Information Theory in Computational Biology: Where We Stand Today

Elucidating the link between binding statistics and Shannon information in biological networks

The response of a biological network to ligand binding is of crucial importance for regulatory control in various cellular biophysical processes that is achieved with information transmission through the different ligand-bound states of such networks. In this work, we address a vital issue regarding the link between the information content of such network states and the experimentally measurable binding statistics. Several fundamental networks of cooperative ligand binding, with the bound states being adjacent in time only and in both space and time, are considered for this purpose using the chemical master equation approach. To express the binding characteristics in the language of information, a quantity denoted as differential information index is employed based on the Shannon information. The index, determined for the whole network, follows a linear relationship with (logarithmic) ligand concentration with a slope equal to the size of the system. On the other hand, the variation of Shannon information associated with the individual network states and the logarithmic sensitivity of its slope are shown to have generic forms related to the average binding number and variance, respectively, the latter yielding the Hill slope, the phenomenological measure of cooperativity. Furthermore, the variation of Shannon information entropy, the average of Shannon information, is also shown to be related to the average binding.

Application of a novel numerical simulation to biochemical reaction systems

Recent advancements in omics and single-cell analysis highlight the necessity of numerical methods for managing the complexity of biological data. This paper introduces a simulation program for biochemical reaction systems based on the natural number simulation (NNS) method. This novel approach ensures the equitable treatment of all molecular entities, such as DNA, proteins, H2O, and hydrogen ions (H+), in biological systems. Central to NNS is its use of stoichiometric formulas, simplifying the modeling process and facilitating efficient and accurate simulations of diverse biochemical reactions. The advantage of this method is its ability to manage all molecules uniformly, ensuring a balanced representation in simulations. Detailed in Python, NNS is adept at simulating various reactions, ranging from water ionization to Michaelis-Menten kinetics and complex gene-based systems, making it an effective tool for scientific and engineering research.

An entropy-based study on the mutational landscape of SARS-CoV-2 in USA: Comparing different variants and revealing co-mutational behavior of proteins

COVID-19 emergency has pushed the international scientific community to use every resource to combat the spread of the virus, to understand its biology and predict its possible evolution in terms of new variants. Since the first SARS-CoV-2 virus nucleotide and amino acid sequences were made available, information theory was used to study how viral information content was changing over time and then trace the evolution of its mutational landscape. In this work we analyzed SARS-CoV-2 sequences collected mainly in the USA in a period from March 2020 until December 2022 and computed mutation profiles of viral proteins over time through an entropy-based approach using Shannon Entropy and Hellinger distance. This representation allows an at-a-glance view of the mutational landscape of viral proteins over time and can provide new insights on the evolution of the virus from different points of view. Non-structural proteins typically showed flat mutation profiles, characterized by a very low Average mutation Entropy, while accessory and structural proteins showed mostly non uniform and high mutation profiles, often coupled with the predominance of variants. Interestingly NSP2 protein, whose function is currently still debated, falls in the same branch of NSP14 and NSP10 in the phylogenetic tree of mutations constructed through correlations of mutation profiles, suggesting a co-evolution of those proteins and a possible functional link with each other. To the best of our knowledge this is the first study based on a massive amount of data (n = 107,939,973) that analyzes from an entropy point of view the mutational landscape of SARS-CoV-2 over time and depicts a mutational temporal profile of each protein of the virus.

Information Theory, Living Systems, and Communication Engineering

Mainstream research on information theory within the field of living systems involves the application of analytical tools to understand a broad range of life processes. This paper is dedicated to an opposite problem: it explores the information theory and communication engineering methods that have counterparts in the data transmission process by way of DNA structures and neural fibers. Considering the requirements of modern multimedia, transmission methods chosen by nature may be different, suboptimal, or even far from optimal. However, nature is known for rational resource usage, so its methods have a significant advantage: they are proven to be sustainable. Perhaps understanding the engineering aspects of methods of nature can inspire a design of alternative green, stable, and low-cost transmission.

