Theory in Biosciences最新文献

The Price equation provides a formal account of selection building on a right-total mapping between two classes of individuals, which is usually interpreted as a parent-offspring relation. This paper presents a new formulation of the Price equation in terms of fuzzy set-mappings to account for structures where the targets of selection may vary in the degree to which they belong to the classes of "parents" and "offspring," and in the degree to which these two classes of individuals are related. The fuzzy set formulation widens the scope of the Price equation such that it equally applies to natural selection, cultural selection, operant selection, and selection in physical systems.

In this study, we conduct a mathematical and numerical investigation of a density-dependent model for the anaerobic digestion process, described by a system of four nonlinear ordinary differential equations, featuring an indirect feedback loop. Our analysis focuses on the acetogenesis and hydrogenotrophic methanogenesis phases. The model incorporates two microbial populations, acetogenic bacteria and hydrogenotrophic methanogens, and two substrates, volatile fatty acids (VFA) and hydrogen, with a specific emphasis on the inhibition of acetogen growth by methanogens. Using a broad class of nonmonotonic growth functions, we establish the necessary and sufficient conditions for the existence and stability of the system's steady states through rigorous mathematical analysis. Operating diagrams are constructed as functions of inlet substrate concentrations and the dilution rate. Numerical simulations further reveal the range of dynamic behaviors, highlighting the impact of methanogen-induced inhibition on acetogen dynamics. Contrary to the findings of Di and Yang in (JRSI 16:20180859, 2019), we demonstrate that when inhibition is sufficiently strong and VFA concentrations are high, the microbial community exhibits damped oscillations that converge to a positive steady state. These results illustrate the system's ability to stabilize at a coexistence equilibrium, even under the influence of an indirect feedback loop.

Due to predicted global climate change, there have been significant alterations in agricultural production patterns, which had a negative impact on ecosystems as well as the commercial and export prospects for the production of grapevines. The natural biochemistry of grapevines, including their chlorophyll content, net photosynthetic rate, Fv/Fm ratio, photorespiration, reduced yield, and quality is also anticipated to be negatively impacted by the various effects of light, temperature, and carbon dioxide at elevated scales. Grapevine phenology, physiology, and quality are impacted by the inactivation of photosystems (I and II), the Rubisco enzyme system, pigments, chloroplast integrity, and light intensity by temperature and increasing CO₂ levels. Grape phenological events are considerably altered by climatic conditions; in particular, berries mature earlier, increasing the sugar-to-acid ratio. In enology, the sugar-to-acid ratio is crucial since it determines the wine's final alcohol concentration and flavour. As light intensity and CO₂ levels rise, the biosynthesis of anthocyanins and tannins declines. As the temperature rises, the production of antioxidants diminishes, affecting the quality of raisins. Table grapes are more sensitive to temperature because of physiological problems like pink berries and a higher sugar-to-acidity ratio. Therefore, the systemic impact of light intensity, temperature, and increasing CO₂ levels on grapevine physiology, phenology, photosystems, photosynthesis enzyme system, and adaptive strategies for grape producers and researchers are highlighted in this article.

Various types of symmetry of polynucleotide sequences and methods of their algebraic description are considered. Among the methods of description, the main attention is paid to the application of semigroup theory (in particular, group theory). For convenience, all symmetry is divided into types. Combinatorial symmetry, first of all, it is associated with the explicit and hidden periodicity of the arrangement of identical nucleotides in subsequences. The above is generalized to the case of color symmetry, when different types of nucleotides or their associations can transform into each other upon shift. Fractal symmetry can also be added to this. Biofunctional symmetry means the presence of sequence factors of different nature (and size), which can be interchanged (swap places) solely due to their biological equivalence in the strand. A number of issues that are indirectly related to symmetry are also touched upon, for example, the presence of closed loops in polynucleotide (or polypeptide) chains and some physicochemical aspects.

Cancer therapies often face the challenge of resistance, which arises from the selective pressures exerted by conventional treatment protocols such as the maximum tolerated dose (MTD). Adaptive therapy adjusts treatment intensity based on tumor response, which emerges as a promising alternative for managing tumor growth and delaying resistance. This study presents a multi-scale computational model that integrates cellular-level processes, tumor population dynamics, and adaptive therapy protocols to explore tumor growth under different therapeutic strategies. Through simulations, we compare the efficacy of MTD and adaptive therapy in controlling tumor size, managing resistance, and optimizing patient survival. Our findings highlight the potential of adaptive therapy to stabilize tumor size and delay resistance while maintaining a diverse population of tumor cells. Additionally, these findings suggest that adaptive therapy could be a promising alternative to MTD, offering improved tumor control and delayed resistance in clinical settings. Moreover, this study underscores the potential of adaptive therapy to provide a more sustainable approach to cancer treatment, offering a better quality of life for patients by delaying the development of resistance. By preserving tumor heterogeneity, adaptive therapy could optimize patient outcomes and offer a more effective long-term solution compared to conventional MTD treatments.

We construct and analyze an SIRI+Q model with a piecewise smooth system of ordinary differential equations for the epidemic dynamics of a reinfectious disease, in which a limited capacity of isolation is incorporated. To consider the relation of the limited isolation capacity to the epidemic consequence, we derive the condition that the isolation reaches the capacity at finite time along the path of the epidemic process, and that the disease becomes endemic. We investigate in particular how the endemicity, the endemic size, or the final epidemic size could depend on the isolation capacity. From the obtained mathematical results, we find theoretical implications on the relevance of the isolation capacity and the difficulty of its measure to control the spread of the disease in the community.

