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. Author manuscript; available in PMC: 2014 Aug 30.
Published in final edited form as: Chem Phys. 2012 Aug 14;422:229–237. doi: 10.1016/j.chemphys.2012.08.005

Table 1.

Comparison of the parameters from experimental data obtained from the maximum likelihood method and the donor-acceptor cross correlation function.a

GdmCl (M)
2.5 3 3.5 4 4.5
Maximum
Likelihood
Method		 2-state EF 0.91
( 0.002)		 0.90
( 0.002)		 0.88
( 0.002)		 0.84
( 0.004)		 0.77
( 0.005)
EU 0.57
( 0.008)		 0.56
( 0.005)		 0.51
( 0.003)		 0.47
( 0.003)		 0.43
( 0.004)
k (ms−1) 50.0 ( 2.3) 41.3 ( 1.3) 37.7 ( 0.9) 45.0 ( 1.2) 49.1 ( 1.7)
pF 0.77
( 0.009)		 0.68
( 0.008)		 0.55
( 0.007)		 0.39
( 0.008)		 0.35
( 0.011)
2-state
with
acceptor
blinking
(4-state
kinetic
model)		 EF 0.92
( 0.003)		 0.92
( 0.003)		 0.90
( 0.003)		 0.88
( 0.005)		 0.81
( 0.006)
EU 0.60
( 0.009)		 0.58
( 0.006)		 0.53
( 0.004)		 0.52
( 0.004)		 0.48
( 0.005)
k (ms−1) 35.8 ( 1.9) 34.2 ( 1.2) 32.2 ( 0.8) 34.3 ( 1.1) 36.1 ( 1.5)
pF 0.78
( 0.009)		 0.69
( 0.009)		 0.56
( 0.007)		 0.38
( 0.009)		 0.35
( 0.012)
kon (ms−1) 860 ( 110) 1170 ( 140) 1050 ( 110) 620 ( 70) 730 ( 80)
Pb 0.98
( 0.002)		 0.97
( 0.002)		 0.96
( 0.002)		 0.95
( 0.003)		 0.94
( 0.004)
ln Lb 95 140 182 233 180
BICc −164 −255 −338 −441 −336
Donor-
Acceptor
Cross
Correlation		 Experiment A 0.055
( 0.015)		 0.087
( 0.008)		 0.093
( 0.006)		 0.093
( 0.005)		 0.058
( 0.006)
k (ms−1) 11.6 ( 9.9) 30.4 ( 9.6) 25.1 ( 5.8) 31.4 ( 5.6) 24.6 ( 8.9)
Recolored A 0.070
( 0.006)		 0.074
( 0.004)		 0.108
( 0.003)		 0.094
( 0.003)		 0.058
( 0.003)
k (ms−1) 28.8 ( 6.2) 24.0 ( 3.8) 31.3 ( 2.7) 37.0 ( 3.2) 31.4 ( 5.1)
a

Errors are standard deviations obtained from the diagonal elements of the covariance matrix calculated from the likelihood function (maximum likelihood method) or chi-square function (donor-acceptor cross-correlation calculation).

b

ln L = ln L (4-state) - ln L (2-state).

c

Baysian inference criterion (BIC) was calculated by BIC = -2ln L + nln Np, where n is the number of parameters and Np is the number of photons. BIC = BIC (4-state) - BIC (2-state).