Protein kinetics: structures of intermediates and reaction mechanism from time-resolved x-ray data.
ABSTRACT We determine the number of authentic reaction intermediates in the later stages of the photocycle of photoactive yellow protein at room temperature, their atomic structures, and a consistent set of chemical kinetic mechanisms, by analysis of a set of time-dependent difference electron density maps spanning the time range from 5 micros to 100 ms. The successful fit of exponentials to right singular vectors derived from a singular value decomposition of the difference maps demonstrates that a chemical kinetic mechanism holds and that structurally distinct intermediates exist. We identify two time-independent difference maps, from which we refine the structures of the corresponding intermediates. We thus demonstrate how structures associated with intermediate states can be extracted from the experimental, time-dependent crystallographic data. Stoichiometric and structural constraints allow the exclusion of one kinetic mechanism proposed for the photocycle but retain other plausible candidate kinetic mechanisms.
Article: A molecular movie at 1.8 A resolution displays the photocycle of photoactive yellow protein, a eubacterial blue-light receptor, from nanoseconds to seconds.[show abstract] [hide abstract]
ABSTRACT: The photocycle of the bacterial blue-light photoreceptor, photoactive yellow protein, was stimulated by illumination of single crystals by a 7 ns laser pulse. The molecular events were recorded at high resolution by time-resolved X-ray Laue diffraction as they evolved in real time, from 1 ns to seconds after the laser pulse. The complex structural changes during the photocycle at ambient temperature are displayed in a movie of difference electron density maps relative to the dark state. The step critical to entry into the photocycle is identified as flipping of the carbonyl group of the 4-hydroxycinnamic acid chromophore into an adjacent, hydrophobic environment rather than the concomitant isomerization about the double bond of the chromophore tail. The structural perturbation generated at the chromophore propagates throughout the entire protein as a light-induced "protein quake" with its "epicenter" at the carbonyl moiety of the chromophore.Biochemistry 12/2001; 40(46):13788-801. · 3.42 Impact Factor
Article: Protein conformational relaxation and ligand migration in myoglobin: a nanosecond to millisecond molecular movie from time-resolved Laue X-ray diffraction.[show abstract] [hide abstract]
ABSTRACT: A time-resolved Laue X-ray diffraction technique has been used to explore protein relaxation and ligand migration at room temperature following photolysis of a single crystal of carbon monoxymyoglobin. The CO ligand is photodissociated by a 7.5 ns laser pulse, and the subsequent structural changes are probed by 150 ps or 1 micros X-ray pulses at 14 laser/X-ray delay times, ranging from 1 ns to 1.9 ms. Very fast heme and protein relaxation involving the E and F helices is evident from the data at a 1 ns time delay. The photodissociated CO molecules are detected at two locations: at a distal pocket docking site and at the Xe 1 binding site in the proximal pocket. The population by CO of the primary, distal site peaks at a 1 ns time delay and decays to half the peak value in 70 ns. The secondary, proximal docking site reaches its highest occupancy of 20% at approximately 100 ns and has a half-life of approximately 10 micros. At approximately 100 ns, all CO molecules are accounted for within the protein: in one of these two docking sites or bound to the heme. Thereafter, the CO molecules migrate to the solvent from which they rebind to deoxymyoglobin in a bimolecular process with a second-order rate coefficient of 4.5 x 10(5) M(-1) s(-1). Our results also demonstrate that structural changes as small as 0.2 A and populations of CO docking sites of 10% can be detected by time-resolved X-ray diffraction.Biochemistry 12/2001; 40(46):13802-15. · 3.42 Impact Factor
Protein kinetics: Structures of intermediates and
reaction mechanism from time-resolved x-ray data
Marius Schmidt*†‡, Reinhard Pahl§, Vukica Srajer†§, Spencer Anderson§, Zhong Ren¶, Hyotcherl Ihee†?,
Sudarshan Rajagopal†, and Keith Moffat†§**
*Physikdepartment E17, Technische Universita ¨t Mu ¨nchen, 85747 Garching, Germany;†Department of Biochemistry and Molecular Biology,§Consortium
for Advanced Radiation Sources, and **Institute of Biophysical Dynamics, University of Chicago, Chicago, IL 60637;¶Renz Research, Des Plaines, IL 60018;
and?Department of Chemistry and School of Molecular Science (BK21), Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
