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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Leveraging public AI tools to explore systems biology resources in mathematical modeling

Predictive mathematical modeling is an essential part of systems biology and is interconnected with information management. Systems biology information is often stored in specialized formats to facilitate data storage and analysis. These formats are not designed for easy human readability and thus require specialized software to visualize and interpret results. Therefore, comprehending modeling and underlying networks and pathways is contingent on mastering systems biology tools, which is particularly challenging for users with no or little background in data science or system biology. To address this challenge, we investigated the usage of public Artificial Intelligence (AI) tools in exploring systems biology resources in mathematical modeling. We tested public AI’s understanding of mathematics in models, related systems biology data, and the complexity of model structures. Our approach can enhance the accessibility of systems biology for non-system biologists and help them understand systems biology without a deep learning curve.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model

The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model’s parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

A Mathematical Model of the Dynamics of Cytokine Expression and Human Immune Cell Activation in Response to the Pathogen Staphylococcus aureus

Cell-based mathematical models have previously been developed to simulate the immune system in response to pathogens. Mathematical modeling papers which study the human immune response to pathogens have predicted concentrations of a variety of cells, including activated and resting macrophages, plasma cells, and antibodies. This study aims to create a comprehensive mathematical model that can predict cytokine levels in response to a gram-positive bacterium, S. aureus by coupling previous models. To accomplish this, the cytokines Tumor Necrosis Factor Alpha (TNF-α), Interleukin 6 (IL-6), Interleukin 8 (IL-8), and Interleukin 10 (IL-10) are included to quantify the relationship between cytokine release from macrophages and the concentration of the pathogen, S. aureus, ex vivo. Partial differential equations (PDEs) are used to model cellular response and ordinary differential equations (ODEs) are used to model cytokine response, and interactions between both components produce a more robust and more complete systems-level understanding of immune activation. In the coupled cellular and cytokine model outlined in this paper, a low concentration of S. aureus is used to stimulate the measured cellular response and cytokine expression. Results show that our cellular activation and cytokine expression model characterizing septic conditions can predict ex vivo mechanisms in response to gram-negative and gram-positive bacteria. Our simulations provide new insights into how the human immune system responds to infections from different pathogens. Novel applications of these insights help in the development of more powerful tools and protocols in infection biology.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Bioelectrochemical reactor to manage anthropogenic sulfate pollution for freshwater ecosystems: Mathematical modeling and experimental validation

Anthropogenic sulfate loading into otherwise low-sulfate freshwater systems can cause significant ecological consequences as a biogeochemical stressor. To address this challenge, in situ bioremediation technologies have been developed to leverage naturally occurring microorganisms that transform sulfate into sulfide rather than implementing resource-intensive physio-chemical processes. However, bioremediation technologies often require the supply of electron donors to facilitate biological sulfate reduction. Bioelectrochemical systems (BES) can be an alternative approach for supplying molecular hydrogen as an electron donor for sulfate-reducing bacteria through water electrolysis. Although the fundamental mechanisms behind BESs have been studied, limited research has evaluated the design and operational parameters of treatment systems when developing BESs on a scale relevant to environmental systems. Further, this study aimed to develop an application-based mathematical model to evaluate the performance of BESs across a range of reactor configurations and operational modes. The model was based on sulfate transformation by hydrogenotrophic sulfate-reducing bacteria coupled with the recovery of solid iron sulfide species formed by the oxidative dissolution of dissolved ferrous iron from a stainless steel anode. Sulfate removal closely corresponded to the rate of electrolytic hydrogen production and hydraulic residence time but was less sensitive to specific microbial rate constants. The mathematical model results were compared to experimental data from a pilot-scale BES tested with nonacidic mine drainage as a case study. The close agreement between the mathematical model and the pilot-scale BES experiment highlights the efficacy of using a mathematical model as a tool to develop a conceptual design of a scaled-up treatment system.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Mechanistic within-host mathematical model of inhalational anthrax

