A method for analyzing molecular vibration and hydrogen bond network

Abstract

This invention relates to the field of spectroscopic analysis technology, specifically to a method for molecular vibration and hydrogen bond network analysis. This method involves acquiring terahertz absorption spectra of samples at different temperatures; acquiring Raman scattering spectra of samples; constructing a unit cell model of the target peptide and calculating its theoretical vibrational spectrum; obtaining the evolution of frequency offset parameters and full width at half maximum (FWHM) parameters with temperature, and performing mathematical fitting; comparing the terahertz absorption and Raman scattering spectra with the theoretical vibrational spectrum to identify the molecular vibrational modes corresponding to each characteristic absorption and scattering peak; performing mode decomposition on the calculated multiple infrared active vibrational modes to quantitatively distinguish the contribution ratios of intermolecular translation, intermolecular rotation, and intramolecular vibration in each vibrational mode; and analyzing the relative changes in bond length and bond angle of intermolecular hydrogen bonds within the target peptide unit cell. This invention systematically analyzes the vibrational behavior of peptide molecules, especially KLVFF peptides.

Description

Technical Field

[0001] This invention relates to the field of spectroscopic analysis technology, and more specifically, to a method for analyzing molecular vibrations and hydrogen bond networks. Background Technology

[0002] Protein folding, considered the "second genetic code," is a key physical process driving the formation of specific three-dimensional structures through intermolecular interactions. The pathogenesis of Alzheimer's disease (AD) is closely related to the misfolding and aggregation of amyloid-beta (Aβ). Although different amyloid proteins lack significant homology in their polypeptide sequences, the formation of amyloid aggregations is often closely associated with a 5-15 amino acid aggregation-prone region (APR). Aβ protein, a biomarker of AD, originates from the enzymatic processing of amyloid precursor protein (APP) and typically contains 40-42 amino acids, with the hydrophobic core sequence KLVFF identified as its key APR.

[0003] Currently, numerous studies have focused on KLVFF, but most utilize it as a coupling agent, transport carrier, or inhibitor. However, in-depth analysis of KLVFF, particularly elucidating the dynamic evolution of its hydrogen bond network from the perspective of intermolecular interactions, remains significantly insufficient. This is primarily due to the bandwidth limitations of existing THz-TDS technology. Therefore, overcoming bandwidth constraints and systematically acquiring key vibrational mode parameters (such as characteristic peak positions and intensity variations) and hydrogen bond length and angle evolution patterns of KLVFF over a wide frequency range is crucial for revealing the core mechanism by which the hydrogen bond network drives and regulates the early aggregation behavior of Aβ protein from the perspective of intermolecular interactions.

[0004] In view of this, the present invention is hereby proposed. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing molecular vibrations and hydrogen bond networks, which can systematically resolve the vibrational behavior of polypeptide molecules, especially KLVFF polypeptides.

[0006] In order to achieve the above-mentioned objectives of the present invention, the following technical solution is adopted: A method for analyzing molecular vibrational and hydrogen bond networks includes the following steps: (a) Using synchrotron broadband terahertz spectroscopy, terahertz absorption spectra of the target peptide sample at different temperatures were collected in the frequency range of 2–18 THz to obtain temperature-dependent terahertz fingerprints; Raman spectroscopy was used in the wavenumber range of 0–1800 cm⁻¹. -1Within the specified range, Raman scattering spectra of the target peptide sample are collected to obtain Raman fingerprints; based on solid-state density functional theory, a unit cell model of the target peptide is constructed, and its theoretical vibrational spectrum is calculated. (b) Quantitatively analyze the temperature-dependent terahertz fingerprint spectrum, extract the frequency offset parameter and full width at half maximum (FWHM) parameter of at least one characteristic absorption peak, obtain the evolution law of the frequency offset parameter and the FWHM parameter with temperature, and perform mathematical fitting on the evolution law to obtain characteristic coefficients that quantitatively describe the molecular vibrational thermodynamic behavior. (c) Compare the terahertz absorption spectrum and the Raman scattering spectrum with the theoretical vibrational spectrum to identify the molecular vibrational modes corresponding to each characteristic absorption peak and scattering peak; perform mode decomposition on the calculated multiple infrared active vibrational modes to quantitatively distinguish the contribution ratio of intermolecular translation, intermolecular rotation and intramolecular vibration in each vibrational mode. (d) Based on the results of mode decomposition, the relative changes in bond length and bond angle of intermolecular hydrogen bonds in the unit cell of the target polypeptide are analyzed to reveal the deformation law of hydrogen bond network under different vibrational frequencies.

