A FINITE ELEMENT MODEL OF THE SYNTHESIS, DEGRADATION, AND SPATIAL SPREAD OF cAMP

A small number of intracellular signals, including cyclic adenosine monophosphate (cAMP) signals, control virtually all cellular phenomena. However, it remains unclear how information is encoded within these signals. In the last decade several groups have proposed mathematical descriptions of cAMP signals and signaling pathways to better understand how information is relayed within cells. Here, we propose a finite element model based upon a linearized version of the equations that govern the synthesis, degradation, and spatial diffusion of cAMP to estimate agonist-induced changes in cAMP within a cell. A simplified circular cell was used to numerically test the validity of this model. Simulations indicate that cAMP rapidly equilibrates within cells with effective diffusion coefficients of 30 mm 2 =s, that finite element analysis (FEA) approaches will be effective tools in the study of the spatial distribution of cAMP levels in more complex cellular geometries, and that these approaches may allow us to better understand information content of cAMP signals.

[1]  R D Kamm,et al.  Mechanical stress is communicated between different cell types to elicit matrix remodeling , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[2]  L. Laitinen,et al.  Airway morphology: epithelium/basement membrane. , 1994, American journal of respiratory and critical care medicine.

[3]  Wolfgang A Wall,et al.  Structured Tree Impedance Outflow Boundary Conditions for 3D Lung Simulations , 2010, Journal of biomechanical engineering.

[4]  M. Zaccolo,et al.  The Role of Type 4 Phosphodiesterases in Generating Microdomains of cAMP: Large Scale Stochastic Simulations , 2010, PloS one.

[5]  Y. Zhao,et al.  Steady inspiratory flow in a model symmetric bifurcation. , 1994, Journal of biomechanical engineering.

[6]  B. Zhu,et al.  Assessment of cellular mechanisms contributing to cAMP compartmentalization in pulmonary microvascular endothelial cells. , 2012, American journal of physiology. Cell physiology.

[7]  Y Liu,et al.  Modeling the bifurcating flow in an asymmetric human lung airway. , 2003, Journal of biomechanics.

[8]  Eric C Greenwald,et al.  Mechanisms of cyclic AMP compartmentation revealed by computational models , 2014, The Journal of general physiology.

[9]  John B. West,et al.  Pulmonary Pathophysiology: The Essentials , 1982 .

[10]  N. Pride,et al.  Pulmonary Mechanics in Fibrosing Alveolitis , 2015 .

[11]  D. Dantzker,et al.  Flow partitioning in symmetric cascades of branches. , 1981, Journal of applied physiology: respiratory, environmental and exercise physiology.

[12]  M. Kojic.  Stress integration procedures for inelastic material models within the finite element method , 2002 .

[13]  K. Bathe.  Finite Element Procedures , 1995 .

[14]  A. Baker,et al.  Effects of varying inspiratory flow waveform and time in intermittent positive pressure ventilation. II: Various physiological variables. , 1977, British journal of anaesthesia.

[15]  D. Cooper,et al.  A uniform extracellular stimulus triggers distinct cAMP signals in different compartments of a simple cell , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Charles Hirsch,et al.  Anatomically based three-dimensional model of airways to simulate flow and particle transport using computational fluid dynamics. , 2005, Journal of applied physiology.

[17]  Manolis Papadrakakis,et al.  A method for the automatic evaluation of the dynamic relaxation parameters , 1981 .

[18]  Clement Kleinstreuer,et al.  Computational analyses of a pressurized metered dose inhaler and a new drug-aerosol targeting methodology. , 2007, Journal of aerosol medicine : the official journal of the International Society for Aerosols in Medicine.

[19]  H. Horinouchi,et al.  Respiratory flow in a realistic tracheostenosis model. , 2003, Journal of biomechanical engineering.

[20]  E. Weibel.  Morphometry of the Human Lung , 1965, Springer Berlin Heidelberg.

[21]  Arne Erik Holdø,et al.  Numerical simulation of respiratory flow patterns within human lung , 2002, Respiratory Physiology & Neurobiology.

[22]  M. Jaafar,et al.  Vibration Analysis of Circular Membrane Model of Alveolar Wall in Examining Ultrasound-induced Lung Hemorrhage , 2013 .

[23]  M J Tobin,et al.  How is mechanical ventilation employed in the intensive care unit? An international utilization review. , 2000, American journal of respiratory and critical care medicine.

[24]  N. Pride,et al.  Pulmonary mechanics in fibrosing alveolitis: the effects of lung shrinkage. , 1977, The American review of respiratory disease.

[25]  J. Turner,et al.  Effects of varying inspiratory flow waveform and time in intermittent positive pressure ventilation: pulmonary oedema. , 1982, British journal of anaesthesia.

[26]  P. Jeffery.  Histological features of the airways in asthma and COPD. , 1992, Respiration; international review of thoracic diseases.

[27]  Albert C. Holt,et al.  Static and Dynamic Pore‐Collapse Relations for Ductile Porous Materials , 1972 .

[28]  Mark L. Wilkins,et al.  Use of artificial viscosity in multidimensional fluid dynamic calculations , 1980 .

[29]  P. A. Taylor,et al.  A Multi-Level Code for Metallurgical Effects in Metal-Forming Processes , 1997 .

[30]  Jin W. Lee,et al.  Dispersion of aerosol bolus during one respiration cycle in a model of lung airways , 2002 .

[31]  R. D. Krieg,et al.  Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model , 1977 .

[32]  Milan Jirásek,et al.  Inelastic Analysis of Structures , 2001 .

[33]  H. Y. Luo,et al.  Particle deposition in obstructed airways. , 2007, Journal of biomechanics.

[34]  Ramana M. Pidaparti,et al.  Inhalation induced stresses and flow characteristics in human airways through fluid-structure interaction analysis , 2008 .

[35]  R. Hyatt,et al.  Static mechanical properties of bronchi in normal excised human lungs. , 1978, Journal of applied physiology: respiratory, environmental and exercise physiology.

[36]  Yael A. Glickman,et al.  Regional distribution of acoustic-based lung vibration as a function of mechanical ventilation mode , 2007, Critical care.

[37]  E. P. Popov,et al.  Accuracy and stability of integration algorithms for elastoplastic constitutive relations , 1985 .

[38]  R. Hill.  The mathematical theory of plasticity , 1950 .

[39]  F. Martinez,et al.  Global strategy for the diagnosis, management, and prevention of chronic obstructive pulmonary disease: GOLD executive summary. , 2007, American journal of respiratory and critical care medicine.

[40]  D Olivieri,et al.  Airways remodeling is a distinctive feature of asthma and is related to severity of disease. , 1997, Chest.

[41]  Werner Riedel,et al.  Numerical assessment for impact strength measurements in concrete materials , 2009 .

[42]  W. Herrmann.  Constitutive Equation for the Dynamic Compaction of Ductile Porous Materials , 1969 .

[43]  J. Parrillo,et al.  Critical Care Medicine: Principles of Diagnosis and Management in the Adult , 2001 .

[44]  M. Conti,et al.  Cellular mechanisms underlying prostaglandin-induced transient cAMP signals near the plasma membrane of HEK-293 cells. , 2007, American journal of physiology. Cell physiology.