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Label-free sensing of the binding state of MUC1 peptide and anti-MUC1 aptamer solution in fluidic chip by terahertz spectroscopy

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Abstract

The aptamer and target molecule binding reaction has been widely applied for construction of aptasensors, most of which are labeled methods. In contrast, terahertz technology proves to be a label-free sensing tool for biomedical applications. We utilize terahertz absorption spectroscopy and molecular dynamics simulation to investigate the variation of binding-induced collective vibration of hydrogen bond network in a mixed solution of MUC1 peptide and anti-MUC1 aptamer. The results show that binding-induced alterations of hydrogen bond numbers could be sensitively reflected by the variation of terahertz absorption coefficients of the mixed solution in a customized fluidic chip. The minimal detectable concentration is determined as 1 pmol/μL, which is approximately equal to the optimal immobilized concentration of aptasensors.

© 2017 Optical Society of America

1. Introduction

MUC1 is a cell-membrane-associated glycoprotein in the mucin family with high molecular weight. It comprises an extracellular domain composed of a region including nearly identical 20-amino-acid-long repeats, a cytoplasmic domain of 69 amino acids, and a hydrophobic membrane-spanning domain of 31 amino acids [1]. In particular, the 9-amino-acid-long peptide sequence APDTRPAP often belongs to the variable tandem repeat (VTR) domain from the epitope within a highly immunogenic region of MUC1 [2]. As a well-known tumor biomarker associated with disease severity, MUC1 is up-regulated and aberrantly glycosylated in a variety of human epithelial cancer cells, and often free-floats in the bloodstream [3], thus making liquid biopsy for MUC1 potentially helpful in cancer diagnosis.

Judicious selection of biomolecules that bind specifically and tightly to biomarkers can offer a useful tool for disease diagnostics, drug screening, and biosecurity applications. Despite wide use of antibodies [4–6], they still suffer from chemical instability, synthesis difficulty, large size, and high cost. Aptamers, single-stranded RNA or DNA oligonucleotide selected by the systematic evolution of ligands by exponential enrichment (SELEX) methodology, interact with targets by forming special three-dimensional conformations. Since the concept of aptamer was first proposed by Ellington in 1990 [7], it has been presented as a regnant bioreceptor for the construction of various aptasensors to detect ions [8, 9], proteins [1, 10], and cells [11, 12], as aptamers possess high affinity, exquisite specificity, reduced immunogenicity, increased stability, and good reproducibility. Moreover, aptamers could be massively synthesized and easily modified via chemical processes, which is more cost-effective [13].

Based on existing anti-MUC1 antibodies (e.g., SM3 antibody), the SELEX library was synthesized to provide 425 different species of DNA for selection of anti-MUC1 aptamers [13]. Subsequently, an aptamer (anti-MUC1 S2.2) has been confirmed as a functional molecule, specifically binding to a common sequence (APDTRPAPG) of the VTR region of MUC1. To date, this MUC1 and aptamer binding reaction has led to discerning diagnostic aptasensors for detecting and monitoring tumor progression [1, 10–12]. In particular, the presence of divalent metal ions (e.g., Mg2+, Ca2+) was indispensable for an aptamer to form the characteristic secondary structure, contributing to the selection process of aptamers and regeneration of aptasensors, in contrast to most existing biosensors [11]. However, an overwhelming majority of the above aptasensors were labeled methods, such as enzyme-linked assay and chemiluminescence assay, rendering them complex as well as laborious.

Recent developments in terahertz (THz, 0.1-10 THz) biomedical applications have garnered much interest in label-free research, owing to its unique spectral advantages [14–17]. THz photon energy meshes well with the energy levels of low-frequency molecular motions including rotation, vibration, and relative translation of the molecular skeleton, and particularly the hydrogen bonds between biomolecules and water [18]. There have been several experimental methods characterizing hydrogen bond network dynamics of liquid water, including IR pump–probe spectroscopy [19], NMR spectroscopy [20], quasi-elastic neutron scattering [21], inelastic neutron, and X-ray scattering [22, 23], whereas THz absorption spectroscopy may be mutually complementary with these existing approaches. Equally important, it could offer a brand-new perspective of collective water dynamics: the analysis of hydration water and bulk water can potentially reveal distinct THz absorption features on the sub-picosecond time scale due to the fundamentally unique collective intermolecular vibrations of the hydrogen bond network and re-orientations of the associated molecular dipoles [24]. Moreover, the THz absorption of most solutions far surpass that of the solutes as a result of the intermolecular vibrations of the hydrogen bond network. Consequently, owing to the presence of a solute molecule, even a small perturbation of the hydrogen bond network could be sensitively detected by THz spectroscopy in a label-free manner.

