COPASI--a COmplex PAthway SImulator

Chemical reaction network knowledge graphs: the OntoRXN ontology

The organization and management of large amounts of data has become a major point in almost all areas of human knowledge. In this context, semantic approaches propose a structure for the target data, defining ontologies that state the types of entities on a certain field and how these entities are interrelated. In this work, we introduce OntoRXN, a novel ontology describing the reaction networks constructed from computational chemistry calculations. Under our paradigm, these networks are handled as undirected graphs, without assuming any traversal direction. From there, we propose a core class structure including reaction steps, network stages, chemical species, and the lower-level entities for the individual computational calculations. These individual calculations are founded on the OntoCompChem ontology and on the ioChem-BD database, where information is parsed and stored in CML format. OntoRXN is introduced through several examples in which knowledge graphs based on the ontology are generated for different chemical systems available on ioChem-BD. Finally, the resulting knowledge graphs are explored through SPARQL queries, illustrating the power of the semantic approach to standardize the analysis of intricate datasets and to simplify the development of complex workflows.

Kinetic Rationalization of Nonlinear Effects in Asymmetric Catalytic Cascade Reactions under Curtin-Hammett Conditions

Observations of nonlinear effects of catalyst enantiopurity on product enantiomeric excess in asymmetric catalysis are often used to infer that more than one catalyst species is involved in one or more reaction steps. We demonstrate here, however, that in the case of asymmetric catalytic cascade reactions, a nonlinear effect may be observed in the absence of any higher order catalyst species or any reaction step involving two catalyst species. We illustrate this concept with an example from a recent report of an organocatalytic enantioselective [10 + 2] stepwise cyclization reaction. The disruption of pre-equilibria (Curtin-Hammett equilibrium) in reversible steps occurring prior to the final irreversible product formation step can result in an alteration of the final product ee from what would be expected based on a linear relationship with the enantiopure catalyst. The treatment accounts for either positive or negative nonlinear effects in systems over a wide range of conditions including "major-minor" kinetics or the more conventional "lock-and-key" kinetics. The mechanistic scenario proposed here may apply generally to other cascade reaction systems exhibiting similar kinetic features and should be considered as a viable alternative model whenever a nonlinear effect is observed in a cascade sequence of reactions.

Modeling Calcium Signaling in S. cerevisiae Highlights the Role and Regulation of the Calmodulin-Calcineurin Pathway in Response to Hypotonic Shock

Calcium homeostasis and signaling processes in Saccharomyces cerevisiae, as well as in any eukaryotic organism, depend on various transporters and channels located on both the plasma and intracellular membranes. The activity of these proteins is regulated by a number of feedback mechanisms that act through the calmodulin-calcineurin pathway. When exposed to hypotonic shock (HTS), yeast cells respond with an increased cytosolic calcium transient, which seems to be conditioned by the opening of stretch-activated channels. To better understand the role of each channel and transporter involved in the generation and recovery of the calcium transient—and of their feedback regulations—we defined and analyzed a mathematical model of the calcium signaling response to HTS in yeast cells. The model was validated by comparing the simulation outcomes with calcium concentration variations before and during the HTS response, which were observed experimentally in both wild-type and mutant strains. Our results show that calcium normally enters the cell through the High Affinity Calcium influx System and mechanosensitive channels. The increase of the plasma membrane tension, caused by HTS, boosts the opening probability of mechanosensitive channels. This event causes a sudden calcium pulse that is rapidly dissipated by the activity of the vacuolar transporter Pmc1. According to model simulations, the role of another vacuolar transporter, Vcx1, is instead marginal, unless calcineurin is inhibited or removed. Our results also suggest that the mechanosensitive channels are subject to a calcium-dependent feedback inhibition, possibly involving calmodulin. Noteworthy, the model predictions are in accordance with literature results concerning some aspects of calcium homeostasis and signaling that were not specifically addressed within the model itself, suggesting that it actually depicts all the main cellular components and interactions that constitute the HTS calcium pathway, and thus can correctly reproduce the shaping of the calcium signature by calmodulin- and calcineurin-dependent complex regulations. The model predictions also allowed to provide an interpretation of different regulatory schemes involved in calcium handling in both wild-type and mutants yeast strains. The model could be easily extended to represent different calcium signals in other eukaryotic cells.

Monopersulfate in water treatment: Kinetics

The kinetics of monopersulfate based systems in the elimination of potential harmful contaminants has been assessed from a theoretical point of view. A detailed reaction mechanism sustained in the generation of radicals (mainly hydroxyl and sulfate), propagation and termination stages has been proposed. The system of first order differential equations derived has numerically been solved. The effect of main influencing parameters such as contaminant and peroxymonosulfate initial concentrations, intermediate generation, presence of organic matter, role played by anions, has been theoretically obtained. Discussion of simulated results has been accomplished by comparison with experimental data found in the literature. At the sight of the theoretical and empirical data, use of simplistic pseudo first order kinetics is discouraged. Despite considering a significant number of elemental reactions, modelling of the system reveals that a high fraction of them can be neglected due to their insignificant role played in the mechanism. The entire mechanism has been tested when peroxymonosulfate has been activated by UV radiation, although results can be fairly extrapolated to other activation strategies. Finally, a generic model capable of accounting for the effect of a diversity of parameters is proposed. No theoretical background is behind the model, however the generic model clearly improves the results obtained by simple first order kinetics.

BioUML-towards a universal research platform

BioUML (https://www.biouml.org)—is a web-based integrated platform for systems biology and data analysis. It supports visual modelling and construction of hierarchical biological models that allow us to construct the most complex modular models of blood pressure regulation, skeletal muscle metabolism, COVID-19 epidemiology. BioUML has been integrated with git repositories where users can store their models and other data. We have also expanded the capabilities of BioUML for data analysis and visualization of biomedical data: (i) any programs and Jupyter kernels can be plugged into the BioUML platform using Docker technology; (ii) BioUML is integrated with the Galaxy and Galaxy Tool Shed; (iii) BioUML provides two-way integration with R and Python (Jupyter notebooks): scripts can be executed on the BioUML web pages, and BioUML functions can be called from scripts; (iv) using plug-in architecture, specialized viewers and editors can be added. For example, powerful genome browsers as well as viewers for molecular 3D structure are integrated in this way; (v) BioUML supports data analyses using workflows (own format, Galaxy, CWL, BPMN, nextFlow). Using these capabilities, we have initiated a new branch of the BioUML development—u-science—a universal scientific platform that can be configured for specific research requirements.

