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Several simple growth and decay models use concepts and measures from fractal geometry. Kinetic models relevant to condensed matter observations arerecalled. They should be specifically adapted with appropriate degrees of freedom in order to reproduce power law behaviors, e.g. of species extinctions, cloud fracture, financial crashes. This allows one to illustrate scientific problems relevant to the growth and control of epidemias, and other event or entity propagation in biology, ecology, traffic and economy.
Redox biology underpins signalling, metabolism, immunity, and adaptation, yet lacks a unifying theoretical framework capable of formalising structure, function, and dynamics. Current interpretations rely on descriptive catalogues of molecules and reactions, obscuring how redox behaviour emerges from constrained biochemical organisation. Here, we present a mathematical theory of redox biology that resolves this gap by treating redox systems as finite, compositional, dynamical, and spatially embedded objects. We define a structured redox state space in which admissible molecular transformations form a neutral algebra of possibilities. Biological function emerges when this structure is embedded within a wider molecular network and interpreted through weighted flux distributions. Time-dependent reweighting of these transformations generates redox dynamics, while spatial embedding enforces locality and causality, yielding a distributed redox field. Within this framework, context dependence, nonlinearity, hysteresis, and memory arise naturally from bounded state spaces and irreversible transformations, without requiring ad hoc assumptions. This theory provides a working, predictive inter
Quantum science and biology now intersect in three complementary directions: quantum in biology, quantum for biology, and biology for quantum. This review provides a structured narrative evidence map of that interface rather than an exhaustive catalogue or formal systematic review. For each topic, we ask what the mechanistic or technological claim is, which quantum resource is invoked, what the strongest experiments and models establish, which classical alternatives or engineering confounds remain competitive, and what decisive tests or benchmarks would most strongly change confidence. The most mature quantum-in-biology cases remain mechanistically constrained tunneling in some enzymatic hydrogen-transfer reactions and radical-pair spin chemistry as a viable framework for magnetoreception, whereas several higher-visibility topics remain suggestive but unresolved under physiological conditions. In quantum for biology, the central issue is whether quantum-enabled tools improve biological inference relative to strong classical baselines under realistic calibration, dose, throughput, and uncertainty constraints. In biology for quantum, the strongest claims arise when biomolecular struc
The rapid evolution of large language models (LLMs) has expanded their capabilities from basic dialogue to advanced scientific reasoning. However, existing benchmarks in biology often fail to assess a critical skill required of researchers: the ability to integrate experimental results with contextual knowledge to derive meaningful conclusions. To address this gap, we introduce BABE(Biology Arena BEnchmark), a comprehensive benchmark designed to evaluate the experimental reasoning capabilities of biological AI systems. BABE is uniquely constructed from peer-reviewed research papers and real-world biological studies, ensuring that tasks reflect the complexity and interdisciplinary nature of actual scientific inquiry. BABE challenges models to perform causal reasoning and cross-scale inference. Our benchmark provides a robust framework for assessing how well AI systems can reason like practicing scientists, offering a more authentic measure of their potential to contribute to biological research.
Some astrobiological models suggest that molecular clouds may serve as habitats for extraterrestrial life. This study reviews recent theoretical work addressing the physical and biochemical prerequisites for life in such environments, with particular focus on three subjects: (1) bioenergetic pathways under extreme low-temperature conditions; (2) the emergence and preservation of biomolecular chirality; and (3) detection methodologies for potential biosignatures. In this paper, we formally introduce the molecular cloud biology concept, which integrates all physicochemical and metabolic processes hypothesized to sustain life within molecular clouds. As a potential branch of astrobiology, molecular cloud biology warrants interdisciplinary collaborative research to validate its foundational assumptions and explore its scientific implications.
This technical monograph provides a comprehensive overview of the field of quantum biology. It approaches quantum biology from a physical perspective with core quantum mechanical concepts presented foremost to provide a theoretical foundation for the field. An extensive body of research is covered to clarify the significance of quantum biology as a scientific field, outlining the field's long-standing importance in the historical development of quantum theory. This lays the essential groundwork to enable further advances in nanomedicine and biotechnology. Written for academics, biological science researchers, physicists, biochemists, medical technologists, and students of quantum mechanics, this text brings clarity to fundamental advances being made in the emerging science of quantum biology.
