Entropy

Artificial intelligence (AI) assistants can improve individual performance but may weaken unaided performance and limit interest diversity, raising questions about their long-term effects on collective intelligence (CI). Here, we consider an evolutionary model in which individuals predict, consult AI, and imitate better-performing peers. Classic reward structures that promote CI without AI can fail under Chatbot AI, whose predictions depend on users' interests, by reducing interest diversity or propagating bias. Directly rewarding or penalizing AI use does not reliably mitigate these effects. Instead, a balanced incentive that preserves minority expertise and rewards collective contributions can promote CI, but an additional incentive is needed to restore unaided collective accuracy. Our framework offers an explanation for emerging evidence of AI's societal impact and clarifies its long-term implications.

A central goal of neuroscience is to establish how similar (or different) brain networks are across individuals, development, psychiatric conditions, and even between biological and artificial brains. Whenever one such comparison is made, it relies on the assumption that we have a measure that produces an accurate and plausible similarity score. Yet, the field lacks one such measure, and the wide variety of existing measures often produces conflicting results. To address this problem, we perform a systematic comparison of 16 established similarity measures. First, we show that different measures consistently disagree on which brain networks are most similar. Second, we rank all measures according to multiple criteria such as biological plausibility, computational efficiency, and sensitivity. We show that DeltaCon is the most accurate measure in terms of parameter recovery, and that it ranks among the fastest and most noise-tolerant. For this reason, we conclude that DeltaCon is the best general-purpose similarity measure. However, no measure ranks best on more than two of the five criteria we assessed, and different measures should be preferred depending on the exact research question. Measure selection can now be made on evidence and should be a crucial decision in any study that compares brain networks.

The genetic code is the rule that (apart from minor modifications) is used by all contemporary life on Earth to translate genes into proteins. It is summarized by a 4x4x4 table which maps the 64 possible triplet RNA codons to the 20 canonical amino acids ("AAs"). Understanding the origin of this code is a fundamental open problem in biology. We review the idea of a comma-free code, and put forward a general reason to suspect the primordial code was comma-free (even though the modern code is not). We explain why this primordial code should then persist as a comma-free subcode within the modern code, and identify the five optimal candidates for such a subcode. We then introduce the idea of "compatible comma-free codes" and explain how they allow multiple codes to evolve in parallel, circumventing a standard argument suggesting that code evolution should effectively freeze when the associated genome becomes sufficiently complex. In particular, we highlight the possibility that the original code was a comma-free doublet code, which was then overtaken by a compatible comma-free triplet code, which finally evolved (after the evolution of the start codon and ribosome) to the modern saturated triplet code. To assess this idea, we classify all inequivalent compatible comma-free doublet-triplet codes and, among these, identify the three most promising predecessors of the modern code. Consistency between these three best codes and the "wobble rules" in gene translation provide non-trivial evidence for this possibility.

Biological populations have been evolving in multi-dimensional trait spaces. Ecological interactions can induce the evolutionary diversification of a biological population into distinct multiple populations, which is called evolutionary branching in adaptive dynamics theory. If possible mutations are restricted to certain directions due to developmental, physiological, or physical constraints, the resulting evolutionary dynamics may be restricted to subspaces with fewer dimensions than the original trait spaces. In general, such constraints are also evolving slowly, due to rare and slight mutational deviations from the constraint subspaces. In this sense, constraints are not strict. However, the method for describing non-strict constraints that is globally consistent has yet to be developed. This study proposes a general and flexible method for constructing a non-strict constraint subspace from the corresponding strict constraint subspace. This method enables efficient analysis of adaptive evolution including evolutionary branching under non-strict constraints in the framework of adaptive dynamics theory. Applying this method to a resource competition model shows that the shape of the carrying capacity distribution can be treated as a non-strict constraint curve, and that the likelihood of evolutionary branching is affected not only by the shape of the constraint curve but also by its slow evolution.

We develop a general geometrical framework for growth processes in which the growth rate depends exponentially on the number of active growth-supporting components. The framework separates the fraction of active components from the size of the accessible component space, allowing qualitatively different growth laws to arise from the same underlying construction. Bacterial population growth provides an example of a fixed-size component space controlled primarily by activation and deactivation, whereas examples such as human population growth or speciation provide an expanding component space in which interactions between individuals promote further growth. This motivates a Replicative geometrical law, dX/dt= X exp({beta} X^{gamma}), whose exponent characterizes the scaling of the effective growth-supporting component space and is tested against historical human-population regimes and eukaryotic lineage-through-time data. For innovation indicators such as patents and arXiv manuscript submissions, where an existing item need not itself reproduce, the same construction motivates a Direct Geometrical production law without the prefactor X. The framework therefore provides a common description of fixed and expanding component spaces while distinguishing Replicative from Direct Geometrical growth.

