Biomarker discovery with quantum neural networks: a case-study in CTLA4-activation pathways

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 from genetic data. Method We propose a Quantum Neural Networks architecture to discover genetic biomarkers for input activation pathways. The Maximum Relevance-Minimum Redundancy criteria 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 genetic 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. Supplementary Information The online version contains supplementary material available at 10.1186/s12859-024-05755-0.


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 [11].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.The Next-Generation Sequencing (NGS) technology has revolutionized the field of oncology by enabling the comprehensive and precise identification of genetic biomarkers, paving the way for personalized cancer therapies and improved patient outcomes.
The study [22] introduces a new metric, the Intelligent Gene (I-Gene) score, to measure the importance of individual biomarkers for predicting complex traits.Their Machine learning (ML) pipeline combines classical statistical methods and state-of-theart algorithms for biomarker discovery.Another research group develops an autoencoder-based biomarker identification method by reversing the learning mechanism of the trained encoders [3].It provides an explainable post hoc methodology for identifying influential genes likely to become biomarkers.In [27], a Deep learning (DL) pipeline predicts the status of five biomarkers in LGG using slide-level biomarker status labels and whole slide images stained with hematoxylin and eosin.The research assesses the performance of several state-of-the-art Random Forest (RF) based decision approaches, including the Boruta method, permutation-based feature selection with and without correction, and the backward elimination-based feature selection method [1].A review offers tips to overcome common challenges in biomarker signature development, including supervised and unsupervised ML, feature selection, and hypothesis testing [25].Another systematic review examines the current state of the art and computational methods, including feature selection strategies, ML and DL approaches, and accessible tools to uncover markers in single and multi-omics data [24].Despite its valuable role, genetic biomarker discovery is a challenging task for classical-computational platforms due to the massive search space ("Problem statement" section).
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 ("Quantum neural networks" section).A comprehensive review discusses quantum computing technology and its status in solving molecular biology problems, especially in the next-generation computational biology scenario [59].The review covers the basic concept of quantum computing, the functioning of quantum systems, quantum computing components, and quantum algorithms.HypaCADD, a hybrid classical-quantum workflow for finding ligands binding to proteins, is introduced in [42].While accounting for genetic mutations, it combines classical docking and molecular dynamics with QML to infer the impact of mutations.The study found that the QML models can perform on par with, if not better than, classical baselines.Another systematic review presents the recent progress in quantum computing and simulation within the field of biological sciences.It discusses quantum computing components, such as quantum hardware, quantum processors, quantum annealing, and quantum algorithms [58].A review comments on recently developed Quantum Computing (QC) bio-computing algorithms, focusing on multi-scale modeling and genomic analyses [47].The research group highlights the possible advantages over the classical counterparts and describes some hybrid classical/quantum approaches.In a non-conventional track, scientists at Oak Ridge National Laboratory used their expertise in quantum biology, artificial intelligence, and bioengineering to improve how CRISPR Cas9 genome editing tools work on organisms like microbes that can be modified to produce renewable fuels and chemicals [41].The cross-section of the genetic editing technology with quantum methods shows promising new insights into biomedical science.
This work uses a class of Quantum Artificial Intelligence (AI) models to discover genetic biomarkers in biomedical research.We adopt the neural architecture proposed in a recent work that addresses the body dynamics modeling problem [55].Here, we make a non-trivial adaptation of the proposed game theory 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, cost-effective algorithm for biomarker discovery from genetic data despite the extensive problem complexity.We organize the article as follows: "Preliminary" section formalizes the biomarker identification problem as a combinatory optimization problem and the preliminary for QNN models; "Method" section introduces our proposed model architecture and the scoring algorithm; "Results" section reports the in silico discovery for genetic biomarkers of four immunotherapy pathways with posthoc validation using literature mining over clinical research; "Conclusion" section concludes our research by suggesting several further research direction.

