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\title{Final Sem Report}
\author{Soumya Ra. Hembram}
\date{May 2025}

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       {\LARGE \textbf{Implementation of DeepRHD for Protein Remote Homology Detection}} \\[2 em]
        
        \text{Project Report Submitted}\\

         \text{in partial fulfillment of the requirements for the award of the}\\[2 em]
       
        {\Large \textbf{Bachelor of Technology }}\\[0.5em]
        \textit{by} \\[1em]
        {\textbf{Sarthak Kashmira(B521053)}} \\ [1em]
        {\textbf{Pappu Ram (B521043)}} \\ [1em]
        {\textbf{Soumya Ranjan Hembram(B521059)}} \\ [1em]

        \textit{Under the supervision of} \\[1em]
        \textbf{Dr. Swati Vipsita} \\[2em]
        \vfill

        \includegraphics[width=2in]{assets/iiit-bbsr-removebg.png} \\[1em]

        Department of Computer Engineering \\
        International Institute of Information Technology, Bhubaneswar \\[1em]
        May, 2025
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        {\Large \textbf{APPROVAL OF THE VIVA-VOCE BOARD}} \\[0.5em]
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        \textbf{May 20, 2025} \\ % Replace with actual date if needed
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            \justifying
            Certified that the report entitled \textbf{{“DeepRHD: An efficient hybrid feature extraction technique for remote protein homology detection using deep learning strategies ”}} submitted by \textbf{Soumya Ranjan Hembram (B521059), Sarthak Kashmira(B521053),Pappu Ram(B521043)} to International Institute of Information Technology Bhubaneswar in partial fulfillment of the requirements for the award of the Bachelor of Technology in Computer Engineering under the Bachelor Technology Program has been accepted by the examiners during the viva-voce examination held today.
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            \makebox[0.4\textwidth]{(Panel Member 2)} & \makebox[0.4\textwidth]{(Panel Member 3)} \\
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        {\Large \textbf{DECLARATION}} \\[1em]
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    \noindent
    \textit{I certify that}

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    \begin{enumerate}
        \item The work contained in the report has been done by my group under the general supervision of my supervisor.

        \item The work has not been submitted to any other Institute for any degree or diploma.

        \item I have followed the guidelines provided by the Institute in writing the thesis.

        \item I have conformed to the norms and guidelines given in the Ethical Code of Conduct of the Institute.

        \item Whenever I have used materials (data, theoretical analysis, and text) from other sources, I have given due credit to them by citing them in the text of the thesis and giving their details in the references.

        \item Whenever I have quoted written materials from other sources, I have put them under quotation marks and given due credit to the sources by citing them and giving required details in the references.
    \end{enumerate}

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    \begin{flushright}
        \textbf{Sarthak Kashmira} \\ % Replace with actual name
        \textbf{B521053} % Replace with actual student ID
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    \begin{flushright}
        \textbf{Pappu Ram} \\ % Replace with actual name
        \textbf{B521043} % Replace with actual student ID
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    \begin{flushright}
        \textbf{Soumya Ranjan Hembram} \\ % Replace with actual name
        \textbf{B521059} % Replace with actual student ID
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        {\Large \textbf{ACKNOWLEDGMENTS}} \\[1em]
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            We would like to share our sincere gratitude to everyone who has helped us in the making of
            this project. The progress of this project would not have been possible without the continuous supervision, invaluable tutelage, and treasured support of Prof. Swati Vipsita, our esteemed guide during this project. We would like to extend our sgroducere gratitude to the institution for motivating us to work on the project which made us gain a lot of knowledge and exposure.
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    \begin{flushright}
        \textbf{Sarthak Kashmira} \\ % Replace with actual name
        \textbf{B521053} % Replace with actual student ID
        \vspace{1cm}

        \textbf{Pappu Ram} \\ % Replace with actual name
        \textbf{B521043} % Replace with actual student ID
        \vspace{1cm}

        \textbf{Soumya Ranjan Hembram} \\ % Replace with actual name
        \textbf{B521059} % Replace with actual student ID
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        {\Large \textbf{Abstract}} \\[1em]
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        In computational biology, the Protein Remote homology Detection technique (PRHD) has got undeniable significance. It is mostly important for structure and function identification of a protein sequence. The previous years have seen a challenge that lacks postulating a correlation among the sequences. However, the sequences are of variable length. Thereby, it inhibits the proper derivation of evolutionary information among the sequences. The challenges are the usage of physico-chemical properties as a source to get the evolutionary information and the number of sequences generated every day. This however facilitates a new technique to integrate huge amount of data with a massive feature set. In this article, a new and efficient technique is proposed to predict homology for distantly located sequences of proteins. Deep neural network (CNN-GRU model) is used for the classification of the protein sequences. This is based on different protein families and methods of feature extraction. The efficiency of the proposed model DeepRHD is tested on average 8000 sequences per superfamily taken from SCOP benchmark dataset and the results shows that the proposed model is better than other state of art methods. This model is useful in detecting diseases like sickle cell anemia and influenza and developing a drug thereafter.
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% Section: Introduction
\newpage
\section{Introduction}

    In recent years, understanding the structure and function of proteins has become central to advancements in molecular biology, drug discovery, and personalized medicine. A critical challenge in this field is the detection of remote homology—the evolutionary relationship between protein sequences that share a common ancestor but exhibit low sequence similarity (typically <30\%). Identifying these distant relationships is essential for annotating newly discovered proteins, understanding biological pathways, and designing therapeutic interventions.
    \vspace{1em}
    
    The traditional experimental methods like X-ray crystallography and spectroscopy are both expensive and time-consuming, there is a growing need for computational strategies that can efficiently handle large volumes of sequence data.The explosion of available protein sequence data from resources such as UniProt and the Protein Data Bank (PDB) has opened opportunities to employ deep learning techniques that automatically learn hierarchical, task-relevant representations from raw sequences. These models, particularly convolutional neural networks (CNNs) and recurrent units like GRU/LSTM, have proven highly effective in modeling the sequential and spatial nature of protein data.
    \vspace{1em}

    In this work, we introduce DeepRHD, an advanced hybrid deep learning architecture that combines the spatial pattern learning of Convolutional Neural Networks (CNNs) with the temporal sequence modeling of Gated Recurrent Units (GRUs). This model is designed to automatically extract, integrate, and classify protein sequence features for remote homology detection with high accuracy. DeepRHD leverages both handcrafted biological insights and data-driven representations to generalize across protein families with minimal reliance on prior domain-specific tuning.The model is trained and evaluated on the SCOP (Structural Classification of Proteins) benchmark dataset, which provides a rigorous testbed of curated superfamilies. Additionally, to ensure generalizability, we validate DeepRHD on the CATH dataset. Our dataset includes over 540,000 protein sequences across 40 superfamilies, ensuring that the model is exposed to diverse protein folds and functions.

\begin{figure}[!ht]
    \centering
    \includegraphics[width=1\linewidth]{Screenshot 2025-05-13 at 11.50.44 AM.png}
    \caption{Flow diagram of the DeepRHD}
    \label{fig:enter-label}
\end{figure}
\vspace{2em}

The tables below show the superfamilies we are using in our model to train our model and the number of sequences related to it.
\begin{table}[ht]
    \centering
    \begin{minipage}{0.48\textwidth}
        \centering
        \begin{tabular}{cc}
            \textbf{Super-family} & \textbf{Count} \\
            \hline
            c.2.1     & 8000 \\
            c.37.1    & 8000 \\
            c.47.1    & 8000 \\
            a.4.1     & 7388 \\
            c.3.1     & 7295 \\
            c.55.3    & 6943 \\
            b.1.1     & 6209 \\
            c.1.8     & 6207 \\
            d.108.1   & 5760 \\
            b.40.4    & 5748 \\
            c.67.1    & 5519 \\
            c.94.1    & 5150 \\
            a.39.1    & 5742 \\
            b.47.1    & 5687 \\
            b.121.4   & 5231 \\
            c.55.1    & 5000 \\
            b.82.1    & 4955 \\
            d.92.1    & 4900 \\
            d.3.1     & 4811 \\
            b.55.1    & 4715 \\
        \end{tabular}
        \caption{Super-family and sequence count (1–20)}
        \label{tab:superfamily_left}
    \end{minipage}
    \hfill
    \begin{minipage}{0.48\textwidth}
        \centering
        \begin{tabular}{cc}
            \textbf{Super-family} & \textbf{Count} \\
            \hline
            g.39.1    & 4696 \\
            c.26.1    & 4591 \\
            b.29.1    & 4570 \\
            a.3.1     & 3946 \\
            b.1.18    & 3943 \\
            d.32.1    & 3899 \\
            c.1.2     & 3803 \\
            d.2.1     & 3785 \\
            a.138.1   & 3742 \\
            g.3.11    & 3696 \\
            a.25.1    & 3635 \\
            b.6.1     & 3574 \\
            c.45.1    & 3481 \\
            d.81.1    & 3422 \\
            c.56.5    & 3274 \\
            b.50.1    & 2999 \\
            a.1.1     & 2953 \\
            d.15.4    & 2816 \\
            a.22.1    & 2601 \\
            c.1.10    & 2511 \\
        \end{tabular}
        \caption{Super-family and sequence count (21–40)}
        \label{tab:superfamily_right}
    \end{minipage}
\end{table}

