Journal of Theoretical Biology最新文献

Varroa destructor is a significant European honeybee pest, impacting agricultural industries globally. Since arriving in 2022, Australia faces the possibility that Varroa will become established in European honeybee colonies nationally. Australia initially pursued a strategy of testing and subsequently eliminating hives infested with Varroa. These management efforts raise interesting questions about the interplay between hive testing and elimination, and the spread of Varroa between hives. This study uses mathematical modelling to investigate how combined hive testing and elimination strategies impact the spread of Varroa through a network of European honeybee hives. We develop a model of both within-hive reproduction of Varroa and hive testing, and between-hive movement of Varroa on a network of hives. This model is used to assess the impact of various testing and hive elimination strategies on the total number of hives eliminated on the network of hives. Each model simulation starts with a single infested hive, and from this we observed one of two dynamics: either the infestation is caught before spreading, or Varroa spreads extensively through the network before being caught by testing. Within our model we implement two common hive testing methods - sugar shake and alcohol testing. A shared limitation of these testing methods is that they can only detect mites in a specific stage of their lifecycle. As such, testing is not only dependent on how many Varroa mites are in a hive, but also on what lifecycle stage the mites are in at the time of testing. By varying testing and movement parameters, we see that this testing limitation greatly impacts the number of hives eliminated in various scenarios. Furthermore, testing earlier, or testing more frequently, does not guarantee a smaller invasion. Our model results suggest irregular testing schedules, e.g. testing multiple times in close succession rather than just once in a given timeframe, may help overcome the limitations of common hive testing strategies.

In this study, we revisit the Canham-Helfrich energy to analytically determine the equilibrium configurations of the red blood cell (RBC). By extending the work of Au and Wan Au and Wan (2003), we establish a sufficient analytical condition ensuring the existence of the biconcave equilibrium shape. This result provides a rigorous complement to previous asymptotic arguments, clarifying the mechanical balance underlying RBC morphology. Moreover, the analytical derivation of the equilibrium shape function from the Helfrich energy naturally reproduces the empirical contour equation proposed by Evans and Fung Evans and Fung (1972). This demonstrates that their experimental results can be obtained via the energy-minimization framework, thereby linking experimental observations with a consistent theoretical foundation. The present results provide both a mathematical completion and a physical unification of previous models, confirming that the biconcave RBC geometry arises as an equilibrium configuration governed by simple curvature constraints.

Ovarian cancer is the deadliest gynaecological cancer and the fourth leading cause of cancer deaths in women. High-grade serous ovarian cancer (HGSOC) accounts for 75% of cases, and chemotherapy resistance and relapse occur in 85% of patients, leading to a 5-year survival of 45%. Currently, the literature lacks comprehensive immunobiological models of HGSOC, and developing such models could provide critical insights into the disease's underlying mechanisms and interactions within the tumour microenvironment. We address this by constructing an immunobiological model using delay differential equations and then optimise chemotherapy regimens to maximise efficacy, minimise toxicity, and improve treatment efficiency for first-line treatment. The model consists of two compartments, the tumour site and tumour-draining lymph node, with immune processes such as dendritic cell (DC) maturation, T cell priming and proliferation, and cytokine interactions modelled. Parameter values are estimated using experimental data from ovarian cancer tissue samples as well as the TCGA OV database. The results indicate that low-dose, more frequent chemotherapy provides comparable results to the standard regimen with a lower toxicity, and alternative dosing strategies with rest weeks can allow patients to recover from the toxic side effects of chemotherapy.

Cleaner shrimp engage in a mutualistic relationship with reef fish, providing cleaning services in exchange for nutritional benefits. These shrimp inhabit stationary sea anemones, forming "cleaning stations" that rely on mobile fish clients to locate and revisit them. To investigate how fish movement behaviors influence the spatial distribution of cleaning stations, we developed an individual-based model that explicitly incorporates both stochastic fish movement and two forms of directed fish movement strategies: taxis (i.e. gradient-following) and memory-based movement. Our results reveal that directed movement, whether through taxis or memory, promotes the formation of spatially clustered cleaning stations, but only when the range of directed movement outweighs the homogenizing effects of random dispersal. Specifically, memory-based clustering requires the memory range to exceed dispersal distance, while taxis-based clustering emerges even with taxis-based movement ranges exceeded by dispersal distance. By parameterizing the model with empirical data on client fish visitation frequencies, we further show that reefs dominated by "Choosy" fish (those willing to travel farther for preferred stations) exhibit stronger station clustering compared to reefs with "Resident" fish (territorial species with limited movement). These findings highlight how client behavior shapes the spatial ecology of cleaning mutualisms, with implications for understanding partner encounter dynamics in other species interactions.