Can biophysical models of dendritic spines be used to explore synaptic changes associated with addiction?

Effective treatments that prevent or reduce drug relapse vulnerability should be developed to relieve the high burden of drug addiction on society. This will only be possible by enhancing the understanding of the molecular mechanisms underlying the neurobiology of addiction. Recent experimental data have shown that dendritic spines, small protrusions from the dendrites that receive excitatory input, of spiny neurons in the nucleus accumbens exhibit morphological changes during drug exposure and withdrawal. Moreover, these changes relate to the characteristic drug-seeking behavior of addiction. However, due to the complexity of the dendritic spines, we do not yet fully understand the processes underlying their structural changes in response to different inputs. We propose that biophysical models can enhance the current understanding of these processes by incorporating different, and sometimes, discrepant experimental data to identify the shared underlying mechanisms and generate experimentally testable hypotheses. This review aims to give an up-to-date report on biophysical models of dendritic spines, focusing on those models that describe their shape changes, which are well-known to relate to learning and memory. Moreover, it examines how these models can enhance our understanding of the effect of the drugs and the synaptic changes during withdrawal, as well as during neurodegenerative disease progression such as Alzheimer's disease.

Origin of iodine preferential attack at sulfur in phosphorothioate and subsequent P-O or P-S bond dissociation

Iodine-induced cleavage at phosphorothioate DNA (PT-DNA) is characterized by extremely high sensitivity (∼1 phosphorothioate link per 106 nucleotides), which has been used for detecting and sequencing PT-DNA in bacteria. Despite its foreseeable potential for wide applications, the cleavage mechanism at the PT-modified site has not been well established, and it remains unknown as to whether or not cleavage of the bridging P-O occurs at every PT-modified site. In this work, we conducted accurate ωB97X-D calculations and high-performance liquid chromatography-mass spectrometry to investigate the process of PT-DNA cleavage at the atomic and molecular levels. We have found that iodine chemoselectively binds to the sulfur atom of the phosphorothioate link via a strong halogen-chalcogen interaction (a type of halogen bond, with binding affinity as high as 14.9 kcal/mol) and thus triggers P-O bond cleavage via phosphotriester-like hydrolysis. Additionally, aside from cleavage of the bridging P-O bond, the downstream hydrolyses lead to unwanted P-S/P-O conversions and a loss of the phosphorothioate handle. The mechanism we outline helps to explain specific selectivity at the PT-modified site but also predicts the dynamic stoichiometry of P-S and P-O bond breaking. For instance, Tris is involved in the cascade derivation of S-iodo-phosphorothioate to S-amino-phosphorothioate, suppressing the S-iodo-phosphorothioate hydrolysis to a phosphate diester. However, hydrolysis of one-third of the Tris-O-grafting phosphotriester results in unwanted P-S/P-O conversions. Our study suggests that bacterial DNA phosphorothioation may more frequently occur than previous bioinformatic estimations have predicted from iodine-induced deep sequencing data.

Dynamic publication media with the COPASI R Connector (CoRC)

In this article we show how dynamic publication media and the COPASI R Connector (CoRC) can be combined in a natural and synergistic way to communicate (biochemical) models. Dynamic publication media are becoming a popular tool for authors to effectively compose and publish their work. They are built from templates and the final documents are created dynamically. In addition, they can also be interactive. Working with dynamic publication media is made easy with the programming environment R via its integration with tools such as R Markdown, Jupyter and Shiny. Additionally, the COmplex PAthway SImulator COPASI (http://www.copasi.org), a widely used biochemical modelling toolkit, is available in R through the use of the COPASI R Connector (CoRC, https://jpahle.github.io/CoRC). Models are a common tool in the mathematical biosciences, in particular kinetic models of biochemical networks in (computational) systems biology. We focus on three application areas of dynamic publication media and CoRC: Documentation (reproducible workflows), Teaching (creating self-paced lessons) and Science Communication (immersive and engaging presentation). To illustrate these, we created six dynamic document examples in the form of R Markdown and Jupyter notebooks, hosted on the platforms GitHub, shinyapps.io, Google Colaboratory. Having code and output in one place, creating documents in template-form and the option of interactivity make the combination of dynamic documents and CoRC a versatile tool. All our example documents are freely available at https://jpahle.github.io/DynamiCoRC under the Creative Commons BY 4.0 licence.

BioSANS: A software package for symbolic and numeric biological simulation

Modeling biochemical systems can provide insights into behaviors that are difficult to observe or understand. It requires software, programming, and understanding of the system to build a model and study it. Softwares exist for systems biology modeling, but most support only certain types of modeling tasks. Desirable features including ease in preparing input, symbolic or analytical computation, parameter estimation, graphical user interface, and systems biology markup language (SBML) support are not seen concurrently in one software package. In this study, we developed a python-based software that supports these features, with both deterministic and stochastic propagations. The software can be used by graphical user interface, command line, or as a python import. We also developed a semi-programmable and intuitively easy topology input method for the biochemical reactions. We tested the software with semantic and stochastic SBML test cases. Tests on symbolic solution and parameter estimation were also included. The software we developed is reliable, well performing, convenient to use, and compliant with most of the SBML tests. So far it is the only systems biology software that supports symbolic, deterministic, and stochastic modeling in one package that also features parameter estimation and SBML support. This work offers a comprehensive set of tools and allows for better availability and accessibility for studying kinetics and dynamics in biochemical systems.

The Atypical Cobalamin-Dependent S-Adenosyl-l-Methionine Nonradical Methylase TsrM and Its Radical Counterparts

Cobalamin (Cbl)-dependent S-adenosyl-l-methionine (AdoMet) radical methylases are known for their use of a dual cofactor system to perform challenging radical methylation reactions at unactivated carbon and phosphorus centers. These enzymes are part of a larger subgroup of Cbl-dependent AdoMet radical enzymes that also perform difficult ring contractions and radical rearrangements. This subgroup is a largely untapped reservoir of diverse chemistry that requires steady efforts in biochemical and structural characterization to reveal its complexity. In this Perspective, we highlight the significant efforts over many years to elucidate the function, mechanism, and structure of TsrM, an unexpected nonradical methylase in this subgroup. We also discuss recent achievements in characterizing radical methylase subgroup members that exemplify how key tools in mechanistic enzymology are valuable time and again. Finally, we identify recent enzyme activity studies that have made use of bioinformatic analyses to expand our definition of the subgroup. Additional breakthroughs in radical (and nonradical) enzymatic chemistry and challenging transformations from the unexplored space of this subgroup are undoubtedly on the horizon.