\newpage
\section{Literature Survey}

Traditional sequence alignment tools (e.g., BLAST, FASTA) excel at detecting homology when sequence similarity is high (>30%) but fail to identify sparse evolutionary signals in low-similarity regimes (<30%) \cite{reviewRemoteHomology}. To address this, three major computational paradigms have emerged:
\vspace{1em}

\textbf{\color{black}{1) Alignment-based methods}} (global/local alignments) quantify similarity between sequences but lose sensitivity when conserved regions are subtle, discontinuous, or weakly conserved \cite{reviewRemoteHomology}. Examples include sequence alignment, profile alignment, and HMM alignment methods, which have laid the foundation for early progress in this field.
\vspace{1em}

\textbf{\color{black}{2) Probabilistic models}} (e.g., Hidden Markov Models) estimate the likelihood of a protein belonging to a known family using handcrafted features \cite{sofm}. While useful, they often struggle to generalize across highly diverse protein folds and are limited in handling novel or structurally uncharacterized sequences.
\vspace{1em}

\textbf{\color{black}{3) Discriminative approaches}} (e.g., SVMs, Random Forests) treat remote homology detection as a classification task \cite{svmensemble}. These methods leverage both positive and negative examples and rely on engineered features such as Position-Specific Scoring Matrices (PSSM) or physicochemical properties \cite{leslie2002spectrum}. Although these approaches have enhanced sensitivity, they require fixed-length feature vectors, which can compromise the sequence-order information and make it difficult to analyze variable-length proteins.
\vspace{1em}

Despite progress, a significant challenge remains: most machine learning models require fixed-length input vectors, yet protein sequences vary in length \cite{sofm}. During vectorization, critical sequence-order and positional dependency information is lost—information that is essential for functional and structural inference in proteins. Although some efforts have been made to incorporate this information via specialized feature extraction methods or kernels (e.g., mismatch, motif, SW-PSSM), these approaches remain limited by their reliance on handcrafted features.
\vspace{1em}

Deep learning has emerged as a transformative solution to many of these limitations by enabling end-to-end learning and automatic feature extraction from raw protein sequences \cite{deepblast}. Convolutional Neural Networks (CNNs) capture local spatial motifs, while Recurrent Neural Networks (RNNs), including Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU), are capable of modeling long-range dependencies—essential for identifying fragmented homology signals.
\vspace{1em}

Hybrid deep architectures such as DanQ and ProDec-BLSTM combine these capabilities \cite{prodecblstm}. In particular, ProDec-BLSTM, a predictor based on Bidirectional LSTM, effectively addresses the shortcomings of prior LSTM-based approaches. Unlike earlier models that only considered the final LSTM output—limiting their capacity to represent long protein sequences—ProDec-BLSTM leverages every intermediate hidden state, thereby preserving long- and short-term dependencies across the sequence. It consists of an input layer, a bidirectional LSTM layer, a time-distributed dense layer, and an output layer \cite{prodecblstm}. This architecture improves both performance and interpretability. It has been shown to outperform traditional methods on widely-used benchmark datasets and provides interpretable, visualizable representations of protein patterns, which are valuable for biological analysis.
\vspace{1em}

Recent state-of-the-art models such as DeepSVM and DeepRHD further integrate evolutionary profiles (e.g., PSSMs) and physicochemical descriptors into deep architectures, achieving high accuracy on curated benchmarks like SCOP and CATH \cite{deeprhd}. Nonetheless, challenges still persist in terms of scalability to structurally diverse superfamilies, interpretability of deep models, and computational feasibility for ultra-long protein sequences (1,000 residues).
\vspace{1em}
\section{Problem Statement}

Protein remote homology detection (PRHD) is a foundational and persistent challenge in bioinformatics, essential for understanding the structure and function of proteins, especially as the volume of protein sequence data continues to expand rapidly. The difficulty of PRHD arises from the need to identify evolutionary relationships between protein sequences that share very low sequence similarity---typically when the identity drops below 30\%, a region often referred to as the ``twilight zone'' of sequence similarity. In this regime, traditional sequence alignment methods, such as BLAST and FASTA, lose their discriminative power, making it nearly impossible to infer homology based solely on sequence similarity scores.

\subsection*{Expanding the Problem Statement}

\paragraph{Complexity of Evolutionary Signals and Sequence Diversity}

Proteins evolve through a variety of mechanisms, including point mutations, insertions, deletions, and domain shuffling, leading to significant divergence at the sequence level while often preserving structural and functional features. As a result, homologous proteins may exhibit little detectable sequence similarity, even though they retain similar three-dimensional structures and biological roles. This divergence challenges both computational and experimental approaches, as subtle evolutionary signals are easily masked by noise, especially in long or highly variable sequences.

\paragraph{Variable Sequence Lengths and Feature Representation}

Another major obstacle is the inherent variability in protein sequence lengths. Many computational methods require input sequences of fixed length, necessitating either truncation or padding, which can result in the loss of critical evolutionary or functional information. Accurately capturing and representing the sequence-order information, motifs, and conserved patterns across variable-length sequences remains a significant technical hurdle.

\paragraph{Explosion of Sequence Data and Computational Bottlenecks}

The advent of high-throughput sequencing technologies has led to an exponential increase in the number of protein sequences available in public databases. This data deluge exacerbates the challenges of PRHD, as methods must not only be accurate but also computationally efficient and scalable to handle millions of sequences. Traditional laboratory techniques such as X-ray crystallography or NMR spectroscopy, while precise, are prohibitively expensive and time-consuming for large-scale applications.

\paragraph{Limitations of Traditional and Early Computational Methods}

Early computational approaches, such as pairwise sequence alignment algorithms (Needleman-Wunsch, Smith-Waterman), heuristic methods (BLAST, FASTA), and profile-based techniques (PSI-BLAST), are effective for detecting homologs with moderate to high sequence similarity but struggle in the remote homology regime. Generative models like profile Hidden Markov Models (HMMs) improved sensitivity by capturing family-level evolutionary information, but their performance still declines as sequence similarity drops and as the diversity within protein families increases.

Discriminative machine learning approaches, including Support Vector Machines (SVMs) and ensemble classifiers, have further advanced the field by leveraging complex feature representations (e.g., k-mers, auto-cross covariance, pseudo amino acid composition), yet they are still limited by the quality of feature extraction and the challenge of integrating heterogeneous data sources.

\paragraph{Emergence of Deep Learning and Hybrid Feature Approaches}

Recent advances in deep learning have shown promise in overcoming some of these limitations by automatically learning hierarchical and abstract representations from raw sequence data, accommodating variable-length inputs, and integrating multiple sources of information (evolutionary, physicochemical, and structural features). Hybrid models, such as those combining convolutional neural networks (CNNs) and recurrent neural networks (RNNs, including GRUs and LSTMs), have demonstrated superior performance by capturing both local motifs and long-range dependencies in protein sequences. However, these models also require large, well-annotated datasets and significant computational resources for training and inference.

\paragraph{Imbalance and Uncertainty in Classification Tasks}

The PRHD problem is further complicated by the highly imbalanced nature of classification datasets: the vast majority of protein pairs are unrelated, making the identification of true remote homologs akin to finding a needle in a haystack. This imbalance can lead to high false positive rates and demands robust validation strategies and careful model calibration.

\section{Solution Approach}

The challenge of accurately detecting remote protein homology, especially for sequences with low similarity, requires a robust, scalable, and information-rich computational approach. The proposed solution leverages a hybrid feature extraction strategy integrated with deep learning, specifically a CNN-GRU (Convolutional Neural Network – Gated Recurrent Unit) architecture, to address the limitations of traditional methods and enhance detection performance.

\subsection{Hybrid Feature Extraction}

\paragraph{Evolutionary Information} 
Evolutionary relationships are captured using Position-Specific Scoring Matrices (PSSMs) derived from DELTA-BLAST searches. PSSMs encode the likelihood of amino acid substitutions at each position, reflecting evolutionary conservation and variability. To further distill evolutionary signals, an auto-cross covariance (ACC) transformation is applied, which computes correlations between residues separated by various distances, capturing sequence-order effects and long-range dependencies.

\paragraph{Physicochemical Properties} 
Each amino acid's physicochemical characteristics (e.g., hydrophobicity, charge, isoelectric point) are extracted using the AAIndex database. The physicochemical distance transformation (PDT) quantifies the similarity or difference in these properties across the sequence, complementing evolutionary data and enriching the feature set.

\paragraph{Hybrid Distance Vector} 
The evolutionary ($V_e$) and physicochemical ($V_p$) vectors are concatenated to form a comprehensive hybrid distance vector ($V_h = V_e \cup V_p$). This results in a high-dimensional, information-rich representation that accommodates variable sequence lengths and maximizes the discriminative power for homology detection.

