A Statistical Testing Strategy Accounting for Random and Nonrandom (Skewed) X-Chromosome Inactivation Identifies Lung Cancer Susceptibility Loci among Smokers.

INTRODUCTION: Lung cancer is the most common cancer worldwide in mortality and the second in incidence. Epidemiological studies found a higher lung cancer risk for smoking women in comparison to men, but these sex differences, irrespective of smoking habits, remain controversial. One of the hypotheses concerns the genetic contribution of the sex chromosomes. However, while genome-wide association studies identified many lung cancer susceptibility loci, these analyses have excluded X-linked loci. METHODS: To account for nongenetic factors, we first presented an association test based on an additive-multiplicative hazard model accounting for random/nonrandom X-inactivation process. A simulation study was performed to investigate the properties of the proposed test as compared with the Wald test from a Cox model with random X-inactivation process and the partial likelihood ratio test proposed by Xu et al. accounting for nonrandom X-inactivation process. Then, we performed an X chromosome-wide association study on 9,261 individuals from the population-based cohort CARTaGENE to identify susceptibility loci for lung cancer among current and past smokers. We adjusted for the PLCOm2012 lung cancer risk score used in screening programs. RESULTS: Simulation results show the good behavior of the proposed test in terms of power and type I error probability as compared to the Xu et al. and the Wald test. Using the proposed test statistic and adjusting for the PLCOm2012 score, the X chromosome-wide statistical analysis identified two SNPs in low-linkage disequilibrium located in the IL1RAPL1 (IL-1 R accessory protein-like) gene: rs12558491 (p = 2.75×10-9) and rs12835699 (p = 1.26×10-6). For both SNPs, the minor allele was associated with lower lung cancer risk. Adjusting for multiple testing, no signal was detected using the Wald or the Xu et al. likelihood ratio tests. CONCLUSION: By taking into account smoking behavior and the X-inactivation process, the investigation of the X chromosome has shed a new light on the association between X-linked loci and lung cancer. We identified two loci associated with lung cancer located in the IL1RAPL1 gene. This finding would have been overlooked by examining only results from other test statistics.

Identification of skewed X chromosome inactivation using exome and transcriptome sequencing in patients with suspected rare genetic disease.

BACKGROUND: X-chromosome inactivation (XCI) is an epigenetic process that occurs during early development in mammalian females by randomly silencing one of two copies of the X chromosome in each cell. The preferential inactivation of either the maternal or paternal copy of the X chromosome in a majority of cells results in a skewed or non-random pattern of X inactivation and is observed in over 25% of adult females. Identifying skewed X inactivation is of clinical significance in patients with suspected rare genetic diseases due to the possibility of biased expression of disease-causing genes present on the active X chromosome. The current clinical test for the detection of skewed XCI relies on the methylation status of the methylation-sensitive restriction enzyme (Hpall) binding site present in proximity of short tandem polymorphic repeats on the androgen receptor (AR) gene. This approach using one locus results in uninformative or inconclusive data for 10-20% of tests. Further, recent studies have shown inconsistency between methylation of the AR locus and the state of inactivation of the X chromosome. Herein, we develop a method for estimating X inactivation status, using exome and transcriptome sequencing data derived from blood in 227 female samples. We built a reference model for evaluation of XCI in 135 females from the GTEx consortium. We tested and validated the model on 11 female individuals with different types of undiagnosed rare genetic disorders who were clinically tested for X-skew using the AR gene assay and compared results to our outlier-based analysis technique. RESULTS: In comparison to the AR clinical test for identification of X inactivation, our method was concordant with the AR method in 9 samples, discordant in 1, and provided a measure of X inactivation in 1 sample with uninformative clinical results. We applied this method on an additional 81 females presenting to the clinic with phenotypes consistent with different hereditary disorders without a known genetic diagnosis. CONCLUSIONS: This study presents the use of transcriptome and exome sequencing data to provide an accurate and complete estimation of X-inactivation and skew status in a cohort of female patients with different types of suspected rare genetic disease.

Characterization of a novel heterozygous frameshift variant in NDP gene that causes familial exudative vitreoretinopathy in female patients.

