Mechanistic models in systems biology enable biophysically-backed testing of hypothesised mechanisms. However, determination of their parameter values is highly challenging, and the data available for calibration is frequently qualitative in nature. Acknowledging this, many approaches abandon mechanistic description, avoiding parameterisation and simulating biological network behaviours in a qualitative fashion. Appealing are the methods that capture some of the best of both types of approach, maintaining a qualitative perspective while using mechanistic models that naturally generalise to quantitative data and carry biochemical implications. Here, using a pea branching network model as an exemplar, we demonstrate the conversion of biological hypotheses into simplified, parameter-free mathematical models, elucidating the biophysical assumptions implicitly made by this approach and analysing the exemplar model's behaviour. Using likelihood-free Bayesian calibration, we compare the parameter-free model to the set of plausible calibrations of its parameterised analog, hence demonstrating that almost all of the qualitative conclusions given data - including both suitability of a hypothesised network structure, and sensitivity analysis - are obtained by the parameter-free paradigm. Altogether, our findings highlight the usefulness of parameter-free treatments of quantitative models, and also deepen understanding of branching network function across mutant and grafted plants.

Cytotoxicity originates at the amorphous intermediate stage during amyloid-like oligomerization of serum albumin under mild denaturing conditions.

Infrared drying characteristics and mathematical modeling of Camellia oleifera seeds

We present a new method to quantify the reaction kinetics of oil-in-water rare-earth solvent extraction systems. The method aims to analyze the trajectory of an oil drop rising in a paramagnetic aqueous phase when the drop is exposed to a magnetic stray field. The latter generates a repulsive Kelvin force on the oil droplet, counteracting its buoyancy, thereby enabling a magnetic levitation in a paramagnetic aqueous phase containing trivalent dysprosium cations Dy(III). With the extractant PC88A dissolved in the oil phase, Dy(III) cation exchange proceeds continuously at the oil-water interface. The depletion of Dy(III) in the aqueous phase and the concurrent formation of Dy-complexes in the organic phase alter both the droplet’s magnetic susceptibility and its density. Consequently, the force balance acting on the droplet shifts, driving an uni-directional ascend toward the magnetic pole. By tracking the droplet motion with far-field optical microscope, we develop a quantitative model that correlates the droplet displacement with the time-resolved Dy(III) extraction rate. Scaling analysis reveals a first-order dependence of the reaction rate on both the Dy(III) and extractant concentrations, and a negative first-order dependence on hydrogen ion concentration. The kinetic rate law is further extended to account for the reverse reaction using reaction equilibrium data. Numerical simulations of the droplet trajectory based on the complete rate law show excellent agreement with experiment. This work establishes a rapid and accurate method for quantifying rare-earth extraction kinetics using a non-contact, single-droplet approach. The method is resource-efficient and readily adaptable to high throughput kinetic analysis of magnetically susceptible systems. • Interfacial rare-earth extraction kinetics can be quantitatively inferred from droplet trajectories. • Magnetic levitation enables accurate determination of kinetic rate laws without physical contact. • Mathematical modelling resolves the coupling of mass transport and force balance. • Extraction kinetics are independent of droplet size, confirming interface-controlled reactions. • The framework enables resource-efficient, high-throughput kinetic screening relevant to rare-earth separation and recycling.

This study explores how vaccination, immune memory, and long-term immunity shape the transmission dynamics of measles by developing a fractional-order mathematical model. Caputo-Fabrizio fractional-order SEITR-VL model is formulated, in which population is divided into susceptible, exposed, infectious, treated, recovered, vaccinated, and lifelong immunity classes. The model incorporates memory effects so that past disease and immunity states can influence current transmission behavior. Basic mathematical properties such as positivity, boundedness, and the existence of solutions are verified. The effective reproduction number is derived using the next-generation matrix approach, and numerical solutions are obtained through the Laplace-Adomian Decomposition Method. Numerical experiments showed that increasing vaccination coverage, as well as improving recovery rates, leads to a clear decline in infection levels. In addition, the fractional-order structure introduces memory effects that moderate sharp epidemic peaks and slow the overall spread of the disease, resulting in smoother outbreak patterns. Since some parameters are not estimated from data, these findings are interpreted mainly at a qualitative level. The results emphasize the importance of vaccination and immune memory in controlling measles transmission. While the fractional-order framework provides a useful way to capture long-term and memory-dependent effects, further validation using real epidemiological data would be necessary for predictive or policy-oriented applications.

A model for a population of trees structured by phenological traits.

Region-specific modeling of refugia and anthelmintic resistance dynamics in gastrointestinal nematodes of Nigerian small ruminants.

Physics-informed neural networks enable patient-specific tumor microenvironment modeling: Identifying parameters in combined immune therapy with integer- and fractional-order dynamics

Collaborative optimization of integrated energy systems in energy-intensive industrial clusters considering carbon-green-certificate trading

Applied mathematical modelling of Ball formula in commercial sterilisation design using household pressure cooker to extend the shelf life of Jamu and herbal drinks

A three-phase mathematical model to monitor alcoholic fermentation and phenolic extraction of Vitis Vinifera L. red wines

The rapid expansion of lithium-ion battery (LIB) production, driven by the rise of electric vehicles and renewable energy storage, has led to growing concerns about end-of-life management and critical material recovery. In this context, biotechnological processes represent an environmentally sustainable alternative to conventional recycling methods such as pyrometallurgy and hydrometallurgy, offering reduced impacts on both ecosystems and human health. However, the performance of bioleaching systems depends heavily on microbial tolerance to toxic metals released from LIBs. This study focuses on assessing the toxicological effects of Co, a key strategic metal in LIBs, on Acidithiobacillus ferrooxidans, a model organism for bioleaching applications. Experimental findings reveal that Co exhibits greater toxicity than Cu, Cd, Ni, Zn, and As, but is less toxic than Cr. Co concentrations exceeding 5g/L result in a 260% increase in Fe2+ oxidation time and an 80% reduction in the Fe oxidation rate. Additionally, elevated Co levels significantly prolong the exponential growth phase, indicating metabolic stress. A predictive mathematical model was developed and validated to describe bacterial growth and Fe2+ oxidation under varying Co concentrations, achieving a determination coefficient (R2) above 0.95. This model serves as a practical tool for optimizing process parameters in the bio-recycling of LIBs, enabling more efficient and scalable engineering applications. These findings contribute to the advancement of greener technologies for critical raw material recovery and support the integration of bio-based methods into circular economy strategies for battery waste management.

Coupled transport and retention dynamics of microplastics in porous media.

Effects of square-wave excited alternating magnetic fields on calcium carbonate crystallization and their application in scale inhibition.

Coherent optical neural network chip with novel computing model for large-scale matrix-vector multiplication.

A comprehensive mathematical model of Nipah virus transmission dynamics: Stability analysis and numerical simulations

Research on the design method of an optical system for star sensors with low centroid drift under under-corrected aberrations.

A variable universe fuzzy control method for the HCOTSG feedwater system of small pressurized water reactor

Long-term clonal analysis using stochastic models reveals heterogeneity and quiescence of hematopoietic stem cells.

A Fkh1/2 binding site array in the WHI5 promoter drives sub-scaling transcription.