Biomarker Discovery with Quantum Neural Networks: A Case-study in
  CTLA4-Activation Pathways
Biomarker discovery is a challenging task due to the massive search space.
Quantum computing and quantum Artificial Intelligence (quantum AI) can be used
to address the computational problem of biomarker discovery tasks. We propose a
Quantum Neural Networks (QNNs) architecture to discover biomarkers for input
activation pathways. The Maximum Relevance, Minimum Redundancy (mRMR) criteria
is used to score biomarker candidate sets. Our proposed model is economical
since the neural solution can be delivered on constrained hardware. We
demonstrate the proof of concept on four activation pathways associated with
CTLA4, including (1) CTLA4-activation stand-alone, (2) CTLA4-CD8A-CD8B
co-activation, (3) CTLA4-CD2 co-activation, and (4)
CTLA4-CD2-CD48-CD53-CD58-CD84 co-activation. The model indicates new biomarkers
associated with the mutational activation of CLTA4-associated pathways,
including 20 genes: CLIC4, CPE, ETS2, FAM107A, GPR116, HYOU1, LCN2, MACF1,
MT1G, NAPA, NDUFS5, PAK1, PFN1, PGAP3, PPM1G, PSMD8, RNF213, SLC25A3, UBA1, and
WLS. We open source the implementation at:
https://github.com/namnguyen0510/Biomarker-Discovery-with-Quantum-Neural-Networks.
Nam Nguyen
# Biomarker Discovery with Quantum Neural Networks: A Case-study in _Ctla4_-Activation Pathways

###### Abstract

**Background:** Biomarker discovery is a challenging task due to the massive search space. Quantum computing and quantum Artificial Intelligence (quantum AI) can be used to address the computational problem of biomarker discovery tasks.

**Method:** We propose a Quantum Neural Networks (QNNs) architecture to discover biomarkers for input activation pathways. The Maximum Relevance -- Minimum Redundancy (mRMR) criteria is used to score biomarker candidate sets. Our proposed model is economical since the neural solution can be delivered on constrained hardware.

**Results:** We demonstrate the proof of concept on four activation pathways associated with _CTLA4_, including (1) _CTLA4_-activation stand-alone, (2) _CTLA4-CD8A-CD8B_ co-activation, (3) _CTLA4-CD2_ co-activation, and (4) _CTLA4-CD2-CD48-CD53-CD58-CD84_ co-activation.

**Conclusion:** The model indicates new biomarkers associated with the mutational activation of _CLTA4_-associated pathways, including 20 genes: _CLJC4_, _CPE_, _ETS2_, _FAM107A_, _GPR116_, _HYOU1_, _LCN2_, _MACF1_, _MT1G_, _NAPA_, _NDUFSS_, _PAK1_, _PFN1_, _PGAP3_, _PPM1G_, _PSMD8_, _RNF213_, _SLC25A3_, _UBA1_, and _WLS_. We open source the implementation at: [https://github.com/namnguyen0510/Biomarker-Discovery-with-Quantum-Neural-Networks](https://github.com/namnguyen0510/Biomarker-Discovery-with-Quantum-Neural-Networks).

## 1 Introduction

A biomarker, a molecular marker or signature molecule, refers to a biological substance or characteristic found in body fluids, tissues, or blood that indicates the presence of a condition, disease, or abnormal process. Biomarkers can be measured to assess how well the body responds to treatment for a particular disease or condition [1]. Biomarkers play a crucial role in drug discovery and development by providing essential information on the safety and effectiveness of drugs. These measurable indicators can be categorized into diagnostic, prognostic, or predictive biomarkers, and they are utilized to choose patients for clinical trials or track patient response and treatment efficacy. Despite its valuable role, biomarker discovery is a challenging task for classical-computational platforms due to the massive search space (**Section**2.1).

Quantum computing is an emerging technology that utilizes the principles of quantum mechanics to solve problems beyond classical computers' capabilities. Quantum Machine Learning and Quantum Neural Networks are an advanced class of machine intelligence on quantum hardware, which promises more powerful models for myriad learning tasks (**Section**2.2).

This work uses a class of Quantum Artificial Intelligence (AI) models to discover biomarkers in biomedical research. We adopt the neural architecture proposed in a contemporary work that addresses the body dynamics modeling problem. Here, we make a non-trivial adaptation of the proposed game-theoric to tackle a different class of problems. The main contribution of this study is summarized as follows:
1. The proposed quantum AI model is a general, cost-efficient, and cost-effective algorithm for biomarker discovery, despite the extensive problem complexity.
2. The model outcomes suggest novel biomarkers for the mutational activation of the notable target in immunotherapy - _CLTA4_, including \(20\) genes: _CLIC4_, _CPE_, _ETS2_, _FAM107A_, _GPR116_, _HYOU1_, _LCN2_, _MACF1_, _MT1G_, _NAPA_, _NDUFS5_, _PAK1_, _PFN1_, _PGAP3_, _PPM1G_, _PSMD8_, _RNF213_, _SLC25A3_, _UBA1_ and _WLS_.

