CASQ1 also regulates store-operated Ca2+ entry (SOCE) by binding to stromal interaction molecule 1 (STIM1). Abnormal SOCE and/or abnormal expression or mutations in CASQ1, STIM1, or STIM2 are associated with human skeletal, cardiac, or smooth muscle diseases. However, the functional relevance of CASQ1 along with STIM2 has not been studied in any tissue, including skeletal muscle. First, in the present study, it was found by biochemical approaches that CASQ1 is bound to STIM2 via its 92 N-terminal amino acids (C1 region). Next, to examine the functional relevance of the CASQ1-STIM2 interaction in skeletal muscle, the full-length wild-type CASQ1 or the C1 region was expressed in mouse primary skeletal myotubes, and the myotubes were examined using single-myotube Ca2+ imaging experiments and transmission electron microscopy observations. The CASQ1-STIM2 interaction via the C1 region decreased SOCE, increased intracellular Ca2+ release for skeletal muscle contraction, and changed intracellular Ca2+ distributions (high Ca2+ in the SR and low Ca2+ in the cytosol were observed). Furthermore, the C1 region itself (which lacks Ca2+-buffering ability but has STIM2-binding ability) decreased the expression of Ca2+-related proteins  and induced mitochondrial shape abnormalities. Therefore, in skeletal muscle, CASQ1 plays active roles in Ca2+ movement and distribution by interacting with STIM2 as well as Ca2+ sensing and buffering.Calsequestrin 1 (CASQ1) in skeletal muscle buffers and senses Ca In addition to the Ca2+-buffering ability, CASQ1 has a Ca2+-sensing ability. CASQ1 senses the degree of Ca2+ depletion from the SR and modulates Ca2+ release from the SR to the cytosol via RyR1 in a conformation -dependent manner  or fluo-4-AM (Invitrogen) for other measurements in imaging buffer  at 37 °C for 45 min, as previously described [2+] and Im1 for other results, v5.29, Intracellular Imaging Inc., Cincinnati, OH, USA). To measure releasable Ca2+ from the SR, thapsigargin  dissolved in dimethyl sulfoxide  in the absence of extracellular Ca2+ was applied to myotubes. For the SOCE measurement, Ca2+ in the SR was depleted with TG (2.5 μM) in the absence of extracellular Ca2+, and once the cytosolic Ca2+ level returned to baseline, Ca2+ (2 mM) was added to myotubes to measure SOCE. To analyze Ca2+ movement, the peak amplitudes (which exhibited similar changes in peak areas) were measured. For long-term Ca2+ movements such as SOCE or the response to TG, the area under the curve was analyzed. To analyze the initial rate of responses, the slope at the rising phase of the response was examined by a linear equation that was obtained from a linear fitting of the rising phase [2+ imaging were obtained from Sigma–Aldrich.Single-myotube Caescribed ,44,45,46ng phase ,41,44,45For TEM observations, myotubes were fixed, embedded in epoxy resin (Epon 812), sectioned using an ultramicrotome , and examined under TEM  at 60 kV, as previously described . To analThe 3D structure of human CASQ1 (PDB ID: 3UOM) is presented as a ribbon diagram using iCn3D (NCBI’s web-based 3D structure viewer) .t-test .The results are presented as the mean ± SEM for the number of myotubes or experiments shown in the figure legends or the table parentheses. Significant differences were analyzed using an unpaired test for B or one-To examine whether CASQ1 binds to STIM2, a triad sample obtained from rabbit skeletal muscle was subjected to a coimmunoprecipitation assay with anti-CASQ1 antibody, and the immunoprecipitate was subjected to immunoblot analysis with anti-CASQ1 or anti-STIM2 antibody A. STIM2 To identify which region of CASQ1 is involved in binding to STIM2, cDNAs for five regions of mouse CASQ1  or the C1 region (C1) was expressed in mouse primary skeletal myotubes instead of heterologous expression systems to avoid possible artifacts and variations in expression introduced by the cell system. Myotubes that were transfected with empty vectors were used as a negative control . WT CASQ1 or C1 was successfully expressed A. To con2+ in the SR of the myotubes in the absence of extracellular Ca2+ was depleted with TG to avoid extracellular Ca2+ entry during SR depletion, and extracellular Ca2+ was then applied to the myotubes to measure SOCE using single-myotube Ca2+ imaging  in the absence of extracellular Ca2+ was measured by depleting the SR with TG  was applied to the myotubes, and intracellular Ca2+ release from the SR to the cytosol through RyR1 was measured. Intracellular Ca2+ release in response to membrane depolarization in skeletal myotubes mimics intracellular Ca2+ release that is needed for the contraction of skeletal muscle [2+ release in response to membrane depolarization without a change in the initial rate of the Ca2+ release  to the 2+ movements or distribution of the myotubes that expressed WT CASQ1 or C1 was caused by a change in the expression level of proteins that regulate or mediate SOCE or EC coupling but were instead due to the CASQ1-STIM2 interaction.To assess the expression levels of fifteen proteins that regulate or mediate SOCE or EC coupling in skeletal muscle, immunoblot assays were conducted with the myotube lysate . There wTo examine whether the expression of WT CASQ1 or C1  reduces Orai1-STIM2 interaction, the myotube lysate was subjected to a coimmunoprecipitation assay with anti-Orai1 antibody, and the immunoprecipitate was subjected to immunoblot analysis with anti-Orai1 or anti-STIM2 antibody D. SignifInterestingly, among four TRPCs that are known to be expressed in skeletal muscle , the exTo examine the cause of the short and swelling mitochondria, the expression level of proteins that mediate mitochondrial fission or fusion was examined by immunoblot assays using the lysate of C1-expressing myotubes. The expression of the dynamin-1-like protein (Drp-1), which mediates the fission process of mitochondria, was significantly increased . HoweverThe N-terminal C1 region of CASQ1 is colored yellow in the 3D structure of human CASQ1 A. The C12+ release through RyR1 for skeletal muscle contraction and Ca2+ amount in the SR but decreases extracellular Ca2+ entry via the SOCE mechanism and cytosolic Ca2+ level at rest. Considering that the amount of CASQ1 in fast-twitch skeletal muscle fibers is approximately three times greater than that in slow-twitch skeletal muscle fibers [In the present study, we found that the N-terminal region of CASQ1 (C1 region) binds to STIM2. Expression of the C1 region in mouse primary skeletal myotubes induces similar influences on the expression of full-length CASQ1, i.e., the CASQ1-STIM2 interaction increases intracellular Cae fibers , these iIn skeletal muscle, STIM1 and Orai1 are the main SOCE-mediating proteins, and STIM2 plays fine-tuning roles in SOCE in addition to STIM1 ,13. The 2+-buffering and sensing protein of the SR but also an active long-range communicator with Orai1 via binding to STIM2, although it is a trapped protein in the SR. Considering that Ca2+ via the SOCE mechanism plays a secondary role in skeletal muscle contraction  [2+ in the SR Ca2+ store and to lower useful Ca2+ in the cytosol than in normal situations and to release Ca2+ from the SR to the cytosol when it is needed  , the lon2+ amount in the SR. The increased Ca2+ amount in the SR has two explanations. First, it is possible that an increase in total Ca2+-buffering capacity by the expression of WT CASQ1 could contribute to the increased Ca2+ amount in the SR. However, the C1 region has a similar effect on the Ca2+ amount in the SR, although it almost lacks the Ca2+-buffering ability. Therefore, free CASQ1 may be increased in C1-expressing myotubes because, on behalf of endogenous CASQ1, the C1 region binds to STIM2, which is a similar condition to WT CASQ1 expression. Indeed, the expression of CASQ1 in C2C12 skeletal myotubes showed an increase in Ca2+ amount in the SR [2+ amount in the SR [2+ in the SR and low Ca2+ in the cytosol. The less Orai1-STIM2 interaction in WT CASQ1 or C1-expressing myotubes  in the present study increased the Can the SR , and conn the SR . Second,n the SR  (which in the SR ). The atmyotubes D support2+ movement and distribution that we present in this study. Interestingly, WT CASQ1 or C1-expressing myotubes have a similar tendency to STIM2-knockdown myotubes [2+ levels and increases in RyR1 activity and Ca2+ amount in the SR were seen. However overexpression or knockdown of STIM1 in mouse skeletal myotubes does not change the cytosolic Ca2+ level or Ca2+ amount in the SR [2+ movement and distribution are due to STIM1 or CASQ1-STIM1 interaction. This is the other different aspect of STIM2 from STIM1.STIM1 (a homolog of STIM2) or CASQ1-STIM1 interaction may be involved in the changes of Camyotubes : decreasn the SR , suggest2+ overload [2+ store in skeletal muscle and are closely localized in triad junctions to functionally communicate with the SR [2+ amount in the SR was increased by the CASQ1-STIM2 interaction and that the C1 region is almost lacking Ca2+-buffering ability, an excessively high Ca2+ amount in the SR due to the C1-STIM2 interaction could not be buffered in C1-expressing myotubes and could induce mitochondrial Ca2+ overload to maintain a Ca2+ balance between the SR and mitochondria  or CaM1 (a Ca2+-dependent protein) is decreased in C1-expressing myotubes  [Additionally, TAM is a skeletal muscle disease that is found in patients with mutated CASQ1 or CASQ1-null mice ,30. Howedomains) . However2+-buffering or sensing protein within the SR but also, by interacting with STIM2, an active player in spatiotemporal cellular Ca2+ movements in skeletal muscle . Furthermore, STIM2 in skeletal muscle is not an extra or alternative protein of STIM1 that mediates SOCE but is a functionally equivalent protein by regulating Ca2+-related cellular events by interacting with other proteins, such as CASQ1 rather than Orai1.In conclusion, CASQ1 is not only a passive Ca


