The move towards personalized treatment and digital twins for cancer therapy requires a complete understanding of the mathematical models upon which these optimized simulation-based strategies are formulated. This study investigates the influence of mathematical model selection on the optimization of chemotherapy and radiotherapy protocols. By examining three chemotherapy models (log-kill, Norton-Simon, and maximum efficacy), and three radiotherapy models (linear-quadratic, proliferation saturation index, and continuous death-rate), we identify similarities and significant differences in the optimized protocols. We demonstrate how the assumptions built into the model formulations heavily influence optimal treatment dosing and sequencing, potentially leading to contradictory results. Further, we demonstrate how different model forms influence predictions in the adaptive therapy setting. As treatment decisions increasingly rely on simulation-based strategies, unexamined model assumptions can introduce bias, leading to model-dependent recommendations that may not be generalizable. This study highlights the importance of adding model selection, not simply information criterion, into uncertainty quantification, as chosen functional forms can be just as significant to predicted outcomes as parameter sensitivity, practical parameter identifiability, and/or inferred parameter posteriors, as a part of the uncertainty quantification process. Understanding how model choice impacts predictions guiding personalized treatment planning with sufficient uncertainty quantification analysis, will lead to more robust and generalizable predictions.
Systemic therapies for advanced cancers often induce initial responses but rarely achieve durable cures due to acquired resistance. Drug-tolerant persister (DTP) cells survive treatment without additional genetic mutations. We previously showed that melanoma DTP cells globally suppress mRNA translation while selectively maintaining translation of specific mRNAs, but the basis of this selectivity remained unclear. Here, we integrate stochastic modeling with experimental analyses to define the principles governing selective translation in DTP cells. We identify translational reprogramming as a conserved feature of DTP cells across cancer types and treatments. Reduced MYC-dependent ribosome biogenesis limits ribosome availability, creating a translational bottleneck. Modeling reveals that ribosome scarcity drives competition among mRNAs, thereby shaping selective translation. This framework uncovers a ribosome-dependent survival checkpoint in DTP cells and highlights ribosome thresholds as a potential vulnerability for overcoming therapy resistance.
An agent-based model of therapeutic neural stem cell (NSC) migration is developed and used to predict the migration of NSCs in naïve mouse brain. The model utilizes generalized q-sampling imaging which resolves white matter fibers that cross in the brain and is shown to better account for variations in NSC migration patterns as compared to diffusion tensor imaging. In calibrating the model to experimental data, we show that the model is able to reproduce the spatial distribution of NSCs in the mouse brain. In addition, we show that the spatial distribution of NSCs in the mouse brain is sensitive to the location of NSC injection. Persistent distribution of NSCs to the olfactory bulb, consistent with developmental pathways including the rostral migratory stream, suggests that future models of therapeutic NSCs in the naïve brain may need to include other factors such as chemotaxis or blood flow to account for variations in NSC migration paths. The results highlight the usefulness of the model in predicting which injection locations may provide the best distribution of NSCs to a given target location.
The opioid epidemic continues to devastate communities across the United States. Treatment options for opioid use disorder (OUD) include Medication-Assisted Treatment (MAT) and non-medication approaches, with MAT demonstrating superior outcomes including lower morbidity and fatal overdose rates, reduced HIV and HCV transmission, and decreased criminal activity. However, treatment access remains limited, and recent federal policies may worsen these barriers. This study employs a system of ordinary differential equations to model the relationship between these treatment modalities and OUD population dynamics. Beyond deriving closed-form equilibrium solutions, our analysis reveals that expanding MAT access alone, while beneficial for reducing OUD prevalence, is insufficient as a standalone policy intervention. Our findings indicate that effective OUD reduction requires a comprehensive approach: enhanced prevention programs, increased access to all treatment types, and improved treatment efficacy. The model also suggests that recent federal policies (e.g., Medicaid cuts) may have unintended negative consequences for population-level outcomes.
