Fig. 3.

The dual-color FCS cross-correlation function differences for a simple four-state cycle kinetics: 1 ⇌ 2 ⇌ 3 ⇌ 4 ⇌ 1. The probe X is specific for state 1. The second probe, Y, is specific for state 2 (a and b) or state 3 (c and d). It is shown that the peak in G_XY(t) - G_YX(t) appears earlier for the former than the latter, as expected. Two cases, one weakly irreversible (b and d) and one strongly irreversible (a and c) are shown. The correlation functions are computed according to

if Y labels state 2, and

if Y labels state 3. The λ values are the eigenvalues of the matrix in Eq. 4 with n = 4. For the weakly irreversible case, all k_ij = 1 except k₂₁ = k₄₃ = 0.5. Then, λ values are 3.5, 2, and 1.5, all real. For a strongly irreversible case, all forward rate constants are 1, backward rate constants are 0, and λ values are 2, 1 ± i.