A strategy combining denoising and cryo-EM single particle analysis.

In cryogenic electron microscopy (cryo-EM) single particle analysis (SPA), high-resolution three-dimensional structures of biological macromolecules are determined by iteratively aligning and averaging a large number of two-dimensional projections of molecules. Since the correlation measures are sensitive to the signal-to-noise ratio, various parameter estimation steps in SPA will be disturbed by the high-intensity noise in cryo-EM. However, denoising algorithms tend to damage high frequencies and suppress mid- and high-frequency contrast of micrographs, which exactly the precise parameter estimation relies on, therefore, limiting their application in SPA. In this study, we suggest combining a cryo-EM image processing pipeline with denoising and maximizing the signal's contribution in various parameter estimation steps. To solve the inherent flaws of denoising algorithms, we design an algorithm named MScale to correct the amplitude distortion caused by denoising and propose a new orientation determination strategy to compensate for the high-frequency loss. In the experiments on several real datasets, the denoised particles are successfully applied in the class assignment estimation and orientation determination tasks, ultimately enhancing the quality of biomacromolecule reconstruction. The case study on classification indicates that our strategy not only improves the resolution of difficult classes (up to 5 Å) but also resolves an additional class. In the case study on orientation determination, our strategy improves the resolution of the final reconstructed density map by 0.34 Å compared with conventional strategy. The code is available at https://github.com/zhanghui186/Mscale.

Comparing methods for statistical inference with model uncertainty.

Probability models are used for many statistical tasks, notably parameter estimation, interval estimation, inference about model parameters, point prediction, and interval prediction. Thus, choosing a statistical model and accounting for uncertainty about this choice are important parts of the scientific process. Here we focus on one such choice, that of variables to include in a linear regression model. Many methods have been proposed, including Bayesian and penalized likelihood methods, and it is unclear which one to use. We compared 21 of the most popular methods by carrying out an extensive set of simulation studies based closely on real datasets that span a range of situations encountered in practical data analysis. Three adaptive Bayesian model averaging (BMA) methods performed best across all statistical tasks. These used adaptive versions of Zellner's g-prior for the parameters, where the prior variance parameter g is a function of sample size or is estimated from the data. We found that for BMA methods implemented with Markov chain Monte Carlo, 10,000 iterations were enough. Computationally, we found two of the three best methods (BMA with g=√n and empirical Bayes-local) to be competitive with the least absolute shrinkage and selection operator (LASSO), which is often preferred as a variable selection technique because of its computational efficiency. BMA performed better than Bayesian model selection (in which just one model is selected).

Phase plane dynamics of ERK phosphorylation.

The extracellular signal-regulated kinase (ERK) controls multiple critical processes in the cell and is deregulated in human cancers, congenital abnormalities, immune diseases, and neurodevelopmental syndromes. Catalytic activity of ERK requires dual phosphorylation by an upstream kinase, in a mechanism that can be described by two sequential Michaelis-Menten steps. The estimation of individual reaction rate constants from kinetic data in the full mechanism has proved challenging. Here, we present an analytically tractable approach to parameter estimation that is based on the phase plane representation of ERK activation and yields two combinations of six reaction rate constants in the detailed mechanism. These combinations correspond to the ratio of the specificities of two consecutive phosphorylations and the probability that monophosphorylated substrate does not dissociate from the enzyme before the second phosphorylation. The presented approach offers a language for comparing the effects of mutations that disrupt ERK activation and function in vivo. As an illustration, we use phase plane representation to analyze dual phosphorylation under heterozygous conditions, when two enzyme variants compete for the same substrate.

Addressing current limitations of household transmission studies by collecting contact data.

Modeling studies of household transmission data have helped characterize the role of children in influenza and COVID-19 epidemics. However, estimates from these studies may be biased since they do not account for the heterogeneous nature of household contacts. Here, we quantified the impact of contact heterogeneity between household members on the estimation of child relative susceptibility and infectivity. We simulated epidemics of SARS-CoV-2-like and influenza-like infections in a synthetic population of 1,000 households assuming heterogeneous contact levels. Relative contact frequencies were derived from a household contact study according to which contacts are more frequent in the father-mother pair, followed by the child-mother, child-child, and finally child-father pairs. Child susceptibility and infectivity were then estimated while accounting for heterogeneous contacts or not. When ignoring contact heterogeneity, child relative susceptibility was underestimated by approximately 20% in the two disease scenarios. Child relative infectivity was underestimated by 20% when children and adults had different infectivity levels. These results are sensitive to our assumptions of European-style household contact patterns; but they highlight that household studies collecting both disease and contact data are needed to assess the role of complex household contact behavior on disease transmission and improve estimation of key biological parameters.

