The sampling of scale-free networks in Molecular Biology is usually achieved by growing networks from a seed using recursive algorithms with elementary moves which include the addition and deletion of nodes and bonds. These algorithms include the Barabasi-Albert algorithm. Later algorithms, such as the Duplication-Divergence algorithm, the Solé algorithm and the iSite algorithm, were inspired by biological processes underlying the evolution of protein networks, and the networks they produce differ essentially from networks grown by the Barabasi-Albert algorithm. In this paper the mean field analysis of these algorithms is reconsidered, and extended to variant and modified implementations of the algorithms. The degree sequences of scale-free networks decay according to a powerlaw distribution, namely $P(k) \sim k^{-γ}$, where $γ$ is a scaling exponent. We derive mean field expressions for $γ$, and test these by numerical simulations. Generally, good agreement is obtained. We also found that some algorithms do not produce scale-free networks (for example some variant Barabasi-Albert and Solé networks).
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.
Achieving complete reproducibility in science, particularly in research fields such as biodiversity, is challenging due to analytical choices, bias and interpretation. Here, we examine examples of reproducibility in biological systematics, ecology, and molecular biology. To mitigate the impact of interpretation and analytical choices, Artificial Intelligence (AI) has provided potential tools. In the present work, while emphasizing the need for methodological rigor and transparency, we acknowledge the role of interpretation in activities such as coding biological characters and detecting morphological patterns in nature. We explore the opportunities and limitations associated with the synergy between big data and AI in molecular biology, emphasizing the need for a more comprehensive and integrated approach based on dataset quality and usefulness. We conclude by advocating for AI-based tools to assist biologists, reinforcing consilience as a criterion for scientific validity without hindering scientific progress.
Understanding the biological mechanisms of disease is crucial for medicine, and in particular, for drug discovery. AI-powered analysis of genome-scale biological data holds great potential in this regard. The increasing availability of single-cell RNA sequencing data has enabled the development of large foundation models for disease biology. However, existing foundation models only modestly improve over task-specific models in downstream applications. Here, we explored two avenues for improving single-cell foundation models. First, we scaled the pre-training data to a diverse collection of 116 million cells, which is larger than those used by previous models. Second, we leveraged the availability of large-scale biological annotations as a form of supervision during pre-training. We trained the \model family of models comprising six transformer-based state-of-the-art single-cell foundation models with 70 million, 160 million, and 400 million parameters. We vetted our models on several downstream evaluation tasks, including identifying the underlying disease state of held-out donors not seen during training, distinguishing between diseased and healthy cells for disease conditions and
AlphaFold 3 represents a transformative advancement in computational biology, enhancing protein structure prediction through novel multi-scale transformer architectures, biologically informed cross-attention mechanisms, and geometry-aware optimization strategies. These innovations dramatically improve predictive accuracy and generalization across diverse protein families, surpassing previous methods. Crucially, AlphaFold 3 embodies a paradigm shift toward differentiable simulation, bridging traditional static structural modeling with dynamic molecular simulations. By reframing protein folding predictions as a differentiable process, AlphaFold 3 serves as a foundational framework for integrating deep learning with physics-based molecular
The molecular machinery of life is largely created via self-organisation of individual molecules into functional assemblies. Minimal coarse-grained models, where a whole macromolecule is represented by a small number of particles, can be of great value in identifying the main driving forces behind self-organisation in cell biology. Such models can incorporate data from both molecular and continuum scales, and their results can be directly compared to experiments. Here we review the state of the art of models for studying the formation and biological function of macromolecular assemblies in cells. We outline the key ingredients of each model and their main findings. We illustrate the contribution of this class of simulations to identifying the physical mechanisms behind life and diseases, and discuss their future developments.
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other but play transparent roles when applied to statistical ensembles (i.e., identically prepared sets) of symbolic sequences. Such an approach can distinguish between entropy and information in genes, predict the secondary structure of ribozymes, and detect the covariation between residues in folded proteins. We also review applications to molecular sequence and structure analysis, and introduce new tools in the characterization of resistance mutations, and in drug design.
Information is a key concept in evolutionary biology. Information is stored in biological organism's genomes, and used to generate the organism as well as to maintain and control it. Information is also "that which evolves". When a population adapts to a local environment, information about this environment is fixed in a representative genome. However, when an environment changes, information can be lost. At the same time, information is processed by animal brains to survive in complex environments, and the capacity for information processing also evolves. Here I review applications of information theory to the evolution of proteins as well as to the evolution of information processing in simulated agents that adapt to perform a complex task.
Quantum computers can in principle solve certain problems exponentially more quickly than their classical counterparts. We have not yet reached the advent of useful quantum computation, but when we do, it will affect nearly all scientific disciplines. In this review, we examine how current quantum algorithms could revolutionize computational biology and bioinformatics. There are potential benefits across the entire field, from the ability to process vast amounts of information and run machine learning algorithms far more efficiently, to algorithms for quantum simulation that are poised to improve computational calculations in drug discovery, to quantum algorithms for optimization that may advance fields from protein structure prediction to network analysis. However, these exciting prospects are susceptible to "hype", and it is also important to recognize the caveats and challenges in this new technology. Our aim is to introduce the promise and limitations of emerging quantum computing technologies in the areas of computational molecular biology and bioinformatics.