In a previous study, the vibrational modes of water molecules at an active site were found to take along the distinctive fingerprints of the substrate in unique enzyme–substrate complexes [25]. This suggests the existence of a heterogeneous hydrogen bond network that assists molecular recognition and binding. Meaningful molecular details for MUC1 peptide and aptamer binding were successfully obtained by molecular dynamics (MD) simulation, which showed the number of hydrogen bonds in and around the aptamer changed with the binding process [26]. On account of hydration shell alteration, the binding reaction of hemagglutinin (HA) subtypes H9 with a human HA-specific neutralizing monoclonal antibody F10 was detected by THz spectroscopy [27]. These findings provide motivation for further investigation into a more promising binding reaction, the MUC1 peptide and anti-MUC1 aptamer, by THz spectroscopy to meet the demand of label-free detection and the SELEX methodology. In this vein, the present study is undertaken to combine MD simulation and THz absorption spectroscopy to evaluate and quantify the change of the collective vibration mode of hydrogen bond network dynamics caused by the binding state of MUC1 and the anti-MUC1 aptamer.

2. Materials and methods

2.1 Spectroscopy system

The THz spectra measurement was carried out on a T-Ray 5000 THz time-domain spectroscopy system (Advanced Photonix, Inc., Roanoke, VA, USA) in transmission mode (Fig. 1(a)). In this system, the femtosecond Yb-fiber laser can emit pulses with a central wavelength of 1064 nm and a 100 MHz repetition frequency. The electric field of ultrashort THz pulses was generated and detected by a low-temperature grown GaAs photoconductive transmitter and detector, respectively. The whole spectroscopy system was filled with pure nitrogen gas to decrease the humidity to less than 2%, so as to exclude the effect of water vapor (Fig. 1(c)).

 figure: Fig. 1

Fig. 1 Schematic diagram of the THz Spectrometer: (a) setup of the THz time-domain spectroscopy system, (b) three-dimensional model of the fluidic chip, and (c) THz frequency-domain spectrum (Frequency range: 0.1–3 THz, average power: 130 nW, peak frequency: 0.13 THz).

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2.2 Fluidic chip design and fabrication

A novel fluidic chip based on SU-8 photoresist was designed as a storage device for THz detection of minute biological samples (Fig. 1(b)) [28]. The chip includes two 1-mm-thick quartz windows with the purpose of alleviating the attenuation of THz energy. The photoresist layer forms a designed structure for sample storage on one quartz window and the layer thickness was determined as 55 μm to match the THz optical path. The fabrication process comprised the steps of substrate pretreatment, spin-coating, soft baking, exposure, and post-exposure baking, followed by developing. A controlled hard bake was then used to further cross-link the imaged SU-8 2050 photoresist structures. All samples were measured in the fluidic chip fixed with a Bruker A140-H sample holder. The sample area in the fluidic chip was approximately 2 cm2. Hence, the requisite volume of the measured sample was approximately 10 μL.

2.3 Molecular dynamics simulation

The software package AMBER 12 [29] was used to simulate the MUC1 and anti-MUC1 binding reaction in a physiological solvent under conditions akin to those of the experiment. The symbolic change of the hydrogen bond network was analyzed along with the binding process. The MUC1 structure (APDTRPAPG) generated via LEaP program as a linear peptide was energy-minimized and continuously heated to 300 K in vacuum; subsequently, the system was maintained at a constant temperature using Langevin dynamics for 10 ns to form a stable configuration, which was saved as a PDB file. The anti-MUC1 aptamer structure was obtained from the protein data bank (PDB ID: 2l5k) with a base sequence of 5′-GCAGTTGATCCTTTGGATACCCTGG-3′. The two PDB files were then combined to form an initial configuration system of MUC1 peptide–aptamer complex. In order to neutralize the negative electric charges of the aptamer, 22 Na+ ions were added to the simulation system. The system was then solvated in explicit TIP3P water in a cubic box of 80.7 × 80.7 × 80.7 Å3 with periodic boundary conditions. Considering that 0.15 M (mole per liter) NaCl in the simulation system can closely imitate the experimental conditions, an additional 46 Na+ and 46 Cl- ions were added. All the above models were constructed using ff12SB force field [30]. At this point, the system contains 122 atoms of the peptide, 728 atoms of the aptamer, 68 Na+, 46 Cl-, as well as 17048 water molecules. The energy minimization, temperature and density equilibrium were followed in accordance with previous strategies and parameters for biological systems [31]. In this way, under standard atmospheric pressure (1.0 bar), the temperature was stable around 300 K, and the density relaxed to 1.003 g/cm−3. Finally, the MUC1 peptide–aptamer combination was simulated in an NVT ensemble for 100 ns. All simulations were conducted using a 2-fs time step.

