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Biomolecular condensates are formed by liquid-liquid phase separation (LLPS) of multivalent molecules. LLPS from a single (\"homotypic\") constituent is governed by buffering: above a threshold, free monomer concentration is clamped, with all added molecules entering the condensed phase. However, both experiment and theory demonstrate that buffering fails for the concentration dependence of multicomponent (\"heterotypic\") LLPS. Using network-free stochastic modeling, we demonstrate that LLPS can be described by the solubility product constant (Ksp): the product of free monomer concentrations, accounting for the ideal stoichiometries governed by the valencies, displays a threshold above which additional monomers are funneled into large clusters; this reduces to simple buffering for homotypic systems. The Ksp regulates the composition of the dilute phase for a wide range of valencies and stoichiometries. The role of Ksp is further supported by coarse-grained spatial particle simulations. Thus, the solubility product offers a general formulation for the concentration dependence of LLPS.

The BioModels Repository contains over 1000 manually curated mechanistic models from published literature, most often encoded in the Systems Biology Markup Language (SBML). This community-based standard formally specifies each model, but does not describe the computational experimental conditions to run a simulation and collect data. Therefore, it can be challenging to reproduce any figure or result from a publication with an SBML model alone. The Simulation Experiment Description Markup Language (SED-ML) provides a solution: a standard way to specify exactly how to run an experiment corresponding to a specific figure or result. BioModels was established years before SED-ML, and both systems evolved over time, both in content and acceptance. Hence, only about half of the entries in BioModels contained SED-ML files, and these files reflected the version of SED-ML that was available at the time. Additionally, almost all of these SED-ML files had at least one minor mistake that made them impossible to run. To make these models and their results more reproducible, we report here on our work updating, correcting and generating new SED-ML files for 1055 curated mechanistic models in BioModels. In addition, because SED-ML is implementation-independent, it can be used for verification, demonstrating that results hold across multiple simulation engines. We tested, corrected, and improved over 450 existing SED-ML files in the BioModels database, and created basic files for the rest of the entries. Then, we used a wrapper architecture for interpreting SED-ML, and report verification results across five different ODE-based biosimulation engines, after further improving the models, the wrappers, and the engines themselves. Our work with SED-ML and the BioModels collection aims to improve the utility of these models by making them more reproducible and credible. Improved reproducibility means these models are now even more fit for re-use, such as in new investigations and as components of multiscale models.

[...]novel mathematical and computational approaches enabled a deeper understanding of biological systems. Biological networks are usually described as graphs with nodes representing biological entities (e.g., genes, proteins, functional complexes) and connecting edges representing influences on their behavior. [...]graph-theoretical methods are under constant development, as illustrated by the two manuscripts in this Research Topic. In summary, the Research Topic, Network-based Mathematical Modeling in Cell and Developmental Biology, gathered many state-of-the-art studies that will guide future directions.

Predictive mathematical modeling is an essential part of systems biology and is interconnected with information management. Systems biology information is often stored in specialized formats to facilitate data storage and analysis. These formats are not designed for easy human readability and thus require specialized software to visualize and interpret results. Therefore, comprehending modeling and underlying networks and pathways is contingent on mastering systems biology tools, which is particularly challenging for users with no or little background in data science or system biology. To address this challenge, we investigated the usage of public Artificial Intelligence (AI) tools in exploring systems biology resources in mathematical modeling. We tested public AI’s understanding of mathematics in models, related systems biology data, and the complexity of model structures. Our approach can enhance the accessibility of systems biology for non-system biologists and help them understand systems biology without a deep learning curve.

Live poultry markets (LPMs) are regarded as hubs for avian influenza virus (AIV) transmission in poultry and are a major risk factor in human AIV infections. We performed an AIV surveillance study at a wholesale LPM, where different poultry species were sold in separate stalls, and nine retail LPMs, which received poultry from the wholesale LPM but where different poultry species were sold in one stall, in Guangdong province from 2017 to 2019. A higher AIV isolation rate was observed at the retail LPMs than the wholesale LPM. H9N2 was the dominant AIV subtype and was mainly present in chickens and quails. The genetic diversity of H9N2 viruses was greater at the retail LPMs, where a complex system of two-way transmission between different poultry species had formed. The isolated H9N2 viruses could be classed into four genotypes: G57 and the three novel genotypes, NG164, NG165, and NG166. The H9N2 AIVs isolated from chickens and quails at the wholesale LPM only belonged to the G57 and NG164 genotypes, respectively. However, the G57, NG164, and NG165 genotypes were identified in both chickens and quails at the retail LPMs. We found that the replication and transmission of the NG165 genotype were more adaptive to both poultry and mammalian models than those of its precursor genotype, NG164. Our findings revealed that mixed poultry selling at retail LPMs has increased the genetic diversity of AIVs, which might facilitate the emergence of novel viruses that threaten public health.

