4.5 Conclusions
5.1.3 Optimal dynamic discrimination of human IgG and HSA . 97
spectroscopies we carry out a single-objective optimization to achieve optimal dis-crimination of immunoglobulin and albumin. During this stage proteins are in the separate flow cells. The target objective for the optimization algorithm is defined as the ratio between the signals simultaneously generated by the studied proteins.
The learning algorithm feedback functionJ(τ)is expressed by:
J(τ) = δIgG(τ)
δHSA(τ) +ε+αδIgG (5.5)
where parametersδIgG,δHSA are the fluorescence depletion1signals of IgG human and HSA, respectively, determined for a specific delay. To avoid artefacts, for example, the division by zero or the convergence to solutions yielding small intensities, the offsetεis added to the denominator and a term α, proportional to the quantity to be maximized. τ , α are set at ε = 0.1, α = 0.2. Figure 5.5 shows the evolution driven by the optimization. It consists of 45 generations. At the beginning, objectiveJis maximized, and after approximately 35 generations it reaches a steady value. The optimization outcome was evaluated by measuring the fluorescence depletion signals as a function of time-delay for IgG human and HSA using shaped optimal pulse.
1fluorescence depletion is defined byδi= (Fiundepl−Fidepl(τ))/(Fiundepl)
1.0
Figure 5.4:Fluorescence depletion traces of human IgG (A) and HSA (B) under the excitation with FT-limited pulse fit-ted with double exponential decay function.
Figure 5.6 demonstrates the result of successful optimization aiming to increase the magnitude of the depletion ratio of IgG and HSA. The best discrimination was reached for an optimization performed at time delayτ ∼500 fs. As one can see from the Figure 5.6 optimally shaped UV pulse affects both proteins. Fluorescence depletion of HSA is enhanced for time-delays at∼ 0 ≤ τ ≤ 3ps, while optimal UV pulse minimize the absolute depletion value of IgG so that depletion peak
0 10 20 30 40
−0.075
−0.065
−0.055
−0.045
−0.035
Generation
Depletion, [a.u.]
Figure 5.5:Evolution of the objective during the optimization. The black dots representJref and redJopt.
vanishes .
The same optimally shaped UV pulse is applied 5 times to the molecular pair IgG and HSA in order to evaluate the robustness and stability of the observed effect. Subsequently, the corresponding depletion traces are recorded along the time-delays−2ps < τ < 8psbetween the shaped UV and IR with time resolu-tion of 50 fs. Figure 5.7 shows the resulting histogram obtained with an optimally shaped pulse at the time delay, where the maximum discrimination is achieved.
The plot contains also the results measured with unshaped UV pulse for compar-ison. Blue columns represent data obtained for HSA under the excitation of opti-mal discrimination pulse, beige columns correspond to the IgG. The columns with dashed lines indicate the depletion values acquired upon illumination of unshaped UV pulse. The histograms obtained with discrimination pulse have a separation of∼ 72 %, defined by100(µHSA-µIgG) , where µHSA and µIgG are the mean depletion values, corresponding to 0.62 and 1.34. This separation is equal 8.5σ, where (µHSA-µIgG)/σ = 8.5 andσ = q(σHSA2 +σ2IgG)/2. σHSA andσIgG are the standard deviations of associated probabilities densities in Figure 5.7.
The outcome observed with a shaped pulse is repeatable, showing the enhanced difference between depletion values of studied molecules. In contrast, the
un-0 2 4 6 8
−0.085
−0.08
−0.075
−0.07
−0.065
Time, [ps]
Depletion, [a.u.]
0 2 4 6 8
−0.085
−0.08
−0.075
−0.07
Time, [ps]
Depletion, [a.u.]
A
B
Figure 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 aver-ages of the date over 10 points.
shaped pulse yields similar levels of fluorescence depletion signals.
Figure 5.7: Histograms of fluorescence depletions for human IgG (A) and HSA (C) resulted from a single-channel opti-mization aiming to increase the ratio of depletion signals.
B: reference depletion of human IgG obtained with un-shaped pulses. D: reference depletion of HSA obtained with unshaped pulses.
To get a further insight into the discrimination mechanism, we measured the retrieved optimal spectral fields using a down-conversion X-FROG. The traces of retrieved spectral phase for two pair of IgG and albumin are reported in the Figure 5.8. The optimized pulse sequences obtained by the GA bear a multi-pulse struc-ture. These X-FROG traces are measured just after the close-loop optimizations and measurements of the biomolecules under the excitation of optimal pulses. The experimental conditions for independent experiments on molecular pairs are kept identical. Zero time-delay corresponds to the case when IR and UV pulses are
temporally overlapped, as determined by the maximum of the frequency mixing in a nonlinear crystal; positive time-delays correspond to UV pulse preceding IR when fluorescence depletion is observed; at the negative delays, there is only fluo-rescence emitted by the molecules. X-FROG conttains subpulses spaced by 0.273 ps, 0.238 ps, 0.339 ps, 0.351 ps, which corresponds to∼122cm−1, 140cm−1, 98cm−1, 95cm−1, as assessed by Fourier transforming the optimal UV intensity envelope. The time resolution of X-FROG spectrogram is∼0.15 ps.
