A Statistical Framework to Identify Deviation from Time Linearity in Epigenetic Aging

The Multi-State Epigenetic Pacemaker enables the identification of combinations of factors that influence DNA methylation

Epigenetic clocks, DNA methylation-based predictive models of chronological age, are often utilized to study aging associated biology. Despite their widespread use, these methods do not account for other factors that also contribute to the variability of DNA methylation data. For example, many CpG sites show strong sex-specific or cell-type-specific patterns that likely impact the predictions of epigenetic age. To overcome these limitations, we developed a multidimensional extension of the Epigenetic Pacemaker, the Multi-state Epigenetic Pacemaker (MSEPM). We show that the MSEPM is capable of accurately modeling multiple methylation-associated factors simultaneously, while also providing site-specific models that describe the per site relationship between methylation and these factors. We utilized the MSEPM with a large aggregate cohort of blood methylation data to construct models of the effects of age-, sex-, and cell-type heterogeneity on DNA methylation. We found that these models capture a large faction of the variability at thousands of DNA methylation sites. Moreover, this approach allows us to identify sites that are primarily affected by aging and no other factors. An analysis of these sites reveals that those that lose methylation over time are enriched for CTCF transcription factor chip peaks, while those that gain methylation over time are associated with bivalent promoters of genes that are not expressed in blood. These observations suggest mechanisms that underlie age-associated methylation changes and suggest that age-associated increases in methylation may not have strong functional consequences on cell states. In conclusion, the MSEPM is capable of accurately modeling multiple methylation-associated factors, and the models produced can illuminate site-specific combinations of factors that affect methylation dynamics.

Privacy-preserving biological age prediction over federated human methylation data using fully homomorphic encryption

DNA methylation data play a crucial role in estimating chronological age in mammals, offering real-time insights into an individual's aging process. The epigenetic pacemaker (EPM) model allows inference of the biological age as deviations from the population trend. Given the sensitivity of this data, it is essential to safeguard both inputs and outputs of the EPM model. A privacy-preserving approach for EPM computation utilizing fully homomorphic encryption was recently introduced. However, this method has limitations, including having high communication complexity and being impractical for large data sets. The current work presents a new privacy-preserving protocol for EPM computation, analytically improving both privacy and complexity. Notably, we employ a single server for the secure computation phase while ensuring privacy even in the event of server corruption (compared to requiring two noncolluding servers in prior work). Using techniques from symbolic algebra and number theory, the new protocol eliminates the need for communication during secure computation, significantly improves asymptotic runtime, and offers better compatibility to parallel computing for further time complexity reduction. We implemented our protocol, demonstrating its ability to produce results similar to the standard (insecure) EPM model with substantial performance improvement compared to prior work. These findings hold promise for enhancing data security in medical applications where personal privacy is paramount. The generality of both the new approach and the EPM suggests that this protocol may be useful in other applications employing similar expectation-maximization techniques.

Identifying epigenetic aging moderators using the epigenetic pacemaker

Epigenetic clocks are DNA methylation-based chronological age prediction models that are commonly employed to study age-related biology. The difference between the predicted and observed age is often interpreted as a form of biological age acceleration, and many studies have measured the impact of environmental and disease-associated factors on epigenetic age. Most epigenetic clocks are fit using approaches that minimize the error between the predicted and observed chronological age, and as a result, they may not accurately model the impact of factors that moderate the relationship between the actual and epigenetic age. Here, we compare epigenetic clocks that are constructed using penalized regression methods to an evolutionary framework of epigenetic aging with the epigenetic pacemaker (EPM), which directly models DNA methylation as a function of a time-dependent epigenetic state. In simulations, we show that the value of the epigenetic state is impacted by factors such as age, sex, and cell-type composition. Next, in a dataset aggregated from previous studies, we show that the epigenetic state is also moderated by sex and the cell type. Finally, we demonstrate that the epigenetic state is also moderated by toxins in a study on polybrominated biphenyl exposure. Thus, we find that the pacemaker provides a robust framework for the study of factors that impact epigenetic age acceleration and that the effect of these factors may be obscured in traditional clocks based on linear regression models.