Using Sequence Analyses to Quantitatively Measure Oropharyngeal Swallowing Temporality in Point-of-Care Ultrasound Examinations: A Pilot Study

(1) Background: Swallowing is a complex process that comprises well-timed control of oropharyngeal and laryngeal structures to achieve airway protection and swallowing efficiency. To understand its temporality, previous research adopted adherence measures and revealed obligatory pairs in healthy swallows and the effect of aging and bolus type on the variability of event timing and order. This study aimed to (i) propose a systemic conceptualization of swallowing physiology, (ii) apply sequence analyses, a set of information-theoretic and bioinformatic methods, to quantify and characterize swallowing temporality, and (iii) investigate the effect of aging and dysphagia on the quantified variables using sequence analyses measures. (2) Method: Forty-three participants (17 young adults, 15 older adults, and 11 dysphagic adults) underwent B-mode ultrasound swallowing examinations at the mid-sagittal plane of the submental region. The onset, maximum, and offset states of hyoid bone displacement, geniohyoid muscle contraction, and tongue base retraction were identified and sorted to form sequences which were analyzed using an inventory of sequence analytic techniques; namely, overlap coefficients, Shannon entropy, and longest common subsequence algorithms. (3) Results: The concurrency of movement sequence was found to be significantly impacted by aging and dysphagia. Swallowing sequence variability was also found to be reduced with age and the presence of dysphagia (H(2) = 52.253, p < 0.001, η2 = 0.260). Four obligatory sequences were identified, and high adherence was also indicated in two previously reported pairs. These results provided preliminary support for the validity of sequence analyses for quantifying swallowing sequence temporality. (4) Conclusions: A systemic conceptualization of human deglutition permits a multi-level quantitative analysis of swallowing physiology. Sequence analyses are a set of promising quantitative measurement techniques for point-of-care ultrasound (POCUS) swallowing examinations and outcome measures for swallowing rehabilitation and evaluation of associated physiological conditions, such as sarcopenia. Findings in the current study revealed physiological differences among healthy young, healthy older, and dysphagic adults. They also helped lay the groundwork for future AI-assisted dysphagia assessment and outcome measures using POCUSs. Arguably, the proposed conceptualization and analyses are also modality-independent measures that can potentially be generalized for other instrumental swallowing assessment modalities.

Pathway analysis through mutual information

MOTIVATION

In pathway analysis, we aim to establish a connection between the activity of a particular biological pathway and a difference in phenotype. There are many available methods to perform pathway analysis, many of them rely on an upstream differential expression analysis, and many model the relations between the abundances of the analytes in a pathway as linear relationships.

RESULTS

Here, we propose a new method for pathway analysis, MIPath, that relies on information theoretical principles and, therefore, does not model the association between pathway activity and phenotype, resulting in relatively few assumptions. For this, we construct a graph of the data points for each pathway using a nearest-neighbor approach and score the association between the structure of this graph and the phenotype of these same samples using Mutual Information while adjusting for the effects of random chance in each score. The initial nearest neighbor approach evades individual gene-level comparisons, hence making the method scalable and less vulnerable to missing values. These properties make our method particularly useful for single-cell data. We benchmarked our method on several single-cell datasets, comparing it to established and new methods, and found that it produces robust, reproducible, and meaningful scores.

AVAILABILITY AND IMPLEMENTATION

Source code is available at https://github.com/statisticalbiotechnology/mipath, or through Python Package Index as "mipathway."

Optimal entropic properties of SARS-CoV-2 RNA sequences

The reaction of the scientific community against the COVID-19 pandemic has generated a huge (approx. 106 entries) dataset of genome sequences collected worldwide and spanning a relatively short time window. These unprecedented conditions together with the certain identification of the reference viral genome sequence allow for an original statistical study of mutations in the virus genome. In this paper, we compute the Shannon entropy of every sequence in the dataset as well as the relative entropy and the mutual information between the reference sequence and the mutated ones. These functions, originally developed in information theory, measure the information content of a sequence and allows us to study the random character of mutation mechanism in terms of its entropy and information gain or loss. We show that this approach allows us to set in new format known features of the SARS-CoV-2 mutation mechanism like the CT bias, but also to discover new optimal entropic properties of the mutation process in the sense that the virus mutation mechanism track closely theoretically computable lower bounds for the entropy decrease and the information transfer.