## 2 Preliminary

### Problem Statement

The learning task involves identifying the best combinations of biomarkers from a given set of genes (represented as \(\mathcal{G}\)) to select those that are (1) most relevant to a specific pathway (represented as \(\mathbf{Y}\)) and (2) optimal for machine learning algorithms. This criterion is commonly referred to as minimizing redundancy and maximizing relevancy for selected feature sets, as proposed in [43] (See **Appendix** A).

In this context, it is worth noting that each individual has unique patterns of mutational alterations that lead to distinct sets of biomarkers. Considering all the possibilities, the number of candidate biomarker sets is the sum of all possible combinations, which can be expressed as

\[\sum_{i=0}^{N}\binom{N}{k}=2^{N} \tag{1}\]

Since the human genome contains around 20,000 to 25,000 genes, this results in a massive search space of \(3.2019\times 10^{6577}\) candidate biomarker set for any biomarker identification algorithm. This search space grows exponentially with the number of input genes, making it an incredibly challenging problem for conventional computing methods.

### Quantum Neural Networks

QNNs represent input data using wavefunction representations, typically using qubits or "qurons" [51], in the form of:

\[\ket{\psi}=\alpha\ket{0}+\beta\ket{1},\alpha\text{ and }\beta\in\mathbb{C}. \tag{2}\]

This distinguishes QNNs from classical ANNs as they capture physical events discretely [33] and offer insight into representation learning [6].

QNNs have been proposed to offer two advantages over classical ANNs [52]. Firstly, quantum feature maps can represent exponentially larger data sets than classical neural networks, with an \(n\)-qubit system representing \(2^{n}\) bits [40]. Secondly, quantum feature maps inherit wavefunction uncertainty from quantum mechanics, allowing measurements of quantum states to return values of \(0\) or \(1\) with probability values of \(\mathbb{P}(0)=|\alpha|^{2}\) and \(\mathbb{P}(1)=|\beta|^{2}\). In our previous papers, we discuss the role of epistemic uncertainty estimation from quantum maps [38] and the effect of entanglement layouts on the classifier's performance.

The typical design for QNNs [5, 19, 27, 47, 53] involves a stack of identical ansatz structures, given by a global unitary transformation:

\[U_{\mathbf{\theta}}(\mathbf{x})=\mathcal{U}^{(l)}(\mathbf{\theta}l)\mathcal{V}(\mathbf{x}) \ldots\mathcal{V}(\mathbf{x})\mathcal{U}^{(0)}(\mathbf{\theta}0), \tag{3}\]

where \(\mathbf{x}\) represents input features, \(\mathbf{\theta}\) represents model weights, \(\mathcal{U}^{(l)}(.)\) represents identical-parameterized circuits serving as variational (trainable neural) blocks, and \(\mathcal{V}(.)\) represents feature-embedding blocks. From our perspective, QNNs are advanced mathematical models in the language of representation theory (See **Appendix** B); thus, we are using mathematics to enable cancer discoveries.

## 3 Method

### Model Architecture

We depict the ansatz structure of our QNN model in **Figure**1. Each neural block in our proposed model includes (1) a parameterized RZ-rotation based on time-domain variables \(t\in[0,2\pi]\), given by

\[\mathbf{R}_{Z}(t)=\begin{bmatrix}e^{-i\frac{t}{2}}&0\\ 0&e^{i\frac{t}{2}}\end{bmatrix} \tag{4}\]
and (2) trainable RX-rotation and RY-rotation gates

\[\mathbf{R}_{X}(\alpha)=\begin{bmatrix}\cos(\frac{\alpha}{2})&-i\sin(\frac{\alpha}{2}) \\ -i\sin(\frac{\alpha}{2})&\cos(\frac{\alpha}{2})\end{bmatrix} \tag{5}\]

and

\[\mathbf{R}_{Y}(\beta)=\begin{bmatrix}\cos(\frac{\beta}{2})&-\sin(\frac{\beta}{2}) \\ \sin(\frac{\beta}{2})&\cos(\frac{\beta}{2})\end{bmatrix} \tag{6}\]

The parameterized wavefunction of the 1-layer model is given

\[\ket{\psi_{\Theta}}=\ket{\psi_{(\mathbf{\alpha},\mathbf{\beta})}(\mathbf{t})}=\text{CNOT}( \Lambda)\mathbf{R}_{X}(\mathbf{\alpha})\mathbf{R}_{Y}(\mathbf{\beta})\mathbf{R}_{Z}(\mathbf{t})H\ket{ 0}^{\otimes n}, \tag{7}\]

\(n\) is the number of qubits, and \(\Lambda\) is the architecture parameter of the entanglement layout constructed by CNOT gates, illustrated in **Figure**1.

### Algorithm

#### 3.2.1 Computations of Gene Scores (GSCORE\({}^{\Theta}\))

We train the proposed QNNs to learn the optimal sampling distribution based on mRMR criteria (See **Appendix** A). In other words, the search algorithm will assign higher probabilities for the more important markers. Thus, the search algorithm will more often select more important biomarkers. Specifically, the output electronic wavefunction of parameterized QML model is given by

\[\ket{\psi_{\Theta}}=\mathcal{U}_{n}(\Theta), \tag{8}\]

with \(n\) is the number of prepared qubits and \(\Theta\) is the model parameter. The sampled probability density is given by

\[p(\Theta)=\ket{\Psi(\Theta)}^{2}=\Psi^{*}\Psi \tag{9}\]

where \(\ket{\Psi^{*}}\) is the conjugate-transpose of the output wavefunction. In other words, we compute the probability amplitude; or the square modulus of the wavefunction.