Familial exudative vitreoretinopathy (FEVR) is a severe inherited disease characterized by defective retinal vascular development. With genetic and clinical heterogeneity, FEVR can be inherited in different patterns and characterized by phenotypes ranging from moderate visual defects to complete vision loss. This study was conducted to unravel the genetic and functional etiology of a 4-month-old female FEVR patient. Targeted gene panel and Sanger sequencing were utilized for genetic evaluation. Luciferase assays, western blot, quantitive real-time PCR, and immunocytochemistry were performed to verify the functional defects in the identified candidate variant. Here, we report a 4-month-old girl with bilateral retinal folds and peripheral avascularization, and identified a novel frameshift heterozygous variant c.37dup (p.Leu13ProfsTer13) in NDP. In vitro experiments revealed that the Leu13ProfsTer13 variant led to a prominent decrease in protein levels instead of mRNA levels, resulting in compromised Norrin/ß-catenin signaling activity. Human androgen receptor assay further revealed that a slight skewing of X chromosome inactivation could partially cause FEVR. Thus, the pathogenic mechanism by which heterozygous frameshift or nonsense variants in female carriers cause FEVR might largely result from a loss-of-function variant in one X chromosome allele and a slightly skewed X-inactivation. Further recruitment of more FEVR-affected females carrying NDP variants and genotype-phenotype correlation analysis can ultimately offer valuable information for the prognosis prediction of FEVR.

X-linked chronic granulomatous disease secondary to skewed X-chromosome inactivation in female patients.

BACKGROUND: Chronic granulomatous disease (CGD) is a heterogeneous primary immunodeficiency. X-linked (XL) CGD caused by gene defects of CYBB is the most prevalent type of CGD. OBJECTIVE: We aim to understand the clinical and molecule features of XL-CGD secondary to skewed X-chromosome inactivation (XCI) in female. METHODS: We retrospectively reviewed the medical records of a female patient diagnosed with XL-CGD. Flow cytometry was used to detect the respiratory burst function. After restriction enzyme digestion of DNA, XCI was calculated by detecting fluorescent PCR products with capillary electrophoresis. The previously published female XL-CGD cases secondary to skewed XCI was summarized. RESULTS: Clinical data were available for 15 female subjects. The median age of diagnosis was 16 years. Consistent with XL-CGD in males, infection was the most frequent manifestation in the female patients. Catalase-positive pathogens including Serratia marcescens and Staphylococcus aureus infections were the most common pathogens. Autoimmune/autoinflammation manifestations were observed in five patients. Dihydrorhodamine (DHR) assay showed that median %DHR+ values were 6.5% and the values varying with age were observed in 2 patients. All patients had a skewing XCI and there was no consistency between the daughter and carrier mother. Anti-infective treatment was effective in majority and there was no mortality reported in XL-CGD female patients to date. CONCLUSION: XL-CGD should not be neglected in female patients manifested as CGD phenotype and it is necessary to make periodic clinical evaluation of CGD female carriers as the neutrophil oxidative function may decline with aging and increase the risk for infection.

Use of allopurinol to manage skewed 6-mercaptopurine metabolism in pediatric maintenance acute lymphoblastic leukemia treatment.

BACKGROUND: 6-mercaptopurine is a cornerstone of maintenance therapy for pediatric ALL. Response to 6MP is typically determined by the ANC. Therapeutic ANC range while receiving 6MP is between 500 and 1500/µL. In addition to desired myelosuppression, 6MP is associated with multiple adverse drug effects. Increased doses of 6MP can lead to therapeutic ANC values; however, patients may experience adverse effects before obtaining therapeutic myelosuppression, often deemed "skewed metabolism." Allopurinol may potentially correct skewed 6MP metabolism. PROCEDURE: Pediatric patients with ALL with 6MMP and 6TGN metabolites drawn during maintenance therapy were analyzed for allopurinol use. The primary outcome evaluated the percentage of time spent in therapeutic ANC range before and after allopurinol initiation. In addition, the difference in 6MMP:6TGN ratios before and after allopurinol initiation, incidence of hepatotoxicity, and rates of relapse, were analyzed. RESULTS: Ninety-five patients were included for analysis. Thirty-two (34%) patients received allopurinol. There were no significant differences in baseline demographics between the patients who received allopurinol and those who did not. When comparing ANC values pre- and post-allopurinol initiation, a statistically significant increase in the percentage of time spent in therapeutic range was observed (27% vs. 43%; p = .03). In addition, when comparing metabolite ratios pre- and post-allopurinol initiation, a statistically significant decrease in 6MMP:6TGN metabolite ratio values was observed (86.7 vs. 3.6; p < .0001). CONCLUSIONS: Allopurinol significantly increased the percent time in therapeutic ANC range and can be safely utilized to significantly lower the ratio of 6MMP:6TGN metabolites, alleviating the undesirable side effects of 6MMP, and optimizing the anti-leukemic effects associated with 6TGN.

