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Whiteley JP, Brown CP, Gaffney EA. Sensitivity of cartilage mechanical behaviour to spatial variations in material properties. J Mech Behav Biomed Mater 2024; 156:106575. [PMID: 38824865 DOI: 10.1016/j.jmbbm.2024.106575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Revised: 02/28/2024] [Accepted: 05/08/2024] [Indexed: 06/04/2024]
Abstract
Articular cartilage tissue exhibits a spatial dependence in material properties that govern mechanical behaviour. A mathematical model of cartilage tissue under one dimensional confined compression testing is developed for normal tissue that takes account of these variations in material properties. Modifications to the model representative of a selection of mechanisms driving osteoarthritic cartilage are proposed, allowing application of the model to both physiological and pathophysiological, osteoarthritic tissue. Incorporating spatial variations into the model requires the specification of more parameters than are required in the absence of these variations. A global sensitivity analysis of these parameters is implemented to identify the dominant mechanisms of mechanical response, in normal and osteoarthritic cartilage tissue, to both static and dynamic loading. The most sensitive parameters differ between dynamic and static mechanics of the cartilage, and also differ between physiological and osteoarthritic pathophysiological cartilage. As a consequence changes in cartilage mechanics in response to alterations in cartilage structure are predicted to be contingent on the nature of loading and the health, or otherwise, of the cartilage. In particular the mechanical response of cartilage, especially deformation, is predicted to be much more sensitive to cartilage stiffness in the superficial zone given the onset of osteoarthritic changes to material properties, such as superficial zone increases in permeability and reductions in fixed charge. In turn this indicates that any degenerative changes in the stiffness associated with the superficial cartilage collagen mesh are amplified if other elements of osteoarthritic disease are present, which provides a suggested mechanism-based explanation for observations that the range of mechanical parameters representative of normal and osteoarthritic tissue can overlap substantially.
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Affiliation(s)
- Jonathan P Whiteley
- Department of Computer Science, University of Oxford, Parks Road, OX1 3QD, Oxford, United Kingdom.
| | - Cameron P Brown
- MMPE, MERF, Faculty of Engineering, Queensland University of Technology, QLD 4000, Brisbane, Australia.
| | - Eamonn A Gaffney
- Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, OX2 6GG, Oxford, United Kingdom.
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2
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Saxton H, Xu X, Schenkel T, Clayton RH, Halliday I. Convergence, sampling and total order estimator effects on parameter orthogonality in global sensitivity analysis. PLoS Comput Biol 2024; 20:e1011946. [PMID: 39018334 DOI: 10.1371/journal.pcbi.1011946] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Revised: 07/29/2024] [Accepted: 06/13/2024] [Indexed: 07/19/2024] Open
Abstract
Dynamical system models typically involve numerous input parameters whose "effects" and orthogonality need to be quantified through sensitivity analysis, to identify inputs contributing the greatest uncertainty. Whilst prior art has compared total-order estimators' role in recovering "true" effects, assessing their ability to recover robust parameter orthogonality for use in identifiability metrics has not been investigated. In this paper, we perform: (i) an assessment using a different class of numerical models representing the cardiovascular system, (ii) a wider evaluation of sampling methodologies and their interactions with estimators, (iii) an investigation of the consequences of permuting estimators and sampling methodologies on input parameter orthogonality, (iv) a study of sample convergence through resampling, and (v) an assessment of whether positive outcomes are sustained when model input dimensionality increases. Our results indicate that Jansen or Janon estimators display efficient convergence with minimum uncertainty when coupled with Sobol and the lattice rule sampling methods, making them prime choices for calculating parameter orthogonality and influence. This study reveals that global sensitivity analysis is convergence driven. Unconverged indices are subject to error and therefore the true influence or orthogonality of the input parameters are not recovered. This investigation importantly clarifies the interactions of the estimator and the sampling methodology by reducing the associated ambiguities, defining novel practices for modelling in the life sciences.