SLC22A2), are sensitive to inhibition by select tyrosine kinase inhibitors (TKIs). We hypothesized that TKIs may differentially interact with the renal transporter MATE1 (SLC47A1) and influence the elimination and toxicity of the MATE1 substrate oxaliplatin. Interactions with FDA-approved TKIs were evaluated in transfected HEK293 cells, and in vivo pharmacokinetic studies were performed in wild-type, MATE1-deficient, and OCT2/MATE1-deficient mice. Of 57 TKIs evaluated, 37 potently inhibited MATE1 function by >80% through a non-competitive, reversible, substrate-independent mechanism. The urinary excretion of oxaliplatin was reduced by about 2-fold in mice with a deficiency of MATE1 or both OCT2 and MATE1 (p < 0.05), without impacting markers of acute renal injury. In addition, genetic or pharmacological inhibition of MATE1 did not significantly alter plasma levels of oxaliplatin, suggesting that MATE1 inhibitors are unlikely to influence the safety or drug-drug interaction liability of oxaliplatin-based chemotherapy.The membrane transport of many cationic prescription drugs depends on facilitated transport by organic cation transporters of which several members, including OCT2 ( Membrane-transporters are key regulators of selective cellular permeability , and medSLC22A2) and MATE1 (SLC47A1) have particular relevance in this connection, since they are highly expressed at the basolateral and luminal membranes of renal tubular cells, respectively, and these proteins are considered major transporters in the secretion of organic cations from the circulation into the kidney and then from the kidney into the tubular lumen. The tissue distributions of OCT2 and MATE1 in mice are generally consistent with that in humans, with the exception of MATE2-K being absent in the kidney of mice  mice, and mice additionally deficient for OCT1 and OCT2 [OCT1/2/MATE1(−/−)], following an established protocol . All anid by PCR , and thed by PCR ,29, by iIn order to examine the influence of transporter deficiency on the elimination of total platinum after oxaliplatin administration, male wild-type, MATE1(−/−), and OCT1/2/MATE1(−/−) mice were kept individually in Nalgene metabolic cages for a period of 3 days prior to oxaliplatin administration . Animals had free access to a standard diet and water, and were housed in a temperature- and light-controlled environment. Changes in the animals’ appearance , behavior , and/or activity  were monitored throughout the experiments. The bodyweight of each individual mouse was recorded before and during the experiment. Urine samples were collected in sterile 1.5 mL Eppendorf tubes at 8, 24, 48, and 72 h post-administration of oxaliplatin. Drug levels in urine were analyzed by a validated method based on flameless atomic absorption spectrometry , and urig for 15 min. The supernatant was re-centrifuged and used for determination of total protein content by a BCA assay kit. For the immunoblotting, the membrane was blocked with 5% skim milk in 0.05% PBS-tween, and then incubated overnight with a primary antibody (NGAL # 0351) obtained from Santa Cruz Biotechnology , and with an HRP-conjugated secondary anti-rabbit antibody (7074) obtained from Cell Signaling Technology .Kidneys were isolated from mice, then minced and incubated in 500 µL of RIPA buffer  containing 1% SDS and protease and phosphatase inhibitors. After sonication, the lysate was incubated for 10 min on ice, and then centrifuged at 15,000× 2), leucovorin (400 mg/m2), and 5-fluorouracil (400 mg/m2 by i.v. bolus and 2400 mg/m2 by infusion over 46 h). Dasatinib was administered in combination with standard doses of oxaliplatin given every 14 days, 24 h before and 30 min before each oxaliplatin infusion. In order to assess the degree of MATE1 inhibition by dasatinib, analyses of N-methylnicotinamide (see below) were performed in plasma samples collected at serial time points (up to 24 h after the end of infusion). Plasma samples were also subjected to dasatinib analysis by liquid chromatography with tandem mass spectrometric detection (LC-MS/MS) . O. O33]. OTo further probe if and how these TKIs interact with MATE1, we computationally docked them to an atomic structural model of MATE1 predicted by AlphaFold2 (access code AF-Q96FL8-F1) . The docNext, we evaluated the influence of MATE1-inhibitory TKIs on post-translational and transcriptional regulatory pathways as potential explanations for the observed inhibitory profiles. We previously reported that the transporter OCT2 is sensitive to inhibition by several FDA-approved TKIs through a mechanism that involves YES1-mediated tyrosine phosphorylation  Since OCin vitro and found that dasatinib and nilotinib (in increasing order) downregulated the expression of MATE1  for human and mouse MATE1 was determined for several TKIs, including ibrutinib, imatinib, and nilotinib. These studies indicated that mouse MATE1 was more resistant to TKI-mediated inhibition than the human transporter; for example, the IC50 for nilotinib against human MATE1 was >100 times lower than that against mouse MATE1  . The finding that the MATE1-inhibitory property of certain xenobiotics is species-dependent is not unprecedented [50 for human MATE1, 1.1 µM; IC50 for mouse MATE1, 101 µM) [In advance of evaluating the influence of TKIs on MATE1 function in mice, the comparative concentration associated with 50% inhibition of transport (ICctively) A. It is cedented , and has 101 µM) . This suin vivo, levels of the endogenous dual OCT2/MATE1 substrate 1-N-methyl-nicotinamide (NMN) were measured as a potentially TKI-sensitive biomarker at baseline in mice that were either wild-type or deficient in MATE1 [bona fide biomarker for directional renal organic cation transport, a conclusion that is in line with a recent clinical report [To directly assess the influence of dasatinib on the function of MATE1 in MATE1 , OCT1 anin MATE1 , or bothin MATE1 . We founl report .in vitro model systems. The plausibility of dasatinib-mediated in vivo inhibition of MATE1 is further underscored by the notion that TKIs tend to accumulate in cells (administration of imatinib 25 µM resulted in 4.2 mM intracellular concentrations in K562 cells) [in vitro, suggesting that concurrent treatment with such TKIs warrants caution, these interactions are not necessarily associated with a deleterious effect on renal function.We next evaluated the impact of dasatinib on concentrations of NMN in mice and found that oral administration of the TKI at a dose of 15 mg/kg resulted in a transient, statistically significant increase in the plasma levels of NMN in wild-type mice to a degree that resembles those observed in MATE1-deficient mice at baseline B. Furthe2 cells)  and dasa2 cells) . In viewin vivo, the plasma pharmacokinetic profile and urinary excretion of the anticancer drug oxaliplatin were examined in mice. Oxaliplatin is a small-molecule platinum coordination complex used for the treatment of several gastrointestinal cancers that is cleared from plasma predominantly by renal elimination, with urinary excretion accounting for >50% of the dose and fecal excretion for about 2% of the dose [in vitro studies provided confirmation of the notion that oxaliplatin is a transported substrate of mouse and human OCT2 and mouse and human MATE1, where overexpression of the murine  and neutrophil gelatinase-associated lipocalin (NGAL) compared with the values observed in wild-type mice . These fes MATE1 ,60,61.The notion that oxaliplatin lacks nephrotoxic properties similar to those observed with cisplatin has been ascribed to comparative differences in transport kinetics for MATE1 in both mice and humans, and with a corresponding increase in luminal efflux into the urine . This, iin vivo as evidenced from their ability to modulate urinary excretion of the prototypical substrate, oxaliplatin, as well as systemic levels of the endogenous biomarker, NMN. These findings provide novel insight into the regulation of MATE1 and suggest that caution is warranted with polypharmacy regimes involving the use of certain MATE1 substrates given in combination with TKIs. Developing a comprehensive physiologically based pharmacokinetics (PBPK) model is required in order to predict TKIs and MATE1 mediated drug-drug interactions in humans. This is particularly relevant in view of the fact that a large proportion of approved prescription drugs are organic cations, and that the membrane transport of many of these agents depends on facilitated carriers such as MATE1 [In the present study, we identified MATE1 as a transporter that is sensitive to potent inhibition by a remarkably large number of small molecule drugs in the class of TKIs, and demonstrated through functional validation studies using genetic and pharmacological approaches that the observed inhibitory properties are potentially related to an effect on transcription. In addition, we found that some of these TKIs can inhibit renal MATE1 function as MATE1 .