Multi-Server Multi-Function Distributed Computation.

The work here studies the communication cost for a multi-server multi-task distributed computation framework, as well as for a broad class of functions and data statistics. Considering the framework where a user seeks the computation of multiple complex (conceivably non-linear) tasks from a set of distributed servers, we establish the communication cost upper bounds for a variety of data statistics, function classes, and data placements across the servers. To do so, we proceed to apply, for the first time here, Körner's characteristic graph approach-which is known to capture the structural properties of data and functions-to the promising framework of multi-server multi-task distributed computing. Going beyond the general expressions, and in order to offer clearer insight, we also consider the well-known scenario of cyclic dataset placement and linearly separable functions over the binary field, in which case, our approach exhibits considerable gains over the state of the art. Similar gains are identified for the case of multi-linear functions.

Modelling count, bounded and skewed continuous outcomes in physical activity research: beyond linear regression models.

BACKGROUND: Inference using standard linear regression models (LMs) relies on assumptions that are rarely satisfied in practice. Substantial departures, if not addressed, have serious impacts on any inference and conclusions; potentially rendering them invalid and misleading. Count, bounded and skewed outcomes, common in physical activity research, can substantially violate LM assumptions. A common approach to handle these is to transform the outcome and apply a LM. However, a transformation may not suffice. METHODS: In this paper, we introduce the generalized linear model (GLM), a generalization of the LM, as an approach for the appropriate modelling of count and non-normally distributed (i.e., bounded and skewed) outcomes. Using data from a study of physical activity among older adults, we demonstrate appropriate methods to analyse count, bounded and skewed outcomes. RESULTS: We show how fitting an LM when inappropriate, especially for the type of outcomes commonly encountered in physical activity research, substantially impacts the analysis, inference, and conclusions compared to a GLM. CONCLUSIONS: GLMs which more appropriately model non-normally distributed response variables should be considered as more suitable approaches for managing count, bounded and skewed outcomes rather than simply relying on transformations. We recommend that physical activity researchers add the GLM to their statistical toolboxes and become aware of situations when GLMs are a better method than traditional approaches for modeling count, bounded and skewed outcomes.

Better performance for right-skewed data using an alternative gamma model.

BACKGROUND: The Maximum Likelihood Estimator (MLE) for parameters of the gamma distribution is commonly used to estimate models of right-skewed variables such as costs, hospital length of stay, and appointment wait times in Economics and Healthcare research. The common specification for this estimator assumes the variance is proportional to the square of the mean, which underlies estimation and specification tests. We present a specification in which the variance is directly proportional to the mean. METHODS: We used simulation experiments to investigate finite sample results, and we used United States Department of Veterans Affairs (VA) healthcare cost data as an empirical example comparing the fit and predictive ability of the models. RESULTS: Simulation showed the MLE based on a correctly specified alternative has less parameter bias, lower standard errors, and less skewness in distribution than a misspecified standard model. The application to VA healthcare cost data showed the alternative specification can have better R square, smaller root mean squared error, and smaller mean residuals within deciles of predicted values. CONCLUSIONS: The alternative gamma specification can be a useful alternative to the standard specification for estimating models of right-skewed continuous variables.

Confounding-adjustment methods for the causal difference in medians.

BACKGROUND: With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation (population mean) may no longer be meaningful. In practice the typical approach is to continue defining the estimand this way or transform the outcome to obtain a more symmetric distribution, although neither approach may be entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate the causal difference in medians is limited. In this study we described and compared confounding-adjustment methods to address this gap. METHODS: The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression (another form of IPW) and two little-known implementations of g-computation for this problem. Methods were evaluated within a simulation study under varying degrees of skewness in the outcome and applied to an empirical study using data from the Longitudinal Study of Australian Children. RESULTS: Simulation results indicated the IPW estimator, weighted quantile regression and g-computation implementations minimised bias across all settings when the relevant models were correctly specified, with g-computation additionally minimising the variance. Multivariable quantile regression, which relies on a constant-effect assumption, consistently yielded biased results. Application to the empirical study illustrated the practical value of these methods. CONCLUSION: The presented methods provide appealing avenues for estimating the causal difference in medians.

