Overview

Our project aimed to develop a novel eye drop based on engineered manganese superoxide dismutase (Mn-SOD) for the early prevention of cataracts. In our initial Design-Build-Test-Learn (DBTL) cycle, we addressed the challenge of Mn-SOD’s tendency to form inclusion bodies in prokaryotic expression systems by implementing a low-temperature induction (16°C) strategy and chaperone co-expression. This approach significantly enhanced soluble expression, providing a solid foundation for scalable production. Furthermore, leveraging a Transformer-based deep learning model, we rationally designed mutations and obtained high-performance variants including G93H (which exhibited a 15.15% increase in enzyme activity) and D107L (showing a 22.26% improvement in thermal stability). These modifications substantially boosted both catalytic efficiency and structural robustness of Mn-SOD. Additionally, we also constructed a multi-scale mathematical model from microcatalytic kinetics to macroscopic 0-dimensional homogeneous system and then to 1-dimensional spatial reaction-diffusion, aiming to simulate and optimize the process of Mn-SOD eye drops from molecular mechanism to in vivo spatiotemporal efficacy, thereby significantly improving the efficiency and accuracy of formula screening and drug delivery protocol design. These engineering advances not only ensure high enzymatic activity and stability of Mn-SOD in ocular formulations but also establish an integrated workflow—from computational design to efficient enzyme production—enabling the development of potent antioxidant eye drops with strong translational potential. Moving forward, we will focus on combining beneficial mutations to achieve synergistic improvements in enzyme performance and explore targeted ocular delivery strategies to accelerate the application of Mn-SOD-based therapeutics.

Cycle 1: Preliminary Experimental Design

Design 1.0

Our project obtained the original gene sequence of manganese superoxide dismutase (Mn-SOD) from the iGEM Part Registry (Part ID: BBa_K4907023). Guided by rational design principles, we performed comprehensive codon optimization to replace rare codons with those preferentially used in Escherichia coli (E. coli) BL21 (DE3), thereby significantly enhancing translational efficiency. Replacing rare codons can significantly improve translation efficiency and protein yield, which is crucial for the future industrial production of core active ingredients in eye drops, laying the foundation for large-scale production and reducing manufacturing costs, ensuring the economic viability and scale potential of our therapies.

The optimized sequence was commercially synthesized to produce a high-purity linear DNA fragment, which was then seamlessly assembled with a linearized pET28a expression vector using the Gibson Assembly method, resulting in the successful construction of the recombinant plasmid pET28a-Mn-SOD (Figure1).

Figure1. Construction of pET28a-Mn-SOD recombinant plasmid and gene circuit design.

Build 1.0

The recombinant plasmid pET28a-Mn-SOD was introduced into Escherichia coli BL21 (DE3) by thermal shock transformation, and then the transformation product was coated in LB solid medium containing kanamycin (Kan) and incubated in a 37℃ constant temperature incubator for 16 hours. Single colonies with regular edges were selected from the cultured plates and identified by colony PCR, and the results (Figure2) were consistent with the expected band size of interest (606 bp).

Figure2. Bacterial solution PCR result of pET28a-Mn-SOD recombinant plasmid.

Test 1.0

Single colonies identified as positive by colony PCR were selected and inoculated into LB(Kan) liquid medium for activation culture, followed by expanded culture and induced expression of the protein of interest. The induction conditions were set to: 37 °C, 180 rpm oscillation culture for 16 hours. After the induction, the bacteria were collected, the supernatant and precipitate were separated by ultrasonic fragmentation, and the expression and solubility of the target protein were analyzed by SDS-PAGE. The theoretical molecular weight of the target protein (Mn-SOD) was 27.9 kDa. The SDS-PAGE results showed that the induced expression of Mn-SOD mainly existed in the precipitate after cell fragmentation in the form of inclusions, and the proportion of soluble expression was low, which complicated the subsequent study of its enzymatic properties (Figure3). Soluble proteins were a key prerequisite for the preparation of liquid pharmaceutical formulations, especially eye drops. This was a key obstacle to our goal of developing liquid formulation eye drops, as the proteins in inclusions are inactive and difficult to use directly in eye drops formulations. Therefore, how to obtain high-yield, soluble active Mn-SOD has become a core engineering problem that we must solve in the next cycle.

Figure3. SDS-PAGE result of pET28a-Mn-SOD.M: Protein Marker; Lane1, 3, 5: Precipitation of Mn-SOD; Lane2, 4, 6: Supernatant of Mn-SOD.

Learn 1.0

The target protein Mn-SOD mainly exists in the form of inclusions in the expression system of Escherichia coli, and the main reasons include the following aspects: first, Escherichia coli, as a prokaryotic expression system, lacks the complex molecular mechanism and intracellular environment that assists in the correct folding of proteins in eukaryotes; Secondly, driven by strong promoters (such as T7), the expression rate of the target protein is too fast, and a large number of newly synthesized peptide chains cannot obtain the necessary folding assistance in time, resulting in the accumulation of intermediates. In addition, the redox environment in prokaryotic cells is different from that of the eukaryotic system, which is not conducive to the formation of active conformations in proteins.