[0007] This invention systematically studied the KLVFF peptide, obtaining its terahertz absorption spectrum in the range of 2–18 THz, and combined it with Raman spectroscopy in the range of 0–1800 cm⁻¹. -1 The characteristic peaks within the wavenumber range collectively reveal the vibrational properties of the molecule. Combined with temperature-dependent experimental results, a comprehensive explanation of the molecular vibrational behavior was provided through Bose-Einstein fitting and FWHM analysis of the characteristic peak frequency shifts. Based on THz experiments and theoretical simulations, the THz fingerprint of the KLVFF peptide was characterized and interpreted from the perspective of intermolecular interactions. Using a Gaussian-based peak fitting mathematical method, the fitting results were found to be highly consistent with the experimental spectra and correspond well with the theoretically calculated vibrational modes, thus more accurately determining the characteristic vibrational modes of the absorption peaks.

[0008] This invention employs temperature-dependent synchrotron radiation broadband terahertz (SRBB-THz) spectroscopy to acquire typical fingerprints and spectral evolution data of KLVFFs from 30 K to room temperature within a wide frequency range of 2–18 THz. Furthermore, the Raman spectra of KLVFFs in the range of 0–1800 cm⁻¹ were measured using a LabRAMHR HR Evolution spectrometer. -1By comparing the wavenumber range of Raman spectra, richer vibrational information was obtained. Furthermore, for the THz vibrational spectra, the frequency offset and full width at half maximum (FWHM) parameters of the characteristic frequencies as a function of temperature were extracted to quantitatively analyze the molecular vibrational modes.

[0009] By combining solid-state density functional theory (ss-DFT) calculations, the correlation between the characteristic absorption peaks of KLVFF and specific molecular vibrational modes was analyzed in depth, and the vibrational composition of its infrared activity was quantitatively determined by decoupling vibrational modes.

[0010] Furthermore, by statistically analyzing the relative changes in hydrogen bond length and angle, the vibrational characteristics of hydrogen bonds between KLVFF molecules were clarified, providing important experimental and theoretical basis for understanding the early aggregation mechanism of Aβ protein at the atomic level.

[0011] Temperature-dependent terahertz fingerprint spectrum refers to the spectral set composed of terahertz absorption spectra collected at multiple different temperature points, and the evolution of the characteristic peak position, peak shape, and intensity in the spectral set as a function of temperature.

[0012] Furthermore, the target polypeptide sample includes: KLVFF polypeptide.

[0013] Furthermore, the different temperatures mentioned in step (a) range from 30 to 300 K, and terahertz absorption spectra are collected every 10 to 20 K.

[0014] Furthermore, the evolution law of the frequency offset parameter in step (b) includes: the frequency offset parameter of the characteristic absorption peak at 8.05 THz does not change with temperature within the temperature range, exhibiting the characteristic of a fixed frequency.

[0015] Further, the mathematical fitting in step (b) includes: fitting the frequency offset parameter using a Bose-Einstein model to obtain the characteristic temperature Tc and coefficient A; and fitting the half-width at half-maximum parameter using a quadratic polynomial model to obtain the quadratic coefficient a, the linear coefficient b, and the constant term c.

[0016] Furthermore, in step (c), identifying the molecular vibrational modes corresponding to each characteristic absorption peak and scattering peak includes comparing the characteristic peak positions in the experimental spectrum with the theoretically calculated spectrum to determine whether they belong to one or more of collective vibration, group rocking, group twisting, group stretching, or group out-of-plane vibration.

[0017] Furthermore, the modal decomposition of multiple infrared active vibration modes in step (c) includes: We performed quantitative calculations on 62 infrared active vibrational modes in the frequency range of 2–18 THz, and statistically analyzed the percentage contributions of intermolecular translation, intermolecular rotation, and intramolecular vibration in each mode.

[0018] Furthermore, step (d) analyzes the relative changes in the bond lengths and bond angles of intermolecular hydrogen bonds, including: The percentage changes in bond length and bond angle of the six intermolecular hydrogen bonds within the unit cell in each vibrational mode were statistically analyzed, and the distribution spectrum of hydrogen bond deformation as a function of frequency was plotted.

[0019] Furthermore, among the six intermolecular hydrogen bonds, the bond length and bond angle of the first hydrogen bond HB-1 and the sixth hydrogen bond HB-6 have significantly higher variation ranges than the other four hydrogen bonds, and they have been identified as key kinetic hub sites regulating the conformational dynamics of the polypeptide.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention quantifies the vibrational composition of 62 infrared vibrational modes. The results show that within modes 0–20 (before 7.8 THz), only the proportion of frequency-shifting vibrations fluctuates, with changes within 1%. After mode 20, the proportions of each component remain constant. This pattern reveals the complex dynamic characteristics of the collective vibration of KLVFFs in the terahertz band and also reflects the relatively rigid structure of the molecules. Terahertz waves exhibit high sensitivity to different intermolecular hexagonal bonds (HBs) and display different characteristic responses. In modes <25, significant HBs bond length stretching is observed, and the vibrational modes show strong vibrational intensities, which is related to the preference for translational motion along the crystal's X-axis in these modes. In modes 25–45, significant synergistic changes in HBs bond length and bond angle are observed, reflecting a flexible adjustment of the overall molecular configuration within the hydrogen bond network. This partitioning phenomenon provides direct kinetic evidence for the combined rigidity and flexibility of the hydrogen bond network in the crystal. Furthermore, research indicates that HB-1 and HB-6 may be important sites driving relative orientation or local lattice rearrangement between peptide chains, while the remaining four hydrogen bonds are the main intermolecular forces maintaining their molecular conformation. These analyses demonstrate that molecular geometry is significantly regulated by intermolecular HB interactions. This study enriches our understanding of intracrystalline molecular dynamics and intermolecular interactions, fills a theoretical gap in the role of intermolecular interactions in KLVFF at the THz band in promoting Aβ misfolding, and provides a new perspective for understanding the aggregation behavior of Aβ proteins. It is expected to provide stronger theoretical support for research in related fields and offer new ideas and strategies for treating Alzheimer's disease (AD). Attached Figure Description