Skewed multifractal scaling of stock markets during the COVID-19 pandemic.

This article proposes a new paradigm of asymmetric multifractality in financial time series, where the scaling feature varies over two adjacent intervals. The proposed approach first locates a change-point and then performs a multifractal detrended fluctuation analysis (MF-DFA) on each interval. The study investigates the impact of the COVID-19 pandemic on asymmetric multifractal scaling by analyzing financial indices of the G3+1 nations, including the world's four largest economies, from January 2018 to November 2021. The results show common periods of local scaling with increasing multifractality after a change-point at the beginning of 2020 for the US, Japanese, and Eurozone markets. The study also identifies a significant transition in the Chinese market from a turbulent multifractal state to a stable monofractal state. Overall, this new approach provides valuable insights into the characteristics of financial time series and their response to extreme events.

A Comparative Study on the Impact of Lexical Inferencing, Extended Audio Glossing, and Frequency Mode of Input Instruction on EFL Learners' Lexical Collocation Knowledge.

This study shed light on the effects of four modes of vocabulary instruction, i.e., extended audio glossing, lexical inferencing, lexical translation, and frequency manipulation of input on the learning of lexical collocations by Iranian intermediate EFL learners. In so doing, 80 L1 Persian EFL students were divided into four 20-participant comparison groups: Lexical Inferencing (LI), Extended Audio Glossing (EAG), Frequency Manipulation of Input (FM), and the Lexical Translation group (LT). LI, EAG, FM, and LT were treated through lexical inferencing, extended audio glossing, skewed frequency of input, and lexical translation techniques, respectively. The participants were pretested and posttested through a piloted multiple-choice lexical collocation test and instructed for ten instructional sessions. The results of the data, analyzed through repeated measures ANCOVA, showed that all the techniques examined in this study were effective on learners' achievement in lexical collocations. Comparatively, FM treated through frequency manipulation of input, significantly outperformed the other groups in lexical collocation improvement. The ANCOVA results and paired comparisons also indicated that EAG had the least achievement in lexical collocation compared to the other three groups. These results can hopefully inform language teachers, learners, and syllabus designers.

BEXCIS: Bayesian methods for estimating the degree of the skewness of X chromosome inactivation.

BACKGROUND: X chromosome inactivation (XCI) is an epigenetic phenomenon that one of two X chromosomes in females is transcriptionally silenced during early embryonic development. Skewed XCI has been reported to be associated with some X-linked diseases. There have been several methods measuring the degree of the skewness of XCI. However, these methods may still have several limitations. RESULTS: We propose a Bayesian method to obtain the point estimate and the credible interval of the degree of XCI skewing by incorporating its prior information of being between 0 and 2. We consider a normal prior and a uniform prior for it (respectively denoted by BN and BU). We also propose a penalized point estimate based on the penalized Fieller's method and derive the corresponding confidence interval. Simulation results demonstrate that the BN and BU methods can solve the problems of extreme point estimates, noninformative intervals, empty sets and discontinuous intervals. The BN method generally outperforms other methods with the lowest mean squared error in the point estimation, and well controls the coverage probability with the smallest median and the least variation of the interval width in the interval estimation. We apply all the methods to the Graves' disease data and the Minnesota Center for Twin and Family Research data, and find that SNP rs3827440 in the Graves' disease data may undergo skewed XCI towards the allele C. CONCLUSIONS: We recommend the BN method for measuring the degree of the skewness of XCI in practice. The R package BEXCIS is publicly available at https://github.com/Wen-YiYu/BEXCIS .

Skewed X-Chromosome Inactivation as a Possible Marker of X-Linked CNV in Women with Pregnancy Loss.

Skewed X-chromosome inactivation (sXCI) can be a marker of lethal genetic variants on the X chromosome in a woman since sXCI modifies the pathological phenotype. The aim of this study was to search for CNVs in women with miscarriages and sXCI. XCI was assayed using the classical method based on the amplification of highly polymorphic exon 1 of the androgen receptor (AR) gene. The XCI status was analysed in 313 women with pregnancy loss and in 87 spontaneously aborted embryos with 46,XX karyotype, as well as in control groups of 135 women without pregnancy loss and 64 embryos with 46,XX karyotype from induced abortions in women who terminated a normal pregnancy. The frequency of sXCI differed significantly between women with miscarriages and women without pregnancy losses (6.3% and 2.2%, respectively; p = 0.019). To exclude primary causes of sXCI, sequencing of the XIST and XACT genes was performed. The XIST and XACT gene sequencing revealed no known pathogenic variants that could lead to sXCI. Molecular karyotyping was performed using aCGH, followed by verification of X-linked CNVs by RT-PCR and MLPA. Microdeletions at Xp11.23 and Xq24 as well as gains of Xq28 were detected in women with sXCI and pregnancy loss.

