurements ,
the assembled t4 lysozyme on the coverslip was further 
 incubated with 25.0 g / ml substrate for half an hour at room 
 temperature in pbs buffer solution ( ph 7.3 ) to fulfill the engagement . 

the effective trolox - oxygen scavenger solution , which contains 0.8% d - glucose , 1.0 mg / ml glucose oxidase , 0.04 mg / ml catalase , and 
 1.0 mm trolox ( 6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid ) , was added to the above sample chamber to prevent the possible photobleaching 
 or quenching of the cy3-cy5-labeled t4 lysozyme molecules . frster resonance energy 
 transfer ( fret ) refers to the nonradiative energy transfer from a 
 donor molecule to an acceptor molecule , arising from a dipole 
energy transfer occurs when the oscillations of an optically induced 
 electronic coherence on the donor are resonant with the electronic 
 energy gap of the acceptor .
fret efficiency is sensitive to the interdistance between the donor 
 and acceptor in the range of 3080  , although fret is 
 not necessarily accurate in measuring absolute distances , as often 
 being specified as a 
, single - molecule fret is sensitive 
 to probe the temporal fluctuation dynamics of the distance changes , 
 such as the conformational changes of the biomolecules .
the energy 
 transfer efficiency ( efret ) is given by2where r is the separate distance 
 between donor and acceptor and r0 ( the 
 frster radius ) is the critical distance at which energy transfer 
 is equal to 50% .
r0 , as expressed in eq 3 , is a function of the orientation factor  , the donor  acceptor spectral overlap j , the donor quantum yield d , and the refractive 
 index of the medium n.  is the orientation factor that varies between 0 and 4 and 
 is defined by the relative orientation of the donor emission and acceptor 
 absorption dipoles . for molecules which rotate very fast ,
 is taken its average value  , 
 which equals 2/3 for isotropic rotation .
in general ,  is given by eq 4 , in which t is the angle between the donor emission dipole and the acceptor 
 absorption dipole , d is the angle between the donor  acceptor 
 connection line and the donor emission dipole , and a is the angle between the donor  acceptor connection line and 
 the acceptor absorption dipole.34 any process that influences the distance 
 of donor - to - acceptor affects the fret rate or efficiency , which enables 
 us to probe the conformational fluctuation dynamics of dna , rna , and 
 proteins . for example , fret can be used to sense the distance changes between 
 donor and acceptor that have been labeled on a host molecule or two 
 different molecules , and then the conformational changes of one host 
 molecule or the relative motions of two molecules can be monitored 
 by tracing the fret efficiency . in single - molecule fret measurements ,
efret from donor to acceptor reflects mutual 
 distance changes , resulting in the capability of probing single molecules 
 conformational dynamics in real time by tracking efret changes .
the detection 
 of efret , usually by 
 ratio - metric methods , can be generally classified into intensity - based 
 fret and lifetime - based fret.5where ia is the 
 acceptor fluorescence intensity and i d is the donor fluorescence intensity in fret process .
da and d are donor lifetime in the presence 
 ( da ) and in absence ( d ) of acceptor , 
 respectively .
fret detection on the basis of 
 donor lifetime is more effective and less sensitive to local environment 
 fluctuations , especially in afm tip - enhanced 
 single - molecule spectroscopic and imaging measurements where amplified 
 fluorescence signal by metal tip reflection exists .
in the photon stamping spectroscopy , each detected photon is stamped 
 with two parameters : a chronic arrival time and a delay time related 
 to femtosecond laser pulse excitation . in this work ,
we treat photons 
 distributions detected in each 10 ms ( ms ) bins as a poisson distribution 
 which gives the mean of delay times in each distribution as the lifetime 
 da .
fluorescence 
 anisotropy is 
 capable of determining the rotational correlation time of the fluorescence 
 probe , thus providing insights into the motions of probe , and orientation / rotation 
 or mobility of subdomains or the entire molecule .
changes in probe s orientation reflect 
 the rotation or mobility of the target macromolecule where the probe 
 is attached .
the fluorescence anisotropy r(t ) is defined as the difference between the vertically and 
 horizontally polarized fluorescence emission divided by the total 
 fluorescence emission , given by6where i ( t ) and i(t ) are the fluorescence intensities of the parallelly (  ) 
 and horizontally (  ) polarized emission components under vertically 
 polarized excitation .
g is the correct coefficient 
 compensation for the different instrumental detection efficiencies 
 of the various polarized components of the emission , accounting for 
 the ratio of the detection system sensitivities for vertically and 
 horizontally polarized light . in our experiments ,
bright fluorescence 
 microspheres ( 0.1 m , 540/560 nm orange spheres , invitrogen 
 molecular probes ) were used to measure the g factor 
 by using horizontally polarized excitation . with the horizontally 
 polarized excitation ,
the excited - state distribution of the molecules 
 is rotated to lie along this observation axis , so that both the horizontally 
 and vertically polarized components are orthogonal to the incident 
 polarization and the intensities of collected signal are equivalent .
g factors are averagely estimated to be 1.36 and 
 2.36 for donor and acceptor , respectively .
the unbalanced g factor for donor and acceptor are most likely due to the 
 detection discrepancy of different detectors and the bias of the optics 
 response to different colors .
typical anisotropy values are in the 
 range from 0.2 for probes with unrestricted motion to 0.4 
 for those that are immobile .
several factors can depolarize the measured 
 anisotropy to values lower than 0.4 ( the maximum theoretical values ) , 
 such as the numerical aperture of the objective , the angle difference 
 between the absorption and emission dipole , molecular rotation related 
 rotational diffusion , and et al . in terms of rotational diffusion process ,
the expected anisotropy 
 is given by the perrin equation7where r0 ( assumed 
 to be 0.40 here ) is the fundamental anisotropy in the absence of rotational 
 diffusion , rda is donor s anisotropy , 
 and  is the rotational correlation time for the diffusion process . 

