Figure 1.
The structure and mechanical coupling network of subtilisin.
(a) A ribbon representation of the X-ray structure of subtilisin (PDB ID: 1OYV). The bound Ca2+ is shown in ball. The secondary structural elements are labeled and the residues of the catalytic triad are listed. A sequential conformational change that represents a pathway of intra-protein communication induced by Ca2+ binding is shown via orange arrows. (b) Residues exhibit significant mechanical coupling in subtilisin. Residues cover the upper-right half are colored red and those cover the lower-left are colored green. (c) The root of mean square fluctuation (RMSF) of Cα atoms in Å calculated from the first 4 ns of Ca2+-bound (top) and apo (down) simulations. (d) Contour plot of the difference in inter-residue force constant (kcal/mol/Å2) between Ca2+-bound and apo simulations. Force constants are calculated from the first 4 ns of Ca2+-bound and apo simulations.
Figure 2.
Mechanical coupling variation of subtilisin due to Ca2+ binding.
(a) Differences in the force constant of each residue between the Ca2+-bound and apo simulations of subtilisin as a function of time, (kcal/mol/Å2). Residues with large mechanical coupling variation are highlighted in the y-axis. See text for the definition of
's. (b) The location of the residues highlighted in (a) and (c). Residues specified by red fonts: residues have large mechanical coupling variation to Ca2+ binding, i.e. the average of
's is larger than 20 kcal/mol/Å2. Residues specified by red and boldfaced fonts: residues with large mechanical coupling variation and cover the mutation sites listed in (c) to within ±1. Residues specified by red and not boldfaced fonts: residues with large mechanical coupling variation but are not within ±1 of any of the mutation sites listed in (c). Residues specified by orange fonts: mutation sites listed in (c) with significant but not large mechanical coupling variation due to Ca2+ binding, i.e., the time average of
's is in between 10–20 kcal/mol/Å2. Residues specified by light blue fonts: mutation sites listed in (c) with medium or weak mechanical coupling variation, i.e., the time average of
's is less than 10 kcal/mol/Å2. (c) Mutation sites reported in protein engineering literature that can enhance the stability of subtilisin and the activity in a non-aqueous solvent. The residues are colored and boldfaced according to the criteria described in (b).
Figure 3.
Changes in the local conformation and mechanical coupling of each residue in subtilisin between neighboring time windows.
(a) Conformational changes in the Ca2+-bound simulation. (b) Conformational changes in the apo simulation. The change in inter-site distance in Å between two neighboring time windows, and t, is
and the local conformational change of residue I is defined as
. Variation in the mechanical coupling of each residue between neighboring time windows for (c) the Ca2+ simulation and (d) the apo simulation. Mechanical coupling variation of residue I between two neighboring time windows,
and t, is defined as
.
is the number of ij pairs associate with residue I and with at least one of
or
has positive value. The time window
for calculating
and
is 4 ns.
Figure 4.
Sequence correlation in subtilisin.
(a) The residues of subtilisin exhibit high correlation in our multiple sequence alignment determined by a statistical coupling analysis (SCA). Residues with high correlation in sequence variation are divided into three sectors, blue, red, and green according to the eigenvectors of the correlation matrix of sequence conservation [38]. Several residues that are not covered by the selection from the Ca2+-bound fluctuogram are highlighted. (b) The residues that satisfy either of the three criteria discussed in the text from the Ca2+-bound fluctuogram and cover the co-evolved residues shown in (a); color codes are the same as in (a). The parameters of the selection criteria are: = 10,
= 2.5,
= 11,
= 8.0, and
= 0.8. (c) The residues selected from the Ca2+-bound fluctuogram based on the parameters listed in (b). Lime: residues that cover the co-evolved residues from SCA. Brown: the co-evolved residues from SCA that are not covered by the residues selected from the Ca2+-bound fluctuogram. Pink: residues selected from the Ca2+-bound fluctuogram but do not cover any of the co-evolved residues. (d) The residues selected from the Ca2+-bound fluctuogram based on the parameters listed in (b). Blue: residues selected by Criterion-A. Red: residues selected from Criterion-B. Green: residues selected from Criterion-C. See text for the definitions of each criterion.
Figure 5.
Correlating the fluctuograms of subtilisin with co-evolution.
The calculated hit rates ('s) and coverages (
's) by using Criterion-A, (eq.(2)). (a)
's from the apo fluctuogram. (b)
's from the Ca2+-bound fluctuogram. Hit rates achieved by randomly picking the same numbers as the selected residues based on
= 8 are shown for comparison. The profiles correspond to other
values are quantitatively close. (c)
's from the apo fluctuogram. (d)
's from the Ca2+-bound fluctuogram.
Figure 6.
The calculated hit rates ('s) and coverages (
's) by using Criterion-B, (eq.(3)).
(a) 's and
's from the apo fluctuogram. Hit rates achieved by randomly picking the same numbers as the selected residues are shown for comparison. (b)
's and
's from the Ca2+-bound fluctuogram.
Figure 7.
The calculated hit rates ('s) and coverages (
's) by using Criterion-C, (eq.(4)).
(a) 's from the apo fluctuogram. (b)
's from the Ca2+-bound fluctuogram. Hit rates achieved by randomly picking the same numbers as the selected residues based on
= 7 kcal/mol/Å2 are also shown for comparison. The profiles correspond to other
values are quantitatively close. (c)
's from the apo fluctuogram. (d)
's from the Ca2+-bound fluctuogram.
Figure 8.
Correlating the fluctuograms of EG1 with co-evolution.
(a) The highly correlated residues observed in a multiple sequence alignment and SCA using EG1 as the query sequence and the residues selected from the fluctuogram satisfying either of the three criteria with the following parameters: = 8,
= 2.5,
= 17,
= 8.0, and
= 0.8. Lime: residues that cover the co-evolved residues from SCA. Brown: co-evolved residues from SCA that are not covered by the residues selected from the fluctuogram. Pink: residues selected from the fluctuogram but do not cover any co-evolved residue. (b) the same as (a) but view from a different angle. The calculated hit rates and coverages from the fluctuogram of EG1 by using (c) Criterion-A, (eq.(2)), (d) Criterion-B, (eq.(3)), and (e) Criterion-C, (eq.(4)).