We further use the Softmax function with tunable temperature to normalize our density. Besides, using the Softmax function also allows us to control the conservative of the search engine as the low temperature will encourage the model confidence. In contrast, high temperatures encourage less conservative predictions. Thus, the biomarker score is the sampling probability of each gene given by

\[\text{GSCORE}^{\Theta}=\hat{p}(\Theta)=\text{SoftMax}\bigg{(}\frac{\sqrt{p( \Theta)}}{\text{temp}}\bigg{)}, \tag{10}\]

where temp is the function temperature. Finally, we select the candidate marker set by parameterized thresholding with \(\bar{p}=1\) if \(\hat{p}\geq\tau\), otherwise \(0\). We interpret the GSCORE\({}^{\Theta}\) that the more important genes have a higher chance to be selected by the sampler, resulting in a higher probability over the output of quantum ansatzes.

#### 3.2.2 Objective Function

We adopt the efficient loss function of the Quadratic Programming Feature Selection (QPFS) method [46], given as

\[\min_{\mathbf{\Theta}}\bigg{(}\lambda\mathbf{p}^{\intercal}\mathbf{H}\mathbf{p}-\mathbf{p}\mathbf{F} \bigg{)},\sum_{i=1}^{n}p_{i}=1,p_{i}>0, \tag{11}\]

where \(\mathbf{F}_{n\times 1}\) is the relevancy to target variables and \(\mathbf{H}_{n\times n}\) is the pairwise redundancy computed from the feature set. Both natural and normalized quantum distributions \(p(\Theta)\) and \(\hat{p}(\Theta)\) satisfy the conditions for \(p_{i}\) in QPFS. For further analysis, we consider \(\lambda=1\), i.e., the balanced loss between redundant-relevant criteria.

Figure 1: **The Ansatz Circuit of Our Proposed QNN Models using Four Qubits with Four Neural Blocks**. We use \(11\)-quit ansatz in the final setting to score \(2^{11}=2,048\) genes.
#### 3.2.3 Pseudo-code

We implement the proposed model using the quantum simulation package Pennylane [7] with Pytorch 3.7 [41]. The mutual information criteria are computed by Scikit-learn [42], and model optimization is conducted by Optuna [2] with Tree Parzen Estimators [8]. The pseudo-code is given in the following algorithm:

```
1importpenmylaneasqml
2importtorch
3importnumpyasnp
4q=11#NumberofQubits
5dev=qml.device("default.qubit",wires=q)
6device=torch.device("cuda:0"
7iftorch.cuda.is_available()else"CPU")
8qml.qnode(dev,interface=torch")
9defquantum_sampler(a,b,n):
10t=torch.tensor(np.linspace(0,np.pi,n))
11foriinrange(q):
12qml.Hadamard(wires=i)
13fork,dtinenumerate(t):
14foriinrange(q):
15qml.RZ(dt,wires=i)
16qml.RY(a,k,i),wires=i)
17qml.RX([k,i],wires=i)
18foriinrange(0,q-1,2):
19qml.CNOT(wires=[i,i+1])
20foriinrange(1,q-1,2):
21qml.CNOT(wires=[i,i+1])
22qml.CNOT(wires=[q-1,0])
23returnqml.state()
```

Listing 1: Model Architecture

#### 3.2.4 Hyper-parameter and Training Protocol

We report the hyper-parameters for our search engine powered by proposed QNNs in **Table**1. Noteworthy, we adopt the Tree Parzen Estimator with Sequential Model-based Optimization [8] (SMBO) to train our model. We learned from our previous works - CSNAS [37] and BayesianQNN [38] that the used optimization is a cost-efficient algorithm, which enables effective search on a massive search space.

## 4 Results

### Case-study

#### 4.1.1 _Ctla4_-activation Pathways

_CTL4_ - The gene is part of the immunoglobulin superfamily and produces a protein that transmits a signal to inhibit T cells. Mutations in this gene have been linked to various autoimmune diseases, including insulin-dependent diabetes mellitus, Graves disease, Hashimoto thyroiditis, celiac disease, systemic lupus erythematosus, and thyroid-associated orbitopathy [20].

In this study, we investigate four pathways regarding the co-occurrence of mutational activation, including:

\begin{table}
\begin{tabular}{|c|c|c|} \hline
**Parameters** & **Range** & **Role** \\ \hline Number of Qubits & \(11\) & Sampler for \(2^{11}=2048\) genes \\ \(\mathbf{\alpha}\) & \(-2\pi,2\pi\) & \(\mathbf{R}_{X}\) rotation \\ \(\mathbf{\beta}\) & \(-2\pi,2\pi\) & \(\mathbf{R}_{Y}\) rotation \\ \(\epsilon\) & \([\pi 96,\pi/24]\) & Standard Deviation of Model Weight \\ \(\tau\) & \([0.5,0.7]\) & Threshold Value \\ temp & \([1/10^{3},2\times 10^{3}]\) & SoftMax Temperature \\ \hline \end{tabular}
\end{table}
Table 1: **Hyper-parameter of Our Model Optimization.**
1. **Pathway 1**: _CTLA4_-activation stand-alone.
2. **Pathway 2**: _CTLA4-CD8A-CD8B_ activated simultaneously.
3. **Pathway 3**: _CTLA4-CD2_ activated simultaneously.
4. **Pathway 4**: _CTLA4-CD2-CD48-CD53-CD58-CD84_ activated simultaneously.

