## 3 Results and Discussion
### Performance Comparison with Hybrid Features  
To explore the potential of integrating complementary features for enhancing prediction accuracy, a series of ablation experiments were conducted to evaluate the performance of different feature combinations. Initially, combinations of traditional features, PSSM-based features, and embeddings from large models like ESM-1b and ESM2 were tested. While these combinations improved prediction accuracy, strategic feature selection emphasizing evolutionary information and structural properties further enhanced performance. To systematically evaluate the contribution of each feature type, ablation experiments were performed using optimal traditional features, PSSM features, and large model embeddings. Specific combinations tested included traditional features alone, PSSM features alone, large model embeddings alone, and their pairwise combinations. It is noteworthy that among the tested large model embeddings, ProtBERT features (Figure 4j) showed comparatively lower performance than ESM2 for this task, leading us to prioritize ESM2 for further feature combinations. Results indicated that while each feature type individually contributed to prediction accuracy, their combinations offered complementary perspectives on protein sequence characteristics, leading to further enhancements.  
As detailed in Table 2, the combination of DDE and ESM2 features achieved the highest performance across most evaluation metrics, with an accuracy of 94.78% and an MCC of 0.896. This result highlights the powerful synergy between traditional, sequence-derived statistics and modern, deep learning-based representations. The DDE feature effectively captures local compositional biases, while the ESM2 embeddings provide rich, context-aware information about global evolutionary and structural properties. This fusion of complementary information proved to be the most effective strategy, outperforming other combinations, including those incorporating PSSM-based features.  
The DDE + ESM2 combination demonstrated the highest prediction accuracy, underscoring the importance of integrating features that provide complementary insights into protein sequences. The DDE feature encapsulates both amino acid composition and dipeptide composition within an evolutionary context, while the ESM2 embeddings capture detailed structural and functional information. This synergy between evolutionary and structural properties proved to be the most effective in our experiments.  
In conclusion, our ablation study confirms that integrating DDE features with ESM2 embeddings creates a highly discriminative feature set for FRP prediction. This finding underscores the value of a hybrid approach, which leverages diverse feature types to capture a multifaceted view of protein sequences, ultimately leading to more accurate and robust predictive models.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Feature Combination** & **Acc (\%)** & **Sn (\%)** & **F1-Score (\%)** & **MCC** \\ \hline DDE & 93.26 & **95.65** & 93.19 & 0.866 \\ AADP-PSSM & 94.57 & 94.35 & 94.56 & 0.891 \\ ESM2 & 93.91 & 93.91 & 93.91 & 0.878 \\ DDE + AADP-PSSM & 93.91 & 94.78 & 93.90 & 0.878 \\
**DDE + ESM2** & **94.78** & 95.22 & **94.78** & **0.896** \\ AADP-PSSM + ESM2 & 93.91 & 94.78 & 93.90 & 0.878 \\ DDE + AADP-PSSM + ESM2 & 93.70 & 93.91 & 93.69 & 0.874 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance of different feature combinations on the independent test set.