We present a mathematical model of the dynamics of Bacillus anthracis bacteria within the lymph nodes and blood of a host, following inhalation of an initial dose of spores. We also incorporate the dynamics of protective antigen, which is the binding component of the anthrax toxin produced by the bacteria. The model offers a mechanistic description of the early infection dynamics of inhalational anthrax, while its stochastic nature allows us to study the probabilities of different outcomes (for example, how likely it is that the infection will be cleared for a given inhaled dose of spores) in order to explain dose-response data for inhalational anthrax. The model is calibrated via a Bayesian approach, using in vivo data from New Zealand white rabbit and guinea pig infection studies, enabling within-host parameters to be estimated. We also leverage incubation-period data from the Sverdlovsk 1979 anthrax outbreak to show that the model can accurately describe human time-to-symptoms data under reasonable parameter regimes. Finally, we derive a simple approximate formula for the probability of symptom onset before time t, assuming that the number of inhaled spores has a Poisson distribution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Development and validation of a mathematical model of heart rate response to fluid perturbation

Physiological closed-loop controlled (PCLC) medical devices monitor and automatically adjust the patient’s condition by using physiological variables as feedback, ideally with minimal human intervention to achieve the target levels set by a clinician. PCLC devices present a challenge when it comes to evaluating their performance, where conducting large clinical trials can be expensive. Virtual physiological patients simulated by validated mathematical models can be utilized to obtain preclinical evidence of safety and assess the performance of the PCLC medical device during normal and worst-case conditions that are unlikely to happen in a limited clinical trial. A physiological variable that plays a major role during fluid resuscitation is heart rate (HR). For in silico assessment of PCLC medical devices regarding fluid perturbation, there is currently no mathematical model of HR validated in terms of its predictive capability performance. This paper develops and validates a mathematical model of HR response using data collected from sheep subjects undergoing hemorrhage and fluid infusion. The model proved to be accurate in estimating the HR response to fluid perturbation, where averaged between 21 calibration datasets, the fitting performance showed a normalized root mean square error (NRMSE) of 7.41 ± 2.8%. The model was also evaluated in terms of model predictive capability performance via a leave-one-out procedure (21 subjects) and an independent validation dataset (6 subjects). Two different virtual cohort generation tools were used in each validation analysis. The generated envelope of virtual subjects robustly met the defined acceptance criteria, in which 95% of the testing datasets presented simulated HR patterns that were within a deviation of 50% from the observed data. In addition, out of 16000 and 18522 simulated subjects for the leave one-out and independent datasets, the model was able to generate at least one virtual subject that was close to the real subject within an error margin of 9.56 ± 3.15% and 11.1 ± 1.22% NRMSE, respectively. In conclusion, the model can generate valid virtual HR physiological responses to fluid perturbation and be incorporated into future non-clinical simulated testing setups for assessing PCLC devices intended for fluid resuscitation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Insights into pathological mechanisms and interventions revealed by analyzing a mathematical model for cone metabolism

This work analyzes a mathematical model for the metabolic dynamics of a cone photoreceptor, which is the first model to account for energy generation from fatty acids oxidation of shed photoreceptor outer segments (POS). Multiple parameter bifurcation analysis shows that joint variations in external glucose, the efficiency of glucose transporter 1 (GLUT1), lipid utilization for POS renewal, and oxidation of fatty acids affect the cone’s metabolic vitality and its capability to adapt under glucose-deficient conditions. The analysis further reveals that when glucose is scarce, cone viability cannot be sustained by only fueling energy production in the mitochondria, but it also requires supporting anabolic processes to create lipids necessary for cell maintenance and repair. In silico experiments are used to investigate how the duration of glucose deprivation impacts the cell without and with a potential GLUT1 or oxidation of fatty acids intervention as well as a dual intervention. The results show that for prolonged duration of glucose deprivation, the cone metabolic system does not recover with higher oxidation of fatty acids and requires greater effectiveness of GLUT1 to recover. Finally, time-varying global sensitivity analysis (GSA) is applied to assess the sensitivity of the model outputs of interest to changes and uncertainty in the parameters at specific times. The results reveal a critical temporal window where there would be more flexibility for interventions to rescue a cone cell from the detrimental consequences of glucose shortage.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Mathematical Modeling of the Potential and Time Dependence of Ir Dissolution from Hydrous Ir Oxide Oxygen Evolution Catalysts