Of note, advanced ML or Quantum AI has yet to study these mutational activation pathways to extend our knowledge. We summarize the biological meaning of quantified targets in **Appendix** C.

#### 4.1.2 Datasets

We use The Cancer Genome Atlas (TCGA [58]) with RNA expression data and Copy Number of Variation (CNV). We score \(2,048\) biomarkers based on its expression, which is equivalent to \(2^{11}\) dimensional embedding generated by \(11\)-qubit system (**Section**3.2.3). The evaluated cohort includes \(9,136\) patients, considered a Big Data in the context of a cancer genetic study. The expression set \(\mathbf{X}\) is normalized using Min-Max normalization, and the mutational signals are created from CNV with \(\mathbf{Y}=1\) if CNV \(\neq 0\), otherwise \(\mathbf{Y}=0\). The evaluated expressions are continuous values, while the activation signals are binary.

#### 4.1.3 Experimental Settings

All experiments were carried out using Python \(3.7.0\), numpy \(1.21.5\), sci-kit-learn \(1.0.2\), and PyTorch \(1.11\) on an Intel i9 processor (2.3 GHz, eight cores), 16GB DDR4 memory and GeForce GTX \(1060\) Mobile GPU with 6GB memory. Besides, we made our implementation available at: [https://github.com/namnguyen0510/Biomarker-Discovery-with-Quantum-Neural-Networks](https://github.com/namnguyen0510/Biomarker-Discovery-with-Quantum-Neural-Networks); and all experimental history available at [https://tinyurl.com/55x77w4h](https://tinyurl.com/55x77w4h). We train our sampler for \(600\) trials with paralleled computing using ten CPU workers for each pathway.

### Quantum AI-driven Biomarkers for _Ctla4_-activation Pathways

We summarize the case-study of _CTLA4_-activation pathways in **Figure**2(A). The full reports for each pathway is given in **SuppFig**1, 2, 3 and 4 in **Appendix** D. We only consider the top 20 biomarkers for further analysis. Of note, the

Figure 2: **(A) Activation Pathways Analyzed in Our Case-study. (B) Venn Diagram of Discovered Biomarker Sets regarding The Quantified Targeted Pathways. _MACF1_ is addressed as a common biomarker for _CTLA4_ and _CTLA4_-_CD8A_-_CD8B_; while _HSPA1B_ is the common biomarker for _CTLA4_-_CD8A_-_CD8B_ and _CTLA4_-_CD2_.
discovered biomarker sets are distinctive for each studied pathway. Specifically, only one biomarker _MACF1_ is founded as the driver for _CTLA4_ and _CTLA4-CD8A-CD8B_ activation pathways (**Figure**2(B)). Similarly, _HSPA1B_ is addressed as a common biomarker for the pathways _CTLA4-CD8A-CD8B_ and _CTLA4-CD2_. Apart from _MACF1_ and _HSPA1B_, the remaining drivers are distinctively associated with the quantified targets.

### Convergence Analysis

We construct an end-to-end explainable quantum AI, illustrated in the results in **SuppFig**1, 2, 3 and 4. Of note, we are addressing a complex problem beyond the capacity of classical computers; thus, our proposed algorithm will likely suggest a sub-optimal solution. We show in these results of **SuppFig**1, 2, 3 and 4 that the proposed algorithm can effectively score genes and sampling biomarker sets as the sampling loss is reducing. Of note, training beyond \(600\) trials does not guarantee better solutions as most of the best loss is found by trial \(400^{th}\). We average top-\(50\%\) models to have a more robust inference of GSCORE\({}^{\Box}\), which shows that higher GSCORE\({}^{\Box}\) tends to have higher score variation since the markers are more frequently sampled by the quantum model. However, the score variation is extremely small with under \(200\mu=2\times 10^{-6}\), indicating the well-convergence of neural solutions.

Furthermore, the output panels in **SuppFig**1, 2, 3 and 4 also report the landscape of hyper-optimization protocol, in which model configuration with the lower score is in a darker color (purple) and model configuration with a higher score is in brighter color (yellow). This analysis significantly reduces the cost of model deployment on actual quantum computers, as we can select the optimal design of quantum ansatz circuits based on analytical solutions using classical simulations.

