M O D E L

The Results for Molecular Dynamics Simulation

In order to characterize our split enzyme system (take TEV as an example) first, we have conducted the 10-ns OPLS-AA/L all-atom force field molecular dynamics through GROMACS, under the NPT equilibrium for a 300K, 1 bar, ion-neutral (balanced ions are Na+ and Cl-) environment. The following is the validation of our manipulation (Figure 1): 

1. The energy minimization (EM) process before the manipulation.
2. The NVT equilibrium under the average of 300 K.
3. The NPT equilibrium under the average of 1 bar.
4. The density of the manipulation system

Following by the analyses of the trajectory results for TEV (Video 1), the Gibbs energy landscape (with principal component values to be gyration radius and RMSD) can be calculated and plotted (Figure 2).

1. The gyration radius of the TEV.
2. The RMSD of the TEV.
3. the Gibbs energy landscape constructed through Rg and RMSD of the TEV.

As shown in the trajectory results, our system eventually converges to a compact and (local) energetic minimized state. We further investigate the flexibility of the TEV through its b-factor and electrostatic properties (Figure 3).

1. The electrostatic properties of the TEV (red: negative; blue: positive).
2. The b-factor of the TEV, with the b-factor growing from lower (blue, rigid) to higher (white, flexible).

First of all, we can immediately extract the diffusion constant through the regression of the MSD (Figure 4), while the diffusion constant is an important physical parameters to be considered in our modeling for the split-enzyme system. The process to derive the relationship between the slop of MSD curve and the diffusion constant will be illustrated in the measurements part.

Furthermore, by applying the same analyses logic to the nTEV and cTEV protein (10-ns OPLS-AA/L all-atom force field MD, Video 2 and Video 3), we have found some possible Phe sites for the clicking reaction which is vital to the linkage between the split enzyme and the aptamer. Eventually, we choose a pair of plausible Phe sites each on either nTEV or cTEV, due to the fact that they are away from the reaction core of the enzyme and lie in the flexible loop of the protein (Figure 5).

1. The chosen Phe site on the nTEV protein.
2. The chosen Phe site on the cTEV protein.
3. The pair of chosen Phe sites on the TEV (with the b-factor the same as Figure. MD4).

Alternatively, we also perform the MD simulation for the PPV system as follows (Video 4 and Video 5), and eventually choose out the appropriate Phe sites for clicking reaction in Figure 6.

The Results of ODEs model for the biochemical system

We first construct the aptamer censoring system as follows (Figure 7), based on a few assumptions that:

1. There is no cooperativity between Apt. 1 and Apt. 2;
2. Compared to Aptamer, the target molecule is relative stable;
3. Ignore the inequilibrim effect given rise to the diffusion process;

We then construct the ODEs according to the basic chemical kinetics equations (Figure 8).

In Figure 9 (set the blue line as check-out line, the same for the following figures), we mimic such situation that both the aptamer A and aptamer B will die down quickly (with a relative high degradation rate compared with the target molecules), which we think will be the common cases for practical usage.

For the Figure 10, we decrease the initial ratio of both the aptamer A and aptamer B compared to the case above, in order to mimic the case when there only exist few targeting molecules in the sample.

In Figure 11, we assume that we have found better aptamer with higher affinity for the target molecules, which bring about both higher value of k1 and k2.

In Figure 12, the initial concentration of both aptamer A and B are identical, while aptamer A has a higher affinity over than aptamer B. As depicted in the figure, this asymmetry of the binding affinity can also bring about sharp peak of the checking out system.

Eventually, if the targeting molecules in the sample were at rather low concentration, and the amount of both aptamers were not enough, we would be confronted with the worst case for being unable to check out(Figure 13).

Furthermore, we construct our down-stream amplification system under the guidance of basic Michaelis-Menten equation, while introducing the flipping: considering the enzyme can be flipping between either inactive and active states (Figure 14).

Considering the aptamer censoring system, we further assume that the whole amount of the enzyme will be constraint to exponential degradation:

And then we mimic for the amplification system as well:

If the degradation rate is high (Figure 15), the down-stream amplification can be inadequate. However, at a relative large parameter space volume, the amplification system can be robust and effective (Figure 16).

1. The relative concentration of the product and the reagent in the fast-degradation case.
2. The different form of enzyme in the fast-degradation case.

1. The relative concentration of the product and the reagent in the normal case.
2. The different form of enzyme in the fast-degradation case.