Mathematical modeling of the interaction between yolk utilization and fish growth in zebrafish, Danio rerio.

Optimal embryonic development plays a major role in the health of an individual beyond the developmental stage. Nutritional perturbation during development is associated with cardiovascular and metabolic disease later in life. With both nutritional uptake and overall growth being risk factors for eventual health, it is necessary to understand not only the behavior of the processes during development but also their interactions. In this study, we used differential equations, image analyses, curve fittings, parameter estimation and laboratory experiments to quantify the rate of yolk absorption and its effect on early development of a vertebrate model (Danio rerio). Findings from this study establish a nonlinear functional relationship between nutrient absorption and early fish growth. We found that the rate of change in fish length and yolk utilization is logistic, that is the yolk decays rapidly for a period of time before leveling out. An interesting finding from this study is that yolk utilization reaches its maximum at 84 h post-fertilization. We validated our mathematical models against experimental observations, making them powerful tools for replication and future simulations.

A protocol for dynamic model calibration.

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.

Bias-reduced neural networks for parameter estimation in quantitative MRI.

PURPOSE: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. THEORY AND METHODS: We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. RESULTS: In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least-squares fitting, while state-of-the-art NNs show larger deviations. CONCLUSION: The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models.

Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.

Development of a model for the ethanol concentration limit as a function of temperature and initial substrate concentration using the yeast Saccharomyces cerevisiae.

In this study, a model was developed to simulate the effect of temperature ( T $T$ ) and initial substrate concentration ( S 0 ${S}_{0}$ ) on the ethanol concentration limit ( P max ${P}_{\max }$ ) using the yeast Saccharomyces cerevisiae. To achieve this, regressions were performed using data provided by other authors for P max ${P}_{\max }$ to establish a model dependent on T $T$ and S 0 ${S}_{0}$ capable of predicting results with statistical significance. After constructing the model, a response surface was generated to determine the conditions where P max ${P}_{\max }$ reaches higher values: temperatures between 28°C and 32°C and an initial substrate concentration around 200 g/L. Thus, the proposed model is consistent with the observations that increasing temperatures decrease the ethanol concentration obtained, and substrate concentrations above 200 g/L lead to a reduction in ethanol concentration even at low temperatures such as 28°C.

Multi-cell-line learning for the data-driven construction of mechanistic metabolic models.

Mammalian cells are commonly used as hosts in cell culture for biologics production in the pharmaceutical industry. Structured mechanistic models of metabolism have been used to capture complex cellular mechanisms that contribute to varying metabolic shifts in different cell lines. However, little research has focused on the impact of temporal changes in enzyme abundance and activity on the modeling of cell metabolism. In this work, we present a framework for constructing mechanistic models of metabolism that integrate growth-signaling control of enzyme activity and transcript dynamics. The proposed approach is applied to build models for three Chinese hamster ovary (CHO) cell lines using fed-batch culture data and time-series transcript profiles. Leveraging information from the transcriptome data, we develop a parameter estimation approach based on multi-cell-line (MCL) learning, which combines data sets from different cell lines and trains the individual cell-line models jointly to improve model accuracy. The computational results demonstrate the important role of growth signaling and transcript variability in metabolic models as well as the virtue of the MCL approach for constructing cell-line models with a limited amount of data. The resulting models exhibit a high level of accuracy in predicting distinct metabolic behaviors in the different cell lines; these models can potentially be used to accelerate the process and cell-line development for the biomanufacturing of new protein therapeutics.

Modelling count data with partial differential equation models in biology.

Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is often bounded above by some carrying capacity that arises through biological competition for space or nutrients. Parameter estimation, parameter identifiability, and making model predictions usually involves working with a measurement error model that explicitly relating experimental measurements with the solution of a mathematical model. In many biological applications, a typical approach is to assume the data are normally distributed about the solution of the mathematical model. Despite the widespread use of the standard additive Gaussian measurement error model, the assumptions inherent in this approach are rarely explicitly considered or compared with other options. Here, we interpret scratch assay data, involving migration, proliferation and delays in a population of cancer cells using a reaction-diffusion PDE model. We consider relating experimental measurements to the PDE solution using a standard additive Gaussian measurement error model alongside a comparison to a more biologically realistic binomial measurement error model. While estimates of model parameters are relatively insensitive to the choice of measurement error model, model predictions for data realisations are very sensitive. The standard additive Gaussian measurement error model leads to biologically inconsistent predictions, such as negative counts and counts that exceed the carrying capacity across a relatively large spatial region within the experiment. Furthermore, the standard additive Gaussian measurement error model requires estimating an additional parameter compared to the binomial measurement error model. In contrast, the binomial measurement error model leads to biologically plausible predictions and is simpler to implement. We provide open source Julia software on GitHub to replicate all calculations in this work, and we explain how to generalise our approach to deal with coupled PDE models with several dependent variables through a multinomial measurement error model, as well as pointing out other potential generalisations by linking our work with established practices in the field of generalised linear models.

