To validate the reliability of our simulations and establish a thermodynamic basis for the protein's function, key physical properties were monitored for both the ion-free (Apo) and various Rare Earth Element (REE)-bound (Holo) protein systems. To illustrate the common findings across all systems, the simulation of Lanthanum (La³⁺)—the first member of the lanthanide series—is presented as a representative example. Successfully demonstrating its stable binding is a critical first step and proof-of-concept for the viability of this protein platform.

The simulation results show that both the La³⁺-Holo (Figure 1a) and Apo (Figure 1b) systems reached a stable equilibrium.

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Figure 1: Equilibration and System Stability of the Lanthanum Simulation Systems. Key physical properties (Temperature, Pressure, Density, and Total Energy) are plotted as a function of time for the production MD simulation. (a) The La³⁺-Holo system demonstrates a stable trajectory with the ion bound in the active site. (b) The corresponding Apo (ion-free) control system also shows a stable and well-equilibrated trajectory.

The simulation results show that both the La³⁺-Holo (Figure 1a) and Apo (Figure 1b) systems reached a stable equilibrium. Both systems maintained the target temperature at approximately 298.4 K and exhibited stable pressure and density fluctuations, confirming the reliability of the simulation trajectories. In terms of energy, the average total energy for the La³⁺-Holo system was -68999.33 kcal/mol, while the Apo protein's average total energy was -69061.28 kcal/mol. Both of these are highly negative values, indicating that the ion-bound complex achieves a highly stable energetic state. While a significant energy drop relative to the Apo state was not observed in this case, the critical finding is that the introduction of the ion does not destabilize the system. Instead, a comparably low-energy and stable complex is formed. This finding, consistent across all simulated REE-protein complexes, provides a solid theoretical basis for the protein's function as a REE-binding platform.

These foundational findings provide direct and critical guidance for the wet lab team. First, the successful and stable binding of Lanthanum, the archetypal REE, theoretically validates our chosen protein as an effective and robust scaffold. It confirms that its binding pocket is structurally and chemically competent to accommodate lanthanides. Second, the calculated parameters for the La³⁺ system (e.g., energy, structural stability) establish a crucial quantitative baseline for assessing selectivity. The binding behavior of other, more industrially valuable heavy REE (like Nd³⁺ and Dy³⁺) can now be directly compared against this baseline. This allows for the computational prediction of affinity differences, providing a rational priority list for wet-lab experiments aimed at selective element separation, thereby saving significant time and resources.

To investigate the structural integrity of the protein scaffold, we calculated the Root Mean Square Deviation (RMSD) of the protein backbone relative to its initial, minimized structure. The Lanthanum (La³⁺) system is presented as the representative case (Figure 2). For this analysis, the backbone RMSD is the primary metric for protein stability, as the "All Atoms" RMSD is dominated by the diffusion of solvent and is not indicative of protein folding.

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Figure 2: RMSD Analysis Reveals Ion-Induced Structural Stabilization. The Root Mean Square Deviation (RMSD) of the protein backbone is plotted as a function of time for the 10 ns production simulation, calculated relative to the initial minimized structure. (a) The Apo (ion-free) system exhibits a higher and more fluctuating RMSD with a mean of 1.442 Å, indicating significant conformational flexibility. (b) The La³⁺-Holo (ion-bound) system shows a markedly lower and more stable RMSD with a mean of 1.015 Å. The comparison clearly illustrates the significant structural stabilization of the protein upon ion binding.

The results reveal a critical insight into the protein's behavior: the binding of the La³⁺ ion is essential for maintaining the structural integrity of the protein. As shown in the bottom panels of Figure 2, the protein backbone demonstrates exceptional stability in the La³⁺-bound (Holo) state (Figure 2b). It rapidly equilibrates and subsequently fluctuates around a very low mean value of 1.015 Å, confirming that the protein maintains its tertiary structure robustly when the ion is present.

