The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro.

During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in vitro.

Engineering tertiary chirality in helical biopolymers.

Tertiary chirality describes the handedness of supramolecular assemblies and relies not only on the primary and secondary structures of the building blocks but also on topological driving forces that have been sparsely characterized. Helical biopolymers, especially DNA, have been extensively investigated as they possess intrinsic chirality that determines the optical, mechanical, and physical properties of the ensuing material. Here, we employ the DNA tensegrity triangle as a model system to locate the tipping points in chirality inversion at the tertiary level by X-ray diffraction. We engineer tensegrity triangle crystals with incremental rotational steps between immobile junctions from 3 to 28 base pairs (bp). We construct a mathematical model that accurately predicts and explains the molecular configurations in both this work and previous studies. Our design framework is extendable to other supramolecular assemblies of helical biopolymers and can be used in the design of chiral nanomaterials, optically active molecules, and mesoporous frameworks, all of which are of interest to physical, biological, and chemical nanoscience.

Deciphering the underlying mechanisms of the pharyngeal pumping motions in Caenorhabditis elegans.

The pharynx of the nematode Caenorhabditis elegans is a neuromuscular organ that exhibits typical pumping motions, which result in the intake of food particles from the environment. In-depth inspection reveals slightly different dynamics at the various pharyngeal areas, rather than synchronous pumping motions of the whole organ, which are important for its effective functioning. While the different pumping dynamics are well characterized, the underlying mechanisms that generate them are not known. In this study, the C. elegans pharynx was modeled in a bottom-up fashion, including all of the underlying biological processes that lead to, and including, its end function, food intake. The mathematical modeling of all processes allowed performing comprehensive, quantitative analyses of the system as a whole. Our analyses provided detailed explanations for the various pumping dynamics generated at the different pharyngeal areas; a fine-resolution description of muscle dynamics, both between and within different pharyngeal areas; a quantitative assessment of the values of many parameters of the system that are unavailable in the literature; and support for a functional role of the marginal cells, which are currently assumed to mainly have a structural role in the pharynx. In addition, our model predicted that in tiny organisms such as C. elegans, the generation of long-lasting action potentials must involve ions other than calcium. Our study exemplifies the power of mathematical models, which allow a more accurate, higher-resolution inspection of the studied system, and an easier and faster execution of in silico experiments than feasible in the lab.

Proteome characterization of liver-kidney comorbidity after microbial sepsis.

Sepsis is a life-threatening condition that occurs when the body responds to an infection but subsequently triggers widespread inflammation and impaired blood flow. These pathologic responses can rapidly cause multiple organ dysfunction or failure either one by one or simultaneously. The fundamental common mechanisms involved in sepsis-induced multiple organ dysfunction remain unclear. Here, employing quantitative global and phosphoproteomics, we examine the liver's temporal proteome and phosphoproteome changes after moderate sepsis induced by cecum ligation and puncture. In total, 4593 global proteins and 1186 phosphoproteins according to 3275 phosphosites were identified. To characterize the liver-kidney comorbidity after sepsis, we developed a mathematical model and performed cross-analyses of liver and kidney proteome data obtained from the same set of mice. Beyond immune response, we showed the commonly disturbed pathways and key regulators of the liver-kidney comorbidity are linked to energy metabolism and consumption. Our data provide open resources to understand the communication between the liver and kidney as they work to fight infection and maintain homeostasis.

The Potential Benefits of Delaying Seasonal Influenza Vaccine Selections for the Northern Hemisphere: A Retrospective Modeling Study in the United States.