[0021] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0022] Figure 1 The images show the terahertz absorption and Raman scattering spectra of KLVFF at room temperature. (a) is the THz fingerprint spectrum of KLVFF in the range of 2–18 THz, and (b) is the THz fingerprint spectrum in the range of 0–600 cm⁻¹. -1 Raman scattering spectra in the wavenumber range; Figure 2 The THz spectrum of KLVFF in a three-dimensional coordinate system, with a temperature range of 30~300K; Figure 3 The curves showing the frequency shift of the KLVFF characteristic peak as a function of temperature and the Bose-Einstein fitting curves are shown. (a) is at 8.57 THz, and (b) is at 15.37 THz. The pink area represents the 95% confidence band. Figure 4 The graphs show the temperature-dependent full width at half maximum (FWHM) variation and quadratic fitting curves of KLVFF. (a) is the 8.57 THz mode, and (b) is the 15.37 THz mode. The pink area represents the 95% confidence band. Figure 5 The molecular structure, intracellular hydrogen bond distribution, and experimental and theoretical spectra of KLVFF are shown in (a) the molecular structure of KLVFF, including atomic labels and intermolecular hydrogen bond positions, but not directions; (b) the positions and directions of the six hydrogen bonds between two molecules within the unit cell; and (c) a comparison of experimental spectra (red curve at 300 K, blue curve at 30 K) and theoretical calculated spectra (black curve). The green bars represent theoretical vibrational modes, and the green vertical lines at the bottom indicate the 62 vibrational modes to be decoupled later. Figure 6 The diagram shows the vibration modes of KLVFF at key characteristic frequencies: (a) 2.53 THz, (b) 4.67 THz, (c) 6.64 THz, (d) 8.05 THz, (e) 8.57 THz and (f) 15.37 THz. Figure 7 The experimental and theoretical comparisons of the single-molecule structure and Raman spectrum of KLVFF are shown in (a) and (b) respectively. The experimental spectrum is shown in red and the theoretical calculated spectrum is shown in black. Figure 8The modal decomposition quantization results of 62 infrared active vibrational modes of KLVFF in the range of 2~18 THz are shown. (a) Intermolecular translation, (b) Intermolecular rotation, and (c) Intramolecular vibration. Figure 9 The results of hydrogen bond quantification analysis of 62 infrared active vibrational modes of KLVFF in the range of 2~18 THz include six intermolecular HBs. (a) shows the relative changes in bond length of intermolecular HBs, and (b) shows the relative changes in bond angle of intermolecular HBs. Detailed Implementation

[0023] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. However, those skilled in the art will understand that the embodiments described below are some embodiments of the present invention, but not all embodiments, and are only used to illustrate the present invention, and should not be regarded as limiting the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Where specific conditions are not specified in the embodiments, conventional conditions or conditions recommended by the manufacturer shall be followed. Where the manufacturers of reagents or instruments are not specified, they are all conventional products that can be purchased commercially.

[0024] Example (1) Terahertz spectroscopy and Raman spectroscopy Figure 1 The THz spectrum of the KLVFF peptide KLVFF in the frequency range of 2~18 THz and the spectrum in the frequency range of 0~600 cm⁻¹ -1 Raman spectra within the wavenumber range. Experimental results show that distinct absorption peaks are observed in the terahertz spectrum at multiple frequencies, including 6.64, 8.05, 8.57, 10.10, 12.47, and 15.37 THz; while in the Raman spectrum, significant absorption peaks are observed at 264.71, 407.65, 443.03, and 488.80 cm⁻¹. -1 Significant scattering peaks appeared at positions such as 155.13 cm⁻¹. Notably, this peak was observed at 155.13 cm⁻¹. -1 233.23 cm -1 With 407.65 cm -1The Raman peaks at certain frequencies are quite close to the absorption peaks at 4.67 THz, 6.64 THz, and 12.47 THz in the THz spectrum. However, theoretical analysis shows that these seemingly corresponding peaks actually originate from different molecular vibrational modes. This phenomenon also confirms the spectroscopic principle that molecules typically do not simultaneously exhibit Raman and infrared activity at the same frequency. The experimental results clearly demonstrate that the broadband THz fingerprint spectrum and Raman spectrum of KLVFF provide different spectral characteristics within the same frequency range. These complementary information collectively constitutes a richer molecular vibrational fingerprint.

