A hybrid quantum-classical fusion neural network to improve
  protein-ligand binding affinity predictions for drug discovery
The field of drug discovery hinges on the accurate prediction of binding
affinity between prospective drug molecules and target proteins, especially
when such proteins directly influence disease progression. However, estimating
binding affinity demands significant financial and computational resources.
While state-of-the-art methodologies employ classical machine learning (ML)
techniques, emerging hybrid quantum machine learning (QML) models have shown
promise for enhanced performance, owing to their inherent parallelism and
capacity to manage exponential increases in data dimensionality. Despite these
advances, existing models encounter issues related to convergence stability and
prediction accuracy. This paper introduces a novel hybrid quantum-classical
deep learning model tailored for binding affinity prediction in drug discovery.
Specifically, the proposed model synergistically integrates 3D and spatial
graph convolutional neural networks within an optimized quantum architecture.
Simulation results demonstrate a 6% improvement in prediction accuracy relative
to existing classical models, as well as a significantly more stable
convergence performance compared to previous classical approaches.
L. Domingo, M. Chehimi, S. Banerjee, S. He Yuxun, S. Konakanchi, L. Ogunfowora, S. Roy, S. Selvaras, M. Djukic, C. Johnson
A Hybrid Quantum-Classical Fusion Neural Network to Improve Protein-Ligand Binding Affinity Predictions for Drug Discovery

###### Abstract

The field of drug discovery hinges on the accurate prediction of binding affinity between prospective drug molecules and target proteins, especially when such proteins directly influence disease progression. However, estimating binding affinity demands significant financial and computational resources. While state-of-the-art methodologies employ classical machine learning (ML) techniques, emerging hybrid quantum machine learning (QML) models have shown promise for enhanced performance, owing to their inherent parallelism and capacity to manage exponential increases in data dimensionality. Despite these advances, existing models encounter issues related to convergence stability and prediction accuracy. This paper introduces a novel hybrid quantum-classical deep learning model tailored for binding affinity prediction in drug discovery. Specifically, the proposed model synergistically integrates 3D and spatial graph convolutional neural networks within an optimized quantum architecture. Simulation results demonstrate a 6% improvement in prediction accuracy relative to existing classical models, as well as a significantly more stable convergence performance compared to previous classical approaches.

S. Banerjee\({}^{1}\), S. He Yuxun\({}^{1}\), S. Konakanchi\({}^{1}\), L. Ogunfowora\({}^{1}\), S. Roy\({}^{1}\), S. Selvaras\({}^{1}\),

L. Domingo\({}^{2*}\), M. Chehimi\({}^{2}\), M. Djukic\({}^{2}\) and C. Johnson\({}^{2*}\)+\({}^{1}\) Purdue University, The Data Mine, USA,

\({}^{2}\) Ingenii Inc., New York, USA,

\({}^{*}\)Corresponding Authors' Emails: {laia,christine}@ingenii.dev

Quantum machine learning (QML), drug discovery, binding affinity, quantum fusion model.

## 1 Introduction

The healthcare landscape has undergone a transformative shift, notably marked by advancements in drug discovery through the integration of emerging technologies. Through complex molecular interactions and precise computational modeling of compound interactions, novel drugs are rigorously designed and identified. Central to this design process is the understanding of proteins and their role in disease mechanisms [1].

In the field of drug discovery, it is imperative to identify proteins that are instrumental in the cascade of molecular interactions leading to a specific disease [2]. Upon the identification of such a target protein, a list of prospective drug candidates is generated. These candidates, often described as small molecules or compounds termed _ligands_, have the potential to modulate the target protein's activity through binding interactions [3]. Ideal ligands are chosen based on their high binding affinity to the target protein, coupled with minimal off-target interactions with other proteins. However, quantifying such binding affinities is a resource-intensive endeavor [4], both in terms of time and financial investment. This is particularly true considering that the initial screening process often encompasses thousands of compounds [4, 5].

The transition from conventional laboratory methods to computer-aided design (CAD) has markedly improved the efficiency and accuracy of drug discovery and binding affinity prediction. This advancement has been further bolstered by the incorporation of artificial intelligence (AI) and machine learning (ML) algorithms, which facilitate exhaustive analyses of large-scale datasets, uncovering previously undetected patterns related to the atomic features of protein-ligand molecular complexes [6]. Furthermore, recent strides in quantum computing have added another layer of sophistication to drug discovery efforts, offering unprecedented parallelized computational capabilities [7]. Quantum machine learning (QML) models, in particular, are well-suited to manage the challenges of exponentially increasing data dimensionality, often outperforming traditional ML models under specific conditions. Taken together, these technological advancements make QML and hybrid quantum-classical models highly promising for navigating the complex, high-dimensional challenges intrinsic to drug discovery [8].