One of the main degradation mechanisms of hydrous iridium oxide acidic oxygen evolution reaction (OER) catalysts is dissolution and loss into the acidic membrane. While degradation models have been proposed, there is a gap in understanding the potential and time dependence of the iridium dissolution reaction and its mechanistic underpinnings. In this work, Ir dissolution rates measured as a function of time and potential via time-resolved inductively-coupled plasma mass spectrometry (ICP-MS) in aqueous acidic electrolyte are used to establish a mathematical model for Ir dissolution. The mathematical model is generated using proposed formation and dissolution reactions for Ir species. Through comparison with the ICP-MS data and existing information on the potential-dependent Ir phase, we find that the potential and time-dependence of dissolution can be modeled as dissolution of an oxide phase, here represented as IrO 2 , with potential dependent kinetics and formation of a passivating species, a process with a rate-limiting step that is not potential dependent. This understanding of the potential dependence of dissolution and passivation kinetics using aqueous electrolyte half-cell measurements can be used to predict the degradation of Ir oxide in operating energy conversion devices relying on the OER, such as proton-exchange membrane water electrolyzers.

Kariuki, Nancy N. [Argonne National Laboratory (AN↗
DOE OSTI2022

Characteristics and mathematical modeling of apple slice drying in an electrohydrodynamic system with a needle‐plate electrode

Abstract The drying of apple slices in an electrohydrodynamic (EHD) system with a needle‐plate electrode was characterized and mathematically modeled at voltages of 30, 40, and 50 kV and with distances between needles of 5, 6, and 7 cm. The results showed that the drying rate, effective water diffusion coefficient, and rehydration ratio of the apple slices, and specific energy consumption of drying, all increased with increasing voltage. Initially, there was a period when the drying rate was approximately constant in the low‐voltage EHD, but not in the high voltage conditions. At the same voltage, the drying rate was highest when the distance between needles was 6 cm. The voltage and distance between needles had a significant ( p < .05) interactive effect on the effective water diffusion coefficient and specific energy consumption, but not on the rehydration ratio. General mathematical models for drying can be used to represent the drying behavior of apple slices. The Midilli and Kucuk model and the Logarithmic model had the best fits, with correlation coefficients of 0.998803 and 0.998267, respectively. Predictive functions for the moisture ratio of apple slices based on voltage and distance between needles were established and verified. The results indicated that the Logarithmic model could more accurately predict the moisture ratio of apple slices dried using the EHD method. Practical Applications As a new drying technology, electrohydrodynamic (EHD) drying has unequaled advantages. According to the results, using the appropriate voltage and distance between needles improves not only drying efficiency, but also the rehydration ratio of apple slices, which reflects the quality of dried products. The Logarithmic model can accurately predict the EHD drying behavior of apple slices, which is of great significance in optimizing actual production.

Li, Bowen↗
DOE OSTI2024

Machine learning mathematical models for incidence estimation during pandemics

Accurate estimates of the incidence of infectious diseases are key for the control of epidemics. However, healthcare systems are often unable to test the population exhaustively, especially when asymptomatic and paucisymptomatic cases are widespread; this leads to significant and systematic under-reporting of the real incidence. Here, we propose a machine learning approach to estimate the incidence of a pandemic in real-time, using reported cases and the overall test rate. In particular, we use Bayesian symbolic regression to automatically learn the closed-form mathematical models that most parsimoniously describe incidence. We develop and validate our models using COVID-19 incidence values for nine different countries, confirming their ability to accurately predict daily incidence. Remarkably, despite the differences in epidemic trajectories and dynamics across countries, we find that a single model for all countries offers a more parsimonious description and is more predictive of actual incidence compared to separate models for each country. Our results show the potential to accurately model incidence in real-time using closed-form mathematical models, providing a valuable tool for public health decision-makers.