## 5 Significance of Discovered Biomarkers

### Statistical Significance

Using the cBioPortal [12] databases from nine projects [9, 25, 35, 45, 48, 50, 59, 64] with a total of \(73,717\) samples, we validated the statistical significance of the top-5 biomarkers for each pathway (**SuppMat-S1**). We found that only a small proportion of the total samples contained mutations in certain biomarkers, with the highest mutated biomarkers being _PAK1_ (\(1.5\%,n=858\)) and _RNF213_ (\(0.3\%,n=62\)). However, the remaining biomarkers accounted for an extremely small proportion of all mutations, making it insufficient to use mutational profiles alone to study the relationship between these biomarkers and targets. We also found co-occurrence of mutations in certain biomarkers with significant statistical evidence regarding the _CTLA4_-activation pathway (SuppDoc-S). Specifically, _UBA1_, _HYOU1_, and _RNF213_ mutations were co-occurring in this pathway. Additionally, mutations in _MAFC1_, _WLS_, _PSMD8_, and _PAK1_ were co-occurring in the _CTLA4-CD8A-CD8B_ pathways, while mutations in _NAPA_, _PGAP3_, _CLIC4_, and _PPM1G_ were co-occurring in the activation of _CTLA4-CD2_. Lastly, the extended activation pathway four was associated only with the co-activation of _LCN2_ and _FAM107A_ mutations.

### Clinical Significance

We perform literature mining from the PubMed.gov library regarding \(19\) top-5 biomarkers, excluding CPE due to similar abbreviations (**SuppMat-S2**). The analysis is on publications over the three years from \(2020\) to \(2023\), up to 12/05/2023. **SuppTab**2 shows that \(12\) over \(19\) biomarkers are rarely known in clinical-associated literature but addressed as significant drivers by our proposed model.

#### 5.2.1 Pathway 1: _Ctla4_

Hypoxia upregulated protein 1 is a protein that in humans is encoded by the _HYOU1_ gene. The protein encoded by this gene belongs to the heat shock protein 70 family. This gene uses alternative transcription start sites. Using a type of bone-forming cell called MC3T3-E1, the study [70] demonstrated that high levels of glucose decrease the ability of the cells to survive and cause them to undergo programmed cell death. The high glucose levels also cause endoplasmic reticulum stress (ERS) by increasing the movement of calcium and the production of a protein called binding immunoglobulin protein (BiP) in the endoplasmic reticulum. This results in the activation of eukaryotic initiation factor 2 alpha (elF2alpha) downstream of a protein called PKR-like ER kinase (PERK). This, in turn, leads to the activation of a transcription factor called _ATT4_ and an increase in the production of a protein called C/EBP-homologous protein (CHOP), which is involved in the regulation of apoptosis in response to ER stress, as well as other proteins like _DNAJC3_, _HYOU1_, and _CALR_. Besides, the discovered _HYOU1_ and _HSPA1A_ (in the _HSPA1B_ family) and _DNAJB11_, _CALR_, _ERP29_, _GANAB_, _HSP90B1_, _HSPA5_, _LMAN1_, _PDIA4_ and _TXNDC5_ were involved in the endoplasmic reticulum (ER) stress [16]. The analysis of how proteins interact with each other revealed certain genes, such as _PTBP1_,
_NUP98_, and _HYOUI_, that are linked to breast cancer brain metastasis [3]. _HYOUI_ plays a role in supporting the growth, spreading, and metabolic activity of papillary thyroid cancer by increasing the stability of _LDHB_ mRNA [56].

Apart from its significant protective function in the formation and progression of tumors, _HYOUI_ can be a promising target for treating cancer. It may serve as an immune-stimulating additive because it can trigger an antitumor immune response. Additionally, it can be a molecular target for treating various endoplasmic reticulum-related ailments [44]. The study [29] found that the secretion of certain substances in response to a communication between lung cancer cells and endothelial cells (ECs) led to an increase in the expression of _HYOUI_ in lung cancer spheroids. Additionally, direct interaction between ECs and lung cancer cells caused an upregulation of _HYOUI_ in multicellular tumor spheroids (MCTSs). When inhibiting _HYOUI_ expression, it reduced the malignant behavior and stemness of the cancer cells, facilitated apoptosis, and made the MCTSs more sensitive to chemotherapy drugs in lung cancer.

_ETS2_ is responsible for producing a transcription factor that controls the activity of genes related to both development and apoptosis. The protein it produces is not only a proto-oncogene but has also been found to play a role in regulating telomerase. Additionally, a non-functional copy of this gene, known as a pseudogene, is located on the X chromosome. Due to alternative splicing, various transcript variants of this gene are generated. The transcription factor _ETS2_ controls the expression of genes responsible for various biological processes such as development, differentiation, angiogenesis, proliferation, and apoptosis. The transcription factor _ETS2_ has been shown to downregulate the expression of cytokine genes and HIV-1 in resting T-cells. [15] have investigated whether _ETS2_ also regulates the expression of lymphotropic factors (LFs) that are involved in T-cell activation/differentiation and the kinase _CDK10_, which controls Ets-2 degradation and repression activity. In vitro experiments demonstrated that Ets-2 overexpression increased the expression of certain LFs while decreasing _CDK10_ levels in both stimulated and unstimulated T-cells. These findings suggest that Ets-2 may regulate cytokine gene expression and HIV-1 latency in virus-infected T-cells.

