protocol-for-analysis-consolidation-trackmate-outputs-for-measuring

Protocol for Analysis and Consolidation of TrackMate Outputs for Measuring Two-Dimensional Cell Motility using Nuclear Tracking

Collective cellular migration plays a key role in many fundamental biological processes including development, wound healing, and cancer metastasis. To ...

University of Colorado Boulder

The bacterial pathogen Klebsiella pneumoniae is a cause of community- and hospital-acquired lung, urinary tract and blood stream infections. It is a common contaminant of indwelling catheters and it is theorized in that context that systemic infection follows shedding of aggregates off of surface-adherent biofilm colonies. In an effort to better understand bacterial proliferation in the host bloodstream, we develop a PDE model for the flocculation dynamics of Klebsiella pneumoniae in suspension. Existence and uniqueness results are provided, as well as a brief description of the numerical approximation scheme. We generate artificial data and illustrate the requirements to accurately identify proliferation, aggregation, and fragmentation of flocs in the experimental domain of interest.

Klebsiella pneumoniae flocculation dynamics.

With an in vitro system that used a luminescent strain of Klebsiella pneumoniae to assess bacterial metabolic activity in near-real-time, we investigated the dynamics of complement-mediated attack in healthy individuals and in patients presenting to the emergency department with community-acquired severe sepsis. A novel mathematical/statistical model was developed to simplify light output trajectories over time into two fitted parameters, the rate of complement activation and the delay from activation to the onset of killing. Using Factor B-depleted serum, the alternative pathway was found to be the primary bactericidal effector: In the absence of B, C3 opsonization as measured by flow cytometry did not progress and bacteria proliferated near exponentially. Defects in bacterial killing were easily demonstrable in patients with severe sepsis compared with healthy volunteers. In most patients with sepsis, the rate of activation was higher than in normal subjects but was associated with a prolonged delay between activation and bacterial killing (P < 0.05 for both). Theoretical modeling suggested that this combination of accentuated but delayed function should allow successful bacterial killing but with significantly greater complement activation. The use of luminescent bacteria allowed for the development of a novel and powerful tool for assessing complement immunology for the purposes of mechanistic study and patient evaluation.

Dynamics of human complement-mediated killing of Klebsiella pneumoniae.

While the importance of fluid dynamical conditions is well recognized in the growth of biofilms, their role during bacteremia is unknown. We examined the impact of physiological fluid shear forces on the development of multicellular aggregates of Klebsiella pneumoniae.

Multicellularity and antibiotic resistance in Klebsiella pneumoniae grown under bloodstream-mimicking fluid dynamic conditions.

Diabetes cases worldwide have risen steadily over the past few decades, lending urgency to the search for more efficient, effective, and personalized ways to treat the disease. Current treatment strategies, however, may fail to maintain oscillations in blood glucose concentration that naturally occur multiple times per day, an important element of normal human physiology. Building upon recent successes in mathematical modeling of the human glucose-insulin system, we show that both food intake and insulin therapy likely demand increasingly precise control over insulin sensitivity if oscillations at a healthy average glucose concentration are to be maintained. We then model and describe personalized treatment options for patients with diabetes that maintain these oscillations. We predict that for a person with type II diabetes, both blood glucose levels can be controlled and healthy oscillations maintained when the patient gets an hour of daily exercise and is placed on a combination of Metformin and sulfonylurea drugs. We note that insulin therapy and an additional hour of exercise will reduce the patient׳s need for sulfonylureas. Results of a modeling analysis suggest that, with constant nutrition and controlled exercise, the blood glucose levels of a person with type I diabetes can be properly controlled with insulin infusion between 0.45 and 0.7μU/mlmin. Lastly, we note that all suggested strategies rely on existing clinical techniques and established treatment measures, and so could potentially be of immediate use in the design of an artificial pancreas. 

Determination of personalized diabetes treatment plans using a two-delay model.