To address this challenge and enhance the soluble expression ratio, we implemented two primary strategies for systematic optimization. First, chaperone proteins were co-expressed to simulate a eukaryotic-like folding environment, assisting Mn-SOD in achieving proper three-dimensional assembly and thereby significantly minimizing inclusion body formation. Second, the protein synthesis rate was reduced through fermentation temperature optimization, which provided a more sufficient time window for correct peptide chain folding. These approaches established a critical foundation for achieving high-level soluble expression of Mn-SOD and supported subsequent functional studies.

Cycle 2: Optimizing Soluble Expression of Mn-SOD

Design 2.1

Chaperones are a class of proteins that can defold, degrade, and label misfolded proteins to maintain protein homeostasis, which can promote correct protein folding and soluble expression, effectively reduce the formation of inclusions, but do not affect the activity of proteins. In this part of the experiment, we selected three chaperone plasmids (pGro7, pKJE7, pTf16) and pET28a-Mn-SOD to co-introduce them into Escherichia coli BL21 (DE3), so that the chaperone proteome can act synergistically and participate in protein folding. By assisting the correct folding of foreign proteins in prokaryotic cells, the soluble expression ratio of foreign proteins was increased, which laid the foundation for obtaining sufficient soluble Mn-SOD target proteins and subsequent biological function studies.

Build 2.1

Three chaperone plasmids procured from TaBaRa company were co-introduced into E. coli BL21 (DE3) host cells through thermal shock transformation with pET28a-Mn-SOD plasmids, and the transformation products were coated on bi-resistant screening plates containing kanamycin (Kan) and chloramphenicol (Cm) for preliminary screening.

Test 2.1

Positive single colonies were selected and inoculated into LB (Kan+Cm) liquid medium for activation and expansion culture. The induction conditions were set to: 37 ℃, 180 rpm oscillation culture for 16 hours. After the induction of expression, bacterial fragmentation and protein purification were performed. The supernatant and pellet after cell fragmentation were collected and protein expression and solubility were analyzed by SDS - polyacrylamide gel electrophoresis (Figure4). The theoretical molecular weight of the target protein (Mn-SOD) was 27.9 kDa. In the case of non-co-expression of chaperones, most of Mn-SOD formed insoluble inclusions, and very few soluble molecules were observed (Figure4 Lane1 and 2). This suggested that the protein struggled to fold correctly on its own in the prokaryotic system. Co-expression of pGro7 significantly increased the soluble expression of Mn-SOD (Figure4 Lane3 and 4). A large amount of protein was transferred from the pellet to the supernatant. Co-expression of pKJE7 also proved highly effective in promoting the soluble expression of Mn-SOD (Figure4 Lane7 and 8). In contrast, co-expression of pTf16 had a certain effect on improving the solubility of Mn-SOD (Figure4 Lane5 and 6), but its effect was not as pronounced as that of the other two chaperone systems.

Figure4. SDS-PAGE result of pET28a-Mn-SOD and Chaperones co-expression.M: protein marker; Lane 1: Precipitation of Mn-SOD; Lane 2: supernatant of Mn-SOD; Lane 3: Precipitation of pGro7/Mn-SOD; Lane 4: supernatant of pGro7/Mn-SOD; Lane 5: Precipitation of pTf16/Mn-SOD; Lane 6: supernatant of pTf16/Mn-SOD; lane 7: precipitation of pKJE7/Mn-SOD; Lane 8: supernatant of pKJE7/Mn-SOD

In order to further quantify the expression level of the target protein, the SDS-PAGE gel was detected by optical density spectrometry, and the expression levels of the target protein in different treatment groups were quantitatively compared by grayscale value, so as to clarify the effect of chaperone co-expression on the soluble expression of Mn-SOD. The protein solubility of pGro7/Mn-SOD and pTf16/Mn-SOD was increased by 1.48 times compared with Mn-SOD, and the density value of protein bands in the prelet was also reduced. The conclusions show that the addition of molecular chaperones significantly improves the solubility of the target protein (Figure5).

Figure5. Quantitative analysis of SDS-PAGE results.A: Optical density analysis of Mn-SOD supernatant and precipitate components co-expressing chaperone proteins;B: Comparison of the percentage soluble expression of Mn-SOD in co-expressed chachaper proteins.

Learn 2.1

Three molecular chaperones (pGro7, pKJE7, and pTf16) were co-expressed, and the correct folding of helper proteins could improve the soluble expression of Mn-SOD protein in the prokaryotic expression system

Design 2.2

The difference in induction temperature can significantly affect the expression abundance, folding efficiency, and growth status of the target protein. Recombinant E. coli BL21 (DE3) was inoculated with suitable medium and cultured at 37°C at 200 rpm. When the optical density (OD600) of the bacterial culture reached 0.6 at 600 nm, isopropyl thiogalactoside (IPTG) was added at a final concentration of 0.5 mM for induction. Subsequently, the cultures were placed at 16°C, 25°C, 30°C, 37°C and incubated for 16 h at 180 rpm oscillation conditions to induce the expression of Mn-SOD enzymes.