Wildlife-vehicle collisions (WVC) threaten both biodiversity and human safety worldwide. Despite empirical efforts to characterize the major determinants of WVC risk and optimize mitigation strategies, we still lack a theoretical framework linking traffic, landscape, and individual movement features to collision risk. Here, we introduce such a framework by leveraging recent advances in movement ecology and reaction-diffusion stochastic processes with partially absorbing boundaries. Focusing on range-resident terrestrial mammals-responsible for most fatal WVCs-we model interactions with a single linear road and derive exact expressions for key survival statistics, including mean collision time and road-induced lifespan reduction. These quantities are expressed in terms of measurable parameters, such as traffic intensity or road width, and movement parameters that can be robustly estimated from relocation data, such as home-range crossing times, home-range sizes, or distance between home-range center and road. Therefore, our work provides an effective theoretical framework integrating movement and road ecology, laying the foundation for data-driven, evidence-based strategies to mitigate WVCs and promote safer, more sustainable transportation networks.
Environmental conditions fundamentally shape host-pathogen interactions; however, how multiple extreme abiotic stressors combine to influence infection outcomes remains poorly understood. All living beings have evolved under specific gravitational and radiation regimes; deviations from these conditions-whether in extreme terrestrial environments or beyond Earth-may alter physiological homeostasis, including immune function and pathogen replication. In this study, we investigated the effects of reduced gravity and lowered muon flux on Orsay virus infection in the nematode Caenorhabditis elegans. We employed a fully factorial experimental design, examining how each factor, alone and in combination, influences fecundity and developmental traits and viral load. While below-background radiation radically affected viral accumulation dynamics, reduced gravity had a minor effect. Both factors significantly impacted reproduction and morphology, with some effects magnified by viral infection. These results reveal how even partial modifications of Earth-like gravity and radiation levels can alter host-pathogen interactions. By integrating experimental observations with mathematical modeling, we suggest that these environmental stressors may primarily affect prezygotic reproductive processes and modulate viral replication through distinct and sometimes antagonistic mechanisms. Although this work does not encompass the full complexity of space environments, where cosmic radiation includes high-energy protons and heavy ions, it provides insight into how adjustable models of reduced gravity and radiation can advance our understanding of biological adaptation beyond standard terrestrial conditions.IMPORTANCEUnderstanding how extreme environmental conditions affect host-pathogen interactions is critical for exploring fundamental principles of stress biology. This study demonstrates that reduced gravity and diminished muon radiation flux can significantly alter viral infection dynamics and host physiology in Caenorhabditis elegans. By integrating experimental data with mathematical modeling, we propose that these abiotic stresses impact prezygotic reproductive processes and modulate viral replication in distinct and sometimes antagonistic ways. Our findings suggest that even partial deviations from Earth-like conditions can reshape infection outcomes and developmental trajectories, highlighting the need for deeper mechanistic insights into biological adaptation beyond terrestrial norms. These results have implications for space biosciences, evolutionary virology, radiation hormesis, and the design of countermeasures to preserve organismal health in extreme or non-terrestrial habitats.
Intercellular coupling between core PCP proteins is essential for unidirectional polarization of epithelial cells, known as planar cell polarity (PCP). While imbalances in core PCP protein levels between adjacent cells disrupt PCP in some tissues, other tissues maintain PCP despite containing multiple cell types with distinct core PCP protein abundance. How such tissues tolerate these imbalances remains unclear. Here, we analyzed how the spatial distribution of cell types contributes to PCP maintenance using a previously established mathematical model. Systematic simulations showed that the accuracy of PCP maintenance under core PCP protein imbalance strongly depends on cell-type distribution patterns. We then applied deep learning and statistical modeling to identify critical features, revealing that the orientation of cell-type alignment is a key determinant of PCP robustness. Such directional cell-type alignment was observed in the mouse oviduct. Our findings highlight an overlooked role of tissue cell-type organization in PCP maintenance.
The Ebola outbreak represents one of the most severe global health crises in recent history. In this study, we develop and analyze a new fractional-order mathematical model for the transmission dynamics of the Ebola virus, incorporating an extended Atangana-Baleanu Caputo fractional operator. The model's foundational properties-such as existence, uniqueness, positivity, and well-posedness of solutions are established through fixed point theorems. A detailed investigation of the basic reproduction number is carried out, accompanied by a sensitivity analysis to highlight influential parameters affecting disease spread. To ensure the stability of the system, chaos control methods and Lyapunov functions are employed, alongside first and second derivative tests, to demonstrate global stability. Additionally, the convergence and uniqueness of the models solution are explored. For the numerical approximation, we apply Lagranges interpolation polynomials method, known for its effectiveness in generating accurate and convergent solutions. This approach offers a novel analytical framework for fractional-order epidemiological models. The findings demonstrate that fractional order derivatives are more dependable and efficient than classical orders when it comes to explaining biological processes.