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Affiliation(s)
- Harry Saxton
- Materials & Engineering Research Institute, Sheffield Hallam University, Sheffield, United Kingdom
| | - Xu Xu
- Department of Computer Science, Faculty of Engineering, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - Torsten Schenkel
- Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield, United Kingdom
| | - Richard H Clayton
- Department of Computer Science, Faculty of Engineering, University of Sheffield, Sheffield, United Kingdom
- Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom
| | - Ian Halliday
- Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, United Kingdom
- Clinical Medicine, School of Medicine and Population Health, University of Sheffield, Sheffield, United Kingdom
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3
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Jegatheesan T, Moorthy AS, Eberl HJ. A mathematical model of competition between fiber and mucin degraders in the gut provides a possible explanation for mucus thinning. J Theor Biol 2024; 587:111824. [PMID: 38604595 DOI: 10.1016/j.jtbi.2024.111824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2023] [Revised: 03/14/2024] [Accepted: 04/06/2024] [Indexed: 04/13/2024]
Abstract
The human gut microbiota relies on complex carbohydrates (glycans) for energy and growth, primarily dietary fiber and host-derived mucins. We introduce a mathematical model of a glycan generalist and a mucin specialist in a two-compartment chemostat model of the human colon. Our objective is to characterize the influence of dietary fiber and mucin supply on the abundance of mucin-degrading species within the gut ecosystem. Current mathematical gut reactor models that include the enzymatic degradation of glycans do not differentiate between glycan types and their degraders. The model we present distinguishes between a generalist that can degrade both dietary fiber and mucin, and a specialist species that can only degrade mucin. The integrity of the colonic mucus barrier is essential for overall human health and well-being, with the mucin specialist Akkermanisa muciniphila being associated with a healthy mucus layer. Competition, particularly between the specialist and generalists like Bacteroides thetaiotaomicron, may lead to mucus layer erosion, especially during periods of dietary fiber deprivation. Our model treats the colon as a gut reactor system, dividing it into two compartments that represent the lumen and the mucus of the gut, resulting in a complex system of ordinary differential equations with a large and uncertain parameter space. To understand the influence of model parameters on long-term behavior, we employ a random forest classifier, a supervised machine learning method. Additionally, a variance-based sensitivity analysis is utilized to determine the sensitivity of steady-state values to changes in model parameter inputs. By constructing this model, we can investigate the underlying mechanisms that control gut microbiota composition and function, free from confounding factors.
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Affiliation(s)
- Thulasi Jegatheesan
- Department of Mathematics and Statistics, University of Guelph, 50 Stone Rd E, Guelph, N1G 2W1, ON, Canada; Biophysics Interdepartmental Group, University of Guelph, 50 Stone Rd E, Guelph, N1G 2W1, ON, Canada
| | - Arun S Moorthy
- Biophysics Interdepartmental Group, University of Guelph, 50 Stone Rd E, Guelph, N1G 2W1, ON, Canada; Department of Forensic Science, Trent University, 1600 West Bank Drive, Peterborough, K9L 0G2, ON, Canada
| | - Hermann J Eberl
- Department of Mathematics and Statistics, University of Guelph, 50 Stone Rd E, Guelph, N1G 2W1, ON, Canada; Biophysics Interdepartmental Group, University of Guelph, 50 Stone Rd E, Guelph, N1G 2W1, ON, Canada.
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4
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Claes E, Heck T, Coddens K, Sonnaert M, Schrooten J, Verwaeren J. Bayesian cell therapy process optimization. Biotechnol Bioeng 2024; 121:1569-1582. [PMID: 38372656 DOI: 10.1002/bit.28669] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 11/17/2023] [Accepted: 01/22/2024] [Indexed: 02/20/2024]
Abstract
Optimizing complex bioprocesses poses a significant challenge in several fields, particularly in cell therapy manufacturing. The development of customized, closed, and automated processes is crucial for their industrial translation and for addressing large patient populations at a sustainable price. Limited understanding of the underlying biological mechanisms, coupled with highly resource-intensive experimentation, are two contributing factors that make the development of these next-generation processes challenging. Bayesian optimization (BO) is an iterative experimental design methodology that addresses these challenges, but has not been extensively tested in situations that require parallel experimentation with significant experimental variability. In this study, we present an evaluation of noisy, parallel BO for increasing noise levels and parallel batch sizes on two in silico bioprocesses, and compare it to the industry state-of-the-art. As an in vitro showcase, we apply the method to the optimization of a monocyte purification unit operation. The in silico results show that BO significantly outperforms the state-of-the-art, requiring approximately 50% fewer experiments on average. This study highlights the potential of noisy, parallel BO as valuable tool for cell therapy process development and optimization.