Build 2.2

The approximate method was the same as Build 1.0, with only the induced temperature gradient set (16°C, 25°C, 30°C, and 37°C).

Test 2.2

1.Mn-SOD Soluble expression detection

After the induction of expression, bacterial fragmentation and protein purification were performed. The supernatant and pellet after cell fragmentation were collected and protein expression and solubility were analyzed by SDS - polyacrylamide gel electrophoresis (Figure6). The theoretical molecular weight of the target protein (Mn-SOD) was 27.9 kDa. At 37°C, most of the Mn-SOD proteins expressed formed insoluble inclusions, which were not properly folded and dissolved into the supernatant (Figure6 Lane1 and 2). As the induction temperature gradually decreases from 30°C to 16°C, a clear trend can be observed: the band strength in the precipitate gradually decreases, while the band strength in the supernatant increases significantly.

Figure6. SDS-PAGE results under different induction temperature conditions.M：protein marker；Lane 1: Precipitation of Mn-SOD after 37°C induction; Lane 2: Supernatant of Mn-SOD after 37°C induction; Lane 3: Precipitation of Mn-SOD after 30°C induction; Lane 4: Supernatant of Mn-SOD after 30°C induction; Lane 5: Precipitation of Mn-SOD after 20°C induction; Lane 6: Supernatant of Mn-SOD after 20°C induction; Lane 7: Precipitation of Mn-SOD after 16°C induction. Lane 8: Supernatant of Mn-SOD after 16°C induction.

In order to further quantify the expression level of the target protein, the SDS-PAGE gel was detected by optical density spectrometry, and the expression changes of the target protein in different treatment groups were quantitatively compared by grayscale value, so as to clarify the effect of fermentation temperature optimization on the soluble expression of Mn-SOD. The results showed that the protein solubility expression of Mn-SOD was increased at 16°C and 20°C temperatures, and it was 4.48 times higher than that at 16°C under 20°C. In addition, the density values of protein bands in the pellet are greatly reduced. This provides additional validation for the inference that selecting the appropriate induction temperature can effectively promote the solubility of the target protein.

Figure7. Quantitative analysis of SDS-PAGE results under different induction temperature conditions.A: Optical density analysis of Mn-SOD supernatant and precipitate components under different induction temperature conditions;B: Comparison of the percentage soluble expression of Mn-SOD under different induction temperature conditions.

2. Mn-SOD Enzymatic Properties Test

Considering the potential interference of chaperone co-expression on the subsequent determination of Mn-SOD enzymatic properties, we finally selected 16°C as the induction temperature to achieve efficient soluble expression of the target protein. The Mn-SOD expressed under these conditions was isolated and purified, and the results showed that we successfully purified the Mn-SOD protein (Figure8). The theoretical molecular weight of the target protein (Mn-SOD) was 27.9 kDa.

Figure8. SDS-PAGE results after purification of Mn-SOD protein under 16 degrees Celsius induction conditions.M: Protein marker; Lane1, 4: Precipitation of Mn-SOD; Lane2, 5: supernatant crude enzyme solution of Mn-SOD; Lanes 3 and 6: Purified and concentrated Mn-SOD

The enzymatic properties of purified Mn-SOD were determined, and the enzyme activity of Mn-SOD was detected by othalicol autooxidation method. The results showed (as shown in Table 1) that the specific enzyme activity of Mn-SOD after purification was 552.131 U/mg.

Table 1 Specific enzyme activity assays for Mn-SOD after purification

Sample	△A325	△A'325	Inhibition rate	Total enzyme activity	Concentration	Sample dosage	Ratio Enzyme activity
Repeat 1	0.0613	0.0426	0.3051	0.6101	0.055	0.02	554.649
Repeat 2	0.0601	0.0419	0.3028	0.6057	0.055	0.02	550.597
Repeat 3	0.0607	0.0423	0.3031	0.6063	0.055	0.02	551.146

Subsequently, To quickly assess the conformational stiffness of purified Mn-SOD and predict its storage stability as a pharmaceutical component, we performed an accelerated thermal stability experiment. By measuring its activity decay rate at high temperatures (60°C and 70°C), its shelf life under milder storage conditions can be deduced, which is standard practice in pharmaceutical formulation development and is the basis for future testing experiments under other temperature conditions (e.g., 4°C or 25°C). The enzyme solution was first diluted to a concentration of 0.05 mg/mL, and then incubated at constant temperature at 60°C and 70°C, respectively, with incubation intervals of 15 min, 30 min, 45 min, and 60 min. After incubation at each time point, the samples were immediately cooled to room temperature to terminate the thermal inactivation reaction, and residual SOD activity was detected according to the standard enzyme activity assay described above. The relative activity of Mn-SOD at different temperatures and different incubation times was determined by calculating the percentage of residual activity and initial activity of each treatment group with 100% enzyme activity at the initial moment (unheated). The results showed that the purified Mn-SOD could still retain 29.92% of its residual activity after 1 hour of incubation at 60°C. However, after incubation at 70°C for the same time, the residual activity decreased significantly, retaining only 10.2% (Figure9).

