. Author manuscript; available in PMC: 2019 Nov 15.

Published in final edited form as: J Phys Chem B. 2019 Aug 15;123(34):7302–7312. doi: 10.1021/acs.jpcb.9b04729

Table 2.

Generalized Two-State Results^a

parameter	k₊	k₋	$k_{+}^{'}$	$k_{-}^{'}$	β	β′
Without noise
true values	0.3	0.5	2.0	4.0	0.5	0.15
estimated values	0.2991	0.5000	2.0012	4.0001	0.5000	0.1501
standard deviation	0.0023	0.0001	0.0016	0.0004	0.0008	0.0005
σ² = 0.05 for the noise
true values	0.3	0.5	2.0	4.0	0.5	0.15
estimated values	0.3055	0.5101	2.0192	4.0501	0.4938	0.1471
standard deviation	0.0234	0.0005	0.0737	0.0403	0.0062	0.0043
σ² = 0.1 for the noise
true values	0.3	0.5	2.0	4.0	0.5	0.15
estimated values	0.2795	0.4316	1.7738	4.2755	0.5729	0.1421
standard deviation	0.1064	0.1884	0.1348	0.1229	0.1261	0.1087
σ² = 0.2 for the noise
true values	0.3	0.5	2.0	4.0	0.5	0.15
estimated values	0.1993	0.6909	1.7047	3.2478	0.4247	0.1967
standard deviation	0.1231	0.1983	0.1801	0.1293	0.1129	0.0915

Results of parameter estimation for the generalized two-state system with and without considering noise (the rates are in units of min ⁻¹). See Table 1 for details on the standard deviation.