Entropy-Driven, Integrative Bioinformatics Approaches Reveal the Recent Transmission of the Monkeypox Virus from Nigeria to Multiple Non-African Countries

Monkeypox virus (mpox) has currently affected multiple countries around the globe. This study aims to analyze how the virus spread globally. The study uses entropy-driven bioinformatics in five directions to analyze the 60 full-length complete genomes of mpox. We analyzed the topological entropy distribution of the genomes, principal component analysis (PCA), the dissimilarity matrix, entropy-driven phylogenetics, and genome clustering. The topological entropy distribution showed genome positional entropy. We found five clusters of the mpox genomes through the two PCA, while the three PCA elucidated the clustering events in 3D space. The clustering of genomes was further confirmed through the dissimilarity matrix and phylogenetic analysis which showed the bigger size of Cluster 1 and size similarity between Clusters 2 and 4 as well as Clusters 3 and 5. It corroborated with the phylogenetics of the genomes, where Cluster 1 showed clear segregation from the other four clusters. Finally, the study concluded that the spreading of the mpox is likely to have originated from African countries to the rest of the non-African countries. Overall, the spreading and distribution of the mpox will shed light on its evolution and pathogenicity of the mpox and help to adopt preventive measures to stop the spreading of the virus.

Bioinformatics tools for the sequence complexity estimates

We review current methods and bioinformatics tools for the text complexity estimates (information and entropy measures). The search DNA regions with extreme statistical characteristics such as low complexity regions are important for biophysical models of chromosome function and gene transcription regulation in genome scale. We discuss the complexity profiling for segmentation and delineation of genome sequences, search for genome repeats and transposable elements, and applications to next-generation sequencing reads. We review the complexity methods and new applications fields: analysis of mutation hotspots loci, analysis of short sequencing reads with quality control, and alignment-free genome comparisons. The algorithms implementing various numerical measures of text complexity estimates including combinatorial and linguistic measures have been developed before genome sequencing era. The series of tools to estimate sequence complexity use compression approaches, mainly by modification of Lempel-Ziv compression. Most of the tools are available online providing large-scale service for whole genome analysis. Novel machine learning applications for classification of complete genome sequences also include sequence compression and complexity algorithms. We present comparison of the complexity methods on the different sequence sets, the applications for gene transcription regulatory regions analysis. Furthermore, we discuss approaches and application of sequence complexity for proteins. The complexity measures for amino acid sequences could be calculated by the same entropy and compression-based algorithms. But the functional and evolutionary roles of low complexity regions in protein have specific features differing from DNA. The tools for protein sequence complexity aimed for protein structural constraints. It was shown that low complexity regions in protein sequences are conservative in evolution and have important biological and structural functions. Finally, we summarize recent findings in large scale genome complexity comparison and applications for coronavirus genome analysis.

Cellular shortening and calcium dynamics are improved by noisy stimulus in a model of cardiomyopathy

Noise is present in cell biology. The capability of cells to respond to noisy environment have become essential. This study aimed to investigate whether noise can enhance the contractile response and Ca2+ handling in cardiomyocytes from a cardiomyopathy model. Experiments were conducted in an experimental setup with Gaussian white noise, frequency, and amplitude control to stimulate myocytes. Cell shortening, maximal shortening velocity, time to peak shortening, and time to half relaxation variables were recorded to cell shortening. Ca2+ transient amplitude and raise rate variables were registered to measure Ca2+ transients. Our results for cell shortening, Ca2+ transient amplitude, and raise rate suggest that cell response improve when myocytes are noise stimulated. Also, cell shortening, maximal shortening velocity, Ca2+ transient amplitude, and raise improves in control cells. Altogether, these findings suggest novel characteristics in how cells improve their response in a noisy environment.

Predicting chromosomal compartments directly from the nucleotide sequence with DNA-DDA

Three-dimensional (3D) genome architecture is characterized by multi-scale patterns and plays an essential role in gene regulation. Chromatin conformation capturing experiments have revealed many properties underlying 3D genome architecture, such as the compartmentalization of chromatin based on transcriptional states. However, they are complex, costly and time consuming, and therefore only a limited number of cell types have been examined using these techniques. Increasing effort is being directed towards deriving computational methods that can predict chromatin conformation and associated structures. Here we present DNA-delay differential analysis (DDA), a purely sequence-based method based on chaos theory to predict genome-wide A and B compartments. We show that DNA-DDA models derived from a 20 Mb sequence are sufficient to predict genome wide compartmentalization at the scale of 100 kb in four different cell types. Although this is a proof-of-concept study, our method shows promise in elucidating the mechanisms responsible for genome folding as well as modeling the impact of genetic variation on 3D genome architecture and the processes regulated thereby.

