Thesis
Reference
Optical coherent discrimination of peptides and plasma proteins
KISELEVA, Svetlana
Abstract
Cette thèse présente l'application du contrôle cohérent pour la discrimination et l'identification des biomolécules dans la phase condensée. Les expériences de contrôle cohérent sont effectuées dans le cadre de la discrimination optimale dynamique (ODD), qui est basée sur la modification de phase d'impulsions femtosecondes dans l'ultraviolet profond. L'objectif principal de ce travail est de démontrer que la fluorescence intrinsèque des acides aminés naturellement présents dans les protéines peut être utilisée comme indicateur pour leur dosage, ce qui permet d'éliminer l'utilisation de tout autre marqueur fluorescent supplémentaire. Dans la première partie, nous utilisons l'ODD pour moduler sélectivement l'extinction de la fluorescence des paires de dipeptides contenant du tryptophane:
alanine-tryptophane, cyclo(glycine-tryptophane) et cyclo(leucine-tryptophane). Dans la deuxième partie, nous étendons l'approche ODD par l'application d'impulsions UV modulées en phase pour des protéines du plasma sanguin. Ces expériences montrent que notre approche pourrait être développée plus loin pour [...]
KISELEVA, Svetlana. Optical coherent discrimination of peptides and plasma proteins. Thèse de doctorat : Univ. Genève, 2014, no. Sc. 4733
URN : urn:nbn:ch:unige-465695
DOI : 10.13097/archive-ouverte/unige:46569
Available at:
http://archive-ouverte.unige.ch/unige:46569
Disclaimer: layout of this document may differ from the published version.
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G P A Professeur J.-P. Wolf
Optical Coherent Discrimination of Peptides and Plasma Proteins
THÈSE
présenté à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention physique
par
Svetlana Kiseleva Afonina de Sarov, Fédération de Russie
ThèseN◦4733
GENÈVE
Atelier de reproduction de la Section de physique 2014
Acknowledgements
First of all, I sincerely express my gratitude to my advisor, Prof. Jean-Pierre Wolf, who gave me the possibility to join his group and lead this project, for pro- viding an excellent atmosphere for doing research. A am very thankful to my co-superviser, Luigi Bonacina, who guided me at all the stages of my PhD. His support strongly motivated me and was fundamental to attain the success. Luigi is a great teacher, I am very grateful for the opportunity to work with him, for all the knowledge I gained in the areas of Femtosecond Spectroscopy and Biophotonics during my thesis.
I am honoured that Prof. Colin Self, Prof. Thomas Feurer, Prof. Eric Vauthey accepted to take part to my examination board and appreciated my work.
I am really grateful to all my former and actual colleagues: Jerome Extermann, Ariana Rondi, Mary Matthews, Davide Staedler, Andrii Rogov, Andrey Stepanov, Denis Kiselev, Julien Gateau, Sylvain Hermelin, Michel Moret, Ondrej Nenadl, Nicolas Berti, Elise Schubert, Sebastien Courvoisier, Thibaud Magouroux, Wahb Ettoumi, Francois Pomel, Stephanie Hwu, Nadege Marchiando, Iris Crassee, Ste- fano Henin, Massimo Petrarca. Especially I would like to thank Jerome Extermann and Ariana Rondi, who shared their experience at the beginning of my PhD pro- gram, their support and guidance was specially essential during the lab relocation from the Ecole de Medicine building to Pinchat. I would like to thank Davide Staedler for his support in the biomedical area, for his advice and guidance in the manipulation of proteins. I was very pleased to work with Ondrej Nenadl, Julien Gateau and Sylvain Hermelin, in spite of a very short period.
A special mention to the GAP secretaries, Isabel, Laurence, Nathalie and Dra- gana for helping me in solving various administrative problems.
A particular acknowledgement to the neighbours of GAP-optics, and particu- larly to Natalia Bruno, Valentina Caprara Vivoli, Thiago Guerreiro, Tomer Barnea, Tommaso Lunghi, Bruno Sanguinetti, Pierre Jobez, Cyril Laplane, Denis Rosset for the thoughtful discussions, and for making a good atmosphere in GAP.
I would like to dedicate this work to my family, for their help and support to my education.
Summary
The fast development of laser techniques, in particular, the generation of ultra- short femtosecond pulses opens up new frontiers and various experimental tools for biomedical and point-of-care applications. The combination of pulse shaping technique and quantum control is a very promising tool based on coherent manip- ulation of wavepackets on an ultrafast time scale. It can be used, for example, in label-free cellular imaging and label-free optical bio sensing of human fluids like plasma, serum and saliva.
This thesis reports on application of quantum control for discrimination and identification of biomolecules in the condensed phase. The quantum control ex- periments are performed in the frame of Optimal Dynamic Discrimination (ODD) approach based on the phase-shaping of deep ultraviolet femtosecond pulses. The main objective of this work is to demonstrate that intrinsic fluorescence of amino- acids naturally present in cells, can be used as a reporter for protein diagnosis, thereby allowing eliminating the use of any additional fluorescent tags.
In the first part, we address the ODD to selectively modulate the time-resolved fluorescence depletion of pairs of tryptophan-containing dipeptides: alanine-tryptophan, cyclo(-glycine-tryptophan), and cyclo(-leucine-tryptophan). The spectroscopic prop- erties of these molecules are dominated by those of tryptophan, and they present identical absorption and strongly overlapping florescence spectra, making their dis- crimination by linear spectroscopy and time-resolved approaches (i.e. fluorescence depletion) nearly impossible. Our results, on the other hand, indicate that phase- sensitive excitation allows their differential identification using fluorescence as ob- servable, beyond the limits of linear and time-resolved spectroscopy.
In the second part, we extend the ODD approach by applying phase-shaped UV pulses, which are generated by a Genetic Algorithm in a closed-loop scheme, for blood plasma proteins: Immunoglobulin G, Immunoglobulin M and Albumin (Hu- man Serum Albumin and Bovine Serum Albumin). We demonstrate that using tryptophan as a local probe, it is possible discriminate them. Moreover, we show that discrimination pulses can be further used for protein identification in their mix- ture. These experiments serve as proof-of-principle and they are challenging. On
the other hand, they show that our approach might be further developed for protein identification directly in human plasma.
Résumé
Le développement rapide des techniques de laser, en particulier la génération d’impulsions femtosecondes, ouvre de nouvelles frontières et divers nouveaux out- ils expérimentaux pour des applications biomédicales et des tests de diagnostic rapide (mis en place en centre de soins). La combinaison de la technique de mise en forme d’impulsion et le contrôle cohérent est un outil très prometteur basé sur la manipulation cohérente de paquets d’ondes sur une échelle de temps ultra-rapide.
Il peut être utilisé par exemple dans l’imagerie cellulaire et la détection optique de fluides humains comme le plasma, le sérum et la salive, sans injection de mar- queurs.
Cette thèse pr´sente l’application du contrôle cohérent pour la discrimination et l’identification des biomolécules dans la phase condensée. Les expériences de contrôle cohérent sont effectuées dans le cadre de la discrimination optimale dy- namique (ODD), qui est basée sur la modulation de phase d’impulsions femtosec- ondes dans l’ultraviolet profond. L’objectif principal de ce travail est de démon- trer que la fluorescence intrinsèque des acides aminés naturellement présents dans les protéines peut être utilisée comme indicateur pour leur dosage, ce qui permet d’éliminer l’utilisation de tout autre marqueur fluorescent supplémentaire.