Edited by Johann Deisenhofer, University of Texas Southwestern Medical Center, Dallas, TX, and approved January 23, 2004 (received for review
September 17, 2003)
We determine the number of authentic reaction intermediates in
the later stages of the photocycle of photoactive yellow protein at
room temperature, their atomic structures, and a consistent set of
chemical kinetic mechanisms, by analysis of a set of time-depen-
dent difference electron density maps spanning the time range
from 5 ?s to 100 ms. The successful fit of exponentials to right
singular vectors derived from a singular value decomposition of
the difference maps demonstrates that a chemical kinetic mecha-
nism holds and that structurally distinct intermediates exist. We
identify two time-independent difference maps, from which we
refine the structures of the corresponding intermediates. We thus
demonstrate how structures associated with intermediate states
can be extracted from the experimental, time-dependent crystal-
lographic data. Stoichiometric and structural constraints allow the
exclusion of one kinetic mechanism proposed for the photocycle
but retain other plausible candidate kinetic mechanisms.
chemical, kinetic mechanism ? time-resolved crystallography
must be determined if the structural basis of function is to be
fully understood. Models for such states are normally deter-
to greatly increase the lifetime of a particular state and to trap
a structurally homogeneous species (1–4). However, the trap-
ping techniques themselves may perturb the mechanism and the
observed species may still not be structurally homogeneous (5).
If homogeneous structures along the reaction path could be
determined directly by using unmodified protein and reactants
at near-physiological temperatures, the difficulties associated
with trapping could be overcome.
The reaction pathway of a protein is typically described by a
chemical kinetic mechanism populated by a reactant state, a set
of ISs, and a product state. For such a mechanism to hold, the
transit time of an individual molecule from each state to its
neighboring state(s) must be short, compared with the lifetimes
of the states themselves. That is, equilibration across all other
degrees of freedom must be fast with respect to progress along
the reaction pathway. The time scales of structural transitions in
proteins range from picoseconds for side-chain relaxations (6) to
several nanoseconds for protein backbone relaxations (7). Such
protein-specific motions are thought to enable both the transi-
tions between protein conformations or substates within a single
state (8, 9), and those between ISs. If the lifetime of an IS is short
compared with the time scales of protein-specific motions, a
simple chemical kinetic mechanism (10) is unlikely to hold. If the
converse is true, those distinct ISs that accumulate to sufficiently
high concentration will be observable. If first-order reactions are
considered, the rise and fall of the concentration of each state
will be describable by a sum of exponentials.
With time-resolved Laue x-ray crystallography (11), we are
able to collect accurate structure amplitudes to high resolution,
he protein structures associated with short-lived intermedi-
ate states (ISs) that form and decay along a reaction pathway
covering the time scale from 100 ps to hours after reaction
initiation (12). By comparing the structure amplitudes before
initiation with those after a time delay, we obtain time-
dependent difference electron density maps that provide a
detailed picture of the structural changes as the reaction pro-
ceeds, without any trapping (13–18). However, whether or not a
simple chemical mechanism holds, several ISs are likely to be
populated at all time delays; the difference electron density
features associated with each intermediate overlap in each map.
Our goal is to identify the number of intermediates and obtain
the time-independent structure of each. The time-dependent
difference maps must therefore be separated into a small set of
homogeneous, time-independent difference maps, one per in-
termediate. The initial stages of this separation are achieved by
applying singular value decomposition (SVD) to the series of
experimental, time-dependent difference maps (19). SVD anal-
matrix A into left singular vectors (lSVs) in matrix U, each of
which contains time-independent structural information; right
singular vectors (rSVs) in matrix VT, each of which contains the
time dependence of the corresponding lSV; and the SVs in the
diagonal matrix S, which serve as weighting factors (19, 20),
according to the equation A ? USVT.