Figure9. Thermal stability analysis of Mn-SOD under different temperature conditions

Learn 2.2

In the prokaryotic expression of Mn-SOD, a large amount of Mn-SOD exists in the form of inclusions due to the lack of eukaryotic protein folding auxiliary mechanism, strong promoters, and unsuitable intracellular environment. In order to solve this problem, two strategies were used to achieve its soluble expression: first, three molecular chaperones, pGro7, pKJE7, and pTf16, were co-expressed, and the accessory protein was folded correctly; The second is to optimize the induction temperature (16°C, 25°C, 30°C, 37°C), and finally determine 16°C as the optimal condition. Subsequent purification assays showed that the specific activity of Mn-SOD reached 552.131 U/mg, but the thermal stability was limited (29.92% residual activity for 1 h incubation at 60°C and only 10.2% at 70 °C).

While we have successfully achieved soluble expression and obtained enzymatically active Mn-SOD, its limited thermal stability presents a significant challenge for our final product. For an eye drop formulation, stability during storage (often at room temperature or under refrigeration) is paramount for shelf-life and efficacy. A protein that degrades quickly would lose its antioxidant potency before ever reaching the patient’s eye.Therefore, our next engineering goal is not just a better enzyme in the abstract, but specifically one with enhanced thermal robustness. To achieve this, we will employ machine learning to rationally design Mn-SOD variants with improved stability, directly addressing this formulation constraint.

Cycle 3.0: Rational design of Mn-SOD based on Transformer deep learning model

Design 3.0

Although traditional directed evolution can screen out functionally optimized enzyme molecules, it has obvious shortcomings: it is necessary to build a huge mutation library, rely on high-throughput screening, be time-consuming, labor-intensive, and have strong randomness, making it difficult to accurately locate key sites in adaptive evolution, especially the recessive co-evolution law of enzyme molecules is insufficient. Therefore, this project aims to use the transformer deep learning model to efficiently capture the potential associations between sequences based on Mn-SOD homology sequences and mutation-functional association data, mine evolutionary laws from massive enzyme sequences, and accurately capture site synergies, locate the adaptive evolutionary hot sites of Mn-SOD, and provide clear modification targets for improving enzymatic properties such as enzyme activity and thermal stability.

The identified Mn/FeSOD protein sequences were first retrieved and obtained from IPR001938 entries in the InterPro database. Considering that Mn/FeSOD functions in the form of dimers under physiological conditions, all extracted sequences are repeated to simulate its natural state of action to improve the accuracy of model training. In the process of sequence adaptive distance modeling, a codec structure neural network based on Transformer encoder is adopted. In the training phase, 40% of amino acid residues are randomly masked to enhance the generalization ability of the model. The model training parameters were set as follows: using the Adam optimizer, the learning rate was 3×10⁻⁴, the training round was 20, and the batch size was 32. After the training was completed, all residue sites were sorted according to the logit, and the top 50 residue sites with the highest average scores were selected as potential key candidates for the adaptive evolution of Mn-SOD (Figure10).

Figure10. Transformer model architecture and model prediction results.

Based on the computational predictions, we designed precise single-point mutations to rationally engineer Mn-SOD variants with enhanced enzymatic properties. Using the previously constructed pET28a-Mn-SOD plasmid as a template, we generated each mutant (D107L, K46S, and G93H) via site-directed PCR amplification with specifically designed primers (Figure11).

Figure11. Construction of pET28a-mutation-Mn-SOD recombinant plasmid and gene circuit design.

Build 3.0

After PCR amplification to obtain the target fragments carrying the specific single-point mutations, the products were purified and recovered. The purified products were then transformed into E. coli BL21(DE3) competent cells, which were incubated upside down at 37°C for 16 hours. Single colonies exhibiting regular morphology were selected from the transformation plate for colony PCR identification. The nucleic acid gel electrophoresis results (Fig. 14) showed that the colonies corresponding to the three mutation groups (K46S, G93H, and D107L) all produced clear bands consistent with the expected size (approximately 606 bp). This indicated that the target plasmid had been successfully introduced into the bacterial cells, and the three single-point mutant plasmids (D309L, K46S, and G93H) were successfully constructed (Figure12).

Figure12. Bacterial solution PCR result of pET28a-mutation-Mn-SOD recombinant plasmid.