Dans la première partie, nous utilisons l’ODD pour moduler sélectivement l’extinction de la fluorescence des paires de dipeptides contenant du tryptophane: alanine- tryptophane, cyclo(glycine-tryptophane) et cyclo(leucine-tryptophane). Les pro- priétés spectroscopiques de ces molécules sont dominées par le tryptophane, elles possèdent une absorption identique et leurs spectres de fluorescence se chevauchent fortement, ce qui rend leur discrimination par la spectroscopie linéaire ou par des approches type pompe-sonde (par exemple l’extinction de fluorescence) presque impossible. D’autre part nos résultats montrent que l’excitation, sensible à la phase, permet leur identification différentielle au-delà des limites de la spectro- scopie linéaire et résolue dans le temps en utilisant la fluorescence comme observ- able.
Dans la deuxième partie, nous étendons l’approche ODD par l’application d’impulsions UV modulées en phase, qui sont générées par un algorithme génétique dans un système en boucle fermée, pour des protéines du plasma sanguin: immunoglobu-
line G, immunoglobuline M et albumine (albumine de sérum humain, albumine de sérum bovin). Nous démontrons qu’il est possible de les discriminer en utilisant le tryptophane comme sonde locale. En outre, nous montrons que les impulsions de discrimination peuvent aussi être utilisées pour l’identification de protéines dans un mélange. Ces expériences servent de preuve de principe. D’autre part, elles mon- trent que notre approche pourrait être développée plus loin pour l’identification des protéines directement dans le plasma humain.
1 Introduction 21
1.1 Blood Components . . . 22
1.1.1 Blood plasma . . . 22
1.1.2 Blood cells . . . 24
1.2 Target molecules . . . 25
1.2.1 Albumin . . . 26
1.2.2 Immunoglobulin G . . . 27
1.2.3 Immunoglobulin M . . . 31
1.3 Methods of protein detection . . . 32
1.3.1 Enzyme-Linked Immunosorbent Assay . . . 33
1.3.2 Biosensor based on Surface Plasmon Resonance . . . 34
2 Basic concepts 37 2.1 Introduction . . . 37
2.2 Dynamics of molecular wave packets . . . 39
2.3 Optimal quantum control . . . 44
2.4 Trp as a fluorescence reporter for protein dynamics . . . 47
3 Experimental 51 3.1 Laser sources . . . 51
3.2 Pulse characterization . . . 53
3.2.1 Autocorrelation . . . 53
3.2.2 Cross-correlation . . . 53
3.2.3 Frequency-Resolved Optical Gating . . . 55
3.3 Pulse shaping . . . 57
3.3.1 Introduction . . . 57
3.3.2 MEMS micromirror array for temporal pulse-shaping . . . 58 9
3.3.3 Background theory of temporal pulse shaping . . . 59
3.3.4 Reflective geometry of pulse-shaper . . . 60
3.3.5 Spectral resolution of the pulse shaper . . . 62
3.3.6 MEMS shaping design in the experiment . . . 64
3.4 Optimization Algorithm . . . 65
3.4.1 Multiobjective Genetic Algorithm . . . 65
3.4.2 Single-objective algorithm . . . 67
3.5 Experimental setups . . . 68
3.6 Sample preparation and handling . . . 71
4 Optimal Dynamic Discrimination of Trp-containing dipeptides 73 4.1 Preliminary measurements . . . 74
4.2 Excited-state dynamics of Trp and Trp-containing dipeptides . . . 75
4.3 Quantum control and optimal coherent discrimination . . . 79
4.4 The track towards molecular discriminability criteria . . . 87
4.5 Conclusions . . . 89
5 Optimal Dynamic Discrimination of proteins 91 5.1 Immunoglobulin G and Human Serum Albumin . . . 92
5.1.1 Steady-state spectroscopy . . . 92
5.1.2 Time-resolved fluorescence spectroscopy . . . 94
5.1.3 Optimal dynamic discrimination of human IgG and HSA . 97 5.2 Human Immunoglobulin G vs Human Immunoglobulin M . . . . 102
5.3 Discrimination of IgG and BSA under excitation of 295 nm . . . 105
5.4 Discussion . . . 111
5.5 Conclusions . . . 117
6 ODD application for protein identification 119 6.1 Introduction . . . 119
6.2 Diagnostics of Immunoglobulin G . . . 120
6.2.1 Methodology . . . 121
6.3 Experimental results . . . 122
6.3.1 Human IgG and HSA . . . 122
6.3.2 Rabbit IgG and BSA . . . 125
6.3.3 Time-delay dependence . . . 125
6.4 Discussion . . . 127
6.5 Conclusions . . . 130
7 Conclusions and Outlook 133
Bibliography 137
1.1 Electron micrographs of Erythrocytes (A), Leukocytes (B), Platelets (C). Source: [1]. . . 25 1.2 Three-dimensional structures of HSA and BSA with tryptophan
residues in orange color. Source: [2]. . . 27 1.3 Schematic representation of five IgG classes. Source: [3]. . . 28 1.4 Schematic representation of a typical immunoglobulin structure. It
is formed of four chains, two heavy VH and two light VL. The binding regions of the antibody are at the ends of the variable do- mains VH and VL, located at the ends of the heavy and light chains respectively. . . 29 1.5 Left: the immunoglobulin fold. Right: TheVH domain. At the end
of both theVH and theVLdomains are three hypervariable loops, highlighted in red. Source: [4]. . . 30 1.6 Three-dimensional structure of human Immunoglobulin M. Source:
[2]. . . 32 1.7 ELISA model. A: a captured antibody is immobilised at the plate
surface. B: a sample, that need to be analysed, is added. C: a detection antibody specific for a target antigen is added. D: adding of an additional antibody linked to an enzyme. E: a chemical is added, and is converted by enzyme to detectable form. . . 34 1.8 Principal scheme of SPR biosensor. . . 35 2.1 Quantum control pump-dump Tannor-Kosloff-Rice scheme. First
pump pulse creates a wavepacket on the first excited state potential energy surface. Second laser pulse dumps the wavepacket into the desired product channel [5,6,7,8]. . . 38
13
2.2 Schematic energy level diagram. Blue (absorption) and green (emis- sion) arrows show electronic transitions, grey arrows illustrate non- radiative vibrational relaxation from the out of equilibrium posi- tion, where the molecule is found immediately after an electronic transition. . . 40 2.3 Explanation for wavepacket dispersion. a) The wavepacket is ex-
cited att0 by an unchirped laser pulse. Because the vibrational spacing in the high energy range∆EH is smaller than the vibra- tional spacing in the low-energy range∆EL, thereby the oscilla- tion timesTH are longer thanTL. Thus after some oscillations at a timet1>t0, the lower-energy parts of the wavepacket advance the higher-energy parts. b) The dispersion can be suppressed by chip- ping a laser pulse in the way to start the ’slow’ blue components earlier than the ’fast’ red ones. Adapted from [9]. . . 41 2.4 Absorption spectra of Trp in PH 7 aqueous solution. Inset: Schematic
representation of fluorescence depletion. Picture is taken from [10]. 43 2.5 Fluorescence depletion traces for Trp (a) and Tyr (b) under excita-
tion with FT-limited pulse represented in black triangles. Picture is taken from [10] . . . 43 2.6 Graphic representation of the ODD mechanism.Left: Initial state,
before the excitation by the laser fieldεc(t). The state vectorscν are the wave function components.Right: An optimal control laser field, prepares a statecξthat will be parallel to the detection state D, and all the other vectors will be orthogonal to the detection state.
