Empirical Determination of the Tolerable Sample Size for Ols Estimator in the Presence of Multicollinearity (<i>ρ</i>)

This paper investigates the tolerable sample size needed for Ordinary Least Square (OLS) Estimator to be used when there is presence of Multicollinearity among the exogenous variables of a linear regression model. A regression model with constant term (β0) and two independent variables (with β1 and β2 as their respective regression coefficients) that exhibit multicollinearity was considered. A Monte Carlo study of 1000 trials was conducted at eight levels of multicollinearity (0, 0.25, 0.5, 0.7, 0.75, 0.8, 0.9 and 0.99) and sample sizes (10, 20, 40, 80, 100, 150, 250 and 500). At each specification, the true regression coefficients were set at unity while 1.5, 2.0 and 2.5 were taken as the hypothesized value. The power value rate was obtained at every multicollinearity level for the aforementioned sample sizes. Therefore, whether the hypothesized values highly depart from the true values or not once the multicollinearity level is very high (i.e. 0.99), the sample size needed to work with in order to have an error free estimation or the inference result must be greater than five hundred.

Stepwise Method Based on Confidence Bound and Information Incorporation for Identifying the Maximum Tolerable Dose

The primary goal of a phase I clinical trial is to find the maximum tolerable dose of a treatment. In this paper, we propose a new stepwise method based on confidence bound and information incorporation to determine the maximum tolerable dose among given dose levels. On the one hand, in order to avoid severe even fatal toxicity to occur and reduce the experimental subjects, the new method is executed from the lowest dose level, and then goes on in a stepwise fashion. On the other hand, in order to improve the accuracy of the recommendation, the final recommendation of the maximum tolerable dose is accomplished through the information incorporation of an additional experimental cohort at the same dose level. Furthermore, empirical simulation results show that the new method has some real advantages in comparison with the modified continual reassessment method.

Endoscopic ultrasound sedation in the United Kingdom: Is life without propofol tolerable?

There is compelling evidence to support the quality,cost effectiveness and safety profile of non-anesthesiologist-administered propofol for endoscopic ultrasound (EUS). However in the United Kingdom, it is recommended that the administration and monitoring of propofol sedation for endoscopic procedures should be the responsibility of a dedicated and appropriately trained anaesthetist only. The majority of United Kingdom EUS procedures are performed with opiate and benzodiazepine sedation rather than anaesthetist led propofol lists due to anaesthetist resource availability. We sought to prospectively determine the tolerability and safety of EUS with benzodiazepine and opiate sedation in single United Kingdom centre. Two hundred consecutive patients undergoing either EUS or oesophago-gastroduodenoscopy (OGD) with conscious sedation were prospectively recruited with a 1:1 enrolment ratio. Patients completed questionnaires pre and post procedure detailing anticipated and actual pain experienced on a 1-10 visual analogue scale. Demographics, procedure duration, sedation doses and willingness to repeat the procedure were also recorded. EUS procedures lasted significantly longer than OGDs(15 min vs 6 min, P < 0.0001), however, there was no difference in anticipated pain scores between the groups(EUS 3.37/10 vs OGD 3.47/10, P = 0.46). Pain scores indicated EUS was better tolerated than OGD(1.16/10 vs 1.88/10, P = 0.03) although higher doses of sedation were used for EUS procedures. There were no complications identified in either group. We feel our study demonstrates that the tolerability of EUS with opiate and benzodiazepine sedation is acceptable.

Is a split-dose regimen of 2 L polyethylene glycol plus ascorbic acid tolerable for colonoscopy in an early morning visit to a comprehensive medical check-up?

To evaluate the effectiveness and tolerability of a split-dose 2 L polyethylene glycol (PEG)/ascorbic acid (AA) regimen for healthy examinees who visited for comprehensive medical check-up in the early morning.METHODSFrom February 2015 to March 2015, examinees of average risk who were scheduled for a colonoscopy in the morning were retrospectively enrolled.RESULTSThe 189 examinees were divided into split-dose and non-split-dose groups. The adequacy of bowel preparation for the split-dose group vs the non-split-dose group was 96.8% vs 85.2%, respectively, P < 0.001, and the compliance of the last meal restriction was 74.6% vs 58.2%, respectively, P < 0.001. The sleep disturbance (P < 0.001) was more prevalent in the split-dose group, however the willingness to repeat the same preparation method (P = 0.243) was not different in both groups. The split-dose regimen was the most important factor influencing adequate bowel preparation in multivariate analysis (HR = 10.89, 95%CI: 6.53-18.17, P < 0.001).CONCLUSIONA split-dose regimen of 2 L PEG/AA for an early morning colonoscopy was more effective and showed better compliance for diet restriction without any difference in satisfaction and discomfort. Introducing a split-dose regimen of 2 L PEG/AA to morning colonoscopy examinees is effective and tolerable in a comprehensive medical check-up setting.