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Affiliation(s)
- Evan Claes
- Antleron, Leuven, Belgium
- Biovism, Department of Data Analysis and Mathematical Modelling, Faculty of Bioscience Engineering, Ghent University, Gent, Belgium
| | | | | | | | | | - Jan Verwaeren
- Biovism, Department of Data Analysis and Mathematical Modelling, Faculty of Bioscience Engineering, Ghent University, Gent, Belgium
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5
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Stadt MM, Layton AT. A modeling analysis of whole body potassium regulation on a high-potassium diet: proximal tubule and tubuloglomerular feedback effects. Am J Physiol Regul Integr Comp Physiol 2024; 326:R401-R415. [PMID: 38465401 DOI: 10.1152/ajpregu.00283.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Revised: 02/15/2024] [Accepted: 03/05/2024] [Indexed: 03/12/2024]
Abstract
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.
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Affiliation(s)
- Melissa M Stadt
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
| | - Anita T Layton
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada
- Department of Biology, University of Waterloo, Waterloo, Ontario, Canada
- Department of Pharmacy, University of Waterloo, Waterloo, Ontario, Canada
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6
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Gasior KI, Cogan NG. Untangling the Molecular Interactions Underlying Intracellular Phase Separation Using Combined Global Sensitivity Analyses. Bull Math Biol 2024; 86:60. [PMID: 38641666 DOI: 10.1007/s11538-024-01288-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 03/27/2024] [Indexed: 04/21/2024]
Abstract
Liquid-liquid phase separation is an intracellular mechanism by which molecules, usually proteins and RNAs, interact and then rapidly demix from the surrounding matrix to form membrane-less compartments necessary for cellular function. Occurring in both the cytoplasm and the nucleus, properties of the resulting droplets depend on a variety of characteristics specific to the molecules involved, such as valency, density, and diffusion within the crowded environment. Capturing these complexities in a biologically relevant model is difficult. To understand the nuanced dynamics between proteins and RNAs as they interact and form droplets, as well as the impact of these interactions on the resulting droplet properties, we turn to sensitivity analysis. In this work, we examine a previously published mathematical model of two RNA species competing for the same protein-binding partner. We use the combined analyses of Morris Method and Sobol' sensitivity analysis to understand the impact of nine molecular parameters, subjected to three different initial conditions, on two observable LLPS outputs: the time of phase separation and the composition of the droplet field. Morris Method is a screening method capable of highlighting the most important parameters impacting a given output, while the variance-based Sobol' analysis can quantify both the importance of a given parameter, as well as the other model parameters it interacts with, to produce the observed phenomena. Combining these two techniques allows Morris Method to identify the most important dynamics and circumvent the large computational expense associated with Sobol', which then provides more nuanced information about parameter relationships. Together, the results of these combined methodologies highlight the complicated protein-RNA relationships underlying both the time of phase separation and the composition of the droplet field. Sobol' sensitivity analysis reveals that observed spatial and temporal dynamics are due, at least in part, to high-level interactions between multiple (3+) parameters. Ultimately, this work discourages using a single measurement to extrapolate the value of any single rate or parameter value, while simultaneously establishing a framework in which to analyze and assess the impact of these small-scale molecular interactions on large-scale droplet properties.
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Affiliation(s)
- Kelsey I Gasior
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA.