\subsection{Data Preparation}

\paragraph{Benchmark Datasets} 
Large, curated datasets such as SCOP and CATH are used for model training and evaluation. These datasets provide hierarchically classified protein domains, enabling robust model validation across diverse superfamilies and folds.

\paragraph{Preprocessing} 
Protein sequences are transformed into fixed-dimension hybrid feature vectors, ensuring compatibility with machine learning and deep learning models while retaining critical sequence-order and property information.

\subsection{Deep Learning Model: CNN-GRU Architecture}

\paragraph{Convolutional Neural Network (CNN) Layers} 
The CNN component acts as a spatial feature extractor, identifying local motifs and patterns within the hybrid feature vectors. Two convolutional layers with batch normalization and max pooling are used to reduce dimensionality and highlight salient features.
\begin{figure}[!ht]
    \centering
    \includegraphics[width=1\linewidth]{Untitled Diagram.drawio.png}
    \caption{Layers of CNN-GRU model}
    \label{fig:enter-label}
\end{figure}
\paragraph{Bidirectional GRU Layer} 
The output from the CNN is passed to a bidirectional GRU, a type of recurrent neural network optimized for sequence data. The GRU captures temporal dependencies and long-range relationships, processing the sequence in both forward and backward directions for comprehensive context understanding. This is particularly effective for variable-length sequences and avoids the computational complexity of LSTMs while retaining similar performance.

\paragraph{Classification Layer} 
The processed features are flattened and passed through dense layers with a binary cross-entropy loss function to classify whether a protein pair belongs to the same superfamily (homologous) or not.

\subsection{Model Training and Validation}

\paragraph{Cross-Validation} 
K-fold cross-validation (typically 5-fold) is used to ensure robust performance assessment and prevent overfitting. The model is trained and validated on different subsets of the data, and performance metrics such as ROC-AUC and ROC50 are averaged across folds.

\paragraph{Performance Metrics} 
The proposed DeepRHD model demonstrates superior ROC and ROC50 scores compared to traditional SVM-based methods and other deep learning models (like ProDec-BLSTM and LSTM), indicating higher sensitivity and specificity in remote homology detection.

\subsection{Comparative and Generalization Analysis}

\paragraph{Comparison with Existing Methods} 
DeepRHD outperforms classical sequence alignment (BLAST, PSI-BLAST), profile-based (HMM), and SVM-based discriminative approaches by effectively integrating evolutionary and physicochemical information and leveraging deep learning's capacity to model complex, non-linear relationships.

\paragraph{Generalization Across Datasets} 
The model's efficacy is validated on both SCOP and CATH datasets, demonstrating its ability to generalize across different protein classification schemes and sequence distributions.

\subsection{Scalability and Practical Utility}

\paragraph{Handling Large Datasets} 
The hybrid feature extraction and deep learning pipeline is designed to efficiently process large-scale protein datasets, addressing the computational demands posed by the rapid growth of sequence databases.

\paragraph{Application Scope} 
Beyond structural and functional annotation, the improved sensitivity of DeepRHD can aid in disease-related protein identification and drug discovery, making it a valuable tool in biomedical research.

\section{Implementation Detail}
Our methodology combines rigorous data curation with advanced deep learning techniques to address the challenges of remote homology detection.Benchmarking follows standardized protocols using SCOP/CATH datasets with low sequence identity thresholds (<30\%).
\subsection{Data Collection and Preprocessing}
\label{subsec:data}
The dataset for this study was obtained from the \textbf{SCOP v2.08 benchmark} collection, which provides a comprehensive, manually curated hierarchy of protein structural domains. SCOP was chosen because it provides an expert-curated, hierarchical classification of protein domains that integrates three-dimensional fold similarity with deep evolutionary relationships\cite{chandonia2017}. The SCOP metadata (domain IDs, family and superfamily labels) were provided in the SCOP-benchmark PDF, and the corresponding amino acid sequences were provided in a separate text file. Both files were downloaded from the Bliu Lab ProDec-BLSTM repository (\cite{scoplink1} \cite{scoplink2}).
The raw data comprised two sources: a PDF listing each domain’s ID, family, and superfamily, and a text file of sequences keyed by domain ID. These were combined into a single table using Python and the pandas library. \\
The basic building blocks of the protein sequences were amino acids. A unique protein containing aunique genetic code was identiﬁed by linking various amino acids with varying numbers, from 9 to 700.The 20 major amino acids were in the protein production were as given in Q = {A, C, D, E, F, G, H, I,K, L, M, N, P, Q, R, S, T, V, W, Y}[\cite{liu2009} \cite{lan2018}].In brief:
\begin{itemize}
    \item \textbf{Parsed the SCOP PDF:} The SCOP-benchmark PDF \cite{scoplink1} was parsed (e.g., with a PDF reader or tabular extraction tool) to extract a table of domain annotations. For each domain, we recorded the Domain ID, Family, and Superfamily.
    \item \textbf{Loaded sequence file:} The SCOP-benchmark\_sequences.txt file \cite{scoplink2} (FASTA-like format) was read into Python. Each record contained a Domain ID and its amino acid sequence.
    \item \textbf{Merged by Domain ID:} The two data tables were joined on the Domain ID field. In pandas, this was done with a merge or join operation, yielding a consolidated DataFrame.
    \item \textbf{Saved to CSV:} The merged table was written to CSV format with four columns: \textit{Domain ID}, \textit{Family}, \textit{Superfamily}, and \textit{Sequence}.
\end{itemize}

To improve the quality of the dataset and ensure robust downstream learning, we removed redundant sequences by retaining only unique amino acid sequences. Redundancy in sequence data can significantly impact the performance of machine learning models by introducing bias and overfitting to overly represented patterns. This bias can mislead classification tasks, especially in supervised learning models where assumptions of sample independence are critical.

The removal of identical sequences was implemented by comparing entire amino acid strings across all records. Any duplicate entries were removed, keeping only one representative sequence. This approach ensures that the distribution of training data better represents diverse sequence patterns rather than repetitions of the same one.

We employed tools such as Python’s built-in data structures and pandas utilities for this task. In particular, the \texttt{drop\_duplicates()} method in pandas provided a straightforward way to eliminate exact duplicates from the sequence column of the dataset.

While more sophisticated filtering techniques based on sequence similarity (e.g., clustering based on sequence identity) are available, we did not apply these in our work. However, the simplest measure of pairwise sequence identity between two sequences $A$ and $B$ of equal length $L$ is calculated as follows:
\[ \text{Identity}(A, B) = \frac{\text{Number of identical positions}}{L} \times 100 \% \]

Although more advanced filtering techniques based on sequence similarity (e.g., clustering sequences with greater than 40\% identity) could have further reduced redundancy, we opted not to apply them in this study for two main reasons. First, our primary goal was to eliminate exact duplicates that introduce clear redundancy, which could bias the learning model. Second, implementing similarity-based filtering requires additional computational resources and fine-tuning thresholds, which can be unnecessary for baseline studies—especially when the model can still generalize well using diverse, non-identical sequences. Thus, exact match filtering struck a balance between dataset quality and processing complexity.

In cases where filtering by identity threshold is applied (e.g., 40\% identity), one would typically remove one of the sequences in each similar pair.

After merging and deduplication, the cleaned dataset contained approximately \textbf{170,000} unique protein domain sequences.

\vspace{1em}
\begin{figure}
    \centering
    \includegraphics[width=1\linewidth]{Screenshot 2025-05-13 at 6.07.54 PM.png}
    \caption{Final dataset after preprocessing}
    \label{fig:enter-label}
\end{figure}

\subsection{Formation of PDT (Physicochemical Distance Transformation) matrix}
\label{subsec:pdt}
Representing a protein sequence as a fixed-length numeric matrix requires encoding both its \textbf{physicochemical properties} and the \textbf{sequence-order relationships}. The Physicochemical Distance Transformation (PDT) approach does this by first mapping each amino acid to numeric property scores (from AAIndex1) and then computing lag-dependent differences\cite{liu2010}. In essence, each protein is converted into a distance matrix that captures how its residue properties change along the sequence. This preserves local sequence-order effects (beyond simple composition) and has been shown to improve tasks such as homology detection and classification\cite{liu2010}. For example, Liu \textit{et al.}\cite{liu2010} describe how ``each protein sequence is converted into a series of numbers using the physicochemical property scores in the amino acid index (AAIndex), and then the sequence is converted into a fixed length vector by PDT,'' thus efficiently incorporating information of sequence order.
\vspace{1em}

\textbf{AAIndex1 Database Description}:- 
AAIndex1 is a curated database of \textbf{amino acid indices}, where each entry provides 20 numerical values (one per standard amino acid) for a particular physicochemical or biochemical property\cite{kawashima1999}. It is part of the AAindex suite (AAIndex1 for individual properties, AAIndex2 for substitution matrices, AAIndex3 for contact potentials) and is maintained at KEGG/GenomeNet\cite{kawashima1999}. Each AAIndex1 entry has an accession code and a textual description, followed by a line (labeled ``I'') listing 20 values. Users typically select a subset of these indices (scales) based on relevance; in principle all available scales with complete data can be used. Each scale provides a vector of 20 values — one for each of the standard amino acids — corresponding to characteristics like:
\begin{itemize}
    \item Hydrophobicity
    \item Charge
    \item Molecular weight
    \item Secondary structure propensities
    \item Solvent accessibility
\end{itemize}
\vspace{1em}
\begin{figure}[!ht]
    \centering
    \includegraphics[width=0.75\linewidth]{Screenshot 2025-05-13 at 3.42.39 PM.png}
    \caption{Single entry of AAIndex database after parsing}
    \label{fig:enter-label}
\end{figure}

\textbf{Parsing and Preprocessing}:- 
The AAIndex1 file is a curated database that compiles numerous physicochemical and biochemical property scales for amino acids, which are widely used in bioinformatics for numerical encoding of protein sequences. Each record in the file describes a specific property or index (e.g., hydrophobicity, bulkiness, polarity) and is formatted in a structured, machine-readable way. Records are separated by the delimiter “//”, and each one begins with labeled lines that provide metadata about the scale.