Estimation of Fading Statistics of Nakagami Channel with Weibull Distributed Tolerable Outage Time

Characterization of a mobile radio channel plays an important role in designing a reliable wireless communication system. Such channels are analyzed by two state model, namely satisfactory and outage state. This paper presents the analysis to estimate fading parameters of wireless channel with omission of certain outage durations which are considered as “Tolerance time”. Minimum outage duration which can be tolerated by a wireless fading channel to achieve desired packet error rate is defined as tolerance time. Normally a system with tolerable minimum outage time is analyzed based on Fade Duration Distribution (FDD) function over Rayleigh channel. In this paper Weibull function is used as FDD for varying tolerance time. The approach is simple and in general applicable from Rayleigh to Nakagami channels. The analysis is extended to study the effect of Tolerance time on channel fading statistics such as Average Fade Duration (AFD) and frequency of outage. Further the effects of various fade margin and Doppler spread on fading parameters are also investigated. The analysis can also be used in case of timeout expiration, connection resetting and congestion window control.

Bi-criteria Optimal Fault-Tolerable Control for SY-II Remote Operated Vehicle

This paper proposed a bi-criteria weighting approach for fault tolerant control(FTC)of SY-II remote operated vehicle(ROV).This approach integrates the minimum kinetic energy(2-norm optimal)approach with the infinity-norm approach through a weighting coefcient,on the basis of SY-II ROV force allocation model.For the realization of fault tolerable control,this approach converts a quadratic programming problem into primaldual neural network.From the motion control simulations and experiments,bi-criteria optimization approach outperforms minimum kinetic energy optimization in FTC,SY-II ROV can realize 2-degree of freedom(DOF)horizontal fault tolerant control with one main thruster and any of horizontal ones.Therefore,this scheme is proved to be of superiority and computational efciency,both the reliability and safety for ROV have been improved.

An Environment‑Tolerant Ion‑Conducting Double‑Network Composite Hydrogel for High‑Performance Flexible Electronic Devices

High-performance ion-conducting hydrogels(ICHs)are vital for developing flexible electronic devices.However,the robustness and ion-conducting behavior of ICHs deteriorate at extreme tempera-tures,hampering their use in soft electronics.To resolve these issues,a method involving freeze–thawing and ionizing radiation technology is reported herein for synthesizing a novel double-network(DN)ICH based on a poly(ionic liquid)/MXene/poly(vinyl alcohol)(PMP DN ICH)system.The well-designed ICH exhibits outstanding ionic conductivity(63.89 mS cm^(-1) at 25℃),excellent temperature resistance(-60–80℃),prolonged stability(30 d at ambient temperature),high oxidation resist-ance,remarkable antibacterial activity,decent mechanical performance,and adhesion.Additionally,the ICH performs effectively in a flexible wireless strain sensor,thermal sensor,all-solid-state supercapacitor,and single-electrode triboelectric nanogenerator,thereby highlighting its viability in constructing soft electronic devices.The highly integrated gel structure endows these flexible electronic devices with stable,reliable signal output performance.In particular,the all-solid-state supercapacitor containing the PMP DN ICH electrolyte exhibits a high areal specific capacitance of 253.38 mF cm^(-2)(current density,1 mA cm^(-2))and excellent environmental adaptability.This study paves the way for the design and fabrication of high-performance mul-tifunctional/flexible ICHs for wearable sensing,energy-storage,and energy-harvesting applications.