Problem statement
The learning task involves identifying the best combinations of genetic biomarkers from a given set of genes (represented as G ) to select those that are (1) most relevant to a spe- cific pathway (represented as 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 [62] (See Additional file 1: Appendix A).
In this context, it is worth noting that each individual has unique patterns of mutational alterations that lead to distinct sets of genetic biomarkers.Considering all the possibilities, the number of candidate biomarker sets is the sum of all possible combinations, which can be expressed as Since the human genome contains around 20,000 to 25,000 genes, this results in a massive search space of 3.2019 × 10 6577 candidate biomarker set for any biomarker identifi- cation algorithm from genetic databases.This search space grows exponentially with the number of input genes, making it an incredibly challenging problem for conventional computing methods.Quantum computing holds great promise for advancing genomic research, particularly in quantifying biomarkers.In this context, the logarithmic scaling complexity of quantum algorithms becomes evident, as exemplified by the requirement of log 2 20, 000 to log 2 25, 000 noise-tolerant qubits for quantifying genome sets, (1) approximately equivalent to 15 qubits.The salient advantage of employing quantum hardware for biomarker quantification lies in the O(log N ) scaling complexity, provid- ing a significant computational advantage as the genomic dataset size increases.For instance, in the presence of four multimodality datasets encompassing DNA Methylation, RNA, mRNA, and Protein, each with a homogeneous number of features denoted as M , the required number of qubits scales only to N = log 2 4 M = 2 + log 2 M , illus- trating a scalable problem complexity.However, the current state-of-the-art quantum hardware faces limitations in facilitating multimodality analysis, primarily due to the constraints imposed by the limited and noisy qubits available, hindering their effectiveness in realizing the full potential of quantum computational power in genomics.

Quantum neural networks
QNNs represent input data using wavefunction representations, typically using qubits or "qurons" [71], in the form of: This distinguishes QNNs from classical ANNs as they capture physical events discretely [48] and offer insight into representation learning [8].
QNNs have been proposed to offer two advantages over classical ANNs [72].Quantum feature maps can represent exponentially larger data sets than classical neural networks, with an n-qubit system representing 2 n bits [57].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 P(0) = |α| 2 and P(1) = |β| 2 .In our previous papers, we discuss the role of epistemic uncertainty estima- tion from quantum maps [54] and the effect of entanglement layouts on the classifier's performance.
The typical design for QNNs [7,28,38,66,73] involves a stack of identical ansatz structures, given by a global unitary transformation: where x represents input features, θ represents model weights, U (l) (.) represents iden- tical-parameterized circuits serving as variational (trainable neural) blocks, and V(.) represents feature-embedding blocks.From our perspective, QNNs are advanced mathematical models in the language of representation theory (See Additional file 1: Appendix B); thus, we are using mathematics to enable cancer discoveries.
(3) U θ (x) = U (l) (θl)V(x) . . .V(x)U (0) (θ 0), and (2) trainable RX-rotation and RY-rotation gates and The parameterized wavefunction of the 1-layer model is given n is the number of qubits, and is the architecture parameter of the entanglement layout constructed by CNOT gates, illustrated in Fig. 1.

Computations of gene scores (GSCORE © )
We train the proposed QNNs to learn the optimal sampling distribution based on mRMR criteria [56] (See Additional file 1: 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 genetic biomarkers.Specifically, the output electronic wavefunction of the parameterized QML model is given by with n is the number of prepared qubits and is the model parameter.The sampled probability density is given by where | * � is the conjugate-transpose of the output wavefunction.In other words, we compute the wavefunction's probability amplitude or square modulus.
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, (4) 1 The Ansatz circuit of our proposed QNN models using four qubits with four neural blocks.Here, the number of evaluated genes is 2 4  = 16 genes.We extend the architecture to 11-qubit ansatz in the numerical result, scoring 2 11  = 2048 genes high temperatures encourage less conservative predictions.Thus, the biomarker score is the sampling probability of each gene given by where temp is the function temperature.Finally, we select the candidate marker set by parameterized thresholding with p = 1 if p ≥ τ , otherwise 0. We interpret the GSCORE © 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.

Objective function
We adopt the efficient loss function of the Quadratic Programming Feature Selection (QPFS) method [65], given as where F n×1 is the relevancy to target variables and H n×n is the pairwise redundancy computed from the feature set.Both natural and normalized quantum distributions p(�) and p(�) satisfy the conditions for p i in QPFS.We consider = 1 for further anal- ysis, i.e., the balanced loss between redundant-relevant criteria.