Identifying Cancer Driver Pathways Based on the Mouth Brooding Fish Algorithm

Identifying the driver genes of cancer progression is of great significance in improving our understanding of the causes of cancer and promoting the development of personalized treatment. In this paper, we identify the driver genes at the pathway level via an existing intelligent optimization algorithm, named the Mouth Brooding Fish (MBF) algorithm. Many methods based on the maximum weight submatrix model to identify driver pathways attach equal importance to coverage and exclusivity and assign them equal weight, but those methods ignore the impact of mutational heterogeneity. Here, we use principal component analysis (PCA) to incorporate covariate data to reduce the complexity of the algorithm and construct a maximum weight submatrix model considering different weights of coverage and exclusivity. Using this strategy, the unfavorable effect of mutational heterogeneity is overcome to some extent. Data involving lung adenocarcinoma and glioblastoma multiforme were tested with this method and the results compared with the MDPFinder, Dendrix, and Mutex methods. When the driver pathway size was 10, the recognition accuracy of the MBF method reached 80% in both datasets, and the weight values of the submatrix were 1.7 and 1.89, respectively, which are better than those of the compared methods. At the same time, in the signal pathway enrichment analysis, the important role of the driver genes identified by our MBF method in the cancer signaling pathway is revealed, and the validity of these driver genes is demonstrated from the perspective of their biological effects.

An exploratory study of CT radiomics using differential network feature selection for WHO/ISUP grading and progression-free survival prediction of clear cell renal cell carcinoma

Objectives

To explore the feasibility of predicting the World Health Organization/International Society of Urological Pathology (WHO/ISUP) grade and progression-free survival (PFS) of clear cell renal cell cancer (ccRCC) using the radiomics features (RFs) based on the differential network feature selection (FS) method using the maximum-entropy probability model (MEPM).

Methods

175 ccRCC patients were divided into a training set (125) and a test set (50). The non-contrast phase (NCP), cortico-medullary phase, nephrographic phase, excretory phase phases, and all-phase WHO/ISUP grade prediction models were constructed based on a new differential network FS method using the MEPM. The diagnostic performance of the best phase model was compared with the other state-of-the-art machine learning models and the clinical models. The RFs of the best phase model were used for survival analysis and visualized using risk scores and nomograms. The performance of the above models was tested in both cross-validated and independent validation and checked by the Hosmer-Lemeshow test.

Results

The NCP RFs model was the best phase model, with an AUC of 0.89 in the test set, and performed superior to other machine learning models and the clinical models (all p &lt;0.05). Kaplan-Meier survival analysis, univariate and multivariate cox regression results, and risk score analyses showed the NCP RFs could predict PFS well (almost all p &lt; 0.05). The nomogram model incorporated the best two RFs and showed good discrimination, a C-index of 0.71 and 0.69 in the training and test set, and good calibration.

Conclusion

The NCP CT-based RFs selected by differential network FS could predict the WHO/ISUP grade and PFS of RCC.

Characterizing the variation in chromosome structure ensembles in the context of the nuclear microenvironment

Inside the nucleus, chromosomes are subjected to direct physical interaction between different components, active forces, and thermal noise, leading to the formation of an ensemble of three-dimensional structures. However, it is still not well understood to what extent and how the structural ensemble varies from one chromosome region or cell-type to another. We designed a statistical analysis technique and applied it to single-cell chromosome imaging data to reveal the heterogeneity of individual chromosome structures. By analyzing the resulting structural landscape, we find that the largest dynamic variation is the overall radius of gyration of the chromatin region, followed by domain reorganization within the region. By comparing different human cell-lines and experimental perturbation data using this statistical analysis technique and a network-based similarity quantification approach, we identify both cell-type and condition-specific features of the structural landscapes. We identify a relationship between epigenetic state and the properties of chromosome structure fluctuation and validate this relationship through polymer simulations. Overall, our study suggests that the types of variation in a chromosome structure ensemble are cell-type as well as region-specific and can be attributed to constraints placed on the structure by factors such as variation in epigenetic state.