Metastasis remains the decisive event in most solid cancers, yet the mathematical tools we use to describe it are still largely tied to tumor size. In the curent work, we recast metastatic spread in terms of tumor age and generational ancestry, turning an implicit notion into the main organizing principle of the model. Building on the classical Iwata-Kawasaki-Shigesada (IKS) framework, we construct a transformation from size to age and derive a hierarchy of integral equations indexed by metastatic generation. Our reformulation yields closed-form expressions for first-generation metastases and simple one-dimensional recursive integrals for higher generations, avoiding direct numerical solution of the original size-structured partial differential equation (PDE) with its nonlocal boundary condition. Using Gompertzian growth and power-law metastatic emission, we show that the age-generation model reproduces IKS predictions over clinically relevant time scales while offering improved numerical stability and interpretability. The generational decomposition reveals a robust pattern: lesions seeded directly from the primary dominate early in the disease course, whereas successively younger generations, emitted by existing metastases, come to dominate the total lesion count at small sizes, leaving older generations to occupy the macroscopic tail of the distribution. Introducing an explicit detection threshold naturally separates a small number of radiologically visible macrometastases from a much larger, unseen pool of micrometastases. Together, these results provide a transparent and computationally efficient framework that links primary-tumor growth, metastatic seeding across generations, and the hidden microscopic burden that underlies clinical presentation.

The global ecological dominance of angiosperms represents a major evolutionary success. This study suggests that their ascendance is not due to a single trait but to a deeply integrated hydraulic design that maximizes performance and resilience. A model is developed, and based on the constructal law, the leaf vascular architecture of three major plant lineages, angiosperms, gymnosperms, and ferns is compared. The model evaluates performance based on two foundational parameters: the branching exponent which accounts for the supply efficiency, and the vein placement ratio, which controls water distribution. The results demonstrate that the angiosperm architecture is superior across all modeled metrics. This design minimizes the energetic cost of water transport, ensures uniform water distribution, and enables rapid hydraulic responsiveness. Significantly, the model reveals that this profound efficiency generates a bioenergetic surplus that funds a resilient, redundant vascular network. This fault-tolerant design provides a decisive advantage against physical damage, ensuring that high photosynthetic capacity is a sustained reality rather than a fragile state. It is this synergistic system that provides a quantitative explanation for the enduring global supremacy of angiosperms.

Modeling biological systems with Boolean networks (BNs) is a well-established approach that enables reasoning about the qualitative dynamics of such systems, such as gene and signaling networks. Several semantics for BNs, i.e., scheduling of component updates, have been proposed that can significantly affect the predicted dynamic behaviors. The synchronous and asynchronous ones are the most popular, but they fail to capture some of the behaviors observed in reality and accounted for by quantitative models. Recently, the most permissive semantics has been introduced, guaranteed not to miss any behavior achievable by a quantitative model following the same logic as the BN, and, in addition, significantly reducing the computational complexity of dynamical analysis. But this time, it appears too permissive and tolerates spurious behaviors in many real situations. After clarifying the relationships between existing semantics, we define the threshold semantics whose dynamic behaviors are all those given by a single threshold network, a subclass of multivalued networks, for any possible threshold map. The spurious behaviors are excluded by the threshold semantics, whose qualitative behaviors appear as a proper abstraction of real biological processes founded on activation and inhibition influences regulated by single thresholds whose values are unknown, which is generally the case. We show that threshold semantics is stricter (for reachability between Boolean configurations) than the cuttable extended semantics (called here linear semantics) and stricter than a given constrained version of the most permissive semantics. We then seek to operationalize this threshold semantics. For this, we equip the constrained version of the most permissive semantics with a system of symbolic constraints, attached to any given trajectory and verifiable by a satisfiability solver. The satisfiability of this set of constraints ensures the consistency of the formal threshold conditions associated with the transitions along the trajectory. It defines a new operational semantics at the level of trajectories. Then we prove that this semantics is equivalent to the threshold semantics. Finally, we prove that the computational complexity of this semantics is the same as that of classical semantics, i.e., PSPACE, and we state several conjectures for future work.