"All models are wrong, but some are useful."
--George Box.
Our project on designing Silinkers to construct a standardized interface platform for silica surface modification brought us some fascinating issues worth studying in a modeling way.From the initial protein design, to the processing and analysis of wet experimental data in the the experiment, to exploring the downstream application of modified mesoporous silica nanoparticles, we found that modeling methods such as machine learning, differential equations, and cellular automata can provide good assistance in studying these problems.
On the one hand, our modeling results provide guidance for the promotion of wet experiments; on the other hand, data from wet experiments also help us verify the results of the model and make appropriate adjustments to the model’s parameters.
In the Protein Structure part, we used algorithms such as AlphaFold2, SELCON3, and CONTINLL for protein structure prediction and experimental data analysis.
Figure:the structure prediction of Basic Silinker
We used AlphaFold2 to predict the three-dimensional structure of proteins based on several groups of protein amino acid sequences provided by the experimental group. The prediction results helped the experimental group to preliminarily verify that the designed Silinkers can maintain the correct three-dimensional structure. At the same time, during the modeling process, we also discovered problems in the original Twisted Silinker protein design, which prompted the experimental group to make a completely new design for Twisted Silinker.
We relied on Dichroweb platform to analyze circular dichroism experimental data using SELCON3 and CONTINLL algorithms, and obtained the proportion of specific secondary structures in Basic Silinker. This helped us evaluate the rationality of AlphaFold2’s protein structure prediction; meanwhile, it also helped the experimental group to confirm that connecting new peptide segments would not cause significant impact on the secondary structure of the original protein region.
In the Loading and Modification part, we employed an Ordinary Differential Equations (ODE) model to simulate the process of drug loading into mesoporous silica particles and subsequent modification.
Figure 丨Basic Silinker Workflow Diagram. ① Load paclitaxel drug into mesoporous silica(MSN). ② Attach Basic Silinker protein to the drug-loaded mesoporous silica nanoparticles (MSN) and formulate the BS-Pac-MSN system. ③ Bioconjugate the biotinylated insulin-like growth factor onto the BS-Pac-MSN system and formulate the Insulin-like growth factor-bio-BS-Pac-MSN system. ④ Transport and deliver the drug delivery system to the target cells.
Figure丨Twisted Silinker Workflow Diagram. ① Attach Twisted Silinker protein to the mesoporous silica nanoparticles (MSN) ② Bioconjugate the biotinylated protein onto the TS-MSN system. ③ Load drug into the TS-MSN system. ④ When the ambient calcium ion concentration increases, calmodulin, calcium ions, and calmodulin-binding peptide interact with each other, effectively reducing the physical distance to achieve the function of blocking MSN pores and controlling drug release. ⑤ Transport and deliver the drug delivery system to the target cells. As the calcium ion concentration near the target cells decreases, the Twisted Silinker configuration expands, enabling targeted drug release.
We used ODEs to simulate the surface protein modification and drug loading process of mesoporous silica nanoparticles. By setting different parameters, we inferred results such as suitable drug loading time and possible leakage ratio of drugs, which helped us design appropriate processes in wet experiments and use appropriate concentrations of reagents.
In the Transport and Release part, we used NETLOGO to establish a cellular automaton model to demonstrate the differences in drug loading and drug release processes. We provided visual results and quantitative analysis to explore the maintenance time of possible effective drug concentration.
In this model, Basic Silinker protein cannot block MSN, so there is drug leakage caused by free diffusion during the transport process. Cut Silinker protein can ensure that drugs do not leak during transport, and when Cut Silinker protein reaches the target site, it can be cleaved by the corresponding enzyme, allowing the drugs to freely diffuse near the target site. Twisted Silinker protein can undergo conformational changes upon specific binding with Ca2+ ions, enabling controlled drug release. When the surrounding drug concentration is too high, the Twisted Silinker protein can be regulated by environmental factors, thereby ensuring a more stable drug release.
Protein structure and function are closely interrelated. A protein's structure is determined by its amino acid sequence, while its function is dictated by its structural arrangement. Different protein structures confer distinct functions and activities. Specific structural features enable proteins to interact with other molecules, thereby facilitating their specific functions.