[0025] (2) Temperature-dependent terahertz spectroscopy To further investigate the thermodynamics of KLVFF, the spectral evolution of KLVFF in the range of 2–18 THz was obtained, and the results are as follows: Figure 2 As shown, the THz spectra of KLVFF were measured at 15 K intervals within the temperature range of 30–300 K.

[0026] from Figure 2 As can be observed, the overall changes in the spectrum are not very significant. This is mainly because longer peptide chains contain more amino acids, resulting in a richer variety of vibrational modes. The coupling between these modes makes the spectrum complex and difficult to resolve. However, a low-frequency shift in characteristic frequencies with increasing temperature can still be observed. Taking the characteristic peak at 15.41 THz as an example, its position gradually shifts from 15.41 THz to 15.37 THz, which is essentially a redshift caused by increasing temperature. This phenomenon originates from the thermal expansion of the crystal lattice: as the temperature rises, the distance between atoms and molecules increases, leading to a decrease in the associated bonding elastic constant, thus causing the vibrational modes dependent on these bonds to shift to lower frequencies.

[0027] In addition to the classical description of how lattice thermal expansion alters the elastic constants of bonds, this transformation can also be explained using Bose-Einstein fitting, supplementing the commonly used analytical methods mentioned above. Two prominent characteristic peaks, 8.57 THz and 15.37 THz, were selected for curve fitting, and the fitted curve is shown below. Figure 3 As shown in Table 1.

[0028] Table 1. Bose-Einstein Fitting Parameters

[0029] from Figure 3As can be seen, in the lower temperature range, temperature changes are insufficient to cause significant changes in peak position. Only when the temperature reaches a sufficiently high level can phonon states be significantly excited, leading to a noticeable redshift. This is because the thermal energy must be high enough to elevate phonons to higher energy levels. During this process, anharmonic effects cause the energy differences between levels to gradually decrease, making transitions between phonons easier. This means that when absorbing or emitting energy, phonons are more likely to choose transition paths with smaller energy differences. Since these paths typically involve lower energy changes, the absorption or emission frequencies shift towards lower energies. From the perspective of the Bose-Einstein fit, the larger Tc value of the 15.37 THz mode indicates higher phonon energy, while the smaller Tc value of the 8.57 THz mode reflects its low-energy phonon characteristics. The difference in Tc values ​​quantifies the significant difference between the two modes, which is directly related to their response to temperature changes.

[0030] However, a somewhat anomalous phenomenon occurs at 8.05 THz: the frequency position remains constant within this temperature range. This may be because the interatomic potential energy experienced by the localized vibrations is closer to a harmonic potential. Even at high temperatures, atomic displacements remain primarily within the range of linear restoring forces, and changes in interatomic distance are insufficient to significantly alter the force constant of this particular vibrational mode. Therefore, the energy difference required to excite higher phonon states remains essentially constant, meaning the critical temperature for significantly exciting phonon states has not been reached.

[0031] Meanwhile, the fitting parameter A is likely related to the degree to which a particular mode depends on specific intermolecular and interatomic interactions. Specifically, the 8.57 THz mode has a large A value of 4.667, exhibiting a significant frequency change with increasing temperature; while the 15.37 THz mode, although having a smaller A value of 2.218, results in a relatively smaller response to temperature changes.

[0032] Furthermore, the temperature dependence of FWHM was fitted using a Gaussian method at 8.57 and 15.37 THz, as shown below. Figure 4 As shown in Table 2. The fitting parameters are shown in Table 2. It is affected by a variety of factors and follows a quadratic fit as shown in the following formula.

[0033] ; Where a, b, and c are three constants, with units of THz and K respectively. -2 , THzK -1 , THz.

[0034] Table 2 Parameters of FWHM Quadratic Fitting Curve

[0035] As can be seen, the observed spectral lines broaden with increasing sample temperature. This is because when numerous isolated atoms combine to form a crystal, each atom's energy level simply corresponds to an energy band. With increasing temperature, the crystal volume expands, increasing the distance between atoms and causing the periodic potential field to become weaker relative to electrons, thus narrowing the band gap. This phenomenon causes the gap between phonons with gradually increasing energy levels to gradually decrease, making phonon transitions easier and allowing the phonon population to spread widely across all energy bands. Since each energy state corresponds to a unique frequency, when these energy states couple to a unified frequency, a longer tail effect is produced, broadening the absorption. Alternatively, from the perspective of the Bose-Einstein distribution, at low temperatures, phonons are not significantly excited and are mainly confined to the lowest energy band. However, as the temperature rises, the number of atoms participating in vibration increases, and phonons are significantly excited. Multiple low-frequency phonons couple to form a high-frequency phonon. At high temperatures, the interaction between phonons becomes more frequent, which is reflected in the frequency of the coupled phonon, exhibiting a longer tail effect. Therefore, it can be observed that the absorption gradually becomes wider as the temperature increases.