Expression and function of TMEM16A is upregulated in ADPKD which causes enhanced intracellular Ca2+ signaling, cell proliferation, and ion secretion. We analyzed kidneys from Pkd1 knockout mice and found a more pronounced phenotype in males compared to females, despite similar levels of expression for renal tubular TMEM16A. Cell proliferation, which is known to be enhanced with loss of Pkd1−/−, was larger in male when compared to female Pkd1−/− cells. This was paralleled by higher basal intracellular Ca2+ concentrations in primary renal epithelial cells isolated from Pkd1−/− males. The results suggest enhanced intracellular Ca2+ levels contributing to augmented cell proliferation and cyst development in male kidneys. Enhanced resting Ca2+ also caused larger basal chloride currents in male primary cells, as detected in patch clamp recordings. Incubation of mouse primary cells, mCCDcl1 collecting duct cells or M1 collecting duct cells with dihydrotestosterone (DHT) enhanced basal Ca2+ levels and increased basal and ATP-stimulated TMEM16A chloride currents. Taken together, the more severe cystic phenotype in males is likely to be caused by enhanced cell proliferation, possibly due to enhanced basal and ATP-induced intracellular Ca2+ levels, leading to enhanced TMEM16A currents. Augmented Ca2+ signaling is possibly due to enhanced expression of Ca2+ transporting/regulating proteins.Autosomal dominant polycystic kidney disease (ADPKD) is caused by loss of function of PKD1 (polycystin 1) or PKD2 (polycystin 2). The Ca Male gender is a risk factor for progression of autosomal-dominant polycystic kidney disease (ADPKD) ,2. Affec2+-activated Cl− channel transmembrane 16A (TMEM16A). Support for a pro-secretory role of CFTR in ADPKD came from a number of in vitro studies i than outward currents and are in the range of 1 µM and higher. However, Ca2+ concentrations related to channel activity are typically obtained by Ca2+-sensing dyes, which measure global cytosolic Ca2+ concentrations, such as Fura-2. These global [Ca2+]i do not reflect the true Ca2+ levels in the TMEM16A-containing subapical compartment. We now know that TMEM16A is a membrane tether that binds the receptor for inositol trisphosphate (IP3) and thereby enhances local Ca2+ levels in close proximity to TMEM16A i was calculated from the 340/380 nm fluorescence ratio after background subtraction. The formula used to calculate [Ca2+]i was [Ca2+]i = Kd × (R − Rmin)/(Rmax − R) × (Sf2/Sb2), where R is the observed fluorescence ratio. The values Rmax and Rmin (maximum and minimum ratios) and the constant Sf2/Sb2 (fluorescence of free and Ca2+-bound Fura-2 at 380 nm) were calculated using 1 µmol/L ionomycin , 5 µmol/L nigericin, 10 µmol/L monensin , and 5 mmol/L EGTA to equilibrate intracellular and extracellular Ca2+ in intact Fura-2-loaded cells. The dissociation constant for the Fura-2•Ca2+ complex was taken as 224 nmol/L.Cells were loaded with 2 µM Fura-2/AM and 0.02% Pluronic F-127  in Ringer solution (mmol/L: NaCl 145; KHt test for unpaired samples and ANOVA were used for statistical analysis. p < 0.05 was accepted as the significant difference. Data are expressed as mean ± SEM. Differences among groups were analyzed using one-way ANOVA, followed by a Bonferroni test for multiple comparisons. An unpaired t test was applied to compare the differences between the two groups. All compounds used were of highest available grade of purity. Data are reported as mean ± SEM. Student’s


Mentoring is a highly personal and individual process, in which mentees take advantage of expertise and experience to expand their knowledge and to achieve individual goals. The emerging use of AI in mentoring processes in higher education not only necessitates the adherence to applicable laws and regulations  but further requires a thorough understanding of ethical norms, guidelines, and unresolved issues . Mentoring in Higher Education requires one of the highest degrees of trust, openness, and social–emotional support, as much is at the stake for mentees, especially their academic attainment, career options, and future life choices. However, ethical compromises seem to be common when digital systems are introduced, and the underlying ethical questions in AI-supported mentoring are still insufficiently addressed in research, development, and application. One of the challenges is to strive for privacy and data economy on the one hand, while Big Data is the prerequisite of AI-supported environments on the other hand. How can ethical norms and general guidelines of AIED be respected in complex digital mentoring processes? This article strives to start a discourse on the relevant ethical questions and in this way raise awareness for the ethical development and use of future data-driven, AI-supported mentoring environments in higher education. Mentoring is widely accepted as a very beneficial, personal, and individual support, in which mentees take advantage of expertise and experience to expand their knowledge and to achieve individual goals. However, the emerging use of AI in mentoring processes in higher education not only necessitates the adherence to applicable laws and regulations  but also further requires a thorough understanding of ethical norms, guidelines, and unresolved issues .The current boom of AI is accompanied by new institutes, initiatives, university courses, books, and papers which deal with the topics of tech ethics and AI ethics . HoweverRelated Work: Mentoring Ethics and Artificial Intelligence Ethics section will give an overview about the recent discourse in the fields of mentoring ethics and AI ethics. Subsequently, the Ethical Principles and Questions of Artificial Intelligence-Supported Mentoring in Higher Education section will connect these two fields and establish ethical principles of AI-supported mentoring and raising ethical questions that derived from one use case in higher education. Final conclusions and future work will be discussed in the last section. Regarding the key terminology, first, for the purposes of this article, our definition of AI will be provided in the Artificial Intelligence Ethics section. Second, we define AI-supported mentoring as a digitally enhanced and scalable process involving the typical topics of a mentoring relationship as follows: career support, support with expert knowledge, and socio-emotional support. In such processes, AI tools take over and automate mentors’ responsibilities, such as giving individual feedback or personal recommendations, helping to design individual learning paths or career strategies, all on the basis of the collected and analyzed data.To begin with, the In this section, we will first outline the ethical questions raised and the guidelines stipulated in the context of face-to-face mentoring in recent literature. Second, we will describe the ethical concerns and guidelines regarding the increasing application of AI.Despite the lack of a consistent definition of mentoring, numerous articles and books have emphasized the positive impact mentoring can have on individuals by enabling them to benefit from the knowledge of a more-experienced individual in various contexts, for example, in sports, at work, or in education . SpecifyWhile conventional mentoring relationships are often relatively intimate and therefore not easy to observe , dysfunc1. Beneficence: to do good, specifically to provide knowledge, wisdom, and developmental support to mentees2. Nonmaleficence: to avoid harming mentees through the exercise of power3. Autonomy: to inform mentees about all the actions that one undertakes on their behalf and to ask for their consent4. Confidentiality: to keep information about mentees’ confidential, to respect the mentees’ right of privacy, and to give them control about their information5. Fairness: to avoid discrimination and to ensure that benefits and potential burdens to mentees are fairly distributed6. Loyalty: to avoid conflicts of interests7. Concern: to exercise a caring but fair partiality toward mentees and their interestsList 1: Mentors’ Obligations Ia) In their article, “The Ethics of Mentoring,” b) In comparison to Moberg and Velazquez’ business ethics perspective, the second discipline home to numerous works on mentoring ethics is psychology. 1. Beneficence: promote mentees’ best interests whenever possible.2. Nonmaleficence: avoid harm to mentees .3. Autonomy: work to strengthen mentee independence and maturity.4. Fidelity: keep promises and remain loyal to those you mentor.5. Justice: ensure fair and equitable treatment of all mentees .6. Transparency: encourage transparency and open communication regarding expectations.7. Boundaries: avoid potentially harmful multiple roles with mentees and discuss overlapping roles to minimize risk for exploitation or bad outcomes.8. Privacy: protect information shared in confidence by a mentee and discuss all exceptions to privacy.9. Competence: establish and continue developing competence.List 2: Mentors’ Obligations IIJust as The APA’s Ethical Principles of Psychologists and Code of Conduct “can be seen as an aspirational guide to appropriate interactions with others in many situations, including mentoring.” It is subdivided into five general principles and 10 standards . In the 1. Principle A, Beneficence and Nonmaleficence: Mentors and mentees should try to help others and be careful not to harm them. Both help and harm in the mentoring relationship may be hard to define and will depend on the purpose and context of the mentoring relationship.2. Principle B, Fidelity and Responsibility: Leads the mentor to clarify the roles of each party to the relationship (the mentor will help the mentee and not just use the mentee to further his or her own career). The roles may evolve over time, and mentees and mentors should be aware of the possible changes in both roles and responsibilities.3. Principle C, Integrity: Follows from the previous principle. Both the mentor and mentee need to do what they have agreed to do when establishing the relationship. If a point of conflict or confusion arises, each person should be willing to resolve that issue.4. Principle D, Justice: Calls mentors and mentees to aspire to fairness, and to ensure that access is free from inappropriate bias. By virtue of Principle D, psychologists consider choices they make regarding with whom they will enter a mentoring relationship, and explore their reasons for choosing a particular mentee as opposed to other possible individuals who may desire such a relationship.5. Principle E, Respect for People's Rights and Dignity: Guides both the mentor and mentee to consider personal differences so that any differences do not bias their interactions. This principle also serves as a reminder that in some mentoring relationships, there may be a power differential that could impact the process.List 3: Mentors’ and Mentees’ Obligations Based on the APA’s Guide for Mentors and Mentees (summarized), 2002APA’s principles give a broader overview of potential ethical problems, but sum up similar issues as 1. Voluntariness: mentee and mentor take part voluntarily in the mentoring program2. Independence: mentee and mentor are not in a direct dependent relationship, for example, PHD supervisor and PHD student3. Defined time span: the relationship evolves over a defined program time, but may be carried forward afterward4. Personal contact: face-to-face contact is important for the success of the relationship, and may be supplemented by e-mail, chat, video calls, etc.5. Confidentiality: mentoring conversations take place in a safe environment, and all shared information is confidential6. Commitment and liability: mentor and mentee comply with agreements and appointments7. Expectations and agreements: mentor and mentee communicate about concrete expectations and agreements.List 4: Prerequisites for a Mentoring Relationship Based on Forum Mentoring e.V. (Summarized and Translated)c) Finally, to include a general education perspective, we want to state the principles of the German Federal Association “Forum Mentoring e.V.” , a natio“Forum Mentoring e.V.” adopts a more practically oriented approach and the standards refer to