In our designs, our proteins can only perform the required functions when they are exposed to the specific secondary structural regions as follows.
Figure 1 | rigid-linker
We require a rigid sequence as a linker to separate functional domains within the Silinker family, ensuring the efficient exposure of all structural domains. The α-helix within the linker constitutes a stable secondary structure(Figure 1), formed by hydrogen bonds within the helix, contributing to protein stability and compact folding. It aids in maintaining the specific spatial configuration of proteins, ensuring proper functionality and resistance, enhancing protein stability, and enabling resilience to environmental changes.
Figure 2| Cam
CaM contains multiple α-helical structures, each capable of binding to calcium ions. These α-helical structures are in an open state in the absence of calcium ions, but undergo structural changes and adopt a tighter closed conformation upon calcium ion binding. The transition of the α-helical structure is a key step for CaM's involvement in signal transduction processes [1].
Figure 3| mSA(Barrel-shaped β-fold structure)
The β-fold can form binding sites for interactions with ligand molecules. In many proteins, the β-fold structure is employed for specific binding to other proteins, DNA, RNA, and small molecules. This binding capability enables proteins to participate in signal transduction, catalysis, and structural support functions.
Monomeric Streptavidin (mSA) contains a binding site for very tight binding to biotin. Each binding site consists of a domain composed of β-fold structures called the biotin-binding pocket. This domain contains a long chain of folded β-strands, forming a specific groove that matches the structure of the biotin molecule [2].
The β-fold structure imparts stability and specificity to the biotin-binding pocket. By encapsulating and constraining the movement of the biotin molecule, the biotin-binding pocket can establish strong interactions with the biotin molecule. To validate whether our designed protein correctly folds to ensure the proper exposure of functional sites, we also utilized AlphaFold2 predictions.
Therefore, analyzing the structure of proteins can help in the design and optimization of protein molecules for improved functionality.
AlphaFold 2.0 is a protein structure prediction algorithm developed by DeepMind.
Its operation is quite simple: for a given protein sequence, it predicts its three-dimensional structure. This is currently the most accurate method for predicting the structure of unknown proteins. It accomplishes this by training specialized neural networks on the evolutionary, physical, and geometric constraints of protein structures [1], and it utilizes the Protein Data Bank (PDB) as a reference database.
The working mechanism can be simplified as shown in the following diagram (Figure 4):
Input: An amino acid sequence, where each element at each position represents an amino acid unit along the chain.
Output: The topological structure of the protein.
Figure 4| AlphaFold algorithm flow chart
The AlphaFold predictions indicate that several proteins can expose the requisite secondary structural regions(Figure 5), allowing them to perform their required functions effectively.
Basic Silinker
Pairing Silinker
Nucleotide Silinker
Cut Silinker1
Cut Silinker2
Cut Silinker3
Figure 5| Structures of several silinkers
Once we had designed the structure of the Twisted Silinker in a preliminary manner, We conducted dry lab validation and utilized the Alpha Fold 2 software for protein modeling to obtain the protein model of Twisted Silinker (Figure 6). It is noteworthy that the flexible linker fails to provide sufficient support, resulting in spatial proximity between the silica-binding peptide and streptavidin. This proximity may lead to cross-interference, impeding the normal functionality of the structure.
Figure 6| Twisted Silinker(before modification)
Recognizing that the flexible linker is excessively pliable and unpredictable, and may become entangled with CBP, thereby hindering proper structural extension, we opted to modify the linker sequence by replacing it with a rigid counterpart to ensure the normal functionality of the structural domain.
After a comprehensive review of the literature, we ultimately selected a combination of calmodulin and calmodulin-binding peptide, as detailed in [link to ENGINEERING], resulting in the current structure of Twisted Silinker (Figure 7). Subsequently, we conducted dry lab validation using AlphaFold 2 for simulation, and the results were consistent with the expected structural functionality.