Mechanistic exploration of CO2 conversion to dimethoxymethane (DMM) using transition metal (Co, Ru) catalysts: an energy span model

The conversion of CO₂ to DMM is an important transformation for various reasons. Co and Ru-based triphos catalysts have been investigated using density functional theory (DFT) calculations to understand the mechanistic pathways of the CO₂ to DMM conversion and the role of noble/non-noble metal-based catalysts. The reaction has been investigated sequentially through methylformate (MF) and methoxymethane (MM) intermediates as they are found to be important intermediates. For the hydrogenation of CO₂ and MF, the hydrogen sources such as H₂ and methanol have been investigated. The calculated reaction free energy barriers for all the possible pathways suggest that both hydrogen sources are important for the Co-triphos catalyst. However, in the case of the Ru-triphos catalyst, molecular H₂ is calculated to be the only hydrogen source. Various esterification and acetalization possibilities have also been explored to find the most favorable pathway for the conversion of CO₂ to DMM. We find that the hydride transfer to the CO₂ is the rate determining step (RDS) for the overall reaction. Our mechanistic investigation reveals that the metal center is the active part for the catalysis rather than the Brønsted acid and the redox triphos ligand plays an important role through the push-pull mechanism. The implemented microkinetic study shows that the reaction is also quite dependent on the concentration of the gaseous reactants and the rate constant increases exponentially above 363 K.

BioCRNpyler: Compiling chemical reaction networks from biomolecular parts in diverse contexts

Biochemical interactions in systems and synthetic biology are often modeled with chemical reaction networks (CRNs). CRNs provide a principled modeling environment capable of expressing a huge range of biochemical processes. In this paper, we present a software toolbox, written in Python, that compiles high-level design specifications represented using a modular library of biochemical parts, mechanisms, and contexts to CRN implementations. This compilation process offers four advantages. First, the building of the actual CRN representation is automatic and outputs Systems Biology Markup Language (SBML) models compatible with numerous simulators. Second, a library of modular biochemical components allows for different architectures and implementations of biochemical circuits to be represented succinctly with design choices propagated throughout the underlying CRN automatically. This prevents the often occurring mismatch between high-level designs and model dynamics. Third, high-level design specification can be embedded into diverse biomolecular environments, such as cell-free extracts and in vivo milieus. Finally, our software toolbox has a parameter database, which allows users to rapidly prototype large models using very few parameters which can be customized later. By using BioCRNpyler, users ranging from expert modelers to novice script-writers can easily build, manage, and explore sophisticated biochemical models using diverse biochemical implementations, environments, and modeling assumptions.

This paper describes a new software package BioCRNpyler (pronounced “Biocompiler”) designed to support rapid development and exploration of mathematical models of biochemical networks and circuits by computational biologists, systems biologists, and synthetic biologists. BioCRNpyler allows its users to generate large complex models using very few lines of code in a way that is modular. To do this, BioCRNpyler uses a powerful new representation of biochemical circuits which defines their parts, underlying biochemical mechanisms, and chemical context independently. BioCRNpyler was developed as a Python scripting language designed to be accessible to beginning users as well as easily extendable and customizable for advanced users. Ultimately, we see Biocrnpyler being used to accelerate computer automated design of biochemical circuits and model driven hypothesis generation in biology.

An Arsenic-76 radiotracer to study the routes of assimilation, hemolymph distribution, and tissue inventories in the bioindicator organism Pomacea canaliculata

The aim of this work was to study the absorption, distribution through the hemolymph, and bioaccumulation of arsenic by the freshwater Pomacea canaliculata using a short-lived tracer (⁷⁶As, t_1/2: 1.07 d) with high specific activity. Arsenic travels mainly dissolved in the plasma of the snail's hemolymph. This element is transferred from the hemolymph to the tissues (87%) 4 h after the inoculation of 50 μL of a 0.04 g/L of ⁷⁶As radiotracer solution, being the digestive gland, kidney, and head-foot the main places of arsenical inventories. Snails exhibited a rapid arsenic accumulation response in a wide range of concentrations (from 1 to 1000 μg/L) of the metalloid dissolved in water and in a concentration-dependent manner. Also, snails incorporated As from the digestive system when they received a single safe dose of ~2 μg of ⁷⁶As inoculated in a fish food pellet. The (semi) physiologically based toxicokinetic model developed in this study is based on anatomical and physiological parameters (blood flow, irrigation, tissue volume and other). Together, these findings make P. canaliculata an excellent sentinel organism to evaluate freshwater bodies naturally contaminated with As.

Hybrid modelling of biological systems: current progress and future prospects

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.

Vivarium: an interface and engine for integrative multiscale modeling in computational biology

MOTIVATION

This article introduces Vivarium-software born of the idea that it should be as easy as possible for computational biologists to define any imaginable mechanistic model, combine it with existing models and execute them together as an integrated multiscale model. Integrative multiscale modeling confronts the complexity of biology by combining heterogeneous datasets and diverse modeling strategies into unified representations. These integrated models are then run to simulate how the hypothesized mechanisms operate as a whole. But building such models has been a labor-intensive process that requires many contributors, and they are still primarily developed on a case-by-case basis with each project starting anew. New software tools that streamline the integrative modeling effort and facilitate collaboration are therefore essential for future computational biologists.

RESULTS

Vivarium is a software tool for building integrative multiscale models. It provides an interface that makes individual models into modules that can be wired together in large composite models, parallelized across multiple CPUs and run with Vivarium's discrete-event simulation engine. Vivarium's utility is demonstrated by building composite models that combine several modeling frameworks: agent-based models, ordinary differential equations, stochastic reaction systems, constraint-based models, solid-body physics and spatial diffusion. This demonstrates just the beginning of what is possible-Vivarium will be able to support future efforts that integrate many more types of models and at many more biological scales.