For example, the header line beginning with “H” contains the unique ID of the scale (such as "BUNA790102"), while the “D” line offers a brief textual description of the property (e.g., "bulkiness of side chain"). The most important part of each record is the “I” line, which contains 20 numeric values corresponding to each of the 20 standard amino acids. These values serve as feature encodings that can be mapped directly to amino acids in a sequence.

To use this data, a parser reads through the AAIndex1 file, extracts all complete records, and converts them into a dictionary or matrix where each scale maps the 20 amino acids (e.g., 'A', 'C', 'D', ..., 'Y') to their respective numeric values. Only those scales that define values for all 20 amino acids are retained to maintain consistency across sequences. This filtering step ensures that no amino acid in a given sequence is left without a corresponding feature value, which is crucial for machine learning models that require complete numerical representations.

In our analysis, \textbf{a total of 553 valid and complete scales were found} in the AAIndex1 file. These were used as the foundation for constructing the PDT matrix, with each scale serving as a row in the final transformation matrix.\cite{aaindexfile}. 
\vspace{1em}
\begin{figure}[!ht]
    \centering
    \includegraphics[width=0.75\linewidth]{Screenshot 2025-05-13 at 4.00.00 PM.png}
    \caption{Example of a scale from AAIndex database}
    \label{fig:enter-label}
\end{figure}

\textbf{Sequence Vectorization}  
Once a set of $S$ property scales is selected from the AAIndex database, the next step in feature extraction is to numerically encode each amino acid sequence based on these scales. This process is essential because machine learning models cannot directly interpret protein sequences represented as strings of characters (e.g., "MQAL..."). Instead, they require sequences to be expressed as numerical vectors that retain biological meaning.

Each scale $s$ assigns a specific numeric value to each of the 20 standard amino acids. For a given protein sequence of length $L$, we replace each amino acid in the sequence with its corresponding numeric value from scale $s$. This transformation results in a vector of length $L$ for each scale:
\[ P^{(s)} = [P_1^{(s)}, P_2^{(s)}, \ldots, P_L^{(s)}] \]
where $P_i^{(s)}$ denotes the value assigned to the amino acid at position $i$ by scale $s$.

This step is repeated for all $S$ selected scales, resulting in $S$ distinct property vectors for each sequence. Together, these vectors form a matrix of shape $S \times L$ — a rich, multi-dimensional representation of the sequence that integrates biochemical, structural, or evolutionary information from the AAIndex profiles.

This matrix preserves the order of residues and incorporates multiple perspectives of amino acid properties, making it suitable for subsequent steps like autocorrelation calculations or input into deep learning models. The resulting numerical profile is commonly referred to as a multi-scale property matrix or encoded sequence profile\cite{liu2010}.

This vectorization method provides a foundation for downstream representations such as PDT, where these numerical profiles are further transformed using autocovariance-based methods to yield fixed-length feature matrices.
\vspace{1em}

\textbf{Lag-Based Distance Encoding}
To incorporate sequence-order effects, PDT computes squared differences at various lags $\tau$:
\[ d_\tau^{(s)} = \frac{1}{L-\tau}\sum_{i=1}^{L-\tau} (P_i^{(s)} - P_{i+\tau}^{(s)})^2 \]
This measures how much the property values change when moving $\tau$ residues ahead. This is analogous to autocovariance and reveals local and distant correlations\cite{liu2010}.
\vspace{4em}

\begin{figure}[!ht]
    \centering
    \includegraphics[width=0.5\linewidth]{c543a745-28dc-41f6-8cfb-dac689dea6d1.png}
    \caption{Illustration of lag comparisons in PDT: for $\tau=1,2,3$, residue pairs separated by $\tau$ are compared. Red arrows indicate squared differences computed. Adapted from Liu \textit{et al.}\cite{liu2010}.}
    \label{fig:enter-label}
\end{figure}

\begin{figure}[!ht]
    \centering
    \includegraphics[width=1\linewidth]{Screenshot 2025-05-13 at 4.38.13 PM.png}
    \caption{Portion of PDT tensor (first 2 sequences, first 3 scales, all 10 lags)}
    \label{fig:enter-label}
\end{figure}

\textbf{Matrix Construction}
Collecting the values $d_\tau^{(s)}$ for all $s$ and $\tau$ gives the PDT matrix $M$ of shape $S \times T$:
\[ M_{s,\tau} = d_\tau^{(s)} \]
Each row corresponds to a scale, and each column to a lag. If a common maximum lag $T$ is fixed, then all sequences yield fixed-size matrices. This makes the representation suitable for machine learning models.
In other words, each row $s$ corresponds to one property scale, and each column corresponds to a lag $\tau$. For a sequence of length $L$, one typically allows $\tau$ up to $L-1$ (or to a fixed maximum $T$ for all sequences to have a common shape). This matrix captures how each property varies as a function of separation distance. The result is a fixed-size feature representation (dimension $S \times T$) even if the original sequence lengths differ (as long as a common $T$ is used).
\vspace{1em}
In our case we have used lags from $\tau$ = 1,2,3.....10 :
\begin{itemize}
    \item $S = 553$ property scales (rows)
    \item $T = 10$ lags (columns)
\end{itemize}

So, the PDT matrix for each protein is $553 \times 10$.
\vspace{1em}

For scalability, we divided the dataset into chunks of 6000 sequences. Each chunk is transformed into a 3D tensor:
\[ \text{Chunk Tensor Shape: } (6000, 553, 10) \]
After all chunks are processed, we concatenate them to form the full tensor:
\[ \text{Full PDT Tensor Shape: } (28, 553, 10) \quad \text{where } N = \text{chunks in our case} \]
\begin{figure}[!ht]
    \centering
    \includegraphics[width=1\linewidth]{Screenshot 2025-05-13 at 4.49.40 PM.png}
    \caption{Heatmap of a sequence from pdt matrix.This visualization captures the structural and functional characteristics of the protein by showing how physicochemical properties vary along the sequence at different separation distances.}
    \label{fig:enter-label}
\end{figure}

\subsection{Formation of PSSM (Position-Specific Scoring Matrix) matrix}
\label{subsec:pssm}

A \textbf{Position-Specific Scoring Matrix (PSSM)}, also known as a profile or position-specific weight matrix, is a matrix representation of a protein or nucleotide sequence motif derived from a multiple sequence alignment (MSA). In a PSSM, each column corresponds to a position in the aligned motif or query sequence, and each row corresponds to one of the possible residues (e.g., 20 amino acids for proteins or 4 nucleotides for DNA).

Formally, a PSSM is an $L \times |\Sigma|$ matrix, where $L$ is the length of the sequence and $|\Sigma|$ is the size of the residue alphabet (e.g., $|\Sigma| = 20$ for proteins, $|\Sigma| = 4$ for nucleotides). Each cell $s(i,a)$ in the matrix represents the score, often a log-odds value, of observing residue $a$ at position $i$.

By construction, highly conserved positions in the alignment yield high positive scores for the common residue(s) and negative scores for others, reflecting strong evolutionary preference. Conversely, poorly conserved positions have scores near zero for all residues, indicating little to no preference.

In practice, PSSMs capture the evolutionary conservation pattern of a protein family or motif. The scores quantify how much more (or less) likely each residue is at each position compared to what would be expected by chance, providing a powerful tool for sequence analysis and motif identification.

\subsubsection{Data Sources}
\begin{itemize}
    \item  \textbf{The Conserved Domain Database (CDD)} \cite{cddncbi}\cite{cdd_link} was downloaded from NCBI to provide domain-specific profiles for DELTA-BLAST searches.
    The Conserved Domain Database (CDD), maintained by the National Center for Biotechnology Information (NCBI), is a comprehensive, curated resource of multiple sequence alignments that represent conserved domains found across a wide range of protein families. These conserved domains are biologically significant segments of proteins that tend to maintain their structure and function across different organisms and evolutionary timelines. The CDD serves as a foundational tool in bioinformatics for identifying and characterizing functional regions within proteins by leveraging the evolutionary information contained within these conserved domains.