Figure 7| Twisted Silinker(after modification)
To validate the accuracy of AlphaFold's structure predictions, including the exposure of specific sites and their congruence with the initial design, we conducted circular dichroism (CD) experiments. These experiments yielded structural information, which was subsequently utilized in conjunction with data from Multiple Sequence Alignment (MSA) and Basic Silinker analysis for further validation.
The experimental principle of CD is relatively simple. Since proteins are composed of amino acids linked together through peptide bonds, the peptide bonds, aromatic amino acid residues, and disulfide bridges in the structure are all functional groups with optical activity. Moreover, the optical activity of proteins is influenced by their secondary and tertiary structures. This phenomenon is known as protein circular dichroism , which follows certain patterns in CD spectra. Thus we can accomplish the above through CD experiments (PBS strongly absorbs at wavelengths below approximately 200 nm, which prevents the collection of CD data at these wavelengths. Therefore, all CD data were collected in water).
Figure 8|The compositional analysis of the secondary structure of Basic Silinker
Figure 9|Far-UV spectra of Basic Silinker in water at a concentration
Figure 10|The compositional analysis of the secondary structure of mSA
Figure 11|Far-UV spectra of mSA in water at a concentration
We are focusing on the β-sheet segments of the protein because the functional structure of the protein is a barrel-shaped β-fold structure in the mSA region, as shown in Figure 3. In this figure, all parts of the mSA segment are of the strand1 secondary structure. However, the bs segment has 0.17% of peptide segments. We speculate that this is because the SBP sequence is a peptide segment without secondary structure. However, the sequence lacks alpha helix, which we speculate is due to incomplete removal of the trx tag, resulting in a very low proportion of alpha helix. It can be observed that in the secondary structures of both proteins, β-sheets dominate the main segments, indicating that the mSA region still retains its original biological activity.
The results closely align with the predictions made by AlphaFold, and the structural integrity of mSA remained unchanged both before and after the binding process.
[1] Zhang, M. & Horst, R. (2016). Structural and functional evolution of the DRE/DREB transcription factor family in plants. Trends in Plant Science, 21(6), 524-534.
[2]Schmidt TGM, Eichinger A, Schneider M, Bonet L, Carl U, Karthaus D, Theobald I, Skerra A. The Role of Changing Loop Conformations in Streptavidin Versions Engineered for High-affinity Binding of the Strep-tag II Peptide. J Mol Biol. 2021 Apr 30;433(9):166893. doi: 10.1016/j.jmb.2021.166893. Epub 2021 Feb 24. PMID: 33639211.
[3]Jumper, J., Evans, R., Pritzel, A., Green, T., Figurnov, M., Ronneberger, O., ... & Hassabis, D. (2021). Highly accurate protein structure prediction with AlphaFold. Nature, 596(7873), 583-589.
Targeted release of drugs is one of the important downstream applications of the mesoporous nanosilica particles modified by different types of silinkers obtained in our project. The simulation of this process can guide future wet experiment design, improve work efficiency, and predict quantitative results in processes such as drug loading and protein modification.
Figure 1| Basic Silinker Workflow Diagram. ① paclitaxel drug into mesoporous silica(MSN). ② Attach Basic Silinker protein to the drug-loaded mesoporous silica nanoparticles (MSN) and formulate the BS-Pac-MSN system. ③ Bioconjugate the biotinylated insulin-like growth factor onto the BS-Pac-MSN system and formulate the Insulin-like growth factor-bio-BS-Pac-MSN system.
Figure 2| Twisted Silinker Workflow Diagram. ① Attach Twisted Silinker protein to the mesoporous silica nanoparticles (MSN) ② Bioconjugate the biotinylated protein onto the TS-MSN system. ③ Load drug into the TS-MSN system. ④ When the ambient calcium ion concentration increases, calmodulin, calcium ions, and calmodulin-binding peptide interact with each other, effectively reducing the physical distance to achieve the function of blocking MSN pores and controlling drug release.
To understand the process of drug molecule entering mesoporous silica nanoparticles (MSN) and the modification of MSN by two different Silinkers, Basic Silinker (BS) and Twisted Silinker (TS), we developed a concise ODE model using MATLAB and solved the model using the solver ode45.
