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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.
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.
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
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.
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Structural biology aims at characterizing the structural and dynamic properties of biological macromolecules at atomic details. Gaining insight into three dimensional structures of biomolecules and their interactions is critical for understanding the vast majority of cellular processes, with direct applications in health and food sciences. Since 2010, the WeNMR project (www.wenmr.eu) has implemented numerous web-based services to facilitate the use of advanced computational tools by researchers in the field, using the high throughput computing infrastructure provided by EGI. These services have been further developed in subsequent initiatives under H2020 projects and are now operating as Thematic Services in the European Open Science Cloud (EOSC) portal (www.eosc-portal.eu), sending >12 millions of jobs and using around 4000 CPU-years per year. Here we review 10 years of successful e-infrastructure solutions serving a large worldwide community of over 23,000 users to date, providing them with user-friendly, web-based solutions that run complex workflows in structural biology. The current set of active WeNMR portals are described, together with the complex backend machinery that
A public preprint server such as arXiv allows authors to publish their manuscripts before submitting them to journals for peer review. It offers the chance to establish priority by making the results available upon completion. This article presents the arXiv section Quantitative Biology and investigates the advantages of preprint publications in terms of reception, which can be measured by means of citations. This paper focuses on the publication and citation delay, citation counts and the authors publishing their e-prints on arXiv. Moreover, the paper discusses the benefit for scientists as well as publishers. The results that are based on 12 selected journals show that submitting preprints to arXiv has become more common in the past few years, but the number of papers submitted to Quantitative Biology is still small and represents only a fraction of the total research output in biology. An immense advantage of arXiv is to overcome the long publication delay resulting from peer review. Although preprints are visible prior to the officially published articles, a significant citation advantage was only found for the Journal of Theoretical Biology.
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
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.
The optimization-based damage detection and damage state digital twinning capabilities are examined here of a novel conditional-labeled generative adversarial network methodology. The framework outperforms current approaches for fault anomaly detection as no prior information is required for the health state of the system: a topic of high significance for real-world applications. Specifically, current artificial intelligence-based digital twinning approaches suffer from the uncertainty related to obtaining poor predictions when a low number of measurements is available, physics knowledge is missing, or when the damage state is unknown. To this end, an unsupervised framework is examined and validated rigorously on the benchmark structural health monitoring measurements of Z24 Bridge: a post-tensioned concrete highway bridge in Switzerland. In implementing the approach, firstly, different same damage-level measurements are used as inputs, while the model is forced to converge conditionally to two different damage states. Secondly, the process is repeated for a different group of measurements. Finally, the convergence scores are compared to identify which one belongs to a different da
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
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Classical molecular dynamics (MD) simulations will be able to reach sampling in the second timescale within five years, producing petabytes of simulation data at current force field accuracy. Notwithstanding this, MD will still be in the regime of low-throughput, high-latency predictions with average accuracy. We envisage that machine learning (ML) will be able to solve both the accuracy and time-to-prediction problem by learning predictive models using expensive simulation data. The synergies between classical, quantum simulations and ML methods, such as artificial neural networks, have the potential to drastically reshape the way we make predictions in computational structural biology and drug discovery.
A number of X-ray analyses of an enzyme involved in a key early stage of tetrapyrrole biosynthesis are reported. Two structures of human 5-aminolaevulinate dehydratase (ALAD), native and recombinant, have been determined at 2.8 Å resolution, showing that the enzyme adopts an octameric quaternary structure in accord with previously published analyses of the enzyme from a range of other species. However, this is in contrast to the finding that a disease-related F12L mutant of the human enzyme uniquely forms hexamers [Breinig et al. (2003[Breinig, S., Kervinen, J., Stith, L., Wasson, A. S., Fairman, R., Wlodawer, A., Zdanov, A. & Jaffe, E. K. (2003). Nature Struct. Biol. 10, 757-763.]), Nature Struct. Biol. 10, 757–763]. Monomers of all ALADs adopt the TIM-barrel fold; the subunit conformation that assembles into the octamer includes the N-terminal tail of one monomer curled around the (α/β)8 barrel of a neighbouring monomer. Both crystal forms of the human enzyme possess two monomers per asymmetric unit, termed A and B. In the native enzyme there are a number of distinct structural differences between the A and B monomers, with the latter exhibiting greater disorder in a number of loop regions and in the active site. In contrast, the second monomer of the recombinant enzyme appears to be better defined and the active site of both monomers clearly possesses a zinc ion which is bound by three conserved cysteine residues. In native human ALAD, the A monomer also has a ligand resembling the substrate ALA which is covalently bound by a Schiff base to one of the active-site lysines (Lys252) and is held in place by an ordered active-site loop. In contrast, these features of the active-site structure are disordered or absent in the B subunit of the native human enzyme. The octameric structure of the zinc-dependent ALAD from the hyperthermophile Pyrobaculum calidifontis is also reported at a somewhat lower resolution of 3.5 Å. Finally, the details are presented of a high-resolution structure of the Escherichia coli ALAD enzyme co-crystallized with a noncovalently bound moiety of the product, porphobilinogen (PBG). This structure reveals that the pyrrole side-chain amino group is datively bound to the active-site zinc ion and that the PBG carboxylates interact with the enzyme via hydrogen bonds and salt bridges with invariant residues. A number of hydrogen-bond interactions that were previously observed in the structure of yeast ALAD with a cyclic intermediate resembling the product PBG appear to be weaker in the new structure, suggesting that these interactions are only optimal in the transition state.