| | - Nicholas G Cogan
- Department of Mathematics, Florida State University, Tallahassee, FL, USA
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7
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Bisesi AT, Möbius W, Nadell CD, Hansen EG, Bowden SD, Harcombe WR. Bacteriophage specificity is impacted by interactions between bacteria. mSystems 2024; 9:e0117723. [PMID: 38376179 PMCID: PMC11237722 DOI: 10.1128/msystems.01177-23] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 01/20/2024] [Indexed: 02/21/2024] Open
Abstract
Predators play a central role in shaping community structure, function, and stability. The degree to which bacteriophage predators (viruses that infect bacteria) evolve to be specialists with a single bacterial prey species versus generalists able to consume multiple types of prey has implications for their effect on microbial communities. The presence and abundance of multiple bacterial prey types can alter selection for phage generalists, but less is known about how interactions between prey shape predator specificity in microbial systems. Using a phenomenological mathematical model of phage and bacterial populations, we find that the dominant phage strategy depends on prey ecology. Given a fitness cost for generalism, generalist predators maintain an advantage when prey species compete, while specialists dominate when prey are obligately engaged in cross-feeding interactions. We test these predictions in a synthetic microbial community with interacting strains of Escherichia coli and Salmonella enterica by competing a generalist T5-like phage able to infect both prey against P22vir, an S. enterica-specific phage. Our experimental data conform to our modeling expectations when prey species are competing or obligately mutualistic, although our results suggest that the in vitro cost of generalism is caused by a combination of biological mechanisms not anticipated in our model. Our work demonstrates that interactions between bacteria play a role in shaping ecological selection on predator specificity in obligately lytic bacteriophages and emphasizes the diversity of ways in which fitness trade-offs can manifest. IMPORTANCE There is significant natural diversity in how many different types of bacteria a bacteriophage can infect, but the mechanisms driving this diversity are unclear. This study uses a combination of mathematical modeling and an in vitro system consisting of Escherichia coli, Salmonella enterica, a T5-like generalist phage, and the specialist phage P22vir to highlight the connection between bacteriophage specificity and interactions between their potential microbial prey. Mathematical modeling suggests that competing bacteria tend to favor generalist bacteriophage, while bacteria that benefit each other tend to favor specialist bacteriophage. Experimental results support this general finding. The experiments also show that the optimal phage strategy is impacted by phage degradation and bacterial physiology. These findings enhance our understanding of how complex microbial communities shape selection on bacteriophage specificity, which may improve our ability to use phage to manage antibiotic-resistant microbial infections.
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Affiliation(s)
- Ave T. Bisesi
- Department of Ecology, Evolution and Behavior, University of Minnesota, St. Paul, Minnesota, USA
| | - Wolfram Möbius
- Living Systems Institute, University of Exeter, Exeter, United Kingdom
- Department of Physics and Astronomy, University of Exeter, Exeter, United Kingdom
| | - Carey D. Nadell
- Department of Biological Sciences, Dartmouth College, Hanover, New Hampshire, USA
| | - Eleanore G. Hansen
- Department of Food Science and Nutrition, University of Minnesota, St. Paul, Minnesota, USA
| | - Steven D. Bowden
- Department of Food Science and Nutrition, University of Minnesota, St. Paul, Minnesota, USA
| | - William R. Harcombe
- Department of Ecology, Evolution and Behavior, University of Minnesota, St. Paul, Minnesota, USA
- BioTechnology Institute, University of Minnesota, St. Paul, Minnesota, USA
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8
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Oliveira RHDM, Annex BH, Popel AS. Endothelial cells signaling and patterning under hypoxia: a mechanistic integrative computational model including the Notch-Dll4 pathway. Front Physiol 2024; 15:1351753. [PMID: 38455844 PMCID: PMC10917925 DOI: 10.3389/fphys.2024.1351753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 02/12/2024] [Indexed: 03/09/2024] Open
Abstract
Introduction: Several signaling pathways are activated during hypoxia to promote angiogenesis, leading to endothelial cell patterning, interaction, and downstream signaling. Understanding the mechanistic signaling differences between endothelial cells under normoxia and hypoxia and their response to different stimuli can guide therapies to modulate angiogenesis. We present a novel mechanistic model of interacting endothelial cells, including the main pathways involved in angiogenesis. Methods: We calibrate and fit the model parameters based on well-established modeling techniques that include structural and practical parameter identifiability, uncertainty quantification, and global sensitivity. Results: Our results indicate that the main pathways involved in patterning tip and stalk endothelial cells under hypoxia differ, and the time under hypoxia interferes with how different stimuli affect patterning. Additionally, our simulations indicate that Notch signaling might regulate vascular permeability and establish different Nitric Oxide release patterns for tip/stalk cells. Following simulations with various stimuli, our model suggests that factors such as time under hypoxia and oxygen availability must be considered for EC pattern control. Discussion: This project provides insights into the signaling and patterning of endothelial cells under various oxygen levels and stimulation by VEGFA and is our first integrative approach toward achieving EC control as a method for improving angiogenesis. Overall, our model provides a computational framework that can be built on to test angiogenesis-related therapies by modulation of different pathways, such as the Notch pathway.