BACKGROUND: Antigenic similarity between vaccine viruses and circulating viruses is crucial for achieving high vaccine effectiveness against seasonal influenza. New non-egg-based vaccine production technologies could revise current vaccine formulation schedules. We aim to assess the potential benefit of delaying seasonal influenza vaccine virus selection decisions. METHODS: We identified seasons where season-dominant viruses presented increasing prevalence after vaccine formulation had been decided in February for the Northern Hemisphere, contributing to their antigenic discrepancy with vaccine viruses. Using a SEIR (susceptible-exposed-infectious-recovered) model of seasonal influenza in the United States, we evaluated the impact of updating vaccine decisions with more antigenically similar vaccine viruses on the influenza burden in the United States. RESULTS: In 2014-2015 and 2019-2020, the season-dominant A(H3N2) subclade and B/Victoria clade, respectively, presented increasing prevalence after vaccine decisions were already made for the Northern Hemisphere. Our model showed that the updated A(H3N2) vaccine could have averted 5000-65 000 influenza hospitalizations in the United States in 2014-2015, whereas updating the B/Victoria vaccine component did not substantially change influenza burden in the 2019-2020 season. CONCLUSIONS: With rapid vaccine production, revising current timelines for vaccine selection could result in substantial epidemiological benefits, particularly when additional data could help improve the antigenic match between vaccine and circulating viruses.

Characteristics of the Sexual Networks of Men Who Have Sex With Men in Montréal, Toronto, and Vancouver: Insights from Canada's 2022 Mpox Outbreak.

BACKGROUND: The 2022-2023 global mpox outbreak disproportionately affected gay, bisexual, and other men who have sex with men (GBM). We investigated differences in GBM's sexual partner distributions across Canada's 3 largest cities and over time, and how they shaped transmission. METHODS: The Engage Cohort Study (2017-2023) recruited GBM via respondent-driven sampling in Montréal, Toronto, and Vancouver (n = 2449). We compared reported sexual partner distributions across cities and periods: before COVID-19 (2017-2019), pandemic (2020-2021), and after lifting of restrictions (2021-2023). We used Bayesian regression and poststratification to model partner distributions. We estimated mpox's basic reproduction number (R0) using a risk-stratified compartmental model. RESULTS: Pre-COVID-19 pandemic distributions were comparable: fitted average partners (past 6 months) were 10.4 (95% credible interval: 9.4-11.5) in Montréal, 13.1 (11.3-15.1) in Toronto, and 10.7 (9.5-12.1) in Vancouver. Sexual activity decreased during the pandemic and increased after lifting of restrictions, but remained below prepandemic levels. Based on reported cases, we estimated R0 of 2.4 to 2.7 and similar cumulative incidences (0.7%-0.9%) across cities. CONCLUSIONS: Similar sexual partner distributions may explain comparable R0 and cumulative incidence across cities. With potential for further recovery in sexual activity, mpox vaccination and surveillance strategies should be maintained.

The Fading of the Mpox Outbreak Among Men Who Have Sex With Men: A Mathematical Modelling Study.

BACKGROUND: In the Netherlands, the number of mpox cases started declining before mpox vaccination was initiated. Most cases were men who have sex with men (MSM). We investigated whether the decline in mpox could be attributed to infection-induced immunity or behavioral adaptations. METHODS: We developed a transmission model and accounted for possible behavioral adaptations: fewer casual partners and shorter time until MSM with mpox refrain from sexual contacts. RESULTS: Without behavioral adaptations, the peak in modelled cases matched observations, but the decline was less steep than observed. With behavioral adaptations in the model, we found a decline of 16%-18% in numbers of casual partners in June and 13%-22% in July 2022. Model results showed a halving of the time before refraining from sex. When mpox vaccination started, 57% of MSM with very high sexual activity in the model had been infected. Model scenarios revealed that the outbreak could have waned by November 2022 even without vaccination. CONCLUSIONS: The limited duration of the mpox outbreak in the Netherlands can be ascribed primarily to infection-induced immunity among MSM with high sexual activity levels. The decline was accelerated by behavioral adaptations. Immunity among those most sexually active is essential to impede mpox resurgence.

Renal handling of albumin in rats with early stage diabetes: A theoretical analysis.

