Theory in Biosciences最新文献

Leukemia is a blood cancer characterized by the abnormal proliferation of blood cells and chronic myeloid leukemia (CML) is a type of leukemia disease that is noted by inappropriate increase of leukemic stem cell in hematopoietic niche. Mathematical modeling gives a strict conceptualization of disease development and the assessment of possible therapeutic reactions. This paper introduces the comparative study and analysis of the three known models of CML including Niche competition, Niche independent, and partial Niche dependence (PND). In case of every model, we determine the equilibrium points, calculate the basic reproduction number $R_0$ , and examine the local stability. We can compare the mathematical frameworks of the models, even though they have mathematical differences, and identify the essence of the role that niche interactions play in the persistence of leukemia. Numerical simulations, which were conducted by the fourth-order Runge-Kutta (RK-4) method, demonstrate the threshold dynamics of and shows clear qualitative behavior in different models. PND model proves to be the most biologically consistent behavior which is consistent with the known CML niche ecology. Our results give us a coherent understanding of CML modeling and a solid basis of the PND framework on the development of more clinically sound models that consider immune interactions, effects of treatment, and patient heterogeneity.

The newly described CIRDD and IROD clusters of Type 2 Diabetes represent clinically meaningful phenotypes, yet no subtype-specific molecular or omics datasets currently exist to define their mechanisms. This study introduces a predictive extrapolation framework to infer how phytocompounds from Andrographis paniculata may interact with these subtypes by mapping established pathways of insulin resistance, β-cell dysfunction, and obesity-driven inflammation onto CIRDD- and IROD-relevant axes. From the broader T2DM network, ten hub proteins (INS, AKT1, TNF, IL6, MMP9, and others) were prioritized based on functional importance and subsequently assigned to each subtype according to their documented physiological roles. Docking analysis, supported by redocking validation against high-resolution crystallographic complexes, enabled assessment of theoretical ligand-protein interactions. The model predicts that CIRDD may be primarily modulated through β-cell regulatory hubs (INS, AKT1), whereas IROD appears more strongly influenced through inflammatory-metabolic hubs (TNF, TLR4, MMP9). Apigenin and andrographolide displayed the strongest predicted affinities (binding energies ≤ -8.5 kcal/mol), and redocking yielded RMSD values below 2.0 Å, supporting the reliability of the docking protocol. Overall, this work proposes a theoretical, biologically anchored framework for predicting subtype-specific phytochemical mechanisms in the absence of direct molecular datasets. While experimental validation is required, the approach offers a rational basis for prioritizing plant-derived candidates for CIRDD and IROD.

Plants exhibit rapid, coordinated responses to environmental stimuli despite lacking a central nervous system, prompting interest in non-classical signaling mechanisms. Recent findings in quantum biology indicate that quantum coherence and entanglement, previously considered too ephemeral for the hot, humid biological medium, could be the basis for certain types of plant signal transduction. This review integrates present knowledge on plant signaling networks and describes theoretical frameworks in which quantum behavior could be involved. Theoretical models, including site-based Hamiltonians for exciton transport in photosynthetic complexes, spin-Hamiltonian models of radical-pair processes in cryptochromes, and quantum percolation theories of plasmodesmatal transport, are reviewed. These models propose that plants might utilize quantum correlations to increase signal fidelity, energy efficiency, and adaptive response between tissues. Experimental evidence for coherence in photosynthesis and cryptochrome-mediated magnetoreception supports these models. Quantum entanglement is proposed to improve long-distance communication and energy transfer in plants. Implications for practical applications range from quantum-informed crop breeding, precision farming, and efficient resource management. Future research directions, including experimental verification of quantum signatures in vivo, are outlined, with implications for bio-inspired quantum engineering in agriculture. Combining quantum mechanics and plant biology provides a paradigm-changing view of plant communication and opens new interdisciplinary horizons in fundamental science and agricultural innovations.