we treat donor s anisotropy in the similar way to donor lifetime 
 described in eq 5 : rda is the mean of fluorescence anisotropy in each 10 ms bins measured 
 based on eq 6 .
fluorescence anisotropy provides 
 information about detailed motions of cy3 or cy5 and conformational 
 dynamics of the t4 lysozyme system being studied here .
the time - dependent correlation strength 
 of lifetime as well as anisotropy trajectory is evaluated by autocorrelation 
 function given by8where xi is the donor lifetime ( da ) or anisotropy 
 ( rda ) , the signal variable in time - dependent 
 lifetime or anisotropy trajectory ; i is the index 
 number of data point ; t is the time lag ; x is the mean value of lifetime or anisotropy in 
 each calculation . by using autocorrelation analysis ,
the donor lifetime 
 and anisotropy fluctuation decays (  ) or rates ( 1/ ) can be identified , providing insights into the t4 lysozyme conformational 
 fluctuation dynamics . combining fret , lifetime , polarization , and
anisotropy 
 at single - molecule 
 sensitivity , we show our compact design for probing multidimensional 
 conformational motions .
compared to two - color or 
 two - polarization concepts , our new approach 
 combines color discrimination and polarization using a four - channel 
 single - molecule epi - illuminated microscopy , as shown in figure 2a . in short , a femtosecond pulse laser ( ti :
is combined with an optical parametric 
 oscillator ( opo basic , coherent inc . ) as well as frequency doubling 
 -barium borate crystal ( bbo ) to generate linear - polarized pulse 
 laser .
the 532 nm linearly polarized pulse laser is aligned and focused 
 into coverslip - solution interface by a confocal objective ( plan - apochromat , 
 1.40 na , 63  , carl zeiss ) to excite molecules .
a piezoelectric 
 scanning stage ( nano - h100 , mcl ) with a positioning resolution of 0.2 
 nm is further used to scan the coverslip surface and locate individual 
 molecules .
the fluorescence signals from single molecule are separated 
 to two pathways ( two color ) in wavelength ranges below and above 640 
 nm after passing through a filter ( hq545lp , chroma ) and two dichroic 
 mirrors ( 545dcxru , 640dcxr , chroma ) .
signals in each pathway are further 
 divided into four - channel parallel and perpendicular components for 
 each color by using two polarizing beam splitter cubes ( pbs 201 420680 
 nm , pbs 202 6201000 nm , respectively ) .
the photons from four - channel 
 ( parallel and perpendicular for both donor and acceptor ) are detected 
 by four apds - si avalanche photodiode ( spcm - aqr-14 , perkinelmer optoelectronics ) . 