Our differential equation model is based on Fick’s law of diffusion[1,2]. It was proposed by German physiologist Adolf Fick in the 19th century. The law describes the rate at which material diffuses through a concentration gradient. The diffusion of drug molecules and protein connections can be approximated as a dynamic process that depends on concentration and ultimately achieves steady-state equilibrium.
It is worth noting that the model construction of BS comes from real experimental data due to the influence of experimental progress, while the model construction of TS is directly based on parameter estimation on BS. We hope that the model results of TS can help experimental group students to design experiments more effectively in the future.
The details of our ODE model are as follws.
Figure 1-1丨Drug Loading. The 10ml Pac (1mg/ml) and 50ml MSN (1mg/ml) solutions are stirred in the dark for 24 hours. Then we can obtain the Pac-MSN system but this system has the issue of drug leakage
The differential equations can be rewritten as follows,
Figure 1-1丨Drug Loading. The 10ml Pac (1mg/ml) and 50ml MSN (1mg/ml) solutions are stirred in the dark for 24 hours. Then we can obtain the Pac-MSN system but this system has the issue of drug leakage
Then we can get the result.
Figure 1-1丨Drug Loading. The 10ml Pac (1mg/ml) and 50ml MSN (1mg/ml) solutions are stirred in the dark for 24 hours. Then we can obtain the Pac-MSN system but this system has the issue of drug leakage
The result shows changes in paclitaxel concentration in MSN over time.
Figure 1-2丨Surface Modification of Mesoporous Silica with Basic Protein. The extensive surface modification of MSN with Basic Silinker protein, among which silica-binding peptide (SBP) greatly facilitates the binding of Basic Silinker protein to silicon surfaces through non-specific physical adsorption. But the BS-Pac-MSN system also has the drug leakage problem.
The differential equations can be rewritten as follows,
Then we can get the result.
The result shows changes in paclitaxel concentration in MSN and the proportion of modified MSNs over time.
Figure 1-3丨Conjugate biotinylated insulin-like growth factor to the drug delivery system. Add 1mL of prepared soluble insulin-like growth factor protein to each tube and rotat at room temperature with the connected BS-Pac-MSN and we can get the Insulin-like growth factor-bio-BS-Pac-MSN system
The differential equations can be rewritten as follows,
Then we can get the result.
The result shows changes in paclitaxel concentration in BS-MSN and the proportion of modified BS-MSNs over time.
Figure 2-1丨Surface Modification of Mesoporous Silica with Twisted Protein. The extensive surface modification of MSN with Basic Silinker protein, among which silica-binding peptide (SBP) greatly facilitates the binding of Basic Silinker protein to silicon surfaces through non-specific physical adsorption.
The differential equations can be rewritten as follows,
Then we can get the result.
The result shows changes in the proportion of modified MSNs over time.
Figure 2-2丨Conjugate biotinylated insulin-like growth factor to the drug delivery system. Add 1mL of prepared soluble insulin-like growth factor protein to each tube and rotat at room temperature with the connected TS-MSN and we can get the Insulin-like growth factor-bio-TS-MSN system.
The differential equations can be rewritten as follows,
Then we can get the result.
The result shows changes in the proportion of modified TS-MSNs over time.
Figure 2-3丨Drug Loading. The 10ml Pac (1mg/ml) and 50ml MSN (1mg/ml) solutions are stirred in the dark for 24 hours. Then we can Load paclitaxel drug into the growth factor-bio-TS-MSN system and formulate the growth factor-bio-TS- Pac-MSN.
The differential equations can be rewritten as follows,
Then we can get the result.
The result shows changes in paclitaxel concentration in ILGF-TS-MSN over time.
Figure 2-4丨Induced calcium concentration. When the ambient calcium ion concentration increases, calmodulin, calcium ions, and calmodulin-binding peptide interact with each other, effectively reducing the physical distance to achieve the function of blocking MSN pores and controlling drug release.
The differential equations can be rewritten as follows,
Then we can get the result.
