Influence of triplet states on single donor-acceptor pair fluorescence

Chemical Physics 525 (2019) 110401

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Influence of triplet states on single donor-acceptor pair fluorescence I.S Osad'ko

T

Institute for Spectroscopy, RAS, Troitsk, Moscow, Russia

ABSTRACT

Single donor-acceptor (D-A) pairs whose molecules have both singlet and triplet states are considered. Fluorescence of such D-A pair has two types of fluctuations: fluctuations due to singlet-triplet transitions and fluctuations because of energy transfer in D-A pair. Both types of fluctuations manifest themselves in the duration of on/off intervals in fluorescence trajectories. Triplet state in the donor molecule creates off-intervals in D- and A-fluorescence. However, it does not influence FRET efficiency E. Another picture we will observe if we take into account triplet state in the acceptor molecule. This state influences FRET efficiency distribution S(E) considerable. 1) Acceptor triplet state hampers energy transfer in D-A pair and changes expression for S(E). 2) Acceptor triplet state is responsible for appearance offintervals in A-fluorescence and dual D-fluorescence: bright and moderate. Fluctuating D- and A-fluorescence are simulated with the help of Monte Carlo method. Dual D-fluorescence of single D-A pair creates FRET efficiency distribution S(E) with two maxima.

1. Introduction Single molecule spectroscopy [1,2] stimulated developing many problems of molecular spectroscopy on more detailed level. In particular, single molecule spectroscopy enabled one to consider the problem of energy transfer between single donor (D) and single acceptor (A) molecule. In this case by measuring efficiency E of Fluorescence Resonance Energy Transfer (FRET) we can find a distance R between molecules of the D-A pair. Changes in the distance R can be detected by measuring changes FRET efficiency. It opened new possibility to detect conformational changes of biomolecules with the help of fluorescence of single D-A pair attached to such biomolecules [3–16]. This new method of using FRET has been also applied to fluorescent proteins in living cells [17–20]. Expression for FRET efficiency E of single D-A pair has been presented in the following form [19,20]:

E (R ) =

IA 1 = IA + ID 1 + (R/ RF )6

(1)

IntensitiesID, A of the donor and acceptor fluorescence in Eq. (1) are expressed via intensities JD, A measured in an experiment with the help of the following formulas: ID, A = JD, A / D, A D, A . Here D, A are quantum yields of donor and acceptor fluorescence and D, A are quantum efficiencies for the detection of D- and A-photons. Eq. (1) can be derived with the help of the Förster formula (2)

F = C / R6

for rate of the energy transfer between exited singlet levels of D- and A-molecule and equation

E = F /[F +

D]

(3)

for FRET efficiency. Here D is rate of relaxation of the donor exited state without acceptor molecule. Inserting Eq. (2) into Eq. (3) we arrive at Eq. (1) with the following expression for Förster radius: RF = (C / D)1/6 . Coefficient C in Eq. (2) includes overlapping of the donor emission spectrum and the acceptor absorption spectrum. If these spectra have been measured in single molecule experiments coefficient C can be calculated [20–22]. Eqs. (1–3) have been derived for D-A pairs by using only singlet electron-vibrational states. However, dye molecules used in a D-A pair include also triplet states. Dexter in 1953 considered energy transfer between two molecules via their triplet states [23]. He has found that energy transfer via triplet states between two molecules separated by few nanometers is negligible as compared with the energy transfer via singlet states. Therefore Eq. (1) was used in practice by experimentalists and theoreticians in many works. However, if we can neglect triplet-triplet transfer in D-A pairs this fact does not mean that we can omit these states at all. Existence of triplet states in molecules will influence quantum dynamics of D-A pair [15,24] considerably. For instance, if acceptor molecule has a triplet state Eq. (3) changes considerably and therefore, Eq. (1) becomes incorrect. Acceptor molecule with triplet state is not able to obtain full electronic energy from the donor molecule even this acceptor molecule is situated very close to the donor molecule. This result is true for arbitrary value of D, A and D, A . However, this result has not been taken into account, in fact, in all papers on energy transfer in D-A pairs. We will consider in this paper fluorescence of single D-A pair. We will calculate influence of triplet states on time instances of D- and Aphoton emission. These random time instances we will find by treating rate equations for D-A pair with the help of Monte Carlo method.