In early diabetic nephropathy (DN), recent studies have shown that albuminuria stems mostly from alterations in tubular function rather than from glomerular damage. Several factors in DN, including hyperfiltration, hypertrophy and reduced abundance of the albumin receptors megalin and cubilin, affect albumin endocytosis in the proximal tubule (PT). To assess their respective contribution, we developed a model of albumin handling in the rat PT that couples the transport of albumin to that of water and solutes. Our simulations suggest that, under basal conditions, ∼75% of albumin is retrieved in the S1 segment. The model predicts negligible uptake in S3, as observed experimentally. It also accurately predicts the impact of acute hyperglycaemia on urinary albumin excretion. Simulations reproduce observed increases in albumin excretion in early DN by considering the combined effects of increased glomerular filtration rate (GFR), osmotic diuresis, hypertrophy, and megalin and cubilin downregulation, without stipulating changes in glomerular permselectivity. The results indicate that in isolation, glucose-elicited osmotic diuresis and glucose transporter upregulation raise albumin excretion only slightly. Enlargement of PT diameter not only augments uptake via surface area expansion, but also reduces fluid velocity and thus shear stress-induced stimulation of endocytosis. Overall, our model predicts that downregulation of megalin and cubilin and hyperfiltration both contribute significantly to increasing albumin excretion in rats with early-stage diabetes. The results also suggest that acute sodium-glucose cotransporter 2 inhibition lowers albumin excretion only if GFR decreases sufficiently, and that angiotensin II receptor blockers mitigate urinary albumin loss in early DN in large part by upregulating albumin receptor abundance. KEY POINTS: The urinary excretion of albumin is increased in early diabetic nephropathy (DN). It is difficult to experimentally disentangle the multiple factors that affect the renal handling of albumin in DN. We developed a mathematical model of albumin transport in the rat proximal tubule (PT) to examine the impact of elevated plasma glucose, hyperfiltration, PT hypertrophy and reduced abundance of albumin receptors on albumin uptake and excretion in DN. Our model predicts that glucose-elicited osmotic diuresis per se raises albumin excretion only slightly. Conversely, increases in PT diameter and length favour reduced albumin excretion. Our results suggest that downregulation of the receptors megalin and cubilin in PT cells and hyperfiltration both contribute significantly to increasing albumin excretion in DN. The model helps to better understand the mechanisms underlying urinary loss of albumin in early-stage diabetes, and the impact of specific treatments thereupon.

The evolution of chemodiversity in plants-From verbal to quantitative models.

Plants harbour a great chemodiversity, that is diversity of specialised metabolites (SMs), at different scales. For instance, individuals can produce a large number of SMs, and populations can differ in their metabolite composition. Given the ecological and economic importance of plant chemodiversity, it is important to understand how it arises and is maintained over evolutionary time. For other dimensions of biodiversity, that is species diversity and genetic diversity, quantitative models play an important role in addressing such questions. Here, we provide a synthesis of existing hypotheses and quantitative models, that is mathematical models and computer simulations, for the evolution of plant chemodiversity. We describe each model's ingredients, that is the biological processes that shape chemodiversity, the scales it considers and whether it has been formalized as a quantitative model. Although we identify several quantitative models, not all are dynamic and many influential models have remained verbal. To fill these gaps, we outline our vision for the future of chemodiversity modelling. We identify quantitative models used for genetic variation that may be adapted for chemodiversity, and we present a flexible framework for the creation of individual-based models that address different scales of chemodiversity and combine different ingredients that bring this chemodiversity about.

Public Health Impact of Paxlovid as Treatment for COVID-19, United States.

We evaluated the population-level benefits of expanding treatment with the antiviral drug Paxlovid (nirmatrelvir/ritonavir) in the United States for SARS-CoV-2 Omicron variant infections. Using a multiscale mathematical model, we found that treating 20% of symptomatic case-patients with Paxlovid over a period of 300 days beginning in January 2022 resulted in life and cost savings. In a low-transmission scenario (effective reproduction number of 1.2), this approach could avert 0.28 million (95% CI 0.03-0.59 million) hospitalizations and save US $56.95 billion (95% CI US $2.62-$122.63 billion). In a higher transmission scenario (effective reproduction number of 3), the benefits increase, potentially preventing 0.85 million (95% CI 0.36-1.38 million) hospitalizations and saving US $170.17 billion (95% CI US $60.49-$286.14 billion). Our findings suggest that timely and widespread use of Paxlovid could be an effective and economical approach to mitigate the effects of COVID-19.