The result shows changes in paclitaxel concentration in ILGF- TS-MSN and the proportion of Folded TS over time.
[1]Trucillo,P.(2022). Drug Carriers: A Review on the Most Used Mathematical Models for Drug Release. Processes, 10(6), 1094.
[2]Elmas, A., Akyüz, G., Bergal, A., Andaç, M., & Andaç, Ö., (2020). Mathematical modelling of drug release. Research on Engineering Structures and Materials , vol.6, no.4, 327-350.
To demonstrate the differences in drug loading and drug release processes on different platforms, we modeled the processes of drug transport and release using Cellular Automaton for Mesoporous Silica Nanoparticles (MSN). The Cellular Automaton model was implemented using NetLogo. Basic Silinker protein cannot block MSN, so there is drug leakage caused by free diffusion during the transport process. Cut Silinker protein can ensure that drugs do not leak during transport, and when Cut Silinker protein reaches the target site, it can be cleaved by the corresponding enzyme, allowing the drugs to freely diffuse near the target site. Twisted Silinker protein can undergo conformational changes upon specific binding with Ca2+ ions, enabling controlled drug release. When the surrounding drug concentration is too high, the Twisted Silinker protein can be regulated by environmental factors, thereby ensuring a more stable drug release.
First, we set target patches as blue, purple balls as purple, and green squares as green. Then we generate a certain number of drug entities to visualize the internal environment of drug delivery to the target site. In each time step, the system checks the position and moves one unit distance towards the target point if the system has not reached the target point yet. Once the system reaches the target point, it stops moving forward. At the same time, the drug behaviors are simulated based on the properties of the three different proteins.
Basic Silinker protein mainly functions to connect MSN with biotinylated target proteins. In the drug delivery simulation, we modified insulin-like growth factor (IGF) with biotin and attached it to the surface of MSN using Basic Silinker. When the insulin-like growth factor in the system bound to insulin-like growth factor receptors on the surface of MCF7 cells, the entire system would be targeted to the vicinity of MCF7 cells, and the loaded drugs in the system would also be released near the MCF7 cells. However, it should be noted that drug release in the Basic Silinker system was continuous. To investigate the realistic process of drug movement and binding to the target after reaching the BS system, we simulated the free release of drugs. In each time step, we calculated the release rate based on the current drug remaining and randomly selected the corresponding number of drug entities to move in a random direction.
Figure 1| Basic Silinker Changes in Drug Concentration over Time. This graph depicts the change in drug concentration over time near the target site, with the x-axis representing the time steps of the simulation process and the y-axis representing the drug content. It demonstrates the variation of drug release in the BS system, showing a relatively stable release but with a smaller overall quantity.
Figure 2| Cut SIlinker Changes in Drug Concentration over Time. The graph in question illustrates the variation of drug concentration over time near the target site in the CS system. The x-axis represents the time steps of the simulation process, while the y-axis represents the drug content. It demonstrates that the drug release in the CS system rapidly increases initially and then gradually decreases over time, resulting in a relatively short effective duration.
According to the different enzymes in the environment, Cut Silinker protein can be cleaved by the corresponding enzyme to release the modified silica surface protein. In the drug delivery simulation, we used Cut Silinker to modify the biotinylated cell surface receptors onto the surface of MSN. Due to the steric hindrance caused by the size of Cut Silinker itself, the release of drugs during the movement was blocked. However, our simulation considered the presence of MMP2 enzyme in the cellular microenvironment. This enzyme bound to the PLGVR site in Cut Silinker, cleaving Cut Silinker and causing drug release. Therefore, drug release occurde only in each time step after the CS system reached the cellular target point, following a diffusion function.