AVAILABILITY AND IMPLEMENTATION

The specific models, simulation pipelines and notebooks developed for this article are all available at the vivarium-notebooks repository: https://github.com/vivarium-collective/vivarium-notebooks. Vivarium-core is available at https://github.com/vivarium-collective/vivarium-core, and has been released on Python Package Index. The Vivarium Collective (https://vivarium-collective.github.io) is a repository of freely available Vivarium processes and composites, including the processes used in Section 3. Supplementary Materials provide with an extensive methodology section, with several code listings that demonstrate the basic interfaces.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

In silico Prediction on the PI3K/AKT/mTOR Pathway of the Antiproliferative Effect of O. joconostle in Breast Cancer Models

The search for new cancer treatments from traditional medicine involves developing studies to understand at the molecular level different cell signaling pathways involved in cancer development. In this work, we present a model of the PI3K/Akt/mTOR pathway, which plays a key role in cell cycle regulation and is related to cell survival, proliferation, and growth in cancer, as well as resistance to antitumor therapies, so finding drugs that act on this pathway is ideal to propose a new adjuvant treatment. The aim of this work was to model, simulate and predict in silico using the Big Data-Cellulat platform the possible targets in the PI3K/Akt/mTOR pathway on which the Opuntia joconostle extract acts, as well as to indicate the concentration range to be used to find the mean lethal dose in in vitro experiments on breast cancer cells. The in silico results show that, in a cancer cell, the activation of JAK and STAT, as well as PI3K and Akt is related to the effect of cell proliferation, angiogenesis, and inhibition of apoptosis, and that the extract of O. joconostle has an antiproliferative effect on breast cancer cells by inhibiting cell proliferation, regulating the cell cycle and inhibiting apoptosis through this signaling pathway . In vitro it was demonstrated that the extract shows an antiproliferative effect, causing the arrest of cells in the G2/M phase of the cell cycle. Therefore, it is concluded that the use of in silico tools is a valuable method to perform virtual experiments and discover new treatments. The use of this type of model supports in vitro experimentation, reducing the costs and number of experiments in the real laboratory.

A Poisson Process Generator Based on Multiple Thermal Noise Amplifiers for Parallel Stochastic Simulation of Biochemical Reactions

In this paper, we propose a novel Poisson process generator that uses multiple thermal noise amplifiers (TNAs) as a source of randomness and controls its event rate via a frequency-locked loop (FLL). The increase in the number of TNAs extends the effective bandwidth of amplified thermal noise and hence enhances the maximum event rate the proposed architecture can generate. Verilog-A simulation of the proposed Poisson process generator shows that its maximum event rate can be increased by a factor of 26.5 when the number of TNAs increases from 1 to 10. In order to realize parallel stochastic simulations of the biochemical reaction network, we present a fundamental reaction building block with continuous-time multiplication and addition using an AND gate and a 1-bit current-steering digital-to-analog converter, respectively. Stochastic biochemical reactions consisting of the fundamental reaction building blocks are simulated in Verilog-A, demonstrating that the simulation results are consistent with those of conventional Gillespie algorithm. An increase in the number of TNAs to accelerate the Poisson events and the use of digital AND gates for robust reaction rate calculations allow for faster and more accurate stochastic simulations of biochemical reactions than previous parallel stochastic simulators.

Structure-Activity Relationships of Novel Tau Ligands: Passive Fibril Binders and Active Aggregation Inhibitors

Intrinsically disordered proteins (IDPs) are core components of many biological processes and are central players in several pathologies. Despite being important drug targets, attempts to design small-molecule ligands that would help understand and attenuate their behavior are frustrated by the structural diversity exhibited by these flexible proteins. To accommodate the dynamic nature of IDPs, we developed a procedure that efficiently identifies active small-molecule ligands for disordered proteins. By exploring the chemical space around these ligands, we refined their effect on aggregation and identified molecular features critical for activity and affinity. Notably, the discovery of this new family of disordered protein ligands was achieved more quickly and with less expense than conventional high-throughput screening (HTS) or docking alone would have allowed. The resulting ligands include tau aggregation inhibitors as well as at least one compound that binds fibrils potently but does not appear to perturb the extent of kinetics of aggregation.

Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2

We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism.

NOT Gates Based on Protein Degradation as a Case Study for a New Modular Modeling via SBML Level 3—Comp Package

In 2008, we were among the first to propose a method for the visual design and modular modeling of synthetic gene circuits, mimicking the way electronic circuits are realized in silico. Basic components were DNA sequences that could be composed, first, into transcription units (TUs) and, then, circuits by exchanging fluxes of molecules, such as PoPS (polymerase per second) and RiPS (ribosomes per seconds) as suggested by Drew Endy. However, it became clear soon that such fluxes were not measurable, which highlighted the limit of using some concepts from electronics to represent biological systems. SBML Level 3 with the comp package permitted us to revise circuit modularity, especially for the modeling of eukaryotic networks. By using the libSBML Python API, TUs—rather than single parts—are encoded in SBML Level 3 files that contain species, reactions, and ports, i.e., the interfaces that permit to wire TUs into circuits. A circuit model consists of a collection of SBML Level 3 files associated with the different TUs plus a “main” file that delineates the circuit structure. Within this framework, there is no more need for any flux of molecules. Here, we present the SBML Level 3-based models and the wet-lab implementations of Boolean NOT gates that make use, in the yeast Saccharomyces cerevisiae, of the bacterial ClpX-ClpP system for protein degradation. This work is the starting point towards a new piece of software for the modular design of eukaryotic gene circuits and shows an alternative way to build genetic Boolean gates.

Spatial and Temporal Resolution of Luminescence Quenching in Small Upconversion Nanocrystals

Luminescent upconversion nanocrystals (UCNCs) have become one of the most promising nanomaterials for biosensing, imaging, and theranostics. However, their ultimate translation into robust luminescent probes for daily use in biological and medical laboratories requires comprehension and control of the many possible deactivation pathways that cause upconversion luminescence (UCL) quenching. Here, we demonstrate that thorough modeling of UCL rise and decay kinetics using a freely accessible software can identify the UCL quenching mechanisms in small (<40 nm) UCNCs with spatial and temporal resolution. Applied to the most relevant β-NaYF₄:Yb³⁺,Er³⁺ UCNCs, our model showed that only a few distinct nonradiative low-energy transitions were deactivated via specific solvent and ligand vibrations with a strong downstream effect on the population and depopulation dynamics of the emitting states. UCL quenching could penetrate ca. 4 nm inside the UCNC, which resulted in significant size-dependent changes of UCL intensities and spectra. Despite the large surface-to-volume ratios and UCL quenching via the UCNC surface, we found strong contributions of the outer layers to the overall UCL, which will be highly important for the design of UCNPs to investigate biomolecular interactions via distance-dependent energy transfer methods. Our advanced kinetic model is easily scalable to different UCNC architectures, environments, and energy transfer interactions such that relatively simple modeling of UCL kinetics can be used for efficiently optimizing UCNCs for their final application as practical luminescent probes.