Compositional and Hollow Engineering of Silicon Carbide/Carbon Microspheres as High-Performance Microwave Absorbing Materials with Good Environmental Tolerance

Microwave absorbing materials(MAMs)characterized by high absorption efficiency and good environmental tolerance are highly desirable in practical applications.Both silicon carbide and carbon are considered as stable MAMs under some rigorous conditions,while their composites still fail to produce satisfactory microwave absorption performance regardless of the improvements as compared with the individuals.Herein,we have successfully implemented compositional and structural engineering to fabricate hollow Si C/C microspheres with controllable composition.The simultaneous modulation on dielectric properties and impedance matching can be easily achieved as the change in the composition of these composites.The formation of hollow structure not only favors lightweight feature,but also generates considerable contribution to microwave attenuation capacity.With the synergistic effect of composition and structure,the optimized SiC/C composite exhibits excellent performance,whose the strongest reflection loss intensity and broadest effective absorption reach-60.8 dB and 5.1 GHz,respectively,and its microwave absorption properties are actually superior to those of most SiC/C composites in previous studies.In addition,the stability tests of microwave absorption capacity after exposure to harsh conditions and Radar Cross Section simulation data demonstrate that hollow SiC/C microspheres from compositional and structural optimization have a bright prospect in practical applications.

MIR1868 negatively regulates rice cold tolerance at both the seedling and booting stages

Low temperature causes rice yield losses of up to 30%–40%,therefore increasing its cold tolerance is a breeding target.Few genes in rice are reported to confer cold tolerance at both the vegetative and reproductive stages.This study revealed a rice-specific 24-nt miRNA,miR1868,whose accumulation was suppressed by cold stress.Knockdown of MIR1868 increased seedling survival,pollen fertility,seed setting,and grain yield under cold stress,whereas its overexpression conferred the opposite phenotype.Knockdown of MIR1868 increased reactive oxygen species(ROS)scavenging and soluble sugar content under cold stress by increasing the expression of peroxidase genes and sugar metabolism genes,and its overexpression produced the opposite effect.Thus,MIR1868 negatively regulated rice cold tolerance via ROS scavenging and sugar accumulation.

Making wheat salt tolerant:What is missing?

The growing global population presents a significant challenge to ensuring food security,further compounded by the increasing threat of salinity to agricultural productivity.Wheat,a major staple food providing 20%of the total caloric intake for humans,is susceptible to salinity stress.Developing new salttolerant wheat cultivars using wheat breeding techniques and genetic modifications is crucial to addressing this issue while ensuring the sustainability and efficiency of wheat production systems within the prevailing climate trend.This review overviews the current landscape in this field and explores key mechanisms and associated genetic traits that warrant attention within breeding programs.We contend that traditional approaches to breeding wheat for Na^(+)exclusion have limited applicability across varying soil salinity levels,rendering them inefficient.Moreover,we question current phenotyping approaches,advocating for a shift from whole-plant assessments to cell-based phenotyping platforms.Finally,we propose a broader use of wild wheat relatives and various breeding strategies to tap into their germplasm pool for inclusion in wheat breeding programs.

PHD17 acts as a target of miR1320 to negatively control cold tolerance via JA-activated signaling in rice

Plant Homeo Domain(PHD)proteins are involved in diverse biological processes during plant growth.However,the regulation of PHD genes on rice cold stress response remains largely unknown.Here,we reported that PHD17 negatively regulated cold tolerance in rice seedlings as a cleavage target of miR1320.PHD17 expression was greatly induced by cold stress,and was down-regulated by miR1320 overexpression and up-regulated by miR1320 knockdown.Through 5'RACE and dual luciferase assays,we found that miR1320 targeted and cleaved the 3'UTR region of PHD17.PHD17 was a nuclearlocalized protein and acted as a transcriptional activator in yeast.PHD17 overexpression reduced cold tolerance of rice seedlings,while knockout of PHD17 increased cold tolerance,partially via the CBF cold signaling.By combining transcriptomic and physiological analyses,we demonstrated that PHD17 modulated ROS homeostasis and flavonoid accumulation under cold stress.K-means clustering analysis revealed that differentially expressed genes in PHD17 transgenic lines were significantly enriched in the jasmonic acid(JA)biosynthesis pathway,and expression of JA biosynthesis and signaling genes was verified to be affected by PHD17.Cold stress tests applied with MeJA or IBU(JA synthesis inhibitor)further suggested the involvement of PHD17 in JA-mediated cold signaling.Taken together,our results suggest that PHD17 acts downstream of miR1320 and negatively regulates cold tolerance of rice seedlings through JA-mediated signaling pathway.