Recent work has revealed principles of how chromosomes are folded and structured inside the human nucleus. It is now even possible to microscopically trace the path of chromosomes in 3D in individual cells. With this data, we can start to examine how much variation exists in chromosome structure and what biological factors may restrict or enhance this variation. Are chromosomes stuck in just a few possible positions or do they move around more freely, sampling many configurations? Here, we use a mathematical approach to compare chromosome structure variation in different cell types, at different locations along the genome, and when key structural proteins are removed. Through these comparisons and dynamic simulations of chromosome behavior, we identify factors that may constrain or promote variation in chromosome structure.

Disentangling single-cell omics representation with a power spectral density-based feature extraction

Emerging single-cell technologies provide high-resolution measurements of distinct cellular modalities opening new avenues for generating detailed cellular atlases of many and diverse tissues. The high dimensionality, sparsity, and inaccuracy of single cell sequencing measurements, however, can obscure discriminatory information, mask cellular subtype variations and complicate downstream analyses which can limit our understanding of cell function and tissue heterogeneity. Here, we present a novel pre-processing method (scPSD) inspired by power spectral density analysis that enhances the accuracy for cell subtype separation from large-scale single-cell omics data. We comprehensively benchmarked our method on a wide range of single-cell RNA-sequencing datasets and showed that scPSD pre-processing, while being fast and scalable, significantly reduces data complexity, enhances cell-type separation, and enables rare cell identification. Additionally, we applied scPSD to transcriptomics and chromatin accessibility cell atlases and demonstrated its capacity to discriminate over 100 cell types across the whole organism and across different modalities of single-cell omics data.

Identification of the associations between genes and quantitative traits using entropy-based kernel density estimation

Genetic associations have been quantified using a number of statistical measures. Entropy-based mutual information may be one of the more direct ways of estimating the association, in the sense that it does not depend on the parametrization. For this purpose, both the entropy and conditional entropy of the phenotype distribution should be obtained. Quantitative traits, however, do not usually allow an exact evaluation of entropy. The estimation of entropy needs a probability density function, which can be approximated by kernel density estimation. We have investigated the proper sequence of procedures for combining the kernel density estimation and entropy estimation with a probability density function in order to calculate mutual information. Genotypes and their interactions were constructed to set the conditions for conditional entropy. Extensive simulation data created using three types of generating functions were analyzed using two different kernels as well as two types of multifactor dimensionality reduction and another probability density approximation method called m-spacing. The statistical power in terms of correct detection rates was compared. Using kernels was found to be most useful when the trait distributions were more complex than simple normal or gamma distributions. A full-scale genomic dataset was explored to identify associations using the 2-h oral glucose tolerance test results and γ-glutamyl transpeptidase levels as phenotypes. Clearly distinguishable single-nucleotide polymorphisms (SNPs) and interacting SNP pairs associated with these phenotypes were found and listed with empirical p-values.

An Epistatic Network Describes oppA and glgB as Relevant Genes for Mycobacterium tuberculosis

Mycobacterium tuberculosis is an acid-fast bacterium that causes tuberculosis worldwide. The role of epistatic interactions among different loci of the M. tuberculosis genome under selective pressure may be crucial for understanding the disease and the molecular basis of antibiotic resistance acquisition. Here, we analyzed polymorphic loci interactions by applying a model-free method for epistasis detection, SpydrPick, on a pan–genome-wide alignment created from a set of 254 complete reference genomes. By means of the analysis of an epistatic network created with the detected epistatic interactions, we found that glgB (α-1,4-glucan branching enzyme) and oppA (oligopeptide-binding protein) are putative targets of co-selection in M. tuberculosis as they were associated in the network with M. tuberculosis genes related to virulence, pathogenesis, transport system modulators of the immune response, and antibiotic resistance. In addition, our work unveiled potential pharmacological applications for genotypic antibiotic resistance inherent to the mutations of glgB and oppA as they epistatically interact with fprA and embC, two genes recently included as antibiotic-resistant genes in the catalog of the World Health Organization. Our findings showed that this approach allows the identification of relevant epistatic interactions that may lead to a better understanding of M. tuberculosis by deciphering the complex interactions of molecules involved in its metabolism, virulence, and pathogenesis and that may be applied to different bacterial populations.

massiveGST: A Mann-Whitney-Wilcoxon Gene-Set Test Tool That Gives Meaning to Gene-Set Enrichment Analysis

Gene-set enrichment analysis is the key methodology for obtaining biological information from transcriptomic space’s statistical result. Since its introduction, Gene-set Enrichment analysis methods have obtained more reliable results and a wider range of application. Great attention has been devoted to global tests, in contrast to competitive methods that have been largely ignored, although they appear more flexible because they are independent from the source of gene-profiles. We analyzed the properties of the Mann–Whitney–Wilcoxon test, a competitive method, and adapted its interpretation in the context of enrichment analysis by introducing a Normalized Enrichment Score that summarize two interpretations: a probability estimate and a location index. Two implementations are presented and compared with relevant literature methods: an R package and an online web tool. Both allow for obtaining tabular and graphical results with attention to reproducible research.