Related Works.Several prior works [9, 10, 11, 12, 13] addressed the problem of binding affinity prediction in drug discovery using tools from both classical ML and QML. For instance, the work in [9] leveraged 3D-convolutional neural networks (3D-CNNs) to perform protein-ligand binding affinity predictions in a faster and more efficient manner relative to other ML models. Moreover, the work in [10] enhanced the model proposed in [9] by predicting binding affinities using an ensemble of several independently-trained 3D-CNN network layers. Furthermore, the work in [11] introduces a classical fusion model combining a 3D-CNN and a spatial graph CNN (SG-CNN). The model in [11] enhances binding affinity prediction by concurrently processing grid-based, context-based, and graph-based protein features. However, the models proposed in [9, 10, 11] suffer from issues with convergence stability, and their predictive accuracy stands to gain from further optimization.
Additionally, the work in [12] uses quantum support vector machines for virtual drug screening. Although the hybrid QML model in [12] outperforms classical counterparts, its focus on a limited subset of protein-ligand features restricts model accuracy and scalability to larger datasets. Finally, the work in [13] proposes a hybrid QML architecture, modifying a classical CNN by replacing a classical convolutional layer with an optimized quantum circuit. While the work in [13] successfully tackles the computational complexity inherent in classical neural networks, it does not yield an improvement in binding affinity predictive accuracy, thus achieving a comparable performance to classical models. To the best of our knowledge, no existing research has effectively tackled the issue of binding affinity prediction in drug discovery by capitalizing on the benefits of QML while simultaneously achieving high accuracy and ensuring smooth, stable convergence.

Contributions.The main contribution of this paper is the development of a novel hybrid quantum fusion model aimed at enhancing the binding affinity predictions in drug discovery. The proposed model strategically integrates 3D-CNNs and SG-CNNs to leverage their respective strengths in processing diverse facets of the training data. The proposed quantum architecture is meticulously designed for optimal accuracy. Simulation results demonstrate the superior performance of the proposed hybrid quantum fusion model relative to state-of-the-art classical models. Particularly, the proposed model achieves a 6% improvement in the binding affinity prediction accuracy, and exhibits faster, smoother, and more stable convergence, thereby boosting its generalization capacity.

## 2 System Model

This section describes the proposed hybrid quantum fusion model, its components, the data used in training the model, and the necessary pre-processing steps.

### Proposed Hybrid QML Architecture

The proposed hybrid quantum fusion architecture builds upon the classical fusion model introduced in [11] while integrating quantum neural networks (QNNs) into the model design. In particular, the protein-ligand complex data (see Section 2.2) is initially fed into a 3D-CNN and an SG-CNN, simultaneously. Then, late-late fusion is performed by feeding the outputs from the second-to-last layer of each of the two respective CNNs into a quantum fusion model, which incorporates a QNN. Let us now briefly introduce the individual components of the proposed architecture, which is shown in Fig. 1.

#### 2.1.1 3d-Cnn

CNNs are deep learning models specifically designed for processing and analyzing high-dimensional arrays such as images, volumes, or series data. Because of their ability to automatically learn and extract features from input data, they are a cornerstone of modern computer vision applications. The adopted 3D-CNN model in this work is based on the ResNet architecture with two residual blocks [14]. After each layer, the output is passed through a batch normalization followed by a nonlinear ReLU activation function. The output from the convolutional layers is then pooled, flattened, and fed through a sequence of fully connected layers, producing the final output of the model. The exact architecture of the adopted 3D-CNN is shown in Fig. 1(a).

