Phase Space Bottlenecks in Enzymatic Reactions

Abstract

The definition of a transition state on an individual reactive trajectory is made via a committor analysis. In the past, the bottleneck definition has often been applied in configuration space. This is an approximation, and in order to expand this definition, we are revisiting an enzyme in which we had identified a fast subpicosecond motion that makes the reaction possible. First we used a time-series analysis method to identify the exact time when this motion initiates donor-acceptor compression. Then we modified the standard committor analysis of transition path sampling to identify events in phase space and found that there is a dividing surface in phase space significantly earlier than the configurationally defined transition-state crossing.

Figure 1

Active site of LDH: substrate (pyruvate) and cofactor (NAD) in cyan. Also shown are three residues along the axis that connects donor and acceptor. Two atoms that are in close proximity are highlighted: a nitrogen in Arg106 and an oxygen in pyruvate. The hydride donor and acceptor atoms are marked with gray.

Figure 2

Distances between donor–acceptor, Ile252–donor, 106–acceptor, and 31–donor during the chemical barrier crossing.

Figure 3

Construction of an instantaneous mode for EMD analysis: one forms envelopes that bound the signal from above and below and takes their average, which is an IM. This IM is subtracted from the signal to form a new signal, and the process is then repeated.

Figure 4

Empirical mode decomposition of the time series of Figure 2. These are plots of the frequency component (vertical axis) vs time (horizontal axis), while the color indicates the power density of the signal. From top to bottom: donor–acceptor, Ile252–donor, 31–donor, and 106–acceptor. The donor–acceptor distance compression in Figure 2 started at ∼120 fs. The Ile252–donor distance seems to be dynamically coupled to the donor–acceptor motion; note the change in frequencies of these two motions at 100 fs.

Figure 5

Same distances as in Figure 2, for a different trajectory.

Figure 6

Empirical mode decomposition of the time series of Figure 5. These are plots of the frequency component (vertical axis) vs time (horizontal axis), while the color indicates the power density of the signal. From top to bottom: donor–acceptor, Ile252–donor, 31–donor, and 106–acceptor. The donor–acceptor distance compression in Figure 5 started at ∼200 fs. The Arg106–acceptor distance seems to be dynamically coupled to the donor–acceptor motion; note the change in frequencies of these two motions at 200 fs.

Figure 7

Committor functions generated by fixing momenta of selected atoms (in addition to fixing the coordinates of all atoms) before performing the committor analysis. The location of the committor function calculated in coordinate space alone is marked with black dots. Blue dots mark the committor when the momenta of the QM atoms are fixed before calculated the committor. Fixing the momenta of atoms of nearby residues results in the committors indicated with red and green dots.