Browsing by Author "Peercy, Bradford E."
Now showing 1 - 13 of 13
Results Per Page
Sort Options
Item Distribution of Chemoattractants in a Heterogeneous Tissue and its Impact on Cell Cluster Migration(2017) Cooley, Jessica; George, Aaron; Mekus, Zachary; Sabo, Victoria; Strzegowski, Morgan; Peercy, Bradford E.; Starz-Gaiano, MichelleCell migration is the process in living organisms by which the body heals and diseases spread, so comprehension of this mechanism is beneficial to understanding its applications. We studied the cluster cell migration in the egg chamber of Drosophila melanogaster, or fruit flies, because it is easy to observe and is relatively simple in that organism. A previous model simulates the cell cluster’s migration using forces to determine movement of many individual cells. We improved and revised this system, creating a geometrically accurate model of the egg chamber and mapping the diffusion of the chemoattractants through that domain using a reaction diffusion system. In addition, the base implementation was updated to more accurately simulate the cell migration process. This model aided us in addressing several uncertainties of cluster cell migration, such as identifying the source and quantity of the chemoattractants, the rate at which they are taken in by other cells in the egg chamber, if at all, and the time needed for them to reach the polar and border cells at the anterior of the chamber that gives the most faithful representation of experimental results.Item Enabling Physiologically Representative Simulations of Pancreatic Beta Cells Imbedded in an Islet(2010) Conde, Sidafa; Lebair, Teresa; Raastad, Christopher; Smith, Virginia; Stern, Kyle; Trott, David; Gobbert, Matthias K.; Peercy, Bradford E.; Sherman, ArthurDiabetes is a collection of diseases marked by high levels of glucose in the blood. The condition results from defects in insulin production or function, which are activities performed by the pancreas. Within the endocrine system of the pancreas lie clusters of cells called islets. Each islet is composed of four different cells, the most prevalent of which being the beta cell. The main function of beta cells is to secrete insulin in response to blood glucose levels. As a result, the behavior of these cells is an issue of ongoing interest in diabetes research. Our research aims to take the next step in implementing the mathematical model governing beta cells by continuing the development of a computational islet. The mechanisms of insulin secretion within beta cells can be modeled with a set of deterministic ordinary differential equations. Considering cell dynamics of a cube of individual heterogeneous cells, the key parameters influencing the time evolution include ionic fluxes, calcium handling, metabolism, and electrical coupling. Capturing sudden changes of cell properties on a millisecond time scale requires the use of a stiff ODE solver. The computational complexity makes the simulation of islet behavior difficult and inefficient without sophisticated software built with careful consideration of robust mathematical numerical techniques. Our research focuses on creating an extensible, efficient, and functional computational beta cell software to aid current and future research in beta cell dynamics. In particular, we adapt existing glycolytic oscillator Matlab code into a numerically robust, modular set of Matlab files. By developing in Matlab, we create code that remains easily modifiable by mathematical biologists for a broad range of future applications. Studies on the cluster tara in the UMBC High Performance Computing Facility demonstrate that simulations up to the desired resolution are now practical. Application simulations of the beta cell islet model led to an unexpected discovery that warrants further study: For certain intermediate values of the coupling strength, a small increase in the number of fast cells acts by first increasing the burst period, before falling into the pattern of reducing the burst period with larger proportions of fast cells again.Item Flipping the switch on the hub cell: Islet desynchronization through cell silencing(PLOS, 2021-04-08) Hogan, Janita P.; Peercy, Bradford E.Pancreatic β cells, responsible for secreting insulin into the bloodstream and maintaining glucose homeostasis, are organized in the islets of Langerhans as clusters of electrically coupled cells. Gap junctions, connecting neighboring cells, coordinate the behavior of the islet, leading to the synchronized oscillations in the intracellular calcium and insulin secretion in healthy islets. Recent experimental work has shown that silencing special hub cells can lead to a disruption in the coordinated behavior, calling into question the democratic paradigm of islet insulin secretion with more or less equal input from each β cell. Islets were shown to have scale-free functional connectivity and a hub cell whose silencing would lead to a loss of functional connectivity and activity in the islet. A mechanistic model representing the electrical and calcium dynamics of β cells during insulin secretion was applied to a network of cells connected by gap junctions to test the hypothesis of hub cells. Functional connectivity networks were built from the simulated calcium traces, with some networks classified as scale-free, confirming experimental results. Potential hub cells were