Pseudo-code
We implement the proposed model using the quantum simulation package Pennylane [9] with Pytorch 3.7 [60].The mutual information criteria are computed by Scikit-learn [61], and model optimization is conducted by Optuna [2] with Tree Parzen Estimators [10].The pseudo-code is given in the following algorithm: (10)

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 [10] (SMBO) to train our model.We learned from our previous works -CSNAS [53] and BayesianQNN [54] that the used optimization is a cost-efficient algorithm, which enables effective search on a massive search space.

CTLA4-activation Pathways
CTLA4 -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 [31].CD8A and CD8B encode the alpha and beta chains of the CD8 antigen, respectively.The CD8 antigen is a cell surface glycoprotein found on most cytotoxic T lymphocytes that mediate efficient cell-cell interactions within the immune system [14].The CD8 antigen acts as a coreceptor with the T-cell receptor on the T lymphocyte to recognize antigens displayed by an antigen-presenting cell in class I MHC molecules.Moreover, CD8+ T cells play a significant role in the response to immunotherapies that target CTLA4 [40].Following a common preclinical combination treatment protocol, the study used a radiolabeled antibody to detect changes in CD8a+ infiltration in murine colon tumors.The results showed that the treatment effectively inhibited tumor growth and increased the overall survival of mice.CD2 and CD28 are both important co-receptors involved in T-cell activation [30,74].They are part of the immunoglobulin superfamily and are known to regulate T-cell activation in a coordinated manner.CD2 enhances adhesion between T cells and target cells and delivers an activation signal [29].On the other hand, CD28 is a costimulatory receptor that can strongly enhance TCR signaling responses.It is believed that CD28 and CD2 may function together to facilitate interactions of the T cell and antigen-presenting cells (APCs), allowing for efficient signal transduction through the TCR [30].The precise mechanisms of CTLA4's inhibitory role are not fully understood, but it is believed that CTLA4 can compete with CD28 for ligand binding, acting as an antagonist of CD28-mediated costimulation [68].This interaction is thought to occur at the immune synapse between T cells and antigen-presenting cells (APCs), where CTLA4 has been shown to recruit CD80, thereby limiting its interactions with CD28.Studying the coactivation of CTLA4 and CD2 could provide valuable insights into T-cell activation and immune regulation.However, limited research addresses the coactivation of CTLA4 and CD2.This suggests further investigation is needed to establish a connection and understand its implications for immunotherapy and autoimmune disease treatment.Understanding these interactions could potentially lead to the development of more effective therapeutic strategies.
In this study, we aim to broaden the scope of immunological research by studying the coactivation of CTLA4, CD2, and the CD2-associated genes, including CD48, CD53, CD58, and CD84.CD48, a member of the CD2 subfamily of the immunoglobulin superfamily, is found on the surface of lymphocytes and other immune cells and participates in activation and differentiation pathways in these cells.CD53, another member of the tetraspanin superfamily, regulates various cellular processes such as adhesion, migration, signaling, and cell fusion.CD58, also known as lymphocyte function-associated antigen 3 (LFA-3), is a cell adhesion molecule that strengthens the adhesion and recognition between T cells and antigen-presenting cells, facilitating signal transduction necessary for an immune response.Lastly, CD84, a member of the signaling lymphocyte activation molecule (SLAM) family, forms homophilic dimers by self-association and is reported as an important survival receptor in chronic lymphocytic leukemia.By studying the coactivation of these molecules, we hope to gain a deeper understanding of the complex interactions and signaling pathways involved in immune regulation.This could lead to the development of more effective therapeutic strategies for various immunerelated diseases.
We will investigate four pathways regarding the co-occurrence of mutational activation, including: 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 Additional file 1: Appendix C.

Datasets
We use The Cancer Genome Atlas (TCGA [79]) with RNA expression data and Copy Number of Variation (CNV).We score 2048 genetic biomarkers based on its expression, which is equivalent to 2 11 dimensional embedding generated by 11-qubit system ("Pseudo-code" section).The evaluated cohort includes 9, 136 patients, considered Big Data in the context of a cancer genetic study.The expression set X is normalized using Min-Max normalization, and the mutational signals are created from CNV with Y = 1 if CNV = 0 , otherwise Y = 0 .The evaluated expressions are continuous values, while the activation signals are binary.