E-mail address: [email protected]. https://doi.org/10.1016/j.chemphys.2019.110401 Received 6 May 2019; Received in revised form 6 June 2019; Accepted 6 June 2019 Available online 07 June 2019 0301-0104/ © 2019 Elsevier B.V. All rights reserved.

Chemical Physics 525 (2019) 110401

I.S. Osad'ko

k +G

1

=

1

By using this relation and taking into account Eq. (6) we can express via on :

1

=

(8)

0

k +G+k

(9)

on

Inserting this equation into Eq. (7) we arrive at the following equation for the duration of on-state:

d dt

Fig. 1. Typical energy diagram for the lowest electronic states of a molecule with two singlet and one triplet levels.

1

1

1

d dt

( + G)

1

d dt 0

=

k

1

off

=

1

+

0

t on

(12)

=

(13)

2

off

=

g

off

(14)

(15)

= 1/ g

(16)

is

the average duration of off-intervals. Ratio = kG/( + G + k ) g kG / g will play important role in the expression for energy transfer.

(4)

off / on

2.2. Model for 3D-2A pair Let us consider now D-A pair in which D-molecule has two singlet and one triplet state. (3D-2A pair). The energy diagram for such 3D-2A pair is shown in Fig. 2. When D-molecule occupies triplet state 3 fluorescence stops because D- and A-molecule cannot be excited by laser light. We can neglect influence of state (DTA*) on pause because it will be weeker as compared with influence of state (DTA) included in the sceme. We can neglect population of state (D*A*) as well because probability of

(5)

The probability of finding the molecule in on-state is described by the following equations: on

exp

on

in which

+ k 0, 0

1

woff = g exp( gt )

+ g 2,

=

(11)

Hence, the distribution of off-states is described by the exponential equation

Here j is a probability of finding the molecule in state j. We are interested in slow on/off kinetics. Equations for on-states. These equations can be found if we neglect in Eq. (4) transition from off state 2 to the ground state 0 . This transition is described by term: g 2 . Then we arrive at the following two equations: d dt 1

G

describes the probability of finding the molecule in off-state. We find the equation for the probability of finding the molecule in off-state if we neglect transition from on-state to off-state, i.e. omit term G 1 in Eq. (4). Hence, dynamics of off-state is described by the following equation:

Energy diagram of a molecule with two singlet and one triplet state and transitions between these states are shown in Fig. 1. Such a molecule being excited by CW laser light with rate k makes jumps between singlet states 0 and 1 creating fluorescence. However, when the molecule gets triplet state 2 its fluorescence stops. Therefore, fluorescence will look as a sequence of groups of photons. Such effect is called “photon bunching”. Fluorescence will consist of intervals with light (on-intervals) and intervals without light (off-intervals). On-intervals include photons with average distance 1/k between photons (fast kinetics). Dynamics of the states shown in Fig. 1 is described by the following equations:

+

k

Equation for off-states. If the molecule gets triplet state its fluorescence stops. Hence the equation

2.1. Blinking fluorescence of single molecule

0

G +G+k

=k

won =

off

k

(10)

determines average duration on of on-interval. The distribution of on-times is described by the exponential function:

Since we intend to consider D-A pairs whose molecules have both singlet and triplet states let us consider peculiarities of fluorescence of a single molecule with singlet and triplet states.

= k 0 ( + G) 1, g 2, 2 = G 1

on on

on

2. Theoretical model

=

=

Here

Statistical treating of these random time instances enables one to find distribution S(E) of FRET efficiency E for various values of Förster rate F. These theoretical distributions can be compared with the distribution measured in experiment.

0

on

(6)

It describes also the probability of finding the molecule in singlet state. After summing two lines in Eq. (5) we find

d dt

on

=

G

1

(7)

At the time exceeding value of life time of the excited singlet state we can use so-called quasistationary approximation by setting: 1 = 0 . In this approximation we find from the first line of Eq. (5) the following relation:

Fig. 2. Diagram for a D-A pair whose donor molecule has singlet and triplet states. Constants G and g describe singlet–triplet transitions. 2

Chemical Physics 525 (2019) 110401

I.S. Osad'ko

finding two excited molecules will be weak at k/ D < < 1. Dynamics of such 3D-2A pair is described by the following equations: 0

=

k

1

=k

0

+

D 1

+

A 2

+ g 3,

( D + G + F ) 1, 0 = F A 2, 2 1 g 3, 3 = G 1

(17)

Slow dynamics in Eq. (17) are caused by singlet-triplet transitions. If signal acquisition time is long enough and it exceeds each relaxation time responsible for on/off processes we can set: d j / dt = 0 . Then taking into account the third line in Eq. (17) we can transform equation for FRET efficiency to the following form:

E = 1/[1 + ID ( )/ IA ( )] = 1/[1 + = 1/[1 +

D 1(

)/

A 2(

Fig. 3. Energy diagram and transitions in 2D-3A pair.