Human-mouse comparison of the multistage nature of radiation carcinogenesis in a mathematical model.

Mouse models are vital for assessing risk from environmental carcinogens, including ionizing radiation, yet the interspecies difference in the dose response precludes direct application of experimental evidence to humans. Herein, we take a mathematical approach to delineate the mechanism underlying the human-mouse difference in radiation-related cancer risk. We used a multistage carcinogenesis model assuming a mutational action of radiation to analyze previous data on cancer mortality in the Japanese atomic bomb survivors and in lifespan mouse experiments. Theoretically, the model predicted that exposure will chronologically shift the age-related increase in cancer risk forward by a period corresponding to the time in which the spontaneous mutational process generates the same mutational burden as that the exposure generates. This model appropriately fitted both human and mouse data and suggested a linear dose response for the time shift. The effect per dose decreased with increasing age at exposure similarly between humans and mice on a per-lifespan basis (0.72- and 0.71-fold, respectively, for every tenth lifetime). The time shift per dose was larger by two orders of magnitude in humans (7.8 and 0.046 years per Gy for humans and mice, respectively, when exposed at ~35% of their lifetime). The difference was mostly explained by the two orders of magnitude difference in spontaneous somatic mutation rates between the species plus the species-independent radiation-induced mutation rate. Thus, the findings delineate the mechanism underlying the interspecies difference in radiation-associated cancer mortality and may lead to the use of experimental evidence for risk prediction in humans.

Guidelines for mechanistic modeling and analysis in cardiovascular research.

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Modeling cerebrovascular responses to assess the impact of the collateral circulation following middle cerebral artery occlusion.

OBJECTIVE: An improved understanding of the role of the leptomeningeal collateral circulation in blood flow compensation following middle cerebral artery (MCA) occlusion can contribute to more effective treatment development for ischemic stroke. The present study introduces a model of the cerebral circulation to predict cerebral blood flow and tissue oxygenation following MCA occlusion. METHODS: The model incorporates flow regulation mechanisms based on changes in pressure, shear stress, and metabolic demand. Oxygen saturation in cerebral vessels and tissue is calculated using a Krogh cylinder model. The model is used to assess the effects of changes in oxygen demand and arterial pressure on cerebral blood flow and oxygenation after MCA occlusion. RESULTS: An increase from five to 11 leptomeningeal collateral vessels was shown to increase the oxygen saturation in the region distal to the occlusion by nearly 100%. Post-occlusion, the model also predicted a loss of autoregulation and a decrease in flow to the ischemic territory as oxygen demand was increased; these results were consistent with data from experiments that induced cerebral ischemia. CONCLUSIONS: This study highlights the importance of leptomeningeal collaterals following MCA occlusion and reinforces the idea that lower oxygen demand and higher arterial pressure improve conditions of flow and oxygenation.

COVID-19 inequalities in England: a mathematical modelling study of transmission risk and clinical vulnerability by socioeconomic status.

