Time Resolved Photoelectron Spectroscopy of Thioflavin T Photoisomerization; A Simulation Study

Abstract

The excited state isomerization of thioflavin T (ThT) is responsible for the quenching of its fluorescence in a non-restricted environment. The fluorescence quantum yield increases substantially upon binding to amyloid fibers. Simulations reveal that the variation of the twisting angle between benzothiazole and benzene groups (ϕ₁) is responsible for the sub-picosecond fluorescence quenching. The evolution of the twisting process can be directly probed by photoelectron emission with energies ε ≥ 1.0 eV before the molecule reaches the ϕ₁-twisted configuration (~300 fs).

1 Introduction

Amyloid fibrils are insoluble filaments formed by proteins with ordered, fibrous structures while share a common series of biophysical and structural properties.^1,2 The accumulation of amyloid fibrils in organism tissues can lead to a number of diseases, such as Alzheimer's and Parkinson's diseases and type II diabetes.^2–7 Detailed information about the fibrillation/aggregation dynamics of amyloid fibrils is required to reveal the fibrillation mechanism, and would be helpful to pathologically overcome these diseases. Traditional analytical techniques, such as X-ray diffraction are impractical for in-vivo investigations. Thioflavin T (ThT) (see Fig. 1), a benzothiazole dye has been used to detect the formation of amyloid fibrils, since it does not interact significantly with folded or unfolded protein monomers and its fluorescence quantum yield is enhanced by about 3 orders of magnitude upon binding to amyloids.⁸

Figure 1.

Geometry of thioflavin T. Twisting in the excited state occurs along ϕ₁ (around C7-C12 single bond) and ϕ₂ (around C15-N18).

Even though the use of ThT as an amyloid sensor has been known for over 50 years,^9–11 the photophysics associated with its fluorescence quenching and the binding mechanism with amyloid fibrils are not well understood. Recent experiments showed that ThT monomer binds to β-sheets such that its long axis is perpendicular to the β-strands.¹⁰ The molecular rotor mechanism supported by both experiments and potential energy surface calculations is the most likely explanation of the fluorescence enhancement upon binding.^8,12 It assumes that the fluorescence is caused by a twisting of the benzothiazole and dimethylaniline groups around the C–C single bond in its first excited state. As shown in Fig. 1, there are two possible twisting coordinates around the C–C and C–N single bonds, corresponding to the dihedral angles between the benzothiazole/benzene (ϕ₁) and benzene/dimethylamino (ϕ₂) groups. According to the potential energy surface calculation of Stsiapura et al.,¹² the rotation barrier for ϕ₂ is 4 times higher than that of ϕ₁, ϕ₁ is thus the more likely candidate. In the ground state S₀, the potential energy minimum is at ϕ₁ ~ 37°, which is a consequence of the π-electron conjugation and the steric effect between the benzothiazole methyl group and the benzene H atom. However, in the first excited state S₁, which is responsible for the fluorescence, the stable configuration has ϕ₁ ~ 90°. Stsiapura et al. proposed that the molecule is photoexcited to its first Franck-Condon locally excited (LE) state and then exhibits an ultrafast twisting to its excited state minima, during which charge transfer to the benzothiazole group occurrs.¹² The fluorescence from the twisted intra-molecular charge transfer (TICT) state is very weak.

The LE → TICT ultrafast excited state dynamics is affected by the friction due to solvent, thus the fluorescence lifetime and quantum yield strongly depend on solvent viscosity or the rigidity of the microenvironment when binding to amyloid fibrils.^13,14 Sub-picosecond fluorescence lifetime in low-viscosity solutions extends to tens of picoseconds in highly viscous solutions.^8,15,16 Huppert el al. found a linear decrease of the excited state decay rate with solvent viscosity.¹⁷ There is little difference between steady state emission maxima of ThT in polar and nonpolar solvents.^8,16

In this paper, we present a simulation of the twisting isomerization dynamics of ThT in S₁ in aqueous solution and how it may be probed by time resolved photoelectron spectra (TRPES). TRPES has been proven to be an valuable technique for the analysis of the photophysics and photochemistry of molecules lie in their excited states.^18–20 Recent developments of photoelectron techniques in liquid phase had extended TRPES to solutions.^21–23 TRPES can reveal the details of the excited state isomerization and the fluorescence quenching mechanism of ThT. We find that the twisting angle ϕ₁ can be directly revealed by the kinetic energy of the high energy (≥1.0 eV) photoelectrons before it reaches its TICT state. Details of isomerization dynamics and photoelectron simulation protocol are given in Sec. 2. The results are presented in Sec. 3 and summarized in Sec. 4.