Picture is taken from [11] . . . 46 2.7 Scheme of an optimal control experiment. . . 47 2.8 Structure of Tryptophan. Figure to the right shows the transition
dipole moments1Laand1Lbthat have an orthogonal orientation. 48 3.1 Scheme of an autocorrelation setup, in nonlinear configuration.
BS: beam splitter. BBO: Beta Barium Borate crystal. DS: delay stage. Dt: detector. . . 54 3.2 Geometry of Self-Diffraction FROG. . . 55 3.3 Scheme of cross-correlation FROG. . . 56
3.4 a) Scanning electron microscope (SEM) image of the mirror array;
b) White-light interferometry image of MEMS micromirror aray with applied parabolic mask. . . 59 3.5 2F geometry shaper with movable mirror array: a) flat phase mask,
no amplitude modification; b) arbitrary phase mask, no amplitude modification; c) flat phase mask, with amplitude modification; d) ar- bitrary phase mask, with amplitude modification. . . 61 3.6 Screen-shot from the program used to calculate the spectral reso-
lution and temporal window of a pulse-shaper. . . 63 3.7 Principal scheme of pulse shaper. Simulation is performed using
Code V. . . 64 3.8 Positions of spectral wavelength’s maximums in the Fourier plane.
Simulation is performed usingCode V. . . 65 3.9 NGSA-II procedure. Adapted from [12]. . . 66 3.10 Crowding-distance calculation for two objectives. Points marked
in filled circles represent solutions of the same nondominated front.
Adapted from [12]. . . 67 3.11 Principal scheme of Third Harmonic Generation. HWP: a half-
wave plate to change a polarization. SHG: second harmonic gener- ation. SFG: sum frequency generation of 266 nm. DS: delay stage used to compensate the group velocity mismatch between 800 nm and 400 nm. . . 68 3.12 Experimental scheme. . . 70 4.1 Normalized absorption and fluorescence spectra, measured for the
four molecules under consideration at the same molar concentra- tion (1 mM) . . . 75 4.2 Pump-probe fluorescence depletion trace for Trp. . . 76 4.3 Pump-probe fluorescence depletion trace of Trp. Probe is set at
400 nm. . . 77 4.4 Relative amplitude of the depletion dip feature∆at short time (B-
A) with respect to the long-term depletion level (C-A) as a function of pump pulse wavelength. . . 78 4.5 Relative fluorescence depletion traces of Trp pumped at different
excitation wavelength: 270 nm, 275 nm, 285 nm, 310 nm. . . 79
4.6 Pump-probe fluorescence depletion traces for trp (a), ala-trp (b), cyclo(-gly-trp) (c) and cyclo(-leu-trp) (d). The corresponding chem- ical structures are also shown asinsets. . . 80 4.7 Example of successful optimization for fluorescence depletion mod-
ulation in case of ala-trp (a) versus trp (b) with multi-objective al- gorithm optimization (c). Histogram of fluorescence depletions for ala-trp and trp. Green (middle column): reference obtained with Fourier-transform pulses,blue(left): maximization of fluorescence depletion forala-trp,red(right): maximization of fluorescence de- pletion for trp . . . 81 4.8 Pareto front of an optimization for trp against ala-trp. Blue dots
represent all the solutions sampled during the optimization,green highlights the starting first generation of solutions and magenta shows the final generation.Redshows the non-optimized reference 82 4.9 Histograms of fluorescence depletions for various pairs of molecules.
Greenreference obtained with Fourier-transform pulses,bluemax- imization of fluorescence depletion for row molecule, red maxi- mization of fluorescence depletion for column molecule . . . 83 4.10 Resulting depletion signal of cyclo(-gly-trp) and trp mixture with
optimized mask for increasing cyclo(-gly-trp) fluorescence and de- creasing cyclo(-leu-trp) fluorescence. a cyclo(-gly-trp) with un- shaped pulse,bcyclo(-leu-trp) with unshaped pulse,c1:1 cyclo(- gly-trp)/trp mixture with unshaped pulse,dcyclo(-leu-trp) with op- timized mask,e trp with mask for cyclo(-gly-trp) and cyclo(-leu- trp), f cyclo(-gly-trp) with optimized mask, g 1:1 cyclo(-glytrp)/
trp mixture with mask for cyclo(-gly-trp) and cyclo(-leu-trp) . . . 85 4.11 X-FROGs of pulse shapes that lead to optimal discrimination. In
each box, the image on thetopis for maximising the fluorescence signal for the molecule in a respective row with the molecule in the respective column being minimised, and vice versa for the image below (same ordering as in Figure 4.9) . . . 86 4.12 Far-infrared absorption spectra of (fromtoptobottom): ala-trp, trp,
cyclo(gly-trp)and cyclo(-leu-trp) . . . 88 5.1 Three-dimensional structure of Human IgG (A) and HSA (B) by
X-ray diffraction and molecular graphics modelling. . . 92
5.2 Human Immunoglobulin G and Human Serum Albumin absorp- tance and fluorescence spectra.Red: IgG human,Black: BSA. . . 93 5.3 Fluorescence depletions of Human IgG and HSA under the excita-
tion with FT-limited pulse. . . 95 5.4 Fluorescence depletion traces of human IgG (A) and HSA (B) un-
der the excitation with FT-limited pulse fitted with double expo- nential decay function. . . 98 5.5 Evolution of the objective during the optimization. The black dots
representJref and redJopt. . . 99 5.6 Result of optimization for (A) HSA and (B) human IgG. Grey:
depletion curves obtained from an unshaped UV pulse. Blue and red: depletion curves obtained with the optimized UV pulse. Solid lines represent moving averages of the date over 10 points. . . 100 5.7 Histograms of fluorescence depletions for human IgG (A) and HSA
(C) resulted from a single-channel optimization aiming to increase the ratio of depletion signals.B: reference depletion of human IgG obtained with unshaped pulses.D: reference depletion of HSA ob- tained with unshaped pulses. . . 101 5.8 X-FROG of the optimal pulse leading to discrimination of human
IgG and HSA. . . 102 5.9 Solution structure of Human Immunoglobulin M by synchrotron
X-ray scattering and molecular graphics modelling. Blue: Trp residues.Red: Tyr residues. . . 103 5.10 Fluorescence and absorption spectra of IgG (black) and IgM (red). 104 5.11 Time-resolved fluorescence depletion traces of IgG and IgM. . . . 104 5.12 Human IgG vs human IgM. a) Relative fluorescence depletion val-
ues obtained with the FT-limited pulse; b) Relative fluorescence depletion values obtained under the excitation of the optimal pulse. 106 5.13 X-FROG trace for retrieved optimal pulse obtained during the close-
loop optimization for discrimination immunoglobulins of human plasma: IgG and IgM. . . 107 5.14 Absorptance and fluorescence spectra of rabbit Immunoglobulin G
and Bovine Serum Albumin.Red: rabbit IgG,Black: BSA. . . . 108 5.15 Pump-probe fluorescence depletion traces of rabbit IgG and BSA
pumped at 295 nm. . . 109
5.16 Fluorescence depletions of rabbit IgG (A) and BSA (B) under the excitation with FT-limited pulse fitted with double exponential de- cay function. . . 110 5.17 Discrimination of rabbit IgG against BSA under single channel
optimization. Excitation UV - 295 nm. a) Rabbit IgG; b) BSA.