Vaccine responses depend on the Darwinian genetic evolution of B cells to generate high-affinity antibodies. However, B cells gain non-genetic heterogeneity while searching for antigen and T helper cells, but then their non-genetic cell states remain stable within proliferative clonal bursts. We explored the functional consequence of this dynamic control of non-genetic variability by developing a mathematical model, integrating a wealth of immunological knowledge. We discovered that variability in B cell fate decisions does not impair but instead accelerates affinity maturation by allowing high-affinity outliers to escape plasma cell differentiation and seed further rounds of Darwinian evolution. During clonal bursts, non-genetic cell state stability further promotes their amplification. The resulting model correctly predicts emergent vaccine response properties in mouse strains with altered B cell fate decision profiles. Our work reconciles classical B cell clonal selection theory with the experimentally observed non-genetic variability, and it provides an interpretable knowledge-based modeling framework to support personalized vaccination strategies.
Most theoretical work on the origin of heredity has focused on how genetic information can be maintained without mutational degradation in the absence of error-proofing systems. A simple and parsimonious solution assumes the first gene sequences evolved inside dividing protocells, which enables selection for functional sets. But this model of information maintenance does not consider how protocells acquired their genetic information in the first place. Clues to this transition are suggested by patterns in the genetic code, which indicate a strong link to autotrophic metabolism, with early translation based on direct physical interactions between amino acids and short RNA polymers, grounded in their hydrophobicity. Here, we develop a mathematical model to investigate how random RNA polymers inside autotrophically growing protocells could evolve better coding sequences for discrete functions. The model tracks a population of protocells that evolve towards two essential functions: CO2 fixation (which drives monomer synthesis and cell growth) and copying (which amplifies replication and translation of sequences inside protocells). The model shows that distinct coding sequences can emerge from random RNA sequences driving increased protocell division. The analysis reveals an important restriction: growth-supporting functions such as CO2 fixation must be more easily attained than informational processes such as RNA copying and translation. This uncovers a fundamental constraint on the emergence of genetic heredity: growth precedes information at the origin of life.
Globally rising cases of malaria have prompted concentrated efforts to control malaria transmission, utilising various mathematical models to support the Roll Back Malaria agenda. Many existing models with their specific modifications exhibit rigidity, limiting their application to inform malaria control interventions. This study addresses this limitation by employing a reduction technique on a comprehensive malaria control model to derive a simplified system that preserves the essential dynamics of the original system. We validate the accuracy of the reduced model by comparing the two models via Bayesian MCMC. Based on a simulation study, parameter identifiability analysis and sensitivity analysis, we compare the two models and show that the reduced system exhibits similar transmission characteristics as the full model. Our results demonstrate that the reduced model effectively captures the essential behaviour of the comprehensive model, while providing flexibility and computational efficiency, making it a valuable tool for evaluating and implementing malaria control strategies.
In our previous work, we introduced the concept of torsion angular bin strings (TABS), which is a discrete vector representation of a conformer's torsional angles. Through this discretization, conformational states can be counted, yielding an estimate of the upper limit of the expected conformational ensemble size (nTABS). Besides nTABS being used as a quantitative measure of molecular flexibility, TABS itself is a way of grouping the conformers of a molecule without picking thresholds. This feature of TABS is especially valuable, as selecting suitable thresholds for metrics such as heavy-atom root-mean-square deviation (RMSD) or shape Tanimoto is highly system-dependent and can thus be challenging when working with large sets of molecules. Here, we describe the update to the nTABS algorithm of the TABS package since the last release. In addition, we present a classification study of conformer ensembles by TABS and compare it to classifications by a shape Tanimoto metric. Scientific contribution In contrast to our previous implementation, which handled molecular topological symmetry by enumerating all possible combinations that were simply permutations of one another, the new implementation treats TABS as mathematical objects governed by group theory, specifically Burnside's Lemma. This approach requires substantially less code and delivers a notable improvement in computational speed. The study also builds upon our previously developed framework for categorization comparisons between TABS and heavy-atom RMSD. Here, we show the results of a similar comparison with a shape Tanimoto metric, which further support the hypothesis that TABS encode the shape of conformers in a meaningful way.