2.4 Sample preparation and measurement

The MUC1 peptide and anti-MUC1 aptamer (HPLC purified) were purchased from Shanghai Bioengineering Company (Shanghai, China). For comparison, a random sequence of 5′-CACGACGTTGTAAAACGACGGCCAG-3′ was purchased and used as the reference to test the specificity in our experiment. Phosphate buffered saline (PBS, without Mg2+, Ca2+) and Dulbecco’s phosphate buffered saline (D-PBS, CaCl2 0.90 mM (mmol/L), MgCl2 0.49mM) were purchased from Sigma-Aldrich (St Louis, MO, USA). The anti-MUC1 aptamer and MUC1 peptide were prepared at different concentrations: 0.1, 0.316, 1.0, 3.16, 10.0, 31.6, and 100.0 pmol/μL dissolved in PBS and D-PBS solutions, respectively. They were then mixed together at the same concentration by 1:1 volume ratio. The random sequence was utilized as the negative control in the same way. In order to allow MUC1 peptide–aptamer binding reaction and complex formation, the mixtures were maintained at room temperature for 1 h and then pipetted into the fluidic chip for THz measurement. The empty fluidic chip was measured as a reference. Each sample was measured five times. Before each measurement the fluidic chip was removed from the sample holder. Both the quartz windows were initially rinsed with absolute ethyl alcohol and ultrapure water in order, and then dried with nitrogen gas. Utilizing the time-dependent electric field as an input, the frequency-dependent power I(ν) of the transmitted THz pulses was acquired via a fast Fourier transformation. The absorption coefficient α(ν) (power attenuation) was obtained on the basis of the following equation [32]:

α(ν)=lnIr(ν)lnIs(ν)d
where d refers to the thickness of the measured sample layer, ν refers to the frequency, and the indices s and r refer to the obtained data of the sample and reference, respectively. We calculated statistical error bars from the population standard deviation and applied it after smoothing the curves via an adjacent averaging method.

3. Results and discussion

3.1 Interference effect of the divalent metal ions

The binding duration of the peptide and aptamer stays at the nanosecond time scale [26], which cannot be monitored in real-time by THz spectroscopy owing to the latter’s millisecond-scale sampling time. The PBS solution and D-PBS solution, showing main discrepancy of divalent metal ions, are selected to control the binding state of the specific aptamer (anti-MUC1) and MUC1 peptide, as divalent metal ions (e.g., Mg2+, Ca2+) are crucial for forming the characteristic secondary structure of the aptamer [11]. Namely, the binding between MUC1 and anti-MUC1 can take place in D-PBS solution but cannot do so in PBS solution. However, ions can modify the polarization properties of water molecules and alter the surrounding water shell, resulting in aberrant absorption compared to double deionized water [33]. Hence, we need to evaluate this interference effect of the divalent metal ions by measuring the THz absorption spectroscopy of the PBS and D-PBS solutions separately.

The THz absorptions of the PBS and D-PBS ionic solutions both exhibit similar features, as shown in Fig. 2, higher than that of double deionized water. Given that D-PBS solution contains 137.93 mM NaCl, 2.67 mM KCl, 8.06 mM Na2HPO4, and 1.47 mM KH2PO4, more ionic vibration in the buffer solution will strengthen the THz absorption compared with that in double deionized water [34]. Moreover, the molar extinction coefficient of CaCl2 is approximately 22 cm−1.M−1 at 1 THz [34], which means that the added redundant divalent metal ions (CaCl2 0.90 mM, MgCl2 0.49 mM) in D-PBS solution can cause a slight change in THz absorption. Consequently, the error bars of the measured absorption coefficients of PBS and D-PBS solutions were essentially indistinguishable, i.e., the absorption difference was not significant. The results demonstrated that divalent metal ions’ interference effect is not prominent. Therefore, the premise of binding state sensing is immune to the bias of the use of divalent ions.

 figure: Fig. 2

Fig. 2 THz absorption spectra of double deionized water, PBS, and D-PBS solution. Error bars represent the standard deviation.