Analysis of the rSVs determines whether or not they can be
represented by a sum of exponentials. If so, a chemical kinetic
mechanism is likely to hold, and the number of relaxation times
is obtained directly (19, 20). This number imposes a powerful
constraint on the mechanisms that are consistent with the data.
We demonstrate here, to our knowledge, the first application
of SVD to experimental, time-resolved crystallographic data,
and the extraction of time-independent intermediate structures.
We investigate structural changes taking place in the photocycle
of photoactive yellow protein (PYP) from Halorhodospira halo-
phila (21). PYP is a blue light photoreceptor believed to be
involved in the regulation of negative phototaxis (22) in various
photosynthetic bacteria (23). Absorption of a photon of blue
light triggers trans-to-cis isomerization of the chromophore of
PYP, p-coumaric acid, and entry into a photocycle containing a
series of at least six spectroscopically distinct states (24–28). The
structures believed to be associated with three of these spectro-
scopic states have been characterized by physical trapping at
cryogenic temperature (ref. 29; PDB ID code 3PYP), by estab-
lishing a photostationary state at room temperature (ref. 30;
This paper was submitted directly (Track II) to the PNAS office.
rSV, right singular vector; lSV, left SV; IS, intermediate state.
Data deposition: The atomic coordinates and structure factors have been deposited in the
Protein Data Bank, www.pdb.org (PDB ID codes 1S4S and 1S4R).
‡To whom correspondence should be addressed at: Physikdepartment E17, Technische
Universita ¨t Mu ¨nchen, James Franck Strasse, 85747 Garching, Germany. E-mail: marius@
© 2004 by The National Academy of Sciences of the USA
April 6, 2004 ?
vol. 101 ?
no. 14 ?
PDB ID code 2PYP), and by examination of a single time point
(ref. 31; PDB ID code 2PYR). A limited, time-dependent set of
difference maps for PYP was subjected only to qualitative
interpretation, and no intermediate structures could be ex-
tracted (15). Here, we quantitatively determine the structures of
intermediates and identify plausible kinetic mechanisms from an
entire time course of difference maps spanning the later stages
of the photocycle of PYP.
Materials and Methods
Laue Data from PYP. Holo-PYP was expressed, purified, and
crystallized as described (15). Typically, crystals of 110 ?m in
diameter and various lengths were used. The reaction was
initiated by an intense 7 ns (full width at half maximum) laser
flash of 485 nm wavelength from a neodymium:yttrium-
aluminum-garnet pumped dye laser. The crystal structure was
probed at 15 time delays by an intense polychromatic x-ray flash.
All Laue data sets were collected at the BioCARS 14-ID
beamline, Advanced Photon Source, Argonne National Labo-
ratory (Argonne, IL), except 9 ?s, 51 ?s, and 8dk, which were
taken from data cited in ref. 15. Raw data were reduced with
LAUEVIEW (32, 33). Data statistics are shown in Tables 1 and 2.
Weighted difference maps, ??(t), were calculated according to
data cited in refs. 15 and 19. Variation of photoactivation due to
fluctuation of the laser power was taken into account by
assuming a constant laser beam diameter and, hence, normal-
izing to a laser pulse energy of 4 mJ. Accordingly, the difference
maps were multiplied before further analysis by a factor 4.0?
Elaser. The factors for the 9- and 51-?s maps were found to be
overestimated, because they appear as outliers in the rSV.
Outliers were corrected as demonstrated (19). The correction
factor for both the 9- and 51-?s maps was 1.3.
SVD-Driven Analysis. SVD flattening with phase recombination
was performed with the time series of difference maps as
outlined in ref. 19 with the following extensions. In the first
round of phase improvement we used ???? ? 2? for the SVD and
gradually decreased this level in subsequent rounds to accept all
grid points of the difference map. For the phase recombination,
we used modified Laue amplitudes: ?F?? ? ?Ft? ? (?FD?calc?