500 0 500 1000 400
390 380 370 360
350
Time, fs
Wavelength, nm
-Figure 5.8: X-FROG of the optimal pulse leading to discrimination of human IgG and HSA.
5.2 Human Immunoglobulin G vs Human Immunoglobu-lin M
In this part different types of antibodies are under investigation: Immunoglobu-lin G (IgG) and ImmunoglobuImmunoglobu-lin M (IgM). The main motivation of selecting IgM as an opponent molecule, underlies in a possible detection of various forms of dis-ease at a very early stage. As mentioned in the previous Chapter (see chapter 1), presence of IgM is often associated with a illness causes by an infection or a virus.
Detection of IgG while IgM is absent indicates past exposure to the virus or vac-cination. Simultaneous identification of IgG and IgM antibodies is often needed mainly to distinguish primarily from secondary infection [161], thus it provides a valuable epidemiological tool for human protection.
Fluorescence emission of human IgM is determined by 141 Trp residues and 293 Tyr residues. A position of each Trp and Tyr in IgM antibody can be observed in Figure 5.9. Like in human IgG, most of the Trp residues are located in the binding pockets of the antibody.
Preliminary measurements
Initially, the samples of IgG and IgM have been examined by steady-state and fluorescence time-resolved spectroscopies. Figure 5.10 illustrates fluorescence and absorption spectra of IgG and IgM. Likewise for IgG antibody, absorption band of IgM is centred at 280 nm. Fluorescence emission of IgM overlaps with IgG spectra and has the emission maximum at∼328 nm. The fluorescence quantum yield of human IgM is estimated to be 0.074 according to the Equation 5.1.
Figure 5.9:Solution structure of Human Immunoglobulin M by syn-chrotron X-ray scattering and molecular graphics mod-elling.Blue: Trp residues.Red: Tyr residues.
Results obtained with time-resolved fluorescence depletion spectroscopy are reported in Figure 5.11. The relaxation time determined by fitting with double-exponential decay function 5.4 is foundτ1 '0.14±0.15ps, which is comparable with the result obtained for IgG antibody.
Figure 5.10: Fluorescence and absorption spectra of IgG (black) and IgM (red).
−5 0 5
−0.08
−0.07
−0.06
−0.05
−0.04
−0.03
−0.02
−0.01 0
Time−delay, ps
Fluorescence depletion, a.u.
−5 0 5
−0.08
−0.07
−0.06
−0.05
−0.04
−0.03
−0.02
−0.01 0
Time−delay, ps
Fluorescence depletion, a.u.
human IgM human IgG
Figure 5.11: Time-resolved fluorescence depletion traces of IgG and IgM.
Optimization aiming to increase IgG/IgM fluorescence depletion ratio Steady-state spectroscopy alone does not allow to distinguish IgG and IgM be-cause of the strongly overlapping spectra of absorption/fluorescence. Moreover, time-resolved spectroscopy shows similar excited-state dynamics of IgG and IgM, measured within 10 ps time window. The further step consists in the extension of optimal control strategy in deep UV for this pair of antibodies. We applied single-objective optimization, as it appears to be less sensitive to the noise issue. The optimization objective is define as the ratio of IgG/IgM, which is intended to be maximized: J(τ) = δδIgG(τ)
IgM(τ)+ε +αδIgG. The experimental setup used here was identical as for the previous experiment.
One of the obstacle in this experiment is the noisy signal from IgM, which can be explained by the formation of aggregates and consequent scattering. Figure 5.12 shows the result obtained with an optimal pulse at a fixed time delay obtained during the optimization. We do see some differences in fluorescence depletion signals, however the effect of discrimination by optimal pulse shape, illustrated in the Figure5.12, is small. The observed discrimination of IgG and IgM is in the order of∼1%, which is equal to 2.8σ. Thereby, a further work is needed to improve the discrimination.
Figure 5.13 shows X-FROG traces obtained for immunoglobulins IgG and IgM.
Similarly as with the serum proteins albumin and IgG, the resulting pulse contains multiple subpulses with different frequency distribution: 196cm−1, 98cm−1, 173 cm−1, 227cm−1, temporally spaced on 170 fs, 340 fs, 193 fs, 147 fs, as assessed by Fourier transforming the optimal UV intensity envelope. We also observe a similar trend with positive chirp.