[0036] Furthermore, the fitting results show that the phonon number n is approximately proportional to the temperature T. Therefore, the T² dependence indicates that the broadening is related to n. 2 This is directly proportional, which confirms the above analysis.

[0037] (3) Theoretical calculation KLVFF molecular structure and spatial arrangement, as well as KLVFF molecular THz spectral data and theoretically calculated spectra, are as follows: Figure 5 As shown.

[0038] Figure 5 In (c), the green vertical line represents the frequency location exhibiting KLVFF vibrational characteristics, and its length is proportional to the vibrational intensity. The red curve represents measurements taken at 300 K; the blue curve represents measurements taken at 30 K; and the black curve represents the theoretically calculated spectrum. Although there are differences in characteristic frequencies between the calculated and experimental spectra, the degree of difference is reasonable. This result indicates that theoretical calculations can reliably reproduce the characteristics of experimental spectra. A detailed description of the aforementioned vibrational modes is shown in Table 3, illustrating the wide distribution of collective vibrational modes in the THz range.

[0039] Table 3. Summary of characteristic peak positions and vibrational modes in the experimental and calculated THz absorption spectra of KLVFF.

[0040] ν represents rotation, r represents in-plane oscillation, ω represents out-of-plane oscillation, t represents translation, and s represents symmetrical stretching vibration.

[0041] Table 3 shows that the absorption peaks exhibit different temperature responses. The vibrational modes corresponding to the more prominent characteristic frequencies are as follows: Figure 6 As shown. Analysis of the THz fingerprint spectrum of KLVFF and theoretical calculations revealed that the specificity of the molecular conformation resulted in distinct resonance peaks. Figure 6 In (a) and (b), the vibrational modes at 2.59 THz and 3.70 THz are attributed to the collective vibration of the KLVFF molecules. Meanwhile, the vibrational changes of the amide bonds in the KLVFF molecules lead to changes in the length and orientation of the intermolecular HBs. Figure 6 (c, d, e, f) show four distinct vibrational modes, primarily originating from the rotational and rocking motions of groups in KLVFF. Slight vibrations of the amide bond also contribute to the deformation of HBs. For comparison with Table 3, before 4.72 THz (corresponding to 4.67 THz in the experimental spectrum), the vibrational modes mainly originate from collective vibrations. After 4.72 THz, the vibrational modes are primarily concentrated in the vibrations of a few specific groups. For example, at 8.20 THz, the vibration is mainly from the rotational vibration of the amino group, and at 6.85 THz, it is mainly from the rotational vibration of the methyl group. The remaining minor vibrations are mainly concentrated in the benzene ring and some vibrations related to the benzene ring, amino group, and methylene group.

[0042] When performing Raman spectroscopy theoretical calculations on the KLVFF molecule, a single-molecule model was constructed. The theoretical calculation results and the single-molecule model are as follows: Figure 7 As shown.

[0043] like Figure 7 (b) shows the range from 0 to 1800 cm. -1 Several characteristic peaks appeared in the Raman scattering spectrum within the range, and the experimental results showed good agreement with the theoretical calculations. A summary of the specific vibrational modes is shown in Table 4. At 1003.57 cm⁻¹ -1 and 1079.33 cm -1 The characteristic wavenumber peaks mainly originate from the stretching vibrations of the benzene ring. These peaks are located at 1588.15 and 1606.63 cm⁻¹. -1 The vibrations at this location also primarily originate from the stretching vibrations of the benzene ring, but their direction and intensity differ significantly. As mentioned earlier, 155.13 cm... -1 233.23 cm -1 and 403.34 cm -1 The Raman peaks at 155.13 cm⁻¹ are relatively close in frequency to the absorption peaks at 4.67 THz, 6.64 THz, and 12.47 THz in the THz spectrum. However, theoretical analysis shows that the peaks at 155.13 cm⁻¹ are much closer in frequency. -1 The Raman vibrational modes mainly originate from amino-N (7)The out-of-plane rocking of H2, while at 4.67 THz, molecular vibrations originate from collective molecular vibrations; at 233.33 cm⁻¹ -1 The Raman vibration mode at that location mainly originates from (-C) (27) H3 and -C (28) The rotational vibrations of the two methyl groups (H3) are present, while at 6.64 THz, the vibrational mode primarily originates from (-C). (27) H3 and -C (62) H3) Rotational vibration of the two methyl groups; at 403.32 cm⁻¹ -1 The Raman vibration mode at that location mainly originates from (-C) (27) H3 and -C (28) The two methyl groups (H3) exhibit out-of-plane rocking, while at 12.47 THz, the vibrational mode primarily originates from the amino (-N) group. (12) H3 + The rotation of ) and methylene (-C (67) H2-) and methyl (-C) (66) The in-plane oscillations of H3. Their vibration modes consist of different vibrational behaviors, which also indicates that infrared and Raman activity cannot coexist at the same frequency.

