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.
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.
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.
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.
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.
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.
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.
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.
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.
Traditional mathematical models of tumor-immune dynamics employ integer-order ordinary differential equations that assume Markovian behavior, wherein the system's instantaneous rate of change depends only on its current state. However, biological processes such as T cell exhaustion and myeloid-derived suppressor cell (MDSC) accumulation exhibit memory effects, where past immunosuppressive exposures create persistent functional states through epigenetic modifications and microenvironmental feedback loops. We develop a fractional-order differential equation framework to quantify these non-Markovian dynamics in human colorectal cancer. By replacing integer-order derivatives with Caputo fractional derivatives of order α ∈ (0, 1] for T cell and MDSC compartments, we incorporate power-law memory kernels that capture temporal persistence of immunosuppressive states. Analyzing gene expression data from 498 patients in The Cancer Genome Atlas, we estimate patient-specific fractional orders from immune signatures and demonstrate substantial inter-patient heterogeneity. Lower fractional orders correlate strongly with T cell exhaustion markers and enable stratification into biologically distinct patient subgroups. Compared to standard integer-order models, the fractional framework achieves threefold higher variance explained in immune signatures. These findings establish fractional calculus as a powerful tool for modeling immune memory in colorectal cancer and suggest potential applications in precision immunotherapy.
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.
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.
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.
A model of an epidemic is investigated with the following population structure: (1) the chronological age of the susceptible population, (2) the chronological age of the infected population, and (3) the infection age of the infected population. The model consists of a system of partial differential equations describing the development of the epidemic in time for these populations. A basic reproduction rate R0(t) for the epidemic is formulated and examples of R0(t) are analyzed and illustrated graphically.
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.
Multiple single-cell and spatial genomics tools have transformed our ability to deconvolve intricate diseases, including cancer. Analysis of complex, multimodal data has provided insights into genomics, cellular states and interactions in tumor ecosystems, enabling the dissection of salient biology and expanding our understanding of drug response, resistance and target discovery. However, several challenges remain before these methods can achieve their full clinical potential. Here, we discuss opportunities, barriers and potential solutions, including sample acquisition and preservation approaches, profiling methods and analytical tools for heterogeneous populations, and we provide recommendations for robust, reproducible use of these technologies in clinical settings.
The risk of pathogen spillover from a natural reservoir to a host population, or from an infectious host population to an environmental reservoir is a major concern in the emergence and re-emergence of infectious diseases. Understanding the source of the pathogen and the environmental conditions driving the emergence or re-emergence are vital to prevention and control. We investigate pathogen spillover in a well-known infectious disease, cholera, where the environment harboring the bacterial pathogen is the natural reservoir. Applying a stochastic seasonal cholera model and methods from continuous-time Markov chains and branching process approximations, the probabilities of spillover and disease emergence are computed. In addition, we propose a new estimate for the risk of disease emergence given there is a spillover. Branching process methods provide new insights about seasonal spillover and disease emergence during the early stages of infection.
Conservation corridors connect natural areas, aiming to mitigate the effects of land transformation. However, their influence on biodiversity, particularly species turnover, remains poorly understood. This study evaluates the impact of conservation corridors on riverine ecosystems and their associated dragonfly assemblages. We assessed species richness and applied the zeta diversity framework to evaluate species turnover across multiple sites, thereby providing insights into how these corridors influence dragonfly community composition relative to natural areas. The research was conducted in the KwaZulu-Natal Midlands of South Africa, covering 104 freshwater sites within natural grasslands and timber plantation corridors. At each site, a 100 m transect adjacent to a river was sampled twice, focusing on recording adult male dragonflies and six environmental variables. Drivers of species richness were analysed using generalised additive models and generalised linear models. Multi-site generalised dissimilarity models were run to examine changes in zeta diversity along environmental gradients and to partition the contributions of different factors to compositional turnover. A total of 37 species were recorded, with one species exclusive to natural areas and four unique to corridors. Dragonfly assemblages were influenced more by stochastic processes than by environmental gradients. Although factors such as site distance, differences in water temperature, dissolved oxygen, shade and rock cover affected turnover, they explained little variation in both rare and common species. Species richness was higher in corridors and consistently declined with increasing shade cover. Neither the presence of corridors nor invasive alien vegetation influenced species turnover, indicating that corridors function similarly to natural habitats. This study demonstrates the crucial role of conservation corridors in preserving dragonfly diversity in altered landscapes. Our findings support continued investment in corridor implementation and management for biodiversity conservation and demonstrate the utility of the zeta diversity framework for understanding species turnover dynamics.