Despite being a powerful tool to model ecological interactions, traditional evolutionary game theory can still be largely improved in the context of population dynamics. One of the current challenges is to devise a cohesive theoretical framework for ecological games with density-dependent (or concentration-dependent) evolution, especially one defined by individual-level events. In this work, I use the notation of reaction networks as a foundation to propose a framework and show that classic two-strategy games are a particular case of the theory. The framework exhibits a strong versatility and provides a standardized language for model design, and I demonstrate its use through a simple example of mating dynamics and parental care. In addition, reaction networks provide a natural connection between stochastic and deterministic dynamics and therefore are suitable to model noise effects on small populations, also allowing the use of stochastic simulation algorithms such as Gillespie's with game models. The methods I present can help to bring evolutionary game theory to new reaches in ecology, facilitate the process of model design, and put different models on a common ground.

In biology, the concept of "living organism" has traditionally been based on the smallest level of organization comprising all the necessary and essential characteristics of life: the cell. Today, this concept is being challenged by the analysis of ambiguous biological entities, located both below and above the level of the living cell, which exhibit some of the characteristics of living organisms. This situation has given rise to an epistemological pluralism of the concepts of "organism", "individual" and "living", for which no clear and unanimous definition has yet been accepted. The aim of this manuscript is to explore new ideas and perspectives for defining the concept of "living organism", in order to eliminate a certain level of pluralism that could generate confusion, particularly in the pragmatic context of biological research. First, I expose the dualism of the concepts of "organism" and "individual" and suggest a fusion of these concepts in order to eliminate a certain level of pluralism. In doing so, I develop a symbiotic and holistic definition of the concept of "living organism", which includes different structural levels of the organism: molecular, cellular and ecosystems. Second, I present the epistemological problem of the concept of "living", which is closely related to the concepts of "organism" and "individual", by analyzing the list and gradational types of definition. In doing so, I propose a new symbiotic, holistic and gradualist model of the concept of "living organism", using a gradation of several properties of the living applied to the different structural levels of the organism developed previously (molecular, cellular, ecosystems).

Can mathematical proofs be employed for the solution of fundamental molecular-level problems in biology? Recently, I mathematically tackled complex mechanistic problems arising during the synthesis of the universal biological currency, adenosine triphosphate (ATP) by the F_OF₁-ATP synthase, nature's smallest rotary molecular motor, using graph-theoretical and combinatorial approaches for the membrane-bound F_O and water-soluble F₁ domains of this fascinating molecule (see Nath in Theory Biosci 141:249‒260, 2022 and Theory Biosci 143:217‒227, 2024). In the third part of this trilogy, I investigate another critical aspect of the molecular mechanism-that of coupling between the F_O and F₁ domains of the ATP synthase mediated by the central γ-subunit of $\sim 1$ nanometer diameter. According to Nath's torsional mechanism of energy transduction and ATP synthesis the γ-subunit twists during ATP synthesis and the release of stored torsional energy in the central γ-stalk causes conformational changes in the catalytic sites that lead to ATP synthesis, with 1 ATP molecule synthesized per discrete 120° rotation. The twisted γ-subunit breaks the symmetry of the molecule, and its residual torsional strain is shown to readily accommodate any symmetry mismatch existing between F_O and F₁. A mathematical number theory proof is developed to quantify the extent of symmetry mismatch at any angular position during rotation and derive the conditions for the regaining of symmetry at the end of a 360° rotation. The many chemical and biological implications of the mechanism and the mathematical proof are discussed in detail. Finally, suggestions for further mathematical development of the subject based on ideas from symmetry and group theory have been made. In sum, the answer to the question posed at the beginning of the Abstract is a resounding YES. There exists new, relatively unexplored territory at the interface of mathematics and molecular biology, especially at the level of molecular mechanism. It is hoped that more mathematicians and scientists interested in interdisciplinary work are encouraged to include in their research program approaches of this type-a mathematical proofs-inspired molecular biology-that have the power to lead to new vistas. Such molecular-scale mechanistic problems in biology have proved extraordinarily difficult to solve definitively using conventional experimental, theoretical, and computational approaches.

The tumor microenvironment constitutes a complex system shaped by the intricate interactions among tumor cells, immune cells, and cytokines. Within this environment, the interplay between immune cells and cytokines is crucial in influencing tumor growth and progression. Despite advancements in clinical tumor immunotherapy, there remains a gap in comprehensive simulations of tumor immune responses, particularly regarding cytokine-driven processes. This study aims to address this gap by investigating the regulatory interactions among tumor cells, immune cells, and cytokines to simulate the complexities of tumor immunotherapy. We develop a comprehensive modeling and computational framework incorporating PD-1 inhibitors and interleukin-10 (IL-10) antibodies. Through detailed mathematical analysis, we elucidate the impact of changes in the immune microenvironment on tumor cells number. Our findings highlight the significant therapeutic effect of anti-PD-1 and IL-10 inhibitors, with increased drug dosage correlating with a reduction in tumor burden. Furthermore, combination therapy demonstrates a marked extension of survival with reduced dosages compared to monotherapy. Based on model simulations, we proposed prognostic predictions by assessing the microenvironmental status before treatment. The findings indicate a promising method for enhancing treatment effectiveness and offering potential advantages to patients receiving tumor immunotherapy.