The relationship between _CELF1_ and _ETS2_ in colorectal cancer (CRC) and chemoresistance to oxaliplatin (L-OHP) is studied in [55]. _CELF1_ was overexpressed in human CRC tissues and positively correlated with _ETS2_ expression. Overexpression of _CELF1_ increased CRC cell proliferation, migration, invasion, and L-OHP resistance, while knockdown of _CELF1_ improved the response of CRC cells to L-OHP. Similarly, overexpression of _ETS2_ increased malignant behavior and L-OHP resistance in CRC cells. The study concluded that _CELF1_ regulates _ETS2_, resulting in CRC tumorigenesis and L-OHP resistance, and maybe a promising target for overcoming chemoresistance in CRC.

_GPR116_ or _ADGRF5_ is the probable G-Protein coupled receptor 116. _GPR116_ has been reported to be involved in cancer progression and predicts poor prognosis in other types of cancer. The study [69] shows that _GPR116_ expression is upregulated in gastric cancer (GC) tissues and is positively correlated with tumor invasion and poor prognosis. _GPR116_ may be a novel prognostic marker and a potential therapeutic target for GC treatment. mRNA and protein expression of _GPR116_ in GC tissues and found that it was significantly upregulated, positively correlated with tumor node metastasis (TNM) staging and tumor invasion, and contributed to poor overall survival in GC patients [26]. _GPR116_ overexpression was also found to be an independent prognostic indicator in GC patients. Enrichment analysis revealed that _GPR116_ co-expression genes were mainly involved in various pathways.

The effect of _GPR116_ receptor on NK cells concerning pancreatic cancer is studied in [21], which found that _GPR116_ mice were able to efficiently eliminate pancreatic cancer through enhancing the proportion and function of NK cells in the tumor. The expression of _GPR116_ receptor was decreased upon the activation of NK cells, and _GPR116_ with NK cells showed higher cytotoxicity and antitumor activity in vitro and in vivo. Downregulation of _GPR116_ receptor also promoted the antitumor activity of NKG2D-CAR-NK92 cells against pancreatic cancer. These findings suggest that downregulation of _GPR116_ receptor could enhance the antitumor efficiency of CAR NK cell therapy.

#### 5.2.2 Pathway 2: _Ctla4-Cdba-Cdb_

The 26S proteasome (_PSMD2_) is a complex enzyme comprising a 20S core and a 19S regulator arranged in a precise structure. The 20S core consists of four rings with 28 different subunits. Two rings contain 7 alpha subunits each, while the other two contain 7 beta subunits each. The 19S regulator consists of a base with six ATPase subunits and two non-ATPase subunits, as well as a lid with up to ten non-ATPase subunits. Proteasomes are found in high concentrations throughout eukaryotic cells and break down peptides through an ATP/ubiquitin-dependent process outside lysosomes. The immunoproteasome, a modified version, plays a critical role in processing class I MHC peptides. This gene codes for one of the non-ATPase subunits in the lid of the 19S regulator. Besides its involvement in proteasome function, this subunit may also participate in the TNF signaling pathway as it interacts with the tumor necrosis factor type 1 receptor. A non-functional copy of this gene has been found on chromosome 1. Multiple transcript variants of this gene are produced through alternative splicing. _PSMD2_ and _PSMD8_ were significantly over-expressed in bladder urothelial carcinoma (BLCA) more than other cancers [49]. Besides, _PSMD8_ with _AUNIP_, _FANCI_, _LASP1_, and _XPO5_ are potential targets for the creation of an mRNA vaccine to combat mesothelioma [67].
_PAK1_ is responsible for producing a member of the PAK protein family, which are serine/threonine p21-activating kinases. PAK proteins connect RhoGTPases to reorganize the cytoskeleton and nuclear signaling. They act as targets for small GTP-binding proteins such as CDC42 and RAC. This particular family member specifically regulates the movement and shape of cells. Different isoforms of this gene have been identified through alternative splicing, resulting in various transcript variants.

Regarding its mechanism, ipomoea batatas polysaccharides specifically encourage the degradation of _PAK1_ through ubiquitination and inhibit its downstream Akt1/mTOR signaling pathway, thereby resulting in an increased level of autophagic flux [11]. _PAK1_ is a serine/threonine kinase gene overexpressed in some human breast carcinomas with poor prognosis, and aberrant _PAK1_ expression is an early event in the development of some breast cancers [18]. The structure of the actin cytoskeleton and protrusions in SW620 cells is related to their ability to move. Ce6-PDT treatment inhibits the migration of SW620 cells by reducing the activity of the _RAC1/PAK1/LIMK1_/cofilin signaling pathway, and this inhibition is improved by decreasing the expression of the _RAC1_ gene [60].

The increased presence of _WLS_ (Wnt Ligand Secretion Mediato) is an important indication of a negative outcome in breast cancer. It may have a vital function in the hormone receptor-positive (HR+) subtype [68]. Reducing the expression of _SNHG17_ in lung adenocarcinoma cells hindered cell growth, migration, and invasion while increasing apoptosis. _SNHG17_ acted as a sponge for miR-485-5p, resulting in increased expression of WLS. Therefore, _SNHG17_ accelerates lung adenocarcinoma progression by upregulating _WLS_ expression through sponging miR-485-5p [30].