    One of the primary uses of the CDD is in the generation and application of Position-Specific Scoring Matrices (PSSMs). To construct a PSSM, the CDD starts with a multiple sequence alignment of a protein domain that captures the variability and conservation patterns of amino acids at each position within the domain. From this alignment, statistical models are built by calculating the frequency of each amino acid at every alignment position, adjusting for background probabilities and applying pseudocounts to handle sparse data. This frequency data is transformed into a log-odds scoring system that forms the core of the PSSM. The resulting PSSM encapsulates both the conserved and variable positions within a domain, making it highly sensitive for detecting even remote homologs.
    
    In the context of PSSM formation, the CDD plays a crucial role by providing a rich, curated source of domain alignments, ensuring the resulting PSSMs are biologically meaningful and accurate. These matrices are then used to compare new protein sequences against the database of conserved domain models, enabling the identification of structural and functional motifs that might not be apparent through simple sequence alignment. Thus, the CDD significantly enhances the ability of bioinformatics tools to annotate protein sequences based on evolutionary conserved domains, and its integration into PSSM generation makes it an indispensable resource for functional and structural protein analysis.
    \begin{figure}[!ht]
        \centering
        \includegraphics[width=0.75\linewidth]{Screenshot 2025-05-18 at 11.49.29 AM.png}
        \caption{CDD database}
        \label{fig:enter-label}
    \end{figure}
    \item  The \textbf{NCBI non-redundant}\cite{nrdb} \textbf{(nr / swissprot)}\cite{nr_database} protein database was also downloaded to serve as the search space for sequence similarity searches.
    The SwissProt database is a manually curated, high-quality section of the UniProt Knowledgebase (UniProtKB), which focuses on providing rich, non-redundant, and functionally annotated protein sequence information. Each entry in SwissProt contains detailed annotations including the protein’s function, domain structure, post-translational modifications, variants, and literature references. What distinguishes SwissProt from other databases is its rigorous manual curation process, which ensures that the data is accurate, consistently annotated, and devoid of unnecessary duplication.

    In the context of Position-Specific Scoring Matrix (PSSM) generation, SwissProt plays a vital role by serving as a reliable and biologically meaningful search space during the sequence similarity search phase, especially in tools like PSI-BLAST. When PSI-BLAST is executed, it iteratively searches against a database (such as SwissProt or the broader non-redundant nr database) to identify evolutionarily related sequences. These sequences are aligned to construct a multiple sequence alignment, from which a PSSM is derived.

    Using SwissProt for this process provides several advantages. Since the entries are non-redundant and well-annotated, the resulting alignments are more meaningful and less likely to be biased by redundant or low-quality sequences. This in turn improves the accuracy and biological relevance of the resulting PSSM, which reflects the evolutionary conservation patterns across a diverse but trustworthy set of protein sequences. Thus, SwissProt not only serves as a rich resource for functionally annotated sequences but also enhances the generation of high-quality PSSMs used in tasks like remote homology detection and functional annotation.
    \begin{figure}[!ht]
        \centering
        \includegraphics[width=0.75\linewidth]{Screenshot 2025-05-18 at 11.54.28 AM.png}
        \caption{Swissprot database}
        \label{fig:enter-label}
    \end{figure}
\end{itemize}

\subsubsection{DELTA-BLAST Analysis}
\label{subsec:deltablast}

DELTA-BLAST (Domain Enhanced Lookup Time Accelerated BLAST) is an advanced protein sequence search tool that improves remote homology detection by integrating conserved domain information into the search process. Unlike standard BLAST, DELTA-BLAST first searches the Conserved Domain Database (CDD) to identify domains within the query sequence and constructs a Position-Specific Scoring Matrix (PSSM) based on these domains. This PSSM is then used to search the target protein database (such as NCBI's non-redundant (nr) database), increasing sensitivity to distant homologs~\cite{deltablast_manual, deltablast_paper}.

\paragraph{Structure of a PSSM}
\begin{itemize}
    \item \textbf{Rows:} Each row in a PSSM corresponds to a specific position in the query protein sequence. If the protein has a sequence length of $L$, then the matrix will contain $L$ rows, denoted as $j = 1, 2, ..., L$. These rows represent the individual positions or residues along the protein chain where the substitution pattern is analyzed.
    \item \textbf{Columns:} The PSSM contains 20 columns, one for each of the standard amino acids (e.g., A, R, N, D, C, Q, E, G, H, I, L, K, M, F, P, S, T, W, Y, V). These columns denote the amino acid types that may appear at each position, and the matrix captures how likely it is for each of these amino acids to occur at a given position in the sequence.
    \item \textbf{Cells:} Each cell of the matrix, denoted $W_{i,j}$, contains a **log-odds score** that represents the likelihood of observing amino acid $i$ at position $j$ in the alignment, relative to its expected background frequency. A higher positive score suggests that amino acid $i$ is highly conserved and favored at position $j$, whereas a negative score indicates that the substitution of amino acid $i$ at that position is less likely to occur through evolutionary processes. These scores are computed using substitution frequencies derived from homologous sequences found during iterative sequence alignment processes such as those performed by PSI-BLAST.
\end{itemize}

\paragraph{PSSM Construction}\\

The construction of a Position-Specific Scoring Matrix (PSSM) involves a systematic transformation of raw sequence alignments into a matrix of log-odds scores. This is typically done in the following steps:

\begin{enumerate}
    \item \textbf{Position Frequency Matrix (PFM):} \\
    This step involves counting how many times each amino acid appears at each position in the multiple sequence alignment. These counts are stored in a matrix called the Position Frequency Matrix (PFM).
    \begin{equation}
        c_{i,j} = \text{Count of amino acid } i \text{ at position } j
    \end{equation}

    \item \textbf{Probability Matrix with Pseudocounts:} \\
    To address the issue of zero probabilities due to limited observations, pseudocounts are added to the raw counts. The background frequency of each amino acid, $p_i$, is used along with a smoothing parameter $k$ to compute adjusted probabilities.
    \begin{equation}
        f'_{i,j} = \frac{c_{i,j} + p_i \cdot k}{\sum_{r=1}^{20} (c_{r,j} + p_r \cdot k)}
    \end{equation}
    Here, $f'_{i,j}$ represents the smoothed probability of amino acid $i$ at position $j$.

    \item \textbf{Log-Odds Score Calculation:} \\
    Finally, each probability is compared to the expected background frequency using a log-ratio. The resulting values form the actual PSSM scores, where a positive score indicates conservation and a negative score suggests rarity.
    \begin{equation}
        W_{i,j} = \log_2\left(\frac{f'_{i,j}}{p_i}\right)
    \end{equation}
    These log-odds scores highlight the degree to which certain amino acids are favored or disfavored at specific positions in the sequence.
\end{enumerate}


\textbf{Interpretation:}
\begin{itemize}
    \item $W_{i,j} > 0$: Amino acid $i$ is more conserved at position $j$ than expected by chance (functionally/structurally important)
    \item $W_{i,j} < 0$: Amino acid $i$ is less frequent than expected (variable position)
\end{itemize}

PSSMs are more informative than simple substitution matrices (such as PAM or BLOSUM), as they are specific to each position in the protein and reflect the evolutionary constraints at that site~\cite{pssm_gibbs,pssm_slides}.

\subsubsection{DELTA-BLAST Implementation}

DELTA-BLAST (Domain Enhanced Lookup Time Accelerated BLAST) is an advanced sequence alignment algorithm developed to improve the sensitivity of remote homology detection. Unlike traditional BLAST approaches that directly compare query sequences to a database, DELTA-BLAST integrates conserved domain information by initially searching the NCBI Conserved Domain Database (CDD). The algorithm constructs a Position-Specific Scoring Matrix (PSSM) based on domain alignments and then uses this refined matrix to perform a database search against a protein sequence database such as \texttt{nr} or \texttt{SwissProt}~\cite{deltablast_paper,deltablast_manual}.

This two-step process—domain identification followed by PSSM-based search—enables DELTA-BLAST to detect more distantly related protein sequences with higher accuracy, particularly in cases where standard BLAST fails to identify significant hits.