The ZOS7-MYB60 module confers drought-stress tolerance in rice

Shanlan upland rice is an important landrace resource with high drought stress(DS)tolerance.Despite its importance,genes responsible for yield in Shanlan upland rice have yet to be discovered.Our previous study identified a drought-responsive zinc finger protein,ZOS7,as highly expressed in Shanlandao upland rice.However,the function of this gene in controlling drought tolerance remains largely unexplored.In this study,we found that overexpressing ZOS7,a drought-responsive zinc finger protein,in rice increased biomass and yield under drought stress.Co-overexpressing ZOS7 and MYB60,encoding a protein with which ZOS7 interacted,intensified the yield increase.ZOS7 and MYB60 appear to form a module that confers drought tolerance by regulating stomatal density and wax biosynthesis.The ZOS7-MYB60module could be used in molecular breeding for drought tolerance in rice.

Abiotic stress treatment reveals expansin like A gene OfEXLA1 improving salt and drought tolerance of Osmanthus fragrans by responding to abscisic acid

Sweet osmanthus(Osmanthus fragrans) is a having general approval aromatic tree in China that is widely applied to landscaping and gardening. However, the evergreen tree adaptability is limited by many environmental stresses. Currently, limited information is available regarding the genetic analysis and functional identification of expansin genes in response to abiotic stress in sweet osmanthus. In this study, a total of 29 expansin genes were identified and divided into four groups by genome-wide analysis from the sweet osmanthus genome. Transcriptome and quantitative Real-time PCR analysis showed that the cell wall-localized protein expansin-like A(OfEXLA1) gene was significantly induced by salt and drought treatment. Histochemical GUS staining of transgenic Arabidopsis lines in which GUS activity was driven with the OfEXLA1 promoter, GUS activity was significantly induced by salt, drought, and exogenous abscisic acid(ABA). In yeast, we found OfEXLA1overexpression significantly improved the population of cells compared with wild-type strains after NaCl and polyethylene glycol(PEG)treatment. Additionally, OfEXLA1 overexpression not only promoted plant growth, but also improved the salt and drought tolerance in Arabidopsis. To gain insight into the role of ABA signaling in the regulation of OfEXLA1 improving abiotic tolerance in sweet osmanthus, four differentially expressed ABA Insensitive 5(ABI5)-like genes(OfABL4, OfABL5, OfABL7, and OfABL8) were identified from transcriptome, and dualluciferase(dual-LUC) and yeast one hybrid(Y1H) assay showed that OfABL4 and OfABL5 might bind to OfEXLA1 promoter to accumulate the OfEXLA1 expression by responding to ABA signaling to improve abiotic tolerance in sweet osmanthus. These results provide the information for understanding the molecular functions of expansin-like A gene and molecular breeding of sweet osmanthus in future.

A Data Intrusion Tolerance Model Based on an Improved Evolutionary Game Theory for the Energy Internet

Malicious attacks against data are unavoidable in the interconnected,open and shared Energy Internet(EI),Intrusion tolerant techniques are critical to the data security of EI.Existing intrusion tolerant techniques suffered from problems such as low adaptability,policy lag,and difficulty in determining the degree of tolerance.To address these issues,we propose a novel adaptive intrusion tolerance model based on game theory that enjoys two-fold ideas:(1)it constructs an improved replica of the intrusion tolerance model of the dynamic equation evolution game to induce incentive weights;and (2)it combines a tournament competition model with incentive weights to obtain optimal strategies for each stage of the game process.Extensive experiments are conducted in the IEEE 39-bus system,whose results demonstrate the feasibility of the incentive weights,confirm the proposed strategy strengthens the system’s ability to tolerate aggression,and improves the dynamic adaptability and response efficiency of the aggression-tolerant system in the case of limited resources.

Boosting oxygen reduction activity and CO_(2) resistance on bismuth ferrite-based perovskite cathode for low-temperature solid oxide fuel cells below 600℃

Developing efficient and stable cathodes for low-temperature solid oxide fuel cells(LT-SOFCs) is of great importance for the practical commercialization.Herein,we propose a series of Sm-modified Bi_(0.7-x)Sm_xSr_(0.3)FeO_(3-δ) perovskites as highly-active catalysts for LT-SOFCs.Sm doping can significantly enhance the electrocata lytic activity and chemical stability of cathode.At 600℃,Bi_(0.675)Sm_(0.025)Sr_(0.3)FeO_(3-δ)(BSSF25) cathode has been found to be the optimum composition with a polarization resistance of 0.098 Ω cm^2,which is only around 22.8% of Bi_(0.7)Sr_(0.3)FeO_(3-δ)(BSF).A full cell utilizing BSSF25 displays an exceptional output density of 790 mW cm^(-2),which can operate continuously over100 h without obvious degradation.The remarkable electrochemical performance observed can be attributed to the improved O_(2) transport kinetics,superior surface oxygen adsorption capacity,as well as O_(2)p band centers in close proximity to the Fermi level.Moreover,larger average bonding energy(ABE) and the presence of highly acidic Bi,Sm,and Fe ions restrict the adsorption of CO_(2) on the cathode surface,resulting in excellent CO_(2) resistivity.This work provides valuable guidance for systematic design of efficient and durable catalysts for LT-SOFCs.