Fifty years of Shannon information theory in assessing the accuracy and agreement of diagnostic tests

Since 1948, Shannon theoretic methods for modeling information have found a wide range of applications in several areas where information plays a key role, which goes well beyond the original scopes for which they have been conceived, namely data compression and error correction over a noisy channel. Among other uses, these methods have been applied in the broad field of medical diagnostics since the 1970s, to quantify diagnostic information, to evaluate diagnostic test performance, but also to be used as technical tools in image processing and registration. This review illustrates the main contributions in assessing the accuracy of diagnostic tests and the agreement between raters, focusing on diagnostic test performance measurements and paired agreement evaluation. This work also presents a recent unified, coherent, and hopefully, final information-theoretical approach to deal with the flows of information involved among the patient, the diagnostic test performed to appraise the state of disease, and the raters who are checking the test results. The approach is assessed by considering two case studies: the first one is related to evaluating extra-prostatic cancers; the second concerns the quality of rapid tests for COVID-19 detection.

The Resolved Mutual Information Function as a Structural Fingerprint of Biomolecular Sequences for Interpretable Machine Learning Classifiers

In the present article we propose the application of variants of the mutual information function as characteristic fingerprints of biomolecular sequences for classification analysis. In particular, we consider the resolved mutual information functions based on Shannon-, Rényi-, and Tsallis-entropy. In combination with interpretable machine learning classifier models based on generalized learning vector quantization, a powerful methodology for sequence classification is achieved which allows substantial knowledge extraction in addition to the high classification ability due to the model-inherent robustness. Any potential (slightly) inferior performance of the used classifier is compensated by the additional knowledge provided by interpretable models. This knowledge may assist the user in the analysis and understanding of the used data and considered task. After theoretical justification of the concepts, we demonstrate the approach for various example data sets covering different areas in biomolecular sequence analysis.

Estimating the variance of Shannon entropy

The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly the most widespread tool is provided by the so-called plug-in estimator, whose statistical properties in terms of bias and variance were investigated since the first decade after the publication of Shannon's seminal works. In the case of an underlying multinomial distribution, while the bias can be evaluated by knowing support and data set size, variance is far more elusive. The aim of the present work is to investigate, in the multinomial case, the statistical properties of an estimator of a parameter that describes the variance of the plug-in estimator of Shannon entropy. We then exactly determine the probability distributions that maximize that parameter. The results presented here allow one to set upper limits to the uncertainty of entropy assessments under the hypothesis of memoryless underlying stochastic processes.

Life's Energy and Information: Contrasting Evolution of Volume- versus Surface-Specific Rates of Energy Consumption

As humanity struggles to find a path to resilience amidst global change vagaries, understanding organizing principles of living systems as the pillar for human existence is rapidly growing in importance. However, finding quantitative definitions for order, complexity, information and functionality of living systems remains a challenge. Here, we review and develop insights into this problem from the concept of the biotic regulation of the environment developed by Victor Gorshkov (1935-2019). Life's extraordinary persistence-despite being a strongly non-equilibrium process-requires a quantum-classical duality: the program of life is written in molecules and thus can be copied without information loss, while life's interaction with its non-equilibrium environment is performed by macroscopic classical objects (living individuals) that age. Life's key energetic parameter, the volume-specific rate of energy consumption, is maintained within universal limits by most life forms. Contrary to previous suggestions, it cannot serve as a proxy for "evolutionary progress". In contrast, ecosystem-level surface-specific energy consumption declines with growing animal body size in stable ecosystems. High consumption by big animals is associated with instability. We suggest that the evolutionary increase in body size may represent a spontaneous loss of information about environmental regulation, a manifestation of life's algorithm ageing as a whole.