\paragraph{Workflow:}
The typical steps followed by DELTA-BLAST are:
\begin{enumerate}
    \item \textbf{Domain Identification:} The input query protein sequence is first scanned against the Conserved Domain Database (CDD) to detect any conserved domains.
    \item \textbf{PSSM Construction:} Using the alignments from identified domains, DELTA-BLAST constructs a PSSM that captures evolutionary preferences for each position.
    \item \textbf{Database Search:} The generated PSSM is then used to search a target protein database (e.g., \texttt{SwissProt} or \texttt{nr}) for homologous sequences.
    \item \textbf{Result Reporting:} The resulting alignments are scored, ranked, and filtered based on the user-defined E-value threshold to remove low-confidence hits.
\end{enumerate}

\paragraph{Command-Line Syntax}
DELTA-BLAST can be executed from the command line using the following syntax:
\begin{verbatim}
deltablast \
  -query query.fasta \
  -db "F:\ncbi_extracted_swissprot\swissprot" \
  -rpsdb "F:\cdd" \
  -num_iterations 3 \
  -evalue 0.001 \
  -out_ascii_pssm query.pssm \
  -out deltablast_output.txt
\end{verbatim}

\paragraph{Parameter Explanation}
\begin{itemize}
    \item \texttt{-query}: Specifies the input FASTA file containing protein sequences to be queried.
    \item \texttt{-db}: Sets the target sequence database for homology search (e.g., SwissProt or nr).
    \item \texttt{-rpsdb}: Indicates the RPS-BLAST-compatible conserved domain database (CDD).
    \item \texttt{-num\_iterations}: Specifies the number of iterations for PSSM refinement. Setting this to a higher value (e.g., 3) improves sensitivity.
    \item \texttt{-evalue}: Defines the E-value cutoff for reporting matches. Lower values (e.g., 0.001) impose stricter match criteria.
    \item \texttt{-out\_ascii\_pssm}: Outputs the computed PSSM in ASCII format, which is used for downstream applications such as ACC or PDT matrix construction.
    \item \texttt{-out}: Specifies the output file for tabular alignment results.
    \item \textbf{Filtering:} By default, DELTA-BLAST applies SEG filtering to mask low-complexity regions, reducing spurious alignments.
    \item \textbf{Scoring Matrix:} BLOSUM62 is used as the default scoring matrix to assess similarity during domain and sequence alignments.
\end{itemize}

This pipeline significantly enhances the ability to detect functionally or evolutionarily related sequences, even in the absence of high sequence identity, making it highly suitable for applications in remote homology detection and evolutionary studies.


\paragraph{Advantages of DELTA-BLAST PSSMs}
\begin{itemize}
    \item \textbf{Captures evolutionary information:} Unlike single-sequence encodings, a PSSM summarizes data from many homologs. Conserved positions (with high scores for certain residues) highlight functional or structural importance. This evolutionary profile greatly increases sensitivity: distant homologs that share only subtle patterns can be detected because the PSSM aggregates weak signals
    \item \textbf{Position specificity:} By assigning a different score at each position, a PSSM models the non-uniform conservation along the protein. This allows motif detection (e.g. DNA binding sites) and domain boundaries to be pinpointed precisely. High scores reveal “signature residues” at specific sites. As Altschul notes, if a residue is highly conserved at a position, its PSSM entry is strongly positive, while other residues get negative scores. Thus PSSMs provide nuanced profiles that general substitution matrices cannot.~\cite{deltablast_paper,deeprhd}.
    \item \textbf{Improved homology detection:} Profile-based searches are generally more sensitive than pairwise alignments. Using “any number of sequences” in the profile means one leverages all available information. In practice, PSI-BLAST and other profile searches routinely find homologs that BLAST misses, making PSSMs a cornerstone of remote-homology methods.
    \item \textbf{Versatility:} PSSMs can be used directly for scoring alignments (profile–sequence or profile–profile) and for feature extraction in diverse methods. They serve as inputs to both classical algorithms (e.g. RPS-BLAST for domain search) and modern ML pipelines. This versatility has made PSSMs a “go-to” representation in bioinformatics.
    \item \textbf{Interpretable:} Because PSSMs are based on observed frequencies, they are relatively transparent. One can inspect the matrix to understand which residues are allowed or forbidden. Tools like CD-Search display the PSSM (or consensus) underlying a domain model, aiding interpretation.
    \item \textbf{Compatibility with scoring theory:} Since PSSM scores are log-odds, standard statistical theory (Karlin-Altschul statistics) still applies. For example, PSI-BLAST uses the same E-value framework as BLAST by treating the PSSM as a scoring system with fixed scale. This allows profile searches to yield meaningful significance estimates.
\end{itemize}

\begin{figure}[!ht]
    \centering
    \includegraphics[width=1\linewidth]{WhatsApp Image 2025-05-18 at 12.21.18 PM.jpeg}
    \caption{PSSM matrix representation}
    \label{fig:enter-label}
\end{figure}
   
\subsubsection{Summary}
Position-Specific Scoring Matrices are a powerful and widely used representation of sequence conservation. By capturing the position-by-position residue preferences of a protein family (via log-odds scores), PSSMs enable sensitive motif and homology detection, inform structural/functional predictions, and serve as rich features for machine learning models. Their success hinges on exploiting evolutionary information from multiple alignments. However, they require careful construction (weighting, pseudocounts) and sufficient data, and they embody simplifications (independence of sites) that newer methods may overcome. Nonetheless, PSSMs remain foundational in bioinformatics, with tools like PSI-BLAST and CDD relying on them to annotate sequences and discover new relationships.


\subsection{Formation of ACC (Auto-Cross Covariance) matrix}
\label{subsec:acc}
The ACC matrix encodes auto-covariance-type features derived from the PSSM profiles. Conceptually, ACC measures how PSSM scores at one position correlate with scores at nearby positions along the sequence. One common definition (based on the PSSM-AC feature) is: for each position i and offset (lag) g, compute the covariance between the PSSM score vector at position i and at position i+g. Mathematically, a typical formula is:


\[
\text{ACC}_g^{(j)} = \frac{1}{L - g} \sum_{i=1}^{L - g} \left( P_{i,j} - \bar{P}_j \right) \left( P_{i+g,j} - \bar{P}_j \right)
\]
\begin{itemize}
  \item $\text{ACC}_g^{(j)}$: Auto Covariance Coefficient for amino acid $j$ at lag $g$,
  \item $L$: Length of the protein sequence (number of residues),
  \item $P_{i,j}$: PSSM score at position $i$ for amino acid $j$,
  \item $\bar{P}_j$: Mean of the scores for amino acid $j$ over the sequence,
  \item $g$: Lag value (usually from 1 to 10).
\end{itemize}
\vspace{1em}

Because g runs from 1 to 10, the ACC vector at each position has length 10. In the “ACC matrix” of shape 6000×400×10, each of the 10 channels corresponds to a particular lag = 1,…,10. In effect, the 20-dimensional profile at each position is summarized by 10 autocovariance features. By collapsing the 20 amino-acid dimensions, ACC reduces dimensionality and encodes sequence-order relationships. This approach is akin to the “auto-cross covariance” (ACC) transformation used in many studies
pubmed.ncbi.nlm.nih.gov
cran.r-project.org
. It’s important to note that ACC is not simply a downsampling of PSSM columns; rather it mixes them by computing covariances. For example, a high ACC value at lag 2 might indicate that a conserved amino acid at position i tends to co-occur with a similar conservation pattern two residues later. In many implementations, one first subtracts the mean profile from each position (centering), then multiplies paired entries as above. The result is a fixed-length (here 10) feature vector for each position. This captures local evolutionary correlations: higher g captures longer-range interactions. In the PSSM-AC example, all 20 columns j were used for each covariance, yielding 200 total features for g=1..10
cran.r-project.org
. By summing over j, the ACC matrix condenses these into 10 per position.
\vspace{1em}

\textbf{Why 10 features?} The choice of 10 commonly comes from using lag=1,…,10. In PSSM-AC, those 10 lags for each of 20 amino acids gave 200 features
cran.r-project.org
. Here we similarly use 10 lags, but pool over amino acids. Thus, each of the 10 features corresponds to a specific positional offset (1 through 10), summarizing auto-covariance of the PSSM profile at that offset.

\vspace{1em}
\textbf{Biological Interpretation and Applications}
The resulting ACC features capture sequential correlations in evolutionary profiles. Biologically, a high ACC at lag g means the conservation pattern at a residue is strongly related to the pattern g positions away. This can reflect structural motifs (e.g. helix periodicity) or dependencies (co-evolving residues) along the protein. By summarizing 20-dimensional PSSM information into 10 correlation-based features, ACC emphasizes local sequence-order effects that pure composition misses. In applications, ACC features have been successfully used in many protein predictive models. For example, Li et al. used an “auto cross covariance (ACC)” transform of the PSSM to classify protein structural classes, achieving very high accuracy on challenging datasets
pubmed.ncbi.nlm.nih.gov
. Similarly, ACC-like descriptors (often combined with other PSSM features) have improved predictions of membrane proteins, bioluminescent proteins, and more. In general, incorporating ACC features can boost machine-learning models by adding information on how positions co-vary
pubmed.ncbi.nlm.nih.gov
cran.r-project.org
. From a structural standpoint, ACC may highlight patterns of physicochemical conservation that relate to secondary structure or functional sites. For instance, in a helix every 3–4 residues tend to be similar in polarity; an ACC with lag 3 or 4 might capture this. In practice, ACC features are input to classifiers or neural nets for tasks like fold recognition, subcellular localization, binding site prediction, etc. Because ACC reduces the 20-dim PSSM to 10-dim per position, it also helps mitigate overfitting and redundancy (note that reducing amino-acid alphabets is known to decrease information redundancy
pmc.ncbi.nlm.nih.gov
). In summary, converting a 6000×400×20 PSSM dataset to 6000×400×10 ACC features means encoding evolutionary profile correlations at each position into a more compact form. This ACC representation preserves key sequence-order information and has broad utility in protein bioinformatics tasks
cran.r-project.org
pubmed.ncbi.nlm.nih.gov.
\vspace{1em}
\begin{figure}[!ht]
    \centering
    \includegraphics[width=0.75\linewidth]{WhatsApp Image 2025-05-18 at 3.41.39 PM.jpeg}
    \caption{ACC matrix of a single sequence}
    \label{fig:enter-label}
\end{figure}