[0044] Table 4 Comparison of characteristic peak positions and vibrational modes in KLVFF experimental and calculated Raman scattering spectra

[0045] ν represents rotation, r represents in-plane oscillation, ω represents out-of-plane oscillation, t represents translation, l represents balance-type vibration, and s represents symmetrical stretching vibration.

[0046] In general, molecules tend to exhibit collective vibrational modes in the THz frequency range, and these low-frequency collective vibrational modes are considered important drivers of biochemical reactions. These modes significantly influence molecular conformational changes and interactions, thus playing a crucial role in physiological and pathological processes. Furthermore, Raman spectroscopy analysis reveals that terahertz absorption spectroscopy and Raman spectroscopy are complementary in analyzing vibrational characteristics in the same region. Therefore, combining terahertz and low-wavenumber Raman spectroscopy can characterize more comprehensive molecular vibrational information, while simultaneously analyzing Raman and infrared activity characteristics, such as collective vibrations, functional vibrations, bond stretching, and intracellular molecular interactions. A deeper understanding of these vibrational modes can better reveal the mechanisms of intermolecular interactions and the rich molecular vibrational information, providing theoretical support for drug design and biomaterial development.

[0047] (4) Mode decomposition and intermolecular hydrogen bond analysis Because this crystal belongs to the P1 space group, the two molecules within the unit cell do not exhibit obvious symmetry, meaning they do not have similar vibrational characteristics in a certain mode. Therefore, the two molecules within the unit cell were calculated together. Figure 8 As shown, a clear trend can be observed: within the vibrational mode range of 0–20 (corresponding to frequencies below 7.8 THz), only the decoupling results of translational vibrations show slight fluctuations, with changes controlled within 1%. This is mainly attributed to the rigidity and symmetry constraints of the molecular structure, resulting in a relatively stable overall distribution of vibrational modes. Beyond the 20th mode, the proportions of various motions in the vibrational mode characteristics of KLVFF remain almost constant: translations along the X, Y, and Z axes account for 7.2%, 5.8%, and 2.4%, respectively; rotations around the x, y, and z axes account for 1.5%, 13.1%, and 23.5%, respectively; and intramolecular vibrations account for 46.5%. This stability reflects the inherent physical properties of the molecule, rather than limitations of the analytical method.

[0048] The decoupling results from these sixty-plus modes show that, during translational motion, molecules tend to move along the X-axis. This indicates that intermolecular forces along the X-axis are relatively weak in the crystal structure. However, six intermolecular hydrogen bonds constrain molecular movement along the X-axis. As a strong interaction force, hydrogen bonds suggest that these six intermolecular hydrogen bonds undergo significant stretching deformation in these modes, a point supported by… Figure 9 This can also be clearly observed in (a). This situation makes molecules more prone to collective slippage or vibration in this direction. During rotational motion, molecules clearly tend to rotate around the z-axis. This suggests that the z-axis is very likely the direction of the molecular principal axis of minimum inertia, and in the crystal structure, the spatial arrangement around the z-axis may be more relaxed than the other two rotational directions, allowing for larger angles of twisting or oscillation. In contrast, rotation around the x-axis or y-axis may cause significant steric collisions between protruding parts of the molecule and adjacent molecules, thus restricting its rotational degrees of freedom.

[0049] These results highlight the complexity of low-frequency vibrational modes, indicating that the low-frequency collective motion of biomolecules involves the synergistic effects of numerous atoms and the coupling of various weak interactions (such as hemispheres). This collective motion is of great significance in biological functions, particularly in promoting protein aggregation, where it plays a crucial role in aggregate formation and stability by regulating intermolecular interactions and conformational dynamics.

[0050] Intermolecular hemispheres (HBs), as key non-covalent interactions, play a central role in driving the folding and stabilizing the conformation of biomacromolecules. THz spectroscopy can directly probe low-frequency vibrational modes associated with HBs, providing a unique and powerful tool for studying their dynamic behavior. Particularly in proteins, intermolecular HBs play a crucial role in promoting specific intermolecular binding, stabilizing aggregate structure, regulating aggregation kinetics, and influencing aggregate toxicity. Synergistically with hydrophobic interactions, HBs significantly enhance aggregate formation and structural stability, with their specific effects finely regulated by protein sequence and environmental conditions. This has profound implications for understanding disease-related protein aggregation and designing novel biomaterials.