The in vitro migration of keratinocyte cell sheets displays behavioral and biochemical similarities to the in vivo wound healing response of keratinocytes in animal model systems. In both cases, ligand-dependent Epidermal Growth Factor Receptor (EGFR) activation is sufficient to elicit collective cell migration into the wound. Previous mathematical modeling studies of in vitro wound healing assays assume that physical connections between cells have a hindering effect on cell migration, but biological literature suggests a more complicated story. By combining mathematical modeling and experimental observations of collectively migrating sheets of keratinocytes, we investigate the role of cell-cell adhesion during in vitro keratinocyte wound healing assays. We develop and compare two nonlinear diffusion models of the wound healing process in which cell-cell adhesion either hinders or promotes migration. Both models can accurately fit the leading edge propagation of cell sheets during wound healing when using a time-dependent rate of cell-cell adhesion strength. The model that assumes a positive role of cell-cell adhesion on migration, however, is robust to changes in the leading edge definition and yields a qualitatively accurate density profile. Using RNAi for the critical adherens junction protein, α-catenin, we demonstrate that cell sheets with wild type cell-cell adhesion expression maintain migration into the wound longer than cell sheets with decreased cell-cell adhesion expression, which fails to exhibit collective migration. Our modeling and experimental data thus suggest that cell-cell adhesion promotes sustained migration as cells pull neighboring cells into the wound during wound healing.

Modeling keratinocyte wound healing dynamics: Cell-cell adhesion promotes sustained collective migration.

Aging in Caenorhabditis elegans is controlled, in part, by the insulin-like signaling and heat shock response pathways. Following thermal stress, expression levels of small heat shock protein-16.2 show a spatial patterning across the 20 intestinal cells that reside along the length of the worm. Here, we present a hypothesized mechanism that could lead to this patterned response and develop a mathematical model of this system to test our hypothesis. We propose that the patterned expression of heat shock protein is caused by a diffusion-driven instability within the pseudocoelom, or fluid-filled cavity, that borders the intestinal cells in C. elegans. This instability is due to the interactions between two classes of insulin-like peptides that serve antagonistic roles. We examine output from the developed model and compare it to experimental data on heat shock protein expression. Given biologically bounded parameters, the model presented is capable of producing patterns similar to what is observed experimentally and provides a first step in mathematically modeling aging-related mechanisms in C. elegans.

Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans.

Infectious Disease Transmission Models to Predict, Evaluate, and Improve Understanding of COVID-19 Trajectory and Interventions.

Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data [6, 39]. Recently, several groups have independently discovered that the weak formulation provides orders of magnitude better robustness to noise. Here we extend our Weak SINDy (WSINDy) framework introduced in [28] to the setting of partial differential equations (PDEs). The elimination of pointwise derivative approximations via the weak form enables effective machine-precision recovery of model coefficients from noise-free data (i.e. below the tolerance of the simulation scheme) as well as robust identification of PDEs in the large noise regime (with signal-to-noise ratio approaching one in many well-known cases). This is accomplished by discretizing a convolutional weak form of the PDE and exploiting separability of test functions for efficient model identification using the Fast Fourier Transform. The resulting WSINDy algorithm for PDEs has a worst-case computational complexity of  for datasets with  points in each of  + 1 dimensions. Furthermore, our Fourier-based implementation reveals a connection between robustness to noise and the spectra of test functions, which we utilize in an  selection algorithm for test functions. Finally, we introduce a learning algorithm for the threshold in sequential-thresholding least-squares (STLS) that enables model identification from large libraries, and we utilize scale invariance at the continuum level to identify PDEs from poorly-scaled datasets. We demonstrate WSINDy's robustness, speed and accuracy on several challenging PDEs. Code is publicly available on GitHub at https://github.com/MathBioCU/WSINDy_PDE.

Article	Year
Klebsiella pneumoniae flocculation dynamics. Bulletin of mathematical biology\| PubMed ID: 18071828	2008
Dynamics of human complement-mediated killing of Klebsiella pneumoniae. American journal of respiratory cell and molecular biology\| PubMed ID: 20008281	2010
Multicellularity and antibiotic resistance in Klebsiella pneumoniae grown under bloodstream-mimicking fluid dynamic conditions. The Journal of infectious diseases\| PubMed ID: 22711903	2012
Determination of personalized diabetes treatment plans using a two-delay model. Journal of theoretical biology\| PubMed ID: 24931673	2014
Modeling keratinocyte wound healing dynamics: Cell-cell adhesion promotes sustained collective migration. Journal of theoretical biology\| PubMed ID: 27105673	2016
Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans. Bulletin of mathematical biology\| PubMed ID: 30097920	2018
Infectious Disease Transmission Models to Predict, Evaluate, and Improve Understanding of COVID-19 Trajectory and Interventions. Annals of the American Thoracic Society\| PubMed ID: 32610024	2020
WEAK SINDY FOR PARTIAL DIFFERENTIAL EQUATIONS. Journal of computational physics\| PubMed ID: 34744183	2021

David M. Bortz

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