In evolutionary biology, phylogenetic networks are graphs that provide a flexible framework for representing complex evolutionary histories that involve reticulate evolutionary events. Recently, phylogenetic studies have started to focus on a special class of such networks called semi-directed networks. These graphs are defined as mixed graphs that can be obtained by de-orienting some of the arcs in some rooted phylogenetic network, that is, a directed acyclic graph whose leaves correspond to a collection of species and that has a single source or root vertex. However, this definition of semi-directed networks is implicit in nature since it is not clear when a mixed-graph enjoys this property or not. In this paper, we introduce novel, explicit mathematical characterizations of semi-directed networks, and also multi-semi-directed networks, that is mixed graphs that can be obtained from directed phylogenetic networks that may have more than one root. In addition, through extending foundational tools from the theory of rooted networks into the semi-directed setting-such as cherry picking sequences, omnians, and path partitions-we characterize when a (multi-)semi-directed network can be obtained by de-orienting some rooted network that is contained in one of the well-known classes of tree-child, orchard, tree-based or forest-based networks. These results address structural aspects of (multi-)semi-directed networks and pave the way to improved theoretical and computational analyses of such networks, for example, within the development of algebraic evolutionary models that are based on such networks.

DNA, or deoxyribonucleic acid, exists in every human cell, including hair, blood, and skin, carrying the genetic blueprint for all living organisms. Comprised of two strands with four nucleotides-adenine (A), thymine (T), cytosine (C), and guanine (G)-DNA forms a double-helix structure that encodes species-specific traits. Its ability to store data and perform logical operations makes it crucial for biological research, particularly in genome sequencing, which involves complex nonlinear mathematical models. To address these challenges, nonlinear partial differential equations (NPDEs) effectively model DNA's dynamic behavior. The Atangana's conformable derivative accommodates memory effects and nonlocal properties, which are crucial in describing the viscoelastic and hereditary nature of biological systems such as DNA. Unlike integer-order derivatives, this approach captures the complexity of the molecular interactions and relaxation phenomena observed in DNA dynamics. Recent literature has supported the use of fractional models for DNA due to their ability to reflect real-world phenomena more accurately (e.g., base pair opening and long-range interactions). In this study, we explore fractional-order derivatives using Atangana's conformable derivative, applying the $\left(\psi -\varphi \right)$ -expansion method to investigate double-chain DNA dynamical patterns. This method provides precise soliton solutions, such as one-soliton kinks, multiple-soliton solutions, and periodic waves, crucial for understanding DNA's optical properties. Solitons represent localized, stable wave packets that maintain their shape while propagating. In the context of DNA, these structures can model energy transmission along the chain without dispersion. This directly corresponds to base pair openings during transcription, where localized energy must be delivered and preserved to break hydrogen bonds selectively. Hence, solitons offer a feasible mathematical abstraction of physical mechanisms observed in transcription and DNA breathing. The visualized soliton solutions from the space-time fractional-order double-chain DNA model underscore the system's biological importance. The findings have potential applications in evaluating systems and refining scientific insights into DNA dynamics.

The establishment of a knowledge system often relies on a set of unfalsifiable axioms. When these foundational assumptions change, they can give rise to entirely new, yet internally consistent frameworks. The emergence of non-Euclidean geometry following the modification of Euclid's fifth postulate offers a compelling example. In this article, we propose a hypothetical world based on the principle of fully acquired heredity. In this envisioned system, DNA is no longer the primary carrier of inheritance. Instead, molecules with a stronger influence on phenotypic expression serve as the basis for heredity. Under such a paradigm, evolution would no longer operate through passive filtering of traits by natural selection, but rather through active adaptation where organisms directly shape their inheritance and respond dynamically to environmental changes. As acquired traits in the previous generation are fully transmitted to the offspring, inter-individual differences would be amplified, potentially rendering the concept of "species" obsolete and promoting asexual reproduction as the dominant mode. Nevertheless, this shift does not preclude the role of natural selection in shaping evolution; the system remains logically coherent and operational. Our article offers a speculative framework to explore not only what the world is, but also what the world could be.