Biological clocks as age estimation markers in animals: a systematic review and meta-analysis

Various biological attributes associated with individual fitness in animals change predictably over the lifespan of an organism. Therefore, the study of animal ecology and the work of conservationists frequently relies upon the ability to assign animals to functionally relevant age classes to model population fitness. Several approaches have been applied to determining individual age and, while these methods have proved useful, they are not without limitations and often lack standardisation or are only applicable to specific species. For these reasons, scientists have explored the potential use of biological clocks towards creating a universal age-determination method. Two biological clocks, tooth layer annulation and otolith layering have found universal appeal. Both methods are highly invasive and most appropriate for post-mortem age-at-death estimation. More recently, attributes of cellular ageing previously explored in humans have been adapted to studying ageing in animals for the use of less-invasive molecular methods for determining age. Here, we review two such methods, assessment of methylation and telomere length, describing (i) what they are, (ii) how they change with age, and providing (iii) a summary and meta-analysis of studies that have explored their utility in animal age determination. We found that both attributes have been studied across multiple vertebrate classes, however, telomere studies were used before methylation studies and telomere length has been modelled in nearly twice as many studies. Telomere length studies included in the review often related changes to stress responses and illustrated that telomere length is sensitive to environmental and social stressors and, in the absence of repair mechanisms such as telomerase or alternative lengthening modes, lacks the ability to recover. Methylation studies, however, while also detecting sensitivity to stressors and toxins, illustrated the ability to recover from such stresses after a period of accelerated ageing, likely due to constitutive expression or reactivation of repair enzymes such as DNA methyl transferases. We also found that both studied attributes have parentally heritable features, but the mode of inheritance differs among taxa and may relate to heterogamy. Our meta-analysis included more than 40 species in common for methylation and telomere length, although both analyses included at least 60 age-estimation models. We found that methylation outperforms telomere length in terms of predictive power evidenced from effect sizes (more than double that observed for telomeres) and smaller prediction intervals. Both methods produced age correlation models using similar sample sizes and were able to classify individuals into young, middle, or old age classes with high accuracy. Our review and meta-analysis illustrate that both methods are well suited to studying age in animals and do not suffer significantly from variation due to differences in the lifespan of the species, genome size, karyotype, or tissue type but rather that quantitative method, patterns of inheritance, and environmental factors should be the main considerations. Thus, provided that complex factors affecting the measured trait can be accounted for, both methylation and telomere length are promising targets to develop as biomarkers for age determination in animals.

Hibernation slows epigenetic ageing in yellow-bellied marmots

Species that hibernate generally live longer than would be expected based solely on their body size. Hibernation is characterized by long periods of metabolic suppression (torpor) interspersed by short periods of increased metabolism (arousal). The torpor–arousal cycles occur multiple times during hibernation, and it has been suggested that processes controlling the transition between torpor and arousal states cause ageing suppression. Metabolic rate is also a known correlate of longevity; we thus proposed the ‘hibernation–ageing hypothesis’ whereby ageing is suspended during hibernation. We tested this hypothesis in a well-studied population of yellow-bellied marmots (Marmota flaviventer), which spend 7–8 months per year hibernating. We used two approaches to estimate epigenetic age: the epigenetic clock and the epigenetic pacemaker. Variation in epigenetic age of 149 samples collected throughout the life of 73 females was modelled using generalized additive mixed models (GAMM), where season (cyclic cubic spline) and chronological age (cubic spline) were fixed effects. As expected, the GAMM using epigenetic ages calculated from the epigenetic pacemaker was better able to detect nonlinear patterns in epigenetic ageing over time. We observed a logarithmic curve of epigenetic age with time, where the epigenetic age increased at a higher rate until females reached sexual maturity (two years old). With respect to circannual patterns, the epigenetic age increased during the active season and essentially stalled during the hibernation period. Taken together, our results are consistent with the hibernation–ageing hypothesis and may explain the enhanced longevity in hibernators.

Species that hibernate generally have longer lifespans than expected based on their body size. The authors show epigenetic ageing patterns from a natural population of hibernating yellow-bellied marmots consistent with the hypothesis that ageing is suspended during hibernation.