Synthetic biology is the engineering of cellular networks. It combines principles of engineering and the knowledge of biological networks to program the behavior of cells. Computational modeling techniques in conjunction with molecular biology techniques have been successful in constructing biological devices such as switches, oscillators, and gates. The ambition of synthetic biology is to construct complex systems from such fundamental devices, much in the same way electronic circuits are built from basic parts. As this ambition becomes a reality, engineering concepts such as interchangeable parts and encapsulation will find their way into biology. We realize that there is a need for computational tools that would support such engineering concepts in biology. As a solution, we have developed the software Athena that allows biological models to be constructed as modules. Modules can be connected to one another without altering the modules themselves. In addition, Athena houses various tools useful for designing synthetic networks including tools to perform simulations, automatically derive transcription rate expressions, and view and edit synthetic DNA sequences. New tools can be i
We developed a theory showing that under appropriate normalizations and rescalings, temperature response curves show a remarkably regular behavior and follow a general, universal law. The impressive universality of temperature response curves remained hidden due to various curve-fitting models not well-grounded in first principles. In addition, this framework has the potential to explain the origin of different scaling relationships in thermal performance in biology, from molecules to ecosystems. Here, we summarize the background, principles and assumptions, predictions, implications, and possible extensions of this theory.
This article frames the relation between biology and physics by characterizing the former as a subdiscipline rather than a special case of the latter. To do this, we posit biological physics as the science of living matter in contrast to classic biophysics, the study of organismal properties by physical techniques. At the scale of the individual cell, living matter is nonunitary, i.e., not composed of aggregated subunits, and has features (e.g., intracellular organizational arrangements and biomolecular condensates) that are unlike any materials of the nonliving world. In transiently or constitutively multicellular forms (social microorganisms, animals, plants), living matter sustains physical processes that are generic (shared with nonliving matter, e.g., subunit communication by molecular diffusion in cellular slime molds), biogeneric (analogous to nonliving matter but realized through cellular activities, e.g., subunit demixing in animal embryos) or nongeneric (pertaining to sui generis materials, e.g., budding of active solids in plants). This "forms of matter" perspective is philosophically situated in the dialectical materialism of Engels and Hessen and the multilevel physica
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.
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled systems, we enforce non-negativity of the solutions, aligning with realistic scenarios in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction in measurement/observation data due to averaging effects, the nonlinear coupling between multiple equations, and the nonlocality arising from fractional-type derivatives. These factors present significant challenges to our inverse problem, and such inverse problems have never been explored in previous literature. To address these challenges, we develop new and effective schemes. Our approach involves properly controlling the injection of different source terms to obtain multiple sets of mean flux data. This allows us to achieve unique identifiability results and accurately determine the unknown parameters. Finally, we establish a connection between our study and practical applications in biology, further highlighting the relevance of our work in real-
Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking. In this paper we formalize these procedures and develop algorithms to solve the relevant problems. In particular, we introduce a new algorithm that solves a "subcoloring" problem for expressing the difference between the taxonomy and phylogeny at a given rank. This algorithm improves upon the current best algorithm in terms of asymptotic complexity for the parameter regime of interest; we also describe a branch-and-bound algorithm that saves orders of magnitude in computation on real data sets. We also develop a formalism and an algorithm for rooting phylogenetic trees according to a taxonomy. All of these algorithms are implemented in freely-available software.
Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown remarkable ability in approximating complex distributions in various domains. However, their application in systems biology for approximating intractable likelihood functions remains unexplored. Here, we elucidate a framework for leveraging normalizing flows to approximate complex likelihood functions inherent to systems biology models. By using normalizing flows in the Simulation-based inference setting, we demonstrate a method that not only approximates a likelihood function but also allows for model inference in the model selection setting. We showcase the effectiveness of this approach on real-world systems biology problems, providing practical guidance for implementation and highlighting its advantages over traditional computational methods.
Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. Results: Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embedded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources
Maximizing a non-negative, monontone, submodular function $f$ over $n$ elements under a cardinality constraint $k$ (SMCC) is a well-studied NP-hard problem. It has important applications in, e.g., machine learning and influence maximization. Though the theoretical problem admits polynomial-time approximation algorithms, solving it in practice often involves frequently querying submodular functions that are expensive to compute. This has motivated significant research into designing parallel approximation algorithms in the adaptive complexity model; adaptive complexity (adaptivity) measures the number of sequential rounds of $\text{poly}(n)$ function queries an algorithm requires. The state-of-the-art algorithms can achieve $(1-\frac{1}{e}-\varepsilon)$-approximate solutions with $O(\frac{1}{\varepsilon^2}\log n)$ adaptivity, which approaches the known adaptivity lower-bounds. However, the $O(\frac{1}{\varepsilon^2} \log n)$ adaptivity only applies to maximizing worst-case functions that are unlikely to appear in practice. Thus, in this paper, we consider the special class of $p$-superseparable submodular functions, which places a reasonable constraint on $f$, based on the parameter
Systems Biology has emerged in the last years as a new holistic approach based on the global understanding of cells instead of only being focused on their individual parts (genes or proteins), to better understand the complexity of human cells. Since the Systems Biology still does not provide the most accurate answers to our questions due to the complexity of cells and the limited quality of available information to perform a good gene/protein map analysis, we have created simpler models to ensure easier analysis of the map that represents the human cell. Therefore, a virtual organism has been designed according to the main physiological rules for humans in order to replicate the human organism and its vital functions. This toy model was constructed by defining the topology of its genes/proteins and the biological functions associated to it. There are several examples of these toy models that emulate natural processes to perform analysis of the virtual life in order to design the best strategy to understand real life. The strategy applied in this study combines topological and functional analysis integrating the knowledge about the relative position of a node among the others in th
We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global aspects of synthetic and biological data. We show examples such as the emergence of giant components in Erdos-Renyi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression data. We provide exact theoretical calculations, numerical approximations and error estimations of entropy, algorithmic probability and Kolmogorov complexity for different types of graphs, characterizing their variant and invariant properties. We introduce formal definitions of complexity for both labeled and unlabeled graphs and prove that the Kolmogorov complexity of a labeled graph is a good approximation of its unlabeled Kolmogorov complexity and thus a robust definition of graph complexity.