Computational Modeling of O-Linked Glycan Biosynthesis in CHO Cells

Glycan biosynthesis simulation research has progressed remarkably since 1997, when the first mathematical model for N-glycan biosynthesis was proposed. An O-glycan model has also been developed to predict O-glycan biosynthesis pathways in both forward and reverse directions. In this work, we started with a set of O-glycan profiles of CHO cells transiently transfected with various combinations of glycosyltransferases. The aim was to develop a model that encapsulated all the enzymes in the CHO transfected cell lines. Due to computational power restrictions, we were forced to focus on a smaller set of glycan profiles, where we were able to propose an optimized set of kinetics parameters for each enzyme in the model. Using this optimized model we showed that the abundance of more processed glycans could be simulated compared to observed abundance, while predicting the abundance of glycans earlier in the pathway was less accurate. The data generated show that for the accurate prediction of O-linked glycosylation, additional factors need to be incorporated into the model to better reflect the experimental conditions.

Interferon-β acts directly on T cells to prolong allograft survival by enhancing regulatory T cell induction through Foxp3 acetylation

Type I interferons (IFNs) are pleiotropic cytokines with potent antiviral properties that also promote protective T cell and humoral immunity. Paradoxically, type I IFNs, including the widely expressed IFNβ, also have immunosuppressive properties, including promoting persistent viral infections and treating T-cell-driven, remitting-relapsing multiple sclerosis. Although associative evidence suggests that IFNβ mediates these immunosuppressive effects by impacting regulatory T (Treg) cells, mechanistic links remain elusive. Here, we found that IFNβ enhanced graft survival in a Treg-cell-dependent murine transplant model. Genetic conditional deletion models revealed that the extended allograft survival was Treg cell-mediated and required IFNβ signaling on T cells. Using an in silico computational model and analysis of human immune cells, we found that IFNβ directly promoted Treg cell induction via STAT1- and P300-dependent Foxp3 acetylation. These findings identify a mechanistic connection between the immunosuppressive effects of IFNβ and Treg cells, with therapeutic implications for transplantation, autoimmunity, and malignancy.

Mechanism and selectivity of photocatalyzed CO2 reduction by a function-integrated Ru catalyst

The phosphine-substituted Ru(II) polypyridyl complex, [Ru^II-(tpy)(pqn)(MeCN)]²⁺ (RuP), was disclosed to be an efficient photocatalyst for the reduction of CO₂ to CO with excellent selectivity. In this work, density functional calculations were performed to elucidate the reaction mechanism and understand the origin of selectivity. The calculations showed that RuP was first excited to the singlet excited state, followed by intersystem crossing to produce a triplet species (3RuIII(L˙-)-S), which was then reduced by the sacrificial electron donor BIH to generate a Ru^II(L˙^-) intermediate. The ligand of Ru^II(L˙^-) was further reduced to produce a Ru^II(L^2-) intermediate. The redox non-innocent nature of the tpy and pqn ligands endows the Ru center with an oxidation state of +2 after two one-electron reductions. Ru^II(L^2-) nucleophilically attacks CO₂, in which two electrons are delivered from the ligands to CO₂, affording a Ru^II-COOH species after protonation. This is followed by the protonation of the hydroxyl moiety of Ru^II-COOH, coupled with the C-O bond cleavage, resulting in the formation of Ru^II-CO. Ultimately, CO is dissociated after two one-electron reductions. Protonation of Ru^II(L^2-) to generate a Ru^II-hydride, a critical intermediate for the production of formate and H₂, turns out to be kinetically less favorable, even though it is thermodynamically more favorable. This fact is due to the presence of a Ru²⁺ ion in the reduced catalyst, which disfavors its protonation.

Bayesian calibration, process modeling and uncertainty quantification in biotechnology

High-throughput experimentation has revolutionized data-driven experimental sciences and opened the door to the application of machine learning techniques. Nevertheless, the quality of any data analysis strongly depends on the quality of the data and specifically the degree to which random effects in the experimental data-generating process are quantified and accounted for. Accordingly calibration, i.e. the quantitative association between observed quantities and measurement responses, is a core element of many workflows in experimental sciences. Particularly in life sciences, univariate calibration, often involving non-linear saturation effects, must be performed to extract quantitative information from measured data. At the same time, the estimation of uncertainty is inseparably connected to quantitative experimentation. Adequate calibration models that describe not only the input/output relationship in a measurement system but also its inherent measurement noise are required. Due to its mathematical nature, statistically robust calibration modeling remains a challenge for many practitioners, at the same time being extremely beneficial for machine learning applications. In this work, we present a bottom-up conceptual and computational approach that solves many problems of understanding and implementing non-linear, empirical calibration modeling for quantification of analytes and process modeling. The methodology is first applied to the optical measurement of biomass concentrations in a high-throughput cultivation system, then to the quantification of glucose by an automated enzymatic assay. We implemented the conceptual framework in two Python packages, calibr8 and murefi, with which we demonstrate how to make uncertainty quantification for various calibration tasks more accessible. Our software packages enable more reproducible and automatable data analysis routines compared to commonly observed workflows in life sciences. Subsequently, we combine the previously established calibration models with a hierarchical Monod-like ordinary differential equation model of microbial growth to describe multiple replicates of Corynebacterium glutamicum batch cultures. Key process model parameters are learned by both maximum likelihood estimation and Bayesian inference, highlighting the flexibility of the statistical and computational framework.

Synthetic biology tools for engineering Goodwin oscillation in Trypanosoma brucei brucei

Kinetoplastid protozoa possess properties that are highly divergent from the mammalian, yeast and bacterial cells more commonly used in synthetic biology and represent a tantalisingly untapped source of bioengineering potential. Trypanosoma brucei brucei (T. b. brucei), an established model organism for studying the Kinetoplastida, is non-pathogenic to humans and provides an interesting test case for establishing synthetic biology in this phylogenetic class. To demonstrate further the tractability of Kinetoplastida to synthetic biology, we sought to construct and demonstrate a Goodwin oscillator, the simplest oscillatory gene network, in T. b. brucei for the first time. We report one completed iteration of the archetypal synthetic biology Design-Build-Test-Learn (DBTL) cycle; firstly, using Ab initio mathematical modelling of the behaviour a theoretical, oscillatory, trypanosomal synthetic gene network (SGN) to inform the design of a plasmid encoding that network. Once assembled, the plasmid was then used to generate a stable transfectant T. b. brucei cell line. To test the performance of the oscillatory SGN, a novel experimental setup was established to capture images of the fluorescent signal from motion-restricted live cells. Data captured were consistent with oscillatory behaviour of the SGN, with cellular fluorescence observed to oscillate with a period of 50 min, with varying amplitude and linear growth trend. This first DBTL cycle establishes a foundation for future cycles in which the SGN design and experimental monitoring setup can be further refined.