Plant roots form a microbiome that interacts at the cell wall extracellular matrix before entering the cell. The root primary and accessory walls present a dynamic, cell-type-dependent scaffold that microbes must navigate, using shared cellulose or contrasting chitin motifs and influencing plant gene responses that encode enzymes for cell wall biosynthesis and degradation. We propose that an interface evolves as microbes reach the root tip and interact with host polymers, potentially driving concurrent degradation of root and microbial cells. Knowledge gaps span diffusion, fluid flow, nutrient exchange, and the physics of microbial motion within the wall boundary. Advances in in situ imaging and mathematical modelling can help understand the dynamics of cell walls to design root microbiomes to function in agroecosystems.
In low tuberculosis (TB) burden settings, recurrent tuberculosis is predominantly driven by relapse. Relapse, defined as the recurrence or re-emergence of a disease or condition after a period of remission or apparent recovery, poses a significant global public health challenge. The variability in the duration of infection and recovery stages among individuals calls for a rigorous mathematical framework to evaluate the impact of this heterogeneity on disease transmission dynamics. To address this, we develop a general integral equation model tailored to low TB burden settings, incorporating arbitrary distributions for the infection and relapse stages, thereby capturing individual variations in sojourn times during disease progression. Our analysis focuses on the existence and stability of equilibrium solutions, which depend on whether the basic reproduction number is less than or greater than one. Additionally, we investigate the reformulation of the integral model into an ordinary differential equation system by assuming exponential or gamma distributions for the sojourn time durations, potentially facilitating further theoretical analysis and numerical computations.
Ovarian cancer is responsible for the most deaths of all gynaecological cancers in the Western world [1]. The symptoms of ovarian cancer are typically subtle and similar to those associated with other diseases found more prevalently in the population, frequently resulting in late diagnoses and advanced tumour stages upon treatment initiation [2]. While surgery and platinum-based treatments can be curative, ovarian cancers found at the latter, metastasised stages are likely to be recurrent and more tailored towards palliative care [3]. Metastasised ovarian cancer spreads to surrounding organs and tissues such as the greater omentum [4], a large fat pad composed of adipose tissue stretching from the stomach and hanging over the intestines. The location of this is key in its role towards ovarian cancer and its progression [5]. In this study, we develop a mathematical model to investigate the role that adipocytes found in adipose tissue can have in ovarian cancer progression. Observations of biological experiments from two ovarian cancer cell lines [6] create foundations to build a multiscale agent-based model in a Physicell framework [7]. The impact of the adipose derived media concentration, treatment dosage, and initial tumour size are explored to find how these conditions affect the spatio-temporal dynamics of cancer tumours.
Releasing Wolbachia-infected mosquitoes to replace the wild mosquito population represents an innovative biocontrol strategy currently implemented in over 15 countries to combat mosquito-borne diseases. This study investigates the population dynamics of Wolbachia invasion under periodic release strategies where only infected males are additionally introduced to accelerate population replacement, a strategy that yields a challenging non-autonomous difference equation model. The analytical complexity stems from the infinite composition of distinct rational maps, which renders conventional methods ineffective. To address this challenge, we develop a novel framework based on Poincaré map theory and geometric analysis. Our approach identifies a critical release threshold α* that fully determines system behavior. The main result reveals a sharp dichotomy. When release ratios surpass α*, the Wolbachia-fixed equilibrium achieves global stability, guaranteeing successful population replacement. Below this threshold, the system maintains bistability. This theoretical advancement establishes a quantitative criterion for optimizing intervention strategies, resolving computational obstacles inherent in non-autonomous systems while providing practical guidance for designing effective Wolbachia-based control programs.
Bananas and plantains are among the world's most important staple food crops and provide daily calories, income, and nutritional security for millions of smallholder households, particularly across sub-Saharan Africa. Accurately estimating epidemiological parameters for major threats such as banana bunchy top virus (BBTV) is essential for predicting disease spread and designing effective management strategies, yet the limited and resource-constrained field data available in smallholder systems make this extremely challenging. Here, we introduce a data-augmented Adaptive Multiple Importance Sampling (DA-AMIS) framework that integrates Bayesian inference with a mechanistic epidemic model to recover key BBTV transmission parameters from small field experiments. Using detailed individual-level observations from a 24-plant experiment in Benin, we jointly infer latent infection times, aphid-mediated dispersal characteristics, and primary and secondary transmission rates. We validate these estimates against independent BBTV datasets from Burundi and Malawi, finding close correspondence between simulated and observed prevalence trajectories, demonstrating the transferability of inferred parameters across regions. Our results indicate that approximately 12% of replanting suckers are infected at planting, emphasizing the high risk of BBTV introduction through planting material, and simulations identify April as the period of peak infection pressure, providing actionable insight for surveillance timing. These findings show that small field experiments, when combined with advanced Bayesian computational methods, can yield robust and generalizable epidemiological parameter estimates.