Blue: fluorescence depletion traces obtained with unshaped UV pulse. Red: fluorescence depletion traces measured with shaped UV pulse. Excitation wavelength is set at 295 nm. . . 112 5.18 X-FROG trace for retrieved optimal pulse obtained during the close-
loop optimization for discrimination of rabbit IgG and BSA. . . . 113 5.19 Fluorescence depletions of IgG under the excitation with FT-limited
pulse at 295 nm (for rabbit IgG) and 270 nm (for human IgG). . . 115 6.1 Retrieved concentrations of IgG human and HSA with optimally
shaped and UV pulse close to FT-limited (unshaped).A: Retrieved level of IgG in the mixture obtained with optimal pulse is indi- cated in green triangles. Black rectangles display values of IgG determined with unshaped pulse. B: Retrieved concentrations of HSA obtained with optimally shaped UV pulse (red triangles) and unshaped pulse (black rectangles). . . 124 6.2 Retrieved concentrations of IgG rabbit and BSA with optimally
shaped and UV pulse close to FT-limited (unshaped).A: Retrieved level of IgG in the mixture obtained with optimal pulse is indicated in green triangles. Black rectangles show values of IgG determined with unshaped pulse.B: Retrieved concentrations of BSA obtained with optimally shaped UV pulse (red triangles) and unshaped pulse (black rectangles). . . 126 6.3 Retrieved concentrations of IgG human and HSA with optimally
shaped UV pulse obtained at different time delays. Retrieved levels of IgG (plotA) and HSA (plotB) obtained with optimal pulse atτ
= 0.85 ps andτ = 1.25 ps, are indicated in blue triangles and green circles, respectively. . . 128 6.4 Relative fluorescence depletion variation of human IgG at different
concentration, varying in the range 1-44 µM/ml. Concentration used for the identification experiment is in the range 16-44µM/ml. 129
3.1 Algorithm parameters used for the optimizations . . . 67 3.2 Concentration of solutions.ε: molar extinction coefficient. . . 71 5.1 Time constants of the double exponential decay functions used to
fit the depletion traces presented in 5.4. (∗): τ2 is fixed to 500 ps for all the traces. . . 97 5.2 Time constants of the double exponential decay function used to fit
the depletion traces presented in 5.16. (∗):τ2 is fixed to 500 ps for all the traces. . . 109 6.1 Evaluation of quantum control based diagnostics technique. Com-
parison of the results obtained under excitation of optimally shaped UV pulse and pulse close to FT-limited . . . 127
19
Introduction
Proteins are the building blocks of living cells. They are polymers consisting of sequence of amino-acids linked together by a polypeptide chain encoded into the 3D structure. Each amino-acid has its own position in the protein, and any small changes or damage in the sequence can mislead the overall protein function and will consequence in some dangerous disease.
Understanding how proteins function requires information of it structure and dynamics. Most of the proteins are resolved by X-ray crystallography and NMR.
Numerous techniques that can be employed for protein investigation have been developed and proposed in the last decade. Circular dichroism (CD) both one- photon and two-photon allow to studying secondary structure, protein folding and binding features [13], [14]. Fluorescence spectroscopy gives a rich insight into the protein organization. It allows the studying of intrinsic fluorescence of individual molecules and living cells. Same as CD spectroscopy, fluorescence spectroscopy is also a powerful tool to investigate binding capabilities of individual chromophores.
With the development of laser spectroscopy, more sophisticated schemes are de- voted to the non-linear regime, where several laser beams can interact non-linearly with matter. Such multidimensional coherent spectroscopies [15] employ ultra- short pulses on the time scales, therefore, makes it capable to explore processes such as electronic and vibrational changes in the excited states of proteins, long- lasting coherences in light harvesting complexes, solvent dynamics [16] and other photochemical processes. Some recent techniques of ultrafast spectroscopy are described in the review by A. Cannizzo [17].
21
In this Chapter we introduce the concept of blood plasma, and describe its main compounds. Further we describe target proteins used in quantum control experi- ments. The next section is devoted to the various methods employed for protein diagnostics.
1.1 Blood Components
Blood contains a complex mixture of many types of compounds with various properties and functions. It is distributed throughout the whole body via the vascu- lar system, and exhibits the following functions:
1. Transport system of various compounds: blood cells, salts, ions, proteins and gas (mainly CO2and O2).
2. Defense system against hostile pathogens such as bacteria, virus, fungi: spe- cialized cells like lymphocytes, monocytes and granulocytes; antibodies;
components of the complement system.
3. The wound sealing and wound healing system, life-saving precautions in the case of injuries: blood cells, e.g. blood platelets; blood coagulation and fibrinolysis
4. The balance of heat distribution throughout the body, thus guaranteeing a constant body temperature.
There are two main parts comprising blood, the blood plasma and the blood cells.
1.1.1 Blood plasma
The blood plasma represents approximately of 55 % of the entire blood, it contains the following groups:
• Water. It is the main component of blood plasma, approximately 90 %.
• Mineral salts and ions.
• Low molecular weight components. For example, there are carbohydrates such as glucose and fructose, amino acids, nucleotides such as ATP1 and
1Adenosine triphosphate (ATP) is a nucleotide that consists of a purine base (adenine), a pentose sugar (ribose), and three phosphate groups. ATP is used in DNA synthesis and energy storage.
cAMP2, vitamins, hormones, fatty acids, lipids and triglycerides, bile acids, urea and ammonia and many more components.
• High molecular weight components. Peptides and proteins, oligosaccha- rides and polysaccharides, DNA and RNA.
• Gases in soluble form. Gases such as oxygen, carbon dioxide and nitric oxide are dissolved in blood.
Among of different water-soluble compounds blood plasma comprise the blood plasma proteins. According to N.G. Anderson and N.L. Anderson [18], plasma proteins can be classified into the proteins secreted by solid tissues, immunoglob- ulins, ’long-distance’ and ’local’ receptor ligands, temporary passengers, tissue leakage products, aberrant secretion and foreign proteins. Based on this classifi- cation these proteins can be further grouped into the following main subclasses [18]:
1. Blood coagulation and fibrinolysis. These kind of proteins comprise fib- rinogen, kinin and the angiotensin/renin system.
2. The complement system. Proteins of the complement system are part of the immune system and are involved in the initiation of the immune response.
3. The immune system. The main proteins of immune system are: Immunoglob- ulin G (IgG) which exists in four subclasses: IgG1 (60%), IgG2 (30%), IgG3 (4%) and IgG4 (6%); Immunoglobulin D (IgD); Immunoglobulin E (IgE), Immunoglobulin A (IgA) which exists in two forms: IgA1 (90%), IgA2(10%); Immunoglobulin M (IgM).
4. Enzymes. These are proteins, which accelerate or catalyse chemical reac- tions. Enzymes control and regulate many biochemical pathways such as blood coagulation and fibrinolysis, the complement system.
5. Lipoproteins. They represent the aggregates of lipids and proteins. They enable transport of water-insoluble lipids via the vascular system to the target cells. Lipoproteins play a key role in homeostasis of cholesterol.
2Cyclic adenosine monophosphate (cAMP) is derived from ATP and used as a intracellular signal transducer. It is comprised of a purine base (adenine), a pentose sugar (ribose), and one phosphate group.
6. Hormones. They are either peptides or proteins, modified amino acids or steroids. Hormones are present in blood plasma in very low concentration (∼pg/ml). They are released by many glands of the endocrine system such as the hypothalamus, the pituitary gland, the parathyroid, the thyroid and pancreas, and by tissues such as the stomach, intestine, liver and placenta.