[0051] Combination Figure 8 and Figure 9 Analysis of the bond length and bond angle changes of the six intermolecular HBs clearly shows that before the 35th vibrational mode (9.66 THz), the changes in HBs bond length mainly originate from the stretching vibrations of HBs. With increasing frequency, in the range of 9.66–18 THz, the deformation of HBs is mainly manifested as changes in bond angles, which are primarily driven by the out-of-plane vibrations of N, H, and O atoms associated with intermolecular HBs. However, several special modes exist; for example, HB-1 exhibits significant changes in bond length and bond angle before mode 35, and in mode 15, N… (11) -H (11C) …O (2A) The intense tensile vibration of (HB-1) caused H (11C) and O (2A) Significant atomic motion along the HBs direction, changing by 4.49%. In the 25th mode, H... (11C) Out-of-plane vibrations of atoms induce N (11) -H (11C) …O (2A) The bond angle of (HB-1) showed a significant distortion, changing by -8.16%. Interestingly, in mode 35, both the bond length and bond angle of HB-6 underwent substantial changes simultaneously, with the bond length showing a positive change and the bond angle a negative change. This may indicate a significant weakening of hydrogen bond strength and a geometric rearrangement of the molecular structure that is unfavorable to hydrogen bond formation. This change is significant for understanding intermolecular interactions and the structural stability of biomolecular structures. Furthermore, another notable feature is that the bond angle of HB-4 exhibited a positive change rate of 1.97% in every vibrational mode. This suggests that HB-4 exhibits a highly consistent trend towards geometric optimization during molecular vibration, reflecting the intrinsic mechanism by which the molecule enhances hydrogen bond stability through systematic adjustment of its geometry during vibration. The increased bond angles tend towards a more ideal linear arrangement, thereby significantly enhancing the stability and strength of hydrogen bonds.

[0052] Further analysis reveals significant variations in hydrogen bond length and bond angle within the vibrational mode range from 25 (8.29 THz) to 45 (12.55 THz). Combined with... Figure 5 (c) It can be seen that the 25-45 mode range corresponds precisely to the region of weaker vibrational intensity in the spectrum. Conversely, before mode 25, the region with more significant bond length changes corresponds to the region of higher vibrational intensity. This reveals that the hydrogen bond network exhibits two different dominant response mechanisms in molecular vibration.

[0053] 1. High-intensity vibrational region (modes <25): dominated by bond length stretching. The molecular vibrations corresponding to these high-intensity vibrational modes are more effectively coupled to the stretching vibrations of hydrogen bonds. Bond length changes require overcoming strong intermolecular barriers, necessitating greater energy input, which directly translates to higher vibrational intensities. The results of vibrational mode decoupling ( Figure 9 (a) further shows that this preference for translational motion along the X-axis of the crystal will cause overall molecular slippage, which will inevitably be accompanied by a significant stretching and adjustment of the hydrogen bond distance between molecules, which is highly consistent with the mechanism dominated by bond length changes.

[0054] 2. Low-intensity vibrational region (modes 25-45): Hydrogen bonds undergo simultaneous changes in both bond length and bond angle. This indicates an overall adjustment of the geometric configuration, reflecting a flexible adjustment of the overall molecular configuration within the hydrogen bond network. This involves the reorganization of the hydrogen bond network rather than the stretching or contraction of individual bonds. This may stem from the flexible nature of the hydrogen bond network. In low-frequency vibrations, the overall molecular configuration adjusts. In weakly interacting systems with hydrogen bonds or van der Waals forces, molecules continuously vibrate and rotate, breaking and forming bonds, resulting in various dynamic transient structures and flexible, variable potential energy surfaces. Under this mechanism, the hydrogen bond network adapts to vibrational perturbations through coordinated geometric changes, rather than the stretching or contraction of individual bonds.

[0055] These two distinct mechanisms provide direct kinetic evidence for the rigidity and flexibility of the hydrogen bond network in crystals. They precisely reveal how molecular vibrational modes of different frequencies selectively excite different degrees of freedom in hydrogen bonds. Understanding this partitioning is crucial for KLVFF, the core pentapeptide of Aβ. Furthermore, high-intensity bond length modes influence its mechanical response, while low-intensity bond angle modes affect its flexibility, energy absorption, and potential conformational switching capabilities. The deformation of HBs stores a significant amount of energy related to large-scale molecular vibrations, and this partitioning may suggest the energy required to excite different vibrations in KLVFF.

[0056] Furthermore, further observation revealed that the bond lengths of HB-1 and HB-6 exhibit a strong and widespread distribution between modes 10 and 45°, with the variation intensity of HB-6 being slightly weaker than that of HB-1. Similarly, the most significant and widespread changes in bond angles were also observed in HB-1 and HB-6, but mainly concentrated between modes 25° and 45°. This interesting finding suggests that HB-1 and HB-6 are likely key kinetic hubs in KLVFF-driven Aβ amyloid assembly. Their prominent responses in molecular vibrational modes indicate that they are core sites for maintaining crystal structure stability and functional flexibility. The extensive and dramatic changes in bond angles between modes 25° and 45° are particularly crucial. These changes in bond angles are directly related to alterations in hydrogen bond directionality and network connectivity, indicating that the geometric adjustments of HB-1 and HB-6 are important mechanisms driving relative orientation or local lattice rearrangement between peptide chains. The remaining four hydrogen bonds are the main intermolecular forces maintaining their molecular conformation.