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Affiliation(s)
| | - Brian H. Annex
- Medical College of Georgia, Augusta University, Augusta, GA, United States
| | - Aleksander S. Popel
- Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, Baltimore, MD, United States
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Day EC, Chittari SS, Bogen MP, Knight AS. Navigating the Expansive Landscapes of Soft Materials: A User Guide for High-Throughput Workflows. ACS POLYMERS AU 2023; 3:406-427. [PMID: 38107416 PMCID: PMC10722570 DOI: 10.1021/acspolymersau.3c00025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 11/02/2023] [Accepted: 11/07/2023] [Indexed: 12/19/2023]
Abstract
Synthetic polymers are highly customizable with tailored structures and functionality, yet this versatility generates challenges in the design of advanced materials due to the size and complexity of the design space. Thus, exploration and optimization of polymer properties using combinatorial libraries has become increasingly common, which requires careful selection of synthetic strategies, characterization techniques, and rapid processing workflows to obtain fundamental principles from these large data sets. Herein, we provide guidelines for strategic design of macromolecule libraries and workflows to efficiently navigate these high-dimensional design spaces. We describe synthetic methods for multiple library sizes and structures as well as characterization methods to rapidly generate data sets, including tools that can be adapted from biological workflows. We further highlight relevant insights from statistics and machine learning to aid in data featurization, representation, and analysis. This Perspective acts as a "user guide" for researchers interested in leveraging high-throughput screening toward the design of multifunctional polymers and predictive modeling of structure-property relationships in soft materials.
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Affiliation(s)
| | | | - Matthew P. Bogen
- Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Abigail S. Knight
- Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
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10
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Nanda P, Budak M, Michael CT, Krupinsky K, Kirschner DE. Development and Analysis of Multiscale Models for Tuberculosis: From Molecules to Populations. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.11.13.566861. [PMID: 38014103 PMCID: PMC10680629 DOI: 10.1101/2023.11.13.566861] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2023]
Abstract
Although infectious disease dynamics are often analyzed at the macro-scale, increasing numbers of drug-resistant infections highlight the importance of within-host modeling that simultaneously solves across multiple scales to effectively respond to epidemics. We review multiscale modeling approaches for complex, interconnected biological systems and discuss critical steps involved in building, analyzing, and applying such models within the discipline of model credibility. We also present our two tools: CaliPro, for calibrating multiscale models (MSMs) to datasets, and tunable resolution, for fine- and coarse-graining sub-models while retaining insights. We include as an example our work simulating infection with Mycobacterium tuberculosis to demonstrate modeling choices and how predictions are made to generate new insights and test interventions. We discuss some of the current challenges of incorporating novel datasets, rigorously training computational biologists, and increasing the reach of MSMs. We also offer several promising future research directions of incorporating within-host dynamics into applications ranging from combinatorial treatment to epidemic response.
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11
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Nanda P, Kirschner DE. Calibration methods to fit parameters within complex biological models. FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS 2023; 9:1256443. [PMID: 38222943 PMCID: PMC10785782 DOI: 10.3389/fams.2023.1256443] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/16/2024]
Abstract
Mathematical and computational models of biological systems are increasingly complex, typically comprised of hybrid multi-scale methods such as ordinary differential equations, partial differential equations, agent-based and rule-based models, etc. These mechanistic models concurrently simulate detail at resolutions of whole host, multi-organ, organ, tissue, cellular, molecular, and genomic dynamics. Lacking analytical and numerical methods, solving complex biological models requires iterative parameter sampling-based approaches to establish appropriate ranges of model parameters that capture corresponding experimental datasets. However, these models typically comprise large numbers of parameters and therefore large degrees of freedom. Thus, fitting these models to multiple experimental datasets over time and space presents significant challenges. In this work we undertake the task of reviewing, testing, and advancing calibration practices across models and dataset types to compare methodologies for model calibration. Evaluating the process of calibrating models includes weighing strengths and applicability of each approach as well as standardizing calibration methods. Our work compares the performance of our model agnostic Calibration Protocol (CaliPro) with approximate Bayesian computing (ABC) to highlight strengths, weaknesses, synergies, and differences among these methods. We also present next-generation updates to CaliPro. We explore several model implementations and suggest a decision tree for selecting calibration approaches to match dataset types and modeling constraints.