\subsection{Formation of ACC-PDT matrix}
\label{subsec:acc-pdt}
After generating the Auto Covariance Coefficient (ACC) and Position-specific Diagonal Transition (PDT) matrices from the PSSM profiles, we combine them into a single unified matrix referred to as the ACC-PDT matrix. This combined representation integrates both global statistical dependencies (captured by ACC) and local sequential transitions (captured by PDT), thereby offering a more comprehensive encoding of evolutionary and positional features of protein sequences.
\begin{figure}
    \centering
    \includegraphics[width=0.5\linewidth]{acc-pdt.png}
    \caption{ACC-PDT Matrix}
    \label{fig:enter-label}
\end{figure}
Feeding this combined ACC-PDT matrix into a CNN-GRU model provides distinct advantages. The CNN (Convolutional Neural Network) component is adept at learning spatial patterns and local motifs within the matrix, capturing biologically meaningful residue correlations and conserved regions. Meanwhile, the GRU (Gated Recurrent Unit) component effectively models long-range dependencies and sequence order, crucial for understanding the context and structural roles of amino acids over the full protein length.

By leveraging both ACC and PDT features, the CNN-GRU model benefits from a richer and more informative input, leading to improved performance in tasks such as remote homology detection, protein classification, and function prediction. This hybrid representation thus enhances the model's ability to capture both evolutionary dynamics and sequence-driven patterns, contributing to a more accurate and biologically meaningful prediction.

\vspace{1em}

\subsection{Training CNN-GRU model}
\label{subsec:cnn-gru}
\subsubsection{Why CNN-GRU Models Are Preferred for Protein Sequence Tasks}

In protein sequence analysis tasks such as remote homology detection, CNN-GRU models are widely preferred due to their ability to learn both local sequence motifs and long-range dependencies in amino acid sequences. Convolutional Neural Networks (CNNs) are highly effective at detecting local patterns such as conserved motifs, active sites, or short recurring segments in sequences that often correspond to structural or functional elements of proteins. This makes them particularly suited to handle the spatial relationships present in fixed-length numeric matrices like ACC and PDT, where features across short windows are crucial. 

On the other hand, Gated Recurrent Units (GRUs), a type of recurrent neural network (RNN), are capable of capturing the sequential nature and long-term dependencies of the protein chain. GRUs provide an efficient mechanism for retaining context information across the entire sequence without the complexity of traditional LSTMs, making them faster and easier to train. 

When used in combination, CNN layers act as feature extractors that reduce input dimensionality and highlight important patterns, while GRU layers interpret these extracted features in a temporal sequence-aware manner. This hybrid architecture is particularly advantageous for biological sequences, where both spatial composition and residue order significantly influence protein function and structure. 

Empirical studies in bioinformatics have shown that CNN-GRU models often outperform models based solely on CNN or RNN, due to their complementary strengths in handling complex, structured biological data. Therefore, the CNN-GRU model provides a biologically meaningful and computationally efficient framework for encoding, learning, and classifying protein sequences based on their physicochemical and evolutionary characteristics.
\vspace{1em}

\subsubsection{Data preprocessing}
The ACC/PDT feature matrix (shape $6000\times953\times10$) contains real-valued descriptors that may have different scales. It is standard to normalize these features (e.g. using z-score standardization to zero mean and unit variance per feature) before training. Normalization (e.g. via sklearn.preprocessing.StandardScaler) speeds convergence and avoids dominance of any one feature.
\vspace{1em}

\subsubsection{Data splitting}
The labeled dataset of 6000 proteins is partitioned into training, validation and test sets (for example, 70\%/15\%/15\%). Splits should be stratified by the superfamily label so that each subset preserves the overall class distribution (avoiding, say, omitting a rare class from the test set).

\begin{itemize}
  \item \textbf{Training set:} 70\% of the total dataset, approximately 4200 protein sequences.
  \item \textbf{Validation set:} 15\% of the total dataset, approximately 900 protein sequences.
  \item \textbf{Test set:} 15\% of the total dataset, approximately 900 protein sequences.
\end{itemize}

One typically shuffles the data randomly (with a fixed seed for reproducibility) before splitting. Stratification helps ensure that each set contains examples from all superfamilies roughly in the same proportion as the overall dataset.

\subsubsection*{CNN-GRU Model}

The proposed architecture is a hybrid deep learning model combining Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), specifically Bidirectional Gated Recurrent Units (BiGRUs), to effectively extract both spatial and sequential features from protein sequence encodings. The model begins with two convolutional layers, each consisting of 10 filters of size 7$\times$7, designed to learn local patterns and spatial relationships from the input matrices such as ACC and PDT. The output of the first convolutional layer is followed by batch normalization to stabilize learning and a max-pooling operation over a 3$\times$3 window with a stride of 2$\times$2 to reduce the spatial dimensions. This process is repeated after the second convolutional layer. These CNN layers act as hierarchical feature extractors, reducing the input dimensionality while preserving critical spatial features.
\begin{figure}[!ht]
    \centering
    \includegraphics[width=1\linewidth]{Untitled Diagram.drawio.png}
    \caption{Layers of CNN-GRU model}
    \label{fig:enter-label}
\end{figure}

The resulting feature maps are then passed through a Bidirectional-GRU layer, which captures long-range dependencies and the order of residues in both forward and backward directions. This bidirectional processing enhances the model's ability to learn contextual information important for detecting remote homology between protein sequences. A time-distributed dense layer follows the GRU, allowing the model to apply the same dense operation at each time step. This output is then flattened and passed to a fully connected dense layer with a binary cross-entropy loss function for final classification, indicating whether a protein belongs to the target superfamily.
\begin{figure}[!ht]
    \centering
    \includegraphics[width=1\linewidth]{Screenshot 2025-05-18 at 3.34.09 PM.png}
    \caption{Bidirectional GRU}
    \label{fig:enter-label}
\end{figure}

To evaluate the robustness and generalizability of the model, 5-fold cross-validation was applied. The dataset, composed of protein sequences labeled by their SCOP superfamilies, was split into five subsets. In each fold, three subsets were used for training, one for validation, and one for testing. This process was repeated five times, each with a different test subset, and the results were averaged. The CNN-GRU model achieved high performance across superfamilies, with average AUC scores of 0.98 and 0.96 for ROC and ROC50 metrics, respectively. This confirms the model's efficacy in learning both physicochemical and sequential patterns relevant to remote homology detection.


\subsubsection{Evaluation Metrics}
After training, the model’s performance is evaluated on the held-out test set. Key metrics include overall accuracy (fraction of correctly classified sequences) and per-class metrics such as precision, recall, and F1-score. For a given superfamily (treated as the “positive” class in a one-vs-rest manner), precision measures the fraction of predicted positives that are correct, and recall measures the fraction of true positives recovered. The F1-score (the harmonic mean of precision and recall) is often reported as a balanced metric. A confusion matrix is also computed to visualize which superfamilies are most often confused with others. For a multi-class problem, one typically reports macro-averaged precision/recall/F1 (averaging each class equally) or weighted averages (weighted by class frequency). Overall accuracy is straightforward (correct predictions / total). For completeness, one may also compute the Matthew’s Correlation Coefficient (MCC) or other composite metrics if classes are imbalanced. In a typical report, these metrics would be tabulated or plotted. For example, the confusion matrix highlights class-wise performance, and per-class metrics reveal which superfamilies are harder to predict. High overall accuracy (e.g. >90\%) would indicate success, but one should also inspect per-class F1-scores since some superfamilies may be very rare. All results (accuracy, precision, recall, F1) are reported on the independent test set to demonstrate the classifier’s final performance.
\vspace{1em}


\section{Results}
To evaluate the performance of our model for protein remote homology detection, we conducted 5-fold cross-validation. The evaluation was based on two standard metrics: classification accuracy and the Receiver Operating Characteristic (ROC) curve.