Gait abnormality detection is critical for the early discovery and progressive tracking of musculoskeletal and neurological disorders, such as Parkinson's and Cerebral Palsy. Especially, analyzing the foot-floor contacts during walking provides important insights into gait patterns, such as contact area, contact force, and contact time, enabling gait abnormality detection through these measurements. Existing studies use various sensing devices to capture such information, including cameras, wearables, and force plates. However, the former two lack force-related information, making it difficult to identify the causes of gait health issues, while the latter has limited coverage of the walking path. In this study, we leverage footstep-induced structural vibrations to infer foot-floor contact profiles and detect gait abnormalities. The main challenge lies in modeling the complex force transfer mechanism between the foot and the floor surfaces, leading to difficulty in reconstructing the force and contact profile during foot-floor interaction using structural vibrations. To overcome the challenge, we first characterize the floor vibration for each contact type (e.g., heel, midfoot, and
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-
Though it goes without saying that linear algebra is fundamental to mathematical biology, polynomial algebra is less visible. In this article, we will give a brief tour of four diverse biological problems where multivariate polynomials play a central role -- a subfield that is sometimes called "algebraic biology." Namely, these topics include biochemical reaction networks, Boolean models of gene regulatory networks, algebraic statistics and genomics, and place fields in neuroscience. After that, we will summarize the history of discrete and algebraic structures in mathematical biology, from their early appearances in the late 1960s to the current day. Finally, we will discuss the role of algebraic biology in the modern classroom and curriculum, including resources in the literature and relevant software. Our goal is to make this article widely accessible, reaching the mathematical biologist who knows no algebra, the algebraist who knows no biology, and especially the interested student who is curious about the synergy between these two seemingly unrelated fields.
Accurate structural response prediction forms a main driver for structural health monitoring and control applications. This often requires the proposed model to adequately capture the underlying dynamics of complex structural systems. In this work, we utilize a learnable Extended Kalman Filter (EKF), named the Neural Extended Kalman Filter (Neural EKF) throughout this paper, for learning the latent evolution dynamics of complex physical systems. The Neural EKF is a generalized version of the conventional EKF, where the modeling of process dynamics and sensory observations can be parameterized by neural networks, therefore learned by end-to-end training. The method is implemented under the variational inference framework with the EKF conducting inference from sensing measurements. Typically, conventional variational inference models are parameterized by neural networks independent of the latent dynamics models. This characteristic makes the inference and reconstruction accuracy weakly based on the dynamics models and renders the associated training inadequate. In this work, we show that the structure imposed by the Neural EKF is beneficial to the learning process. We demonstrate the
Background: Margin assessment of basal cell carcinoma using the frozen section is a common task of pathology intraoperative consultation. Although frequently straight-forward, the determination of the presence or absence of basal cell carcinoma on the tissue sections can sometimes be challenging. We explore if a deep learning model trained on mobile phone-acquired frozen section images can have adequate performance for future deployment. Materials and Methods: One thousand two hundred and forty-one (1241) images of frozen sections performed for basal cell carcinoma margin status were acquired using mobile phones. The photos were taken at 100x magnification (10x objective). The images were downscaled from a 4032 x 3024 pixel resolution to 576 x 432 pixel resolution. Semantic segmentation algorithm Deeplab V3 with Xception backbone was used for model training. Results: The model uses an image as input and produces a 2-dimensional black and white output of prediction of the same dimension; the areas determined to be basal cell carcinoma were displayed with white color, in a black background. Any output with the number of white pixels exceeding 0.5% of the total number of pixels is dee
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