How much is enough? Sampling intensity influences estimates of reproductive variance in an introduced population.

Conservation introductions to islands and fenced enclosures are increasing as in situ mitigations fail to keep pace with population declines. Few studies consider the potential loss of genetic diversity and increased inbreeding if released individuals breed disproportionately. As funding is limited and post-release monitoring expensive for conservation programs, understanding how sampling effort influences estimates of reproductive variance is useful. To investigate this relationship, we used a well-studied population of Tasmanian devils (Sarcophilus harrisii) introduced to Maria Island, Tasmania, Australia. Pedigree reconstruction based on molecular data revealed high variance in number of offspring per breeder and high proportions of unsuccessful individuals. Computational subsampling of 20%, 40%, 60%, and 80% of observed offspring resulted in inaccurate estimates of reproductive variance compared to the pedigree reconstructed with all sampled individuals. With decreased sampling effort, the proportion of inferred unsuccessful individuals was overestimated and the variance in number of offspring per breeder was underestimated. To accurately estimate reproductive variance, we recommend sampling as many individuals as logistically possible during the early stages of population establishment. Further, we recommend careful selection of colonizing individuals as they may be disproportionately represented in subsequent generations. Within the conservation management context, our results highlight important considerations for sample collection and post-release monitoring during population establishment.

A scoping review of statistical methods for trial-based economic evaluations: The current state of play.

The statistical quality of trial-based economic evaluations is often suboptimal, while a comprehensive overview of available statistical methods is lacking. Therefore, this review summarized and critically appraised available statistical methods for trial-based economic evaluations. A literature search was performed to identify studies on statistical methods for dealing with baseline imbalances, skewed costs and/or effects, correlated costs and effects, clustered data, longitudinal data, missing data and censoring in trial-based economic evaluations. Data was extracted on the statistical methods described, their advantages, disadvantages, relative performance and recommendations of the study. Sixty-eight studies were included. Of them, 27 (40%) assessed methods for baseline imbalances, 39 (57%) assessed methods for skewed costs and/or effects, 27 (40%) assessed methods for correlated costs and effects, 18 (26%) assessed methods for clustered data, 7 (10%) assessed methods for longitudinal data, 26 (38%) assessed methods for missing data and 10 (15%) assessed methods for censoring. All identified methods were narratively described. This review provides a comprehensive overview of available statistical methods for dealing with the most common statistical complexities in trial-based economic evaluations. Herewith, it can provide valuable input for researchers when deciding which statistical methods to use in a trial-based economic evaluation.

Spatial Modeling of Precipitation Based on Data-Driven Warping of Gaussian Processes.

Modeling and forecasting spatiotemporal patterns of precipitation is crucial for managing water resources and mitigating water-related hazards. Globally valid spatiotemporal models of precipitation are not available. This is due to the intermittent nature, non-Gaussian distribution, and complex geographical dependence of precipitation processes. Herein we propose a data-driven model of precipitation amount which employs a novel, data-driven (non-parametric) implementation of warped Gaussian processes. We investigate the proposed warped Gaussian process regression (wGPR) using (i) a synthetic test function contaminated with non-Gaussian noise and (ii) a reanalysis dataset of monthly precipitation from the Mediterranean island of Crete. Cross-validation analysis is used to establish the advantages of non-parametric warping for the interpolation of incomplete data. We conclude that wGPR equipped with the proposed data-driven warping provides enhanced flexibility and-at least for the cases studied- improved predictive accuracy for non-Gaussian data.

Improvement in the Between-Class Variance Based on Lognormal Distribution for Accurate Image Segmentation.