Extracellular Electron Transfer Enables Cellular Control of Cu(I)-Catalyzed Alkyne-Azide Cycloaddition

Extracellular electron transfer (EET) is an anaerobic respiration process that couples carbon oxidation to the reduction of metal species. In the presence of a suitable metal catalyst, EET allows for cellular metabolism to control a variety of synthetic transformations. Here, we report the use of EET from the electroactive bacterium Shewanella oneidensis for metabolic and genetic control over Cu(I)-catalyzed alkyne-azide cycloaddition (CuAAC). CuAAC conversion under anaerobic and aerobic conditions was dependent on live, actively respiring S. oneidensis cells. The reaction progress and kinetics were manipulated by tailoring the central carbon metabolism. Similarly, EET-CuAAC activity was dependent on specific EET pathways that could be regulated via inducible expression of EET-relevant proteins: MtrC, MtrA, and CymA. EET-driven CuAAC exhibited modularity and robustness in the ligand and substrate scope. Furthermore, the living nature of this system could be exploited to perform multiple reaction cycles without regeneration, something inaccessible to traditional chemical reductants. Finally, S. oneidensis enabled bioorthogonal CuAAC membrane labeling on live mammalian cells without affecting cell viability, suggesting that S. oneidensis can act as a dynamically tunable biocatalyst in complex environments. In summary, our results demonstrate how EET can expand the reaction scope available to living systems by enabling cellular control of CuAAC.

Multi-omics-based label-free metabolic flux inference reveals obesity-associated dysregulatory mechanisms in liver glucose metabolism

Glucose homeostasis is maintained by modulation of metabolic flux. Enzymes and metabolites regulate the involved metabolic pathways. Dysregulation of glucose homeostasis is a pathological event in obesity. Analyzing metabolic pathways and the mechanisms contributing to obesity-associated dysregulation in vivo is challenging. Here, we introduce OMELET: Omics-Based Metabolic Flux Estimation without Labeling for Extended Trans-omic Analysis. OMELET uses metabolomic, proteomic, and transcriptomic data to identify relative changes in metabolic flux, and to calculate contributions of metabolites, enzymes, and transcripts to the changes in metabolic flux. By evaluating the livers of fasting ob/ob mice, we found that increased metabolic flux through gluconeogenesis resulted primarily from increased transcripts, whereas that through the pyruvate cycle resulted from both increased transcripts and changes in substrates of metabolic enzymes. With OMELET, we identified mechanisms underlying the obesity-associated dysregulation of metabolic flux in the liver.

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We developed OMELET to infer metabolic flux from label-free multi-omic data

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Contributions of metabolites, enzymes, and transcripts for flux were inferred

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Gluconeogenic flux increased in fasting ob/ob mice by increased transcripts

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Increased pyruvate cycle fluxes were led by increased transcripts and substrates

GAMES: A Dynamic Model Development Workflow for Rigorous Characterization of Synthetic Genetic Systems

Mathematical modeling is invaluable for advancing understanding and design of synthetic biological systems. However, the model development process is complicated and often unintuitive, requiring iteration on various computational tasks and comparisons with experimental data. Ad hoc model development can pose a barrier to reproduction and critical analysis of the development process itself, reducing the potential impact and inhibiting further model development and collaboration. To help practitioners manage these challenges, we introduce the Generation and Analysis of Models for Exploring Synthetic Systems (GAMES) workflow, which includes both automated and human-in-the-loop processes. We systematically consider the process of developing dynamic models, including model formulation, parameter estimation, parameter identifiability, experimental design, model reduction, model refinement, and model selection. We demonstrate the workflow with a case study on a chemically responsive transcription factor. The generalizable workflow presented in this tutorial can enable biologists to more readily build and analyze models for various applications.

The principle of detailed balancing, the iron-catalyzed disproportionation of hydrogen peroxide, and the Fenton reaction

The iron-catalyzed disproportionation of H₂O₂ has been investigated for over a century, as has been its ability to induce the oxidation of other species present in the system (Fenton reaction). The mechanisms of these reactions have been under consideration at least since 1932. Unfortunately, little or no attention has been paid to ensuring the conformity of the proposed mechanisms and rate constants with the constraints of the principle of detailed balancing. Here we identify more than 200 publications having mechanisms that violate the principle of detailed balancing. These violations occur through the use of incorrect values for certain rate constants, the use of incorrect forms of the rate laws for certain steps in the mechanisms, and the inclusion of illegal loops. A core mechanism for the iron-catalyzed decomposition of H₂O₂ is proposed that is consistent with the principle of detailed balancing and includes both the one-electron oxidation of H₂O₂ by Fe(III) and the Fe(II) reduction of HO₂˙.

Agent-based models for detecting the driving forces of biomolecular interactions

Agent-based modelling and simulation have been effectively applied to the study of complex biological systems, especially when composed of many interacting entities. Representing biomolecules as autonomous agents allows this approach to bring out the global behaviour of biochemical processes as resulting from local molecular interactions. In this paper, we leverage the capabilities of the agent paradigm to construct an in silico replica of the glycolytic pathway; the aim is to detect the role that long-range electrodynamic forces might have on the rate of glucose oxidation. Experimental evidences have shown that random encounters and short-range potentials might not be sufficient to explain the high efficiency of biochemical reactions in living cells. However, while the latest in vitro studies are limited by present-day technology, agent-based simulations provide an in silico support to the outcomes hitherto obtained and shed light on behaviours not yet well understood. Our results grasp properties hard to uncover through other computational methods, such as the effect of electromagnetic potentials on glycolytic oscillations.

A light-fuelled nanoratchet shifts a coupled chemical equilibrium

Biological molecular machines enable chemical transformations, assembly, replication and motility, but most distinctively drive chemical systems out of-equilibrium to sustain life^1,2. In such processes, nanometre-sized machines produce molecular energy carriers by driving endergonic equilibrium reactions. However, transforming the work performed by artificial nanomachines^3-5 into chemical energy remains highly challenging. Here, we report a light-fuelled small-molecule ratchet capable of driving a coupled chemical equilibrium energetically uphill. By bridging two imine^6-9 macrocycles with a molecular motor^10,11, the machine forms crossings and consequently adopts several distinct topologies by either a thermal (temporary bond-dissociation) or photochemical (unidirectional rotation) pathway. While the former will relax the machine towards the global energetic minimum, the latter increases the number of crossings in the system above the equilibrium value. Our approach provides a blueprint for coupling continuous mechanical motion performed by a molecular machine with a chemical transformation to reach an out-of-equilibrium state.