the time - stamped photon information is recorded through multichannel 
 detector router ( hrt-82 , becker & hickl gmbh ) to a time - correlated 
 single photon counting module ( spc-830 , becker & hickl gmbh ) and 
 a personal computer .
figure 2b shows the single - molecule 
 photon counting images of individual cy3-cy5 labeled t4 lysozymes 
 in which dual - color ( donor and acceptor ) and dual - polarization (  
 and  ) are captured by four apds .
four images are taken simultaneously 
 with an illumination of 532 nm and scanning area of 20 m by 
 20 m .
( a ) 
 experimental home - built four - channel single - molecule setup for measuring 
 multidimensional conformational dynamics . basically , it consists of 
 an inverted confocal epi - illumination configured microscopy , a femtosecond 
 pulse laser , four si avalanche photodiode detectors , a time - correlated 
 single photon counting module , and several optics .
532 nm green linearly 
 polarized pulse laser is used to excite cy3-cy5 labeled t4 lysozyme . 

the emissions ( yellow and red ) from cy3 and cy5 are discriminated 
 by dichroic mirrors .
the polarization of the light emitted is further 
 distinguished into parallel (  ) and vertical (  ) components 
 ( relative to the polarization of the laser excitation ) by two polarizing 
 beam splitter cubes .
( b ) single - molecule photon counting images of 
 individual cy3-cy5 labeled t4 lysozymes .
dual - color ( cy3 and cy5 ) 
 and dual - polarization (  and  ) images are captured . 

dm : dichroic mirror ; apd : avalanche photodiode ; pbs : polarizing beam 
 splitter cubes ; lpf : long pass filter ; wp : wave plate ; l1/l2 : lens ; 
 pc : personal computer .
figure 3 shows the single - molecule studies 
 of multidimensional conformational motions of t4 lysozyme by recording 
 real - time anisotropy trajectory and donor lifetime trajectory . in 
 our single - molecule multiparameter spectroscopy ,
time - resolved fret 
 fluctuations detected by donor lifetime and the correlated fluorescence 
 anisotropy are simultaneously recorded . as described before , each 
 detected photon
is stamped with two parameters : a chronic arrival 
 time and a delay time related to femtosecond laser pulse excitation .
our data analyses are primarily 
 based on those two temporal parameters recorded by single - molecule 
 photon stamping spectroscopy . in this 
 work ,
we have used donor lifetime ( da ) to probe 
 fret fluctuations and fluorescence anisotropy ( rda ) to monitor domain rotational motions of cy3-cy5 labeled t4 lysozyme . 

figure 3b shows a typical single - molecule lifetime 
 trajectory , { da(t)}. the donor 
 lifetime fluctuates from time to time , implying dynamic change of 
 interdomain distance along fret coordinate .
the wide gaussian - like 
 distribution of lifetime ( the right panel in figure 3b ) indicates the existence of multiple conformational intermediate 
 states characterized with different interdomain distance along -helix , 
 from fret perspective .
multiple conformational intermediate 
 states have often been suggested 
 as the general feature of enzymatic mechanisms and protein motions . in single - molecule studies ,
time - binned fret or lifetime trajectory 
 has been reliably used to identify the presence of multiple intermediate 
 states corresponding to well - defined stable fret values in the case of well - separated , low - noise , two - state 
 or three - state 
 systems .
nevertheless , for complex 
 biological systems , due to the influence from local environmental 
 fluctuations , thermal fluctuations , measurement short noise , photophysical 
 effects , and conformational dynamic or static heterogeneity coupled 
 with fluctuating catalytic activity , multiple intermediate states 
 are often buried in a wide - distributed gaussian - like distribution . in this work ,
the single - molecule lifetime trajectories are limited 
 by 10 ms binning time and the other facts discussed above , resulting 
 in that conformational intermediate states do not present clear separation 
 in the lifetime distribution in figure 3b . 