_NDUFS5_ belongs to the NADH dehydrogenase (ubiquinone) iron-sulfur protein family. The protein it encodes is a component of the NADH - ubiquinone oxidoreductase (complex I), which is the initial enzyme complex in the electron transport chain situated in the inner membrane of mitochondria. Through alternative splicing, multiple transcript variants of this gene are generated. Additionally, pseudogrees of this gene have been discovered on chromosomes 1, 4, and 17.

Machine learning algorithms have been used to classify some cancer types, but not lung adenocarcinoma, in which _NDUFS5_, _P2RY2_, _PRPF18_, _CCL24_, _ZNF813_, _MYL6_, _FLJ41941_, _POU5F1B_, _and SUV420H1_ were associated with alive without disease [17]. The study identified _MACF1_ with _FTSJ3_, _STAT1_, _STX2_, _CDX2_ and _RASSF4_ that can be used as a signature to predict the overall survival of pancreatic cancer patients [62]. The poor response of low-grade serous ovarian carcinoma (LGSOC) to chemotherapy calls for a thorough genomic analysis to identify new treatment options. This study, 71 LGSOC samples were analyzed for 127 candidate genes using whole exome sequencing and immunohistochemistry to assess key protein expression. Mutations in _KRAS_, _BRAF_, and _NRAS_ genes were found in 47% of cases. Several new driver genes were identified, including _USP9X_, _MACF1_, _ARID1A_, _NF2_, _DOTIL_, and _ASH1L_[13]. To improve the treatment of glioblastomas and enhance patient survival, _MACF1_ can be used as a specific diagnostic marker that enhances the effectiveness of radiation therapy while minimizing damage to normal tissues [10]. This approach could potentially lead to the development of new combination radiation therapies that target translational regulatory processes, which are often involved in poor patient outcomes. Another study presented data indicating that reduced _MACF1_ expression inhibited melanoma metastasis in mice by blocking the epithelial-to-mesenchymal transition process. Therefore, _MACF1_ could be a potential target for melanoma treatment [57].

_MACF1_ is responsible for producing a substantial protein that consists of multiple spectrin and leucine-rich repeat (LRR) domains. The encoded protein belongs to a family of proteins that connect various cytoskeletal components. Specifically, this protein plays a role in enabling interactions between actin and microtubules at the outer edges of cells, and it also connects the microtubule network to cellular junctions. Multiple transcript variants of this gene are produced through alternative splicing, although the complete structure of some of these variants has yet to be determined [20]. A study included 695 patients with hepatocellular carcinoma (HCC), divided into a training group of 495 patients and a validation group of 200 patients [24]. A nomogram was developed using T stage, age, and the mutation status of _DOCK2_, _EYS_, _MACF1_, and _TP53_. The nomogram was found to have good accuracy in predicting outcomes and was consistent with the actual data. The study also found that T-cell exclusion may be a potential mechanism for malignant progression in the high-risk group. In contrast, the low-risk group may benefit from immunotherapy and _CTLA4_ blocker treatment. In conclusion, the study developed a nomogram based on mutant genes and clinical parameters and identified the underlying association between these risk factors and immune-related processes.

#### 5.2.3 Pathway 3: _Ctla4-cd2_

Fucoxanthin is a natural pigment present in brown seaweeds, and its derivative, fucoxanthin (FxOH), has been shown to effectively induce apoptosis (programmed cell death) in various types of cancer cells. The role of Chloride intracellular channel 4 (_CLIC4_), which plays a crucial role in cancer development and apoptosis, in FxOH-induced apoptosis was also investigated [63]. Treatment with FxOH induced apoptosis in human CRC DLD-1 cells. FxOH treatment downregulated _CLIC4_, integrin beta1, _NHERF2_, and _pSMAD2_ (Ser(465/467)) compared to control cells, without affecting _RAB35_ expression. _CLIC4_ knockdown suppressed cell growth and apoptosis, and apoptosis induction by
FxOH was reduced with _CLIC4_ knockdown. The expression levels of _CLIC4_ and _GAS2L1_ were found to be higher in circulating tumor cells (CTCs) from pancreatic cancer patients compared to peripheral blood mononuclear cells [71]. Besides, the overexpression of _CLIC4_ was associated with unfavorable outcomes in multiple cohorts of CN-AML patients [22].

The role of actin-binding proteins, including profiling, fascin, and ezrin, in the metastasis of non-small cell lung cancer (NSCLC) [28]. The study collected tumor and adjacent normal lung tissue samples from 46 NSCLC patients and used real-time PCR and Western blotting to determine the levels of _PFN1_, _FSCN1_, and _EZR_ mRNAs and proteins. The results showed that patients with lymphatic metastasis had higher expression levels of the profilin, fascin, and ezrin mRNAs and profilin and fascin proteins. In contrast, mRNA and protein expression levels increased in patients with distant metastasis. The activation of AKT signaling in the progression of colorectal cancer (CRC) can be influenced by the lncHCPC9/miR-299-3p/_PFN1_[4]. The loss of _PFN1_ leads to the activation of several signaling pathways, including AKT, NF-(k)B, and WNT. On the other hand, overexpression of PFN1 in cells with high levels of SH3BGRL can counteract SH3BGRL-induced metastasis and tumor growth by upregulating _PTEN_ and inhibiting the PI3K-AKT pathway [66].