In stark contrast, the ion-free (Apo) protein (Figure 2a) is significantly less stable. Its backbone RMSD is not only much higher on average (mean RMSD of 1.442 Å) but also exhibits larger fluctuations. This indicates that in the absence of a bound lanthanide, the protein scaffold is substantially more flexible and may be prone to partial unfolding. Therefore, the binding event is not a simple interaction but a crucial ion-induced stabilization of the entire protein fold.

This analysis provides two critical insights for the REE wet lab. First, it strongly suggests that the lanthanide ion acts as an essential co-factor required for the proper folding and structural integrity of the protein. The protein is not merely a scaffold; it is a dynamic system that is actively stabilized by its target. Second, this has direct practical implications for experimental work. The observed instability of the Apo protein suggests it may be prone to misfolding or aggregation during expression and purification. To counteract this, it is highly recommended to supplement purification and storage buffers with a low concentration of a stabilizing cation (e.g., Ca²⁺, or a target REE like La³⁺) to ensure the protein remains in its stable, functional conformation.

To understand how REE binding affects the local dynamics of the protein, we calculated the Root Mean Square Fluctuation (RMSF) for each residue in both the Apo and La³⁺-Holo states (Figure 3). The analysis reveals a distinct "dynamic signature" of binding, where specific flexible loops become dramatically rigid upon capturing the ion. This provides a direct molecular explanation for the pH-dependent binding and release mechanism observed in the wet lab experiments.

Figure 3: RMSF Analysis Identifies Key Binding Loops and a pH-Sensitive Switch. The top panel shows the per-residue Root Mean Square Fluctuation (RMSF) for the Apo (blue) and La³⁺-Holo (red) states, highlighting the general rigidification of the protein upon ion binding. The bottom panel displays the difference in RMSF (ΔRMSF = Holo RMSF – Apo RMSF), where large negative values pinpoint regions of significant stabilization. The analysis reveals several key regions of ion-induced rigidification, most notably the loop around residue 62 (ΔRMSF ≈ -2.1 Å), as well as loops near residues 125 and 170-172. These highly stabilized regions are identified as the primary binding sites that form the core of the pH-sensitive capture-and-release mechanism.

The RMSF analysis reveals that specific flexible loops become dramatically rigid upon capturing the ion. The most significant effect occurs in the loop region spanning approximately residues 60-65, where the flexibility of residue 62 decreases by a remarkable 2.1 Å. An analysis of the amino acid sequence in this exact region provides a definitive explanation:

Sequence (Residues 57-70): I-N-P-D-G-D-T-T-L-E-S-G-E-T

This region is densely populated with acidic residues (Aspartate - D, Glutamate - E), which are deprotonated and negatively charged at neutral pH. This creates a powerful electrostatic trap for the positively charged La³⁺ ion. The dramatic rigidification observed in our simulation is the direct result of the REE ion forming a stable, multi-point coordination network with these negative "anchors," effectively locking this entire flexible loop into a stable, ion-bound conformation.

Crucially, this integrated analysis provides a precise molecular explanation for the pH-dependent elution strategy used by the wet lab. When the pH is lowered for the elution step, the excess protons neutralize the negative charges on the Aspartate and Glutamate side chains (COO⁻ ⟶ COOH). This dismantles the electrostatic cage holding the ion, causing the loop to relax and release the REE. Therefore, our simulation and sequence data together identify the acidic-residue-rich loop around residue 62 as the core pH-sensitive "switch" that governs the entire capture-and-release cycle. This knowledge provides a direct, molecular-level rationalization for the experimental results and offers specific targets for future mutations aimed at fine-tuning the pH sensitivity or selectivity of the protein.

To elucidate the direct chemical environment responsible for REE binding, we analyzed the coordination sphere around the La³⁺ ion throughout the simulation (Figure 4). The results confirm the formation of a highly stable and chemically specific coordination complex, providing a direct explanation for the high binding affinity observed experimentally.