#### 2.1.2 Sg-Cnn

An SG-CNN capitalizes on the benefits of convolutional layers while leveraging the structural relationships within protein-ligand complexes. They effectively capture and preserve spatial information using a 2D graph representation, where each edge corresponds to a bond between atoms across all molecules. For each molecule within the complex, spatial

Figure 1: a) 3D-CNN architecture. b) SG-CNN architecture c) Proposed hybrid quantum fusion model. In the hybrid fusion model, outputs from the second-to-last layer of each of the 2 classical neural networks trained with the PDBbind dataset are encoded onto quantum states before being fed into a feed-forward quantum neural network (QNN).
information and associated features are initially processed through a graph gated recurrent unit (GGRU), incorporating information from its nearest neighbors. The resulting output vector subsequently enters another GGRU, accumulating information from the next nearest neighbors. This pivotal stage, known as the _graph gather step_, is followed by the data passing through a sequence of fully connected layers, ultimately yielding the final output of the SG-CNN. The exact architecture of the adopted SG-CNN is shown in Fig. 1(b).

#### 2.1.3 Quantum Fusion Model

The quantum fusion model takes the outputs from the second-to-last layer of the two aforementioned CNN models. In particular, this input is a vector of size 16, as it entails the output of 10 nodes from the 3D-CNN and 6 nodes for the SG-CNN (see Fig. 1 c)). By optimally fusing these two pre-final layers, this strategy effectively aggregates the acquired knowledge during the training of the CNNs, thereby achieving superior performance. Unlike the classical fusion model in [11], which is simply a one-layer feed-forward neural network, the quantum fusion model incorporates a QNN that consists of a quantum circuit divided into two blocks. The first block is the _quantum encoding_ part, which maps the input data into a quantum circuit, and the second block is a _parameterized quantum circuit (PQC)_, where quantum operations are applied to retrieve information from the encoded data. In the quantum fusion model, the considered outputs of the 3D-CNN and SG-CNN models are first encoded into quantum states through quantum embedding circuits, then run through the trainable QNN.

Quantum Encoding Techniques.A variety of quantum data encoding techniques have been recently developed in the literature [15]. In this work, we focus on two of the most effective encoding techniques, analyzing and comparing their performance in the context of binding affinity prediction. The two considered methods are:

1. **Amplitude encoding.** where the features are encoded in the amplitudes of the quantum state in the computational basis [16]. This scheme requires only \(\lceil\log_{2}(n)\rceil\) qubits to encode a data sample into a quantum state, where \(n\) represents the input dimension of the QNN. The depth of the embedding circuit grows as \(O(poly(n))\) while the number of parameters subject to optimization scales as \(O(log_{2}(n))\).
2. **Hybrid Angle Encoding (HAE)**, where amplitude encoding is implemented using parallel blocks of independent qubits [15]. The features are divided into \(b\) blocks of size \(2^{m}-1\), where \(m\) represents is the number of qubits. Accordingly, \(b\times m\) qubits are required to encode the whole data sample into a quantum state.

PQC ArchitectureAfter encoding the data into quantum states (or qubits), they pass through a PQC. The architecture of the PQC is designed to generate a substantial level of entanglement and expressibility, by creating cross connections between the qubits. The PQC consists of several quantum gates which are controlled by classically-optimized parameters. Several potential PQC architectures were analyzed, and the resulting optimal architecture is composed of 3D generalized rotation gates with all-to-all CNOT connections, catalogued as _strongly entangling layers_.

### Dataset

The PDBbind dataset [17] (2020 version) is adopted as the input to train the proposed quantum fusion model. PDBbind represents an extensive compilation of experimentally determined binding affinity data between proteins and ligands. This dataset meticulously associates protein-ligand complexes with their respective affinity measurements, a curation process executed via manual extraction from peer-reviewed scientific publications. The current latest PDBbind version, released in early 2020, contains a total of 19,443 protein-ligand complexes. Additionally, a meticulously curated subset of 5,316 samples has been compiled, specifically comprising high-quality complexes. Finally, an even higher-quality core set of 285 samples is derived, primarily for validating binding affinity prediction methods. We utilize the refined set in the training and validation phases of our analysis, with 25% of the data reserved for validation. Then, the core set is used for the testing phase.

### Data Pre-processing

Before passing the PDBbind data into the two CNN architectures, it is essential to pre-process the raw data and extract pertinent input features from the 3D structures of proteins and ligands. In this regard, our approach closely aligns with established featurization techniques as outlined in [18, 11, 13], thereby facilitating the comparability of our results with existing state-of-the-art models. Moreover, the PDB files are converted to Mol2 files using the UCSF Chimera software [19].

