A Model of Gastric Mucosal pH Regulation: Extending Sensitivity Analysis Using Sobol' Indices to Understand Higher Moments.

Several recent theoretical studies have indicated that a relatively simple secretion control mechanism in the epithelial cells lining the stomach may be responsible for maintaining a neutral (healthy) pH adjacent to the stomach wall, even in the face of enormous electrodiffusive acid transport from the interior of the stomach. Subsequent work used Sobol' Indices (SIs) to quantify the degree to which this secretion mechanism is "self-regulating" i.e. the degree to which the wall pH is held neutral as mathematical parameters vary. However, questions remain regarding the nature of the control that specific parameters exert over the maintenance of a healthy stomach wall pH. Studying the sensitivity of higher moments of the statistical distribution of a model output can provide useful information, for example, how one parameter may skew the distribution towards or away from a physiologically advantageous regime. In this work, we prove a relationship between SIs and the higher moments and show how it can potentially reduce the cost of computing sensitivity of said moments. We define γ -indices to quantify sensitivity of variance, skewness, and kurtosis to the choice of value of a parameter, and we propose an efficient strategy that uses both SIs and γ -indices for a more comprehensive sensitivity analysis. Our analysis uncovers a control parameter which governs the "tightness of control" that the secretion mechanism exerts on wall pH. Finally, we discuss how uncertainty in this parameter can be reduced using expert information about higher moments, and speculate about the physiological advantage conferred by this control mechanism.

Dory: Computation of persistence diagrams up to dimension two for Vietoris-Rips filtrations of large data sets.

Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patterns across various applications, computational requirements have limited applications to small data sets of a few thousand points. We present Dory, an efficient and scalable algorithm that can compute the persistent homology of sparse Vietoris-Rips complexes on larger data sets, up to and including dimension two and over the field Z2. As an application, we compute the PH of the human genome at high resolution as revealed by a genome-wide Hi-C data set containing approximately three million points. Extant algorithms were unable to process it, whereas Dory processed it within five minutes, using less than five GB of memory. Results show that the topology of the human genome changes significantly upon treatment with auxin, a molecule that degrades cohesin, corroborating the hypothesis that cohesin plays a crucial role in loop formation in DNA.

Geometric and topological characterization of the cytoarchitecture of islets of Langerhans.

The islets of Langerhans are critical endocrine micro-organs that secrete hormones regulating energy metabolism in animals. Insulin and glucagon, secreted by beta and alpha cells, respectively, are responsible for metabolic switching between fat and glucose utilization. Dysfunction in their secretion and/or counter-regulatory influence leads to diabetes. Debate in the field centers on the cytoarchitecture of islets, as the signaling that governs hormonal secretion depends on structural and functional factors, including electrical connectivity, innervation, vascularization, and physical proximity. Much effort has therefore been devoted to elucidating which architectural features are significant for function and how derangements in these features are correlated or causative for dysfunction, especially using quantitative network science or graph theory characterizations. Here, we ask if there are non-local features in islet cytoarchitecture, going beyond standard network statistics, that are relevant to islet function. An example is ring structures, or cycles, of α and δ cells surrounding ß cell clusters or the opposite, ß cells surrounding α and δ cells. These could appear in two-dimensional islet section images if a sphere consisting of one cell type surrounds a cluster of another cell type. To address these issues, we developed two independent computational approaches, geometric and topological, for such characterizations. For the latter, we introduce an application of topological data analysis to determine locations of topological features that are biologically significant. We show that both approaches, applied to a large collection of islet sections, are in complete agreement in the context both of developmental and diabetes-related changes in islet characteristics. The topological approach can be applied to three-dimensional imaging data for islets as well.

Tight basis cycle representatives for persistent homology of large biological data sets.

Persistent homology (PH) is a popular tool for topological data analysis that has found applications across diverse areas of research. It provides a rigorous method to compute robust topological features in discrete experimental observations that often contain various sources of uncertainties. Although powerful in theory, PH suffers from high computation cost that precludes its application to large data sets. Additionally, most analyses using PH are limited to computing the existence of nontrivial features. Precise localization of these features is not generally attempted because, by definition, localized representations are not unique and because of even higher computation cost. Such a precise location is a sine qua non for determining functional significance, especially in biological applications. Here, we provide a strategy and algorithms to compute tight representative boundaries around nontrivial robust features in large data sets. To showcase the efficiency of our algorithms and the precision of computed boundaries, we analyze the human genome and protein crystal structures. In the human genome, we found a surprising effect of the impairment of chromatin loop formation on loops through chromosome 13 and the sex chromosomes. We also found loops with long-range interactions between functionally related genes. In protein homologs with significantly different topology, we found voids attributable to ligand-interaction, mutation, and differences between species.