7. Cytokines and growth factors. Cytokines are the soluble proteins, pro- duced by hematopoietic and nonhematopoietic cells. They are responsible for intercellular communication, and also involved in the development, dif- ferentiation and activation of cells. Growth factors play an essential role in stimulating cellular proliferation and differentiation. Besides, they act as signal transmission proteins between cells.
8. Proteins of transport and storage. These type of proteins includes the serum albumin family, where Human Serum Albumin is the major transport protein, it is also present in a very high concentration (∼ 35-50 mg/ml).
Another class of plasma proteins responsible for transport and storage are globulin family. These are heme-containing proteins, which involved into the binding and transport of oxygen.
1.1.2 Blood cells
The blood cells represents approximately 45 % of entire blood, they are primarily synthesized in the bone marrow. There three main groups of blood cells:
• Erythrocytesorred blood cells. They have a biconcave form (see Figure 1.1), representing flattened cells with a discoed shape. They contain no nu- cleus and have a diameter of∼ 7.5 µm, a thickness of ∼2 µm. Blood contains approximately 4-5 × 109 erythrocytes/ml of blood, representing approximately 96 % of all blood cells. They contain hemoglobin protein, which carries oxygen and defines the red color of blood.
• Leukocytesorwhite blood cells. They represent∼3 % of all blood cells, and appear in concentration of∼4-8×106leukocytes/ml of blood with an approximate size of 7-15µm. Leukocytes are composed by cells from the innate immune system and adaptive immune system, particularly lympho- cytes T and B.
A B C
Figure 1.1:Electron micrographs of Erythrocytes (A), Leukocytes (B), Platelets (C). Source: [1].
• Thrombocytesor platelets. They contain no nucleus and have a discoid shape with a diameter of approximately 1-3 µm. Blood contains approxi- mately 2-3×108 platelets/ml of blood. Platelets are essential in the heal- ing process of vascular injuries, they protect the body by stopping bleeding.
During the coagulation cascade they close the site of injury via intercalation with the fibrin network close. During this process activated platelets change its shape from discoid to spherical, exposing spines termed pseudopodia, which become sticky, thus annealing the injured blood vessel. By clumping together platelets form clots.
Serum
In the next part we will use the notion of serum. This is a blood compound not including blood cells and proteins participating in blood coagulation.
1.2 Target molecules
In this part we characterize serum proteins which are under investigation in the following chapters. Serum proteins are the good indicators for diagnostics [19]. We will focus our study on the serum albumin protein, which is responsible for trans- port of various compounds, proteins of immune system, antibodies, Immunoglob- ulin G (IgG) and Immunoglobulin M (IgM). Antibodies defend the body against foreign substances.
1.2.1 Albumin
Serum albumin is the most abundant protein of plasma and one of the most in- vestigated proteins. It belongs to the serum albumin family and represents 90% of serum proteins. It is synthesized in the liver and it is present in all body fluids in considerably high concentration (35-50 mg/ml). It plays an important role in bind- ing and transporting various types of endogenous and exogenous compounds like fatty acids, ions, heavy metals, hormones, amino acids, toxic metabolites. Further- more, there is a variety of drugs and other compounds that are delivered to their organs through the vascular system by binding with serum albumin.
Human Serum Albumin (HSA) is well known as a marker for good nutrition and longevity. A decrease in a HSA concentration indicates a negative acute-phase marker of inflammation [20] or infection. HSA regulates and maintains colloidal osmotic pressure in blood [21], which is important for the distribution of body fluids between intravascular compartments and tissues. This is very crucial for the regulation of body temperature.
The 3D structure of HSA, which is shown in Figure 1.2, is well determined by X- ray diffraction [22,23,24]. HSA is organized with high content of alpha- helixes ( 67%) and no beta-strands and has a single polypeptide of 585 residues. Its structure consists of three homologous domains I, II and III, which form resembles a heart- shaped structure. Besides of topologically similarities, these domains have also similar 3D structures. They are further divided into sub-domains named IAB, IC, IIAB, IIC, IIIAB, IIIC, respectively [23,25].
Bovine Serum Albumin (BSA) is often used as a model protein mainly because of its structural homology with HSA. Its pairwise sequence alignment structure shares 75% identity and 87% similarity with HAS. However, from the spectro- scopic point of view, the main difference between BSA and HSA is the number of tryptophan residues. BSA has two Trp residues: Trp135, locating on the surface of subdomain IB and Trp214, which is located within the hydrophobic binding pocket of subdomain IIA; while HSA has only one Trp214, located in the hydrophobic pocket (Figure 1.2).
Binding affinities of serum albumin proteins with various compounds is studied widely by numerous techniques [26, 27, 28] including fluorescence [29, 30, 31,
TRP214 TRP214 TRP134
HSA BSA
Figure 1.2:Three-dimensional structures of HSA and BSA with tryptophan residues in orange color. Source: [2].
32], UV - Visible spectroscopy, CD spectroscopy and NMR [33, 34]. In spite of similarities in common properties of albumin subdomains, it is revealed by Trp fluorescence quenching analysis that each subdomain exhibits certain degree of binding specificity.
Understanding the mechanisms affecting the pharmacological effect of drugs during the interaction with HSA is very important. This knowledge can signif- icantly improve drug delivery system through HSA - drug complexes, which is currently very promising. Various examples show that it can be exploited towards reducing side effects of anticancer drags and make their targeting more effective [35,36,37,38,39].
1.2.2 Immunoglobulin G
Antibodies or Immunoglobulins are the hallmark proteins of immune system, whose task is the fine recognition of foreign compounds and various antigenic de- terminants of specifics cells. Immunoglobulins can be found under two forms:
membrane-bound constituent of immune or soluble molecule secreted by B-cells.
There are 5 classes of immunoglobulins differing considerably in their biological function and overall structure: IgG, IgE, IgM, IgD and IgA (Figure 1.3). The most common type of antibody is immunoglobulin G, it composed about 75 % of immunoglobulins.
IgG1 IgG2 IgG3 IgG4 IgM
Figure 1.3:Schematic representation of five IgG classes. Source:
[3].
Antibodies have a common structure that builds up with many structural do- mains. A basic structure of an immunoglobulin is aY-shaped molecule composed of two regions: H and L (Figure 1.4). The first consists of long constant polypep- tide regions (heavy chain) of about 55 kDa, and the second represent a variable region consists of two short or light chains (22 kDa). The H regions consist ofVH, CH1,CH2, and CH3 domains, and the L regions consist ofVLandCLdomains.
The H and L chains are bound by disulphide bonds. The diversity of combinations of variable regions results in the ability to bind different antigens and provides a variety targets of immunoglobulin. The rigidity of these domains ensures a high binding selectivity.
Antigen is recognized by the Fab region, composed of one variable domainsVL in light chains and one VH in heavy (Figure 1.4). This is the part of antibody that gives itY shape. It can also be recognized by hipervariable loops bordering the antigen-binding pocket at the Fab interface (see Figure 1.5). Therefore, vari- able regions has a particular amino-acid sequence and a strict conformation of the loops, hence it determines all the differences in specificity displayed by different immunoglobulins. Each immunoglobulin can only binds to a particular antigen and not the others.
VH VL H L H2N
H2N
L H
VL VH
H2N H2N
CO2H HO2C
CO2H HO2C CL CL
CH1 CH1
CH2 CH2
CH3 CH3
Fc FAB
Figure 1.4:Schematic representation of a typical immunoglobulin structure. It is formed of four chains, two heavy VH and two light VL. The binding regions of the antibody are at the ends of the variable domains VH and VL, located at the ends of the heavy and light chains respectively.