?FD?obs), where ?Ft? are the measured, time-dependent Laue
amplitudes, ?FD?calcare structure amplitudes calculated from the
Table 1. Statistics of the time-dependent Laue data sets
?t laser to x-ray
aResolution limits at ?50% completeness in the last-resolution shell (?dmin? 0.1 Å). All difference maps calculated to 1.9-Å resolution.
bW, wiggler, U, undulator.
cCCD, ADSC Quantum-4 CCD detector; II, Thompson image intensified CCD detector; IP, MAR345 image plate detector.
dEnergy of laser pulse.
eCalculated from single reflections only.
fCalculated from all reflections, including harmonics.
gRmerge(?F?) ? ? ??F? ? ??F????? ?F? where ??F?? is the mean amplitude of multiple observations and symmetry measurements. Rmerge(F2) ? ? ??F?2? ??F?2???? ?F?2where
??F?2? is the mean intensity of multiple observations and symmetry measurements.
hDark data sets used to calculate difference maps; 6dk was also used for the 250- and 500-?s time points, because no dark data were collected on this crystal.
iRscale? ? ??Ft?2? ?FD?2??? ?FD?2after scaling of the time-dependent (?Ft?) to the dark (?FD?) data sets.
jMean of the absolute difference amplitudes.
kMean error of the difference amplitude.
lAverage weight for map calculation.
Table 2. Statistics of the dark Laue data sets
*Resolution limits at ?50% completeness in the last-resolution shell (?dmin?
0.1 Å). All difference maps calculated to 1.9-Å resolution.
†W, wiggler; U, undulator.
‡CCD, ADSC Quantum-4 CCD detector; II, Thompson image-intensified CCD
detector; IP, MAR345 image plate detector.
§Calculated from single reflections only.
¶Calculated from all reflections including harmonics
?Rmerge(?F?) ? ? ??F? ? ??F????? ?F? where ??F?? is the mean amplitude of multiple
observations and symmetry measurements. Rmerge(F2) ? ? ??F?2? ??F?2???? ?F?2
where ??F?2? is the mean intensity of multiple observations and symmetry
www.pnas.org?cgi?doi?10.1073?pnas.0305983101Schmidt et al.
dark-state model (34), and ?FD?obsare structure amplitudes
collected without laser illumination, typically from the same
crystal as ?Ft?. Throughout, we used weighted difference ampli-
tudes, w??Ft? (15, 19). Difference maps ??(t)svdfrom the last step
of the iterative phase improvement established the data matrix
A?, which was used for the final decomposition. The rSVs
were fit by concentrations derived from candidate kinetic
mechanisms. The candidate mechanisms were selected from
the general mechanism, which accounts for the number of
relaxation times observed. The time-independent difference
maps ??Ijwere generated by projection, using the fitted con-
density maps were used to model the structures of the interme-
diates. We calculated difference structure factors ?FIjfor each
IS from a spherical volume of the time-independent difference
map ??Ij with radius 15 Å centered on atom C4 of the PYP
chromophore. We added multiples of ?FIj to the structure
the rSV and for the occupancy values of the intermediates being
?10%. It can be selected so that the map calculated from FIj
does not contain negative features on the phenolate oxygen of
pCA or on residues Arg-52 and Tyr-42. Conventional electron
density maps for each intermediate, ?Ij
against the extrapolated amplitudes by using CNS (35).
calcto generate extrapolated structure factors: FIj
calc? e??FIj. The factor e compensates for the missing scale in
ext, were calculated from
Posterior Analysis. Posterior analysis uses stoichiometric and
structural constraints with the goal of identifying and excluding
mechanisms that are incompatible with the data. The major
difficulty is that a common scale is absent in the rSVs (36). The
central idea of the posterior analysis is to restore a common or
absolute scale by using calculated difference electron density
values, which are equivalent to fractional concentration. This
analysis can be performed after the structures of the interme-
diates are determined. Posterior analysis consists of two parts:
computational and structural. Initially, the relaxation times are
determined from the global analysis of the rSV. The rate
coefficients can be uniquely determined only if the number of
observed relaxation times is larger than or equal to the number
of rate coefficients in the mechanism (37). This result is not
normally the case. This situation may be resolved by putting the
data on an absolute scale, which is equivalent to introducing
stoichiometric constraints. Structural constraints can be intro-
duced to allow a further level of discrimination. Thus, both the
absolute values and the shapes of the functions which describe
the time-dependent concentrations of the intermediates con-
tribute to discrimination between the mechanisms (19).