Appearance of fluorescence from state 4 is fact of great importance. 2D-3A pair has 2 × 3 = 6 quantum states. The diagram in Fig. 3 includes only five states. State (D*A*) for two excited molecules is omitted because the probability of finding two excited molecules simultaneously is small at k < < D . Therefore, this state will influence weakly on quantum dynamics of the system. We can write the following five equations for population of the states shown in the diagram presented in Fig. 3:

)] (18)

D / F (R )]

Inserting Förster rate F (R) = C / R6 into Eq. (18) we arrive at the following equation: (19)

E (R) = 1/[1 + (R/ RF )6]

in which RF = (C / D is Förster radius. Eq. (19) coincides exactly with Eq. (1) discussed earlier. Hence, triplet state in the donor molecule doesn’t manifest itself in the expression for the average FRET efficiency. Consider now dynamics of the system described by Eq. (17). In accordance with Eq. (17) the system has both fast dynamics described by rate constants D and A , and more slow dynamics described by singlet-triplet transitions. We are interested in this slow dynamics. Such slow dynamics we can find setting 1 = 2 = 0 in Eq. (17). Then we arrive at the following two equations for the probabilities describing slow dynamics:

)1/6

0

= G1 0 + g 3 , = G1 0 g 3 ,

3

0 1

=

3

=G 4

D

kG +G+F

(20)

g

G1 0 ,

= 1/ G1,

off

= 1/ g,

1

+ g 4,

A) 2,

+

D 4,

(25)

D) 4 .

2( )

=

1 = 1 + ID ( ) / IA ( )

1 ( ) +G 1+ D A + D 4 A F (R)

(26)

A 2( )

Solving stationary Eq.(25) we find expression for the ratio )/ 2 ( ) . Substituting this ratio to Eq. (26) we arrive at the following expression for FRET efficiency: 4(

E (R ) = 1 +

D A

+G + F (R )

A

D A

g(

D

kG + g + k)

1

(27)

Eq. (27) can be transformed at D, A > > G, k, g with the help of Eqs. (11) and (16) to the following simple form:

(23)

E (R )

These equations describe distribution of off- and on-intervals with such average duration of intervals: on

3

(g +

3

+ g 3,

A 2

(k + g )

2

=k

A

(21)

It describes exponential distribution of off-intervals without light. By setting g = 0 in Eq. (20) we arrive at the following equation for on-intervals:

d 0 / dt =

+

D 1

1 ( ) + 4( ) 1+ D 1

(22)

3

+

E ( ) = IA ( )/[IA ( ) + ID ( )] =

and g determine rates of singlet-triplet transitions. By setting G1 = 0 in Eq. (20) we find the following equation:

d 3 / dt =

0

If signal acquisition time tbin is long enough and it exceeds each relaxation time responsible for dynamics processes, we can set d j / dt = 0 in Eq. (25). In this case Eq. (25) describes stationary situation and we can solve these equations. Expression for FRET efficiency will look as follows:

Here rate constant

G1 =

k

= k 0 [F (R) + D ] (G + 2 = F (R ) 1

1 1+

Gk Ag

1 +

D

F (R )

1+

off on

+

( )

R 6 RF

(28)

Here off / on is a ratio of the average durations of off- and on-intervals in blinking fluorescence of free acceptor molecule. This ratio can be measured in an additional experiment with single acceptor molecule. Eq. (28) differs considerably from Eq. (1) used in many works. This FRET efficiency is shown in Fig. 4 We see that full energy transfer is impossible if acceptor molecule has blinking fluorescence. This conclusion is very important. As a rule, dashed line is used in practice for analysis of experimental data on fluorescent proteins in cell [19,20]. However, use of dashed line will create mistakes if the acceptor fluorescence has blinking character. Hence, fluorescence of single A-molecule has to be measured in preliminary experiment. However, such verification of A-fluorescence has not been made in all works so far. Eq.(25) include fast relaxation rates: A , D and more slow relaxation rates: G, k, g , F . Distribution of on-intervals is dependent solely on slow relaxation rates. Therefore, we can find these distributions considering population of levels 1, 2 and 4 in quasistationary mode by setting 1 = 2 = 4 = 0 in Eq. (28). Then the second, the third and the