A detection of IgG is important to provide information about the health of indi- vidual’s immune system. It helps in diagnostics of various conditions and diseases that affect the levels of IgG classes. IgG is often used as a biomarker of certain viruses, like rotavirus, the leading cause of severe diarrheal infection, Epstein-Barr virus and Herpes simplex virus. IgG identification can be even applied for the diagnosis of Alzheimer’s disease. In most of the cases it is labelled with some flu- orescence dye to enhance fluorescence emission. For example, increased level of immunoglobulin is a result of:
• Infections (bacteria, virus)
• Allergy
• Autoimmune disorders
• Cirrhosis
CH3 CH2
CL VL
VH CH1
VH
Hypervariable loops
Figure 1.5:Left: the immunoglobulin fold. Right: TheVHdomain.
At the end of both theVH and theVLdomains are three hypervariable loops, highlighted in red. Source: [4].
• Chronic inflammation
• Inflammatory disorders
• Hyperimmunization reactions
• Wiskott-Aldrich syndrome
Low level of immunoglobulin indicates on deaseases like:
• Immunosuppressant drugs such as phenytoin, carbamazepine
• Kidney failure or diabetes
• Transient delay in production in newborns
• Nephrotic syndrome-kidney disease
• Burns
• Protein-losing enteropathy-any condition of the gastrointestinal tract that af- fects the digestion or absorption of protein
• Waldenstrom’s macroglobulinemia
• Some types of leukemia
1.2.3 Immunoglobulin M
Another class of antibody produced during the humoral immune response is immunoglobulin M (IgM). IgM accounts for 5 to 10 % of the total serum im- munoglobulins. By far it is the largest type of immunoglobulins with molecular mass of approximately 970 kDa. Normally, IgM presents in concentration of 1.5 mg/ml. IgM is formed by five disulphide-bonded monomeric subunits, structurally resembling IgG, forming a pentamer, joined together by polypeptide known as J chain (Figure 1.6). This class of immunoglobulin contains 10-antigen combining sites on the periphery of the molecule and can bind 10 small antigens. However due to steric restrictions only five large molecules can be bound to one IgM an- tibody. IgM molecule is found also in the form of hexamer. It consists of six monomeric blocks lacking J chain, but the amount of IgM hexamers in serum is no more than 5 % of total IgM. However, study is showing that this type of IgM was detected in patients having various disorders: Waldenstrom’s macroglobuline- mia, a type of cancer affecting B-cells [40], [41], a form of autoimmune hemolytic anemia, and cold agglutinin disease [42], [43], which is characterized by the in- creased concentration of IgM. Changes in composition of IgM were also found in patients suffering from recurrent urinary bacterial infections [44]. Definite role of hexametric antibody however has not been reported yet.
IgM is the first antibody synthesized by immune system followed then by the increased number of longer-lived IgG and IgA after the primary infections or vac- cines. It is also recognized as natural antibody found in serum even before the con- tact with antigen or pathogen [45]. IgM is often associated as a first trait against infections [46], [47]. IgM antibody attracting a lot of interest in therapeutic appli- cations. In some research, it was found that IgM antibodies serve as the indicator of initial stage of severe illness like diarrheal disease, where mucosally derived IgM is the most marked mucosal response [48]. It can be used to identify such diseases like cytomegalovirus typhoid fever pathogen at the early stages.
Numerous reports show that IgM can be used to enhance the response of vac- cines [49], while to date immunoglobulin infusion (IgG) is considered as a treat- ment of various autoimmune deseases. Examples include malaria [50], cancer [51, 52], and leukemia. Thus IgM could be added as a potential vaccine adju- vant to IgG injection to improve the therapeutic efficacy. Understanding the role of IgM antibody and its interaction with different environment might be very helpful
Figure 1.6:Three-dimensional structure of human Immunoglobulin M. Source: [2].
for numerous therapeutic applications.
1.3 Methods of protein detection
The diversity and impact of bio-assays technologies continues to expand in bio- chemical screening applications, which involve protein identification and analysis of protein-protein, protein-peptide, protein-small-molecule, and protein-DNA in- teractions.
There are several classes of biosensing techniques. A first one is based on the tra- ditional analytical chemistry methods such as NMR and mass spectrometry. Other ones are based on molecular interactions (Enzyme-Linked Immunosorbent Assay) and optical techniques relying on the evanescent field interaction with an analyte, which are sensitive, reproducible, able to detect small concentration of studied
protein ( ∼ng/ml). These methods usually require the presence of immobilized biomolecule on the surface of traducer, enzyme or antibody. Some of the com- monly used techniques are described below.
1.3.1 Enzyme-Linked Immunosorbent Assay
One of the most common diagnostic techniques for protein identification is en- zymelinked immunosorbent assay (ELISA). Currently it serves as the etalon in proteomics. It is based on the immunological interaction between the antibody and antigen. Besides of application in serum antibody detection, it is used in various fields including food industry for detection toxins and food allergens, in medical application for quantification of hormones and drugs.
ELISA test is performed in multiple steps which require sample preparation, immobilization into the immunoassay plate, washing steps, and adding additional enzyme linked to the detection antibody. Previous techniques close to ELISA, radioactive labeling, were using radioactive materials instead of using enzymes.
The working principle of ELISA assay is shown Figure 1.7.
1) Wells are coated with captured antibody that will bind an antigen that will be analyzed. Adsorption is achieved through hydrophobic interactions between the microtiter plate and non-polar protein residues ;
2) Blocker buffer to lock non-specific binding sites of antibody ; 3) A measured sample of antigen is added ;
4) Plates are incubated and washed to remove all unbound antigen, thereby removing the entire background signal and improving signal-to-noise ratio;
5) A specific antibody that will bind an antigen is added;
6) Further steps include addition of detecting secondary antibody linked to an enzyme, for example Horseradish peroxidase (HRP) and alkaline phos- phatase (AP), that binds to detecting antibody;
7) All unbound enzyme conjugates are removed;
8) In order to reveal the outcome of the chemical analysis, a chemical is added for converting the occurred reaction into a detectable form;
9) Analysis of the antigen concentration can be based, for example, on the mea- surements of absorbance, fluorescence intensity, or luminescence during the irradiation of microplates by laser with specific wavelength;
A B C D E
Figure 1.7:ELISA model. A: a captured antibody is immobilised at the plate surface. B: a sample, that need to be analysed, is added. C: a detection antibody specific for a target anti- gen is added. D: adding of an additional antibody linked to an enzyme. E: a chemical is added, and is converted by enzyme to detectable form.
1.3.2 Biosensor based on Surface Plasmon Resonance
Other most common technology commercially available is Surface Plasmon Resonance (SPR). SPR optical biosensor is often used for binding kinetics stud- ies, measuring antibody affinity and protein concentration. Figure 1.8 illustrates the principal scheme of SPR biosensor. It consists of a glass slide coated with no- ble metal thin film, which works as a sensor surface. On the sensor surface antigen is immobilized, which serves as transducer for antibody detection.
The principle of SPR is based on the interaction of metals with electromagnetic radiation. The surface charge density oscillations associated with surface plasmons at the interface between a metal and a dielectric can give rise to strongly enhanced optical near-fields specially confined near the metal surface. At a certain reso- nant condition under plasmon excitation, it can be used for immune biosensing applications. When a buffer solution with antibody is immobilized on the dielec- tric surface, it cause changes in the local index of refraction that are subsequently monitored .