Phase separating biopolymers are often described by the sticker-spacer model, which accounts for non-attractive linkers that connect discrete attractive moieties. "Associative polymer" theories describe these systems as two coexisting fluids of stickers and spacers, respectively. In such theories the stickers and spacers are decoupled in the sense that sticker binding does not affect spacer conformations or vice versa. Informed by coarse-grained simulations, we develop a phenomenological mean-field theory to determine the microscopic coupling between the sticker and spacer degrees of freedom. Accounting for linkers connecting adjacent spacers introduces free energy contributions due to conformational entropy of the spacer and the binding combinatorics of the stickers. These contributions have opposite dependencies on spacer length because longer spacers allow a greater volume to search for binding partners but incur a greater entropy cost upon bond formation. The length dependent terms from these contributions cancel leaving a length-independent elastic term arising from the fact that a small amount of spacer stretching lowers the free energy by increasing the number of possible binding partners. The cancellation of spacer length from the theory justifies the decoupling approximation and supports mean-field treatments of heterogeneous spacers.

Recurrent cortical circuits are hypothesized to perform Bayesian posterior sampling through their stochastic dynamics. Yet identifying which sampling algorithm a circuit intrinsically implements, as opposed to mapping manually designing algorithms onto circuits, requires rigorous theoretical analysis of the biological circuit dynamics, and remains a fundamental open challenge because of the analytical intractability of nonlinear recurrent dynamics. Here, we tackle this challenge through comprehensive theoretical analysis of analytically tractable nonlinear recurrent circuit dynamics used in neuroscience research-- the continuous attractor network (CAN). Surprisingly, we find that the circuit, without any non-Gaussian components in its connectivity or internal variability, intrinsically emerges heavy-tailed subspaces dynamics described as scale-mixture Langevin posterior sampling. The mechanism emerges from the circuits own nonlinear dynamics: divisive normalization renders the overall population activation Gamma-distributed which multiplicatively modulates the time constant of the Langevin sampling in the stimulus feature subspace. Eventually, this scale-mixture structure produces a heavy-tailed (Student-t) sampling step size distribution, significantly accelerating the sampling speed. Moreover, the scale-mixture Langevin sampling approaches a Levy-like regime in the weak input limit. Our results analytically identify an intrinsic circuit algorithm embedded in subspaces of nonlinear recurrent dynamics, and establish a minimal circuit mechanism for endogenous heavy-tail statistics without any explicit non-Gaussian components.

In this work, we focus on predicting fold-switching phenomena observed in certain protein structures. Proteins that undergo fold-switching are called metamorphic proteins. We model fold-switch prediction in proteins as a position/residue-wise classification task. We use various features extracted from a protein's sequence as well as structure to train the classifiers. We propose a novel class of handcrafted parametrised features that encode the structural context of a residue. We also use embeddings from existing protein language models (PLMs) to train the classifiers. We train binary and 3-class classifiers, with the 3-class classifiers providing granular information on the type of fold-switch. In our computations, higher classification performance is achieved for binary prediction as compared to 3-class granular prediction. The handcrafted features perform comparably with the PLM embeddings on our standard test set. A rigorous error analysis by us during the review period revealed a critical data-leakage vulnerability in the metamorphic protein test data. This analysis also revealed that the PLM-based classifier suffers sequence-memorisation bias and fails to generalise to novel fold-switching sequences. On the other hand, one of our domain-informed handcrafted feature based classifier detects fold-switching without relying on sequence memory.

In network biology, analyzing pathways is critical to study mechanisms or sequences of biological events. The pathway co-membership approach aims to link proteins belonging to the same pathway inside a network that is a clique. Although this method is great for projecting pathway knowledge onto proteins, it remains unsuitable for some downstream applications relying on graph distances like random walks with restart. To address this limitation, we introduce a weighted pathway co-membership method that incorporates biological distances between proteins. We achieve this by developing an abstraction framework for Reactome pathways, which captures both their hierarchical organization and sequential relationships. By assigning weights to these abstractions, we define a scoring system for proteins within the pathway co-membership clique. We illustrate our approach using a Reactome pathway ("Signaling by TGF-beta receptor complex", R-HSA-170834), and explain how we generate the weighted co-membership cliques of the 29 Reactome top-level pathways. Next, we construct the entire weighted pathway co membership network of the Reactome knowledge base. Validation and evaluation of our method is performed using cancer hallmark gene sets and a random walk with restart experiment, comparing our approach to state-of-the-art methods. We show that our approach outperforms state-of-the-art methods for gene prioritization on cancer hallmarks.

