Modeling FRET systems

Fluorescence emission spectra is taken by exciting a cyan fluorescent protein (CFP) at 430 nm and the emission is observed in the range of 460– 580 nm (Mohsin et al., 2013). Thus, the ratio of the FRET acceptor to FRET donor emission (ratio 535/485) is used to measure the efficiency of the FRET system (Hara et al., 2004). In the present work, two FRET systems were modeled using MatLab, 2022 to determine the relation and possible optimization of the system through different parameters present in the model. The first modeled system is a nucleotide sequence of CusF gene introduced between the enhaced cyan fluorescent protein (ECFP) used as the donor, Venus, a yellow fluorescent protein (YFP), used as the acceptor, and silver (Ag) as substrate (Agrawal et al., 2021). The second system is a leucine binding periplasmic binding protein (LivK) of Escherichia coli K12 flanked with a CFP and YFP, and leucine (Leu) as a substrate (Mohsin et al., 2013).

Regarding the first system, an increase in Ag concentration resulted in an increase in FRET ratio in all treatments (mutants and wild type (WT)). Even though two affinity mutants (H36D and F71W) were tried, the WT displayed the higher FRET ratio (Figure 1) (Mohsin et al., 2013).

Figure 1. FRET ratio vs. silver concentration.

The Logistic Growth model was used for this system. It is characterized by increasing growth in the beginning period, but a decreasing growth at a later stage, as it gets closer to a maximum.

c represents the maximum limiting value, b is the growth rate, the maximum growth rate is at y(t) = c / 2, and the initial value is c / (1 + a). The results of these parameters that best fit each treatment are shown in Table 1.

Even though the mutants (F71W and H36D) displayed higher growth rates, the WT had the highest value on the maximum growth (c/2) and the initial value. Therefore, the WT nanosensor was considered as the most efficient tool for the study (Figure 2).

Table 1. Parameters obtained in the FRET system using Ag.

Furthermore, as we can see in Figure 2, parameter a and c displayed a linear relationship, while b displayed no relation. Parameter a displayed a negative linear relation, where higher values were obtained in less efficient treatments (F71W and H36D). Contrarily, parameter c displayed a positive linear relation, where higher values were obtained in more efficient treatments (WT). Therefore, in this case, the optimization of the system would be having high initial values and maximum growth, along with a low a parameter.