Computational simulation for TiN plasmonic biosensor

Understanding the molecular interaction between the receptors and TiN surface leading to successful functionalization and subsequent biosensing is the most significant attribute of computational modeling. At Rafael Biotechnology, we invested considerably towards the computation resources. There are three open-sourced software packages installed on our cluster i.e.

• Quantum Espresso [1] for DFT calculation based on quantum mechanics,
• GROMACS [2] for molecular dynamics based on classical force fields,
• MEEP [3] for finite difference time domain electromagnetic modeling of TiN nanocube.

With these three packages, we can explore the biochemistry of TiN biosensors from subatomic level to molecular scale then finally in nanometers.

Let's start with an example i.e., functionalization of oligonucleotides on the TiN(200) surface. This is particular important for our LSPR biosensor for molecular diagnostics. We started with the four basic nucleotides i.e., Adenine (A), Gaunine (G), Cytosine (C), and Uracil (U). One of these nucleotides are placed sufficient close to the TiN(200) surface but with different orientation with respect to the sugar ring nomenclature i.e., 1' to 5'. The 1’ end is decorated with one of AGCU which is responsible to the formation of DNA/RNA double helix via hydrogen bonding. The 5’ end is the PO4 functional group which is response for the extension of the DNA/RNA backbone thus formation of the genetic sequence. The standard pseudopotential library was used in the DFT calculation. The model includes a TiN(200) slab with sufficient multiple TiN basic cells, a oligonucleotide with chosen orientation, and a vacuum space above the slab to avoid interaction between adjacent duplicates. The model was fully relaxed to ground state and the final energy of the system is determined in eV. The adsorption energy of each orientation is calculated by the following equation,

 E_{ads =} E_slab+nt - E_slab - E_nt

where E_slab+nt is the final energy of the model with a nucleotide adsorbed on the TiN slab surface, E_slab  is the final energy of the model with the TiN slab surface only, and E_nt is the final energy of the model with the nucleotide only. It is important to state that there are at least 5 orientations in the sugar ring from 1’ to 5’, so there are at least 5 calculations for each nucleotides. By comparison of the adsorption energy, we can estimate the preferred adsorption orientation on TiN surface. The most striking discovery of adsorption energy are summarize in Table 1 below.

Table 1. Adsorption energy of AGCU on TiN(200) surface with 1’ and 5’ orientations

So it is obvious that the adsorption energy via 5’ end is more negative than those via 1’ bases. Therefore, the 5’ end with PO4 is the preferred orientation for AGCU to anchor on the TiN(200) surface. This is actual beneficial to the DNA/RNA sensing scenario as complementary pairs always hybridize via the 1’ base via hydrogen bond. As functionalization binding is preferred via the 5’ end, it does not compete with the hybridization site for binding. Therefore, AGCU nucleotides can be directly used to functionalization the TiN surface for LSPR biosensing. This is an improvement over existing gold based SPR device, since it is simple and robust. Operators are no longer required to activate the sensing surface with unstable thiol chemicals thus save time and cost. The optimized structures of AGCU on TiN(200) with 1’ base and 5’ end are shown in Figure 1 and Figure 2 respectively.

Figure 1. Optimized nucleotides AGCU adsorbed via 1’ bases on TiN(200)

Figure 2. Optimized nucleotides AGCU adsorbed via 5’ end on TiN(200)