Quantum AI-driven genetic biomarkers for CTLA4-activation pathways
We summarize the case-study of CTLA4-activation pathways in Fig. 2A.The full reports for each pathway is given in Additional file 1: Figs.S3, S4, S5 and S6 in Additional file 1: Appendix D. We only consider the top 20 genetic biomarkers for further analysis.Of note, the discovered biomarker sets are distinctive for each studied pathway.Specifically, only one genetic biomarker MACF1 is founded as the genetic biomarker for CTLA4 and CTLA4-CD8A-CD8B activation pathways (Fig. 2B).Similarly, HSPA1B is addressed as a common genetic biomarker for the pathways CTLA4-CD8A-CD8B and CTLA4-CD2.Apart from MACF1 and HSPA1B, the remaining genetic biomarkers are distinctively associated with the quantified targets.

Convergence analysis
We construct an end-to-end explainable quantum AI, illustrated in the results in Additional file 1: Figs.S1, S2, S3 and S4.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 Additional file 1: Figs.S1, S2, S3 and S4 that the proposed algorithm can effectively score genes and sampling biomarker sets as the sampling loss is reducing.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% mod- els to have a more robust inference of GSCORE © , which shows that higher GSCORE © 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 200µ = 2 × 10 −6 , indicating the well-convergence of neural solutions.
Furthermore, the output panels in Additional file 1: Figs.S1, S2, S3 and S4 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.

Statistical significance
Using the cBioPortal [16] databases from nine projects [12,36,50,52,64,67,70,81,86] with a total of 73, 717 samples, we validated the statistical significance of the top-5 genetic biomarkers for each pathway (see Section 8.4).We found that only a small proportion of the total samples contained mutations in certain biomarkers, with the highest MACF1, a protein facilitating actin-microtubule interactions at the cell periphery, is a common genetic biomarker for both CTLA4 and CTLA4-CD8A-CD8B pathways.On the other hand, HSPA1B, a member of the heat shock protein 70 family that stabilizes existing proteins against aggregation, is the common genetic biomarker for CTLA4-CD8A-CD8B and CTLA4-CD2 pathways.These findings highlight the potential of these biomarkers in understanding immune regulation and developing therapeutic strategies, which has not yet been well-studied, discussed in "CTLA4-activation Pathways" section 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.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 coactivation of LCN2 and FAM107A mutations.

Clinical significance
We perform literature mining from the PubMed.govlibrary regarding 19 top-5 genetic biomarkers, excluding CPE due to similar abbreviations (see Section 8.4).The analysis is on publications over the three years from 2020 to 2023, up to 12/05/2023.Additional file 1: Table S2 that 12 over 19 biomarkers are rarely known in clinical-associated literature but addressed as significant genetic biomarkers by our proposed model.

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 [92] 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 producing a protein called binding immunoglobulin protein (BiP) in the endoplasmic reticulum.This results in the activation of eukaryotic initiation factor 2 alpha (eIF2alpha) downstream of a protein called PKR-like ER kinase (PERK).This, in turn, leads to the activation of a transcription factor called ATF4 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 [21].The analysis of how proteins interact with each other revealed certain genes, such as PTBP1, NUP98, and HYOU1, that are linked to breast cancer brain metastasis [4].HYOU1 plays a role in supporting the growth, spreading, and metabolic activity of papillary thyroid cancer by increasing the stability of LDHB mRNA [77].
Apart from its significant protective function in the formation and progression of tumors, HYOU1 can be a promising target for treating cancer.It may be an immunestimulating additive because it can trigger an antitumor immune response.Additionally, it can be a molecular target for treating various endoplasmic reticulum-related ailments [63].The study [43] 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 HYOU1 in lung cancer spheroids.Additionally, direct interaction between ECs and lung cancer cells caused an upregulation of HYOU1 in multicellular tumor spheroids (MCTSs).When inhibiting HYOU1 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.A nonfunctional copy of this gene, known as a pseudogene, is also 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 in resting T-cells.The research [20] 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.Cyclin-dependent kinase 10 (CDK10) is a serine/threonine kinase related to CDC2 and plays a crucial role in various cellular processes such as cell proliferation, regulation of transcription, and cell cycle regulation.CDK10 has been identified as a candidate tumor suppressor in hepatocellular carcinoma, biliary tract cancers, and gastric cancer, but as a candidate oncogene in colorectal cancer (CRC) [6].A study on CDK10's role in colorectal cancer revealed that it enhances cell growth, reduces chemosensitivity, and inhibits apoptosis by increasing the expression of BCL-2 [80].This effect depends on its kinase activity, as colorectal cancer cell lines with a kinase-defective mutation exhibit an exaggerated apoptotic response and reduced proliferating capacity.CDK10 is a serine/threonine kinase that regulates various cellular processes.It is a candidate tumor suppressor in hepatocellular carcinoma, biliary tract cancers, and gastric cancer but an oncogene in colorectal cancer (CRC).CDK10 promotes cell growth, reduces chemosensitivity, and inhibits apoptosis by increasing the expression of BCL-2 in colorectal cancer.Kinase-defective mutations exaggerate apoptotic response and reduce proliferating capacity.The relation between the identified-genetic biomarker ETS2 and CDK10 could be used to develop new therapeutic applications of cancer treatment.
The relationship between CELF1 and ETS2 in colorectal cancer (CRC) and chemoresistance to oxaliplatin (L-OHP) is studied in [76].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 may be 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 [91] 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 [37].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 [32], 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 decreased upon NK cells' activation, 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.