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Affiliation(s)
- Pariksheet Nanda
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI, United States
| | - Denise E. Kirschner
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI, United States
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12
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Gao G, Walter NG. Critical Assessment of Condensate Boundaries in Dual-Color Single Particle Tracking. J Phys Chem B 2023; 127:7694-7707. [PMID: 37669232 DOI: 10.1021/acs.jpcb.3c03776] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/07/2023]
Abstract
Biomolecular condensates are membraneless cellular compartments generated by phase separation that regulate a broad variety of cellular functions by enriching some biomolecules while excluding others. Live-cell single particle tracking of individual fluorophore-labeled condensate components has provided insights into a condensate's mesoscopic organization and biological functions, such as revealing the recruitment, translation, and decay of RNAs within ribonucleoprotein (RNP) granules. Specifically, during dual-color tracking, one imaging channel provides a time series of individual biomolecule locations, while the other channel monitors the location of the condensate relative to these molecules. Therefore, an accurate assessment of a condensate's boundary is critical for combined live-cell single particle-condensate tracking. Despite its importance, a quantitative benchmarking and objective comparison of the various available boundary detection methods is missing due to the lack of an absolute ground truth for condensate images. Here, we use synthetic data of defined ground truth to generate noise-overlaid images of condensates with realistic phase separation parameters to benchmark the most commonly used methods for condensate boundary detection, including an emerging machine-learning method. We find that it is critical to carefully choose an optimal boundary detection method for a given dataset to obtain accurate measurements of single particle-condensate interactions. The criteria proposed in this study to guide the selection of an optimal boundary detection method can be broadly applied to imaging-based studies of condensates.
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Affiliation(s)
- Guoming Gao
- Biophysics Graduate Program, University of Michigan, Ann Arbor, Michigan 48109, United States
- Center for RNA Biomedicine, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Nils G Walter
- Center for RNA Biomedicine, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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13
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Budak M, Cicchese JM, Maiello P, Borish HJ, White AG, Chishti HB, Tomko J, Frye LJ, Fillmore D, Kracinovsky K, Sakal J, Scanga CA, Lin PL, Dartois V, Linderman JJ, Flynn JL, Kirschner DE. Optimizing tuberculosis treatment efficacy: Comparing the standard regimen with Moxifloxacin-containing regimens. PLoS Comput Biol 2023; 19:e1010823. [PMID: 37319311 PMCID: PMC10306236 DOI: 10.1371/journal.pcbi.1010823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Revised: 06/28/2023] [Accepted: 05/17/2023] [Indexed: 06/17/2023] Open
Abstract
Tuberculosis (TB) continues to be one of the deadliest infectious diseases in the world, causing ~1.5 million deaths every year. The World Health Organization initiated an End TB Strategy that aims to reduce TB-related deaths in 2035 by 95%. Recent research goals have focused on discovering more effective and more patient-friendly antibiotic drug regimens to increase patient compliance and decrease emergence of resistant TB. Moxifloxacin is one promising antibiotic that may improve the current standard regimen by shortening treatment time. Clinical trials and in vivo mouse studies suggest that regimens containing moxifloxacin have better bactericidal activity. However, testing every possible combination regimen with moxifloxacin either in vivo or clinically is not feasible due to experimental and clinical limitations. To identify better regimens more systematically, we simulated pharmacokinetics/pharmacodynamics of various regimens (with and without moxifloxacin) to evaluate efficacies, and then compared our predictions to both clinical trials and nonhuman primate studies performed herein. We used GranSim, our well-established hybrid agent-based model that simulates granuloma formation and antibiotic treatment, for this task. In addition, we established a multiple-objective optimization pipeline using GranSim to discover optimized regimens based on treatment objectives of interest, i.e., minimizing total drug dosage and lowering time needed to sterilize granulomas. Our approach can efficiently test many regimens and successfully identify optimal regimens to inform pre-clinical studies or clinical trials and ultimately accelerate the TB regimen discovery process.
