Review
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the photoactive yellow protein.
.................................. 85
2.2.2. Separability .................................................... 85
www.bba-direct.com
Biochimica et Biophysica Acta 1657 (2004) 82–1042.4.1. Global analysis .................................................. 86
2.4.2. Convolution of exponential decay with IRF ................................... 86
2.4.3. Compartmental models .............................................. 86
2.5. Spectral models....................................................... 89
2.5.1. Spectral shapes .................................................. 89
Abbreviations: BR, bacteriorhodopsin; DADS, Decay Associated Difference Spectra; DAS, Decay Associated Spectra; EADS, Evolution Associated2.4. Kinetic models .....................2.3. Inverse problem ...................................................... 85
.................................. 862.2.1. Homogeneity .................D 2004 Elsevier B.V. All rights reserved.
Keywords: Global analysis; Multiway data; Photoactive yellow protein; Spectrotemporal model; Target analysis; Time-resolved spectroscopy
Contents
1. Introduction ............................................................ 83
2. Model for the observations .................................................... 84
2.1. Measurement process.................................................... 84
2.1.1. The instrument response function ......................................... 84
2.1.2. Stochastics .................................................... 85
2.2. Model assumptions ..................................................... 85illustrated with an elaborate case study of the ultrafast dynamics ofGlobal and target analysis of time-resolved spectra
Ivo H.M. van Stokkum
*
, Delmar S. Larsen, Rienk van Grondelle
Department of Physics and Astronomy, Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Received 29 December 2003; received in revised form 29 April 2004; accepted 29 April 2004
Available online
Abstract
In biological/bioenergetics research the response of a complex system to an externally applied perturbation is often studied. Spectroscopic
measurements at multiple wavelengths are used to monitor the kinetics. These time-resolved spectra are considered as an example of
multiway data. In this paper, the methodology for global and target analysis of time-resolved spectra is reviewed. To fully extract the
information from the overwhelming amount of data, a model-based analysis is mandatory. This analysis is based upon assumptions regarding
the measurement process and upon a physicochemical model for the complex system. This model is composed of building blocks
representing scientific knowledge and assumptions. Building blocks are the instrument response function (IRF), the components of the
system connected in a kinetic scheme, and anisotropy properties of the components. The combination of a model for the kinetics and for the
spectra of the components results in a more powerful spectrotemporal model. The model parameters, like rate constants and spectra, can be
estimated from the data, thus providing a concise description of the complex system dynamics. This spectrotemporal modeling approach is0005-2728/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.bbabio.2004.04.011
Difference Spectra; ESA, Excited State Absorption; ESI, Excited State Intermediate; GSA, Ground State Absorption; GSB, Ground State Bleach; GSI, Ground
State Intermediate; I
0
, first photocycle intermediate of PYP; I
1
, second photocycle intermediate of PYP; IRF, instrument response function; MA, magic angle;
mOD, milli optical density; NLLS, nonlinear least squares; pCA, p-coumaric acid; PYP, photoactive yellow protein; SADS, Species Associated Difference
Spectra; SAS, Species Associated Spectra; SE, Stimulated Emission; SVD, Singular Value Decomposition
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Dedicated to Hans Spoelder, y 1.4.2003, who pioneered this field.
* Corresponding author. Tel.: +31-20-4447868; fax: +31-20-4447899.
E-mail address: ivo@nat.vu.nl (I.H.M. van Stokkum).

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the proton pump bacteriorhodopsin (BR) [3,4] and the
photodetector photoactive yellow protein (PYP) [5,6].A
of multiway data [9,10].
To unravel the processes underlying the observable
I.H.M. van Stokkum et al. / Biochimica et Biophysica Acta 1657 (2004) 82–104 83key question in these chromophore–protein complexes is
how the chromophore dynamics are modified by the protein
[7,8]. This question can be adressed by time-resolved
spectroscopy in combination with global and target analy-
sis. Here global refers to a simultaneous analysis of all
measurements, whereas target refers to the applicability of a
particular target model. Phenomena occurring on a variety
of time scales ranging from femtoseconds to seconds can be
studied. The input to the system usually consists of a short
pulse of high energy which is absorbed and triggers a series
of reactions. These reactions are often accompanied by
changes in the UV, visible or IR spectroscopic properties
of the system which can be measured. The output of the
system is thus a collection of measurements of a spectro-
scopic property, like absorption or emission, as a function
of time and wavelength, which is called a time-resolved
spectrum.
A time-resolved spectrum is the most well-known exam-
ple of two-way data. These data are a collection of measure-
ments in two dimensions (ways). The first dimension is the
independent experimental spectral variable: wavelength k or
spectroscopic changes, which result in overwhelming
amounts of data, a model-based analysis of the measure-
mentsismandatory.Fromananalysisperspectivetwo
problems can be distinguished: (a) when a parameterized
model of the observations is available, the parameters have
to be estimated in a statistically sound way; (b) when only a
class of models is known, in addition also the ‘‘best’’ model
needs to be determined.
Previously several methodological reviews have been
written on global and target analysis by Beechem and co-
workers [11–13], Ameloot et al. [14], Holzwarth [15] and
Dioumaev [16]. These reviews demonstrate the importance
of simultaneous (global) analysis of multiple decay traces.
The combination of global analysis with testing of a photo-
physical or photochemical model is often called target
analysis [11,15]. Reviews discussing global analysis in
combination with experimental techniques are Refs.
[1,17]. In addition, the BR photocycle has been a model
system also for global and target analysis [18–22]. Recently
five-way data (wavelength, time, temperature, polarization
dependence, acidity) from this photocycle were subjected tochromophoreprotein complexes traverse a photocycle, e.g. er, many of the methods are also applicable for other types2.6. Model for the observations in matrix notation ....
2.6.1. Estimation of the number of components ..
2.6.2. Equivalence of spectral or kinetic models ..
2.6.3. Projecting the data upon singular vectors ..
2.7. Spectrotemporal models. ...............
2.7.1. Spectral shape model and kinetic model ..
2.7.2. A priori spectral knowledge and kinetic mode
2.7.3. A priori band amplitude knowledge and spec
2.7.4. Spectrotemporal model for a photocycle ..
2.7.5. Anisotropy models. .............
2.7.6. Multi-pulse excitation models ........
3. Parameter estimation .....................
3.1. Incorporating multiple experiments ..........
3.2. Software .......................
4. Case study: ultrafast dynamics of PYP............
4.1. Residual analysis of MA data. ............
4.2. Global analysis of MA data: DADS and EADS ...
4.3. Target analysis of anisotropy data: SAS .......
4.4. Target analysis of multipulse data: SADS ......
5. Conclusion ..........................
Acknowledgements ........................
References .............................
1. Introduction
Time-resolved spectroscopy is a widely used tool in
photophysics, photochemistry and photobiology to investi-
gate the dynamic properties of complex systems [1,2].
Examples of such systems are chromophore–protein com-
plexes essential for photosynthesis and photodetection,
which are important model systems in bioenergetics. Manywave number r¯, or magnetic field strength B, etc. The................................ 90
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odel ............................. 92
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second dimension is an independent experimental variable
to monitor spectral change: time t after excitation, temper-
ature T, polarization dependence, acidity pH or pD, excita-
tion wavelength, or quencher concentration [Q]. Adding a
third dimension results in three-way data, of which the
combination of time and wavelength with temperature or
with quencher concentration are the most well known. In
this paper we concentrate on time-resolved spectra, howev-a comprehensive target analysis [23]. In this paper, an