_PPMIG_ codes for a large protein that contains spectrin and leucine-rich repeat (LRR) domains. It belongs to a family of proteins that act as bridges between different cytoskeletal elements. Specifically, this protein facilitates the interaction between actin and microtubules at the periphery of cells and links the microtubule network to cellular junctions. The level of _PPMIG_ expression in LIHC may be influenced by promoter methylation, CNVs, and kinases and could be linked to immune infiltration. High _PPMIG_ expression was found to be related to mRNA splicing and the cell cycle according to GO terms. These findings suggest that _PPMIG_ could be a prognostic indicator for liver hepatocellular carcinoma patients and may play a role in the tumor immune microenvironment [31]. Besides, the irc-_PGAP3_ plays a significant role in the growth and advancement of triple-negative breast cancer (TNBC), thus making it a potential target for the treatment of TNBC patients.

#### 5.2.4 Pathway 4: _Ctla4-CD2-CD48-CD53-CD58-CD84_

_MTIG_ (Metallothioneen 1G) and _MTIH_ have the potential to suppress tumor growth and are regulated by DNA methylation in their promoter regions. In addition, they are associated with serum copper levels and may be linked to the survival rate of patients with hepatocellular carcinoma [54]. Besides, _MTIG_, _CXCL8_, _IL1B_, _CXCL5_, _CXCL11_, and _GZMB_ are over-expressed in colorectal cancer tissues compared to normal tissues [34]. Three genes (_SLC7A11_, _HMOX1_, and _MT1G_) were identified as differentially expressed genes (DEGs) associated with renal cancer prognosis using survival analysis screening [14]. _SLC7A11_ and _HMOX1_ were found to be upregulated in renal cancer tissues, while _MTIG_ was downregulated. The combination of receiver operating characteristic (ROC) curves, Kaplan-Meier analysis, and Cox regression analysis revealed that high expression of _SLC7A11_ was a prognostic risk factor for four different types of renal cancers, low expression of _HMOX1_ was a poor prognostic marker for patients, and increased expression of _MTIG_ increased the prognostic risk for three additional classes of renal cancer patients, except for those with renal papillary cell carcinoma.

_FAM107A_ (Family With Sequence Similarity 107 Member A) with _ADAM12_, _CEP55_, _LRFN4_, _INHBA_, _ADHIB_, _DPT_, and _LOC100506388_ were analyzed and evaluated as potential prognostic genes for gastric cancer [23]. Among these genes, _LRFN4_, _DPT_, and _LOC100506388_ were identified as having a potential prognostic role in gastric cancer, as determined through a nomogram. Besides, the interaction pairs of _HCG22/EGOT-hsa-miR-1275-FAM107A_ and _HCG22/EGOT-hsa-miR-1246-_Glycerol-3-phosphate dehydrogenase 1 are likely to have a significant role in laryngeal squamous cell carcinoma.

_LCN2_ is responsible for producing a protein classified as a lipocalin family member. Lipocalins are known for their ability to transport small hydrophobic molecules like lipids, steroid hormones, and retinoids. The specific protein encoded by this gene is called neutrophil gelatinase-associated lipocalin (NGAL), and it plays a significant role in innate immunity. NGAL sequesters iron-containing siderophores, which helps limit bacterial growth and infection [20]. Besides, _LCN2_ is an innate immune protein that regulates immune responses by promoting sterile inflammation. _LCN2_ is a biomarker associated with radioresistance and recurrence in nasopharyngeal carcinoma (NPC) [65]. _LCN2_ expression was upregulated in radioresistant NPC tissues and associated with NPC recurrence. Knocking down _LCN2_ enhances the radiosensitivity of NPC cells, while ectopic expression of _LCN2_ confers additional radioresistance. _LCN2_ may interact with _HIF-IA_ and facilitate the development of a radioresistant phenotype. _LCN2_ is a promising target for predicting and overcoming radioresistance in NPC. Moreover, the downregulation of the immune response, influenced by specific metastasis-evaluation genes (_BAMBI_, _F13A1_, _LCN2_) and their associated immune-prognostic genes (_SLIT2_, _CDKN2A_, _CLU_), was found to increase the risk of post-operative recurrence [32]. Higher _LCN2_ expression was associated with poor clinical outcomes and correlated with increased infiltration of various immune cells. _LCN2_ may
serve as a biomarker for immune infiltration and poor prognosis in cancers, suggesting potential therapeutic targets for cancer treatment [61].

## 6 Conclusion

To this end, I have introduced the quantum AI model used for biomarker discovery in biomedical research (**Section**3). The proof of concept is demonstrated in four targeted pathways associating with therapeutic-target _CTL4_ in **Section**4. Our model found clinical-relevant and notably potential biomarkers/targets for cancer treatment, which are extensively validated through statistical methods and literature mining (**Section**5).

I suggest several research directions that can be extended from the study. First, deploying the proposed quantum AI models on real quantum computers is worth investigating in the future, in which the effect of noise should be addressed toward the model's efficiency and effectiveness. Second, extension to other pathway activation is possible as the proposed algorithm is generalized. Finally, in _vivo_ and in _vitro_, validations of the discovered in _silico_ biomarkers will translate the findings to therapeutic solutions for cancer treatment and prevention.