Motivated by correlations between SARS-COV-2 infections and transthyretin (TTR) amyloidosis we use molecular dynamics simulations to study whether three protein fragments from the SARS-CoV-2 virus can initiate dissociation of the transthyretin (TTR) homotetramer as the first step on the pathway to TTR amyloidosis. We find that the peptides reduce the frequency of transient hydrogen bonds at the monomer-monomer interfaces, decreasing in this way the stability of the TTR tetramer.

A major transition in the evolution of eukaryotic cells was phagocytosis: the ability of one cell to engulf another. In some cases, the engulfed cell persists, forming an endosymbiosis which is often mutually beneficial. However, it is unclear whether the interaction between the ancestors was also cooperative. There are clear benefits to developing the ability to eat a competitor, but can it ever be beneficial to eat a cooperator? We use a dynamical systems framework to identify the ecological conditions under which phagocytosis can evolve from a system of cooperating microbes.Beginning with a system of two cooperating species, we use invasion analysis to identify the parameter regimes under which a phagocytosing mutant can invade and the subsequent population dynamics. We identify a critical threshold that determines whether an invading predator will coexist with the cooperative community or replace members. Repeatedly invading with different predators, we find that the system saturates when there are three coexisting species, though this community does not have a single optimal composition. However, if we incorporate additional costs, we find there is a single evolutionarily stable community of two cooperators and a pure predator. Ultimately, we show that it is possible for phagocytosis to evolve from a cooperative community and, moreover, coexist with the original cooperating species.

Oscillatory and saturating dynamics in regulatory gene networks govern processes such as cell cycle timing, circadian rhythms, and inflammatory signaling, and sparse regression methods such as SINDy offer an interpretable method for recovering their governing equations from time-series data. However, these networks are typically governed by Hill-type nonlinearities that become nearly collinear with polynomial candidates over most bounds of an oscillating curve, and placing them in a shared library produces ill-conditioned regressions and unreliable coefficient estimates. Standard approaches such as ridge regularization, library normalization, and orthogonalization can marginally improve conditioning but cannot remove the structural multicollinearity of these systems, in turn limiting our ability to produce accurate parameter estimates. To address this issue, we propose the Regulation-Informed Sparse Identification of Nonlinear Dynamics (RI-SINDy) method, which removes known regulatory terms from the regression and recovers their coefficients directly from an asymptotic drift-balance condition. Because the time averaged derivative of a bounded trajectory approaches zero, the coefficients of regulatory nonlinearities can be computed independently by constraining them to offset the mean contribution of the remaining terms. We demonstrate that this method effectively reduces library collinearity and improves conditioning numbers by 3-45x, substantially improving coefficient recovery and regression accuracy. We test the RI-SINDy method on experimental Hes1 data and on synthetic Goodwin and NF-{kappa}B models. On Hes1, it achieves the lowest trajectory error among the compared methods (Traditional SINDy, SR3, and Nullcline Reconstruction). On the synthetic systems, it recovers the correct sparse structure with lower trajectory error than SR3 and Nullcline Reconstruction, and in a Goodwin noise sweep it recovers all active terms at noise levels up to 15%, where Traditional SINDy and E-SINDy fail to. In conclusion, the RI-SINDy method provides a robust framework to overcome the issue of multicollinearity for system identification in biological systems.

Emerging research on desynchronization reveals strong relations to memory formation and recollection with much of the evidence originating from studies of the hippocampus, a brain region central to memory processing. However, growing evidence emphasizing the role of desynchronization is accompanied by challenges, most notably the synchronization/desynchronization conundrum. The conundrum arises from an apparent contradiction between learning and Shannon's information theory: spike-timing-dependent plasticity (STDP) acquires information via synchronized populational activity whereas information theory suggests that information channel is encoded through higher variability. Both frameworks are well-founded. Learning is widely accepted as the mathematical abstraction of STDP while Shannon's information theory showcases its power ubiquitously across fields from communication systems to neuroscience. Here, we propose that learning and Shannon's information theory are not necessarily opposing principles. Rather, learning plays a critical role in the process of synchronization and desynchronization. To justify our claim, we conduct computational simulations based on a Hodgkin-Huxley neuronal model coupled with NMDA, AMPA, and GABA synapses with inputs of biologically realistic spiking data. Our results show that enabling STDP significantly influences synchronization and desynchronization dynamics. Specifically, we find that STDP and desynchronization form a regulatory loop, in which STDP regulates the level of synchrony, and synchrony regulates subsequent learning strength. Further study reveals STDP is capable of switching neurons from synchronization to desynchronization. This framework mitigates the synchronization/desynchronization conundrum by clarifying the relationship between desynchronization and learning, and offers a new perspective on how synchrony contributes to memory formation and recollection.