Though SPR biosensor has the advantage of measuring binding rates in protein- protein interaction studies and in binding strengths, however some of the dominant
Figure 1.8:Principal scheme of SPR biosensor.
techniques suffer from low throughput in processing different samples, compli- cated microfluidics, expensive chips and limited sensitivity. Problem with sensitiv- ity is especially pronounced when working with protein-small-molecules, as well as with low concentrations, weak binders, and low levels of immobilized com- pounds. This type of biosensor is also limited by analytical specificity and non- specific binding, since any substance binding to the surface causes a change in the refractive index.
Other optical methods such as resonant waveguide grating (RWG) and bio-layer interferometry (BLI) are actively used for biosensing applications. The RWG, also named photonic crystal biosensor, relies on the resonant coupling of light into a waveguide. Such biosensor consits of a substrate and a periodic-embedded waveg- uide thin film. Similar to SPR it utilize evanescent wave interaction with the ana- lyte, as a result changes in local refractive index are measured. Contrary to SPR, BLI optical biosensor, is based on analysis of interference pattern in the reflected light intensity form the biosensor surface. White light irradiates two surfaces: a layer of immobilized protein, and a reference layer (usually glass), and reflected intensity as a function of wavelength is monitored.
Basic concepts
2.1 Introduction
Control over chemical reactions is a fascinating theme in physics and chemistry.
With the invention of laser in the 1960s, remarkable theoretical and experimental progress has been achieved in the area of control of molecular processes. Initially monochromatic lasers were proposed for bond-selective control of chemical reac- tions [53, 54]. The idea was simply to use a laser with a frequency tuned, to a specific chemical bond, so it could absorb radiation that would lead to its cleav- ing without damage of others. However, soon it was realized that the energy ab- sorbed at one bond is redistributed amongst other degrees of freedom of the excited molecule. Early attempts using selective laser excitation were thereby thwarted by fast intramolecular energy redistribution [55,56,57,58,59].
In 1980s femtosecond lasers have become available with the development of mode-locking techniques. So the issue of energy redistribution could be over- come using pulses with the duration of the chemical reaction time. Since then the application of femtosecond laser in new field of femtosecond spectroscopy and femtochemistry has developed rapidly. A Nobel laureate in Chemistry in 1999, Ahmed Zewail proposed to use femtosecond laser to study a motion of atoms and molecules during chemical reactions. A significant step forward was made in at- tempting to control microscopic system on the ultrafast time scale by using tailored laser pulses with femtosecond temporal resolution.
37
Quantum control uses the properties of the laser to create a coherent super- position of vibrational eigenstates in excited molecules. Control of molecular wavepackets on the excited states became possible by manipulation of quantum in- terference of different pathways within a femtosecond time resolution. Several the- oretical methods were introduced and verified experimentally. In the first scheme, proposed theoretically by Brumer and Sharipo in 1986 [60,61], branching ratios in molecular photodissociation were controlled, and experimentally demonstrated in 1990 [62]. In this scenario two monochromatic lasers with tunable frequencies are simultaneously used to excite a continuum of vibronic states of molecule. It was shown that by adjusting the relative phase between two laser fields induces constructive or destructive interference in the desired and undesired reaction path- ways. A second approach introduced by Tannor, Koslov, and Rice [5,6] in 1985 is based on the sequences of femtosecond laser pulses, where control over molec- ular photodissociation was achieved by varying the time-delay. One of the pulses creates a vibrational wavepacket on the excited potential energy surface, while it travels to reach a particular point the second pulse probes at the time to re-excite the population to the ground surface, thereby promoting the desired reaction pathway.
These two schemes by Brumer-Sharipo and Tanor-Kosloff-Rice were implemented experimentally in 1990s with the development of femtosecond lasers [63,64,65].
*
Figure 2.1: Quantum control pump-dump Tannor-Kosloff-Rice scheme. First pump pulse creates a wavepacket on the first excited state potential energy surface. Second laser pulse dumps the wavepacket into the desired product channel [5,6,7,8].
These approaches lead to the idea of designing specific tailored ultrashort laser pulses which can drive a molecule to a particular target state. This idea was relied on the continuous interaction of complex laser field with quantum system during the time of evolution of the molecular wave packet, until a desired outcome is reached [66,67,68,66,69,70]. With the development of pulse shaping techniques to modulate phase and amplitude, considerable progress has been made in fem- tosecond spectroscopy. In 1992, Judson and Rabitz proposed using a pulse shaping device in combination with a searching algorithm [71]. Employing feedback from the molecular system an optimal electric field which optimized a desired outcome can be found. At that time the concept of optimal control was introduced, and opened up numerous research avenues.
In this Chapter we introduce the basic principle of quantum control and show how the manipulation of molecular wave packets on the excited states can be used for the discrimination of molecules that have similar spectroscopic features. Most of the molecular systems that have biological significance, such as proteins, have an important compound Tryptophan (Trp). Trp is an aromatic amino-acid, which is often used as a protein reporter. Hereafter we describe the general properties of this molecule, reported in Section 2.4.
2.2 Dynamics of molecular wave packets
When a molecule is irradiated by an utrashort laser pulse, it is electronically excited. In molecular spectroscopy it is normally assumed that the nuclear con- figuration is fixed due to the relatively slow velocity of the nuclei in comparison with the electronic. This principle is well described within the Franck-Condon approximation. Excitation of the molecule leads to a vertical transition, as it is demonstrated in Figure 2.2.
If laser pulse is short compared with the vibrational period of the molecule, several vibrational levels become populated. As a result it forms a coherent super- position of eigenstates with a well-defined phase evolution. Such a superposition is called a wavepacket, which is spatially localized and its motion can be temporally deciphered using ultrashort laser pulses. The time evolution of eigenfunctions can be described as
Nuclear Coordinate
Energy
S1
S0
Emission Absorption
Figure 2.2:Schematic energy level diagram. Blue (absorption) and green (emission) arrows show electronic transitions, grey arrows illustrate nonradiative vibrational relaxation from the out of equilibrium position, where the molecule is found immediately after an electronic transition.
Ψ(t) =X
n
cnψnexp[−i(wnt−φn)] (2.1) where ψn andωn are the eigenfunction and transition frequency of the n-th vibrational level, respectively;cn andφn represent its amplitude and phase. Ma- nipulation of the amplitudes and phases of the laser pulses allows the control of the quantum amplitude and phases of the molecular wavepacket.
When the molecular wavepacket is formed, it periodically oscillates back and forth in the harmonic potential. If there is no external perturbation, it continues oscillating without losing energy until it decays from the excited state.
In an anharmonic potential, the wavepacket exhibits broadning [72] during a period of time and changes its shape. This occurs because the slower high energy (’blue’) components of the molecular wavepacket are delayed with respect to the faster low energy (’red’) components (see Figure 2.3 a). Using a tailored laser pulse it is possible to suppress broadning, as shown in Figure 2.3 b. It is also observed that after a certain revival time, the wavepacket reforms with its initial phase [73]. This phenomenon is well described theoretically and experimentally,
t
0t
1Internuclear distance
Energy
∆EH
∆EL
t
0t
1=T
optInternuclear distance
Energy
∆EH
∆EL
a) b)
Figure 2.3: Explanation for wavepacket dispersion. a) The wavepacket is excited att0by an unchirped laser pulse.
Because the vibrational spacing in the high energy range
∆EH is smaller than the vibrational spacing in the low- energy range∆EL, thereby the oscillation timesTHare longer thanTL. Thus after some oscillations at a timet1
>t0, the lower-energy parts of the wavepacket advance the higher-energy parts. b) The dispersion can be sup- pressed by chipping a laser pulse in the way to start the
’slow’ blue components earlier than the ’fast’ red ones.
