Editorial: theme issue on complex rheology in biological systems

Schaefer, Charley; McKinley, Gareth H.; McLeish, Tom

doi:10.1098/rsfs.2022.0058

Cited by 2 publications

(1 citation statement)

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“…Biomathematics not only uses mathematical theories to study the problems of biology but also conducts in-depth research on mathematical theories related to biology [8]. Mathematical models can quantitatively describe biological phenomena, and a complex biological problem can be converted into a mathematical problem with the help of a mathematical model [9]. By studying the nature of mathematical model solutions, qualitative analysis, and other methods, problems of living or non-living phenomena can be analyzed.…”

Section: Introductionmentioning

confidence: 99%

A study of periodic solutions of several types of nonlinear models in biomathematics

2024

Applied Mathematics and Nonlinear Sciences

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Biomathematics is a cross-discipline formed by the interpenetration of mathematics with life sciences, biology, and other disciplines, and biomathematical models provide an effective tool for solving problems in the above application areas. Our aim in this paper is to combine mathematical analytical tools and numerical simulation methods to investigate the existence and steady state of periodic solutions in different nonlinear models. Time lags with both discrete and distributed characteristics are introduced into the Lotka-Volterra predator-feeder system, and based on the discussion of the central manifold theorem and canonical type theory, it is proved that the branching periodic solution exists when the discrete time lag parameter τ > τ 0. In the SEIRS infectious disease model with nonlinear incidence term and vertical transmission, the global stability of the disease-free equilibrium point and the local asymptotic stability of the endemic equilibrium point are analyzed through the computation and discussion of the fundamental regeneration number R 0 (p, q). A class of convergence-growth models with nonlinear sensitivity functions is studied, and the global boundedness of classical solutions and their conditions are demonstrated based on global dynamics. A mathematical generalization of the muscular vascular model is made by introducing a centralized parameter, the relationship between periodic solutions and chaotic phenomena is explored utilizing a systematic equivalence transformation, and the equation of the homoscedastic orbitals is deduced to be z 2 = x 2 ( A - 1 2 x 2 ) {z^2} = {x^2}\left( {A - {1 \over 2}{x^2}} \right) .

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Section: Introductionmentioning

confidence: 99%

A study of periodic solutions of several types of nonlinear models in biomathematics

2024

Applied Mathematics and Nonlinear Sciences

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Predicting Rubisco-Linker Condensation from Titration in the Dilute Phase

Payne-Dwyer,

Kumar,

Barrett

et al. 2024

Phys. Rev. Lett.

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The condensation of Rubisco holoenzymes and linker proteins into “pyrenoids,” a crucial supercharger of photosynthesis in algae, is qualitatively understood in terms of “sticker-and-spacer” theory. We derive semianalytical partition sums for small Rubisco-linker aggregates, which enable the calculation of both dilute-phase titration curves and dimerization diagrams. By fitting the titration curves to surface plasmon resonance and single-molecule fluorescence microscopy data, we extract the molecular properties needed to predict dimerization diagrams. We use these to estimate typical concentrations for condensation, and successfully compare these to microscopy observations. Published by the American Physical Society 2024

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Editorial: theme issue on complex rheology in biological systems

Cited by 2 publications

References 20 publications

A study of periodic solutions of several types of nonlinear models in biomathematics

A study of periodic solutions of several types of nonlinear models in biomathematics

Predicting Rubisco-Linker Condensation from Titration in the Dilute Phase

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