In epidemiology studies, control processes are driven by key parameters, such as $R_0$ , the epidemic threshold $\tau$ over a contact network. By network-based models, the knowledge of network structures improves the prediction of $\tau$ , which is a challenge using structural features of a contact network. There are several structural approaches to predict $\tau$ . The common QMF (Quenched Mean-Field) approach uses the spectral radius as a single parameter. However, prediction can be improved using the node number, spectral radius, and Laplacian energy of graph. In this paper, at different levels, we design and experiment a new structural and spectral prediction approach of $\tau$ called KSEL (K Spectral Energy of Laplacian). Theoretical and formal levels establish mathematical foundations, while qualitative, quantitative, and comparative levels compute a descriptive statistics summary, some data analytics, and visualisation through a large and heterogeneous dataset. Results show that the new approach effectively predicts $\tau$ . It captures the full network structure, connectivity, and network diffusion features. KSEL is similar, shares a common rolling trend, and performs really good compared to the previous structural prediction approaches, including the most commonly used QMF. There is a strong positive correlation and similar value distribution between KSEL and the previous structural prediction approaches that accepted the null hypothesis by ANOVA analysis. Therefore, the new approach is structurally enriched; it extends the structural and spectral area to analyse and control spreading processes over a network. The results can have practical interests to advise an effective epidemiological control policy.

An optimal representation constitutes an efficient set. It is known that for an aggregating system if the cost of representation increases linearly with the number of bases, ternary coding is superior to binary, and coding in e is optimal. This paper investigates the relative efficiency of bases for the cases when the cost complexity is affine (slope-intercept linear), exponential, and logistic and presents new results. It is shown that for representation of structure in logistic maps, which applies often to biological systems and is true for input-output maps of neurons, the optimal base value is near 1.7632, which is consistent with the unary and space coding of information in songbirds. It is shown that the mathematical basis of this result is the solution to the equation $b^b=e.$

Traditionally, disease spread is attributed to direct individual contact. However, various mechanisms influence transmission. This paper formulates a delay-induced reaction-diffusion system where predators significantly contribute to disease spread in prey populations. Theoretical analyses include boundedness, equilibrium existence and stability, Turing bifurcation, Turing instability, and Hopf bifurcation. Species exhibit both spatially homogeneous and heterogeneous distributions. Predators accelerate disease transmission, hindering species coexistence. A positive Lyapunov exponent confirms chaotic attractors, while random species movement destabilizes the system due to predator influence. In contrast, prey movement remains stable without predators. Increasing infectious delay shifts the system from oscillatory to stable dynamics, and a specific delay controls homogeneous periodic behavior. Thus, time delay has both stabilizing and destabilizing effects. Moreover, healthy prey cannot persist if disease transmission surpasses infected prey mortality in the absence of predators. The study suggests that predator-mediated disease spread, control strategy, complexities, and chaotic behavior can provide deeper insights to understand the complexity of the system in the presence of delay and diffusion.

In this paper, an innovative passive formulation has been developed for a wide range of nonlinear systems. During this formulation, a stable and passive state-observer is provided which leads to have a passive closed-loop system. Some remarkable definitions and charts are presented for time-invariant and time-varying Lipschitz systems in four different control scenarios. From a different perspective, a novel interconnection has been established which links the passivity of subsystems with passivity/stability of the closed-loop system. All definitions have been arranged according to the systematic approach named "virtually Euler-Lagrange" form of passivation. Since some design conditions will be released due to using the mentioned method and definitions, the process of analysis and design will be simplified. The proposed passivity-based controller has been applied to treat hepatitis B virus infection disease in several scenarios. All the proposed definitions have been validated by the simulation results.