Mathematical modeling of adipocyte size distributions: Identifiability and parameter estimation from rat data.

Fat cells, called adipocytes, are designed to regulate energy homeostasis by storing energy in the form of lipids. Adipocyte size distribution is assumed to play a role in the development of obesity-related diseases. These cells that do not have a characteristic size, indeed a bimodal size distribution is observed in adipose tissue. We propose a model based on a partial differential equation to describe adipocyte size distribution. The model includes a description of the lipid fluxes and the cell size fluctuations and using a formulation of a stationary solution fast computation of bimodal distribution is achieved. We investigate the parameter identifiability and estimate parameter values with CMA-ES algorithm. We first validate the procedure on synthetic data, then we estimate parameter values with experimental data of 32 rats. We discuss the estimated parameter values and their variability within the population, as well as the relation between estimated values and their biological significance. Finally, a sensitivity analysis is performed to specify the influence of parameters on cell size distribution and explain the differences between the model and the measurements. The proposed framework enables the characterization of adipocyte size distribution with four parameters and can be easily adapted to measurements of cell size distribution in different health conditions.

A mathematical model for wound healing in the reef-building coral Pocillopora damicornis.

Coral reefs, among the most diverse ecosystems on Earth, currently face major threats from pollution, unsustainable fishing practices , and perturbations in environmental parameters brought on by climate change. Corals also sustain regular wounding from other sea life and human activity. Recent reef restoration practices have even involved intentional wounding by systematically breaking coral fragments and relocating them to revitalize damaged reefs, a practice known as microfragmentation. Despite its importance, very little research has explored the inner mechanisms of wound healing in corals. Some reef-building corals have been observed to initiate an immunological response to wounding similar to that observed in mammalian species. Utilizing prior models of wound healing in mammalian species as the mathematical basis, we formulated a mechanistic model of wound healing, including observations of the immune response and tissue repair in scleractinian corals for the species Pocillopora damicornis. The model consists of four differential equations which track changes in remaining wound debris, number of cells involved in inflammation, number of cells involved in proliferation, and amount of wound closure through re-epithelialization. The model is fit to experimental wound size data from linear and circular shaped wounds on a live coral fragment. Mathematical methods, including numerical simulations and local sensitivity analysis, were used to analyze the resulting model. The parameter space was also explored to investigate drivers of other possible wound outcomes. This model serves as a first step in generating mathematical models for wound healing in corals that will not only aid in the understanding of wound healing as a whole, but also help optimize reef restoration practices and predict recovery behavior after major wounding events.

Aß-protein polymerization in Alzheimer disease: Optimal control for nucleation parameter estimation.

In this paper, we are interested in the modeling of Alzheimer's disease from the angle of the amyloid cascade hypothesis, where the pathogenic agent is the Aß protein in its oligomeric form. The formation dynamics of this pathogenic form is modeled by a Becker-Doring type model where APP (Amyloid Precursor Protein) protein, after cleavage by specific enzymes, forms monomeric Aß proteins, which, by polymerization and/or nucleation, lead to the formation of oligomeric Aß. We propose an optimal control problem to estimate the rate of nucleation which seems to be at the base of this amyloid cascade hypothesis and for which no (experimental) measurement exists for the moment.

Parameter estimation and forecasting with quantified uncertainty for ordinary differential equation models using QuantDiffForecast: A MATLAB toolbox and tutorial.

Mathematical models based on systems of ordinary differential equations (ODEs) are frequently applied in various scientific fields to assess hypotheses, estimate key model parameters, and generate predictions about the system's state. To support their application, we present a comprehensive, easy-to-use, and flexible MATLAB toolbox, QuantDiffForecast, and associated tutorial to estimate parameters and generate short-term forecasts with quantified uncertainty from dynamical models based on systems of ODEs. We provide software ( https://github.com/gchowell/paramEstimation_forecasting_ODEmodels/) and detailed guidance on estimating parameters and forecasting time-series trajectories that are characterized using ODEs with quantified uncertainty through a parametric bootstrapping approach. It includes functions that allow the user to infer model parameters and assess forecasting performance for different ODE models specified by the user, using different estimation methods and error structures in the data. The tutorial is intended for a diverse audience, including students training in dynamic systems, and will be broadly applicable to estimate parameters and generate forecasts from models based on ODEs. The functions included in the toolbox are illustrated using epidemic models with varying levels of complexity applied to data from the 1918 influenza pandemic in San Francisco. A tutorial video that demonstrates the functionality of the toolbox is included.