furthermore , we have performed advanced quantitative analysis of lifetime , 
 to be discussed later in this paper ( figures 4 and 5 ) , to further resolve buried multiple 
 intermediate states .
the rotational flexibility of the donor 
 molecule cy3 on t4 lysozyme 
 fluctuates significantly in the course of the enzymatic reaction turnovers , 
 revealed in our single - molecule anisotropy analysis .
figure 3a shows a typical single - molecule anisotropy trajectory , 
 { rda(t ) } showing that 
 the single - molecule anisotropy fluctuates in a wide range from negative 
 to the maximum value of 0.4 .
this is most likely associated with the 
 dye molecule fast spinning motions , the slow subdomain motions , and 
 entire protein motions of the t4 lysozyme tethered with the dye molecule .
those three types of motions are all involved but contribute differently 
 to the overall anisotropy measured from the experiments . if there 
 are no rotational diffusion restrictions from the subdomains or the 
 whole enzyme , the cy3 probe on t4 lysozyme should exhibit fast wobbling 
 spin rotation and the resulting cy3 lifetime should be in the subnanosecond 
 range consistant with a free cy3 dye in solution .
our experimental results of lifetime trajectory and distribution 
 ( figure 3a ) exclude this scenario because most 
 of the measured lifetimes of cy3 are in the nanosecond range instead 
 of the subnanosecond range .
similar behavior of the lack of rotational 
 freedom and nanoseconds lifetime range of tethered dye molecules have 
 also been reported for cy3 covalently linked to dna .
the reported cy3 lifetime is around 10 times larger than 
 the fluorescence lifetime of the free dye in solution , which is similar 
 to the result of cy3 on t4 lysozyme in our measurements .
the lifetime 
 of cy3 is dependent on physical and chemical properties of surroundings . 

the longer lifetime of cy3 is directly related to local environment 
 changes deviated from an aqueous environment , such as viscosity . for 
 example , when cy3 is attached to a strand of dna or a protein , an 
 additional increase in local viscosity may occur , leading to a lifetime 
 increase .
the interaction between cy3 and dna molecules 
 has also been reported to play a role in longer cy3 lifetime than 
 that measured in aqueous solution .
therefore , 
 it is most likely that the increase in local viscosity and the interaction 
 between cy3 and t4 lysozyme result in longer cy3 lifetime which evidence 
 the lack of cy3 free spin and wobbling rotational freedom identified 
 in our anisotropy measurements .
the joint distribution of lifetime 
 and anisotropy ( figure 3c ) further implies 
 that the measured overall anisotropy is not dominated by free dye 
 rotation but rather by restricted rotation , indicating that the cy3 
 dye probe is significantly regulated by interactions with the t4 lysozyme 
 protein matrix . presumably , there are two possibilities that may contribute 
 to the restricted rotation : the enzyme
previous studies have reported that 
 the tethered single t4 lysozyme to the hydrocarbon modified surface 
 is mostly in solution phase , and the interaction between enzyme and 
 surface is weak or insignificant in impacting enzyme rotations , giving 
 rise to the absence of rotational rate fluctuations for most of the 
 time during the measurements .
therefore , 
 the restricted rotation of cy3 characterized by the dynamic and fluctuating 
 anisotropy is most likely regulated by the domain rotations of enzyme . 

