Model
Overview
Cellular Activation miRNA
Experimental Design Setup
Visualization Analysis
Molecular Response Patterns
Interactive Visualization
Morphological Spatial Analysis
Dose Response Optimization
Statistical Validation Metrics
Temporal Dynamics Insights
Computational Sensitivity Analysis
Model Validation Performance
Theoretical Foundation and Mathematical Framework

This study employs an agent-based modeling framework to investigate miR-455-3p and miR-148a-5p therapeutic potential in liver fibrosis, integrating molecular dynamics, cellular behavior, and tissue organization within a unified mathematical system. The framework addresses three fundamental scales through interconnected mathematical formulations capturing fibrosis progression and therapeutic response mechanisms.

At the molecular level, spatiotemporal distribution of signaling molecules follows reaction-diffusion dynamics:

$$\frac{\partial C_i}{\partial t} = \nabla \cdot (D_i(\mathbf{r},t) \nabla C_i) - \lambda_i(\mathbf{r},t) C_i + \sum_{j} R_{ij}(C_1, C_2, ..., C_n) + S_i(\mathbf{r},t)$$
where $D_i(\mathbf{r},t) = D_{i,0} \cdot \mathbf{T}(\mathbf{r}) \cdot f(\phi(\mathbf{r},t))$ incorporates tissue anisotropy and cell density-dependent transport.

Cellular dynamics are governed by stochastic differential equations describing individual hepatic stellate cell evolution within 33-dimensional state space:

$$d\mathbf{X}_\alpha = \mathbf{F}(\mathbf{X}_\alpha, \mathbf{C}(\mathbf{r}_\alpha,t), \mathbf{N}_\alpha) dt + \mathbf{G}(\mathbf{X}_\alpha) d\mathbf{W}_\alpha$$

This formulation captures deterministic biochemical networks and stochastic fluctuations driving cellular behavior emergence.

Cellular Activation and miRNA Regulatory Dynamics

HSC activation exhibits bistable dynamics described through bifurcation theory:

$$\frac{dA_\alpha}{dt} = k_{act} \cdot H(C_{TGF}^{eff}, K_{act}, n_{act}) - k_{deact} \cdot A_\alpha + \xi_\alpha(t)$$
where $C_{TGF}^{eff} = C_{TGF} \cdot (1 - I_{miRNA})$ represents miRNA-modulated TGF-β1 effectiveness.

miRNA regulatory networks follow coupled kinetics:

$$\frac{dM_{455}}{dt} = k_{in,455} \cdot U_{exo} - k_{deg,455} \cdot M_{455} - k_{bind,455} \cdot M_{455} \cdot mRNA_{target}$$
$$\frac{dM_{148}}{dt} = k_{in,148} \cdot U_{exo} - k_{deg,148} \cdot M_{148} - k_{bind,148} \cdot M_{148} \cdot mRNA_{target}$$

Individual inhibitory effects follow Hill kinetics, while synergistic interactions are captured through:

$$I_{total} = I_{455} + I_{148} + \gamma \cdot \frac{(M_{455} \cdot M_{148})^{\beta}}{K_{syn}^{2\beta} + (M_{455} \cdot M_{148})^{\beta}}$$
Experimental Configuration Design

Nine experimental configurations systematically evaluate miR-455-3p and miR-148a-5p therapeutic effects: control (TGF-β1: 2.0 ng/mL, 8% activation), positive control (TGF-β1: 15.0 ng/mL, 75% activation), single miRNA treatments (0.4 dose, 42-38% efficacy), and dual miRNA combinations (1:1, 2:1, 1:2 ratios achieving 68-72% efficacy with synergy factors 2.8-3.1).

Figure 1. Comparative analysis demonstrating superior dual miRNA therapeutic performance.

Visualization Analysis

The computational modeling generates multi-modal visualization outputs including molecular heatmaps, morphological analysis, 3D spatial distributions, time-lapse animations, and interactive visualization platforms. These visualizations provide quantitative assessment of therapeutic mechanisms across molecular, cellular, and tissue scales.

Figure 2. The Control. Configuration - Key Visualization Results - Animation

Figure 3. The Positive Control. Configuration - Key Visualization Results - Animation

Figure 4. The miR-455-3p Only. Configuration - Key Visualization Results - Animation

Figure 5. The miR-148a-5p Only. Configuration - Key Visualization Results - Animation

Figure 6. The Dual miRNA (1:1). Configuration - Key Visualization Results - Animation

Figure 7. The Dual miRNA (2:1). Configuration - Key Visualization Results - Animation

Figure 8. The Dual miRNA (1:2). Configuration - Key Visualization Results - Animation

Molecular and Morphological Response Patterns

The visualization analysis reveals distinct molecular and morphological signatures corresponding to therapeutic mechanisms. Control conditions exhibit uniform molecular landscapes with minimal TGF-β activity, while positive controls demonstrate intense pathological signaling gradients. Single miRNA treatments show mechanism-specific patterns: miR-455-3p reduces cytoskeletal activation markers while miR-148a-5p enhances metabolic activity and reduces collagen synthesis. Dual miRNA combinations create synergistic molecular profiles exceeding individual contributions, with the 1:2 ratio achieving optimal anti-fibrotic conditions.

Morphological analysis quantifies cellular phenotypic changes, demonstrating progressive restoration of quiescent HSC morphology through miRNA interventions, with dual combinations achieving superior normalization compared to single agent treatments.

Interactive Visualization Platforms
3D Cell Visualization Platform

Beyond static images and animations, our computational framework generates sophisticated interactive visualization platforms enabling real-time exploration of multi-dimensional datasets.