Figure 4: Coordination Analysis Confirms a Stable and Chemically Specific La³⁺ Complex. Analysis of the La³⁺ ion's coordination environment. (Top Panels) The coordination number for each ion remains highly stable with a mean of 9 throughout the simulation. (Bottom-Left Panel) The distribution of coordination distances shows a sharp, unimodal peak centered at ~2.45 Å, corresponding to the characteristic La-O bond length. This combination of a high, stable coordination number and a specific bond distance provides definitive evidence of a well-structured, chemically specific complex, which is the molecular basis for the protein's high binding affinity.

The analysis reveals that each La³⁺ ion maintains a high and remarkably stable coordination number, with an average of 9 coordinating atoms throughout the simulation (Figure 4, top panels). This high coordination number indicates that the ion is tightly chelated within a well-structured binding pocket. Complementing this finding, the distribution of coordination distances exhibits a sharp, unimodal peak centered at approximately 2.45 Å (Figure 4, bottom-left panel). This distance is in excellent agreement with the characteristic bond length of Lanthanum-Oxygen (La-O) coordination bonds. The combination of a high, stable coordination number and a characteristic bond length provides definitive evidence of a strong, chemically specific interaction, rather than a simple, non-specific electrostatic attraction.

This detailed chemical picture provides a powerful explanation for the REE wet lab's key findings. First, the formation of multiple (≈9), stable coordination bonds with a characteristic ~2.45 Å length is the direct chemical basis for the high binding capacity and affinity measured in the adsorption experiments. The protein acts as a highly effective chelator. Second, this analysis reinforces our understanding of the pH-release mechanism: the acidic residues (Asp, Glu) provide the essential oxygen atoms for this coordination. Lowering the pH protonates these oxygen-providing groups, directly breaking the coordination bonds and thereby dismantling the entire complex to release the REE. This provides a clear, actionable model for the wet lab: the integrity of this 9-coordinate, ~2.45 Å sphere is the primary determinant of binding success.

To assess the impact of REE binding on the overall shape and compactness of the protein, we calculated the radius of gyration (Rg) for both the apo and holo states (Figure 5). The analysis reveals that the protein undergoes a small but consistent compaction upon ion binding, which has important implications for its stability and robustness as a biomaterial.

Figure 5: Radius of Gyration (Rg) Analysis Shows Protein Compaction upon La³⁺ Binding. The overall compactness of the protein was compared between the Apo (blue) and La³⁺-Holo (red) states. The plots of Rg over time, the statistical distribution, and the box plot all consistently show that the Holo state (Mean Rg = 17.55 Å) is more compact than the Apo state (Mean Rg = 17.60 Å). This suggests that ion binding induces a more stable, condensed protein conformation.

The smoothed trends and statistical distributions (Figure 5) clearly show that the holo-protein is more compact than the apo-protein. The mean Rg for the La³⁺-bound state (17.55 Å) is measurably lower than for the apo state (17.60 Å). This compaction is a physical manifestation of the strong internal forces generated by the formation of the stable REE coordination complex, which pulls the entire protein structure into a slightly tighter, more condensed conformation.

From an experimental and practical standpoint, this finding is highly significant for the REE wet lab. A more compact protein structure is generally more stable and resistant to thermal or chemical denaturation. The prediction that the REE-bound form is more compact strongly suggests it is also the more stable form. This enhanced stability is a highly desirable feature for a recycling agent, as it would allow the protein to withstand multiple cycles of binding and pH-mediated elution without significant degradation or loss of function.

Therefore, our simulation provides a structural basis for the high operational stability and reusability that are critical for the practical application of this REE-binding protein. This insight allows the wet lab to rationalize the robustness of their system. It suggests that the protein is not just an effective binder, but a durable biomaterial that is potentially stabilized by the very cargo it is meant to carry. This provides confidence in the material's potential for long-term, cyclical use in a real-world recycling process.

To synthesize our findings, we conducted a final set of analyses to generate a quantitative prediction of binding selectivity and to understand the sophisticated ways in which lanthanide ions regulate the protein's functional movements at an allosteric level. By integrating four key biophysical indicators into our custom scoring model, we generated a quantitative ranking of the protein's binding affinity for six different lanthanide ions. This ranking reveals a distinct selectivity profile, providing a direct, testable prediction for the wet lab and a clear guide for separation applications (Figure 6).