figure 3b , c gives a broad anisotropy distribution , 
 implying different rotational flexibility of cy3 regulated by t4 lysozyme 
 domain motions .
the different dye rotational flexibility has been 
 found in the study of hiv-1 reverse transcriptase , and they have attributed 
 broad rotational correlation time distribution probably to the clamping 
 of the finger and thumb domains during polymerase activity . in our work , different cy3 rotational flexibility , 
 reflected in the broad anisotropy distribution in figure 3b , c , is likely regulated by t4 lysozyme domain rotations 
 during the interdomain hinge - bending conformational motions .
t4 lysozyme exhibits well - known hinge - bending conformational motions 
 in which the distance changes between the opening and closing of the 
 active site cleft are about 46  , revealed in crystal 
 structure analyses , md simulation , and our previous single - molecule 
 spectroscopic analysis .
conceivably , t4 lysozyme conformational 
 motions involve more than just hinge - bending along its -helix
. 
 furthermore , even the hinge - bending motions themselves are actually 
 complex fluctuating conformational motions involving multiple conformations 
 with distinct domain orientations or hinge - bending angles along multiple 
 nuclear coordinates .
for example , it has been suggested that t4 lysozyme 
 populates multiple intermediates states with distinct hinge - bending 
 angles trapped in the crystal structures of t4 lysozyme mutants
. our single - molecule t4 lysozyme anisotropy 
 fluctuation result ( figure 3 ) suggests that 
 there are a wide range of domain - rotational 
 mobility , indicating different dominant orientations of the domains 
 from time to time , consistent with distinct hinge - bending angles . 
 typically , single - molecule fret spectroscopy only probes the conformational 
 motions associated with the fret donor 
acceptor distance changes , 
 and most likely , such fret probed conformational motions are actually 
 the projections of much more complex conformational motions of the 
 examined enzyme molecules on the fret sensitive coordinate .
nevertheless , 
 besides hinge - bending motions along coordinate probed by single - molecule 
 fret spectroscopy , t4 lysozyme actually exhibits 
 complex and fluctuating rotational motions along multiple orientation 
 coordinates , leading to a comprehension of the multidimensional conformational 
 motions associated with the t4 lysozyme enzymatic reaction turnovers .
multidimensional 
 conformational motions of t4 lysozyme probed by 
 single - molecule multiparameter spectroscopy : dynamic anisotropy and 
 lifetime - based fret .
all the data are collected from single cy3-cy5 
 labeled t4 lysozyme under enzymatic reactions with 25.0 g / ml 
 peptidoglycan and are simultaneously recorded by four - channel single 
 photon stamping spectroscopy .
( a ) single - molecule real - time anisotropy 
 trajectory { rda(t ) } and 
 distribution recorded within 100 s. each dot represents the average 
 anisotropy in every 10 ms binning of cy3 , calculated on the basis 
 of eq 6 .
( b ) single - molecule real - time donor lifetime trajectory 
 { da(t)}. each dot is the average 
 of photon delay times in each 10 ms binning of cy3 collected from 
 single - molecule photon stamping .
( c ) 2d joint distribution between 
 anisotropy in ( a ) and lifetime in ( b ) .
we note that the band widths 
 of both lifetime and anisotropy distributions , 1.0 ns and 0.25 , are 
 significantly larger than the measurement error bars of 0.30 
 ns and 0.05 , respectively .
the broadness of the distributions 
 of the lifetime and anisotropy represent intrinsic physical inhomogeneity 
 beyond the measurement error bars .
t4 lysozyme multidimensional hinge - bending conformational 
 motion 
 dynamics presents dynamic and static inhomogeneity , revealed and identified 
 by autocorrelation analysis of the single - molecule lifetime trajectories 
 { da(t ) } and anisotropy time trajectories 
 { rda(t)}. autocorrelation 
 function analysis has been extensively applied to identify inhomogeneous 
 fluctuation rates of single - molecule electron transfer , energy transfer fluctuations , and protein conformational changes .
we have analyzed the 
 autocorrelation functions , c(t ) , of lifetime and 
 anisotropy trajectories for 40 cy3-cy5 labeled t4 lysozyme molecules 
 under the enzymatic reaction conditions .
figure 4 shows the autocorrelation analysis results of lifetime fluctuation 
 decays ( figure 4a ) and anisotropy fluctuation 
 decays (  ) ( figure 4b ) .
most of the autocorrelation 
 functions of fret donor lifetime trajectories ( figure 4a , inset ) show nonexponential fluctuation decays , implying 
 the dynamic disorder of fret energy transfer , i.e. , the conformational 
 fluctuation rate along fret - probed hinge - bending coordinate changes 
 from time to time under enzymatic condition in one single - molecule 
 measurement .
we have analyzed the autocorrelation functions by biexponential 
 fitting and observed a wide range of fluctuation decays from milliseconds 
 to seconds ( figure 4a ) , suggesting a static 
 disorder of conformational fluctuation rate change from molecule to 
 molecule .
autocorrelation functions of anisotropy trajectories also 
 give similar results in terms of nonexponential and inhomogeneity 
 of fluctuation correlation function decays ( figure 4b ) .
the nonexponential conformational fluctuation dynamics 
 and the wide - range rate constant distributions of the single - molecule 
 anisotropy indicate dynamic disorder and static disorder of conformational 
 rotational fluctuation along multiple orientation coordinates , respectively .
dynamic 
 and static disorder of t4 lysozyme multidimensional conformational 
 fluctuations along fret coordinate and orientation coordinates via 
 autocorrelation analysis of lifetime and anisotropy .
( a ) histogram 
 of fluctuation decays derived from the autocorrelation function of 
 donor lifetime trajectories .
( inset ) typical nonexponential autocorrelation 
 function calculated from a single molecule fluorescence lifetime trajectory 
 { da(t)}. ( b ) histogram of fluctuation 
 decays derived from the autocorrelation function of donor anisotropy 
 trajectories .
( inset ) typical nonexponential autocorrelation function 
 originated from a single molecule fluorescence anisotropy trajectory 
 { rda(t)}. for autocorrelation 
 functions of lifetime or anisotropy ,  represents the fluctuation 
 decay . correspondingly , 1/ represents the fluctuation rate , 
 that is , conformational fluctuation rate along fret coordinate or 
 multiple orientation coordinates under t4 lysozyme enzymatic reactions . 