This study systematically evaluates 27 frontier Large Language Models on eight biology benchmarks spanning molecular biology, genetics, cloning, virology, and biosecurity. Models from major AI developers released between November 2022 and April 2025 were assessed through ten independent runs per benchmark. The findings reveal dramatic improvements in biological capabilities. Top model performance increased more than 4-fold on the challenging text-only subset of the Virology Capabilities Test over the study period, with OpenAI's o3 now performing twice as well as expert virologists. Several models now match or exceed expert-level performance on other challenging benchmarks, including the biology subsets of GPQA and WMDP and LAB-Bench CloningScenarios. Contrary to expectations, chain-of-thought did not substantially improve performance over zero-shot evaluation, while extended reasoning features in o3-mini and Claude 3.7 Sonnet typically improved performance as predicted by inference scaling. Benchmarks such as PubMedQA and the MMLU and WMDP biology subsets exhibited performance plateaus well below 100%, suggesting benchmark saturation and errors in the underlying benchmark data. The
The Lagrangian formalism has attracted the attention of mathematicians and physicists for more than 250 years and has played significant roles in establishing modern theoretical physics. The history of the Lagrangian formalism in biology is much shorter, spanning only the last 50 years. In this paper, a broad review of the Lagrangian formalism in biology is presented in the context of both its historical and modern developments. Detailed descriptions of different methods to derive Lagrangians for five selected population dynamics models are given and the resulting Lagrangians are presented and discussed. The procedure to use the obtained Lagrangians to gain new biological insights into the evolution of the populations without solving the equations of motion is described and applied to the models. Finally, perspectives of the Lagrangian formalism in biology are discussed.
Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure or dynamics of specific subsystems in controlled conditions, compositional systems biology aims to connect these models, asking critical questions about the space between models: What variables should a submodel expose through its interface? How do coupled models connect and translate across scales? How do domain-specific models connect across biological and physical disciplines to drive the synthesis of new knowledge? This approach requires robust software to integrate diverse datasets and submodels, providing researchers with tools to flexibly recombine, iteratively refine, and collaboratively expand their models. This article offers a comprehensive framework to support this vision, including: a conceptual and graphical framework to define interfaces and composition patterns; standardized schemas that facilitate modular data and model assembly; biological templates that integrate detailed submodels that connect molecular processes to the emerg
The convergence of artificial intelligence (AI) and synthetic biology is rapidly accelerating the pace of biological discovery and engineering. AI techniques, such as large language models and biological design tools, are enabling the automated design, build, test, and learning cycles for engineered biological systems. This convergence promises to democratize synthetic biology and unlock novel applications across domains from medicine to environmental sustainability. However, it also poses significant risks around reliability, dual use, and governance. The opacity of AI models, the deskilling of workforces, and the outdated nature of current regulatory frameworks present challenges in ensuring responsible development. Urgent attention is needed to update governance structures, integrate human oversight into increasingly automated workflows, and foster a culture of responsibility among the growing community of bioengineers. Only by proactively addressing these issues can we realize the transformative potential of AI-driven synthetic biology while mitigating its risks.
Systems biology models are useful models of complex biological systems that may require a large amount of experimental data to fit each model's parameters or to approximate a likelihood function. These models range from a few to thousands of parameters depending on the complexity of the biological system modeled, potentially making the task of fitting parameters to the model difficult - especially when new experimental data cannot be gathered. We demonstrate a method that uses structural biology predictions to augment systems biology models to improve systems biology models' predictions without having to gather more experimental data. Additionally, we show how systems biology models' predictions can help evaluate novel structural biology hypotheses, which may also be expensive or infeasible to validate.