Test 3.0

Single colonies of single-point mutant strains were inoculated into LB(Kan) liquid medium for activation culture. After the bacterial density reached the logarithmic growth stage, it was transferred to fresh LB (Kan) medium to expand the culture and induce the expression of the target protein. The induction conditions were set to: 16°C, 180 rpm oscillation culture for 16 hours. After the induction, the bacteria were collected by centrifugation, and the supernatant and precipitate were separated by centrifugation after ultrasonic fragmentation, and the target protein in the supernatant was purified and ultrafiltrated and concentrated. The enzyme activity and thermal stability of the purified mutant proteins were determined by referring to the above experimental methods, and the effects of different single-point mutations on Mn-SOD function were analyzed.

The enzyme activity assay results showed that among the three single-point mutants, the G93H mutant had the most significant increase in enzyme activity: compared with wild-type Mn-SOD, its specific enzyme activity was increased by about 15.15%, indicating that the introduction of histidine at the G93H site had a clear effect on the catalytic efficiency of the enzyme (Figure13).

Figure13. Specific enzyme activity analysis of different Mn-SOD mutants.

The inactivation rate constant (k) of enzymes at high temperatures usually follows the Arrhenius equation, and the higher the temperature, the greater the k value, the faster the inactivation.The results of thermal stability assay showed that the D107L mutant showed the best thermal stability improvement effect: after incubating the mutants and wild type for 60 min at 70°C, the D107L mutant could still retain 11.86% of the residual activity, which was 22.26% higher than that of wild type, indicating that the D107L mutant was replaced with leucine and effectively enhanced the tolerance of the protein structure to high temperature environment (Figure14). This suggested that the D107L mutant enhanced the resistance of protein structures to denaturation, suggesting that it might have a longer shelf life. In subsequent experiments, we will verify this prediction by monitoring its long-term activity at 4°C and 25°C, which is a critical step in formulation development.

Figure14. Thermal stability analysis of different Mn-SOD mutants

Finally, we also tested the total antioxidant capacity of G93H mutant because this mutation significantly enhanced enzyme catalytic activity. The results showed that the total antioxidant capacity of G93H variant was significantly higher than that of wild-type Mn-SOD, indicating that G93H variant had higher efficiency in scavenging free radicals (Figure15).

Figure15. Total antioxidant capacity of G93H mutant and wild-type Mn-SOD

Learn 3.0

In this study, the key modification sites were successfully screened out from the adaptive evolution of Mn-SOD through the transformer deep learning model, and single-point mutants such as D309L, K46S, G93H, and D107L were further constructed. Experimental results confirm that the target mutations predicted by the model can effectively optimize the function of Mn-SOD: the G93H mutation significantly enhances the enzyme-catalytic activity and total antioxidant capacity. The D107L mutation greatly enhances the thermal stability. This result verifies the effectiveness of the transformer model in the rational design of enzyme molecules to accurately locate hot sites. This result not only verified the effectiveness of the transformer model but, more importantly, delivered tangible improvements critical for our application.

Cycle 4.0: Simulating Mn-SOD Eyedrop Efficacy based on Multi-Scale math model

Design 4.0

In order to scientifically design and evaluate the efficacy of Mn-SOD eye drops in practical application, we have constructed a set of multi-scale mathematical models from simple to complex, aiming to quantitatively simulate the "efficacy-time" relationship in the eyeball, and provide a phased and increasingly refined simulation tool for the whole process of Mn-SOD eye drops from early formula screening to precise dosing protocol design. Firstly, we construct a catalytic kinetic model at the molecular mechanism level based on the "Ping-Pong" mechanism to characterize the catalytic reaction mechanism of Mn-SOD catalytic scavenging of ROS. Subsequently, it was embedded into a zero-dimensional (0D) homogeneous system kinetic model describing the "efficacy-time" relationship after administration of eye drops, and ordinary differential equations (ODEs) were established to simulate the dynamic process of drug and ROS concentrations over time. This foundation model is suitable for rapid assessment of dose effects and the impact of formulation formulations. To further improve the prediction accuracy and biorelevance of the model, we introduced a one-dimensional (1D) reaction-diffusion equation to simulate the spatial distribution of drugs within the eye. The geometry of the eyeball is mainly simulated by model construction under the Cartesian coordinate system and the spherical coordinate system, so as to achieve higher fidelity prediction of the spatiotemporal evolution of pharmacodynamics.

Build 4.0

1. Microscopic Catalytic Kinetic Model

Microscopic Catalytic Kinetic Model is based on the Ping-Pong Mechanism in which manganese superoxide dismutase (Mn-SOD) catalyzes the disproportionation reaction of superoxide anion (O2⁻). This mechanism accurately describes the cyclic catalytic process of manganese ions in the enzemic active center between the oxidation state (Mn³⁺-SOD, Eox) and the reducing state (Mn²⁺-SOD, Ered), with each step and a half of the reaction consuming a superoxide molecule and generating the corresponding enzyme-substrate intermediate complex (C1 and C2). The two-and-a-half-step reaction is shown in Figure 16 below. The model derives the total reaction rate equation from the first principles by applying the Briggs-Haldane steady-state approximation (assuming zero rate change in the concentration of the intermediate complex) combined with the flow equilibrium condition of the two-step reaction.

Figure16. Chemical Reaction Mechanism of Mn-SOD Scavenging ROS.