institutionalized mentoring programs. Therefore, the recommendations for a mentoring relationship differ from the aforementioned ethical mentoring principles but also focus on “confidentiality,” “commitment,” “liability,” and “independence.” Some other general conditions of the relationship are mentioned, including “personal contact,” “defined time span,” and “voluntariness” that we would not necessarily include as ethical principles.After discussing and comparing principles regarding mentoring ethics in three disciplines, we will now move on to Artificial Intelligence to approach the question, “which ethical principles need to be added or eliminated when we use AI-supported mentoring?”Before focusing on ethical principles concerning AI, we have to precise the scope of AI in this article. We adopt the definition provided by the Stanford Encyclopedia of Philosophy, a source widely regarded as authoritative in the field of ethics. Accordingly, AI is “any kind of artificial computational system that shows intelligent behaviour, i.e., complex behaviour that is conducive to reaching goals. […] we incorporate a range of machines, including those in ‘technical AI’, that show only limited abilities in learning or reasoning but excel at the automation of particular tasks, as well as machines in ‘general AI’ that aim to create a generally intelligent agent” . This leBefore referring to general AI ethics principles, we want to focus on data ethics as an example. It is not only the data itself, its collection and the selection of appropriate data that raise ethical questions, but also its subsequent use : 75–76. Within all proceedings, the third question of representativity is very sensitive. The problem of algorithmic biases already occurred in the choice of representatives: [...] we will seek for a sufficient presence, a consistent treatment, and a proper representation of items, particularly those belonging to protected or disadvantaged groups . The repThe questions arising in this paragraph frame reflections on AI ethics, as they address the basic problems of representativity and fairness, and they already occur before the processing of data in AI. It is widespread common sense that AI-supported technologies should be used for a common good. AI-supported technologies should not be used to harm or undermine anyone, and should respect widely held values such as fairness, privacy, and autonomy . The amoHuman Rights: A/IS shall be created and operated to respect, promote, and protect internationally recognized human rights.1. Well-being: A/IS creators shall adopt increased human well-being as a primary success criterion for development.2. Data Agency: A/IS creators shall empower individuals with the ability to access and securely share their data, to maintain people’s capacity to have control over their identity.3. Effectiveness: A/IS creators and operators shall provide evidence of the effectiveness and fitness for the purpose of A/IS.4. Transparency: The basis of a particular A/IS decision should always be discoverable.5. Accountability: A/IS shall be created and operated to provide an unambiguous rationale for all the decisions made.6. Awareness of Misuse: A/IS creators shall guard against all potential misuses and risks of A/IS in operation.7. Competence: A/IS creators shall specify and operators shall adhere to the knowledge and skill required for safe and effective operation.8. List 5: Principles According to IEEEs “Ethically Aligned Design,” 2019.a) The IEEE Global Initiative on Ethics of Autonomous and Intelligent Systems published a list of eight principles for a fair, transparent, and human AI, that have been updated in 2019. Their perspective addresses developers in the field of AI and names eight aspects to consider within its development:Interesting in this perspective is the practical view on the realization and development, and the direct address of the stakeholders in the field. Especially, the aspects of “effectiveness,” “competence,” and “knowledge” refer directly to requirements of its realization.1. Human agency and oversight: including fundamental rights, human agency, and human oversight2. Technical robustness and safety: including resilience to attack and security, fall back plan and general safety, accuracy, reliability, and reproducibility3. Privacy and data governance: including respect for privacy, quality and integrity of data, and access to data4. Transparency: including traceability, explainability, and communication5. Diversity, non-discrimination and fairness: including the avoidance of unfair bias, accessibility and universal design, and stakeholder participation6. Societal and environmental well-being: including sustainability and environmental friendliness, social impact, society, and democracy7. Accountability: including auditability, minimization, and reporting of negative impact, trade-offs, and redress.List 6: The Ethics Guidelines for Trustworthy Artificial Intelligence by the European Commission, 2019.b) A more political and juridical perspective is opened up with “The Ethics Guidelines for Trustworthy Artificial Intelligence” by the European Commission. They formulate guiding ethical values and refer to possible guidelines and legal references in the detailed description:This more political position frames even the legal aspects of AI Ethics. They address the respect of fundamental rights and furthermore in this recommendation, especially aspects concerning data and “data governance,” refer directly to the already asserted rights in many European countries.Human Rights (Dignity): human-centered design and respecting humans as a social being1. Self-Determination: a manifestation of individual freedom, right to individual identity, and digital self-determination2. Privacy: safety of human rights, dignity, and preserve integrity3. Safety: safety of privacy, physical, and emotional security4. Democracy: to guarantee human rights and to provide and secure education5. Fairness and Solidarity: accessibility of  resources6. Sustainability: ecological, societal, and economical funding7. c) In the report of the German Commission on Data Ethics instated by the German Federal Government, general rights and principles on AI are communicated. The report then aligns these principles in fundamental, technical, and data referred aspects and specifies especially data processing in algorithmic systems. The following seven principles are displayed in the report and have been summarized and translated into English:List 7: Principles according to the report of the German Commission on Data Ethics, 2019.As well as in the guidelines of the European Commission, in this ethics report, a political and legal view is emphasized and is closely related to the existing German law. Especially, the aspect of informational self-determination refers to aspects guaranteed in the German jurisdiction and the German law on data privacy and protection.Related Work: Mentoring Ethics and Artificial Intelligence Ethics to start a discourse on the lacking principles of AI-supported mentoring. For the first time in this research context, we search for overlapping, redundant, and missing principles to suggest a basis for relevant ethical questions with the main aim to raise awareness for the ethical development, and use of future data-driven AI-supported mentoring environments in higher education.In this section, we will compare the ethical principles of mentoring and AI evaluated in In In In contrast, we also identified principles that are unique in both contexts (highlighted in grey). Because of their focus on the personal relationship, the mentoring ethics principles, listed on the left, do not concentrate on the aspects of “technical robustness” and “safety,” “sustainability” and “equivalent aspects,” “effectiveness,” and “democracy.” However, we argue that traditional face-to-face mentoring can also benefit from considering AI ethics principles that raise more awareness of possible sensitivity of data, which is the basis for all mentoring relationships. The security aspects of the data that a mentee share with mentors go beyond “privacy” and “confidentiality” and can also lead to technical security issues in face-to-face mentorship . Also, aspects like “democracy” and “sustainability” could be easily adapted to mentoring guidelines.Exemplary Ethical Questions of the Use Case section, we will focus on one exemplary use case to illustrate various ethical questions the checklist can raise. The aim of this study was not to answer these questions, but to raise awareness.Reflecting upon our special use case of AI-supported mentoring, both AI ethics principles and mentoring ethics principles need to be considered. As it is an interdisciplinary topic, this comparison of principles can raise awareness of the ethical development and use of future data-driven, AI-supported mentoring environments in higher education. Interestingly, the non-corresponding principles (highlighted in blue) also play an important role and could easily be overlooked by stakeholders with only an educational/mentoring background or an IT/AI background. Therefore, we compiled a checklist for the responsible design of AI-supported mentoring environments and tools . As alreOn the basis of the identified ethical principles of AI-supported mentoring, we would now like to highlight and discuss a few of them in an exemplary use case in the higher education context. The raised questions are only a starting point for a new discourse, and of course, many more questions and arguments are imaginable.“… Suppose you are the head of the career service at a German University. Your university wants to establish a new professional AI-supported mentoring program that suggests students to apply for three job positions based on their information given in several online surveys and the learning data the system collected on their learning management system over the past semester.”a) Would it be ethical to suggest three career options to the mentee without making transparent which of the collected data was used and how?b) Would it be ethical to include a passus in the data protection regulation that permits the university to use the students’ data also as training data for study program marketing purposes to guarantee long-term financial security of the mentoring program?In this question, the center of interest is the principle of “transparency”: first, we have to ask, display and explain which data was collected. According to this we have to ask where the data was collected: which access points in the highly private mentoring process were set, and was there consent on the collection and processing of this data for the consideration of career options? Here, another facet according to the conception of AI-supported systems is affected; the “effectiveness,” which questions the purpose of the use of random data. Second, we should make transparent the representability of the data: whose data were used, which model was used, and what was the scope of the recommendation in the process? In this context, the principle of “fairness” needs to be respected.c) Would it be ethical to store the algorithm on an open server  to save costs and provide a free program for all?We already argued that mentoring requires one of the highest degrees of trust, openness, and socio-emotional support, as much is at stake for mentees, especially their academic attainment, career options, and future life choices. Highly personal data will be shared with the AI-supported mentoring program and not only the alignment with the university’s data protection regulations, but also the principles of “confidentiality and privacy” and “loyalty” need to be respected. If the program includes such a prerequisite in its data protection regulation, maybe students who do not agree will be excluded. However, the university is under constant financial pressure and in alignment with the principle “sustainability” must ensure that the program will run for future cohorts.d) Would it be ethical to free students from the decision-making process behind the searching for positions on the job market they are interested in  and enhance their life choices by providing them