The input data for 3D-CNN consists of spatial representation of 3D structures of atoms of protein-ligand pairs. The atoms are voxelized into a grid of size \(N\times N\times N\) with a voxel size of \(1\) A, and the number of voxels set to \(N=48\) to strike a balance between covering the entire pocket regions and lowering the input data size for the CNN model. \(C=19\) features are extracted for each voxelized atom using OpenBabel [20], bringing the input data for 3D-CNN to a \(C\times N\times N\times N\) matrix. Such features include the atom type, hybridization, number of heavy atom bonds, number of bonds with heteroatoms, structural properties, partial charge, and molecule type (protein vs ligand).

On the other hand, the input data for SG-CNN consists of a spatial graph representation of the protein-ligand complexes, with the atoms forming the nodes, and the bonds between atoms forming the edges, of the graph. As in Ref. [11], covalent bonds are represented by an \(N\times N\) adjacency matrix and non-covalent bonds by an \(N\times M\) matrix, where the element
\(A_{ij}\) of each matrix represents the Euclidean distance between the atoms \(i\) and \(j\).

## 3 Experiments and Results

In this section, the conducted experiments and simulations are presented, and the obtained results are analyzed. To validate the performance of our proposed hybrid quantum fusion model, we benchmark against the classical fusion counterpart model. The binding affinity prediction performance of both fusion models is evaluated using five different metrics: root mean square error (RMSE), mean absolute error (MAE), \(R^{2}\), Pearson coefficient, and Spearman coefficient. Recall that the RMSE and MAE should be minimized to obtain optimal performance, while \(R^{2}\), Pearson and Spearman coefficients should be maximized.

### Experimental Setup

Following a comparative evaluation of various optimizers and hyperparameters, the training of both fusion models was conducted using the ADAM optimizer with a learning rate of \(\eta=0.002\), a batch size of 50 samples, and a mean squared error loss function. Moreover, in the QNN, \(\sigma_{z}\) Pauli operator projection measurements were performed on all qubits to extract the classical measurement outcomes. The final prediction is made with a classical linear layer with a ReLu activation function. Finally, the PQC has a depth of 10 layers.

### Binding affinity prediction performance

First, we compare the performance of the proposed quantum fusion model and its classical counterpart for the five considered metrics, which is summarized in Table 1. From Table 1, we notice that the quantum fusion model provides better performance for all five metrics, which represents an up to 6% improvement over the classical model.

### Convergence of the fusion model

Next, in Fig. 2, we compare the convergence of the loss function in the validation set for the quantum and classical fusion models. We notice from Fig. 2 that the convergence of the loss function for the quantum model is much smoother and stable than that of the classical model. Therefore, the quantum fusion model provides much more reliable predictions, which are less likely to produce overfitting in the training set.

### Impact of quantum encoding

Finally, we compare the performance of the proposed quantum fusion model with amplitude encoding and HAE techniques, as shown in Fig. 3. For HAE, we used \(b=2\) and \(m=4\), corresponding to encoding 30 data points. The 16 features of the QNN input vector were padded with zeros to create a 30-dimensional vector. From Fig. 3, it is clear that the amplitude encoding outperforms the HAE technique.

## 4 Conclusion

In this paper, we have proposed a novel hybrid QML model, offering accurate and reliable binding affinity predictions, which is a critical factor in drug discovery. The proposed model is a quantum fusion model that integrates 3D-CNN and SG-CNN classical models with QNNs. Simulation results validate the superiority of the quantum model relative to the classical fusion counterpart model, demonstrating a 6% accuracy enhancement while achieving faster and smoother convergence, thus mitigating the risk of overfitting.

## 5 Acknowledgment

This research was supported by Ingenii Inc, USA. Authors would also like to thank the Data Mine project at Purdue University, specifically Dr. Mark Daniel Ward.

\begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \hline Method & \(R^{2}\) & MAE & Pearson & Spearman & RMSE \\ \hline \hline Class. Fsn & 0.60 & 1.05 & 0.777 & 0.766 & 1.37 \\ \hline Q’tum Fsn & 0.63 & 1.04 & 0.809 & 0.815 & 1.29 \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of classical and quantum fusion model for the five error metrics.

Figure 3: Comparison of test statistics resulting from two data encoding schemes (amplitude vs. hybrid angle) and strongly entangling layers in the quantum circuits.

Figure 2: Comparison of the convergence of the loss function for the classical and quantum fusion models.