The refined structures of the N intermediates (derived from
the SVD analysis) and the dark state are used to derive structure
factors F1??? FNand FDand time-independent difference struc-
ture factors F1?FD, F2?FD ??? FN?FD. From these factors, N
time-independent difference maps ??
time-dependent difference maps ??(t, k)calccan then be deter-
mined on the absolute scale by using the concentrations cn(t, k)
of each intermediate, which depend on time t, on the candidate
kinetic mechanism itself, and the rate coefficients k in the
particular candidate mechanism (18). The observed difference
maps ??(t)svdwere fit to the calculated difference maps
??(t, k)calcat all time points t (t ? 1???T) by using M map grid
points in the entire protein region (Eq. 1). Minimization was
achieved by varying the rate coefficients k.
calcare calculated. The
?????t??svd????m?t?svd? CPA???m?t, k?calc?23 min
The summation is evaluated at those points m, where the
magnitude of the difference electron density in the observed and
calculated difference maps exceeds 2? or falls below ?2?. The
fit is weighted by the average of the absolute difference electron
density in the observed, SVD-flattened difference maps,
?????t??svd?. CPAcorresponds to the fractional concentration of
activated molecules at the beginning of our analysis and is
equivalent to the constant of integration in the solutions to the
coupled differential equations, which describe the mechanisms.
CPAwas determined from the first two pairs of observed and
calculated difference maps. The uncertainties of the fits were
estimated for each time-point from the overall sigma values ?svd
in the observed, SVD-flattened maps (Eq. 2):
If the assumed mechanism is incorrect, then the concentrations
are also incorrectly determined and the ??(k, t)calcdo not fit the
experimental, difference maps ??(t)svd. That is, significant den-
sity remains in the time-dependent residual maps ???(t, k) ?
??(t)svd? ??(k, t)calc.
Results and Discussion
We probe the time-dependent evolution of structural changes in
PYP by analyzing the 15 Laue data sets at time delays ranging
from 5 ?s to 100 ms after initiation of its photocycle by the ns
laser pulse. The temporal array of the resulting 15 difference
maps constitutes the data matrix A to be decomposed by SVD.
From the 15 SVs and their associated lSVs and rSVs, only four
contain significant structural signals by the criteria of Schmidt et
al. (19). In Fig. 1, the experimental difference maps for three
representative time delays are shown (Fig. 1 A–C) together with
the corresponding SVD-flattened maps (19) reconstructed from
the four significant lSVs (Fig. 1 D–F). Reconstruction with the
remaining 11 lSVs displays only noise (Fig. 1 G–I) and thus
confirms that signal is confined to the first four lSVs. The SVD
procedure results in greatly reduced noise (compare the noise
levels in the time-dependent, experimental time series and the
SVD-derived time series provided by Fig. 6, which is published
as supporting information on the PNAS web site). The four
significant rSVs could be globally fitted by a sum of three
exponentials with relaxation times of 170 ?s, 620 ?s, and 8.5 ms
(Fig. 2). We draw two important conclusions: a simple chemical
kinetic mechanism is likely to hold in this time domain; and the
existence of three relaxation times shows that this mechanism
must contain at least four states (Fig. 3). However, a conse-
quence of the closely spaced relaxation times is that there is no
time range within which the difference electron density is
essentially constant and the underlying structure is homoge-
neous. Even a perfect trapping experiment would yield a het-
erogeneous mixture of structures. A structural interpretation is
extremely difficult, unless the composite is separated into its
pure, authentic components, which can be performed by fitting
kinetic mechanisms to the rSVs (19).
