Theory and Procedures for Finding a Correct Kinetic Model for the Bacteriorhodopsin Photocycle

Abstract

In this paper, we present the implementation and results of new methodology based on linear algebra. The theory behind these methods is covered in detail in the Supporting Information, available electronically (Shrager and Hendler). In brief, the methods presented search through all possible forward sequential submodels in order to find candidates that can be used to construct a complete model for the BR-photocycle. The methodology is limited only to forward sequential models. If no such models are compatible with the experimental data, none will be found. The procedures apply objective tests and filters to eliminate possibilities that cannot be correct, thus cutting the total number of candidate sequences to be considered. In the current application, which uses six exponentials, the total sequences were cut from 1950 to 49. The remaining sequences were further screened using known experimental criteria. The approach led to a solution which consists of a pair of sequences, one with 5 exponentials showing BR* → Lf → Mf → N → O → BR and the other with three exponentials showing BR* → Ls → Ms → BR. The deduced complete kinetic model for the BR photocycle is thus either a single photocycle branched at the L intermediate or a pair of two parallel photocycles. Reasons for preferring the parallel photocycles are presented. Synthetic data constructed on the basis of the parallel photocycles were indistinguishable from the experimental data in a number of analytical tests that were applied.

Simultaneous measurements of fast optical and proton current kinetics in the bacteriorhodopsin photocycle using an enhanced spectrophotometer

“…Table 2 shows the presence of 6 kinetically distinct species with taus near 0.008, 0.05, 0.15, 0.5, 1.9, and 4.9 ms. These are essentially the same components as obtained previously by Hendler et al [14,20] and Chizhov et al [21] using optical data, and by Rodig et al [22] and Morgan et al [23 ] using FTIR data, and by Müller et al using both optical and FTIR data [24]. It is also shown in Table 2 that the component seen optically with a tau near 1.9 ms is absent in the electrical data.…”

“…Based on the parallel cycles model favored by Hendler et al [14,20] at pH near 7 and temperature near 20 °C there are two separate cycles, one containing M f and the other M s .…”

“…Optical data collection-Time-resolved multichannel data were collected as previously described [14,15]. A brief summary is as follows.…”

Electrogenic Proton-Pumping Capabilities of the M-Fast and M-Slow Photocycles of Bacteriorhodopsin

“…These are essentially the same components as obtained previously by us (2,8) B. Electric Data-The raw data for proton currents generated by actinic pulses of different strengths are shown in the range of 0 to 1 ms in Figure 3 and from 0 to 8 ms in Figure 4.…”

“…We suspect that additional light scattering in the gels interferes with obtaining an adequate fit to this fastest transition which is recorded in only the first 3 or 4 time samples. The electrical data show no component for M-fast decay at ≈2 ms, which is always seen in the optical data and is the decay time constant for the M f → N transition (2,8). Therefore, there is one less exponential required for fitting the electrical data than the optical data.…”