Single-cell sequencing provides a rich source of data that can be used to model and estimate the evolution of somatic cells within individuals. Many common models for modeling DNA evolution in phylogenetics are based on continuous-time Markov processes that operate on aligned sites. For haploid DNA, such as found in mitochondria, there are many well established models for these processes but since nuclear DNA is diploid, containing copies of both the maternal and paternal genome, it is natural to develop continuous-time Markov processes adapted to diploid DNA. One possible model is that both the maternal and paternal evolve independently according to haploid models so that, in principle, DNA comes with a phase. i.e. a label that tells if the site was derived from the maternal or paternal sequence. However, this information may not be available in practice and only an unphased diploid genotype is available. That is, an unphased model groups both of the possible maternal-paternal labels into a single state. This grouping process, called ``lumping'', is used by other methods as well and results in a coarser process. Care must be taken so that the coarser process can still be modeled as a continuous-time Markov chain; the lumped process of the original phased Markov chain may or may not be Markovian, depending on restrictions imposed on the generator matrix. Here, we explore the mathematical formulations of phased and unphased Markov processes, as well as a collection of other diploid DNA models from the literature.

Regular environmental cycles such as day and night or the lunar cycle are ubiquitous and drive many biological processes. Many organisms have evolved endogenous time-keeping mechanisms to anticipate these cycles to accurately time their behavior or synchronize physiological processes. The evolution of such synchronization to environmental cycles and their variability is not very well understood. As an example, we use the marine insect Clunio (Diptera, Chironomidae), which synchronize adult emergence and reproduction with the lunar cycle, and show different emergence patterns across populations. We use a model constructed with replicator-mutator dynamics to provide a novel outlook at the evolution of these emergence patterns. In particular, we investigate the effect of two traits of individual phenotypic variability of emergence, the spread and shape, on population-wide emergence patterns. We find that the semilunar and lunar emergence patterns are alternatively stable and occur when the phenotypic distribution has a narrow and is roughly flat. Arrhythmic emergence occurs when the phenotypic distribution is wide and nearly flat. The semi-lunar pattern can only be observed when the parameter of rhythmicity is changed. With our model, we introduce the concepts of frequency-dependent selection and individual phenotypic variability into the theory of chronobiology, which gives us insights into the evolution of rhythmicity in these organisms.

Evolution has given rise to the diversity of life on Earth, but it can also cause species extinctions. While major extinction events are usually associated with external drivers, in this study, we show mechanistically how evolution can trigger abrupt extinction avalanches in ecological networks without any environmental change. In particular, we investigate an eco-evolutionary simulation model of a tripartite mutualistic-antagonistic network, such as a plant-pollinator-herbivore network, with additional intraguild competition. The prevalence of self-organised extinction avalanches depends on a subtle balance of the different interaction types, where antagonism and similarity-based competition are needed for initial diversification while mutualism and trait-independent competition foster evolutionarily driven extinction events. Extinction avalanches are triggered by a mutualist evolving to interact with plants that are not subject to sufficient antagonistic control. Subsequently, the mutualist, its plant partners and their main antagonist potentially outcompete the rest of the community. Our findings point out that evolutionary murder may claim many victims simultaneously and highlight the need to take different interaction types into account to gain a comprehensive understanding of the links between evolution and biodiversity in ecological communities.

A brain's wiring must satisfy conflicting pressures, from the outside world (be capable) and from the inside (stay within finite resources). These pressures often have opposing requirements. Prior work studies these trade-offs mostly between 2-3 pressures at a time, and thus cannot say how many pressures shape brain wiring or for which trade-off brains decide. To see all possible trade-offs at once and to uncover the set of most important pressures, we generate 25,000 synthetic brain networks and describe each by 29 network properties. We then place 635 human (ages 6-22) and 224 mammalian (12 taxonomic orders) brain networks in this property space. The space is triangular, and follows three pressures: computational capability, robustness to damage, and metabolic efficiency. No network is optimal at all three, and biological brains cluster in one small niche of this triangle. There, they accept higher metabolic cost to gain both robustness and capability. Development and evolution move brains in the same direction; additionally, human maturation first raises capability, and later optimizes for efficiency. This study underscores the triangular trade-off between metabolic efficiency, computational capacity and robustness, and the narrow region brains occupy in this trade-off triangle, visible only from a multi-property, cross-species perspective.