Four simpler candidate mechanisms (sequential, semiparallel,
dead end, and parallel) are chosen from the general mechanism
containing four states (Fig. 3A) by setting selected rate coeffi-
cients to 0. For each of the four candidate mechanisms, three
time-independent difference maps, each associated with one of
the ISs IS1, IS2, and IS3, can be obtained by fitting the remaining
the contribution of all four lSVs to each state (see Eqs. 8–10 in
ref. 19). We find that in this case, all four candidate mechanisms
generate three qualitatively similar difference maps. That is, the
maps do not distinguish between correct and incorrect candidate
Schmidt et al.
April 6, 2004 ?
vol. 101 ?
no. 14 ?
mechanisms. However, these maps do enable us to determine
intermediate structure(s) by examining the three corresponding
electron density maps calculated from extrapolated structure
amplitudes. We find that the map representing the IS1 state
populated between 5 and ?200 ?s does not represent a unique
structure (Fig. 4D) and hence a unique atomic model could not
be refined. When we tried to model a single chromophore
conformation (blue in Fig. 4) into the electron density, the
residual map (Fig. 4G) clearly showed the large features ? and
?; we conclude that the chromophore conformation is hetero-
geneous. We believe that this heterogeneity is the result of the
fact that the 5-?s time point occurs in the middle of the
photocycle. An earlier intermediate with a different chro-
mophore conformation may also contribute to the electron
density. Indeed, there is both spectroscopic (27, 28) and struc-
tural (15) evidence of heterogeneity in this time range, associ-
ated with the pR spectroscopic state.
In contrast, the second, IS2, and third, IS3, states both arise
from a unique structure and can be satisfactorily refined (Table
3). IS2 is significantly populated from 200 ?s to ?2 ms. Modeling
it by a unique structure (Fig. 4E) results in a residual map (Fig.
4H) that displays only noise. In this structure, the very stable
hydrogen bond network from Glu-46 and Tyr-42 to the pheno-
late oxygen of the transchromophore present in the ground state
is broken and the cis chromophore is displaced toward the
ence electron density maps at representative time delays of 5 ?s, 500 ?s, and
(D–F) SVD-flattened difference electron density maps reconstituted with the
first four significant singular vectors and values, lSV 1–4 at time delays as in
A–C. Contour level: red?white ?3??4 ?, blue?cyan 3?4 ?. Yellow atomic
structure: structure of the dark state, the chromophore pCA, and the residues
Arg-52, Tyr-42, and Glu-46 are marked. (G–I) SVD-flattened difference elec-
tron density maps reconstituted with the 11 remaining singular vectors. Maps
are at the same time points as in A–C and are reconstituted with the insignif-
icant SVs and vectors, lSV 5–15. Contours on same sigma level as for D–F.
The effect of SVD flattening. (A–C) Experimental, weighted differ-
rSV; X, fourth rSV; lines: global fit by a sum of three exponentials. Three
relaxation times are marked by arrows. (Inset) Magnitude of the SVs, E, and
autocorrelation (AC), ?, of rSVs.
The time dependence of the rSVs. F, first rSV; I, second rSV; Œ, third
mechanism that generates three relaxation times. The state IS1 is the first
observed intermediate after the illumination of the dark state pG. The acti-
vated molecules relax through two ISs, IS2, and IS3, to the dark state pG. The
general scheme compiled by setting certain rate coefficients to 0. (B) S,
Irreversible, sequential mechanism. (C) P, Parallel mechanism. (D) DE, Mech-
anism with a dead end. (E) SP, Semiparallel mechanism.
The chemical, kinetic mechanisms. (A) General chemical, kinetic
www.pnas.org?cgi?doi?10.1073?pnas.0305983101Schmidt et al.
solvent. The phenolate oxygen most likely forms a new hydrogen
bond to N?of Arg-52 (Fig. 4 B and E). Arg-52 has swung into the
solvent (negative feature ? and positive feature ?; Fig. 4B) and
displays two conformations c1 and c2 at nearly equal occupancy.