identified using previously defined centrality measures, but silencing them was unable to desynchronize the islet. Instead, switch cells, which were able to turn off the activity of the islet but were not highly functionally connected, were found via systematically silencing each cell in the network.Item Impact of Calcium Store Overload and Electrical Dynamics on Cardiac Myocytes(2015) Alexander, Amanda M.; DeNardo, Erin K.; Frazier III, Eric; McCauley, Michael; Rojina, Nicholas; Coulibaly, Zana; Peercy, Bradford E.; Izu, Leighton T.The heart's main function of pumping blood to the body is a complicated process separated into two major steps. Initially, the heart is relaxed and blood flows freely into the ventricles and atria from the veins, then the atria contracts and pumps more blood to the ventricles. The atria relaxes and the inlet valves between these and the ventricles close, producing the initial thump of the heartbeat, as pressure builds while the ventricles contract. This pressure also forces the outlet valves open, allowing blood to ow into the arteries and aorta. As the ventricles relax, the outlet valves then close, producing the second thump of the heartbeat. Once the atria and ventricles are relaxed, the inlet valves reopen, allowing the compartments to ll with blood again as the process repeats. If the heart's contractile abilities are impaired in any way, the rest of the body cannot perform properly. Despite advances in cardiology research, cardiac arrhythmia remains an influential cause of morbidity and mortality in the United States. Recent advances involve the application of devices, such as pacemakers or de brillators, and the outlook of antiarrhythmic drug therapy up to this point is grim, so it is necessary to understand how some pathological conditions within cardiac myocytes can lead to dysfunction of these cells. Calcium mishandling can play a major role in disruption of overall cardiac function by preventing the ability of the heart muscles to relax between heartbeats and thus impair their pumping blood to the bodyItem Implementing a Numerical Package to Model Collective Cell Migration(2014-01-27) Stonko, David; Starz-Gaiano, Michelle; Peercy, Bradford E.In this article we present our three dimensional mathematical model of collective cell migration and describe the method by which we developed and implemented this package on the High Performance Computing Facility at UMBC. Specifically, we describe our motivation and the results of a new interface to define initial conditions for the three dimensional system, specify implementation constraints and solutions for the HPCF regarding post-processing, and outline several implementation changes that we made in order to achieve improved computation time.Item The Interaction of Calcium and Metabolic Oscillations in Pancreatic β-cells(Illinois State University, 2017) Aronne, Mary; Clapp, Samantha; Jung, Soohwan; Kramer, Abigail; Wang, William; Patwardhan, Janita; Peercy, Bradford E.; Sherman, ArthurDiabetes is a disease characterized by an excessive level of glucose in the bloodstream, which may be a result of improper insulin secretion. Insulin is secreted in a bursting behavior of pancreatic β -cells in islets, which is affected by oscillations of cytosolic calcium concentration. We used the Dual Oscillator Model to explore the role of calcium in calcium oscillation independent and calcium oscillation dependent modes and the synchronization of metabolic oscillations in electrically coupled β -cells. We implemented a synchronization index in order to better measure the synchronization of the β -cells within an islet, and we studied heterogeneous modes of coupled β-cells. We saw that increasing calcium coupling or voltage coupling in heterogeneous cases increases synchronization; however, in certain cases increasing both voltage and calcium coupling causes desynchronization. To better represent an islet, we altered previous code to allow for a greater number of cells to be simulated.Item The Interaction of Calcium and Metabolic Oscillations in Pancreatic β-cells(2016) Aronne, Mary; Clapp, Samantha; Jung, Soohwan; Kramer, Abigail; Wang, William; Patwardhan, Janita; Peercy, Bradford E.; Sherman, ArthurDiabetes is a disease characterized by an excessive level of glucose in the blood-stream, which may be a result of improper insulin secretion. Insulin is secreted in a bursting behavior of pancreatic β-cells in the islets of Langerhans, which is affected by oscillations of cytosolic calcium concentration. We used the Dual Oscillator Model to explore the role of calcium in calcium oscillation independent and calcium oscillation dependent (CaD) modes as well as the synchronization of metabolic oscillations in electrically coupled β-cells. We also implemented a synchronization index in order to better measure the synchronization of the β-cells within an islet. We observed that voltage or calcium coupling result in increased synchronization and are more effective in CaD modes. Furthermore, we studied heterogeneous modes of coupled β-cells, their arrangements in the islets, and their synchronization. We saw that increasing calcium coupling or increasing voltage coupling in heterogeneous cases increases synchronization; however, in certain cases increasing both voltage and calcium coupling causes desynchronization, primarily in voltage. To better