Fajardo-Fontiveros, Oscar (ORCID:0000000207058972)↗
DOE OSTI2021

Qualitative properties of mathematical model for data flow

In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established. Qualitative properties of these solutions are investigated, both theoretically and numerically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Patient-Specific Mathematical Model of the Clear Cell Renal Cell Carcinoma Microenvironment

The interactions between cells and molecules in the tumor microenvironment can give insight into the initiation and progression of tumors and their optimal treatment options. In this paper, we developed an ordinary differential equation (ODE) mathematical model of the interaction network of key players in the clear cell renal cell carcinoma (ccRCC) microenvironment. We then performed a global gradient-based sensitivity analysis to investigate the effects of the most sensitive parameters of the model on the number of cancer cells. The results indicate that parameters related to IL-6 have high a impact on cancer cell growth, such that decreasing the level of IL-6 can remarkably slow the tumor’s growth.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

A Mathematical Model of Breast Tumor Progression Based on Immune Infiltration

Breast cancer is the most prominent type of cancer among women. Understanding the microenvironment of breast cancer and the interactions between cells and cytokines will lead to better treatment approaches for patients. In this study, we developed a data-driven mathematical model to investigate the dynamics of key cells and cytokines involved in breast cancer development. We used gene expression profiles of tumors to estimate the relative abundance of each immune cell and group patients based on their immune patterns. Dynamical results show the complex interplay between cells and molecules, and sensitivity analysis emphasizes the direct effects of macrophages and adipocytes on cancer cell growth. In addition, we observed the dual effect of IFN-γ on cancer proliferation, either through direct inhibition of cancer cells or by increasing the cytotoxicity of CD8+ T-cells.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

On Soft Mathematical Models of Subjective Time Acceleration with Age

It is a commonplace perception that speed of time subjectively experienced by humans significantly differs from chronological (objective) time and shows a great deal of variability. An often cited example is the phenomenon of the time acceleration with age - subjectively, the time passes faster as we get older. While the exact mechanisms behind it are not yet fully established, here we consider three 'soft' (conceptual) mathematical models that might be applicable to the speeding time phenomenon: two proportionality theories widely discussed in the past and the original model that takes into account the novelty of experience effect. Furthermore, the latter is found the most plausible, as not only it satisfactorily describes the decadal subjective time acceleration, but also offers a reasonable explanation of the human life experience accumulation with age.

acceleration↗
DOE OSTI2023

Ionization detail parameters and cluster dose: a mathematical model for selection of nanodosimetric quantities for use in treatment planning in charged particle radiotherapy

Abstract Objective . To propose a mathematical model for applying ionization detail (ID), the detailed spatial distribution of ionization along a particle track, to proton and ion beam radiotherapy treatment planning (RTP). Approach . Our model provides for selection of preferred ID parameters ( I p ) for RTP, that associate closest to biological effects. Cluster dose is proposed to bridge the large gap between nanoscopic I p and macroscopic RTP. Selection of I p is demonstrated using published cell survival measurements for protons through argon, comparing results for nineteen I p : N k , k = 2, 3, …, 10, the number of ionizations in clusters of k or more per particle, and F k , k = 1, 2, …, 10, the number of clusters of k or more per particle. We then describe application of the model to ID-based RTP and propose a path to clinical translation. Main results . The preferred I p were N 4 and F 5 for aerobic cells, N 5 and F 7 for hypoxic cells. Significant differences were found in cell survival for beams having the same LET or the preferred N k . Conversely, there was no significant difference for F 5 for aerobic cells and F 7 for hypoxic cells, regardless of ion beam atomic number or energy. Further, cells irradiated with the same cluster dose for these I p had the same cell survival. Based on these preliminary results and other compelling results in nanodosimetry, it is reasonable to assert that I p exist that are more closely associated with biological effects than current LET-based approaches and microdosimetric RBE-based models used in particle RTP. However, more biological variables such as cell line and cycle phase, as well as ion beam pulse structure and rate still need investigation. Significance . Our model provides a practical means to select preferred I p from radiobiological data, and to convert I p to the macroscopic cluster dose for particle RTP.