Gastric cancer liver metastasis will reduce the efficacy of immunotherapy

Immune checkpoint inhibitors augment the antitumor activity of T cells by inhibiting the negative regulatory pathway of T cells,leading to notable efficacy in patients with non-small cell lung cancer,melanoma,and other malignancies through immunotherapy utilization.However,secondary malignant liver tumors not only lower the liver's sensitivity to immunotherapy but also trigger systemic immune suppression,resulting in reduced overall effectiveness of immune therapy.Patients receiving immunotherapy for non-small cell lung cancer and melanoma experience reduced response rates,progression-free survival,and overall survival when secondary malignant tumors develop in the liver.Through Liu's retrospective analysis,valuable insights are provided for the future clinical management of these patients.Therefore,in patients with gastric cancer(GC),the occurrence of liver metastasis might be indicative of reduced efficacy of immuno-therapy.Overcoming liver immune tolerance mechanisms and their negative impacts allows for the potential benefits of immunotherapy in patients with GC and liver metastasis.INTRODUCTION Gastric cancer(GC)ranks among the prevalent malignancies affecting the digestive system globally.Based on the latest epidemiological data[1,2],it holds the fifth position for incidence and the fourth position for mortality among all malignant tumors.GC cases and fatalities in China make up roughly half of the worldwide figures.Earlier investigations[3]have demonstrated that the median overall survival(mOS)among advanced GC patients left untreated typically ranges from 3 to 4 months.Systemic chemotherapy recipients often experience a mOS of around one year,accompanied by a marked improvement in the quality of life among patients with advanced GC.The mainstay of treatment for advanced GC patients involves chemotherapeutic medications such as fluoropyrimidines,platinum compounds,and taxanes.However,their efficacy in tumor control is constrained by acquired resistance and primary resistance.The rise of personalized precision therapy has propelled immunotherapy into the spotlight as a crucial component of comprehensive treatment[4].By blocking the negative regulatory pathways of T cells,immune checkpoint inhibitors(ICIs)boost the anti-tumor effect of T cells.Immunotherapy has brought about significant therapeutic benefits for patients diagnosed with non-small cell lung cancer,melanoma,and related illnesses[5,6],instilling newfound hope in those with advanced GC[7].However,phase III clinical trial data[8-12]reveals that the incorporation of immunotherapy into chemotherapy regimens improves overall survival(OS)outcomes for patients with advanced GC.The liver's immune-exempt nature renders it less responsive to immunotherapy when secondary malignant tumors are present,fostering systemic immune suppression and yielding unfavorable outcomes in immune therapy[13-15].In retrospective research[16-20]pertaining to non-small cell lung cancer and melanoma,it has been observed that the presence of secondary liver malignancies may lower the response rate,progression-free survival(PFS),and OS rates in patients treated with immunotherapy,independent of factors such as tumor mutation burden and PD-L1 expression.Despite this,there is a paucity of studies examining whether the existence of secondary malignant liver tumors affects the effectiveness of immunotherapy in patients diagnosed with advanced HER-2 negative GC.

Heterogeneous expression of stearoyl-acyl carrier protein desaturase genes SAD1 and SAD2 from Linum usitatissimum enhances seed oleic acid accumulation and seedling cold and drought tolerance in Brassica napus

Flax(Linum usitatissimum L.)is a versatile crop and its seeds are a major source of unsaturated fatty acids.Stearoyl-acyl carrier protein desaturase(SAD)is a dehydrogenase enzyme that plays a key role in oleic acid biosynthesis as well as responses to biotic and abiotic stresses.However,the function of SAD orthologs from L.usitatissimum has not been assessed.Here,we found that two LuSAD genes,LuSAD1 and LuSAD2,are present in the genome of L.usitatissimum cultivar‘Longya 10’.Heterogeneous expression of either LuSAD1 or LuSAD2 in Arabidopsis thaliana resulted in higher contents of total fatty acids and oleic acid in the seeds.Interestingly,ectopic expression of LuSAD2 in A.thaliana caused altered plant architecture.Similarly,the overexpression of either LuSAD1 or LuSAD2 in Brassica napus also resulted in increased contents of total fatty acids and oleic acid in the seeds.Furthermore,we demonstrated that either LuSAD1 or LuSAD2 enhances seedling resistance to cold and drought stresses by improving antioxidant enzyme activity and nonenzymatic antioxidant levels,as well as reducing membrane damage.These findings not only broaden our knowledge of the LuSAD functions in plants,but also offer promising targets for improving the quantity and quality of oil,and the abiotic stress tolerance of oil-producing crops,through molecular manipulation.