represent an entire islet, we altered previous code by further optimizing run-time and memory usage to allow for a greater number of cells to be simulated for a longer period of time.Item Investigating Oscillation Loss in Computational Islets(2013) Gearhart, Gemma; Jiang, Shuai; May, Thomas J.; Pan, Jane; Khuvis, Samuel; Gobbert, Matthias K.; Peercy, Bradford E.; Sherman, ArthurThe study of pancreatic β -cells comprises a crucial part of the study of the group of diseases known as diabetes. These cells exist in groups known as islets of Langerhans and are responsible for storing and producing insulin. They exhibit electrical bursting behavior during insulin production that correlates with the rate at which insulin is secreted into the bloodstream. Coupling is a natural process within islets that enables the cells to communicate with one another and transfer various ions and electrical currents; coupling of both voltage and metabolites can occur. We model multicellular islets using an existing system of seven ordinary differential equations to model beta cell function. We first treat metabolic coupling as independent and look for combinations of coupling strengths, initial conditions, and parameter values that lead to metabolic oscillation loss, which has been observed in previous studies using a two-cell model. We find examples of each of these three features that can cause β -cells to exhibit oscillation loss at particular values. Next, we simulate cells with mutated KATP channels that remain open indefinitely, which have been described in experimental studies but not yet modeled. Simulations run with these mutations reveal the existence of a bursting death threshold, described by the least percentage of cells in the islet that must be mutated for electrical bursts to completely disappear. We determine that this threshold is independent of coupling strengths, cell distribution, and possibly islet dimension; however, we also determined that this threshold is not independent of the glucose influx rate.Item Linkages of Calcium Induced Calcium Release in a Cardiomyocyte Simulated by a System of Seven Coupled Partial Differential EquationsKroiz, Gerson C.; Barajas, Carlos; Gobbert, Matthias K.; Peercy, Bradford E.Cardiac arrhythmias affect millions of adults in the U.S. each year. This irregularity in the beating of the heart is often caused by dysregulation of calcium in cardiomyocytes, the cardiac muscle cell. Cardiomyocytes function through the interplay between electrical excitation, calcium signaling, and mechanical contraction, an overall process known as calcium induced calcium release (CICR). A system of seven coupled non-linear time-dependent partial differential equations (PDEs), which model physiological variables in a cardiac cell, link the processes of cardiomyocytes. Through parameter studies for each component system at a time, we create a set of values for critical parameters that connect the calcium store in the sarcoplasmic reticulum, the effect of electrical excitation, and mechanical contraction in a physiologically reasonable manner. This paper shows the design process of this set of parameters and then shows the possibility to study the influence of a particular problem parameter using the overall model.Item Long-Time Simulation of Calcium Waves in a Heart Cell to Study the Effects of Calcium Release Flux Density and of Coefficients in the Pump and Leak Mechanisms on Self-Organizing Wave Behavior(2009) Coulibaly, Zana; Muscedere, Michael; Gobbert, Matthias K.; Peercy, Bradford E.Spontaneous calcium sparks can lead to propagation of a self-initiated calcium wave under certain conditions in a heart cell. A model for diffusion waves of calcium ions in a heart cell is given by a system of coupled, time-dependent reaction- diffusion equations. The key term of the model quantifies the release of calcium at the calcium release units by a flux density. The model also includes pump and leak mechanisms that model the extruding and entering of calcium throughout the cell, respectively. Previous simulations for this model with extreme values of the flux density demonstrate that no wave will self-organize for a small value and that a wave will self-organize for a large value; in the latter case, it also becomes apparent that the total concentration of calcium throughout the cell grows without bound. This report shows that the original conclusions with respect to wave self-organization are correct qualitatively, and it identifies the range of values of the flux density quantitatively for which we can be confident about the observation. Additionally, a range of values for the parameters of the pump mechanism is studied. We can conclude that the growth of the total calcium concentration is affected by the choice of coefficients, but that, for the parameters studied here, the growth cannot be avoided for the cases in which a wave self-organizes.Item A Spatial Multi-Cellular Model of the Pancreatic Islet including 𝛼-, β -, and 𝛿-cells(2014) Dai, Annie; Palensky, David; Piatski, Alex; Queen, Kendall; Vockeroth, Gina; Lebair, Teresa; Peercy, Bradford E.; Watts, Margaret; Sherman, ArthurOur goal is to create a computational model of an islet of Langerhans, consisting of 𝛼-, β -, and 𝛿-cells. We will focus on varying the geometries and proportions of the cells in this islet, and study the hormonal secretion and