Adapted from [9].
and is observed in various systems.
Since most chemical reactions take place in the liquid phase, it is important to study the effect of this environment on the molecular systems. Generally, interac- tions with the environment induce dephasing of the coherently formed molecular wavepacket. It can be expressed in two forms: 1) coupling with internal modes of the solute following Internal Vibrational Redistribution (IVR), 2) interaction with solvent molecules leading to efficient depopulation channels of coherently excited vibrational modes. Solute-solvent interaction can change the potential energy sur- faces on which the wavepacket evolves [74], which can result in fast dephasing.
When we deal with an ensemble of molecules in the liquid phase, their excita- tion leads to the formation of a wavepacket whose frequencies are distributed for different molecules. At first they are all in phase and coherence is preserved, but after a certain time, the interaction with the surrounding solute molecules breaks
the initial coherence and all phases become randomized. The dephasing time of an ensemble of wave packets varies in different environments, and it is faster for solvents that undergo a strong interaction with the solutes and have fast fluctuation time scales. To overcome this, instantaneous excitation is necessary. This means that the duration of the laser pulse should be much shorter than the oscillation pe- riod, so that the evolution of the excited wavefunction during the interaction with the field can be considered negligible.
Example
Here we show an example of how a pump-probe approach allows the observation of the evolution of the molecular wavepacket during its motion along a potential energy surface.
As an example investigated by our group [10,75], fluorescence can be used as an observable for this purpose. Here we focus on the molecular systems consisting of the aromatic amino-acids Trp and Tyr. They are two of the 20 amino-acids that made up proteins and the main contributors in protein fluorescence. They have both absorption bands centred at 270 nm. While the second band which is char- acteristic for Trp originates from π −π∗ transition to the 1Ba, 1Ba states, Trp fluorescence originates from the two transitions1La,1Lain the firstπ,π∗ excited singlet state. Figure 2.4 shows a schematic of this process. First, a short UV pulse excites molecules from theS0 toS1 states forming a coherent superposition of vibrational states, i.e. the molecular wavepacket. This evolves in time and fluores- cence is eventually observed. The evolution of the wavepacket can be probed by an IR pulse, which transfers the population to higher lying ionizing and dissociative states, thereby depleting fluorescence.
Fluorescence depletion for Trp and Tyr already exhibits different time-resolved dynamics under the excitation with FT-limed pulses. One can see from Figure 2.5 that Trp undergoes rapid fluorescence depletion reaching a minimum at 600 fs, which can be attributed to the opening of a Franck-Condon window toward higher lying ionizing states. In contrast, Tyr fluorescence decreases until 600 fs and then continues less abruptly until 7 ps. The sampling of the transient dynamical con- figuration explored by the molecular wavepacket allows one to easily discriminate between the two main amino acids, Trp and Tyr, responsible for protein fluores- cence.
1La, 1Lb 1Ba, 1Bb
IR
UV
Absorption
Wavelength [nm]
IR
UV Fluorescence
ionization: φ = 0.2 non-radiative deexcitation SN
S1
S0
ionization: φ = 0.02 non-radiative deexcitation 1 2
1La, 1Lb 1Ba, 1Bb
IR
UV
Absorption
Wavelength [nm]
IR
UV Fluorescence
ionization: φ = 0.2 non-radiative deexcitation SN
S1
S0
ionization: φ = 0.02 non-radiative deexcitation 1 2
Figure 2.4: Absorption spectra of Trp in PH 7 aqueous solution. In- set: Schematic representation of fluorescence depletion.
Picture is taken from [10].
Figure 2.5: Fluorescence depletion traces for Trp (a) and Tyr (b) un- der excitation with FT-limited pulse represented in black triangles. Picture is taken from [10]
This example demonstrates that probing the motion of molecular wavepackets for the two essential amino-acids Trp and Tyr allows to discriminate them using pump-probe technique. Nevertheless, the question rises how to discriminate when time-resolved fluorescence depletion is the same for both molecules, for example in more complex molecules such as peptides and proteins, described in more detail in Chapters 4 and 5.
2.3 Optimal quantum control
Optimal control is based on the ability to optimize properties of the laser pulses such as the phase [76], the amplitude [77] and the polarization [78] which act on a quantum system until a desired product is obtained. The experimental realization the optimal control experiments covers a wide domain, including: control over molecular dissociation and ionization [79,80,81,82] , fragmentation [83,84,85, 80], chemical bond breaking [86] , control over fluorescence of dye molecules [87], shaping of molecular wavefunction [88], quantum information processing [89], control of attosecond dynamics [90, 91], control over izomerization of proteins [92], dynamical processes in the light-harvesting complexes [93], semiconductors [94,95,96,97,98], and many other applications.
One of the challenges and issues emerging, when employing quantum control experiments, is finding the optimal laser pulses, that lead to the desired outcome.
In theory, optimally laser pulse can be calculated by solving the time-dependent Schrödinger equation of the system, and a-priori knowledge of molecular Hamil- tonians is needed. In particular, for a complex system, such as large molecules in the condensed phase, the molecular Hamiltonian is known usually to a limited de- gree, and solving the Schrödinger equation is challenging. However, tailored laser pulses steering the quantum system from its initial state to a desired final state can be found, by using the optimal control introduced by Rabitz and co-workers [71] in 1992. It was proposed to use a feedback from a molecule observable to iteratively optimize the laser pulse characteristics until an optimally shaped laser field is found. In this framework, there is no need to have prior information of the molecular system, the experimental apparatus ’solves’ Schrödinger equation in the laboratory field.
Optimal control can be adapted for the discrimination task of molecular systems even if their spectral properties are very similar. Optimal Dynamic Discrimination (ODD) exploits the dynamics of the molecules, in order to discriminate them. Ul- trafast excitation of the quantum system creates the molecular wavepacket, which is then probed by the second detection laser pulse. The detection pulse projects the molecular wavepacket that has evolved under the influence of the first optimally control field into the detection state. As a result, we observe the dynamical re- sponse of the molecule, that depends on the frequencies of the lasers, polarization and the relative time-delay. The use of a pulse shaping technique combined with a closed-loop approach to control the molecular dynamics differently, is at the basis of ODD.
To introduce the concept of optimal control, let us consider a quantum system described by a wavefunctionΨ(t), for example a molecular wavepacket generated at a potential energy surface. Its evolution under the influence of a control field ε(t)is governed by the time-dependent Schrödinger equation:
i¯hδ
δtΨ(t) =HΨ(t) (2.2)
whereH=H0−µε(t)is the total Hamiltonian comprising molecular Hamilto- nian and the interaction with external light field. The external fieldε(t)influences primarily the phases of molecule. The optimal electric field, which can be gener- ated by pulse-shapers, can guide the quantum system, evolving along the multiple pathways, to the desired state by manipulation over constructive and destructive interferences.
Let us consider example of quantum systems represented by multiple chemi- cal species, that we intend to discriminate. Then for each of them characterized by Ψν0,Ψν1,...,ΨνN−1, there is a detection stateDwhich can describe a final population.
The detection state is associated with the observable such as fluorescence (or fluo- rescence depletion) in the experiment. For each chemical species, the wavepacket is defined by [99]
Ψν(t) =
N−1
X
i=0
cνi(t)Ψνi +dν(t)Dν (2.3) The dynamics of each system is controlled by its Schrödinger equation [99]