Conformation c1 closely resembles that found in the photosta-
tionary state (30). Motion of Arg-52 causes structural changes in
nearby residues. Thr-50 is hydrogen-bonded in the ground state
to Tyr-42; when Thr 50 is displaced, Tyr-42 is pushed out of the
plane (Fig. 4B, negative feature ? and positive feature ?) and its
O?1atom is displaced by 1.2 Å. At the tail of the chromophore,
very prominent negative difference electron density features are
observed (feature ?) also associated with trans-to-cis isomeriza-
tion of the double bond in the tail.
IS3 is the longest-lived IS and decays on the 10-ms time scale.
It can also be satisfactorily refined with a single conformation
(Fig. 4 C, F, and I). Although the two intermediates IS2 and IS3
are similar, several structural features distinguish them. The
features ? and ? in IS2 are nearly absent in IS3 (compare Fig.
4 B and C), which indicates that Tyr-42 has nearly reverted to the
their position and the prominent feature ? near the chro-
mophore carbonyl moiety is greatly reduced in magnitude.
However, the phenolate ring is still displaced toward Arg-52 and
remains hydrogen-bonded to it; and Arg-52 retains the two
conformations c1 and c2, with nearly equal occupancy.
The structurally distinct intermediates IS2 and IS3 may ac-
count for the biphasic decay from a photostationary state (38).
However, the structure of that state, which we designate I2-P
(30), differs in detail from the present structures: in I2-P, the
phenolate ring is further displaced toward Arg-52, which displays
only the c1 conformation. Because the photostationary state
accumulates the longest-lived intermediate, I2-P may represent
an intermediate not populated to a significant extent in a pulsed
experiment. We propose that the intermediates IS2 and IS3
correspond to the spectroscopically observed intermediates I1?
and I2 (21, 27), respectively. The relaxation times and the
spectroscopically proposed structures (27) are in accordance
with our results.
To identify one or more chemical kinetic mechanism(s)
compatible with the data, we employ posterior analysis, which
exploits the absolute scale of the crystallographic data (19). This
Table 3. Refinement of the intermediate structures
Refinement data IS2 IS3
Factor e is defined and determined as described in Materials and Methods.
*Rwork?free? ? ?Fobs? ? ?Fcalc??? ?Fobs?, ?Fobs? are the Laue amplitudes, ?Fcalc? are
calculated from the atomic structure. Rfreewas determined from 5% of the
Table 4. Rate coefficients (1?s) assigned to the mechanisms
1,200 1.0 ? 106
For mechanisms and the rate coefficients, see Fig. 3.
ference electron densities ?? of intermediates IS1, IS2, and IS3, respectively.
structure of the dark state; blue, red, and green atomic structures: structures
of the intermediates IS1, IS2, and IS3, respectively. The chromophore pCA,
features in A–C: negative features ?,?,? and positive features ?, ?, ? are
associated with the chromophore; positive features ?, ?1, ?2and negative
feature ? are associated with Arg-52; features ? (positive) and ? (negative)
intermediate structures IS1, IS2, and IS3, respectively. In D, the same residues
Contour levels: blue-tint 1.6 ?, pink-tint 3 ?. (G–I) FIj
features ? and ? in G indicate an admixture (see text).
The time-independent density maps. (A–C) Time-independent dif-
dependent difference maps ??(t, k)calcfrom the SVD-flattened difference
maps ??(t)svdplotted as a function of log time. Bold solid line and F, fit of
Blue dotted line, no symbols; fit of sequential mechanism, thin solid line and
I, fit of dead-end mechanism; dotted line and Œ, fit of semiparallel mecha-
nism; dotted-dashed line and X, parallel mechanism.
Fit result. Mean square deviation (?2) of the calculated, time-
Schmidt et al.
April 6, 2004 ?
vol. 101 ?
no. 14 ?