The main method process of this model mainly includes the following steps. Firstly, the reactions of each element and their rate equations are written according to the ping-pong mechanism. Subsequently, a steady-state approximation (d[C1]/dt ≈ 0, d[C2]/dt ≈ 0 was applied to the intermediate complexes C1 and C2, and the concentrations of oxidation and reducing enzymes were expressed as intermediate complex concentrations using the condition that the two halves of the reaction flow rate in the catalytic cycle were equal (k₂[C1] = k₄[C2]). These expressions are then substituted into the total enzyme conservation equation (Figure17). The expression of [C1] is finally solved by algebraic rearranging, and the explicit equation of total ROS clearance rate is obtained accordingly, which clearly expresses the dependence of clearance rate on the substrate concentration S and the total enzyme concentration Et.

Figure17. The total enzyme conservation equation.

2. Macroscopic Zero-Dimensional (0D) Homogeneous System Dynamics Model

The model simplifies the aqueous humor environment in the eyeball into an ideal, well-mixed continuous stirred kettle reactor (CSTR), and its core assumption is spatial uniformity, that is, the concentration of drug and ROS in the entire aqueous humor is uniform at any time. The model describes the changes of drug concentration and ROS concentration over time by establishing a coupled ordinary differential equation (ODE) system (Figure 18). Among them, the change of drug concentration is only determined by the purge process (such as degradation and loss), following the exponential decay law; while the change of ROS concentration is controlled by the dynamic balance of its endogenous generation rate and enzyme-catalytic clearance rate. The key model parameters in the zero-dimensional (0D) homogeneous system dynamics model are shown in the fellow Table.

Figure18. Ordinary differential equation (ODE) system in Zero-Dimensional (0D) Homogeneous System Dynamics Model.

Table. Key Model Parameters in Zero-Dimensional (0D) Homogeneous System Dynamics Model.

3. Macroscopic One-Dimensional (1D) Reaction-Diffusion Model

The target that drugs for preventing cataracts need to act on is the lens. Traditional models cannot answer the core questions of "how much drug will reach the lens" and "how long will it take?" In order to directly and dynamically simulate the penetration process of drugs in the anterior chamber, we designed the Macroscopic One-Dimensional (1D) Reaction-Diffusion Model. This model introduces spatial dimensions and diffusion effects. Its principle is based on Fick's second law, which suggests that changes in the concentration of substances in the eye are not only due to local chemical reactions, but also from their diffusion flux between different spatial locations. The model describes this process through the reaction-diffusion partial differential equation (PDE), in which temporal evolution and spatial distribution are coupled (Figure 19). Tthe spherical coordinate system (Figure 20) can more realistically capture the geometric dilution effect caused by the spherical geometry of the eyeball due to the introduction of the (2/r) (∂C/∂r) term, that is, the natural decrease in concentration due to the increase in the area of the sphere through which the material passes when it diffuses outward.

Figure19. The reaction-diffusion partial differential equation.

Figure20. The spherical coordinate system equation.

The main method process of this model mainly includes the following steps. Firstly, the coordinate system is selected according to the geometric characteristics of the simulation domain and the corresponding reaction-diffusion PDE system is established. For the concentration of drugs and ROS C(x,t) or C(r,t), the control equation is ∂C/∂t = D * ∇²C + R(C), where R(C) represents the chemical reaction term (i.e., microscopic engine V). Subsequently, physiologically reasonable initial conditions (e.g., initial distribution of ROS S₀(x) before dosing, drug distribution at the moment of administration) and boundary conditions (e.g., flux input conditions at the corneal boundary to simulate eye drop administration, and no flux conditions at the lens boundary to simulate its physical barrier) were set. Finally, numerical methods (such as finite difference method or finite element method) were used to discretize and solve the PDE to obtain the complete distribution of drug and ROS concentrations in space and time C(x, t).

Test 4.0

1. Microscopic Catalytic Kinetic Model

The core purpose of this microscopic model is to build an accurate "biochemical reaction engine". It quantitatively describes the catalytic efficiency of Mn-SOD from the lowest molecular mechanism, providing fundamental and reliable chemical reaction terms. Without this microscopic engine, any macroscopic simulation would lose its foundation in biochemical authenticity. The steady-state approximation and rate equation derivation process of the model are shown in Figure 21.

Figure21. Derivation process of Microscopic Catalytic Kinetic Model.