2 Simulation Protocol

2.1 Isomerization dynamics

Excited state isomerization dynamics is performed using ab-initio MD trajectories implemented in the Newton-X package.^24,25 In preparing the initial states for the dynamics simulation, nuclear motions are treated as harmonic; The initial coordinates and velocities are generated by random sampling according to the Wigner distribution for quantum harmonic oscillators.^24,25 We used time dependent functional theory (TDDFT) with the B3LYP functional and DZP basis set implemented in the TURBOMOLE package²⁶ to describe the electronic structure. TDDFT is fast and analytical excited state gradients are available, TDDFT with nonlocal hybrid density functionals has been successfully used on the excited state twisting dynamics in good agreement with experiments.^27–30

36 initial configurations of the first excited state are prepared for the 800 fs excited state dynamics simulation with 1 fs time step. The TDDFT dynamics break down when the molecule encounters a geometry that involves multireference character.²⁸ These events are rare for times shorter than 500 fs,³¹ we thus limited our study to this time regime.

2.2 Photoelectron transition probability

In a time-dependent photoelectron process, the molecule is pumped into an excited state and after a variable time delay t is ionized by a short probe pulse with frequency hω_p.¹⁹ It contains a single time delay together with the photoelectron energy provides a two-dimensional (2D) representation of the signals. Allowing the system to interact with a sequence of ultrafast pulses could extend this technique to higher dimensions.³² We assume that the ionization process is fast and vertical, i.e., geometry is preserved during electron ejection. The electronic wave function of the ionized system is written as $\mid {\Psi }_{\alpha }^{N-1}{\Psi }^{\eta }\rangle$, where η represents the ejected electron and N is the total number of electrons in the initial system. Within the dipole approximation, the photoelectron transition probability from the core state C is written as^19,33–35

$$A_C^{N\to N-1}\left(t\right)\propto \sum _{\eta }{A}_{\eta C}^{N\to N-1}$$ (1)

where,

$$A_{\eta C}^{N\to N-1}\propto {\mid \langle {\Psi }^N\mid \widehat{\overrightarrow{\mu }}\mid {\Psi }^{N-1}{\Psi }_C^{\eta }\rangle \mid }^2\times \delta \left(\hslash {\omega }_p+V^N\left(\overrightarrow{R}\left(t\right)\right))-V^{N-1}\left(\overrightarrow{R}\left(t\right)\right)-\epsilon \left(\eta \right)\right)$$ (2)

here $\widehat{\overrightarrow{\mu }}$ is the electronic dipole operator, V^N and V^N–1 are the potential energies of the N and (N – 1)-electron systems, respectively, corresponding to the nuclear configurations $\overrightarrow{R}\left(t\right)$. ε(η) is the photoelectron kinetic energy. The transition dipole matrix elements can then be written as,

$$\begin{array}{cc}\hfill {\mid \langle {\Psi }^N\mid \widehat{\overrightarrow{\mu }}\mid {\Psi }_C^{N-1}{\Psi }^{\eta }\rangle \mid }^2& ={\mid \sum _{a,b}\langle {\Psi }^N\mid {\widehat{c}}_a^{†}{\widehat{c}}_b\mid {\Psi }_C^{N-1}{\Psi }^{\eta }\rangle \langle {\Psi }_a\mid \widehat{\overrightarrow{\mu }}\mid {\Psi }_b\rangle \mid }^2\hfill \\ \hfill & ={\mid \sum _p\langle {\Psi }^N\mid {\widehat{c}}_p^{†}\mid {\Psi }_C^{N-1}\rangle {\overrightarrow{\mu }}_{p\eta }\mid }^2\hfill \end{array}$$ (3)