the flexibility of the hinge - bending conformational coordinates 
 regulated by substrate binding to the enzymatic active site most likely 
 contributes to the inhomogeneous and complex fluctuation dynamics 
 of lifetime and anisotropy .
the flexibility of conformations associated 
 with the process of forming the nonspecific binding complex ( e + s 
  es ) , the process of enzyme closing down to form the active 
 complex of es  es * , and the following enzymatic reaction of 
 es *  ep , involves complex local environment and molecular 
 structures of substrate as well as the enzymatic active site .
the 
 conformational motions involve multiple coordinates in nature and 
 are regulated by a fluctuating multiple coordinate energy landscape 
 defined by the dynamically changing and statically inhomogeneous molecular 
 interactions as well as local electric field in the process of open - close 
 hinge - bending enzymatic turnovers .
donor lifetime decays exhibit 
 two major distributions , associated 
 with t4 lysozyme open and close states during the hinge - bending motions 
 of the enzymatic active site .
mean lifetime trajectory and distribution 
 ( figure 3a ) do not necessarily give a clear 
 separation of multiple intermediate states but rather present a gaussian - like 
 distribution , due to the limitations from the local environment fluctuations 
 and the time - resolution of our single - molecule spectroscopy .
most 
 likely , the convolution of the multiple poisson processes gives rise 
 to the overall wide gaussian - like distribution . to further resolve the intermediate conformational states , 