(24)

The average off-time off coincides with life time of triplet state of the donor molecule. However, the average on-time on depends on rate G of singlet-triplet transition and on Förster rate F. Förster rate F makes the average on-time on longer in comparison with the average on-time of single donor molecule. 2.3. Model for 2D-3A pair Consider now D-A pair in which A-molecule has triplet state (2D-3A pair). Energy diagram for 2D-3A pair is shown in Fig. 3. Level 3 relates to the acceptor molecule in the triplet state in presence of the donor molecule in the ground state (DAT). Level 4 relates to the acceptor molecule in the same triplet state but in presence of the donor molecule in the excited state (D*AT). D is rate of D*-D transition. States 1 and 4 are initial states for two types of D-fluorescence. These two types of D-fluorescence are shown by bold blue arrows in Fig. 3. 3

Chemical Physics 525 (2019) 110401

I.S. Osad'ko

3. Calculation of distributions with the help of Monte Carlo technique By using Monte Carlo method we can calculate random time instances Tdi and Tai of D- and A-photon emission. By substituting values Tdi and Tai in the following equations 105

IA (s ) =

if [(s × 10

3

if [(s × 10

3

< Tai )(Tai < (s + 1) × 10 3), 1, 0]

(36)

i=1 105

ID (s ) =

Fig. 4. Dependence of FRET efficiency on R/RF described by Eq.(28) at off / on = 0 (dashed line), 1 (blue line) and 2 (red line).

Es =

fifth lines in Eq. (25) take the following form:

k

0

[F (R) +

k

3

(g +

D] 1

D) 4

+g

4

= 0, F (R)

1

(G +

A) 2

Rest two equations with derivative can be transformed with the help of Eq. (29) to the following form:

=

0

3

k (R)

= k (R )

0

k

+g 1+ g 1+

0

k (R ) D+g

k

k (R ) D+g

G A + G

S (E ) =

= 3

k (R)

= k (R )

0

F (R) = D + F (R )

1 on (R)

By using Monte Carlo method we can calculate with the help of Eq. (17) random time instances Tdi and Tai of D- and A-photon emission by 3D-2A pair. These time instances are shown in Fig. 5. Triplet state in the donor molecule results in off-intervals both in Dand A-fluorescence of 3D-2A pair. Off-intervals in D- and A-fluorescence coincide with each other. It is easy to understand this fact if we look at Fig. 2. When D-molecule occupies triplet state it cannot emit light and we see off-interval in D-fluorescence. However, D-molecule being in triplet state cannot be excited by laser light and therefore it cannot excite A-molecule. Therefore, off-interval in A-fluorescence emerges simultaneously with off-interval in D-fluorescence. We see that appearance of off- intervals in trajectories of D- and A-fluorescence is main result of the existence of triplet state in the donor molecule. However, this fact does not influence on view of the average value of FRET efficiency and this efficiency is described by Eq. (19). We can calculate trajectory of FRET efficiency by using signal acquisition time (bin time) of 1 ms. These efficiency trajectories for few values of Förster rate F are shown in Fig. 6. Fig. 6 shows that trajectories for a 3D-2A pair include off-intervals in contrast to trajectories for 2D-2A pairs. However, the distribution of FRET efficiency does not feel existence of off-intervals. This fact correlates with Eq. (19) derived for 3D-2A pair which looks like Eq. (1) for energy transfer in 2D-2A pair.

(31)

(32)

g 3.

The distribution of on-intervals can be found with the help of Eq. (32). By omitting g 3 or k (R) 0 in Eq. (32) we arrive at the following exponential equations: 0

=

k (R ) 0 ,

3

=

(33)

g 3,

They describe two types of distributions of on-intervals in D-fluorescence. Times (1) on

= 1/ k (R) =

on

D

+ F (R ) > F (R )

on

(34)

and (2) on

= 1/ g

(39)

3.1. Distribution of time instances in fluorescence of 3D-2A pairs

+ g 3,

0

if [(E < Es )(Es < E + 1/20), 1, 0]

(30)

Eqs. (30) and (31) describe slow dynamics of 2D-3A pair. Due to k k (R ) < < 1, we can write Eq. (30) in the following simple inequality D+g form: 0

(38)

s= 0

3.