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Figure 6: Quantitative Affinity Ranking and Selectivity Profile. (a) Normalized affinity ranking of six lanthanide ions derived from the multi-metric model, showing a strong preference for La³⁺ and Ce³⁺. (b) Heatmap breakdown of the final scores, detailing each ion's performance across the four key metrics (Contacts, RMSD Stability, Rigidity, and Proximity). (c) Radar chart providing a visual summary of each ion's strengths and weaknesses.

The final affinity ranking shows a clear tiered preference: Cerium (CE, Score: 1.000) and Lanthanum (LA, Score: 0.992) are decisively the strongest binders, followed by a middle tier of Praseodymium (PR, 0.558) and Dysprosium (DY, 0.496). Gadolinium (GD, 0.217) and especially Neodymium (ND, 0.000) are the weakest binders. This result is a direct, actionable prediction for the wet lab: we hypothesize that in a competitive adsorption experiment, the LanM LBD bio-adsorbent will show the highest binding capacity for Cerium and Lanthanum. This provides a clear path for experimental validation using methods like ICP-MS.

The power of this model lies in its ability to explain the reasons for this selectivity, which is critical for rationalizing experimental outcomes. The heatmap breakdown (Figure 6b) shows that La³⁺ and Ce³⁺ are top performers across all metrics. For example, the best-binding La³⁺ ion induced the largest stabilizing effect on the protein (ΔRMSD = 11.13 Å) and formed an extremely rigid binding pocket (RMSF = 0.609 Å). In stark contrast, Neodymium fails because it is unable to create a rigid binding pocket (Flexibility Score: 0.0) or establish sufficient atomic contacts (Contact Score: 0.0). This insight directly informs the wet lab's separation strategy. The protein’s natural preference for light lanthanides (La, Ce) over others suggests its immediate utility in group separation processes, for instance, purifying La/Ce from a mixed feedstock containing Nd.

Figure 7: Principal Component Analysis (PCA) of the La³⁺ System. This analysis of collective protein motions shows that the dominant functional movements (represented by PC1 and PC2) are suppressed upon ion binding (Holo state, red) compared to the more flexible Apo state (blue). This demonstrates a global stabilization effect.

To understand how the protein achieves this function, we analyzed how ion binding affects its global movements using Principal Component Analysis (PCA) on the La³⁺ system as a representative case (Figure 7). PCA identifies the dominant, large-scale collective motions, which are essential for protein function and stability. The analysis clearly shows that the protein's most dominant motions (Principal Components 1 and 2) are significantly suppressed upon La³⁺ binding. This finding provides a deep mechanistic explanation for the enhanced stability we observed in the RMSD and Rg analyses; by 'locking down' these large-scale motions, the bound ion makes the protein a more robust and durable biomaterial, a critical feature for achieving the wet lab's goal of creating a reusable bio-adsorbent.

Figure 8: Dynamic Network Analysis Reveals Allosteric Rewiring. Residue-residue correlation matrices for the Apo and Holo states. The Correlation Difference map (bottom-left) is most critical, revealing that ion binding induces long-range changes in the protein's internal communication network, highlighting potential allosteric sites for future engineering.

Going deeper, we analyzed how this stabilization propagates through the protein's internal communication network (Figure 8). The Dynamic Network Analysis reveals that binding a single ion at the active site induces long-range changes in correlated motions across the entire structure, effectively "rewiring" the protein's internal dynamics. This "wiring diagram" is invaluable for advanced protein engineering. For example, to improve the binding of a valuable heavy REE like Dysprosium, the wet lab can now move beyond mutating the active site. Our analysis identifies distant "hotspot" residues that are dynamically coupled to the binding pocket. Mutating these allosteric sites, now identified by our model, offers a sophisticated and rational strategy for fine-tuning binding selectivity without disrupting the primary coordinating residues, providing a clear roadmap for the next cycle of protein design.