where a and b label bound and scattering orbitals, respectively. We ignore the polarization of the probe beam and the angular distribution of photoelectrons, and replace the dipole matrix element ${\overrightarrow{\mu }}_{p\eta }$ by its rotationally averaged value μ_η, the transition dipole matrix is then factorized into a term governed by the difference between electronic structures of the N-electron initial state and (N – 1)-electron final state, and a term associated with the photoelectron kinetic energy, which we assumed to be a constant,^19,36

$${\mid \langle {\Psi }^N\mid \widehat{\overrightarrow{\mu }}\mid {\Psi }_C^{N-1}{\Psi }^{\eta }\rangle \mid }^2={\mid \sum _p\langle {\Psi }^N\mid {\widehat{c}}_p^{†}\mid {\Psi }_C^{N-1}\rangle \mid }^2{\mu }_{\eta }^2$$ (4)

The time resolved photoelectron signal for a given core state is obtained by summing over all the final states with the selected kinetic energy ε,

$$A_C^{N\to N-1}(\epsilon ,t)\propto {\mid \sum _p\langle {\Psi }^N\mid {\widehat{c}}_p^{†}\mid {\Psi }_C^{N-1}\rangle \mid }^2{\mu }_{\eta }{\left(\epsilon \right)}^2\rho \left(\epsilon \right)\delta \left(\hslash {\omega }_p+V^N\left(\overrightarrow{R}\left(t\right)\right))-V^{N-1}\left(\overrightarrow{R}\left(t\right)\right)-\epsilon \left(\eta \right)\right)$$ (5)

where ρ(ε) is the density of states of scattered electrons. The product μ_η (ε)²ρ(ε) in the low energy region only depends weakly on the kinetic energy, since μ_η (ε)² decreases and density of states ρ(ε) increases,³⁷

$$A_C^{N\to N-1}(\epsilon ,t)\propto {\mid \sum _p\langle {\Psi }^N\mid {\widehat{c}}_p^{†}\mid {\Psi }_C^{N-1}\rangle \mid }^2\delta \left(\hslash {\omega }_p+V^N\left(\overrightarrow{R}\left(t\right)\right))-V^{N-1}\left(\overrightarrow{R}\left(t\right)\right)-\epsilon \left(\eta \right)\right).$$ (6)

The total signal is finally obtained by summing over the accessible core states C,

$$A^{N\to N-1}(\epsilon ,t)=\sum _C{A}_C^{N\to N-1}(\epsilon ,t).$$ (7)

3 Results and Discussion

3.1 Geometries and electronic structure

The geometry and electronic structure of the states involved in the evolution are calculated on the (TD)DFT/B3LYP level with 6-311++G(d,p) basis set implemented in the Gaussian 09 package.³⁸ The optimized geometries in its ground and the first excited states are shown in Fig. 2. At the ground state minima, the molecule is twisted with ϕ₁ = 37.6°, and the benzene and the dimethylamino are co-planar with ϕ₂ = 0.0°. The twisted conformation in the ground state is due to the steric interaction between the N–CH₃ group and its nearby benzene H atom. The molecule twists further to ϕ₁ = 91.7° and ϕ₂ = 11.6° in the first excited state, the long axis also bent here. We define the bending of long axis with the angle α between the C7–C12 single bond and the benzthiazole plane as shown in Fig. 2 (b).

Figure 2.

Optimized (a) ground state (S₀) and (b) first excited state (S₁) structures. The dimethylaniline in the ground state minimum (R₀) is planar with ϕ₂ = 0.0°. The long axis of the molecule is straight in R₀ and is bent with an angle of α = 24.6° in R₁. The dimethylaniline group is twisted with ϕ₂=11.6° in R₁.

Fig. 3 depicts the frontier orbitals and natural transition orbitals (NTO)³⁹ of the ThT first electronic transition in its ground and first excited states minima. In the ground state minimum (left panel, R₀), the compositions of the HOMO/hole or LUMO/electron orbitals are almost the same, indicating that the first electronic excitation is dominated by the HOMO-LUMO transition. The transition has clear π-π* character, where all the orbitals presented are delocalized across the molecule, strong π conjugation effect is expected although the structure deviated from planar conformation. The first electronic excitation at the excited state minimum (right panel, R₁) is also dominated by the HOMO-LUMO transition. However, both HOMO and LUMO orbitals are now localized either in the dimethylaniline or the benzothiazole group, indicating considerable charge transfer from dimethylaniline to benzothiazole during the photoexcitaion. The π conjugation is broken at the perpendicular (ϕ₁ ~90°) configuration. In the HOMO of R₁, the state remains delocalized in the dimethylaniline group although the geometry deviates planar configuration.