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3.2 MUC1 and anti-MUC1 aptamer binding reaction

The regeneration ability in dissociating aptamer (antibody)-target molecule complexes plays a pivotal part in the construction of a biosensor. The aptasensor was always regenerated by a gentle regeneration reagent EDTA. Because most aptamers require divalent metal ions to fold characteristic secondary structure and unfold in the presence of EDTA, an aptamer can refold quickly when EDTA is removed and replaced by divalent metal ions [35]. All of these properties highlight the importance of the presence of divalent metal ions for aptamer binding to the target molecule. We see in Fig. 3(a) that the absorption coefficients of the binding state of MUC1 and anti-MUC1 aptamer complexes in D-PBS solution can be unequivocally differentiated from the unbinding state at the concentration of 1 pmol/μL.

 figure: Fig. 3

Fig. 3 THz absorption spectra of (a) anti-MUC1 aptamer and MUC1 in PBS and D-PBS solution at the concentration of 1 pmol/μL, and (b) concentration-dependent anti-MUC1 aptamer and MUC1 in PBS and D-PBS solution at 1 THz. Error bars represent the standard deviation.

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Although it may not always appear possible to acquire distinct spectroscopic features for biomolecule solutions, the variation of THz absorption spectroscopy may be useful to reflect the state of the hydrogen bond network. To find out how the absorption coefficient changes as a function of concentration, we present the concentration-dependent THz absorption for MUC1 peptide binding with anti-MUC1 aptamer at 1 THz, as shown in Fig. 3(b). The concentration-dependent absorption seems to overlap as the concentration of MUC1 and aptamer increase from 0.01 pmol/μL. This continues until the concentration reaches 1 pmol/μL, where the binding and unbinding states were clearly distinguishable.

Owing to the negatively charged DNA phosphate groups and a large quantity of positively charged groups on the protein side, the DNA–protein interface is actually more polar than the protein–protein interface, which guarantees direct interactions between the DNA sequence and protein (i.e., direct hydrogen bonds, electrostatic, and van der Waals interactions) [36]. In addition, water-mediated indirect interactions facilitate specific binding processes between DNA and protein by screening unfavorable electrostatic and hydrogen bond interactions [37]. This suggests that the hydrogen bond network will mediate the specific recognition and experience simultaneous rearrangements when anti-MUC1 aptamer and MUC1 peptide approach each other; thus, as an ascendant method to probe sub-picosecond water network dynamics, THz spectroscopy can sensitively monitor these binding-induced collective vibrations of the hydrogen bond network, of which the key rotational and vibrational motions occur on the picosecond time scale. To clarify such sub-picosecond dynamical processes, we conducted an MD simulation to theoretically assess the alteration of hydrogen bonds in this binding behavior, as discussed next. The detection limit is a vital parameter for biomedical sensing applications. We have obtained a lower detectable concentration than that of a full-scale THz absorption spectrum up to the concentration level of mM. In this experiment, the binding state detection limit was at the concentration of 1 pmol/μL, which is approximately equal to the optimal immobilized concentration of the proposed aptasensors [11].

3.3 Specificity for the binding reaction

A random sequence, proved not to bind with MUC1 peptide, has been used for a reference sensor to reduce the interference from nonspecific binding [11]. From Fig. 4(a), we find that the THz absorption curves of the random sequence in the PBS and D-PBS solutions are almost the same at the concentration of 1 pmol/μL. The concentration-dependent THz absorption spectrum (Fig. 4(b)) at 1 THz demonstrates that the error bars are partially overlapped and mean values start to separate at the concentration of 10 pmol/μL, which indicates that there exists discrepancy but that it is not significant. The THz absorption of MUC1 and random sequence in D-PBS is lower than that in PBS solution, owing to the conformational change of the random sequence in D-PBS solution. Videlicet, different conformations (such as flexible to rigid state [38] or coiled to helical state [31]) form diverse hydrogen bonds with water molecules, which will be mirrored by the variation of the THz absorption coefficients of the corresponding solutions.

 figure: Fig. 4

Fig. 4 THz absorption spectra of (a) random sequence and MUC1 in PBS and D-PBS solution at the concentration of 1 pmol/μL, and (b) concentration-dependent random sequence and MUC1 in PBS and D-PBS solution. Error bars represent the standard deviation.