There are various distributions of image histograms where regions form symmetrically or asymmetrically based on the frequency of the intensity levels inside the image. In pure image processing, the process of optimal thresholding tends to accurately separate each region in the image histogram to obtain the segmented image. Otsu's method is the most used technique in image segmentation. Otsu algorithm performs automatic image thresholding and returns the optimal threshold by maximizing between-class variance using the sum of Gaussian distribution for the intensity level in the histogram. There are various types of images where an intensity level has right-skewed histograms and does not fit with the between-class variance of the original Otsu algorithm. In this paper, we proposed an improvement of the between-class variance based on lognormal distribution, using the mean and the variance of the lognormal. The proposed model aims to handle the drawbacks of asymmetric distribution, especially for images with right-skewed intensity levels. Several images were tested for segmentation in the proposed model in parallel with the original Otsu method and the relevant work, including simulated images and Medical Resonance Imaging (MRI) of brain tumors. Two types of evaluation measures were used in this work based on unsupervised and supervised metrics. The proposed model showed superior results, and the segmented images indicated better threshold estimation against the original Otsu method and the related improvement.

Towards Generalizing the Information Theory for Neural Communication.

Neuroscience extensively uses the information theory to describe neural communication, among others, to calculate the amount of information transferred in neural communication and to attempt the cracking of its coding. There are fierce debates on how information is represented in the brain and during transmission inside the brain. The neural information theory attempts to use the assumptions of electronic communication; despite the experimental evidence that the neural spikes carry information on non-discrete states, they have shallow communication speed, and the spikes' timing precision matters. Furthermore, in biology, the communication channel is active, which enforces an additional power bandwidth limitation to the neural information transfer. The paper revises the notions needed to describe information transfer in technical and biological communication systems. It argues that biology uses Shannon's idea outside of its range of validity and introduces an adequate interpretation of information. In addition, the presented time-aware approach to the information theory reveals pieces of evidence for the role of processes (as opposed to states) in neural operations. The generalized information theory describes both kinds of communication, and the classic theory is the particular case of the generalized theory.

Lack of MECP2 gene transcription on the duplicated alleles of two related asymptomatic females with Xq28 duplications and opposite X-chromosome inactivation skewing.

Xq28 duplication syndrome (MIM# 300815) is a severe neurodevelopmental disorder in males due to MeCP2 overexpression. Most females with MECP2 duplication are asymptomatic carriers, but there are phenotypic heterogeneities. Skewed X-chromosome inactivation (XCI) can protect females from exhibiting clinical phenotypes. Herein we reported two asymptomatic females (mother and grandmother) with interstitial Xq28 duplication. AR and RP2 assays showed that both had extremely skewed XCI, the Xq28 duplicated chromosome was inactivated in the mother, but was surprisingly activated in the grandmother. Interestingly, by combining RNA sequencing and whole-exome sequencing, we confirmed that XIST only expressed in the Xq28 duplication chromosomes of the two females, indicating that the Xq28 duplication chromosomes were inactive. Meanwhile, MECP2 and most XCI genes in the duplicated X-chromosomes were not transcriptionally expressed or upregulated, precluding major clinical phenotypes in the two females, especially the grandmother. We showed that XCI status detected using RNA sequencing was more relevant for establishing the clinical phenotype of MECP2 duplication in females. It suggested that there were other factors maintaining the XCI status in addition to DNA methylation, a possible additional inhibition mechanism occurred at the transcriptional level in the unmethylated X-chromosome, counter balancing the MECP2 duplication's detrimental phenotype effects.

Induction of activity synchronization among primed hippocampal neurons out of random dynamics is key for trace memory formation and retrieval.

Memory is thought to be encoded by sparsely distributed neuronal ensembles in memory-related regions. However, it is unclear how memory-eligible neurons react during learning to encode trace fear memory and how they retrieve a memory. We implemented a fiber-optic confocal fluorescence endomicroscope to directly visualize calcium dynamics of hippocampal CA1 neurons in freely behaving mice subjected to trace fear conditioning. Here we report that the overall activity levels of CA1 neurons showed a right-skewed lognormal distribution, with a small portion of highly active neurons (termed Primed Neurons) filling the long-tail. Repetitive training induced Primed Neurons to shift from random activity to well-tuned synchronization. The emergence of activity synchronization coincided with the appearance of mouse freezing behaviors. In recall, a partial synchronization among the same subset of Primed Neurons was induced from random dynamics, which also coincided with mouse freezing behaviors. Additionally, training-induced synchronization facilitated robust calcium entry into Primed Neurons. In contrast, most CA1 neurons did not respond to tone and foot shock throughout the training and recall cycles. In conclusion, Primed Neurons are preferably recruited to encode trace fear memory and induction of activity synchronization among Primed Neurons out of random dynamics is critical for trace memory formation and retrieval.