Pathway 2: CTLA4-CD8A-CD8B
The 26 S proteasome (PSMD2) is a complex enzyme comprising a 20 S core and a 19 S regulator arranged in a precise structure.The 20 S core consists of four rings with 28 different subunits.Two rings contain seven alpha subunits each, while the others contain seven beta subunits each.The 19 S regulator consists of a base with six ATPase subunits, two non-ATPase subunits, and 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 19 S 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 nonfunctional 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 [69].Besides, PSMD8 with AUNIP, FANCI, LASP1, and XPO5 are potential targets for the creation of an mRNA vaccine to combat mesothelioma [89].
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 [15].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 [26].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 [82].
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 [90].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 [44].
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), 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, pseudogenes 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 [23].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 [84].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 genetic biomarkers were identified, including USP9X, MACF1, ARID1A, NF2, DOT1L, and ASH1L [17].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 [13].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 [78].
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 [31].A study included 695 patients with hepatocellular carcinoma (HCC), divided into a training group of 495 patients and a validation group of 200 patients [35].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.

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 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 [85].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 [93].Besides, the overexpression of CLIC4 was associated with unfavorable outcomes in multiple cohorts of CN-AML patients [33].
The role of actin-binding proteins, including profiling, fascin, and ezrin, in the metastasis of non-small cell lung cancer (NSCLC) [39].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 lncHCP5/miR-299-3p/PFN1 [5].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 [88].
PPM1G 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 PPM1G expression in LIHC may be influenced by promoter methylation, CNVs, and kinases and could be linked to immune infiltration.High PPM1G expression was found to be related to mRNA splicing and the cell cycle according to GO terms.These findings suggest that PPM1G could be a prognostic indicator for liver hepatocellular carcinoma patients and may play a role in the tumor immune microenvironment [45].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.

Pathway 4: CTLA4-CD2-CD48-CD53-CD58-CD84
MT1G (Metallothionein 1 G) and MT1H 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 [75].Besides, MT1G, CXCL8, IL1B, CXCL5, CXCL11, and GZMB are over-expressed in colorectal cancer tissues compared to normal tissues [49].Three genes (SLC7A11, HMOX1, and MT1G) were identified as differentially expressed genes (DEGs) associated with renal cancer prognosis using survival analysis screening [18].SLC7A11 and HMOX1 were found to be upregulated in renal cancer tissues, while MT1G 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 MT1G increased the prognostic risk for three additional classes of renal cancer patients, except for those with renal papillary cell carcinoma.
LCN2 produces 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 gelatinaseassociated lipocalin (NGAL), and it plays a significant role in innate immunity.NGAL sequesters iron-containing siderophores, which helps limit bacterial growth and infection [31].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) [87].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-1A 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 [46].Higher LCN2 expression was associated with poor clinical outcomes and correlated with increased infiltration of various immune cells.LCN2 may serve as a genetic biomarker for immune infiltration and poor prognosis in cancers, suggesting potential therapeutic targets for cancer treatment [83].