In vitro cell models of the gut epithelium, particularly those based on the Caco-2 and HT29-MTX cell lines, play an important role in studying the uptake and metabolism of nutrients and pharmaceuticals. Previous studies using mass spectrometry imaging have shown a distinctive lipidome signature for these cells, alone and in coculture, although only limited information on lipid identities was obtained. A novel method employing limited proteolysis for sampling live, adherent cells using an automated capillary extraction workflow was developed which achieved single-cell sampling of Caco-2 cells although only clusters of HT29-MTX cells could be sampled due to mucus secreted by these cells. The lipidomes of the cell samples were mapped using LC-MS/MS and approximately 150 lipids were putatively identified. Further analysis of these data confirmed the distinctiveness of the Caco-2 and HT29-MTX cell lipidomes. Cell-to-cell heterogeneity was observed, especially in the Caco-2 cells, which may be indicative of variation in their differentiation state. Metabolic pathway analysis showed the distinctive lipidome of Caco-2 cells related to increased glycerol-3-phosphate pathway activity involved in di- and tri- glyceride synthesis. In contrast, HT29-MTX cells exhibited a more active phosphatidylcholine metabolism, related to their mucus-secreting capability. Future studies will explore wider application of the sampling procedure outlined here for single cell lipidomics of other adherent cell lines.
Previous studies have mainly focused on spatiotemporal dynamics near the Turing-Hopf bifurcation point, typically employing normal form theory to partition parameter space and identify classic solutions. However, both Hopf and Turing bifurcations can be classified into supercritical and subcritical types, and the combined effects of their criticality on vegetation dynamics remain unclear. To address this issue, we construct a diffusive vegetation-water model under semi-arid grazing conditions. Our analysis shows that the system admits a unique vegetation equilibrium once the grazing intensity reaches a threshold, and we derive the conditions for the occurrence of both Turing and Hopf bifurcations. By taking the water reduction rate and the water diffusion rate as control parameters, we apply normal form theory to determine the Hopf bifurcation type and employ weakly nonlinear analysis to derive the amplitude equation at the critical wavenumber, thereby identifying the Turing bifurcation type. Numerical simulations further reveal that the Turing and Hopf bifurcations partition the parameter plane into four regions: the vegetation equilibrium stability, pure Turing instability, Turing and Hopf instabilities, and pure Hopf instability. In the supercritical-supercritical case, the system sequentially exhibits a homogeneous steady state, spatial periodic patterns and spatiotemporal periodic solutions. In the subcritical-subcritical case, a bistable region arises where vegetation homogeneous state and spatially periodic state coexist, accompanied by a snaking bifurcation structure that induces localized patterns. Along this snaking bifurcation, a Hopf bifurcation emerges, generating more complex oscillatory localized states. Moreover, under the subcritical-subcritical case, the final state is highly sensitive to initial conditions. Overall, this study not only uncovers rich dynamical behaviors arising from combination of different type of bifurcations, but also provides new theoretical insights into the spatiotemporal evolution and ecological stability of vegetation systems.
The sigmoidal Holling III functional response is particularly suited for generalist predators, which exhibit 'prey-switching' behavior at low prey densities. In this paper, we consider a Leslie-type predator-prey model incorporating generalist predation and Holling III functional response. We first establish the existence of a nilpotent cusp or focus of codimension up to 3, or a weak focus of order at most 3. As parameters vary, the system can undergo a nilpotent cusp or focus bifurcation of codimension 3, or a Hopf bifurcation of codimension 2. Moreover, sufficient conditions for global asymptotic stability of the unique positive equilibrium are derived. Our results demonstrate that the Holling III functional response not only prompts the coexistence of both populations, but also induces richer bifurcation phenomena and dynamics, such as tristability, or three limit cycles. Furthermore, our results highlight the crucial role of generalist predators and their 'prey switching' behavior in regulating intricate dynamics and bifurcation thresholds in ecological systems.