Biomarker discovery from high-dimensional RNA sequencing data remains challenging. Conventional methods such as differential expression analysis, pairwise protein-protein interaction networks, and weighted gene co-expression network analysis suffer from false-positive interactions, transitivity-driven noise, and arbitrary thresholds for feature selection. Addressing these limitations, this study proposed a novel framework, Hypergraph Regularised Fuzzy Rough Gene Selection (HR-FRGS), for knowledge-driven biomarker discovery. This pipeline integrates information-rich protein clustering with entropy filtering and PPI-pruned co-expression interactions to form a dual-layer hypergraph. A hypergraph-based scoring method that combines Random Walk with Restart diffusion and Hypergraph Betweenness Centrality is used to identify genes that are central in the biological network. Furthermore an autonomous fuzzy rough set selection eliminates arbitrary threshold dependency for gene selection. HR-FRGS was applied to four TCGA cancer cohorts: Lung Adenocarcinoma, Head and Neck Cancer, Kidney Clear Cell Carcinoma, and Colon Cancer, which reduced over 60,000 transcripts to compact biomarker panels. Validation using classical Machine Learning algorithms with cross-validation demonstrated that biomarker panels matched or exceeded the classification performance of the full transcriptome (AUC > 0.99, MCC > 0.94) and confirmed generalizability (MCC $\geq$ 0.893). Benchmarking against baseline methods and an ablation study showed the contribution of major parts of the algorithm. Functional enrichment analysis captures established pan-cancer hallmarks and cohort-specific oncogenic mechanisms, confirming the biological relevance of the identified genes.

Protein-protein interactions shape cellular organization and disease processes, but their prediction remains difficult because known interaction networks are incomplete, noisy and highly uneven across proteins. Hyperbolic graph learning is well suited to the hierarchical structure of such networks, yet most methods emphasize learning hyperbolic embeddings and pay less attention to how these embeddings are propagated and decoded for type prediction. Here we introduce the Lorentz Tangent Diffusion Adapter (LTDA), a post-embedding module for PPI type prediction, that is, for predicting which of several interaction types a candidate protein pair undergoes. LTDA learns relation-specific protein representations on the Lorentz manifold, projects them to tangent space, applies lightweight graph diffusion, and decodes the diffused representations directly in tangent space. This design uses the tangent space as a prediction-oriented interface between hierarchical representation learning and interaction classification. On SHS27K and SHS148K under BFS and DFS splits, LTDA consistently improves over representative PPI methods and a reproduced HI-PPI baseline, with average gains of 1.41 percentage points in Micro-F1, 3.21 in AUPR, 1.31 in AUC and 1.25 in accuracy. Ablation, degree-bin and biological-evidence analyses indicate that the gains are not explained by simple smoothing or hub correction. LTDA therefore shows that post-embedding adaptation can make Lorentz representations more effective for PPI type prediction.

Biomolecular condensates are condensed assemblies of biomolecules that form through the process of liquid phase separation. Condensates in biology typically function as membraneless organelles, providing compartmentalization in the absence of a dividing lipid membrane. The molecular make-up of different condensates includes diverse multivalent proteins and nucleic acids as the primary drivers, many of them including significant fractions of intrinsically disordered regions (IDRs). To date, the sequence to phase separation relationship of IDRs has focused largely on one protein at a time, studying single-component condensate formation, or single-component partitioning into condensates. The co-phase separation and mixing of two or more IDRs is considerably more complex as both sequences can vary widely in their self- and cross-interactions, as well as their relative abundance in solution. It is unclear that a rule which predicts how a single sequence behaves will also predict what happens when two sequences are mixed. In this study, we disentangle the influence of sequence from that of composition using a set of 18 LAF-1 RGG variants that keep the same length and amino-acid composition and change only the order of the residues. This lets us vary charge patterning and, to a lesser extent, hydropathy patterning while keeping protein composition fixed. By themselves, the sequences phase separation and single-chain compaction are controlled by their degree of charge and hydropathy patterning. Within single-component condensed phases, each sequence adopts a more extended conformational ensemble, due to a more favorable, selfsolvated environment. We find that mixing two IDRs together into a condensate causes this universal scaling behavior to break, impacted by the relative interactions of the two components and overall composition of the slab. We find two different qualitative behaviors, one characterized by cooperative co-condensation when both sequences are subcritical, and the other by scaffold-client behavior when one sequence is supercritical. The scaffold-client systems generally show a high degree of demixing, while the co-condensing systems are generally quite well-mixed in the dense phase. This is surprising because even in cases where both partners have significantly different patterning parameters, they still mix. Thus, the descriptor that predicts a sequence's behavior alone can help indicate whether it will mix with or separate from a second component, but it does not fully determine the outcome on its own.