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Affiliation(s)
- Maral Budak
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, Michigan, United States of America
| | - Joseph M. Cicchese
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Pauline Maiello
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - H. Jacob Borish
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Alexander G. White
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Harris B. Chishti
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Jaime Tomko
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - L. James Frye
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Daniel Fillmore
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Kara Kracinovsky
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Jennifer Sakal
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Charles A. Scanga
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Philana Ling Lin
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Véronique Dartois
- Center for Discovery and Innovation, Hackensack Meridian Health, Nutley, New Jersey, United States of America
- Department of Medical Sciences, Hackensack Meridian School of Medicine, Nutley, New Jersey, United States of America
| | - Jennifer J. Linderman
- Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, United States of America
| | - JoAnne L. Flynn
- Department of Microbiology and Molecular Genetics and Center for Vaccine Research, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Denise E. Kirschner
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, Michigan, United States of America
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14
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Feng A, Xie Y, Sun Y, Wang X, Jiang B, Xiao J. Efficient Autonomous Exploration and Mapping in Unknown Environments. SENSORS (BASEL, SWITZERLAND) 2023; 23:4766. [PMID: 37430680 DOI: 10.3390/s23104766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Revised: 05/09/2023] [Accepted: 05/12/2023] [Indexed: 07/12/2023]
Abstract
Autonomous exploration and mapping in unknown environments is a critical capability for robots. Existing exploration techniques (e.g., heuristic-based and learning-based methods) do not consider the regional legacy issues, i.e., the great impact of smaller unexplored regions on the whole exploration process, which results in a dramatic reduction in their later exploration efficiency. To this end, this paper proposes a Local-and-Global Strategy (LAGS) algorithm that combines a local exploration strategy with a global perception strategy, which considers and solves the regional legacy issues in the autonomous exploration process to improve exploration efficiency. Additionally, we further integrate Gaussian process regression (GPR), Bayesian optimization (BO) sampling, and deep reinforcement learning (DRL) models to efficiently explore unknown environments while ensuring the robot's safety. Extensive experiments show that the proposed method could explore unknown environments with shorter paths, higher efficiencies, and stronger adaptability on different unknown maps with different layouts and sizes.
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Affiliation(s)
- Ao Feng
- College of Integrated Circuit Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
| | - Yuyang Xie
- College of Electronic and Optical Engineering & College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China
| | - Yankang Sun
- College of Integrated Circuit Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
| | - Xuanzhi Wang
- College of Electronic and Optical Engineering & College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China
| | - Bin Jiang
- College of Electronic and Optical Engineering & College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China
| | - Jian Xiao
- College of Integrated Circuit Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
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15
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Sorokin A, Goryanin I. FBA-PRCC. Partial Rank Correlation Coefficient (PRCC) Global Sensitivity Analysis (GSA) in Application to Constraint-Based Models. Biomolecules 2023; 13:biom13030500. [PMID: 36979435 PMCID: PMC10046323 DOI: 10.3390/biom13030500] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Revised: 02/24/2023] [Accepted: 03/02/2023] [Indexed: 03/11/2023] Open
Abstract
Background: Whole-genome models (GEMs) have become a versatile tool for systems biology, biotechnology, and medicine. GEMs created by automatic and semi-automatic approaches contain a lot of redundant reactions. At the same time, the nonlinearity of the model makes it difficult to evaluate the significance of the reaction for cell growth or metabolite production. Methods: We propose a new way to apply the global sensitivity analysis (GSA) to GEMs in a straightforward parallelizable fashion. Results: We have shown that Partial Rank Correlation Coefficient (PRCC) captures key steps in the metabolic network despite the network distance from the product synthesis reaction. Conclusions: FBA-PRCC is a fast, interpretable, and reliable metric to identify the sign and magnitude of the reaction contribution to various cellular functions.
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Affiliation(s)
- Anatoly Sorokin
- Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan
- Correspondence: (A.S.); (I.G.)
| | - Igor Goryanin
- Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan
- Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin 300308, China
- School of Informatics, The University of Edinburgh, Informatics Forum, Edinburgh EH8 9AB, UK
- Correspondence: (A.S.); (I.G.)
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16
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dePillis L, Caffrey R, Chen G, Dela MD, Eldevik L, McConnell J, Shabahang S, Varvel SA. A mathematical model of the within-host kinetics of SARS-CoV-2 neutralizing antibodies following COVID-19 vaccination. J Theor Biol 2023; 556:111280. [PMID: 36202234 PMCID: PMC9529354 DOI: 10.1016/j.jtbi.2022.111280] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 08/22/2022] [Accepted: 09/14/2022] [Indexed: 10/25/2022]
Abstract
Compelling evidence continues to build to support the idea that SARS-CoV-2 Neutralizing Antibody (NAb) levels in an individual can serve as an important indicator of the strength of protective immunity against infection. It is not well understood why NAb levels in some individuals remain high over time, while in others levels decline rapidly. In this work, we present a two-state mathematical model of within-host NAb dynamics in response to vaccination. By fitting only four host-specific parameters, the model is able to capture individual-specific NAb levels over time as measured by the AditxtScore™ for NAbs. The model can serve as a foundation for predicting NAb levels in the long-term, understanding connections between NAb levels, protective immunity, and breakthrough infections, and potentially guiding decisions about whether and when a booster vaccination may be warranted.