Kinetic and Stoichiometric Modeling-Based Analysis of Docosahexaenoic Acid (DHA) Production Potential by C. cohnii from Glycerol, Glucose and Ethanol

Docosahexaenoic acid (DHA) is one of the most important long-chain polyunsaturated fatty acids (LC-PUFAs), with numerous health benefits. Crypthecodinium cohnii, a marine heterotrophic dinoflagellate, is successfully used for the industrial production of DHA because it can accumulate DHA at high concentrations within the cells. Glycerol is an interesting renewable substrate for DHA production since it is a by-product of biodiesel production and other industries, and is globally generated in large quantities. The DHA production potential from glycerol, ethanol and glucose is compared by combining fermentation experiments with the pathway-scale kinetic modeling and constraint-based stoichiometric modeling of C. cohnii metabolism. Glycerol has the slowest biomass growth rate among the tested substrates. This is partially compensated by the highest PUFAs fraction, where DHA is dominant. Mathematical modeling reveals that glycerol has the best experimentally observed carbon transformation rate into biomass, reaching the closest values to the theoretical upper limit. In addition to our observations, the published experimental evidence indicates that crude glycerol is readily consumed by C. cohnii, making glycerol an attractive substrate for DHA production.

Structure of a B12-dependent radical SAM enzyme in carbapenem biosynthesis

Carbapenems are antibiotics of last resort in the clinic. Owing to their potency and broad-spectrum activity, they are an important part of the antibiotic arsenal. The vital role of carbapenems is exemplified by the approval acquired by Merck from the US Food and Drug Administration (FDA) for the use of an imipenem combination therapy to treat the increased levels of hospital-acquired and ventilator-associated bacterial pneumonia that have occurred during the COVID-19 pandemic1. The C6 hydroxyethyl side chain distinguishes the clinically used carbapenems from the other classes of β-lactam antibiotics and is responsible for their low susceptibility to inactivation by occluding water from the β-lactamase active site2. The construction of the C6 hydroxyethyl side chain is mediated by cobalamin- or B12-dependent radical S-adenosylmethionine (SAM) enzymes3. These radical SAM methylases (RSMTs) assemble the alkyl backbone by sequential methylation reactions, and thereby underlie the therapeutic usefulness of clinically used carbapenems. Here we present X-ray crystal structures of TokK, a B12-dependent RSMT that catalyses three-sequential methylations during the biosynthesis of asparenomycin A. These structures, which contain the two metallocofactors of the enzyme and were determined in the presence and absence of a carbapenam substrate, provide a visualization of a B12-dependent RSMT that uses the radical mechanism that is shared by most of these enzymes. The structures provide insight into the stereochemistry of initial C6 methylation and suggest that substrate positioning governs the rate of each methylation event.

Systems approaches to investigate the role of NF-κB signaling in aging

The nuclear factor-κB (NF-κB) signaling pathway is one of the most well-studied pathways related to inflammation, and its involvement in aging has attracted considerable attention. As aging is a complex phenomenon and is the result of a multi-step process, the involvement of the NF-κB pathway in aging remains unclear. To elucidate the role of NF-κB in the regulation of aging, different systems biology approaches have been employed. A multi-omics data-driven approach can be used to interpret and clarify unknown mechanisms but cannot generate mechanistic regulatory structures alone. In contrast, combining this approach with a mathematical modeling approach can identify the mechanistics of the phenomena of interest. The development of single-cell technologies has also helped clarify the heterogeneity of the NF-κB response and underlying mechanisms. Here, we review advances in the understanding of the regulation of aging by NF-κB by focusing on omics approaches, single-cell analysis, and mathematical modeling of the NF-κB network.

Computational Models for Clinical Applications in Personalized Medicine—Guidelines and Recommendations for Data Integration and Model Validation

The future development of personalized medicine depends on a vast exchange of data from different sources, as well as harmonized integrative analysis of large-scale clinical health and sample data. Computational-modelling approaches play a key role in the analysis of the underlying molecular processes and pathways that characterize human biology, but they also lead to a more profound understanding of the mechanisms and factors that drive diseases; hence, they allow personalized treatment strategies that are guided by central clinical questions. However, despite the growing popularity of computational-modelling approaches in different stakeholder communities, there are still many hurdles to overcome for their clinical routine implementation in the future. Especially the integration of heterogeneous data from multiple sources and types are challenging tasks that require clear guidelines that also have to comply with high ethical and legal standards. Here, we discuss the most relevant computational models for personalized medicine in detail that can be considered as best-practice guidelines for application in clinical care. We define specific challenges and provide applicable guidelines and recommendations for study design, data acquisition, and operation as well as for model validation and clinical translation and other research areas.

ParaCopasi: A package for parallel biochemical simulation and analysis

Biochemical simuflation and analysis play a significant role in systems biology research. Numerous software tools have been developed to serve this area. Using these tools for completing tasks, for example, stochastic simulation, parameter fitting and optimization, usually requires sufficient computational power to make the duration of completion acceptable. COPASI is one of the most powerful tools for quantitative simulation and analysis targeted at biological systems. It supports systems biology markup language and covers multiple categories of tasks. This work develops an open source package ParaCopasi for parallel COPASI tasks and investigates its performance regarding accelerations. ParaCopasi can be installed on platforms equipped with multicore CPU to exploit the cores, scaling from desktop computers to large scale high-performance computing clusters. More cores bring more performance. The results show that the parallel efficiency has a positive correlation with the total workload. The parallel efficiency reaches a level of at least 95% for both homogeneous and heterogenous tasks when computational workload is adequate. An example is illustrated by applicating this package in parameter estimation to calibrate a biochemical kinetics model.

SMGen: A Generator of Synthetic Models of Biochemical Reaction Networks

Several software tools for the simulation and analysis of biochemical reaction networks have been developed in the last decades; however, assessing and comparing their computational performance in executing the typical tasks of computational systems biology can be limited by the lack of a standardized benchmarking approach. To overcome these limitations, we propose here a novel tool, named SMGen, designed to automatically generate synthetic models of reaction networks that, by construction, are characterized by relevant features (e.g., system connectivity and reaction discreteness) and non-trivial emergent dynamics of real biochemical networks. The generation of synthetic models in SMGen is based on the definition of an undirected graph consisting of a single connected component that, generally, results in a computationally demanding task; to speed up the overall process, SMGen exploits a main–worker paradigm. SMGen is also provided with a user-friendly graphical user interface, which allows the user to easily set up all the parameters required to generate a set of synthetic models with any number of reactions and species. We analysed the computational performance of SMGen by generating batches of symmetric and asymmetric reaction-based models (RBMs) of increasing size, showing how a different number of reactions and/or species affects the generation time. Our results show that when the number of reactions is higher than the number of species, SMGen has to identify and correct a large number of errors during the creation process of the RBMs, a circumstance that increases the running time. Still, SMGen can generate synthetic models with hundreds of species and reactions in less than 7 s.