Engineering↗
DOE OSTI2025

A consensus mathematical model of vaccine-induced antibody dynamics for multiple vaccine platforms and pathogens

Introduction: Vaccine platforms used in successful, licensed vaccines have varied among pathogens. However, antibody level is still the main clinical correlate of protection in most approved vaccines. Decisions as to the best vaccine platform to pursue for a given pathogen may be informed through improved understanding of the process of antibody generation and its temporal dynamics, as well as the relationship between these processes and the type of vaccine. Methods: We have analyzed the dynamics of antibody generation for different vaccine platforms against diverse pathogens, and developed a consensus mathematical model that captures antibody dynamics across these diverse systems. Initially, the model was fitted to a rich dataset of antibody and immune cell concentrations in a SARS-CoV-2 vaccine experiment. We then used concepts from machine learning, such as transfer learning, to apply the same model to a variety of systems, involving different pathogens, vaccine platforms, and booster dose use/timing, fixing most parameter values relating to the dynamics of the immune system. Results: The model includes B cell proliferation and differentiation, as well as the generation of plasma cells, which secrete large amounts of antibody, and memory B cells. Overall, the model describes antibody generation in all systems tested well and shows that the main differences across platforms are related to the dynamics of antigen presentation. Discussion: This model can be used to predict antibody generation in pairs of vaccine platform/pathogen, allowing for the use of in silico results to narrow down experimental burden in vaccine development.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Targeted Quantification of Protein Phosphorylation and Its Contributions towards Mathematical Modeling of Signaling Pathways

Post-translational modifications (PTMs) are key regulatory mechanisms that can control protein function. Of these, phosphorylation is the most common and widely studied. Because of its importance in regulating cell signaling, precise and accurate measurements of protein phosphorylation across wide dynamic ranges are crucial to understanding how signaling pathways function. Although immunological assays are commonly used to detect phosphoproteins, their lack of sensitivity, specificity, and selectivity often make them unreliable for quantitative measurements of complex biological samples. Recent advances in Mass Spectrometry (MS)-based targeted proteomics have made it a more useful approach than immunoassays for studying the dynamics of protein phosphorylation. Selected reaction monitoring (SRM)—also known as multiple reaction monitoring (MRM)—and parallel reaction monitoring (PRM) can quantify relative and absolute abundances of protein phosphorylation in multiplexed fashions targeting specific pathways. In addition, the refinement of these tools by enrichment and fractionation strategies has improved measurement of phosphorylation of low-abundance proteins. The quantitative data generated are particularly useful for building and parameterizing mathematical models of complex phospho-signaling pathways. Potentially, these models can provide a framework for linking analytical measurements of clinical samples to better diagnosis and treatment of disease.

mathematical modeling↗
DOE OSTI2022

Estimating the population level impact of a gonococcal vaccine candidate: Predictions from a simple mathematical model

Neisseria gonorrhoeae cross-protection was suggested in a New Zealand meningitis B vaccine. We modeled the potential impact of similar vaccines on gonorrhea prevalence in heterosexuals in the United States. Here, our mathematical model incorporated infection, behavior, and vaccination dynamics. Approximate Bayesian Computation calibrated our model to US prevalence. Primary analyses assumed New Zealand vaccine characteristics: 30% efficacy and 2-year duration of protection. We estimated impact under two vaccine coverages (20%, 50%). Reduction in gonorrhea prevalence ranged from 4.8 to 39.4%, depending on vaccine coverage. Vaccine impact was correlated with both size of the highly sexually active subpopulation and sexual mixing between high and low activity subpopulations. A meningitis vaccine providing low efficacy cross-protection against gonorrhea acquisition and short duration of protection could result in a large reduction in gonorrhea prevalence in the United States. Potential dual protective effects can be considered when making vaccine recommendations.

60 APPLIED LIFE SCIENCES↗