Figure 3.

0.02 au. isosurfaces of the frontier orbitals (HOMO/LUMO) and natural transition orbitals (HOLE/ELEC) of ThT at its ground state (R₀)and first excited state (R₁) optimized goemetries.

3.2 Excited State Isomerization Dynamics

Previous potential energy surface calculations showed no barrier from R₀ to R₁ for the S₁ state.¹² This implies the possible ultrafast evolution from the dipole allowed (strong fluorescence) configuration to a dipole forbidden (non fluorescence) twisted configuration.¹²

Fig. 4 shows the time dependent geometry and electronic properties averaged over the trajectories used in the simulation. Panel (a) displays the evolution of the twisting angles and the bending angle. ϕ₁ varies from 37° at t = 0 fs to ~100° in 400 fs. ϕ₂ also varies significantly, initially it is in the range -45~30°, changing to 15~25° after 400 fs. As found in previous calculations,^8,12 the S₁ state potential energy curve along ϕ₂ has a ~3000 cm^–1 barrier at ϕ₂ = ±60°, which is much higher than that of ϕ₁ (~ 700 cm^–1). The dimethylaniline group is not planar in the S₁ potential energy minima as shown in Fig. 2 (b), where ϕ₂ = 11.6°. ϕ₂ varies by ~10° after 400 fs. We conclude that the variation of ϕ₂ during the evolution is the consequence of the random choice of nuclear coordinates and velocities, which drive ϕ₂ to oscillate in the potential energy well with |ϕ₂| < 50°. The evolution of ϕ₁ and ϕ₂ are related to their vibrational modes: the 96.4 cm^–1 (at R₀) twisting mode between benzothiazole and benzene for ϕ₁ and the 85.8 cm^–1 (at R₀) twisting mode between benzene and dimethyamino for ϕ₂. The molecule bends from straight to 20~25° after 400 fs evolution, and the bending angle α continues increase thereafter. The slower variation of α is the consequence of the fact that it is related to the 32.2 cm^–1 (at R₀) bending mode.

Figure 4.

Time evolution of (a) twist angles and bending angle, (b) Mulliken charge populations in various regions, (c) energy gaps between S₁ and S₀ and (d) S₁ ← S₀ oscillator strengths. All pannels are averaged over 29 trajectories.

The Mulliken charge distribution on the three parts of the molecule is shown in Fig. 4 (b). This reveals a substantial charge transfer from dimethylamino to benzothiazole, where the charge population on the benzene group only varies slightly. The charge transfer is caused by electronic localization on benzothiazole during the twisting as shown in Fig. 3. Panel (c) shows that the energy gap reduces from 3.0 eV to 1.0 eV in 500 fs, and does not lead to degeneracy of these states. The oscillator strength of the S₁-S₀ transition shown in panel (d) rapidly decreases from 0.8 to below 0.2 in 100 fs, and further reduces to less than 0.1 after 300 fs. This suggests that in unrestricted environments, the sub-picosecond fluorescence quenching is mainly due to the ϕ₁ twisting. ThT evolves to a dipole forbidden state in 400~500 fs, before encountering the conical intersection between S₀ and S₁.

3.3 Time-resolved Photoelectron Spectra

TRPES can monitor the evolution of electronic structure in the excited state. We have simulated the TRPES signals of ThT induced by a resonant pump that suddenly excites the molecule from S₀ to S₁ followed by a 125 nm (9.93 eV) UV ionization probe after a variable time delay t. We tunned the probe frequency so that only the first few lowest ionized states are accessible (~2.5 eV higher than the ionization threshold). TRPES were calculated at 10 fs intervals. Core states with energies higher than -10.0 eV are taken into account in the summation in Eq. 7.