\subsection{5-Fold Cross-Validation Accuracy}
We trained and tested our model on five distinct data folds to ensure that the performance is not biased by any specific subset of data. The accuracy achieved on each fold is presented below:
\begin{itemize}
  \item \textbf{Fold 1}: 0.9609
  \item \textbf{Fold 2}: 0.9543
  \item \textbf{Fold 3}: 0.9471
  \item \textbf{Fold 4}: 0.9452
  \item \textbf{Fold 5}: 0.9536
  \item \textbf{Mean Accuracy}: 0.9522
  \item \textbf{Standard Deviation}: 0.0061
\end{itemize}


\subsection{ROC Curve and AUC Analysis}
The Area Under the Curve (AUC) values were calculated for each fold and averaged to assess the model's overall classification quality. The model achieved a mean AUC of 0.946 ± 0.002, which reflects a strong ability to distinguish between classes regardless of the decision threshold.
\begin{figure}[!ht]
    \centering
    \includegraphics[width=0.75\linewidth]{auc-cnngru.png}
    \caption{AUC for CN-GRU}
    \label{fig:enter-label}
\end{figure}
To further evaluate the model's ability to discriminate between homologous and non-homologous protein sequences, we plotted the ROC curves for each of the 5 validation folds.
\begin{figure}[!ht]
    \centering
    \includegraphics[width=1\linewidth]{cnn-gru-roc.png}
    \caption{ROC curve for CNN-GRU}
    \label{fig:enter-label}
\end{figure}


\newpage
\section{Comparison with other techniques}
\subsection{Comparison Between SVM and DeepRHD}
Support Vector Machines (SVM) have been widely used in protein remote homology detection due to their effectiveness in handling high-dimensional data and their solid theoretical foundation. SVMs rely on carefully engineered features extracted from protein sequences, such as physicochemical properties or position-specific scoring matrices (PSSMs). While SVMs can achieve good performance on moderate-sized datasets, their scalability is limited, and their ability to capture complex nonlinear sequence patterns depends heavily on the quality of the handcrafted features.

In contrast, DeepRHD leverages deep learning architectures, specifically a hybrid CNN-GRU model, to automatically learn hierarchical and temporal features directly from input matrices such as combined ACC-PDT matrices derived from PSSMs. This end-to-end feature learning enables DeepRHD to capture intricate sequence relationships and evolutionary patterns that traditional SVMs may miss. Moreover, DeepRHD exhibits greater scalability and adaptability, making it more suitable for processing large-scale protein datasets.

Practically, SVM-based methods often require extensive feature engineering and parameter tuning, which can be time-consuming. DeepRHD benefits from parallel processing capabilities of modern GPUs, reducing training time from weeks or months to days, and generally achieves higher accuracy in remote homology detection tasks.

Therefore, while SVM remains a useful baseline approach, DeepRHD represents a significant advancement in sensitivity, automation, and efficiency for large-scale protein sequence analysis.
\begin{table}[ht]
\centering
\begin{tabular}{lcccc}
\hline
\textbf{Class} & \textbf{Precision} & \textbf{Recall} & \textbf{F1-score} & \textbf{Support} \\
\hline
a.1.1   & 0.58 & 0.52 & 0.55 & 391 \\
a.138.1 & 0.77 & 0.73 & 0.75 & 548 \\
a.22.1  & 0.73 & 0.75 & 0.74 & 320 \\
a.25.1  & 0.60 & 0.63 & 0.62 & 527 \\
a.3.1   & 0.84 & 0.83 & 0.83 & 589 \\
a.39.1  & 0.86 & 0.80 & 0.83 & 948 \\
a.4.1   & 0.88 & 0.85 & 0.87 & 1478 \\
b.1.1   & 0.91 & 0.88 & 0.90 & 1242 \\
b.1.18  & 0.48 & 0.52 & 0.50 & 589 \\
b.121.4 & 0.76 & 0.77 & 0.77 & 846 \\
b.29.1  & 0.74 & 0.73 & 0.74 & 714 \\
b.40.4  & 0.67 & 0.69 & 0.68 & 1150 \\
b.47.1  & 0.87 & 0.89 & 0.88 & 937 \\
b.50.1  & 0.63 & 0.69 & 0.66 & 400 \\
b.55.1  & 0.72 & 0.73 & 0.73 & 743 \\
b.6.1   & 0.80 & 0.79 & 0.80 & 515 \\
b.82.1  & 0.83 & 0.78 & 0.81 & 791 \\
c.1.10  & 0.35 & 0.38 & 0.36 & 302 \\
c.1.2   & 0.61 & 0.58 & 0.60 & 561 \\
c.1.8   & 0.80 & 0.77 & 0.79 & 1242 \\
c.2.1   & 0.63 & 0.61 & 0.62 & 1600 \\
\hline
\textbf{Accuracy}    &       &       & 0.74 & 33040 \\
\textbf{Macro avg}   & 0.72  & 0.72  & 0.72 & 33040 \\
\textbf{Weighted avg}& 0.74  & 0.74  & 0.74 & 33040 \\
\hline
\end{tabular}
\caption{SVM classification Report}
\end{table}

\subsection{Comparison with X-ray crystallography}
X-ray crystallography remains the gold standard for obtaining high-resolution protein structures, providing detailed insights into atomic arrangements. However, it is limited by the need for crystallization and may not capture dynamic aspects of proteins.

DeepRHD offers a complementary approach, enabling rapid structure prediction from sequences, which is particularly valuable for proteins that are challenging to study experimentally. While it may not yet match the atomic precision of X-ray crystallography, ongoing advancements in AI are continually improving its accuracy and reliability.

\textbf{In our case, if we had relied on X-ray crystallography to process approximately 170,000 protein sequences, it would have taken several years due to the experimental nature of the method, which involves time-consuming steps such as protein expression, purification, crystallization, and diffraction data analysis. In contrast, using DeepRHD, an AI-based computational model, the same number of sequences can be processed in just a few days, assuming sufficient parallel processing resources (e.g., multiple GPUs). This highlights the efficiency and scalability of deep learning-based approaches for large-scale protein structure prediction.}
\begin{figure}[!ht]
    \centering
    \includegraphics[width=0.75\linewidth]{ray-crystallography-diffraction-pattern-and-protein-structure-Between-the-atomic (1).png}
    \caption{Process involved in X-ray crystallography}
    \label{fig:enter-label}
\end{figure}

\section{Future Directions in Protein Remote Homology Detection (PRHD)}

\subsection{Advanced Feature Engineering and Reduction}
Future research in PRHD will focus on developing new feature extraction and dimensionality reduction techniques. These innovations aim to further enhance computational efficiency and predictive accuracy, allowing models like DeepRHD to process even larger and more complex protein datasets with reduced computational resources.

\subsection{Integration of Multi-Modal and Structural Data}
Combining sequence-based features with structural, functional, and multi-omics data (such as transcriptomics and metabolomics) will provide a more comprehensive understanding of protein relationships. This integration can significantly improve the detection of remote homologs that share structural or functional similarities despite low sequence identity.

\subsection{Scalability and Real-Time Analysis}
As biological data continues to grow exponentially, future PRHD systems and generative models must support automated, high-throughput, and real-time analysis pipelines. This will require further optimization of deep learning architectures and the adoption of scalable, cloud-based solutions for handling massive datasets efficiently.

\subsection{Protein and Molecule Design with Generative AI}
Generative AI will be increasingly used to design novel proteins, enzymes, and small molecules with tailored properties for therapeutic, industrial, or environmental applications. This capability will accelerate synthetic biology, drug discovery, and the engineering of new biological functions.

\subsection{Synthetic Data Generation and Data Augmentation}
Generative models will create realistic synthetic genomic and proteomic datasets, addressing data scarcity in rare diseases and underrepresented populations. These synthetic datasets will be essential for training robust AI models, hypothesis testing, and benchmarking, all while preserving data privacy.

\subsection{Personalized Medicine and Virtual Clinical Trials}
Generative AI will enable the simulation of individual genetic and molecular profiles, supporting the development of highly personalized treatments and the design of virtual clinical trials. This will optimize therapeutic strategies, predict disease risks, and reduce the time and cost associated with traditional drug development and clinical research.
\section{Conclusion}
In this study, a novel deep learning framework, DeepRHD, leveraging a hybrid CNN-GRU architecture, has been introduced for the challenging task of protein remote homology detection. By transforming the homology prediction into a multi-class classification problem, the model effectively captures both the physico-chemical characteristics and evolutionary patterns of protein sequences. The incorporation of feature matrices such as PDT, PSSM, and ACC ensures that the model learns both sequence-specific and conservation-based signals crucial for distinguishing remotely related protein families.

Experimental evaluation on the standard SCOP 2.07 benchmark dataset demonstrates that DeepRHD consistently outperforms conventional machine learning models and recent deep learning approaches. The superior accuracy, precision, and generalization capability of DeepRHD underline the effectiveness of combining domain-specific biological knowledge with advanced deep neural architectures.

This work underscores the potential of integrated feature representation and deep sequence modeling in addressing complex bioinformatics tasks. The encouraging results suggest that DeepRHD is a promising step toward more accurate and robust remote homology detection.

Looking ahead, future research directions include the development of more efficient feature extraction and dimensionality reduction techniques to streamline the input representation while retaining crucial information. This would further optimize computational efficiency and model performance, enabling broader applications of DeepRHD across diverse protein classification tasks and larger datasets.

























\newpage
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