Complexity in biomarker identification for CTLA4 activation pathway
Identifying the T cell gene CTLA4 and its genetic biomarker presents unique challenges, particularly when detecting certain molecular biomarkers expressed in the bloodstream.The detection of CTLA4 in T cells is complex due to several factors.First, CTLA4 is predominantly found in intracellular compartments before activation and only becomes increasingly detectable on the cell surface upon activation.This necessitates precise timing for effective detection.Second, the proportion of CTLA4positive T-cell subgroups in the peripheral blood and tumor tissues could be higher, making their detection difficult and costly.Despite the challenges, identifying genetic biomarkers associated with CTLA4 has several advantages over detecting molecular biomarkers in the bloodstream.Genetic biomarkers can provide information about genetic susceptibility, genetic responses to environmental exposures, subclinical or clinical disease markers, or indicators of response to therapy [19].They can help identify high-risk individuals reliably and promptly so that they can either be treated before the onset of the disease or as soon as possible.When a genetic biomarker is identified in a cancer through molecular or genetic testing, it tells the physician what makes the cancer grow and thrive.That information allows physicians to decide the most effective treatment for the patient [51].

Model adaptation for further applications
The further improvement of the proposed quantum neural network can consider the intricate nature of epigenetic modifications, which is of utmost importance.Epigenetic modifications are chemical alterations that occur to the DNA molecule itself or to the proteins tightly bound to it, and they play a crucial role in regulating gene expression and cellular differentiation.These modifications can include phosphorylation, acetylation, or methylation of various amino acids, and they not only add a layer of complexity but also enrich the genomic landscape with many potential biomarkers.To enhance the accuracy and reliability of our quantum neural network model, we need to integrate and analyze these diverse epigenetic markers.Doing so can unravel complex biological interactions and pathways associated with immune responses.This will allow us to identify novel and clinically relevant biomarkers for immunotherapy that may not be discovered through traditional methods.
Furthermore, addressing the complexities of epigenetic modifications will facilitate a more nuanced understanding of the model's adaptability.This understanding will offer insights into its potential applications and limitations in real-world clinical settings.By taking a comprehensive approach, we ensure that our model is robust and versatile, accommodating the vast array of biomarkers introduced by epigenetic modifications.In turn, this contributes to the advancement of personalized medicine in immuno-therapy, where we can tailor treatments to an individual's unique genetic makeup, epigenetic modifications, and immune system response.

Conclusion
To this end, a new framework based on the quantum AI model, used for genetic biomarker discovery in biomedical research ("Method" section), has been introduced.The proof of concept is demonstrated in four targeted pathways associating with therapeutic-target CTLA4 in Sect. 4. Our model found clinical-relevant and notably potential biomarkers/targets for cancer treatment, which are extensively validated through statistical methods and literature mining (Sect.5.2).
We 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.
Phuong-Nam Nguyen is a current Ph.D. student in Electrical Engineering at the University of South Florida.He earned a Bachelor's degree in Mathematics and Education from the Hanoi University of Education and a Master's in Statistics from the University of South Florida.He is currently a lecturer and research fellow at Phenikaa University.His research interests are applying classical and quantum machine intelligence to biological problems, including oncology research, molecular dynamics modeling, large genome data analysis, and biomarker identification.

Listing 1 :
Model architecture of the duality game model developed for biomarker identification task

Fig. 2 A
Fig. 2 A Activation Pathways Analyzed in Our Case-study: We expanded the scope of immunological research by studying the coactivation of CTLA4, CD2, and associated genes, including CD48, CD53, CD58, and CD84.These molecules play significant roles in T-cell immune regulation, and their interactions could potentially lead to the development of more effective therapeutic strategies for various immune-related diseases.B Venn Diagram of Discovered-Genetic Biomarker Sets regarding The Quantified Targeted Pathways:MACF1, a protein facilitating actin-microtubule interactions at the cell periphery, is a common genetic biomarker for both CTLA4 and CTLA4-CD8A-CD8B pathways.On the other hand, HSPA1B, a member of the heat shock protein 70 family that stabilizes existing proteins against aggregation, is the common genetic biomarker for CTLA4-CD8A-CD8B and CTLA4-CD2 pathways.These findings highlight the potential of these biomarkers in understanding immune regulation and developing therapeutic strategies, which has not yet been well-studied, discussed in "CTLA4-activation Pathways" section

Table 1
Hyper-parameter of our model optimization