Fig. 5 depicts the time and energy resolved TRPES spectrum for a single trajectory. Vertical slices with t = 0, 100, 200 and 400 fs are shown in the top panels. The peaks are assigned to various ionization channels. The strongest features appear in the low electron energy regime at short decays. This indicates that higher excited states of the ionized molecule are generated in this regime. Since the photoelectron energy is related to the difference between the probe frequency and ionization potential for the ionization channel, the lower energy region corresponds to higher excited states in the ionized molecule. The t = 0 fs slice is dominated by channels D₄ and higher. The weaker features at 2.93, 2.03, and 1.42 eV correspond to channels D₀, D₁, and D₂, respectively. In all channels the signal are dominated by the ionization of the outmost electron in the S₁ state, which is an open-shell singlet with the same ionization probability for α and β electrons. We have only calculated the ionization probability from α orbitals in S₁, which can be factorized into spin polarized contributions from final states with different spins,

$$\begin{array}{cc}\hfill A_{C,p=HOMO}& ={\mid \langle {\Psi }^N\mid {\stackrel{‒}{c}}_{p=HOMO}^{†}\mid {\Psi }^{N-1}\rangle \mid }^2\hfill \\ \hfill & ={\mid \langle {\Psi }_{\alpha }^N\mid {\Psi }_{\alpha }^{N-1}\rangle \mid }^2{\mid \langle {\Psi }_{\beta }^N\mid {\stackrel{‒}{c}}_{p=HOMO}^{†}\mid {\Psi }_{\beta }^{N-1}\rangle \mid }^2\hfill \\ \hfill & ={\mid S_{\alpha }\mid }^2{\mid S_{\beta }\mid }^2\hfill \end{array}$$ (8)

Here S_α and S_β are the overlap matrices between the α spin orbitals in S₁ with the α and β spin orbitals in D_n, respectively. As shown in Fig. 6, the β states of the ionized molecule (right) have the same spatial distribution with the N-electron system (left), which results in a large S_β value near 1. However, the α states of S₁ (middle) has different symmetry than the N-electron system, although in both systems the states are delocalized among the whole molecule, the overlap S_α = 0.015, which is much smaller than S_β ~ 1. For channels D₁, D₂ and D₄, where the final states are the first, second, and fourth excited states of the ionized molecule, respectively, these three final states have considerable contribution from 75α → 76α transition in the configuration interaction (CI) expansions. S_β has the same value in transition D₀ ← S₁, but S_α is much larger since the 76α state has similar spatial distribution and symmetry compared with the 76-th unionized state. Hence the intensities of the D₁, D₂ and D₄ channels only depend on the CI expansion coefficient of 75α → 76α transition. D₄ has the most 75α → 76α component and is the strongest.

Figure 5.

TRPES for a single trajectory. Top, vertical slices at t = 0, 100, 200, and 400 fs. Peaks are assigned to various ionization channels as marked.

Figure 6.

0.02 au. isosurfaces the N-electron (left), (N-1)-electron α (middle), and (N-1)-electron β frontier orbitals at t = 0 fs for the same trajectory used in Fig. 5.

The time slices in Fig. 5 show that the D₀ ← S₁ channel has similar intensities in the first 200 fs and decays a half at t = 400 fs. At t = 200 fs as shown in Fig. 7, all the occupied orbitals are localized and the LUMO (76) state is delocalized. The S₁ excitation is dominated by the 75-76 transition. For D₀ ← S₁, the state pairs 72-73β, 73-74β, 74-72β have similar symmetry and spatial distribution, although their orders are changed. This results in a large S_β ~ 1. Due to the delocalized distribution of state 76, the α overlap S_α = 0.012, comparable with that at t = 0 fs. However, all the channels ending in excited ionized states decay rapidly. This is a consequence of state localization caused by twisting during time evolution. At 200 fs, all the excited ionized states accessible by the ionization probe only contain β transitions, which result in S_β ~ 0.

Figure 7.

Same as Fig. 6 except t = 200 fs.