After successfully deriving the relevant equations of the model, we visually compared the catalytic efficiency of natural Mn-SOD and engineered Mn-SOD in the scavenging of reactive oxygen species (ROS) using the Michaelis-Menten curve. The analysis results showed that the maximum reaction rate (Vmax) of engineered Mn-SOD reached 4000.0 μM/s, which was about 2.67 times higher than that of natural Mn-SOD (1500.0 μM/s). This significant improvement means that our engineered variant can perform the role of scavenger with extreme efficiency when oxidative stress occurs in the eye and ROS concentrations rise sharply, quickly reducing ROS concentrations below safe thresholds, thereby effectively protecting lens proteins from oxidative damage, which will theoretically significantly reduce the time window for the protective effect after eye drop administration. Although its Mie constant (Km) is slightly elevated (12.0 μM → 10.0 μM), indicating a subtle change in substrate affinity, in cataract-related pathological settings (often accompanied by significant increases in ROS concentration), the catalytic capacity gain from extremely high Vmax far outweighs the small effects that Km change may have. In summary, the excellent catalytic efficiency of engineered Mn-SOD has laid a solid theoretical foundation for its potential to achieve low-dose and high-efficacy in the development of subsequent ophthalmic drop formulations, and greatly enhanced the confidence of this project from molecular design to practical application (Figure 22).

Figure22. Plot of the comparative Michaelis-Menten kinetics for Natural vs. Engineered Mn-SOD.

2. Macroscopic Zero-Dimensional (0D) Homogeneous System Dynamics Model

Macroscopic Zero-Dimensional (0D) Homogeneous System Dynamics Model is designed to quickly assess the overall pharmacodynamic profile of dosing regimens and serves as a powerful tool for conducting efficient parameter scanning and preliminary screening. It visualizes the intensity (how low ROS can be suppressed) and duration (how long ROS remains low) for comparing the strengths and weaknesses of different formulations (corresponding to different kclear values), analyzing dose-response relationships, and initially evaluating the dosage adjustment strategies required for different levels of oxidative stress (simulated by adjustment kgen). Its simple and fast calculations make it ideal for high-throughput virtual screening in the early stages of a project.

We systematically evaluated the efficacy boundaries of engineered Mn-SOD eye drops under different pathological conditions. The heat map results visually showed that the final ROS residual concentration (color from purple to yellow indicates high to low) formed a clear efficacy demarcation between different initial Mn-SOD doses (horizontal axis, 0–1 μM) and different oxidative stress levels (vertical axis, 10–70 μM/h). The results showed that ROS could be inhibited at a safe level (yellow region) with very low doses (about 0.2–0.3 μM) of engineered Mn-SOD under low oxidative stress conditions (e.g., physiological aging). In environments with high oxidative stress (e.g., pathological states caused by metabolic diseases), the dose needs to be significantly increased to more than 0.6 μM to achieve effective clearance (breakthrough to the yellow-green region). This simulation result not only quantitatively characterizes the efficacy advantages of engineered Mn-SOD, but more importantly, provides clear dosage window guidance for clinical precision drug use, that is, the need to adopt differentiated drug delivery strategies for different risk groups, thus providing a key theoretical basis for the personalized prevention of cataracts (Figure 23).

Figure23. Heatmap showing efficacy (ROS remaining) for different doses and stress levels.

3. Macroscopic One-Dimensional (1D) Reaction-Diffusion Model

The core purpose of this model is to make a leap from "temporal dynamic" prediction to "spatiotemporal dynamic" prediction to obtain simulation results with higher biological realism and prediction accuracy. It can accurately simulate the spatiotemporal process of how drugs penetrate aqueous humor and finally reach the target (lens) after dripping from the cornea, predicting its actual exposure concentration and history on the target surface, so as to provide the final and most reliable decision-making basis for designing precise dosing regimens (dosage and frequency) that can truly ensure the effectiveness of the target. At the same time, its visualizations, such as heat maps, provide an excellent representation of the spatial dynamics of drug penetration and ROS clearance.

We simulated the spatiotemporal dynamics of engineered Mn-SOD eye drops after dropping into the eye and its scavenging effect on reactive oxygen species (ROS). As shown in Figure 24, the model simulation results reveal changes in SOD and ROS concentrations over time (hours) within the eye (from the cornea to the lens, expressed as normalized distance): the distribution of SOD (Figure 24a) shows that its concentration is relatively uniform spatially, with only slight attenuation over time, indicating that the drug can effectively diffuse and maintain therapeutic concentrations; The dynamics of ROS (Figure 24b) showed a clear spatiotemporal gradient, with a higher initial concentration in the near lens region (bottom), but gradually decreased with the continuous effect of SOD, especially in the later stage of administration. This result confirms that engineered Mn-SOD can efficiently penetrate into the target area and achieve spatiotemporal specific clearance of ROS, which provides a key basis for the optimization of the frequency and dosage of eye drops, and verifies its feasibility and reliability as a cataract prevention strategy.

Figure24. Generates a conceptual plot of the spatiotemporal dynamics from a 1D-PDE model.