Olive Oil Improves While Trans Fatty Acids Further Aggravate the Hypomethylation of LINE-1 Retrotransposon DNA in an Environmental Carcinogen Model

DNA methylation is an epigenetic mechanism that is crucial for mammalian development and genomic stability. Aberrant DNA methylation changes have been detected not only in malignant tumor tissues; the decrease of global DNA methylation levels is also characteristic for aging. The consumption of extra virgin olive oil (EVOO) as part of a balanced diet shows preventive effects against age-related diseases and cancer. On the other hand, consuming trans fatty acids (TFA) increases the risk of cardiovascular diseases as well as cancer. The aim of the study was to investigate the LINE-1 retrotransposon (L1-RTP) DNA methylation pattern in liver, kidney, and spleen of mice as a marker of genetic instability. For that, mice were fed with EVOO or TFA and were pretreated with environmental carcinogen 7,12-dimethylbenz[a]anthracene (DMBA)-a harmful substance known to cause L1-RTP DNA hypomethylation. Our results show that DMBA and its combination with TFA caused significant L1-RTP DNA hypomethylation compared to the control group via inhibition of DNA methyltransferase (DNMT) enzymes. EVOO had the opposite effect by significantly decreasing DMBA and DMBA + TFA-induced hypomethylation, thereby counteracting their effects.

Epigenetic age prediction

Advanced age is the main common risk factor for cancer, cardiovascular disease and neurodegeneration. Yet, more is known about the molecular basis of any of these groups of diseases than the changes that accompany ageing itself. Progress in molecular ageing research was slow because the tools predicting whether someone aged slowly or fast (biological age) were unreliable. To understand ageing as a risk factor for disease and to develop interventions, the molecular ageing field needed a quantitative measure; a clock for biological age. Over the past decade, a number of age predictors utilising DNA methylation have been developed, referred to as epigenetic clocks. While they appear to estimate biological age, it remains unclear whether the methylation changes used to train the clocks are a reflection of other underlying cellular or molecular processes, or whether methylation itself is involved in the ageing process. The precise aspects of ageing that the epigenetic clocks capture remain hidden and seem to vary between predictors. Nonetheless, the use of epigenetic clocks has opened the door towards studying biological ageing quantitatively, and new clocks and applications, such as forensics, appear frequently. In this review, we will discuss the range of epigenetic clocks available, their strengths and weaknesses, and their applicability to various scientific queries.

Estimage: a webserver hub for the computation of methylation age

Methylage is an epigenetic marker of biological age that exploits the correlation between the methylation state of specific CG dinucleotides (CpGs) and chronological age (in years), gestational age (in weeks), cellular age (in cell cycles or as telomere length, in kilobases). Using DNA methylation data, methylage is measurable via the so called epigenetic clocks. Importantly, alterations of the correlation between methylage and age (age acceleration or deceleration) have been stably associated with pathological states and occur long before clinical signs of diseases become overt, making epigenetic clocks a potentially disruptive tool in preventive, diagnostic and also in forensic applications. Nevertheless, methylage dependency from CpGs selection, mathematical modelling, tissue specificity and age range, still makes the potential of this biomarker limited. In order to enhance model comparisons, interchange, availability, robustness and standardization, we organized a selected set of clocks within a hub webservice, EstimAge (Estimate of methylation Age, http://estimage.iac.rm.cnr.it), which intuitively and informatively enables quick identification, computation and comparison of available clocks, with the support of standard statistics.

Disentangling age-dependent DNA methylation: deterministic, stochastic, and nonlinear

DNA methylation variability arises due to concurrent genetic and environmental influences. Each of them is a mixture of regular and noisy sources, whose relative contribution has not been satisfactorily understood yet. We conduct a systematic assessment of the age-dependent methylation by the signal-to-noise ratio and identify a wealth of "deterministic" CpG probes (about 90%), whose methylation variability likely originates due to genetic and general environmental factors. The remaining 10% of "stochastic" CpG probes are arguably governed by the biological noise or incidental environmental factors. Investigating the mathematical functional relationship between methylation levels and variability, we find that in about 90% of the age-associated differentially methylated positions, the variability changes as the square of the methylation level, whereas in the most of the remaining cases the dependence is linear. Furthermore, we demonstrate that the methylation level itself in more than 15% cases varies nonlinearly with age (according to the power law), in contrast to the previously assumed linear changes. Our findings present ample evidence of the ubiquity of strong DNA methylation regulation, resulting in the individual age-dependent and nonlinear methylation trajectories, whose divergence explains the cross-sectional variability. It may also serve a basis for constructing novel nonlinear epigenetic clocks.