Utilizing Provocative Maneuvers Intraoperatively in Conjunction With IVUS to Diagnose vTOS: The New Gold Standard.

Current methodologies of diagnosing and managing venous thoracic outlet syndrome (vTOS) remain controversial, as pertinent studies using modern advancements in medicine are limited. We present a case in which we innovatively used a modified Wright's test during venography coupled with intravascular ultrasound, which allowed us to definitively determine the etiology of a vTOS. (Level of Difficulty: Intermediate.).

Physiological insights into electrodiffusive maintenance of gastric mucus through sensitivity analysis and simulations.

It is generally accepted that the gastric mucosa and adjacent mucus layer are critical in the maintenance of a pH gradient from stomach lumen to stomach wall, protecting the mucosa from the acidic environment of the lumen and preventing auto-digestion of the epithelial layer. No conclusive study has shown precisely which physical, chemical, and regulatory mechanisms are responsible for maintaining this gradient. However, experimental work and modeling efforts have suggested that concentration dependent ion-exchange at the epithelial wall, together with hydrogen ion/mucus network binding, may produce the enormous pH gradients seen in vivo. As of yet, there has been no exhaustive study of how sensitive these modeling results are with respect to variation in model parameters, nor how sensitive such a regulatory mechanism may be to variation in physical/biological parameters. In this work, we perform sensitivity analysis (using Sobol' Indices) on a previously reported model of gastric pH gradient maintenance. We quantify the sensitivity of mucosal wall pH (as a proxy for epithelial health) to variations in biologically relevant parameters and illustrate how variations in these parameters affects the distribution of the measured pH values. In all parameter regimes, we see that the rate of cation/hydrogen exchange at the epithelial wall is the dominant parameter/effect with regards to variation in mucosal pH. By careful sensitivity analysis, we also investigate two different regimes representing high and low hydrogen secretion with different physiological interpretations. By complementing mechanistic modeling and biological hypotheses testing with parametric sensitivity analysis we are able to conclude which biological processes must be tightly regulated in order to robustly maintain the pH values necessary for healthy function of the stomach.

Single-Session Treatment of Upper Extremity Deep Venous Thrombosis and Central Venous Catheter Malfunction Using the ClotTriever System.

Intravenous catheters account for the majority of cases of upper extremity deep vein thrombosis (UEDVT), with a higher incidence in patients suffering from malignancy. Sequelae of UEDVT are similar to that of lower extremity DVT, comprising post-thrombotic syndrome and pulmonary embolism. While there are several treatment options for UEDVT including systemic anticoagulation, catheter-directed thrombolysis, and percutaneous mechanical thrombectomy, due to the absence of consistent guidelines regarding its management, treatment is often individualized based on patient characteristics, clinical factors, and technical considerations. We present a case of a 49-year-old female suffering from breast cancer with a central venous catheter (CVC) who came to the clinic with UEDVT and CVC malfunction and was successfully treated with mechanical thrombectomy using the ClotTriever System (Inari Medical, Irvine, CA). To our knowledge, this is the first report of the ClotTriever System being used to treat UEDVT and simultaneously salvage the CVC in a single session.

Growth Dynamics and Survival of Liberibacter crescens BT-1, an Important Model Organism for the Citrus Huanglongbing Pathogen "Candidatus Liberibacter asiaticus".

Liberibacter crescens is the only cultured member of its genus, which includes the devastating plant pathogen "Candidatus Liberibacter asiaticus," associated with citrus greening/Huanglongbing (HLB). L. crescens has a larger genome and greater metabolic flexibility than "Ca Liberibacter asiaticus" and the other uncultured plant-pathogenic Liberibacter species, and it is currently the best model organism available for these pathogens. L. crescens grows slowly and dies rapidly under current culture protocols and this extreme fastidiousness makes it challenging to study. We have determined that a major cause of rapid death of L. crescens in batch culture is its alkalinization of the medium (to pH 8.5 by the end of logarithmic phase). The majority of this alkalinization is due to consumption of alpha-ketoglutaric acid as its primary carbon source, with a smaller proportion of the pH rise due to NH3 production. Controlling the pH rise with higher buffering capacity and lower starting pH improved recoverability of cells from 10-day cultures by >1,000-fold. We have also performed a detailed analysis of L. crescens growth with total cell numbers calibrated to the optical density and the percentage of live and recoverable bacteria determined over 10-day time courses. We modified L. crescens culture conditions to greatly enhance survival and increase maximum culture density. The similarities between L. crescens and the pathogenic liberibacters make this work relevant to efforts to culture the latter organisms. Our results also suggest that growth-dependent pH alteration that overcomes medium buffering should always be considered when growing fastidious bacteria.IMPORTANCELiberibacter crescens is a bacterium that is closely related to plant pathogens that have caused billions of dollars in crop losses in recent years. Particularly devastating are citrus losses due to citrus greening disease, also known as Huanglongbing, which is caused by "Candidatus Liberibacter asiaticus" and carried by the Asian citrus psyllid. L. crescens is the only close relative of "Ca Liberibacter asiaticus" that can currently be grown in culture, and it therefore serves as an important model organism for the growth, genetic manipulation, and biological control of the pathogenic species. Here, we show that one of the greatest limitations to L. crescens growth is the sharp increase in alkaline conditions it produces as a consequence of consumption of its preferred nutrient source. In addition to new information about L. crescens growth and metabolism, we provide new guidelines for culture conditions that improve the survival and yield of L. crescens.