F (R ) 1 = D + F (R ) on

IA (s ) IA (s ) + ID (s )

4000

3,

Here

k (R ) = k

(37)

we can with the help of Mathcad 15 calculate a trajectory of the efficiency by using signal acquisition time (bin time) of 1 ms. By using efficiency trajectory Es we can calculate FRET efficiency distributions with the help of the following equation taken in Mathcad 15

= 0, (29)

=0

< Tdi)(Tdi < (s + 1) × 10 3), 1, 0]

i=1

(35)

determine the average duration of two types of on-intervals in Dfluorescence.

Fig. 5. Time instances of D- and A-photon emission calculated with the help of Eq. (17) at the following value of constants: k = 10 4s 1 , g = 30s 1, G = 106s 1 andF (R) = 108s 1 4

D

= 2 × 10 8s 1,

A

= 1 × 108s 1,

Chemical Physics 525 (2019) 110401

I.S. Osad'ko

Fig. 6. FRET efficiency trajectories and distributions S(E) relating to these trajectories calculated with the help of Eqs. (36–38) at: D = 2 × 10 8s 1, A = 1 × 108s 1, k = 10 4s 1 , g = 30s 1, G = 106s 1 and F (R) = 6 × 107s 1 (upper panel) F (R) = 108s 1 (middle panel) and F (R) = 5 × 108s 1 (low panel). Distributions S(E) of FRET efficiency were calculated with the help of Eq. (39)

3.2. Distribution of time instances in fluorescence of 2D-3A pair

By applying Monte Carlo method to Eq. (25) we are able to calculate time instances for emission 1-0 and 4-3 photons of D-fluorescence. Fig. 8 shows these time instances for 1-0 photons (upper panel) and for 4-3 photons (lower panel) at various values of Förster rate F ranging from 107s−1 (panels a) up to109s−1 (panels f). It is clearly seen if we increase Förster rate F by moving from a) to f) intensity of 1-0 D-fluorescence decreases but intensity of 4-3 D-fluorescence increases. Such picture emerges because the probability of population of triplet level 3 is increased if we increase Förster rate F. Hence population of level 4 in Fig. 3 increases as well. Therefore, intensity of 4-3 fluorescence increases as well. We have calculated D- and A-trajectories with the help of Eqs. (36) and (37) by taking signal acquisition time of 1 ms. Inserting these Dand A-trajectories into Eq. (38) for FRET efficiency E and carrying out statistical treating of the trajectory E(t) with the help of Eq. (39) we find the following six distribution functions S(E) shown in Fig. 9. Two peaks emerged in the distribution because two types of Dfluorescence there are in 2D-3A pairs: transitions 1-0 and 4-3. Fig. 9a relates to small value of Förster rate F = 107s−1 when energy transfer is almost absent. In this case we have, in fact, only 1-0 fluorescence. On the contrary, Fig. 9f relates to large value of Förster rate F = 109s−1 when large amount of electronic energy was transferred from D-molecule to A-molecule. Therefore, intensity of 4-3 fluorescence is increased.

In order to understand why full energy transfer becomes impossible if the acceptor molecule of D-A pair has triplet state we consider time instances of photon emission in 2D-3A pair. We can calculate time instances of D- and A-photon emission in single 2D-3A pair by using Eq. (25) and a Monte Carlo method. These time instances are shown in Fig. 7. On/off blinking in A-fluorescence emerges due to existence of triplet state in A-molecule. Let us compare energy diagram shown in Fig. 3 for 2D-3A pair with those shown in Fig. 2 for 3D-2A pair. We see two bold blue arrows for D-fluorescence in Fig. 3 and only one bold blue arrow for D-fluorescence in Fig. 2. This means that 2D-3A pair has two types of D-fluorescence relating to 1-0 and 4-3 transitions whereas 3D-2A pair has only one type of D-fluorescence. Transition 1-0 in Fig. 3 is realized when A-molecule occupies the ground singlet state. Transition 4-3 is realized when A-molecules occupies its triplet state. If A-molecule occupies the ground singlet state energy transfer from D-molecule is possible. Therefore, intensity of 1-0 D-fluorescence is reduced because of FRET. If A-molecule occupies triplet state FRET is impossible. Therefore, intensity of 4-3 D-fluorescence is bright. Intensities of D- and A-fluorescence presented in Fig. 7 are related to such situation.