Network biology is an interdisciplinary field bridging computational and biological sciences that has proved pivotal in advancing the understanding of cellular functions and diseases across biological systems and scales. Although the field has been around for two decades, it remains nascent. It has witnessed rapid evolution, accompanied by emerging challenges. These challenges stem from various factors, notably the growing complexity and volume of data together with the increased diversity of data types describing different tiers of biological organization. We discuss prevailing research directions in network biology and highlight areas of inference and comparison of biological networks, multimodal data integration and heterogeneous networks, higher-order network analysis, machine learning on networks, and network-based personalized medicine. Following the overview of recent breakthroughs across these five areas, we offer a perspective on the future directions of network biology. Additionally, we offer insights into scientific communities, educational initiatives, and the importance of fostering diversity within the field. This paper establishes a roadmap for an immediate and long-
Cancer, as the uncontrollable cell growth, is related to many branches of biology. In this review, we will discuss three mathematical approaches for studying cancer biology: population dynamics, gene regulation, and developmental biology. If we understand all biochemical mechanisms of cancer cells, we can directly calculate how the cancer cell population behaves. Inversely, just from the cell count data, we can use population dynamics to infer the mechanisms. Cancer cells emerge from certain genetic mutations, which affect the expression of other genes through gene regulation. Therefore, knowledge of gene regulation can help with cancer prevention and treatment. Developmental biology studies acquisition and maintenance of normal cellular function, which is inspiring to cancer biology in the opposite direction. Besides, cancer cells implanted into an embryo can differentiate into normal tissues, which provides a possible approach of curing cancer. This review illustrates the role of mathematics in these three fields: what mathematical models are used, what data analysis tools are applied, and what mathematical theorems need to be proved. We hope that applied mathematicians and even
Recent advances in Large Language Models (LLMs) have presented new opportunities for integrating Artificial General Intelligence (AGI) into biological research and education. This study evaluated the capabilities of leading LLMs, including GPT-4, GPT-3.5, PaLM2, Claude2, and SenseNova, in answering conceptual biology questions. The models were tested on a 108-question multiple-choice exam covering biology topics in molecular biology, biological techniques, metabolic engineering, and synthetic biology. Among the models, GPT-4 achieved the highest average score of 90 and demonstrated the greatest consistency across trials with different prompts. The results indicated GPT-4's proficiency in logical reasoning and its potential to aid biology research through capabilities like data analysis, hypothesis generation, and knowledge integration. However, further development and validation are still required before the promise of LLMs in accelerating biological discovery can be realized.
It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalized diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field of heterogeneous anomalous transport (HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and NMR), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous t
One possible explanation for magnetosensing in biology, such as avian magnetoreception, is based on the spin dynamics of certain chemical reactions that involve radical pairs. Radical pairs have been suggested to also play a role in anesthesia, hyperactivity, neurogenesis, circadian clock rhythm, microtubule assembly, etc. It thus seems critical to probe the credibility of such models. One way to do so is through isotope effects with different nuclear spins. Here we briefly review the papers involving spin-related isotope effects in biology. We suggest studying isotope effects can be an interesting avenue for quantum biology.
Characterizing structural and dynamic properties of proteins and large macromolecular assemblies is crucial to understand the molecular mechanisms underlying biological functions. In the field of Structural Biology, no single method comprehensively reveals the behavior of biological systems across various spatio-temporal scales. Instead, we have a versatile toolkit of techniques, each contributing a piece to the overall puzzle. Integrative Structural Biology combines different techniques to create accurate and precise multi-scale models that expand our understanding of complex biological systems. This review outlines recent advancements in computational and experimental methods in Structural Biology, with special focus on recent Artificial Intelligence techniques, emphasizes integrative approaches that combine different types of data for precise spatio-temporal modeling, and provides an outlook into future directions of this field.
Linguistic laws, the common statistical patterns of human language, have been investigated by quantitative linguists for nearly a century. Recently, biologists from a range of disciplines have started to explore the prevalence of these laws beyond language, finding patterns consistent with linguistic laws across multiple levels of biological organisation, from molecular (genomes, genes, and proteins) to organismal (animal behaviour) to ecological (populations and ecosystems). We propose a new conceptual framework for the study of linguistic laws in biology, comprising and integrating distinct levels of analysis, from description to prediction to theory building. Adopting this framework will provide critical new insights into the fundamental rules of organisation underpinning natural systems, unifying linguistic laws and core theory in biology.
Molecular biology and biochemistry interpret microscopic processes in the living world in terms of molecular structures and their interactions, which are quantum mechanical by their very nature. Whereas the theoretical foundations of these interactions are very well established, the computational solution of the relevant quantum mechanical equations is very hard. However, much of molecular function in biology can be understood in terms of classical mechanics, where the interactions of electrons and nuclei have been mapped onto effective classical surrogate potentials that model the interaction of atoms or even larger entities. The simple mathematical structure of these potentials offers huge computational advantages; however, this comes at the cost that all quantum correlations and the rigorous many-particle nature of the interactions are omitted. In this work, we discuss how quantum computation may advance the practical usefulness of the quantum foundations of molecular biology by offering computational advantages for simulations of biomolecules. We not only discuss typical quantum mechanical problems of the electronic structure of biomolecules in this context, but also consider t
Astronomers have found the first confirmed atmosphere around a rocky planet in another star’s habitable zone。 The planet, LHS 1140 b, revealed its atmosphere through helium slowly leaking into space。 Located 48 light-years away, the world may have preserved its atmosphere for billions of years, making it a promising target in the search for potenti