Another powerful aspect of computational modeling is to explore potential receptor candidates on specific protein target via dynamic docking. For example, a synthetic molecular receptor of small size 100 Da would be more effective in the capture of targeted protein antigen than a 100 KDa antibody. This is because large antibody is vulnerable to nonspecific binding and gives false positive result. The docking process is essentially performed with molecular dynamics, and it does not matter on where the receptor is placed at the beginning. As computation starts, the receptor moves randomly around the protein target searching for the docking location. Once the docking location is found, the receptor reorients its position to fit into the docking pocket. After that, it stays in the pocket as long as the system temperature remains about the same. To illustrate docking with molecular dynamics, we use the GROMACS open-sourced package to study the interaction between Kelch-like ECH-associated protein 1 (KEAP1) and and a small molecule called LgN from herbal extract. The root mean squared distance (RMSD) of LgN from KEAP1 target is calculated for 200 nanoseconds and plotted in Figure 3. The number is an indicator of the LgN position as the MD simulation runs. With the first 25 nanoseconds, LgN tends to moves randomly to search for the binding site. From 25 to 75 nanoseconds, the RMSD is relatively stable because LgN have attached to a site relatively far from the initial position. However, the first attachment is unstable. So, LgN is detached from the site and restarted searching at about 85 nanoseconds. From 85 to 105 nanoseconds, LgN overcomes the positional barrier and finally arrived on the optimal docking pocket. After 125 nanoseconds, LgN stays in the same docking site as time evolves. Therefore, we are convinced that LgN is a potential candidate as small molecular receptor for the KEAP-1 target. The snapshots at stages A, B and C of RMSD are shown in Figure 4, 5 and 6 respectively. The corresponding animation movie at stages A, B and C can be also found on this page.

Figure 3. RMSD of LgN with least squared fit to KEAP-1 backbone.

Figure 4. Top view of LgN and KEAP-1 at stage A.

Figure 5. Top view of LgN and KEAP-1 at stage B.

Figure 6. Top view of LgN and KEAP-1 at stage C.

Finally, the open-sourced finite difference time domain (FDTD) package MEEP helps to calculate the electromagnetic field as free space light wave interacts with TiN and induces plasmonic resonance. It is well known that plasmonic resonance produces intensified electromagnetic field in close proximity to the nanostructures, but the far field redistribution of wave energy is seldom explored. However, the far field intensity pattern plays a crucial role in the development of LSPR biosensor. Besides, with 3D printing fabrication of substrate, we introduce photo-excited dye molecules as dipole sources to the substrate by optical pumping with LEDs. This is to enable thermoplasmonic heating to unfold DNA/RNA sequences for direct hybridization on the TiN surface. Doing so, we can detect different fragments of DNA/RNA sequences using our LSPR biosensor with thermoplasmonic technology. The computational model includes a TiN nanocube of size 45nm in length and it is partially embedded in a PMMA substrate as shown in Figure 7. With 3D printing, we can adjust the concentration of dye molecules premixed with PMMA monomers, so here we modified the number of excited dipoles in the PMMA substrate from 1 to 10,000. The incident wavelength was set to 638nm and polarized in the XZ plane propagating towards Z direction. Electromagnetic field plane monitors were placed at the center of the XZ and YZ planes to record the light wave amplitude and phase. The computation ran for sufficient long duration until the wave amplitude decays to a prescribed threshold. The results are shown in Figure 8 to 12 with different number of dipole sources from 1 to 10,000. It is obvious that the electromagnetic field intensity in Y direction (|Ey|2) is rather weak because the incident light wave is X polarized. As the number of dipoles increases from 1 to 10,000, |Ey|2 increases from 0.06 to over 200 proportionally. With greater the electromagnetic field, the Joule heating shall increases. This is affirmative that our TiN nanocube is an excellent nanostructure for thermoplasmonic applications.

Figure 7. 3D model of the TiN nanocube partially embedded in the PMMA substrate

Figure 8. EM field intensity of the TiN nanocube at XZ plane with 1 dipole source

Figure 9. EM field intensity of the TiN nanocube at XZ plane with 10 dipole sources

Figure 10. EM field intensity of the TiN nanocube at XZ plane with 100 dipole sources

Figure 11. EM field intensity of the TiN nanocube at XZ plane with 1,000 dipole sources

Figure 12. EM field intensity of the TiN nanocube at XZ plane with 10,000 dipole sources

References

[1] Quantum Espresso, https://www.quantum-espresso.org/

[2] GROMACS, https://www.gromacs.org/

[3] MEEP, https://meep.readthedocs.io/en/latest/