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Affiliation(s)
- Lisette dePillis
- Department of Mathematics, Harvey Mudd College, 301 Platt Blvd., Claremont, CA 91711, United States.
| | - Rebecca Caffrey
- Aditxt, Inc. 737 N. Fifth Street, Suite 200, Richmond, VA 23219, United States
| | - Ge Chen
- Aditxt, Inc. 737 N. Fifth Street, Suite 200, Richmond, VA 23219, United States
| | - Mark D. Dela
- California State Polytechnic University, Pomona, CA, United States
| | - Leif Eldevik
- Aditxt, Inc. 737 N. Fifth Street, Suite 200, Richmond, VA 23219, United States
| | - Joseph McConnell
- Aditxt, Inc. 737 N. Fifth Street, Suite 200, Richmond, VA 23219, United States
| | - Shahrokh Shabahang
- Aditxt, Inc. 737 N. Fifth Street, Suite 200, Richmond, VA 23219, United States
| | - Stephen A. Varvel
- Aditxt, Inc. 737 N. Fifth Street, Suite 200, Richmond, VA 23219, United States
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17
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Dela A, Shtylla B, Pillis L. Multi-method Global Sensitivity Analysis of Mathematical Models. J Theor Biol 2022; 546:111159. [DOI: 10.1016/j.jtbi.2022.111159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2022] [Revised: 04/10/2022] [Accepted: 05/03/2022] [Indexed: 10/18/2022]
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18
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Hult C, Mattila JT, Gideon HP, Linderman JJ, Kirschner DE. Neutrophil Dynamics Affect Mycobacterium tuberculosis Granuloma Outcomes and Dissemination. Front Immunol 2021; 12:712457. [PMID: 34675916 PMCID: PMC8525425 DOI: 10.3389/fimmu.2021.712457] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Accepted: 08/18/2021] [Indexed: 01/01/2023] Open
Abstract
Neutrophil infiltration into tuberculous granulomas is often associated with higher bacteria loads and severe disease but the basis for this relationship is not well understood. To better elucidate the connection between neutrophils and pathology in primate systems, we paired data from experimental studies with our next generation computational model GranSim to identify neutrophil-related factors, including neutrophil recruitment, lifespan, and intracellular bacteria numbers, that drive granuloma-level outcomes. We predict mechanisms underlying spatial organization of neutrophils within granulomas and identify how neutrophils contribute to granuloma dissemination. We also performed virtual deletion and depletion of neutrophils within granulomas and found that neutrophils play a nuanced role in determining granuloma outcome, promoting uncontrolled bacterial growth in some and working to contain bacterial growth in others. Here, we present three key results: We show that neutrophils can facilitate local dissemination of granulomas and thereby enable the spread of infection. We suggest that neutrophils influence CFU burden during both innate and adaptive immune responses, implying that they may be targets for therapeutic interventions during later stages of infection. Further, through the use of uncertainty and sensitivity analyses, we predict which neutrophil processes drive granuloma severity and structure.
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Affiliation(s)
- Caitlin Hult
- Department of Mathematics, Gettysburg College, Gettysburg, PA, United States
| | - Joshua T Mattila
- Department of Infectious Diseases and Microbiology, University of Pittsburgh School of Public Health, Pittsburgh, PA, United States.,Center for Vaccine Research, University of Pittsburgh, Pittsburgh, PA, United States
| | - Hannah P Gideon
- Center for Vaccine Research, University of Pittsburgh, Pittsburgh, PA, United States.,Department of Microbiology and Molecular Genetics, University of Pittsburgh School of Medicine, Pittsburgh, PA, United States
| | - Jennifer J Linderman
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI, United States
| | - Denise E Kirschner
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI, United States
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