The Epigenetic Pacemaker: modeling epigenetic states under an evolutionary framework

SUMMARY

Epigenetic rates of change, much as evolutionary mutation rate along a lineage, vary during lifetime. Accurate estimation of the epigenetic state has vast medical and biological implications. To account for these non-linear epigenetic changes with age, we recently developed a formalism inspired by the Pacemaker model of evolution that accounts for varying rates of mutations with time. Here, we present a python implementation of the Epigenetic Pacemaker (EPM), a conditional expectation maximization algorithm that estimates epigenetic landscapes and the state of individuals and may be used to study non-linear epigenetic aging.

AVAILABILITY AND IMPLEMENTATION

The EPM is available at https://pypi.org/project/EpigeneticPacemaker/ under the MIT license. The EPM is compatible with python version 3.6 and above.

Inference of mutability landscapes of tumors from single cell sequencing data

One of the hallmarks of cancer is the extremely high mutability and genetic instability of tumor cells. Inherent heterogeneity of intra-tumor populations manifests itself in high variability of clone instability rates. Analogously to fitness landscapes, the instability rates of clonal populations form their mutability landscapes. Here, we present MULAN (MUtability LANdscape inference), a maximum-likelihood computational framework for inference of mutation rates of individual cancer subclones using single-cell sequencing data. It utilizes the partial information about the orders of mutation events provided by cancer mutation trees and extends it by inferring full evolutionary history and mutability landscape of a tumor. Evaluation of mutation rates on the level of subclones rather than individual genes allows to capture the effects of genomic interactions and epistasis. We estimate the accuracy of our approach and demonstrate that it can be used to study the evolution of genetic instability and infer tumor evolutionary history from experimental data. MULAN is available at https://github.com/compbel/MULAN.

Epigenetic pacemaker: closed form algebraic solutions

Background

DNA methylation is widely used as a biomarker in crucial medical applications as well as for human age prediction of very high accuracy. This biomarker is based on the methylation status of several hundred CpG sites. In a recent line of publications we have adapted a versatile concept from evolutionary biology - the Universal Pacemaker (UPM) - to the setting of epigenetic aging and denoted it the Epigenetic PaceMaker (EPM). The EPM, as opposed to other epigenetic clocks, is not confined to specific pattern of aging, and the epigenetic age of the individual is inferred independently of other individuals. This allows an explicit modeling of aging trends, in particular non linear relationship between chronological and epigenetic age. In one of these recent works, we have presented an algorithmic improvement based on a two-step conditional expectation maximization (CEM) algorithm to arrive at a critical point on the likelihood surface. The algorithm alternates between a time step and a site step while advancing on the likelihood surface.

Results

Here we introduce non trivial improvements to these steps that are essential for analyzing data sets of realistic magnitude in a manageable time and space. These structural improvements are based on insights from linear algebra and symbolic algebra tools, providing us greater understanding of the degeneracy of the complex problem space. This understanding in turn, leads to the complete elimination of the bottleneck of cumbersome matrix multiplication and inversion, yielding a fast closed form solution in both steps of the CEM.In the experimental results part, we compare the CEM algorithm over several data sets and demonstrate the speedup obtained by the closed form solutions. Our results support the theoretical analysis of this improvement.

Conclusions

These improvements enable us to increase substantially the scale of inputs analyzed by the method, allowing us to apply the new approach to data sets that could not be analyzed before.