Inhibition of the urea-urease reaction by the components of the zeolite imidazole frameworks-8 and the formation of urease-zinc-imidazole hybrid compound

In the past decade, much effort has been devoted to using chemical clock-type reactions in material design and driving the self-assembly of various building blocks. Urea-urease enzymatic reaction has chemical pH clock behavior in an unbuffered medium, in which the induction time and the final pH can be programmed by the concentrations of the reagents. The urea-urease reaction can offer a new alternative in material synthesis, where the pH and its course in time are crucial factors in the synthesis. However, before using it in any synthesis method, it is important to investigate the possible effects of the reagents on the enzymatic reaction. Here we investigate the effect of the reagents of the zeolite imidazole framework-8 (zinc ions and 2-methylimidazole) on the urea-urease reaction. We have chosen the zeolite imidazole framework-8 because its formation serves as a model reaction for the formation of other metal–organic frameworks. We found that, besides the inhibition effect of the zinc ions which is well-known in the literature, 2-methylimidazole inhibits the enzymatic reaction as well. In addition to the observed inhibition effect, we report the formation of a hybrid urease-zinc-2-methylimidazole hybrid material. To support the inhibition effect, we developed a kinetic model which reproduced qualitatively the experimentally observed kinetic curves.

Periodic synchronization of isolated network elements facilitates simulating and inferring gene regulatory networks including stochastic molecular kinetics

Background

The temporal progression of many fundamental processes in cells and organisms, including homeostasis, differentiation and development, are governed by gene regulatory networks (GRNs). GRNs balance fluctuations in the output of their genes, which trace back to the stochasticity of molecular interactions. Although highly desirable to understand life processes, predicting the temporal progression of gene products within a GRN is challenging when considering stochastic events such as transcription factor–DNA interactions or protein production and degradation.

Results

We report a method to simulate and infer GRNs including genes and biochemical reactions at molecular detail. In our approach, we consider each network element to be isolated from other elements during small time intervals, after which we synchronize molecule numbers across all network elements. Thereby, the temporal behaviour of network elements is decoupled and can be treated by local stochastic or deterministic solutions. We demonstrate the working principle of this modular approach with a repressive gene cascade comprising four genes. By considering a deterministic time evolution within each time interval for all elements, our method approaches the solution of the system of deterministic differential equations associated with the GRN. By allowing genes to stochastically switch between on and off states or by considering stochastic production of gene outputs, we are able to include increasing levels of stochastic detail and approximate the solution of a Gillespie simulation. Thereby, CaiNet is able to reproduce noise-induced bi-stability and oscillations in dynamically complex GRNs. Notably, our modular approach further allows for a simple consideration of deterministic delays. We further infer relevant regulatory connections and steady-state parameters of a GRN of up to ten genes from steady-state measurements by identifying each gene of the network with a single perceptron in an artificial neuronal network and using a gradient decent method originally designed to train recurrent neural networks. To facilitate setting up GRNs and using our simulation and inference method, we provide a fast computer-aided interactive network simulation environment, CaiNet.

Conclusion

We developed a method to simulate GRNs at molecular detail and to infer the topology and steady-state parameters of GRNs. Our method and associated user-friendly framework CaiNet should prove helpful to analyze or predict the temporal progression of reaction networks or GRNs in cellular and organismic biology. CaiNet is freely available at https://gitlab.com/GebhardtLab/CaiNet.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04541-6.

On the role of citrate in 12-molybdophosphoric-acid methods for quantification of phosphate in the presence of ATP

Citrate is a useful additive for measuring ATPase activities avoiding the interference of phosphate release after catalysis. In this work we explore this effect, and optimize the malachite green procedure for determination of phosphate.

Fixation can change the appearance of phase separation in living cells

Fixing cells with paraformaldehyde (PFA) is an essential step in numerous biological techniques as it is thought to preserve a snapshot of biomolecular transactions in living cells. Fixed-cell imaging techniques such as immunofluorescence have been widely used to detect liquid-liquid phase separation (LLPS) in vivo. Here, we compared images, before and after fixation, of cells expressing intrinsically disordered proteins that are able to undergo LLPS. Surprisingly, we found that PFA fixation can both enhance and diminish putative LLPS behaviors. For specific proteins, fixation can even cause their droplet-like puncta to artificially appear in cells that do not have any detectable puncta in the live condition. Fixing cells in the presence of glycine, a molecule that modulates fixation rates, can reverse the fixation effect from enhancing to diminishing LLPS appearance. We further established a kinetic model of fixation in the context of dynamic protein-protein interactions. Simulations based on the model suggest that protein localization in fixed cells depends on an intricate balance of protein-protein interaction dynamics, the overall rate of fixation, and notably, the difference between fixation rates of different proteins. Consistent with simulations, live-cell single-molecule imaging experiments showed that a fast overall rate of fixation relative to protein-protein interaction dynamics can minimize fixation artifacts. Our work reveals that PFA fixation changes the appearance of LLPS from living cells, presents a caveat in studying LLPS using fixation-based methods, and suggests a mechanism underlying the fixation artifact.

A Different Polynorbornene Backbone by Combination of Two Polymer Growth Pathways: Vinylic Addition and Ring Opening via β-C Elimination

A new polynorbornene skeleton has been found that contains bicyclic norbornane units and cyclohexenyl methyl linkages. The polymers have been synthesized using a nickel catalyst in the presence of a controlled amount of ligands with low or moderate coordination ability. The backbone structure is the result of a vinylic addition polymerization, via sequential insertions of norbornene into a Ni–C bond (bicyclic units) combined with an unusual ring opening of the norbornene structure by a β-C elimination (cyclohexenyl methyl units) to give a new Ni–C(alkyl) bond that continues the polymerization. The ring opening events are favored when the rate of propagation of the vinylic addition polymerization decreases, and this can be modulated by making the coordination of norbornene to the metal center less favorable using additional ligands.

A new polynorbornene skeleton that contains a mixture of bicyclic norbornane units and cyclohexenylmethyl moieties can be obtained using a nickel catalyst.