Determining dengue infection risk in the Colombo district of Sri Lanka by inferencing the genetic parameters of Aedes mosquitoes.

BACKGROUND: For decades, dengue has posed a significant threat as a viral infectious disease, affecting numerous human lives globally, particularly in tropical regions, yet no cure has been discovered. The genetic trait of vector competence in Aedes mosquitoes, which facilitates dengue transmission, is difficult to measure and highly sensitive to environmental changes. METHODS: In this study we attempt, for the first time in a non-laboratory setting, to quantify the vector competence of Aedes mosquitoes assuming its homogeneity across both species; aegypti and albopictus and across the four Dengue serotypes. Estimating vector competence in relation to varying rainfall patterns was focused in this study to showcase the changes in this vector trait with respect to environmental variables. We quantify it using an existing mathematical model originally developed for malaria in a Bayesian inferencing setup. We conducted this study in the Colombo district of Sri Lanka where the highest number of human populations are threatened with dengue. Colombo district experiences continuous favorable temperature and humidity levels throughout the year creating ideal conditions for Aedes mosquitoes to thrive and transmit the Dengue disease. Therefore we only used the highly variable and seasonal rainfall as the primary environmental variable as it significantly influences the number of breeding sites and thereby impacting the population dynamics of Aedes. RESULTS: Our research successfully deduced vector competence values for the four identified seasons based on Monsoon rainfalls experienced in Colombo within a year. We used dengue data from 2009 - 2022 to infer the estimates. These estimated values have been corroborated through experimental studies documented in the literature, thereby validating the malaria model to estimate vector competence for dengue disease. CONCLUSION: Our research findings conclude that environmental conditions can amplify vector competence within specific seasons, categorized by their environmental attributes. Additionally, the deduced vector competence offers compelling evidence that it impacts disease transmission, irrespective of geographical location, climate, or environmental factors.

A two-variant model of SARS-COV-2 transmission: estimating the characteristics of a newly emerging strain.

BACKGROUND: The Covid-19 pandemic has been characterized by the emergence of novel SARS-CoV-2 variants, each with distinct properties influencing transmission dynamics, immune escape, and virulence, which, in turn, influence their impact on local populations. Swift analysis of the properties of newly emerged variants is essential in the initial days and weeks to enhance readiness and facilitate the scaling of clinical and public health system responses. METHODS: This paper introduces a two-variant metapopulation compartmental model of disease transmission to simulate the dynamics of disease transmission during a period of transition to a newly dominant strain. Leveraging novel S-gene dropout analysis data and genomic sequencing data, combined with confirmed Covid-19 case data, we estimate the epidemiological characteristics of the Omicron variant, which replaced the Delta variant in late 2021 in Philadelphia, PA. We utilized a grid-search method to identify plausible combinations of model parameters, followed by an ensemble adjustment Kalman filter for parameter inference. RESULTS: The model successfully estimated key epidemiological parameters; we estimated the ascertainment rate of 0.22 (95% credible interval 0.15-0.29) and transmission rate of 5.0 (95% CI 2.4-6.6) for the Omicron variant. CONCLUSIONS: The study demonstrates the potential for this model-inference framework to provide real-time insights during the emergence of novel variants, aiding in timely public health responses.

GlyCompute: towards the automated analysis of protein N-linked glycosylation kinetics via an open-source computational framework.

Understanding the complex biosynthetic pathways of glycosylation is crucial for the expanding field of glycosciences. Computer-aided glycosylation analysis has greatly benefited in recent years from the development of tools found in web-based portals and open-source libraries. However, the in silico analysis of cellular glycosylation kinetics is underrepresented in current glycoscience-related tools and databases. This could be partly attributed to the limited accessibility of kinetic models developed using proprietary software and the difficulty in reliably parameterising such models. This work aims to address these challenges by proposing GlyCompute, an open-source framework demonstrating a novel, streamlined approach for the assembly, simulation, and parameterisation of kinetic models of protein N-linked glycosylation. Specifically, given one or more sets of experimentally observed N-glycan structures and their relative abundances, minimum representations of a glycosylation reaction network are generated. The topology of the resulting networks is then used to automatically assemble the material balances and kinetic mechanisms underpinning the mathematical model. To match the experimentally observed relative abundances, a sequential parameter estimation strategy using Bayesian inference is proposed, with stages determined automatically based on the underlying network topology. The proposed framework was tested on a case study involving the simultaneous fitting of the kinetic model to two protein N-linked glycoprofiles produced by the same CHO cell culture, showing good agreement with experimental observations. We envision that GlyCompute could help glycoscientists gain quantitative insights into the effect of enzyme kinetics and their perturbations on experimentally observed glycoprofiles in biomanufacturing and clinical settings.