tailored career paths?Here, some principles and reasons might oppose: we could come to the conclusion that the use of an open system and a good documentation for the further use and development of software affects “sustainability” and that the possibility to access code drives the “transparency” of its use. On the other side, an openly documented code might be an open door for technical intruders and a possibility to hack the system. Especially, when it comes to a sensitive set of personal data in the mentoring process, the system needs to guarantee a high standard of “technical robustness and safety.”On the one hand, this question relates to the mentoring principle “autonomy, independence, and self-determination”; a mentor should try to strengthen the mentee’s independence and maturity, and therefore, should not have such an enormous influence on the career and life of the mentee. On the other hand, AI support could rise above subjective recommendations of parents and teachers that students are exposed anyways. AI could be more objective and could show broader career opportunities. It is also imaginable that AI suggestions could ensure “fairness, justice, and diversity” because students who do not already have a social network that can provide them with internships and career support would also have access to the AI-supported mentoring program. With regard to the principle “competence,” These are only four of the many questions and discussion points that could be raised; of course, much more are imaginable. After considering these exemplary questions , would you like the idea of an AI-supported mentoring program? Would you, as head of the career service, introduce the program? Would you, as an educator, encourage your students to take part? Would you, as a student, rely on the suggested job positions?Technology today “raises fundamental ethical questions about community, democracy, and what it means to be human”  . We arguBoth face-to-face mentoring and AI-supported mentoring bear advantages and disadvantages and ethical challenges: as long as AI cannot feel or interact with empathy and compassion, there will still be a great need for human teachers  and mentThe use of AI in mentoring environments creates new ethical challenges, but both face-to-face and AI mentoring will and can exist simultaneously, inspire one another and improve each other in a positive way. The juxtaposition of ethical principles in AI and mentoring in this article can serve as a basis and check list for further discussions in both disciplines and beyond. Following the idea of value-sensitive design , methods


Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout. Spatially, Ca2+ sparks, the fundamental element of Ca2+-induced-Ca2+-release , are controlled at the nanometer-scale in localized nanodomains referred to as dyads or couplons, yet Ca2+ homeostasis occurs inherently at the cellular-scale where flux balance through the membrane and subcellular transporters determines the total Ca2+ levels in the cell and in the Sarcoplasmic Reticulum . Homeostatic conditions of cardiomyocytes at the cell-level are integrated in the heterogeneous syncytium of cardiac muscle tissue where individual myocytes do not function as isolated entities. Temporally, the gating of Ca2+ channels occurs on sub-millisecond time-frames function  Ca2+ enters the cell through the L-type Ca2+ channels (LTCC) during electrical excitation ; (2) This local rise in Ca2+ activates the ryanodine receptors (RyRs) to trigger a large release of Ca2+ (triggered Ca2+ spark) from the SR; (3) Ca2+ diffuses throughout the myocyte, binds with the contractile apparatus, and initiates cellular contraction; (4) Peak contraction occurs when Ca2+ has diffused sufficiently throughout the cell to permit substantial binding with the contractile apparatus; Ca2+ influx has largely terminated at this point; intracellular Ca2+ is removed into the extracellular space through the sodium-Ca2+ exchanger (NCX) and the plasmalemmal Ca2+ pump, and SR-Ca2+ is restored through the SR-Ca2+ pump (SERCA); (5) As NCX and SERCA reduce the Ca2+ concentration in the intracellular volume, myofilaments release Ca2+ from their binding sites and cellular relaxation occurs; (6) NCX and SERCA continue to act to restore resting Ca2+ levels, ready for the next cycle.Excitation-contraction coupling is mediated by CICR , illustr2+ in the intracellular volume is referred to as the intracellular Ca2+ transient (CaT), and broadly follows the AP  membrane contains multiple invaginations into the cell interior, consisting of the transverse-tubule (TT) and axial-tubule (AT) system (T-system), harboring LTCCs, NCX, and other ion channels  and their involvement in proarrhythmogenic premature focal excitations , potentially inducing the nanodomain-wide event of a spontaneous Ca2+ spark by recruiting further RyRs within the dyad to sustain a release flux. The specific mechanism for this recruitment is either a large flux of Ca2+ through the pore of a channel that stochastically opens, which raises the local Ca2+ sufficiently to trigger the opening of adjacent RyRs, or a cascade of events where a single channel opening increases the probability of opening of a second round of receptors, which triggers more rounds of receptors opening  or, if of sufficient magnitude, a full triggered AP  and can simulate different potential mechanisms of these behaviors. The model structure of the RyR is directly related to the type of behavior that is considered to be behind the appearance of local sparks. In two-state models, refractoriness is not considered relevant in the dynamics of initiation and termination of sparks, whereas refractoriness and more complex gating, that may play critically important roles in the regulation of spark dynamics, can be included in four-state and other models. Previous studies and reviews have compared fundamentally different models of the RyR regarding their ability to reproduce different features of the physiology and/or assess the ability of different proposed mechanisms to explain these features. For example, This section aims to provide a clear indication of the models used in various studies by different groups and explain what the major features of these models’ differences are, in order to guide the reader through the many studies. The focus is primarily on those models which are utilized in whole-cell simulations, rather than those designed specifically to evaluate RyR function in isolation or in bilayers, such as The four-state Markov chain RyR model  which foAnd by definition/conservation:Jrel, is generally given by:Where O, O*, C, and C* represent the four states of the model and correspond to different physical conditions dependent on the specific model implemented . The release flux, Jrelmax is the maximal flux rate and the subscripts SR and i denote the SR and intracellular Ca2+ concentrations. The models have the following symmetries (some of which are broken in further model developments):Where If all of these symmetries are preserved, the description becomes equivalent to a Hodgkin-Huxley model with two independent gating variables.C*–O*, are dependent on the square of local cytosolic Ca2+ (“Cai” from herein for brevity and to avoid confusion with notation of powers); transitions from the top-to-bottom, also symmetric, are linearly dependent on the local Cai:The functional form of these transition rates, including the variables that they depend on and which states correspond to release flux, differ between the different implementations. In the original study by k0–3 are constants. This model is directly used in, for example, Where 2+ (CaSR for brevity) as a gating variable, which will be referred to here as “direct luminal gating.” The transition rates from the closed-to-open states are now functions of CaSR as well as Cai2, and the transitions from active to inactive (top-to-bottom) are dependent on both CaSR and Cai:WhereThis formulation is one of the most-commonly used , 2021.SR influences gating of the RyRs not directly but rather mediated through the SR-Ca2+ buffer calsequestrin (CASQ), as introduced by Jrel [equation (5)] updated accordingly [equation (21)]; (2) The constant for the open transition rate for the lower portion of the model (which now corresponds to CASQ-bound) is smaller than that of the top, breaking one of the symmetries in the previous models [equation (6) is no longer true]:Whereas the above model introduced direct luminal gating, many models include “buffer-mediated luminal gating,” wherein the CaWhereAnd CASQ determines the unbound-bound transition rates:The release flux is now given by:The reader is referred to the work of 2+ spark:In kcp and w are further constants. The majority of the models presented in the field – especially those of whole-cells – implement an RyR model which falls into one of these three broad categories. It is worth noting that the relatively simple functional forms of the transition rates given for the different models above may be modified in studies which aim to fit to experimental data describing RyR open probability, e.g., i and CaSR dependence is still captured in the general forms of the model given above. Further alternatives and updates exist of these baseline models. In Where i is raised by for the closed-to-open (left-to-right) transition rates. Many of the models use a simple coefficient of H = 2. However, single-channel and single-nanodomain studies  are not of the form of a four-state model or (2) introduce further environmental variables to control gating. In te model  was usedte model . In Greete model  was impl2+ spark, as discussed in There is also the question of whether allosteric interactions/cooperativity play a role in RyR gating, with 2+-waves. Thus, deterministic solutions are no longer suitable. Instead, stochastic algorithms that explicitly account for randomness and track individual channels are required.In common-pool models of the cardiomyocyte, the solutions to the RyR/LTCC models are typically numerically approximated using deterministic algorithms such as the forward-Euler method. These numerical solutions correspond to tracking only the average state of the system, i.e., the proportion of open RyRs/LTCCs across the whole-cell; information on the state of individual channels or channel clusters is not preserved in such an approximation. One motivation for the development of detailed spatial models of the dyad or cardiomyocyte is to capture the stochastic (random) nature of individual RyRs/LTCCs as well as their local control, due to the relevance of both of these features for both CICR and more complex emergent dynamics such as Cat) might look like:The most straight-forward method is to implement the Monte-Carlo approach: the state of each individual channel is tracked directly, and state-transitions are determined based on random numbers and the probability of transition. For example, for a two-state RyR model corresponding to only closed (C) and open (O) states, the algorithm at each time-step  of RyRs that open in a given cluster during a triggered Ca2+ spark, as directly addressed in the reformulation presented in 2+ concentrations) but with different parameters governing the transition rates and maximal Ca2+-flux rate may lead to very different outcomes in adaptive function regarding Ca2+-spark dynamics and homeostasis.The disparity between the gating mechanisms of the different models could have important implications for model dynamics and thus mechanistic conclusions drawn from these simulations. Due to inter-model differences in the setup of the whole-cell , it is not necessarily trivial to directly evaluate RyR function, as dynamics are intricately linked with other model parameters such as dyadic cleft volume, LTCC formulation/magnitude, local Ca2+ binding to the RyR and that this plays a significant role in CaT alternans. An important implication of the model choice to either include or omit significant RyR inactivation is the degree to which the junctional SR depletes during a triggered Ca2+-spark: models which do not include RyR inactivation . One reason for the disparities between the model structures is the current debate regarding the fundamental physiological relevance of RyR inactivation , where ton e.g.,  exhibit on e.g., . This fu+ sparks .