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To fold the characteristic conformation is fundamental for binding reaction. For anti-MUC1 aptamer, this conformation change in D-PBS solution leads to a specific binding behavior, which causes alterations in the hydrogen bond network surrounding the MUC1 peptide and anti-MUC1 aptamer complex as well as the generation of new hydrogen bonds between these complexes. Whereas for the random sequence, it cannot bind with MUC1 peptide; thus, the hydrogen bond network around the random sequence changes only slightly compared to the anti-MUC1 aptamer (shown in Fig. 5). Considering that the discrepancy is merely between the anti-MUC1 aptamer and the random sequence in Fig. 5, we can confirm that the absorption variation originates from the binding-induced change of the hydrogen bond network in and around the aptamer-peptide complex. This tendency of biomolecular interaction inducing the decrease of THz absorption coefficients of corresponding solutions, is consistent with previous reports [27, 39]. Furthermore, we see in Fig. 5 that the absorption difference at 1 pmol/μL is greater than those at other concentrations, implying that the alterations of hydrogen bond network caused by different behaviors (binding reaction and conformation change) achieve perfect balance at a low concentration probed by THz absorption spectroscopy. The concentration of 1 pmol/μL may be suitable for biomedical applications, especially the THz-based SELEX methodology which can obtain highly specific aptamers from randomly generated oligonucleotide library. Overall, THz absorption spectroscopy allows a direct evaluation of such hydrogen bond network alterations, in terms of how comprehensive the influence of the binding behavior on the water network is.

 figure: Fig. 5

Fig. 5 Concentration-dependent THz absorption spectra of anti-MUC1 aptamer and random sequence reacting with MUC1 in D-PBS solution. Error bars represent the standard deviation.

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3.4 Molecular dynamics simulation

MD can effectively analyze the role of hydrogen bonds in binding behavior. Hydrogen bonds here are considered to have a donor–acceptor distance < 3.5 Å and an angle between donor-hydrogen-acceptor > 135° [31, 40, 41]. We counted the hydrogen bonds between the MUC1 and anti-MUC1 aptamer, as well as between the biomolecules and surrounding water molecules during the entire binding simulation process (shown in Fig. 6(a)). Figure 6(b) shows the variation of the number of hydrogen bonds formed between MUC1 peptide and aptamer with simulation time. The number of hydrogen bonds increases as the binding continues, and finally tends to stabilize after 50 ns. Figure 6(c) shows the number of hydrogen bonds formed between biomolecules and water. The initial interaction causes the number of hydrogen bonds to decrease, then gradually increase as the complex structure achieves stable conformation corresponding to the final binding combination. The variation of the hydrogen bonds along with the binding process is consistent with the results obtained by Rhinehardt [26]. THz spectra of biological solutions mainly reflect the change in the hydrogen bond network around the biomolecules [42, 43]. From the MD simulation result, the number of hydrogen bonds between the biomolecules and surrounding water decreases by approximately 2% after complete binding. In our experiment, the THz absorption coefficient of the solution decreases by 1–6%, the proportion of the decrease in the THz absorption coefficient essentially corresponds to the decrease in the hydrogen bonds. Because the combination time scales are in the tens of nanoseconds, we could not observe the variation of absorption coefficient in nanoseconds duration. Instead, only the initial and final states can be measured in the actual experiment. However, from the MD simulation, according to the time-dependent change in the number of hydrogen bonds between the biomolecules and water, we can observe the binding process as it occurs, and estimate an approximate binding time of 25 ns [26].

 figure: Fig. 6

Fig. 6 Molecular dynamics simulation of hydrogen bond variations in MUC1 peptide and anti-MUC1 aptamer binding process at significant times. (a) Snapshots of MUC1 peptide (red backbone) and anti-MUC1 aptamer (blue backbone) binding process as observed in molecular dynamics simulation (without water molecules or ions). (b) Number of hydrogen bonds formed between aptamer and peptide. (c) The black line shows the number of hydrogen bonds formed between the peptide–aptamer complex and surrounding solvent; the red line shows the number of hydrogen bonds formed between peptide and aptamer as well as between the peptide–aptamer complex and surrounding solvent. The average number of hydrogen bonds is shown as symbols along with corresponding error bars.