Twisted Silinker protein can undergo conformational changes and adopts a "folded and curled" state upon specific binding with Ca2+ ions. In the drug delivery simulation, we modified the biotinylated cell surface receptors onto the surface of MSN using Twisted Silinker. Under high Ca2+ ion conditions, Twisted Silinker protein bent and folded, blocking the pores of MSN and preventing drug release. Under low Ca2+ ion conditions, the conformation of Twisted Silinker protein was restored, facilitating the release of drugs from MSN. Therefore, drug release in the TS system occured in specific cellular environments with low Ca2+ ion concentration, where drugs acted on the specific cells causing an increase in the Ca2+ ion concentration. Twisted Silinker protein sensed and bound to Ca2+ ions, leading to conformational changes and the cessation of drug delivery in the TS system. In the absence of drug action, the Ca2+ ion concentration decreased in the specific cellular environment, achieving controlled drug release, automatic sensing, and dynamic regulation.
Furthermore, the release of drugs during the movement is also influenced by the protein type. The molecular weight of the protein affects the leakage of drugs during the transport process. The larger the molecular weight of the protein, the less drug leakage occurs during transport. After reaching the target point, drugs initially diffuse according to a diffusion function. In each time step, the drug concentration in the surrounding area of the target point is calculated, and the drug release rate is determined by the remaining drug amount and the environmental concentration, allowing for the regulation of drug release rate.
*Connection between Silicon Dioxide Surface and Basic Silinker's SBP End
After the extensive extraction and purification of the Basic Silinker protein, we attempted to functionally test the protein for future use by iGEM teams.
We initially validated the binding of the Basic Silinker protein to the silicon dioxide surface. To achieve this, we conducted an in vitro co-incubation experiment of Basic Silinker with silicon dioxide and identified protein-containing fractions using SDS-PAGE and Coomassie Brilliant Blue staining. The results are depicted in the following figure: We observed that both Basic Silinker and non-specific proteins were abundant in the supernatant. However, the protein bands of Basic Silinker became progressively lighter in the lanes of the three washes, indicating that most unbound proteins were washed away. To confirm the binding of Basic Silinker to silicon dioxide, we denatured the protein through heating and denaturant treatment, allowing Basic Silinker to be washed out from silicon dioxide, demonstrating that it had bound to the surface. Protein bands of Basic Silinker were evident in both denaturation methods. Thus, we can conclude that Basic Silinker can effectively bind to the silicon dioxide surface.
Figure 3: SDS-PAGE analysis of the in vitro co-incubation of Basic Silinker protein with SiO2. The experiment involved the co-incubation of purified Basic Silinker protein with SiO2 for 3 hours. A protein ladder ranging from 10-190kDa (Blue Plus V Protein Marker) was used for comparison. Lanes 1-6 represent the supernatant, SiO2 wash 1, SiO2 wash 2, SiO2 wash 3, SiO2 co-incubation at 99°C for 20 minutes without loading denaturant, and SiO2 co-incubation at 99°C for 20 minutes with loading denaturant, respectively. Electrophoresis was conducted at 80v for 10 minutes followed by 150v for 20 minutes. The gel was stained with Coomassie Brilliant Blue and subjected to protein analysis.
*Testing the Thermal Stability of Basic Silinker
Figure 3| The Effective Duration of Drug Release in Various Protein Systems. The x-axis of the graph represents different proteins, while the y-axis represents the effective duration of drug release.
For Cut Silinker, there is no regulation mechanism, so the drug concentration initially rises rapidly outside the effective range and gradually decreases to return to the effective range, becoming ineffective after a certain period of time.
Twisted Silinker, on the other hand, is regulated by the drug concentration. Therefore, when the drug concentration is too high, the release of drugs decreases accordingly, resulting in a more stable drug release and a longer overall effective duration. At the same time, if the molecular weight of Twisted Silinker is small, it may lead to excessive drug leakage during the transport process. When binding to the target, the total amount of carried drugs decreases, resulting in a decrease in the overall drug release concentration and a subsequent reduction in the effective duration.
Figure 4| The Changes in Drug Concentration over Time of Twisted Silinker Protein under Different Target Protein Molecular Weights. The concentration changes of drug release in different types of Twisted Silinker have been visualized. In this graph, the x-axis represents the time steps of the simulation process, while the y-axis represents the drug content near the target site. As the molecular weight of the TS system increases, both the total amount of drug release and the effective duration of drug increase.
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