+, Mg2+, Cl–, and the counter-ion fluxes they facilitate during SR-Ca2+ release which help to maintain the trans-SR membrane driving force, especially at rapid pacing rates. It is possible that these dynamics could also influence RyR refractoriness by modulating this driving force.A further factor, which has recently been included in 2+ signaling modulators) can be directly motivated by the aim of the specific study; it is generally the perspective that additional complexity should only be included where specifically required, in order to reduce the influence of the propagation of unknown errors. However, it could also be argued that a non-linear, multi-scale complex system such as this presents the possibility for unpredictable emergent phenomena, which may depend on the interaction of factors such as CaM with other variables. In this case, it can be argued that one should aim to include as many (rigorously derived) components of the system as is feasible. Perspectives on this are ultimately philosophical and it would be unwise to disregard either argument.Considerations of further complexity, such as the inclusion/omission of regulation by CaM  has yet to be performed. Such a study, requiring the whole-cell models described later in this review, could be hugely valuable in understanding the features of the different models and revealing fundamental insight into the physiology of cardiac Ca2+ handling.Whereas the original study of 2+ concentration to RyR activity and quantify the specific fractional opening of RyRs during a typical spark in imaging data, and optical methods are limited to the close proximity of the cell surface. Thus, computational models of the single, spatially distributed dyad are useful to understand the mechanisms of Ca2+ sparks and their dependence on RyR number and arrangement.Only recently have experimental imaging techniques been able to resolve individual RyRs , enablindx = 10 nm; 2+ could diffuse within the dyadic space, the rapid equilibrium approximation was generally implemented in order to improve computational efficiency, a far more pressing constraint in 1999 than presently.In the original paper by 2+ release in heart failure. The model was combined with AP recordings from control and heart failure myocytes. They observed that whereas AP prolongation reduces the driving force for Ca2+ entry through the LTCCs, this is balanced by the increase in RyR sensitivity which results from steady-state increased SR-Ca2+. Thus, they conclude that other factors  underlie the loss of spatial synchrony in the CaT.In 2+ in the cytosol which emphasized the importance of the location of SERCA and its role in facilitating long-lasting Ca2+ sparks.A detailed 3D model of multiple structures surrounding a dyad, reconstructed from electron tomograms of a mouse ventricular myocyte, was presented by 2+ could diffuse in 3D, the RyRs were arranged on a 2D pancake  were not necessary to explain experimental observations, although they do state that they likely still play a role facilitating multiple points of control.A similar model was also presented in 2+), and results support the conclusions of both 2+ spark dynamics and fidelity. 2+ spark occurrence varied with the spatial arrangement, but did not consistently correlate with total RyR number, the magnitude of Ca2+ current or the surface density. This model included allosteric interactions and the authors found RyR coupling strength to be a major factor underlying sparks.In 2+ spark spatio-temporal functional properties. Because of the difficulty in measuring Ca2+ function and underlying sub-cellular structure simultaneously, computational modeling can be useful to help fill in the gaps to relate structure to function, but for the same reasons, challenging to directly validate. It is worth highlighting that the models of single nanodomains do not reproduce well experimentally measured values for the full width half maximum (FWHM) of Ca2+, generally resulting in values of ∼1 μm which are below the 1.8–2.2 μm in experiment. As the experimental structural data improves in resolution and quality it will become more feasible and important to develop models based directly on these data, requiring semi-automated image processing pipelines to produce these geometries in both 2D and 3D. This will enable the models to be applied to more specific conditions including disease states, with many pathologies producing complex and heterogeneous subcellular remodeling. However, there are still numerous challenges in regards to model validation of Ca2+ concentration is relatively large, it does pose a problem at resting/quiescent Ca2+ levels, where the low Ca2+concentration of ∼0.1 μM in small volumes of 10–21–10–18L ; similar considerations may also apply in the junctional SR during CICR when its Ca2+ load has been depleted  required to model RyR distribution: whereas this does not pose a problem during CICR, in which local Ca1–10–18L  correspodepleted . Continuramework , may off2+ spark dynamics. This presents a challenge for the translation to whole-cell modeling, as it is not feasible to simulate ∼20,000 spatially distributed dyads in a whole cell at resolutions of ∼10 nm, even if this high resolution is only adaptively applied in the local dyadic space. Therefore, in order to understand how a heterogeneous system of dyads with different RyR numbers and spatial arrangements coordinates in a whole-cell, coarse-graining methods will need to be developed which capture the features of this dyad heterogeneity at a reduced computational cost.These spatial nanodomain models have demonstrated the importance of specific RyR arrangement – and not just the total number – in determining Ca2+ can diffuse in both the cytosolic and SR spaces. It is useful now to bring in the terminology of a Ca2+-release-unit (CRU). Whereas some studies use this to refer to the dyad or individual RyRs, cellular-scale modeling studies commonly refer to all of the intracellular and SR compartments associated with a single dyad as a CRU, i.e., it can be thought of as the entire volume of cell surrounding each dyad. Typically, this will contain the network SR (NSR), bulk cytoplasmic space (cyto), and the restricted volume of the dyad (treated as a common-pool). It is also common to include a distinct junctional SR compartment (JSR), as well as other optional sub-spaces, such as the sub-sarcolemma volume just below the surface or T-system membrane, included in order to preserve the higher local Ca2+ concentration close to a dyad in regions where the membrane fluxes are located. A major focus of this section is to discuss the various approaches to modeling sub-cellular structure in regards to spatial Ca2+ coupling.Spatial models of the cardiomyocyte describe the cell as a 2D area / 3D volume throughout which dyads are distributed and within which CaCalcium homeostasis in the compartments is described by:Transfer between compartments is given by:And the general form for the reaction terms are:cyto, SS, nSR, ds, and JSR refer to the Ca2+ concentrations in each of the  compartments, β refers to the instantaneous buffering term, ϕ refers to a general reaction term in each compartment, Jx refers to transfer flux between compartments, ∇2 is the spatial Laplacian operator in 2D or 3D, describing coupling between CRUs, D is the diffusion constant, v refers to the volumes of the compartments, and τ to the time constants of diffusion. The concentration in the dyadic space can be described by a quasi-steady-state approximation, motivated by the rapid equilibration of Ca2+ in this small volume. By setting:Where An approximation for equation (27) can be obtained as in krel is defined by Jrel = krel(CaSR-Cads) and therefore corresponds to:Where gRyR is the conductance of a single RyR channel and nRyR_O is the number of open RyRs in the dyad . This approximation enables less constraint on the time-step for the simulation, allowing faster simulations to be performed. A limitation of this approximation is that the introduction of this type of equation leads to a lack of ionic Ca2+ conservation in the models; similar issues arise with the implementation of the rapid buffering approximations [β terms in equations (24) – (28)]. Models that try to analyze homeostatic properties require that the computing algorithm conserves ions at all orders  and other ion-currents/concentrations assumed to be homogeneous throughout the cell. This is justified by the fast diffusion of Vm along the cell membrane, indicating that it is valid to assume all channels “see” the same global voltage, at least, in the time-frames considered by the models; moreover, the Debye length in cardiac cells is approximately 1 nm  or biophysically detailed models of the primary ion currents and global ionic concentrations.In general, it is only the Caely 1 nm . Detaileely 1 nm , are the2+ and voltage systems are coupled through the influence of Vm on the activity of the LTCCs and NCX (and any other voltage-dependent Ca2+ channel), and feedback of Ca2+ into the voltage is captured if a biophysically detailed model of the AP is included, wherein ICaL and INaCa directly influence Vm. Thus, the interaction between global voltage and local Ca2+ dynamics can be described in these models, enabling study of the mechanisms of, for example, Ca2+-induced AP duration (APD) alternans and afterdepolarizations CRU-grid” or “compartmentalized” models, wherein the spatial resolution is ∼ 1 μm × 1 μm × 2 μm and each pixel/voxel corresponds to a single CRU;“(2)Sub-micron” or “free-diffusion” models, wherein the volumes of the SR and cytoplasm, and SS if present, are discretized within each CRU.“2+ diffusion and cellular geometry, and are better suited to direct incorporation of experimental imaging data.Details of each approach are described below. In general, the CRU-grid approach is more computationally efficient and consequently suitable for statistical simulations and high-throughput, population-cohort models of spatial structure and heterogeneity. Its simplified structure also facilitates the dissection of the mechanisms by which various components contribute to macroscopic function. The advantages of the sub-micron approach are that one can more precisely control aspects such as heterogeneous inter-dyad spacing and co-localization of different channels, they have a more accurate recapitulation of CaIn these models, each voxel contains all of the compartments contained within a CRU. Spatial coupling is described using the isotropic finite-difference method (FDM), or approximations thereof. Each CRU is coupled to its four or six nearest-neighbors  along the principal axes:ei refers to the three dimensions , the subscript c refers to any compartment which is spatially coupled , D is the diffusion coefficient and dx is the spatial step . The diffusion term (D/dx2) is often approximated with a time-constant of diffusion between spatially coupled compartments :Where dx2 in equation (40) or τ in equation (41) can be larger in the longitudinal (z) direction compared to the transverse. This therefore introduces an anisotropy  despite the model equations being derived from isotropic approximations.Note that whereas these approximations are derived from the isotropic FDM, the models are often discretized at a larger resolution in the longitudinal direction than the transverse, reflecting the larger spacing of dyads along the cell compared to along a TT. Thus, In these models, each CRU is further discretized into voxels or elements. Not every voxel necessarily contains all compartments. For example, nanodomains/jSR will only be present in a small subset of voxels, and in some models, the T-system or even nSR may also only be present in a subset of voxels. Spatial coupling is solved using FDM [equation (40)] on regular structured grids or using the more complex finite element method (FEM) on structured or unstructured meshes. They can be discretized at different choices of resolution, generally between 0.05 and 0.2 μm , althoug2+ coupling, in part due to the variable peak Ca2+ concentrations in the compartments selected for coupling: compartments which have a smaller volume and are more directly coupled to the dyad exhibit larger CaTs and thus stronger inter-CRU coupling compared to larger compartments which are less directly coupled to the dyad. In this context, coupling strength refers only to the intracellular space, not the SR, the spatial coupling of which is independently controlled. Broadly, there can be considered four different structures which the models follow  act. This subspace has a smaller volume and higher Ca2+ concentrations at peak than the bulk cytoplasm. This sub-space is generally coupled between CRUs in the transverse direction only, i.e., along the TTs. Longitudinal coupling of this sub-space may be present where ATs are modeled, but does not by default occur for every CRU throughout the cell. Coupling strength is higher than the simplest type 1 models due to the larger CaT in this sub-space. Models of this type include Many models also include a sub-sarcolemmal subspace from/into which the other membrane fluxes  were originally designed to represent atrial cells with no T-system: interior compartments did not contain the SL fluxes or associated sub-space. However, models of type 1–3 can be generalized to match this structure by removing these same SL fluxes and associated sub-space (where present) from interior CRUs, e.g., as in 2+ propagation. Broadly, models with weaker inter-CRU Ca2+ coupling (type 1–2 above) tend to contain either a physiologically sized CaT and operate at the threshold of Ca2+ propagation, or contain a substantially larger CaT (>2–8 μM) with more robust Ca2+ propagation (2+ release in some of these models. Models with stronger inter-CRU coupling (type 3–4 above) tend to contain more robust Ca2+ propagation while maintaining physiologically sized CaTs , as in 2+-wave propagation, such as in the atria. The implications of these differences are far-reaching: Ca2+ propagation is relevant for graded release of CICR, the dynamics of CaT alternans, success or failure of triggered Ca2+ wave propagation into regions without T-system, and the dynamics of spontaneous Ca2+ sparks and waves.One major feature of the differences between these models is the relationship between RyR sensitivity, inter-CRU coupling strength and the size of the CaT in normal pacing, which has significant implications for the robustness of inter-CRU Capagation . Alterna2+-voltage interactions during SCRE or alternans, it may be best to prioritize CaT magnitude (as this will determine the degree of Ca2+-induced inactivation of ICaL and the magnitude of INCX which feedback into the voltage) and use a more “functional” description of inter-CRU coupling (types 3–4) in order to maintain robust Ca2+ propagation. However, if the focus of the study is on the mechanisms and implications of inter-CRU coupling then the simpler and  more physiologically justified inter-CRU coupling structures (types 1–2) may be prioritized. These considerations may be particularly relevant for the development of atrial cell models and those with variable T-system density, and will be discussed in this context in more detail in the next section.These features and limitations, generally discussed openly in the original papers, do not detract from the ambitions of the various studies nor question their analyses, as model choices are motivated by the focus of the specific study. It is important to note that all approaches are capable of reproducing all of the phenomena described above, including properties such as the statistics of SCRE and dynamics of alternans, although various model parameters are likely to be substantially different in order to reproduce these same macroscopic features. Nevertheless, it is still important to carefully consider the motivations of the study for model selection. As an oversimplified example, if the ambition is to study Ca2+ coupling. Further to this, it is these authors’ opinion that future studies would do well to implement multiple, disparate models in order to navigate the limitation of model-dependent conclusions.These disparities and compromises indicate that there are fundamental properties of the CaT and inter-CRU coupling which we do not fully understand, and these gaps in our understanding and model differences reflect the large degree of uncertainty in the experimental data on which the models are based. There is an important possibility that different internal structures need different behavior at the dyadic level since weaker coupling generally requires stronger transients to reproduce wave-like propagation. This might lead to important model-dependent conclusions on new research issues. As models become more sophisticated, getting closer to genuine cell- and species- specificity (indeed as more data become available), and are applied in more complex and clinically oriented studies, it will become imperative to solve these issues and develop models which include fully physiologically justified descriptions of RyRs and spatial Ca2+ cycling.Cardiomyocytes demonstrate a large degree of inter-cellular, inter-subject and inter-species heterogeneity in properties such as ion-channel expression and sub-cellular structure, and recent studies have highlighted the importance of including such variabilities in, for example, predictive models of pharmacology . This se2+ sparks will occur only in regions of the cell where LTCCs are closely coupled to RyRs  are primarily regulated by CaSR and were fit to experimental data to describe Ca2+-wave velocity, enabling many features of whole-cell SCRE to be captured at a significantly reduced cost.Where τIn Inter-CRU coupling was described using a spatially exponential function such that the influence of one CRU on its neighbors decays rapidly as distance increases:rj is the Ca2+ released at site j, xi, and xj are the locations of the two coupled CRUs and l is the diffusive length-scale. This model was used to evaluate the influence of CRU connectivity on Ca2+-wave nucleation and propagation.Where 2+ concentrations from one beat to the next . This is a spatial analog of the iterative-map approach described in the next sub-section. Concentrations for beat n+1 are functions of concentrations and fluxes during beat n:In SRx and Caix are the SR and intracellular Ca2+ concentrations at the spatial point x , Rx(n) is the total Ca2+ released from the SR at point x during beat n and Ux(n) is the total Ca2+ pumped back into the SR at point x during beat n. As a simplification, it is assumed that the total Ca2+ is conserved (CaSR + Cai = C) and can be thusly normalized to 1 (arbitrary units). The stochastic dependence of intracellular Ca2+ release (Rx) on voltage can be incorporated by accounting for the probability of release, and intracellular uptake is given as a function of the CaT peak. Ca2+ diffusion was then described by accounting for the average Ca2+ over the nearest neighbors in the 2D lattice of CRUs.Where Ca2+ load and RyR refractoriness on the dynamics of CaT alternans.In Further simplification can be achieved by developing non-spatial (or “0D”) approximations, which have no explicit description of spatial diffusion in the sub-cellular volume and present the opportunity for the largest increases in computational efficiency. Several different techniques have been proposed.In n+) and extinguished (Δn–) at each time-step (Δt):In studies by The number of sparks initiated was determined by the rate at which sparks are recruited (either spontaneous or triggered) and stochasticity was maintained through the use of random number sampling. This used a similar approach to individual CRU recruitment to that of 2+ and voltage properties on a beat-to-beat basis (peak). Thus, the APD at the current cycle (n) depends on the previous cycle (n-1) and is given by:at basis , a whole2+ have been separated: f1 is the APD restitution function and f2 accounts for the coupling strength between Ca2+ and APD (which can be positive or negative). The peak Ca2+ concentration at cycle n can be given by the sum of the diastolic Ca2+ from the previous cycle (Can–1) and the total Ca2+ released from the SR in the current cycle (rn):Where the functions of DI and intracellular Ca2+ released from the SR, rn, is given by:The total Caf3 describes the restitution properties of SR-Ca2+ release  and f4 describes the dependence of Ca2+ release on the SR-Ca2+ load. The reader is referred to the original publication for full details on the parameters and functions involved. This model reproduced the non-linear dynamics of Ca2+ handling including CaT alternans, and this simplification helped to develop a unified theory of CaT alternans in cardiac cells (Where ac cells . FurtherJrel) associated with SCRE was controlled by imposing a waveform defined by two sigmoidal functions, the parameters of which determined the timing, duration and magnitude of SCRE:As an alternative to the above approaches, it is also possible to control spontaneous CaTs in otherwise deterministic cell models by imposing (or clamping) SCRE waveforms . In Xie Gspont is a rate constant , t0 was set to 425 ms and τ1 = 10 ms and τ2 = 30 ms. The model was used to determine the minimum number of cells undergoing DADs in various tissue conditions in order for this to manifest as a focal excitation. Whereas not performed in the original study, the timing and duration parameters  could be randomly sampled from distributions to reproduce stochasticity in independent cellular SCRE. This approach was used in i associated with SCRE was directly controlled, described by a Gaussian-shaped function with equivalent parameters to control timing, magnitude and duration:Where A sets the maximum amplitude, t0 sets the latency (timing) and σ sets the duration. In Where ti is the initiation time  of the SCRE, tf is the end time , tp is the time of the peak of the waveform and NRyR_Opeak is the peak proportion of open RyRs. In this model, NRyR_O [equation (55)] replaces the “O” in the Jrel equation [equation (5)] and so Jrel and the CaT are allowed to dynamically evolve according to their deterministic functions; the magnitude of the CaT associated with the SCRE is therefore dependent on NRyR_Opeak, the SR-Ca2+ and Jrel maximal flux rate. This model demonstrated feedback between re-entry and focal excitation in which the rapid activation during re-entry loads the SR-Ca2+ to promote focal excitations following re-entry termination , but the cost of this inclusion is smaller than the typical differences in computational efficiency between common-pool models which feature a different number of components and governing equations.In all implementations, the parameters defining the distributions which describe SCRE statistics could be set as a function of environmental variables, such as SR-Ca2+ waves and DADs in single cells, and used the 1D fiber model to translate these features to tissue activity. From this, they developed a spatial-average filtering model which aimed to estimate Vm from intracellular release fluxes, enabling the estimation of the probabilities of “extreme”  events in which multiple cells synchronously undergo large-scale SCRE, i.e., the requirements for focal excitations. This type of approach is powerful and important because the generation of a serious arrhythmia in an individual is often a very rare event that cannot be robustly or consistently captured in simulations of a generally normally functioning heart. In agreement with other studies . Nevertheless, the general agreement between models is encouraging and the availability of multiple different models provides the opportunity to comprehensively test hypotheses and explore fundamental theories. As computational power increases, experimental imaging data improves, and more powerful coarse-graining techniques are developed, the relevance, scope and power of these models will only continue to increase.Recent advances in the robustness, complexity and sophistication of computational models of spatial Ca2+ sparks, such as the spatial FWHM, do not necessarily match experimental observations. This is not the only difficulty associated with obtaining a realistic and well-validated