Results of the PDEs model for the diffusion system

To describe the diffusion process in our biological system, we turn to the two-dimensional Fokker-Plank equation for characterizing our diffusion system. Again, we have made some plausible assumptions initially:

1. The oriented−dragging vector is only relate to the time t;
2. The diffusion constants for each biomolecules are not affected by time;

Based on the two-dimensional Fokker-Plank equation as follows:

With relative low dragging force v compared with the diffusion constant, the diffusion process can be rather normal (Video 6).

Nevertheless, when the dragging force v is apparently higher than the diffusion rate, there can be turbulence (i.e. Multiple peaks) within the fixed volume (Video 7).

MAGA:Make Aptamer Generally Applied

Accurate and timely detection of disease biomarkers is crucial for effective diagnosis and treatment across various medical conditions. Traditional methods, such as SELEX, used for screening Aptamers that bind to specific biomarkers, are often slow, costly, and lack the precision needed for diverse applications. To overcome these limitations, we introduce MAGA: Make Aptamer Generally Applied—a universal machine learning-based platform designed to predict Aptamer sequences that can target a wide range of disease biomarkers with high specificity and affinity.

Methodology:

1. Pretrained Feature Extractor:
   • We pretrained protein and nucleic acid feature extractors (encoders) using extensive datasets from publicly available sources such as the Protein Data Bank (PDB) and GenBank. These encoders are designed to capture the complex structural and sequence-based features of proteins and nucleic acids, forming the foundation of our predictive modeling.
2. Affinity Prediction Model:
   • The second component of MAGA involves a predictive model trained to estimate the binding affinity between proteins and corresponding Aptamers. By leveraging the extracted features from the pretrained encoders, our model accurately predicts the strength and specificity of the Aptamer-protein interactions, providing crucial insights into their potential as biomarkers.
3. Monte Carlo Search Optimization:
   • To identify the optimal Aptamer sequences for specific proteins, we employed a Monte Carlo search strategy. This approach systematically explores the sequence space, guided by the predicted affinities, to find the most suitable Aptamers. This method ensures that our predictions are not only accurate but also optimized for practical use in various diagnostic applications.

Result

The MAGA platform’s capabilities were rigorously tested using AlphaFold3, a state-of-the-art tool for predicting protein structures. By integrating our machine learning-driven Aptamer prediction model with AlphaFold3, we were able to simulate the binding interactions between the Aptamer sequences and their target proteins with remarkable precision. The results achieved through these predictions were on par with those obtained from controlled laboratory experiments, underscoring the accuracy and reliability of our system.

As a specific example, we focused on thrombin, a critical enzyme in the blood coagulation process, to evaluate the performance of our approach. Thrombin was chosen due to its well-characterized binding interactions and clinical relevance. Our predictive model not only identified Aptamer sequences that showed high binding affinity to thrombin, but the structural predictions made using AlphaFold3 were also in excellent agreement with experimental data. This alignment between predicted and observed results demonstrates the potential of the MAGA platform to deliver high-accuracy predictions that are comparable to, if not better than, traditional laboratory-based methods.

Furthermore,we employed Electrophoretic Mobility Shift Assay (EMSA) to further validate that the predicted aptamer can indeed bind to the target protein. EMSA is a classic method used to study protein-nucleic acid interactions. By observing the changes in electrophoretic mobility before and after the binding of the aptamer to the target protein, we can directly detect the formation of the complex.

The successful application of the MAGA system to thrombin not only validates our approach but also sets the stage for its expansion to other disease biomarkers. This positions MAGA as a powerful, universal tool for biomarker detection, offering a blend of computational efficiency and experimental precision that could revolutionize the field of diagnostic medicine.

Conclusion:

MAGA represents a novel approach to Aptamer-based biomarker detection, combining advanced machine learning techniques with rigorous optimization strategies. This universal system has the potential to revolutionize how we detect and diagnose a wide range of diseases, offering a scalable, cost-effective, and highly accurate alternative to traditional methods. Future developments will focus on expanding MAGA’s capabilities to cover even more biomarkers and refining its predictive accuracy.

Acknowledgments:

We would like to thank Peking University for their support, as well as our collaborators at Institute for Artificial-Intelligence. Special thanks to our mentors, Long Qian, for their guidance and expertise.

Contact Information:

Email: juntingzhou@stu.pku.edu.cn

Web: zjtpku.github.io