Where to look and how to look: Combining global sensitivity analysis with fast/slow analysis to study multi-timescale oscillations.

Parameterized systems of nonlinear ordinary differential equations, the type of system that is often used in mathematical models for biological systems, can be of sufficient complexity that it can take years to appreciate the full range of behaviors that can be produced. Global sensitivity analysis is one tool that has been developed for determining which parameters have the largest impact on the behavior of the model. Thus, it provides the user with a tool to know where to look in parameter space for important changes in behavior. However, it says nothing about the underlying mechanism mediating a change in behavior. For this, other tools exist. If the system dynamics occur over multiple highly-separated time scales then one useful analysis tool is fast/slow geometric analysis, also known as geometric singular perturbation analysis. This is based on bifurcation analysis of a fast or slow subsystem, and can shed light on the influence that a parameter has on structures of either subsystem, and thus on the system dynamics. Hence, once one knows where to look in parameter space for interesting behavior, this technique describes how to look at the system to extract information about how parameter changes influence the behavior of the system. In this study, we combine the two techniques in the analysis of bursting behavior in a model of insulin-secreting pancreatic ß-cells, with the goal of determining the key parameters setting the period of the bursting oscillations, and understanding why they are so influential. This can be viewed as a case study for combining mathematical techniques to build on the strengths of each and thereby achieve a better understanding of what most influences the range of model behaviors and how this influence is brought about.

A framework for model analysis across multiple experiment regimes: Investigating effects of zinc on Xylella fastidiosa as a case study.

Mathematical models are ubiquitous in analyzing dynamical biological systems. However, it might not be possible to explicitly account for the various sources of uncertainties in the model and the data if there is limited experimental data and information about the biological processes. The presence of uncertainty introduces problems with identifiability of the parameters of the model and determining appropriate regions to explore with respect to sensitivity and estimates of parameter values. Since the model analysis is likely dependent on the numerical estimates of the parameters, parameter identifiability should be addressed beforehand to capture biologically relevant parameter space. Here, we propose a framework which uses data from different experiment regimes to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. Along with building confidence in the parameter estimates, it provides us with variations in the parameters due to changes in the experimental conditions. To determine significance of these variations, we conduct global sensitivity analysis, allowing us to make testable hypothesis for effects of changes in the experimental conditions on the biological system. As a case study, we develop a model for growth dynamics and biofilm formation of a bacterial plant pathogen, and use our framework to identify possible effects of zinc on the bacterial populations in different metabolic states. The framework reveals underlying issues with parameter identifiability and identifies a suitable region in the parameter space, sensitivity analysis over which informs us about the parameters that might be affected by addition of zinc. Moreover, these parameters prove to be identifiable in this region.

A mathematical model for the determination of mouse excisional wound healing parameters from photographic data.

We present a mathematical model to quantify parameters of mouse excisional wound healing from photographic data. The equation is a piecewise linear function in log scale that includes key parameters of initial wound radius (R0 ), an initial wound stasis phase (Ti ), and time to wound closure (Tc ); subsequently, these terms permit calculation of a latter active proliferative phase (Tp ), and the healing rate (HR) during this active phase. A daily photographic record of wound healing (utilizing 6 mm diameter splinted excisional wounds) permits the necessary sampling for robust parameter refinement. When implemented with an automated nonlinear fitting routine, the healing parameters are determined in an operator-independent (i.e., unbiased) manner. The model was evaluated using photographic data from a splinted excisional surgical procedure involving several different mouse cohorts. Model fitting demonstrates excellent coefficients of determination (R2 ) in each case. The model, thus, permits quantitation of key parameters of excisional wound healing, from initial wounding through to wound closure, from photographic data.