Fig. 8 (a) shows that the average number of states accessible by the ionization probe decreases from 7~8 at t = 0 fs to 5~6 in 100 fs, and further decreases to 3-4 after 300 fs. The integrated photoelectron yield shows similar behavior, it decays from 0.25 at t = 0 fs to 0.04 at t = 100 fs, and further decays to 0.01 after 400 fs. The TRPES features shown in Fig. 9 can be divided into three groups. In the first 100 fs, the three groups correspond to electron energies in the range 2.0~3.0, 1.0~2.0, and 0~1.0 eV. Strong signals for the low energy group in the first 100 fs are mainly contributed by the ionization channel D₄ ← S₁ as shown in Fig. 8 (d) and Fig. 10 (a)-(c). The ionization to D₄ rapidly decays to near zero after 100 fs. The features with electron energies 1.0~2.0 eV are mainly contributed by the ionization channels D₁ ← S₁, D₂ ← S₁ and D₃ ← S₁. These features also decay rapidly to near zero after 100 fs. The intensity decay is accompanied by decreasing of electron energies, makes these features can appear in the lower energy region. For instance, there is a significant contribution from channel D₃ ← S₁ at t = 200 fs and t = 400 fs, as shown in Fig. 10. The high energy peak intensities do not decay as fast as those of the lower energy groups. These come from channel D₀ ← S₁, with intensities only decays a half from ~0.02 at t = 0 fs to ~0.01 after 400 fs. This is the consequence of the similar electronic configuration of D₀ and S₁ states. The photoelectron energies decrease from 2.5~3.0 eV at t = 0 fs to 1.4~2.2 at t = 400 fs. Moreover, as shown in Fig. 10, the energy distribution becomes broader during time evolution. This can be rationalized since the trajectories are initiated from random nuclear velocities and coordinates near R₀, as the excited state gradient drives nuclei evolving, trajectories with different initial conditions might apart from each other on the potential energy surface, hence

Figure 8.

Time evolution of (a) The number of ionized states accessible by the 125 nm probe, (b) The energy integrated photoelectron probabilities, (c) high electron energy (E≥1.0 eV, solid) and D₀ ← S₁ probabilities (dashed), and (d) low electron energy (E≤1.0 eV, solid) and D₄ ← S₁ probabilities (dashed). All figures are averaged over 29 trajectories.

Figure 9.

Time resolved photoelectron spectra averaged over 29 trajectories. The signals are shown on a nonlinear scale S̄ = arcsinh(CS), where C is a constant making S̄ near 1, for better visibility.

Figure 10.

Solid lines: Slices of Fig. 9 at various times. Dashed lines: Ionization channel resolved spectra.

The correlation scatter plot of the D₀ photoelectron energy and the ϕ₁ twisting angle is shown in Fig. 11. In the early stage of the evolution (i.e. t ≤ 100 fs), the ε(D₀)–ϕ₁ pairs locate near the line ε(D₀) = –0.258ϕ₁ + 9.71, with an uncertainty Δϕ₁ = ±5° for a specific D₀ energy. After 200 fs, the D₀ energies increases as ϕ₁ apart from 90°, which corresponds to the S₁ state minima. Between 200-300 fs, there is also a linear relation ε(D₀) = 0.258ϕ₁ – 21.07, with an uncertainty Δϕ₁ = ±12°. The uncertainty in determining ϕ₁ twisting angles through the high energy region peak positions comes from the perturbation by other geometry parameters, such as ϕ₂ and α, etc. As shown in Fig. 4 (a), ϕ₂ varies on the same time scale of ϕ₁, but α increases much slower. That means in the early stage of evolution (t ≤ 200 fs), the uncertainty is mainly attributed to the ϕ₂ twisting angle. The correlation between ε(D₀) and ϕ₁ is weaker at times longer than 250 fs.

Figure 11.

Correlation between the D₀ ← S₁ electron energies (ε(D₀)) and ϕ₁ twising angles in varioius time intervals. Solid lines represent the linear correlation at the early stage of evolution.

4 Conclusions

Using excited state isomerization dynamics simulation for ThT, we had calculated the time resolved photoelectron spectra for 500 fs time delays. The calculated fluorescence intensity decays by two orders of magnitude upon ϕ₁ twisting within 400 fs, indicating that the sub-picosecond fluorescence decay in unrestricted environments is mainly due to the twisting between benzothiazole and benzene groups. The subpicosecond fluorescence quenching of ThT in restriction free environment does not necessary indicate an internal conversion from S₁ to S₀. Photoelectron signals originate from channels from S₁ to excited ionized states decays in 100 fs due to the localization of wavefunctions caused by twisting. The D₀ ← S₁ feature decays much slower. The twisting angle ϕ₁ is related to the photoelectron spectra via two linear relations in the early stage of evolution, where the molecular twisting can be directly probed by the photoelectron signals with ε ≥ 1.0 eV.