we have performed analysis of the temporal decays including all the 
 photons in a single - molecule donor lifetime trajectories .
figure 5a shows the representative single - molecule lifetime 
 decay curves of the fret donor .
two - component lifetime decays , a faster 
 one ( 1 ) and a slower one ( 2 ) , 
 are derived from biexponential fits .
we note that the lifetime decays 
 ( 1 and 2 ) in figure 5a reflects different properties of the enzymatic conformational 
 dynamics from the fluctuation decays (  ) in figure 4 . as a lifetime - based fret measurement expressed 
 in eq 5 , fret donor lifetime decays are derived 
 by fitting donor photon delay times histogram , essentially a time - correlated 
 single photon counting distribution , to identify the fret efficiency 
 reflecting the major conformational states along fret coordinates , 
 whereas the fluctuation decays are calculated by the autocorrelation 
 analysis of mean lifetimes da to characterize the 
 conformational fluctuations and conformational flexibility .
we attribute 
 the two - component fret donor lifetime decays corresponding to two 
 different fret efficiency values , to two major conformational states , 
 that is , open and close states along fret coordinates : in each enzymatic 
 reaction cycle , the enzyme active site opens up to interact with the 
 substrate forming a nonspecific enzyme  substrate complex ( e 
 + s  es ) and then closes down to form a specific enzyme 
substrate 
 complex ( es  es * ) ready to react and turnover the substrate 
 to product .
our result of the two - component donor lifetime decays 
 ( figure 5b , c ) corresponding to two distinct 
 fret efficiency 
 distributions is consistent with hinge - bending motion that opens and 
 closes the active site cleft along the -helix . from the distributions of two - component lifetime
decays of donor 
 fluorescence , we have identified narrowly distributed faster component 
 ( 1 ) and widely distributed slower component ( 2 ) ( figure 5b ) .
the results of two - component lifetime decays imply that t4 lysozyme 
 exhibits open - close hinge - bending conformational motions associated 
 with two - component fret donor lifetime : the faster component ( 1 ) , when the active - site is closed and the fret efficiency 
 is high , is relatively narrowly distributed , and the slower component 
 ( 2 ) , when the active - site is open and the fret efficiency 
 is low , is widely distributed .
the distinct distribution of each component 
 gives a further indication that close state is rigid and spatially 
 narrowly distributed , and in contrast , the open states involve flexible 
 and broadly distributed conformational fluctuations . on the basis 
 of michaelis  menten mechanism in eq 1 , in the process of forming the active complex es * ( e + s  
 es  es * ) , the enzyme involves active site opening up to intake 
 the substrate to form the nonspecific enzyme  substrate complex 
 es , and binding down to form the active complex es*. during this whole 
 open - close hinged - bending rate process , the enzyme essentially involves 
 multiple steps associated with multiple conformational intermediate 
 states . in the process of catalytic reaction and product releasing 
 ( es *  ep  e + p ) , corresponding to the rigid and narrowly 
 distributed close states , the enzyme may not exhibit significant enzymatic 
 active site conformational changes . in terms of t4 lysozyme hinge - bending 
 open - close conformational motions
, our result of two - component lifetime 
 decays is consistent with both ensemble - level measurements and single - molecule fluorescence measurements .
the different modes 
 of open and close motions also agree with the recent study of conformational 
 dynamics of t4 lysozyme through an electric circuit by means of attaching 
 single molecules to single - walled carbon nanotube field - effective 
 transistors , that is , t4 lysozyme closes up 
 in a single step while the open process requires a minimum of two 
 steps .
two - component donor lifetime decays associated 
 with two major open 
 and close conformational states .
( a ) the representative histograms 
 of photon delay times of donor in a single - molecule measurement .
biexponential 
 fitting ( red curve ) gives the best estimate to the experimental data 
 ( gray ) , and two - component donor lifetime decays ( 1 and 2 ) are observed .
narrowly distributed faster component ( 1 ) and widely distributed slower component ( 2 ) are revealed .
( c ) statistical results of the two - component feature 
 derived from ( b ) . mean and
the results of two - component lifetime imply that t4 lysozyme 
 exhibits open - close hinge - bending conformational motions characterized 
 with two - component lifetime decays .
the distinct distributions of 
 each component even give a further implication that close state is 
 rigid and spatially narrowly distributed while the open states involve 
 flexible and broadly distributed conformational fluctuations .
our work provides a new insight 
 into t4 lysozyme conformational 
 dynamics from a multiple dimensional perspective . along the domain 
 orientation
coordinates , significantly different t4 lysozyme conformations 
 can have similar or same donor - to - acceptor ( d - a ) distance ; therefore , 
 the different t4 lysozyme conformations may not necessarily be identifiable 
 from the fret signal alone associated with this d  a sensitive 
 coordinate ( figure 6 ) .
typically , fret measurement 
 is sensitive to the projected fret - coordinate changes from the multiple 
 t4 lysozyme intermediates states associated with different domain 
 orientation coordinates .
the multiple intermediate states involved 
 in the active - site open - close hinge - bending motions and the hinge - bending 
 conformational motions are intrinsically multidimensional , allowing 
 for repositioning and reorienting the subdomains in forming the active 
 enzyme  substrate complex conformational state ready for a hydrolysis 
 turnover reaction . while the hinge - bending motions along -helix 
 require spatial proximity of two domains to interact with the substrate 
 within the active site , the domain rotational orientation motions 
 are predicted to be important for the enzyme to function , allowing the substrate to enter and the products to leave the active 
 site .
our results of t4 lysozyme conformational dynamics obtained 
 from the single - molecule multiparameter photon - counting spectroscopy 
 highlight the potential significance of probing the multidimensional 
 conformational motions along multiple coordinates for characterizing 
 the enzyme  substrate interactions and catalytic efficiency .
close hinge - bending motions , involving multiple 
 domain orientation coordinates and fret coordinate .
fret - coordinate 
 projections of multiple t4 lysozyme conformations associated with 
 different domain orientation coordinates are presented .
along domain 
 orientation coordinates , different enzyme conformations can have the 
 same d  a distance , which can be undetectable and hidden in 
 a conventional single - molecule fret spectroscopic measurement . in the past decades , there have 
 been intensive efforts to investigate 
 and understand how the enzymes work and are capable of changing the 
 biological activity pathways and enhancing a biological reaction rate 
 by as much as 10 times . over the years , it has been recognized 
 that the conformational motions are essential for the catalytic functions 
 of enzymes .
for example , molecular dynamics ( md ) simulation and statistical 
 modeling have made significant contributions to characterize conformational 
 motions and reaction fluctuations of enzymes in enzyme - catalyzed reactions .
more often than not , subtle conformational changes even play a crucial 
 role in enzyme functions , and these protein conformations are highly 
 dynamic rather than being static , involving in multiple intermediate 
 states and multiple conformational coordinates .
the approach , experimental results , and discussion presented in 
 this report are probably just a beginning step in expanding the studies 
 and interpretations of new information about dissecting both the spatially 
 and temporally complex enzymatic conformational dynamics under enzymatic 
 reactions . apparently , there is still a long way toward a detailed 
 and quantitative analysis of function - related conformational motions . 

for example , fret and anisotropy results suggest the existence of 
 multidimensional conformational motions that are important to enzymatic 
 activities , such as the hinged - bending motions under t4 lysozyme enzymatic 
 reactions .
additional efforts are still on demand to give direct spatial 
 and temporal characterizations of the exact angles and positions of 
 multidimensional conformational coordinates .
temporal transitions 
 of multiple intermediate states associated with fret coordinate and 
 orientation coordinates or the coupling between them are still unclear . 