Fig. 7. Time instances of D- and A-photon emission by single 2D-3A pair calculated with the help of Eq. (36) and Eq.(37) by a Monte Carlo method at the following value of parameters: D = 2 × 10 8s 1, A = 1 × 108s 1 , k = 10 4s 1 , F (R) = 2 × 108s 1, g = 10s 1, G = 105s 1. 5

Chemical Physics 525 (2019) 110401

I.S. Osad'ko

Fig. 10. Histograms of on-times in D-fluorescence for photons emitted on 1-0 transitions (left) and 4-3 transitions (right) for the case related to Figs. 8f and 9f. These distributions are described by function 30 exp( t /4ms ) shown by line.

of the trajectories coincide well with values given by the theory. In this case we obtain the following value: off / on = 1 for the ratio of average times existing in Eq. (28). 4. Conclusions Although triplet state in D-molecule creates off-intervals in the trajectory for FRET efficiency as Fig. 5 shows, however, this triplet state doesn’t influence the distribution of FRET efficiency as we can see on Fig. 6. Therefore, Eq. (19) derived for 3D-2A pair coincides with Eq. (1) for 2D-2A pair. Influence of triplet state in A-molecule on 2D-3A pair fluorescence is more considerable as Fig. 7 shows. First of all we cannot describe the average FRET efficiency in fluorescence of 2D-3A pair with the help of Eq. (1) because FRET efficiency depends on singlet-triplet transitions in the acceptor molecule. Eq. (28) and solid lines in Fig. 4 show that triplet state in A-molecule hampers transfer of electronic energy to A-molecule. Full energy transfer becomes impossible in presence of triplet state in A-molecule. This result is very important because if we want to use single D-A pair for treating experimental data we must know degree of blinking in fluorescence of single A-molecule. This means that each experiment with single D-A pair has to start with the measurement of fluorescence trajectory of single acceptor molecule. We find in such preliminary experiment value of off / on that should be inserted to Eq. (28). As far as I know nobody made such preliminary experiments with single acceptor molecule. 2D-3A pair has D-fluorescence of two types as bold blue arrows in Fig. 3 demonstrate. Fluorescence 1-0 is emitted when A-molecule occupies the ground singlet state. Intensity of this D-fluorescence is moderate because of energy transfer to A-molecule. 4-3 D-fluorescence is realized when A-molecule occupies triplet state. Due to existence of

Fig. 8. Time instances of D-photons emission via 1-0 transition (upper panel) and via 4-3 transition (lower panel) at various values of Förster rate. F = 107s−1 (a), 5 × 107s−1(b), 8 × 107s−1(c), 2 × 108s−1(d), 5 × 108s−1(e), 109s−1(f) g = 30 s−1, G = 3 × 105s−1.

At intermediate values of Förster rate we have two types of D-fluorescence and the distribution S(E) with two peaks in 2D-3A pair as Fig. 9d shows. 3.3. Distribution of on/off times Let us find now the distribution of on-intervals in D-fluorescence which are realized on 1-0 and 4-3 transitions for the case presented in Fig. 8f and Fig. 9f. These distributions are presented in Fig. 10. (1) = 1/ k (R) = 4ms and In accordance to Eqs. (34) and (35) we find on (2) on = 1/ g = 3.33ms for set of rate constants relating to Fig. 9f. Hence, average values of on-intervals found with the help of statistical treating

Fig. 9. Dependence of FRET efficiency distribution on value of Förster rate F. FRET efficiency trajectories were calculated at: k = 10 4s 1 , D = 2 × 10 8s 1, g = 30s 1, G = 3 × 105s 1 and F = 107s 1 (a), 5 × 107s 1 (b), 8 × 107s 1 (c ), 2 × 10 8s 1 (d) , 5 × 108s 1 (e ), 109s 1 (f ) In all cases off / on = 1. 6

A

= 108s 1,

Chemical Physics 525 (2019) 110401

I.S. Osad'ko

two types of D-fluorescence in single 2D-3A pair the distribution of FRET efficiency can have two maxima. One maximum relates to 4-3 transitions. Another maximum relates to 1-0 transitions shown in Fig. 9.

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