BACKGROUND: The COVID-19 pandemic resulted in major inequalities in infection and disease burden between areas of varying socioeconomic deprivation in many countries, including England. Areas of higher deprivation tend to have a different population structure-generally younger-which can increase viral transmission due to higher contact rates in school-going children and working-age adults. Higher deprivation is also associated with a higher presence of chronic comorbidities, which were convincingly demonstrated to be risk factors for severe COVID-19 disease. These two major factors need to be combined to better understand and quantify their relative importance in the observed COVID-19 inequalities. METHODS: We used UK Census data on health status and demography stratified by decile of the Index of Multiple Deprivation (IMD), which is a measure of socioeconomic deprivation. We calculated epidemiological impact using an age-stratified COVID-19 transmission model, which incorporated different contact patterns and clinical health profiles by decile. To separate the contribution of each factor, we considered a scenario where the clinical health profile of all deciles was at the level of the least deprived. We also considered the effectiveness of school closures and vaccination of over 65-year-olds in each decile. RESULTS: In the modelled epidemics in urban areas, the most deprived decile experienced 9% more infections, 13% more clinical cases, and a 97% larger peak clinical size than the least deprived; we found similar inequalities in rural areas. Twenty-one per cent of clinical cases and 16% of deaths in England observed under the model assumptions would not occur if all deciles experienced the clinical health profile of the least deprived decile. We found that more deaths were prevented in more affluent areas during school closures and vaccination rollouts. CONCLUSIONS: This study demonstrates that both clinical and demographic factors synergise to generate health inequalities in COVID-19, that improving the clinical health profile of populations would increase health equity, and that some interventions can increase health inequalities.

A modeling analysis of whole body potassium regulation on a high-potassium diet: proximal tubule and tubuloglomerular feedback effects.

Potassium (K+) is an essential electrolyte that plays a key role in many physiological processes, including mineralcorticoid action, systemic blood-pressure regulation, and hormone secretion and action. Indeed, maintaining K+ balance is critical for normal cell function, as too high or too low K+ levels can have serious and potentially deadly health consequences. K+ homeostasis is achieved by an intricate balance between the intracellular and extracellular fluid as well as balance between K+ intake and excretion. This is achieved via the coordinated actions of regulatory mechanisms such as the gastrointestinal feedforward effect, insulin and aldosterone upregulation of Na+-K+-ATPase uptake, and hormone and electrolyte impacts on renal K+ handling. We recently developed a mathematical model of whole body K+ regulation to unravel the individual impacts of these regulatory mechanisms. In this study, we extend our mathematical model to incorporate recent experimental findings that showed decreased fractional proximal tubule reabsorption under a high-K+ diet. We conducted model simulations and sensitivity analyses to investigate how these renal alterations impact whole body K+ regulation. Model predictions quantify the sensitivity of K+ regulation to various levels of proximal tubule K+ reabsorption adaptation and tubuloglomerular feedback. Our results suggest that the reduced proximal tubule K+ reabsorption under a high-K+ diet could achieve K+ balance in isolation, but the resulting tubuloglomerular feedback reduces filtration rate and thus K+ excretion.NEW & NOTEWORTHY Potassium homeostasis is maintained in the body by a complex system of regulatory mechanisms. This system, when healthy, maintains a small extracellular potassium concentration, despite large fluctuations of dietary potassium. The complexities of the system make this problem well suited for investigation with mathematical modeling. In this study, we extend our mathematical model to consider recent experimental results on renal potassium handling on a high potassium diet and investigate the impacts from a whole body perspective.

Mathematical model of rabies vaccination in the United States.

Rabies is one of the oldest viral diseases and it has been present on every continent except Antarctica. Within the U.S. human rabies cases are quite rare. In the eastern USA, raccoons are the main reservoir hosts and pet vaccination serves as an important barrier against human rabies exposure. In this paper, we develop a compartmental model for rabies transmission amongst raccoons and domestic pets. We find the disease-free equilibria, reproduction numbers for the raccoons and domestic pets. We also determine the vaccination coverage/rates, both for raccoons and pets, needed to achieve the elimination of rabies.

Spatially-dependent model for rods and cones in the retina.