the complementary md simulations will likely be helpful and supportive 
 to address those issues .
in this report , we have 
 provided a new insight into t4 lysozyme 
 conformational dynamics from a multiple dimensional perspective .
the 
 multidimensional conformational probing from our correlated single - molecule 
 fret and anisotropy measurements implies that t4 lysozyme exhibits 
 much complex conformational motions along multiple orientations and 
 nuclear coordinates beyond hinge - bending coordinate ( -helix ) . 

significant information about the complex conformational motions are 
 hidden by using only a conventional single - molecule one - dimensional 
 fret analysis that is primarily sensitive to the motions projected 
 from the complex and real conformational motions to the fret distance 
 sensitive coordinate .
the results of fret donor lifetime decays and 
 correlated anisotropy suggest that t4 lysozyme open states involve 
 flexible and broadly distributed conformational fluctuations while 
 the close state is more rigid .
in addition , the dynamic and static 
 inhomogeneity of multidimensional conformational fluctuations have 
 been revealed by nonexponential features of autocorrelation functions 
 of both lifetime and anisotropy .
the developed single - molecule multiparameter 
 photon stamping spectroscopy provides a possible access to probe multidimensional 
 conformational motions of complex enzymatic systems , such as t4 lysozyme , 
 by means of simultaneous acquisition of fret , fluorescence anisotropy , 
 and fret donor fluorescence lifetime .
there is still a high call for 
 experimentally technical approaches which are capable of probing the 
 complex enzymatic conformational fluctuations without ensemble - averaging 
 as well as measurement synchronization , and multiple parameter measurements 
 with the sensitivity of analyzing the enzyme rotational motion , translational 
 diffusion , intramolecular domain motions , and intermolecular interactions . 

our approach reported here holds the promise to characterize not only 
 the enzymatic active site conformational fluctuations and enzyme  substrate 
 interactions but also the overall enzyme matrix motions surrounding 
 the active site .
evidently , such overall enzyme conformation fluctuations 
 and multiple coordinate in nature , likely play important roles in 
 establishing the catalytic reaction pathways and the overall enzymatic 
 reaction energy landscape .
 conformational motions of proteins 
 are highly dynamic and intrinsically 
 complex . to capture the temporal and spatial complexity of conformational 
 motions and further to understand their roles in protein functions , 
 an attempt is made to probe multidimensional conformational dynamics 
 of proteins besides the typical one - dimensional fret coordinate or 
 the projected conformational motions on the one - dimensional fret coordinate . 
 
 t4 lysozyme hinge - bending motions between two domains along -helix 
 have been probed by single - molecule fret . nevertheless , the domain 
 motions of t4 lysozyme are rather complex involving multiple coupled 
 nuclear coordinates and most likely contain motions besides hinge - bending . 
 
 it is highly likely that the multiple dimensional protein conformational 
 motions beyond the typical enzymatic hinged - bending motions have profound 
 impact on overall enzymatic functions . in this report , we have developed 
 a single - molecule multiparameter photon stamping spectroscopy integrating 
 fluorescence anisotropy , fret , and fluorescence lifetime . 
 this spectroscopic 
 approach enables simultaneous observations of both fret - related site - to - site 
 conformational dynamics and molecular rotational ( or orientational ) 
 motions of individual cy3-cy5 labeled t4 lysozyme molecules . 
 we have 
 further observed wide - distributed rotational flexibility along orientation 
 coordinates by recording fluorescence anisotropy and simultaneously 
 identified multiple intermediate conformational states along fret 
 coordinate by monitoring time - dependent donor lifetime , presenting 
 a whole picture of multidimensional conformational dynamics in the 
 process of t4 lysozyme open - close hinge - bending enzymatic turnover 
 motions under enzymatic reaction conditions . by analyzing the autocorrelation 
 functions of both lifetime and anisotropy trajectories 
 , we have also 
 observed the dynamic and static inhomogeneity of t4 lysozyme multidimensional 
 conformational fluctuation dynamics , providing a fundamental understanding 
 of the enzymatic reaction turnover dynamics associated with overall 
 enzyme as well as the specific active - site conformational fluctuations 
 that are not identifiable and resolvable in the conventional ensemble - averaged 
 experiment . 
Inroduction
Materials and Methods
Results and Discussion
Conclusions