Learn 4.0

In cycle5.0, we successfully designed, built, and tested a multi-scale mathematical modeling framework that bridges from molecular catalytic kinetics to macroscopic spatiotemporal dynamics. The results from the test phase provide profound insights into the performance of our engineered Mn-SOD and the optimization of eyedrop formulations, while also revealing key limitations and directing future improvements. There are three main aspects：

1. Microscopic Model Confirms Superior Catalytic Efficiency: The Michaelis-Menten analysis unequivocally demonstrated that our engineered Mn-SOD variant achieves a maximum reaction rate (V_max) of 4000.0 μM/s, which is 2.67 times higher than that of natural Mn-SOD (1500.0 μM/s). This significant enhancement in catalytic power means that our variant can rapidly scavenge ROS under oxidative stress, potentially leading to a shorter onset time for therapeutic effects after eyedrop administration. The slight increase in K_m (12.0 μM vs. 10.0 μM) indicates a subtle trade-off in substrate affinity, but in the high-ROS pathological environment of cataract formation, the vastly improved V_max dominates the overall efficacy, validating our protein engineering strategy.

2. 0D Model Defines Dosage Windows for Different Clinical Scenarios: The heatmap generated from the 0D homogeneous model provides a clear, quantitative roadmap for precision dosing. It reveals that under mild oxidative stress (e.g., normal aging), a low dose of 0.2-0.3 μM engineered Mn-SOD is sufficient to suppress ROS to safe levels. In contrast, under severe stress (e.g., diabetic conditions), the dose must be increased to above 0.6 μM to achieve efficacy. This result is crucial for transitioning from a one-size-fits-all approach to a personalized medicine strategy, where dosing can be tailored to an individual's specific risk level.

3. 1D Model Visualizes and Validates Targeted Drug Delivery: The spatiotemporal simulations from the 1D reaction-diffusion model are a landmark achievement. They visually confirm that our Mn-SOD eyedrop can penetrate the aqueous humor, diffuse to the lens surface (the target site), and maintain a therapeutic concentration long enough to achieve significant ROS clearance in the critical region. This proves the fundamental feasibility of using a topical eyedrop to deliver a large enzyme like SOD to its intraocular target, addressing a major translational challenge.

Despite its success, our modeling framework has inherent limitations that guide future work:

1. The 0D Model's Simplicity: Its assumption of a perfectly mixed, homogeneous ocular environment is a significant simplification. It cannot account for spatial gradients, which are crucial for understanding localized drug concentrations and effects at the lens surface. This makes it unsuitable for final dosing predictions but excellent for initial screening.

2. The 1D Model's Parameter Dependency: The accuracy of our high-fidelity 1D model is highly dependent on precise input parameters, such as diffusion coefficients and boundary conditions, which were obtained from literature or in vitro studies. In vivo validation is necessary to calibrate these parameters truly and ensure the model's predictive power reflects biological reality.

3. Biological Complexity: Our current models do not incorporate other physiological factors like tear turnover, lacrimation, protein binding, or the complex barrier properties of the corneal epithelium. These elements could significantly alter drug pharmacokinetics and must be integrated into future model iterations for ultimate realism.

In conclusion, Cycle 5.0 has provided a powerful computational foundation that validates our biological design and guides practical dosing. It has transformed our project from one of molecular discovery to one of predictive therapeutic development, embodying the engineering ethos of iGEM by providing a reusable, rational framework for designing and evaluating enzymatic therapies.

Future work

In the future, we will conduct a systematic evaluation of Mn-SOD's enzymatic performance under varied thermal conditions to bridge the gap between laboratory characterization and real-world application. This endeavor aims to establish a detailed temperature-activity-stability relationship, which is critical for optimizing formulation storage, determining shelf life, and predicting in vivo behavior under physiological temperatures (~35°C). We will measure enzymatic activity across a broad thermal spectrum (e.g., 4°C to 60°C) to identify the optimal operating temperature and assess kinetic parameters (Km, Vmax) shifts, thereby revealing thermal influences on catalytic efficiency. Long-term stability studies will monitor activity retention over weeks to months at clinically relevant storage temperatures (e.g., 4°C for refrigeration, 25°C for room temperature), providing essential data for practical formulation design. The resulting dataset will be integrated into our existing multi-scale mathematical models, allowing us to refine predictive simulations of drug efficacy under realistic ocular temperature conditions, ultimately enabling the design of more robust and effective therapeutic regimens.

In parallel, our research will pivot towards developing advanced targeted delivery strategies to enhance the ocular bioavailability and therapeutic efficacy of Mn-SOD eye drops. The primary objective is to overcome physiological barriers such as rapid tear turnover and corneal impermeability, ensuring that the enzyme not only penetrates the ocular surface efficiently but also achieves sustained release at the lens—the key site of action for cataract prevention. To this end, we will explore innovative approaches including nano-encapsulation of Mn-SOD within lipid-based or polymeric carriers to shield it from degradation and prolong its ocular residence time. These carriers will be further functionalized with cell-penetrating peptides or ligand motifs that specifically bind to lens epithelial cell receptors, enabling active targeting and enhanced cellular uptake. The validation of these strategies will involve a multi-tiered experimental pipeline: initially employing in vitro corneal epithelial cell models to assess permeability and cytotoxicity, followed by ex vivo studies using animal corneas to visualize distribution patterns, and ultimately culminating in in vivo efficacy trials in cataract-prone animal models to quantify improvements in drug delivery and biological outcomes.