We develop a mathematical model for photoreceptors in the retina. We focus on rod and cone outer segment dynamics and interactions with a nutrient source associated with the retinal pigment epithelium cells. Rod and cone densities (number per unit area of retinal surface) are known to have significant spatial dependence in the retina with cones located primarily near the fovea and the rods located primarily away from the fovea. Our model accounts for this spatial dependence of the rod and cone photoreceptor density as well as for the possibility of nutrient diffusion. We present equilibrium and dynamic solutions, discuss their relation to existing models, and estimate model parameters through comparisons with available experimental measurements of both spatial and temporal photoreceptor characteristics. Our model compares well with existing data on spatially-dependent regrowth of photoreceptor outer segments in the macular region of Rhesus Monkeys. Our predictions are also consistent with existing data on the spatial dependence of photoreceptor outer segment length near the fovea in healthy human subjects. We focus primarily on the healthy eye but our model could be the basis for future efforts designed to explore various retinal pathologies, eye-related injuries, and treatments of these conditions.

Kill rates by immune cells: Ratio-dependent, or mass action?

We describe a cell-based fixed-lattice model to simulate immune cell and tumor cell interaction involving MHC recognition, and FasL vs perforin lysis. We are motivated by open questions about the mechanisms behind observed kill rates of tumor cells by different types of effector cells. These mechanisms play a big role in the effectiveness of many cancer immunotherapies. The model is a stochastic cellular automaton on a hexagonal grid.

Flow modeling and structural characterization in fungal pellets.

Fungal pellets are hierarchical systems that can be found in an ample variety of applications. Modeling transport phenomena in this type of systems is a challenging but necessary task to provide knowledge-based processes that improve the outcome of their biotechnological applications. In this work, an upscaled model for total mass and momentum transport in fungal pellets is implemented and analyzed, using elements of the volume averaging and adjoint homogenization methods departing from the governing equations at the microscale in the intracellular and extracellular phases. The biomass is assumed to be composed of a non-Newtonian fluid and the organelles impervious to momentum transport are modeled as a rigid solid phase. The upscaled equations contain effective-medium coefficients, which are predicted from the solution of adjoint closure problems in a three-dimensional periodic domains representative of the microstructure. The construction of these domains was performed for Laccaria trichodermophora based on observations of actual biological structures. The upscaled model was validated with direct numerical simulations in homogeneous portions of the pellets core. It is shown that no significant differences are observed when the dolipores are open or closed to fluid flow. By comparing the predictions of the average velocity in the extracellular phase resulting from the upscaled model with those from the classical Darcy equation (i.e., assuming that the biomass is a solid phase) the contribution of the intracellular fluid phase was evidenced. This work sets the foundations for further studies dedicated to transport phenomena in this type of systems.

A stochastic model for topographically influenced cell migration.

Migrating cells traverse a range of topographic configurations presented by the native extracellular environment to conduct their physiologic functions. It is well documented cells can modulate their behaviour in response to different topographic features, finding promising applications in biomaterial and bioimplant design. It is useful, in these areas of research, to be able to predict which topographic arrangements could be used to promote certain patterns of migration prior to laboratory experimentation. Despite a profusion of study and interest shown in these fields by experimentalists, the related modelling literature is as yet relatively sparse and tend to focus more on either cell-matrix interaction or morphological responses of cells. We propose a mathematical model for individual cell migration based on an Ornstein-Uhlenbeck process, and set out to see if the model can be used to predict migration patterns on 2-d isotropic and anisotropic topographies, whose characteristics can be broadly described as either uniform flat, uniform linear with variable ridge density or non-uniform disordered with variable feature density. Results suggest the model is capable of producing realistic patterns of migration for flat and linear topographic patterns, with calibrated output closely approximating NIH3T3 fibroblast migration behaviour derived from an experimental dataset, in which migration linearity increased with ridge density and average speed was highest at intermediate ridge densities. Exploratory results for non-uniform disordered topographies suggest cell migration patterns may adopt disorderedness present in the topography and that 'distortion' introduced to linear topographic patterns may not impede linear guidance of migration, given its magnitude is bounded within certain limits. We conclude that an Ornstein-Uhlenbeck based model for topographically influenced migration may be useful to predict patterns of migration behaviour for certain isotropic (flat) and anisotropic (linear) topographies in the NIH3T3 fibroblast cell line, but additional investigation is required to predict with confidence migration patterns for non-uniform disordered topographic arrangements.