Human epigenetic ageing is logarithmic with time across the entire lifespan

Epigenetic changes during ageing have been characterized by multiple epigenetic clocks that allow the prediction of chronological age based on methylation status. Despite their accuracy and utility, epigenetic age biomarkers leave many questions about epigenetic ageing unanswered. Specifically, they do not permit the unbiased characterization of non-linear epigenetic ageing trends across entire life spans, a critical question underlying this field of research. Here we provide an integrated framework to address this question. Our model, inspired from evolutionary models, is able to account for acceleration/deceleration in epigenetic changes by fitting an individual's model age, the epigenetic age, which is related to chronological age in a non-linear fashion. Application of this model to DNA methylation data measured across broad age ranges, from before birth to old age, and from two tissue types, suggests a universal logarithmic trend characterizes epigenetic ageing across entire lifespans.

An epigenetic pacemaker is detected via a fast conditional expectation maximization algorithm

AIM

DNA methylation has proven to be a remarkably accurate biomarker for human age, allowing the prediction of chronological age to within a couple of years. Recently, we proposed that the Universal PaceMaker (UPM), a flexible paradigm for modeling evolution, could be applied to epigenetic aging. Nevertheless, application to real data was restricted to small datasets for technical limitations.

MATERIALS & METHODS

We partition the set of variables into to two subsets and optimize the likelihood function on each set separately. This yields an extremely efficient Conditional Expectation Maximization algorithm, alternating between the two sets while increasing the overall likelihood.

RESULTS

Using the technique, we could reanalyze datasets of larger magnitude and show significant advantage to the UPM approach.

CONCLUSION

The UPM more faithfully models epigenetic aging than the time linear approach while methylated sites accelerate and decelerate jointly.

Bounds on Identification of Genome Evolution Pacemakers

Several studies have pointed out that the tight correlation between genes' evolutionary rate is better explained by a model denoted as the Universal PaceMaker (UPM) rather than by a simple rate constancy as manifested by the classical hypothesis of molecular clock (MC). Under UPM, each gene is associated with a single pacemaker (PM) and varies its evolutionary rate according to this PM ticks. Hence, the relative rates of all genes associated with the same PM remain nearly constant, whereas the absolute rates can change arbitrarily according to the PM ticks. A consequent question to that mentioned is finding the gene-PM association only from the gene sequence data. This, however, turns to be a nontrivial task and is affected by the number of variables, their random noise, and the amount of available information. To this end, a clustering heuristic was devised by exploiting the correlation between corresponding edge lengths across thousands of gene trees. Nevertheless, no theoretical study linking the relationship between the affecting parameters was done. We here study this question by providing theoretical bounds, expressed by the system parameters, on probabilities for positive and negative results. We corroborate these results by a simulation study that reveals the critical role of the variances.

Aging in a Relativistic Biological Space-Time

Here we present a theoretical and mathematical perspective on the process of aging. We extend the concepts of physical space and time to an abstract, mathematically-defined space, which we associate with a concept of “biological space-time” in which biological dynamics may be represented. We hypothesize that biological dynamics, represented as trajectories in biological space-time, may be used to model and study different rates of biological aging. As a consequence of this hypothesis, we show how dilation or contraction of time analogous to relativistic corrections of physical time resulting from accelerated or decelerated biological dynamics may be used to study precipitous or protracted aging. We show specific examples of how these principles may be used to model different rates of aging, with an emphasis on cancer in aging. We discuss how this theory may be tested or falsified, as well as novel concepts and implications of this theory that may improve our interpretation of biological aging.

The epigenetic landscape of age-related diseases: the geroscience perspective

In this review, we summarize current knowledge regarding the epigenetics of age-related diseases, focusing on those studies that have described DNA methylation landscape in cardio-vascular diseases, musculoskeletal function and frailty. We stress the importance of adopting the conceptual framework of “geroscience”, which starts from the observation that advanced age is the major risk factor for several of these pathologies and aims at identifying the mechanistic links between aging and age-related diseases. DNA methylation undergoes a profound remodeling during aging, which includes global hypomethylation of the genome, hypermethylation at specific loci and an increase in inter-individual variation and in stochastic changes of DNA methylation values. These epigenetic modifications can be an important contributor to the development of age-related diseases, but our understanding on the complex relationship between the epigenetic signatures of aging and age-related disease is still poor. The most relevant results in this field come from the use of the so called “epigenetics clocks” in cohorts of subjects affected by age-related diseases. We report these studies in final section of this review.