The UDP-glycosyltransferase OsUGT706D2 positively regulates cold and submergence stress tolerance in rice

In a genome-wide association study,we identified a rice UDP-glycosyltransferase gene,OsUGT706D2,whose transcription was activated in response to cold and submergence stress and to exogenous abscisic acid(ABA).OsUGT706D2 positively regulated the biosynthesis of tricin-4’-O-(syringyl alcohol)ether-7-O-glucoside at both the transcriptional and metabolic levels.OsUGT706D2 mediated cold and submergence tolerance by modulating the expression of stress-responsive genes as well as the abscisic acid(ABA)signaling pathway.Gain of function of OsUGT706D2 increased cold and submergence tolerance and loss of function of OsUGT706D2 reduced cold tolerance.ABA positively regulated OsUGT706D2-mediated cold tolerance but reduced submergence tolerance.These findings suggest the potential use of OsUGT706D2 for improving abiotic stress tolerance in rice.

Identification of genes involved in cadmium-ion tolerance in evolutionary Synechocystis sp.PCC 6803 tolerant to both cadmium and high light

Photosynthetic cyanobacteria have shown great potential as“autotrophic cell factories”for the synthesis of fuels and chemicals.However,poor tolerance to various environmental stressors such as high light and heavy metals is an important factor limiting their economic viability.While numerous studies have focused on the tolerance mechanism of cyanobacteria to individual stressors,their response to simultaneous stresses remains to be recovered.To investigate the mechanism of cross tolerance to heavymetal Cd^(2+) and high light,the model cyanobacterium Synechocystis sp.PCC 6803 tolerant to both Cd^(2+) and high light was obtained via about 800 days’cross-adaptive laboratory evolution.Three evolutionary strains capable of tolerating both 5.5 μmol·L^(-1) Cd^(2+) and 600 μmol·m^(-2)·s^(-1) high light were successfully obtained,achieving about 83%enhancement of Cd^(2+) tolerance compared with the parent strain.The different response of parent and evolutionary strains to Cd^(2+) was elucidated via metabolomics.Furthermore,a total of 15 genes that were mutated during evolution were identified by whole-genome re-sequencing.Finally,by single-gene knockout and complementation analysis,four genes including ssl2615,sll1732,ssr1480,and sll1659 involved in the improvement of Cd^(2+) tolerance under high-light condition were successfully identified.This work explored the tolerance mechanism of Synechocystis sp.PCC 6803 to cadmium under high-light condition and provided valuable reference for deciphering multitolerance mechanism of cyanobacteria in the future.

Genome-wide identification,molecular evolution,and functional characterization of fructokinase gene family in apple reveal its role in improving salinity tolerance

Fructokinase(FRK)is a regulator of fructose signaling in plants and gateway proteins that catalyze the initial step in fructose metabolism through phosphorylation.Our previous study demonstrated that MdFRK2 protein exhibit not only high affinity for fructose,but also high enzymatic activity due to sorbitol.However,genome-wide identification of the MdFRK gene family and their evolutionary dynamics in apple are yet to be reported.A systematic genome-wide analysis in this study identified a total of nine MdFRK gene members,which could phylogenetically be clustered into seven groups.Chromosomal location and synteny analysis of MdFRKs revealed that their expansion in the apple genome is primarily driven by tandem and segmental duplication events.Divergent expression patterns of MdFRKs were observed in four source-sink tissues and at five different apple fruit developmental stages,which suggested their potential crucial roles in the apple fruit development and sugar accumulation.Reverse transcription-quantitative PCR(RT-qPCR)identified candidate NaCl or drought stress responsive MdFRKs,and transgenic apple plants overexpressing MdFRK2 exhibited considerably enhanced salinity tolerance.Our results will be useful for understanding the functions of MdFRKs in the regulation of apple fruit development and salt stress response.