Parameter subset reduction for imaging-based digital twin generation of patients with left ventricular mechanical discoordination.

BACKGROUND: Integration of a patient's non-invasive imaging data in a digital twin (DT) of the heart can provide valuable insight into the myocardial disease substrates underlying left ventricular (LV) mechanical discoordination. However, when generating a DT, model parameters should be identifiable to obtain robust parameter estimations. In this study, we used the CircAdapt model of the human heart and circulation to find a subset of parameters which were identifiable from LV cavity volume and regional strain measurements of patients with different substrates of left bundle branch block (LBBB) and myocardial infarction (MI). To this end, we included seven patients with heart failure with reduced ejection fraction (HFrEF) and LBBB (study ID: 2018-0863, registration date: 2019-10-07), of which four were non-ischemic (LBBB-only) and three had previous MI (LBBB-MI), and six narrow QRS patients with MI (MI-only) (study ID: NL45241.041.13, registration date: 2013-11-12). Morris screening method (MSM) was applied first to find parameters which were important for LV volume, regional strain, and strain rate indices. Second, this parameter subset was iteratively reduced based on parameter identifiability and reproducibility. Parameter identifiability was based on the diaphony calculated from quasi-Monte Carlo simulations and reproducibility was based on the intraclass correlation coefficient ( ICC ) obtained from repeated parameter estimation using dynamic multi-swarm particle swarm optimization. Goodness-of-fit was defined as the mean squared error ( χ 2 ) of LV myocardial strain, strain rate, and cavity volume. RESULTS: A subset of 270 parameters remained after MSM which produced high-quality DTs of all patients ( χ 2 < 1.6), but minimum parameter reproducibility was poor ( ICC min = 0.01). Iterative reduction yielded a reproducible ( ICC min = 0.83) subset of 75 parameters, including cardiac output, global LV activation duration, regional mechanical activation delay, and regional LV myocardial constitutive properties. This reduced subset produced patient-resembling DTs ( χ 2 < 2.2), while septal-to-lateral wall workload imbalance was higher for the LBBB-only DTs than for the MI-only DTs (p < 0.05). CONCLUSIONS: By applying sensitivity and identifiability analysis, we successfully determined a parameter subset of the CircAdapt model which can be used to generate imaging-based DTs of patients with LV mechanical discoordination. Parameters were reproducibly estimated using particle swarm optimization, and derived LV myocardial work distribution was representative for the patient's underlying disease substrate. This DT technology enables patient-specific substrate characterization and can potentially be used to support clinical decision making.

Making Predictions Using Poorly Identified Mathematical Models.

Many commonly used mathematical models in the field of mathematical biology involve challenges of parameter non-identifiability. Practical non-identifiability, where the quality and quantity of data does not provide sufficiently precise parameter estimates is often encountered, even with relatively simple models. In particular, the situation where some parameters are identifiable and others are not is often encountered. In this work we apply a recent likelihood-based workflow, called Profile-Wise Analysis (PWA), to non-identifiable models for the first time. The PWA workflow addresses identifiability, parameter estimation, and prediction in a unified framework that is simple to implement and interpret. Previous implementations of the workflow have dealt with idealised identifiable problems only. In this study we illustrate how the PWA workflow can be applied to both structurally non-identifiable and practically non-identifiable models in the context of simple population growth models. Dealing with simple mathematical models allows us to present the PWA workflow in a didactic, self-contained document that can be studied together with relatively straightforward Julia code provided on GitHub . Working with simple mathematical models allows the PWA workflow prediction intervals to be compared with gold standard full likelihood prediction intervals. Together, our examples illustrate how the PWA workflow provides us with a systematic way of dealing with non-identifiability, especially compared to other approaches, such as seeking ad hoc parameter combinations, or simply setting parameter values to some arbitrary default value. Importantly, we show that the PWA workflow provides insight into the commonly-encountered situation where some parameters are identifiable and others are not, allowing us to explore how uncertainty in some parameters, and combinations of parameters, regardless of their identifiability status, influences model predictions in a way that is insightful and interpretable.