reception of each cell at any point in time. We are currently considering basic cubic and spherical models, among others. Besides changing the physical shape of our islet, we will change the sequential ordering of the cell types in our model. We will have three different models (one for each cell type). While β -cells are already electronically wired, 𝛼-cell and 𝛿-cell paracrine interactions depend on a spatial-temporal model. We will use ODEs to model the behavior of these cells. We will use a diffusive PDE equation to model the propagation of the secretions . Out of computational concerns, we will hope to find and assume parameters that would allow us to use an analytical solution to the diffusive PDE. Currently, we are contemplating using the heat kernel to approximate a solution to. However, if such an approximation cannot be realized, we may just end up numerically solving the PDE's despite of the increase in computational complexity. (𝜕u/𝜕t) - Dƍ²u = f(u,t) K(t, x, y) = (1/(4ΠDt)³/²)e⁻⁽ˣ⁻ʸ⁾^²/⁴ᴰᵗ Upon creating a modeling tool, we will be able to model experimental scenarios with similar geometries and proportions to human and mouse islets given in your presentation. We hope to simulate a core and mantle geometry for the mouse model by creating a core of β-cells with an 𝛼 and 𝛿 mantle. We will see which geometries work best for such a simulation. Afterward, we will be prepared to compare our results to experimental data (already done by the NIH). We will also be able to use these models to isolate specif c cell types and compare them to each other at different points in the model, while toggling certain secretions or any system parameter to test if any paracrine interactions tame heterogeneity.Item Spontaneous Calcium Release in Cardiac Myocytes: Store Overload and Electrical Dynamics(Illinois State University, 2015) Alexander, Amanda M.; DeNardo, Erin K.; Frazier III, Eric; McCauley, Michael; Rojina, Nicholas; Coulibaly, Zana; Peercy, Bradford E.; Izu, Leighton T.Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca²⁺) mishandling in cardiac muscle cells. We adapt Izu's et al. mathematical reaction-diffusion model of calcium in cardiac muscle cells, or cardiomyocytes, [14], implemented by Gobbert [12], and analyzed in Coulibaly et al. [8] to include calcium being released from the sarcoplasmic reticulum (SR), the effects of buffers in the SR, particularly calsequestrin, and the effects of Ca²⁺ influx due to voltage across the cell membrane. Based on simulations of the model implemented in parallel using MPI, our findings aligned with known biological models and principles, giving us a thorough understanding of several factors that influence Ca²⁺ dynamics in cardiac myocytes. Speci cally, dynamic calcium store will cap previous calcium blow-up seen in the model. Calcium channels located in spatial opposition of calcium release units produce more predictable intracellular calcium propagation. And we used multi-parametric calcium dynamics tables, which act as a multidimensional bifurcation diagram, to visualize parameter boundaries between different biophysical dynamics.Item Time-stepping techniques to enable the simulation of bursting behavior in a physiologically realistic computational islet(ScienceDirect, 2015-02-14) Khuvis, Samuel; Gobbert, Matthias K.; Peercy, Bradford E.Physiologically realistic simulations of computational islets of beta cells require the long-time solution of several thousands of coupled ordinary differential equations (ODEs), resulting from the combination of several ODEs in each cell and realistic numbers of several hundreds of cells in an islet. For a reliable and accurate solution of complex nonlinear models up to the desired final times on the scale of several bursting periods, an appropriate ODE solver designed for stiff problems is eventually a necessity, since other solvers may not be able to handle the problem or are exceedingly inefficient. But stiff solvers are potentially significantly harder to use, since their algorithms require at least an approximation of the Jacobian matrix. For sophisticated models, systems of several complex ODEs in each cell, it is practically unworkable to differentiate these intricate nonlinear systems analytically and to manually program the resulting Jacobian matrix in computer code. This paper demonstrates that automatic differentiation can be used to obtain code for the Jacobian directly from code for the ODE system, which allows a full accounting for the sophisticated model equations. This technique is also feasible in source-code languages Fortran and C, and the conclusions apply to a wide range of systems of coupled, nonlinear reaction equations. However, when we combine an appropriately supplied Jacobian with slightly modified memory management in the ODE solver, simulations on the realistic scale of one thousand cells in the islet become possible that are several orders of magnitude faster than the original solver in the software Matlab, a language that is particularly user friendly for programming complicated model equations. We use the efficient simulator to analyze electrical bursting and show non-monotonic average burst period between fast and slow cells for increasing coupling strengths. We also find that interestingly, the arrangement of the connected fast and slow heterogeneous cells impacts the peak bursting period monotonically.