Logic-derived modeling has been used to map biological networks and to study arbitrary functional interactions, and fine-grained kinetic modeling can accurately predict the detailed behavior of well-characterized molecular systems; at present, however, neither approach comes close to unraveling the full complexity of a cell. The current data revolution offers significant promises and challenges to both approaches - and could bring them together as it has spurred the development of new methods and tools that may help to bridge the many gaps between data, models, and mechanistic understanding. Have you used logic modeling in your research? It would not be surprising if many biologists would answer no to this hypothetical question. And it would not be true. In high school biology we already became familiar with cartoon diagrams that illustrate basic mechanisms of the molecular machinery operating inside cells. These are nothing else but simple logic models. If receptor and ligand are present, then receptor-ligand complexes form; if a receptor-ligand complex exists, then an enzyme gets activated; if the enzyme is active, then a second messenger is being produced; and so on. Such chains of causality are the essence of logic models (Figure 1a). Arbitrary events and mechanisms are abstracted; relationships are simplified and usually involve just two possible conditions and three possible consequences. The presence or absence of one or more molecule, activity, or function, [some icons in the cartoon] will determine whether another one of them will be produced (created, up-regulated, stimulated) [a 'positive' link] or destroyed (degraded, down-regulated, inhibited) [a 'negative' link], or be unaffected [there is no link]. The icons and links often do not follow a standardized format, but when we look at such a cartoon diagram, we believe that we 'understand' how the system works. Because our brain is easily able to process these relationships, these diagrams allow us to answer two fundamental types of questions related to the system: why (are certain things happening)? What if (we make some changes)?

Digital twins represent a key technology for precision health. Medical digital twins consist of computational models that represent the health state of individual patients over time, enabling optimal therapeutics and forecasting patient prognosis. Many health conditions involve the immune system, so it is crucial to include its key features when designing medical digital twins. The immune response is complex and varies across diseases and patients, and its modelling requires the collective expertise of the clinical, immunology, and computational modelling communities. This review outlines the initial progress on immune digital twins and the various initiatives to facilitate communication between interdisciplinary communities. We also outline the crucial aspects of an immune digital twin design and the prerequisites for its implementation in the clinic. We propose some initial use cases that could serve as “proof of concept” regarding the utility of immune digital technology, focusing on diseases with a very different immune response across spatial and temporal scales (minutes, days, months, years). Lastly, we discuss the use of digital twins in drug discovery and point out emerging challenges that the scientific community needs to collectively overcome to make immune digital twins a reality.

Most computational models in biology are built and intended for “single-use”; the lack of appropriate annotation creates models where the assumptions are unknown, and model elements are not uniquely identified. Simply recreating a simulation result from a publication can be daunting; expanding models to new and more complex situations is a herculean task. As a result, new models are almost always created anew, repeating literature searches for kinetic parameters, initial conditions and modeling specifics. It is akin to building a brick house starting with a pile of clay. Here we discuss a concept for building annotated, reusable models, by starting with small well-annotated modules we call ModelBricks. Curated ModelBricks, accessible through an open database, could be used to construct new models that will inherit ModelBricks annotations and thus be easier to understand and reuse. Key features of ModelBricks include reliance on a commonly used standard language (SBML), rule-based specification describing species as a collection of uniquely identifiable molecules, association with model specific numerical parameters, and more common annotations. Physical bricks can vary substantively; likewise, to be useful the structure of ModelBricks must be highly flexible—it should encapsulate mechanisms from single reactions to multiple reactions in a complex process. Ultimately, a modeler would be able to construct large models by using multiple ModelBricks, preserving annotations and provenance of model elements, resulting in a highly annotated model. We envision the library of ModelBricks to rapidly grow from community contributions. Persistent citable references will incentivize model creators to contribute new ModelBricks.

In a paper in the Aug 2005 issue of Nature Biotechnology, Kitano et al. discuss the use of process diagrams to map signal-transduction cascades; they have used the formalism of process diagrams to specify pathway maps that are both readable and precise, and they have developed a map depicting hundreds of species and reactions involved in signaling by the epidermal growth factor receptor (EGFR)1. However, this map, as expansive as it is, omits the vast majority of species and reactions that could potentially be generated during signaling. Comprehensive process diagrams for this, or any other signaling system, are very likely to be of unmanageable size.