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4. Conclusion

A THz spectroscopy investigation of the binding interaction between aptamer and targeted peptide was considered in this study, both experimentally and by simulation. Divalent ions were used to regulate the binding state of MUC1 peptide and anti-MUC1 aptamer, and their influence on the THz absorption of buffer and biomolecular solutions was discussed. No significant absorption difference was found between PBS and D-PBS solutions in the THz spectral region, indicating that the interference of divalent ions for THz measurement was negligible. On the other hand, for MUC1 and its specific aptamer in PBS and D-PBS solutions, absorption differences were unambiguously observed for the concentration range of 1–100 pmol/μL. By utilizing MD simulation, we observed that the binding reaction induced hydrogen bonds alteration in and around the MUC1 peptide and anti-MUC1 aptamer complex. As a result, the change in the hydrogen bond network around biomolecules could be sensitively quantified and distinguished by THz absorption spectroscopy at the concentration of 1 pmol/μL, which was approximately equal to the optimal immobilized concentration of pre-existing aptasensors. The present work demonstrated that THz absorption spectroscopy combined with MD simulation could offer a comprehensive understanding of the correlation between THz absorption and the hydrogen bond network, the associated biomolecular interaction, and the resulting conformational change. The random sequence used as negative control showed overlapped absorption coefficients and error bars when mixed with the MUC1 peptide, affirming the specificity of the MUC1 peptide–anti-MUC1 aptamer interaction. This work thus provides a foundation for the development of a label-free THz-based methodology, as insights from this work should be helpful in establishing a THz fluidic sensor for high-throughput SELEX screens as well as trace sample analysis. In future work, the underlying mechanism of the binding-induced connection between the variation of THz absorption coefficients and the binding enthalpy should be elucidated, whereas an in-depth study of the relationship between the affinity level of the aptamer and the alteration of the hydrogen bond network would bolster the feasibility of such THz aptasensors in clinical settings.

Funding

National Basic Research Program of China (Program 973) (2015CB755400); National Natural Science Foundation of China (NSFC) (81430054, 81370049, 61605206, 31400625).

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the THz Spectrometer: (a) setup of the THz time-domain spectroscopy system, (b) three-dimensional model of the fluidic chip, and (c) THz frequency-domain spectrum (Frequency range: 0.1–3 THz, average power: 130 nW, peak frequency: 0.13 THz).
Fig. 2
Fig. 2 THz absorption spectra of double deionized water, PBS, and D-PBS solution. Error bars represent the standard deviation.
Fig. 3
Fig. 3 THz absorption spectra of (a) anti-MUC1 aptamer and MUC1 in PBS and D-PBS solution at the concentration of 1 pmol/μL, and (b) concentration-dependent anti-MUC1 aptamer and MUC1 in PBS and D-PBS solution at 1 THz. Error bars represent the standard deviation.
Fig. 4
Fig. 4 THz absorption spectra of (a) random sequence and MUC1 in PBS and D-PBS solution at the concentration of 1 pmol/μL, and (b) concentration-dependent random sequence and MUC1 in PBS and D-PBS solution. Error bars represent the standard deviation.
Fig. 5
Fig. 5 Concentration-dependent THz absorption spectra of anti-MUC1 aptamer and random sequence reacting with MUC1 in D-PBS solution. Error bars represent the standard deviation.
Fig. 6
Fig. 6 Molecular dynamics simulation of hydrogen bond variations in MUC1 peptide and anti-MUC1 aptamer binding process at significant times. (a) Snapshots of MUC1 peptide (red backbone) and anti-MUC1 aptamer (blue backbone) binding process as observed in molecular dynamics simulation (without water molecules or ions). (b) Number of hydrogen bonds formed between aptamer and peptide. (c) The black line shows the number of hydrogen bonds formed between the peptide–aptamer complex and surrounding solvent; the red line shows the number of hydrogen bonds formed between peptide and aptamer as well as between the peptide–aptamer complex and surrounding solvent. The average number of hydrogen bonds is shown as symbols along with corresponding error bars.

Equations (1)

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α ( ν ) = ln I r ( ν ) ln I s ( ν ) d
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