[0057] In summary, the conformational freedom of KLVFF side chains is not only intrinsically constrained by molecular geometry but also significantly regulated by intermolecular hemisphere (HBs) interactions. The vibrational properties of HBs play a crucial role in molecular conformational dynamics and functional regulation. HBs formation and breakage are the core driving forces behind free energy changes during protein folding, directly influencing the transition of proteins from a disordered state to a specific conformation. HBs deformation stores energy associated with large-scale molecular vibrations, driving local folding and global conformational adjustments in protein chains. Furthermore, variations in HBs parameters with frequency may reflect the energy differences required to excite different vibrational modes, thus affecting protein folding path preferences and conformational stability. These findings highlight the unique advantages of terahertz spectroscopy in resolving intermolecular interactions and protein dynamics, providing a new perspective for a deeper understanding of protein folding mechanisms.

[0058] Although the present invention has been illustrated and described with specific embodiments, it should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; those skilled in the art should understand that modifications can be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein, without departing from the spirit and scope of the present invention; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing molecular vibrational and hydrogen bond networks, characterized in that, Includes the following steps: (a) Using synchrotron broadband terahertz spectroscopy, terahertz absorption spectra of the target peptide sample at different temperatures were collected in the frequency range of 2–18 THz to obtain temperature-dependent terahertz fingerprints; Raman spectroscopy was used in the wavenumber range of 0–1800 cm⁻¹. -1 Within the specified range, Raman scattering spectra of the target peptide sample are collected to obtain Raman fingerprints; based on solid-state density functional theory, a unit cell model of the target peptide is constructed, and its theoretical vibrational spectrum is calculated. (b) Quantitatively analyze the temperature-dependent terahertz fingerprint spectrum, extract the frequency offset parameter and full width at half maximum (FWHM) parameter of at least one characteristic absorption peak, obtain the evolution law of the frequency offset parameter and the FWHM parameter with temperature, and perform mathematical fitting on the evolution law to obtain characteristic coefficients that quantitatively describe the molecular vibrational thermodynamic behavior. (c) Compare the terahertz absorption spectrum and the Raman scattering spectrum with the theoretical vibrational spectrum to identify the molecular vibrational modes corresponding to each characteristic absorption peak and scattering peak; perform mode decomposition on the calculated multiple infrared active vibrational modes to quantitatively distinguish the contribution ratio of intermolecular translation, intermolecular rotation and intramolecular vibration in each vibrational mode. (d) Based on the results of mode decomposition, the relative changes in bond length and bond angle of intermolecular hydrogen bonds in the unit cell of the target polypeptide are analyzed to reveal the deformation law of hydrogen bond network under different vibration frequencies.

2. The molecular vibration and hydrogen bond network analysis method according to claim 1, characterized in that, The target polypeptide sample includes: KLVFF polypeptide.

3. The molecular vibration and hydrogen bond network analysis method according to claim 1, characterized in that, The different temperatures mentioned in step (a) are in the range of 30~300 K, and terahertz absorption spectra are collected every 10~20 K.

4. The molecular vibration and hydrogen bond network analysis method according to claim 1, characterized in that, The evolution law of the frequency offset parameter in step (b) includes: the frequency offset parameter of the characteristic absorption peak at 8.05 THz does not change with temperature within the temperature range, exhibiting the characteristic of a fixed frequency.

5. The molecular vibration and hydrogen bond network analysis method according to claim 1, characterized in that, The mathematical fitting in step (b) includes: fitting the frequency offset parameter using a Bose-Einstein model to obtain the characteristic temperature Tc and coefficient A; and fitting the full width at half maximum (FWHM) parameter using a quadratic polynomial model to obtain the quadratic coefficient a, the linear coefficient b, and the constant term c.

6. The molecular vibration and hydrogen bond network analysis method according to claim 1, characterized in that, Step (c) identifies the molecular vibrational modes corresponding to each characteristic absorption peak and scattering peak by comparing the characteristic peak positions in the experimental spectrum with the theoretically calculated spectrum to determine whether they belong to one or more of collective vibration, group rocking, group twisting, group stretching, or group out-of-plane vibration.

7. The molecular vibration and hydrogen bond network analysis method according to claim 1, characterized in that, Step (c) involves modal decomposition of multiple infrared active vibration modes, including: Quantitative calculations were performed on 62 infrared active vibrational modes in the frequency range of 2 to 18 THz, and the percentage contributions of intermolecular translation, intermolecular rotation and intramolecular vibration in each mode were statistically analyzed.

8. The molecular vibration and hydrogen bond network analysis method according to claim 1, characterized in that, Step (d) analyzes the relative changes in the bond lengths and bond angles of intermolecular hydrogen bonds, including: The percentage changes in bond length and bond angle of the six intermolecular hydrogen bonds within the unit cell in each vibrational mode were statistically analyzed, and a distribution spectrum of hydrogen bond deformation as a function of frequency was plotted.

9. The molecular vibration and hydrogen bond network analysis method according to claim 8, characterized in that, Of the six intermolecular hydrogen bonds, the first hydrogen bond HB-1 and the sixth hydrogen bond HB-6 exhibit greater variations in bond length and bond angle than the other four hydrogen bonds, and are thus identified as key kinetic hub sites regulating polypeptide conformation dynamics.

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