description of RyR gating: Integration of spark properties in the context of whole-cell homeostasis is also highly challenging due to the interaction with the wider model system and further constraints on model stability and long-term dynamics.There are a number of challenges and avenues for future development and innovation. Robust validation of the models remains a major difficulty, not-least because of the challenges in obtaining sufficient and congruent experimental data to validate the many interacting model components and emergent functional phenomena. Validation of the governing RyR models themselves, in isolation and in the context of the spatial-nanodomain, is non-trivial - important features of Ca2+ coupling, corresponding to fundamentally different underlying model structures. Each approach has associated features of the CaT and Ca2+-handling dynamics, such as the robustness of Ca2+-wave propagation; certainly, not all of these structures and parameter combinations can simultaneously accurately describe real myocytes, and there are therefore fundamental questions about the mechanisms of inter-CRU Ca2+ diffusion which remain to be resolved. Nevertheless, the success of these models to explain and provide interpretations into experimental results is highly encouraging, especially in the more recent studies which combine experiment and simulation and are indeed beginning to resolve some of these issues.At the whole-cell scale, many approaches have been implemented to describe spatial Ca2+ gradients and channel distribution – combining these models with detailed representations of RyR arrangement in nanodomains, models of counter-ion fluxes, and the electrophysiology of the T-tubule membrane itself presents exciting prospects for powerful and highly accurate models of local control; again, translating these to the whole-cell scale is associated with a number of challenges. Initial success has been achieved in models attempting to preserve the impact of stochastic spatial Ca2+ dynamics in reduced, computationally efficient cell models suitable for tissue simulations, revealing the mechanisms of ectopic excitation, its interaction with re-entry, and dependence on tissue structure. Generalizing these models to naturally capture the dynamics of heterogenous populations of cells, themselves depending on heterogeneous sub-cellular structure, remains a major goal.One of the most exciting and challenging prospects is true multi-scale model integration. The recent spatial models of single nanodomains highlight the importance of specific RyR arrangement and microstructure of the dyad; incorporating these features into a whole-cell model containing tens of thousands of heterogeneous dyads is far from trivial. The detailed models of the local regions of a single T-tubule reveal important features of local CaFinally, there have been substantial advances in approaches for image-based modeling, both for high-throughput, population-cohort simulations, and for direct integration of experimental structures. Closely related to advances in experimental imaging modalities, this is occurring at multiple spatial scales including the nanodomain, localized sub-cellular regions, whole-cells, and whole-heart. The further development and automation of these experimental-simulation frameworks presents exciting prospects for the true mechanistic analysis of structure-function relationships underlying cardiac electrophysiology from the nanometer to the whole-heart.MC conceived the review, drafted and edited the manuscript, and prepared the illustrations. All the authors drafted and edited the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


In computer science, clustering is a technique for grouping data. Ising machines can solve distance-based clustering problems described by quadratic unconstrained binary optimization (QUBO) formulations. A typical simple method using an Ising machine makes each cluster size equal and is not suitable for clustering unevenly distributed data. We propose a new clustering method that provides better performance than the simple method, especially for unevenly distributed data. The proposed method is a hybrid algorithm including an iterative process that comprises solving a discrete optimization problem with an Ising machine and calculating parameters with a general-purpose computer. To minimize the communication overhead between the Ising machine and the general-purpose computer, we employed a low-latency Ising machine implementing the simulated bifurcation algorithm with a field-programmable gate array attached to a local server. The proposed method results in clustering 200 unevenly distributed data points with a clustering score 18% higher than that of the simple method. The discrete optimization with 2000 variables is performed 100 times per iteration, and the overhead time is reduced to approximately 20% of the total execution time. These results suggest that hybrid algorithms using Ising machines can efficiently solve practical optimization problems. Ising machines, which are special-purpose computers for solving combinatorial optimization problems, have attracted significant interest in recent years. Inspired by the first quantum annealer2, several devices have been developed, such as digital processors based on simulated annealing (SA)9, those on simulated bifurcation (SB)12, coherent Ising machines implemented with pulsed lasers18, and other types of optical Ising machines21. Most Ising machines accept an objective function in the form of a Hamiltonian formulated by the Ising model or QUBO formulation. Ising machines return binary solutions that minimize the objective function, although they do not always return optimal solutions because of their heuristic nature. Recent research on the application of Ising machines has shifted from simple combinatorial optimization to hybrid methods using both an Ising machine and a general-purpose computer27. Most hybrid methods are iterative methods that offload the sampling or combinatorial optimization step to an Ising machine.Many combinatorial optimization problems can be described by the Ising model or quadratic unconstrained binary optimization (QUBO) formulations36. Clustering methods using a quantum computer and a quantum annealer have also been proposed and investigated38. A typical simple method using an Ising machine minimizes the distances between data points in the same cluster, resulting in cluster sizes that are approximately equal35. Let us suppose that a small group is away from other large groups. Then, using this method, part of a large group is merged into a small group such that the number of members in each group becomes almost equal. This implies that this method is not suitable for clustering unevenly distributed data.Clustering is a technique for grouping data such that the members in each cluster have similar characteristics. Although there are various types of clustering, this work focuses on non-hierarchical and distance-based clustering. Because clustering can be formulated as a combinatorial optimization problem, several algorithms using Ising machines have been developedIn this work, we propose a clustering method using an Ising machine that applies to unevenly distributed data. We compare the clustering of two data sets, one uniformly distributed and the other unevenly distributed, using the simple method and the proposed method. Employing the average silhouette coefficient, we evaluate clustering performance. The proposed method provides better clustering results than the simple method, especially for unevenly distributed data. The proposed method is a hybrid algorithm that solves discrete optimization problems iteratively. The discrete optimization described in a QUBO formulation is performed by an Ising machine, while a general-purpose  computer calculates parameters for the QUBO formulation in each iteration.12. The low latency of the SB-based machine is advantageous for executing the proposed method. Because the method requires the iterative computation of discrete optimization, a low communication cost between an Ising machine and a general-purpose computer is essential for high performance.The proposed method could be implemented in one of three possible ways: (i) discrete optimization executed on a remote Ising machine provided as a cloud service, (ii) discrete optimization undertaken using a local Ising machine, and (iii) all computations undertaken on a local general-purpose computer. The first approach incurs a high communication cost with the Ising machine, and so is unsuitable for hybrid algorithms. The second implementation option offloads the computation of discrete optimization steps to the accelerator attached to a local server. This approach has the benefit of a much lower communication cost with the Ising machine than the first approach. In this work, we compare the second and third implementations. The Ising machine used is an SB-based machine implemented with a field-programmable gate array (FPGA)This work demonstrates that the proposed hybrid method using an Ising machine provides high-quality results in clustering problems. The method’s effectiveness suggests a new usage that takes advantage of a low-latency Ising machine. Moreover, this work will highly motivate developing iterative hybrid algorithms. Although hybrid algorithms using an Ising machine and a general-purpose computer take extra time for communication, they have many practical applications. The reduction in communication cost enables iterative hybrid algorithms to solve practical optimization problems efficiently. The proposed method will also be applicable as a quantum-classical hybrid algorithm when the communication cost reduces significantly.37 and graph partitioning33 using a quantum annealer still attract some interest. Several methods inspired by classical clustering have been proposed and developed recently. For example, quantum-assisted clustering based on similarities28, K-means31 and K-Medoids32 clustering on a quantum annealer, as well as K-means clustering on a gate-model quantum computer38, have been proposed. K-means-like clustering on a digital Ising machine has also been investigated36.We briefly review some recent works on the clustering method using Ising machines and quantum computers. Simple distance-based clustering is a typical example using an Ising machine or a quantum computer. Simple clustering methods based on the distance between data pointsi and j, N is the number of points, and G is the number of groups. The sum i belongs to group g, We examine two clustering methods. One is the typical simple method in which the Hamiltonian is given asg. The number of nonzero terms in g, i.e., g, where a factor of 2 is omitted for simplicity. In other words, the first term on the right-hand side of Eq.  is a control parameter that increases from zero to ith spin: ith particle, respectively. Classical particles interact in a potential whose shape gradually changes. The sign of SB has several variants, the first of which was adiabatic SB (aSB). The set of equations for aSB is given byd by Eq. . Because12. Instead of the nonlinear term 12.kth time step, and The ballistic SB used in this work was developed to suppress analog errors3 in Eq. , perfectThe hyperparameter mentclass2pt{minim in Eqs.  are tunea(t), that is, In SA, the parameter controlling the annealing time is the number of sweeps or steps, called num_sweeps in the dwave-neal package. In SB, the number of steps  in Eqs.  and 9)..\documeni is defined bya(i) is the mean distance between point i and the other points in the same group, and b(i) is the mean distance between point i and points in the neighboring group. However, if a point belongs to several groups or does not belong to any group, the silhouette coefficient cannot be properly calculated. Therefore, we calculate the silhouette coefficient for a feasible solution in which each point belongs to exactly one group and take the average over all the points in the feasible solution.The silhouette coefficient is defined for each data point, and it is higher when the point belongs to a well-defined cluster. The silhouette coefficient for point