The 3D Cell Visualization Platform enables dynamic manipulation of viewing angles, zoom levels, and temporal progression. Users can interactively explore cellular activation states, migration patterns, and population dynamics throughout the simulation timeline.(Control/Positive Control/miR-455-3p/miR-148a-5p/Dual 1:1/Dual 1:2)

Figure 9. Control 3D Cell Visualization

Figure 10. Positive Control 3D Cell Visualization

Figure 11. miR-455-3p 3D Cell Visualization

Figure 12. miR-148a-5p 3D Cell Visualization

Figure 13. Dual 1:1 3D Cell Visualization

Figure 14. Dual 2:1 3D Cell Visualization

Figure 15. Dual 1:2 3D Cell Visualization

The 3D Cell Visualization Platform enables dynamic manipulation of viewing angles, zoom levels, and temporal progression. Users can interactively explore cellular activation states, migration patterns, and population dynamics throughout the simulation timeline.

Molecular Gradient Visualization System

Figure 16. Control Molecular Gradient Visualization

Figure 17. Positive Control Molecular Gradient Visualization

Figure 18. miR-455-3p Molecular Gradient Visualization

Figure 19. miR-148a-5p Molecular Gradient Visualization

Figure 20. Dual 1:1 Molecular Gradient Visualization

Figure 21. Dual 2:1 Molecular Gradient Visualization

Figure 22. Dual 1:2 Molecular Gradient Visualization

The Molecular Gradient Visualization System provides real-time visualization of molecular concentration fields, diffusion patterns, and reaction kinetics. Interactive features include species selection, concentration threshold adjustment, and temporal navigation enabling comprehensive analysis of molecular transport phenomena.

Time Lapse Animation Series

Figure 23. Control Time Lapse Visualization

Figure 24. Positive Control Time Lapse Visualization

Figure 25. miR-455-3p Time Lapse Visualization

Figure 26. miR-148a-5p Time Lapse Visualization

Figure 27. Dual 1:1 Time Lapse Visualization

Figure 28. Dual 2:1 Time Lapse Visualization

Figure 29. Dual 1:2 Time Lapse Visualization

The Time-Lapse Animation Series integrates cellular dynamics and molecular transport within synchronized temporal frameworks, allowing researchers to correlate cellular behavior changes with molecular concentration variations throughout therapeutic interventions.

Complementary Morphological and Spatial Analysis

Additional detailed morphological assessments provide comprehensive cellular phenotype quantification across all experimental configurations. The complete morphological analysis suite includes the following visualization.

Figure 30. Control Morphological Analysis

Figure 31. Control Morphological Analysis

Figure 32. Control Morphological Analysis

Figure 33. Control Morphological Analysis

These visualizations quantify cellular elongation ratios, stress fiber densities, organelle distributions, and activation marker expressions, enabling precise phenotypic characterization and therapeutic effect assessment.

Dose Response Analysis and Synergistic Optimization

Figure 34. Dose-Response Analysis

It reveals nonlinear miRNA concentration-efficacy relationships with distinct kinetic profiles: miR-455-3p exhibits steep dose-response (EC50 = 0.15, Hill coefficient = 2.3) indicating cooperative binding, while miR-148a-5p shows gradual response (EC50 = 0.22, Hill coefficient = 1.8) suggesting broader therapeutic windows. The 1:2 ratio achieves maximal synergistic enhancement (combination index = 3.1), producing 1.8-fold higher efficacies than predicted additive effects.

Statistical Validation and Performance Metrics

Figure 35. Statistical Analysis

It demonstrates robust model performance with strong correlations between miRNA concentrations and cellular activation (r = -0.89 for miR-455-3p, r = -0.84 for miR-148a-5p). Cross-validation achieves 92-94% prediction accuracy across experimental configurations. Monte Carlo uncertainty quantification reveals narrow confidence intervals (±3.2%) supporting reliable therapeutic predictions. All dual miRNA combinations show statistically significant enhancement over single treatments (p < 0.001).

Temporal Dynamics and Mechanistic Insights

Time-lapse analysis reveals biphasic response kinetics with rapid initial effects (12-24 hours) followed by sustained therapeutic maintenance. miR-455-3p achieves 70% maximal effect within 24 hours through cytoskeletal disruption mechanisms described by:

$$ \alpha_{SMA} = \alpha_{SMA,max} \cdot (1 - I_{455}) \cdot H(A_{level}, K_{morph}, n_{morph})$. miR-148a-5p demonstrates sustained kinetics via metabolic reprogramming: $M_{efficiency} = M_{base} \cdot (1 + \beta_{148} \cdot I_{148}) \cdot f(ATP_{availability}) $$

Synergistic interactions emerge through complementary mechanisms creating multi-target therapeutic approaches addressing both structural and metabolic aspects of HSC activation.

Computational Methods and Parameter Sensitivity
The implementation employs adaptive Runge-Kutta-Fehlberg time-stepping with error tolerances below $10^{-6}$ for molecular concentrations. Spatial discretization uses hybrid finite element/finite volume methods with octree decomposition reducing computational complexity to $O(N \log N)$. Sobol sensitivity analysis identifies miRNA uptake kinetics ($S_{uptake} = 0.34$) and degradation rates ($S_{degradation} = 0.28$) as most influential parameters, while polynomial chaos expansion enables efficient uncertainty quantification.
Model Validation and Predictive Performance

Validation against experimental observations demonstrates strong correlations: cellular activation measurements (r = 0.91-0.94), molecular biomarkers including α-SMA expression (r = 0.88), and metabolic indicators (r = 0.82). Cross-validation analysis confirms robust performance with mean absolute errors below 4.2% and root mean square errors within 6.8%. Prospective validation maintains accuracy levels (r = 0.87, MAE = 5.1%), supporting model generalizability for therapeutic optimization and clinical translation planning.

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