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Time-dependent model to mimic acetylcholine induced vasodilatation in arterial smooth muscle cells

Computational approaches for spatial modeling of dynamics of the intercellular distribution of molecules can parse, simplify, classify and organize the spatiotemporal richness of any biochemical pathway and demonstrate its impact on the cells function by simply coupling it with the downstream effecters. One such online system biology modeling package is Virtual cell that provides a unique open source software and it’s used for making mathematical models to simulate the cytoplasmic control of molecule that interact to produce certain cellular behavior. In our present study, a spatial model for time dependent acetylcholine induced relaxation of vascular endothelial cells lining the lumen of blood vessel that regulate the contractility of the arteries was generated. The time-dependent action of neurotransmitter acetylcholine for total time period for 1 second was studied on the endothelial cell at an interval of every 0.05 seconds. Such time simulated spatial models may be useful for testing and developing new hypotheses, interpretation of results and understand the dynamic behavior of cells.


INTRODUCTION
The development of computational approaches for modeling and understanding the time dependent dynamics of any intracellular physiologies are of profound interest for researchers [1]. In this field a widely used systems biology and computational simulation, software package is Virtual Cell (VCell: http://www.nrcam.uchc.edu/). It is used to model the intracellular biological pathways and understanding the downstream effects of biochemical reactions that impact the overall cellular function in a time-course manner [2].
Virtual Cell has a unique computational environment for modeling and simulation of a cell and has applications in a wide range of scientific disciplines ranging from experimental cell biology to theoretical biophysics. The models can be based on experimental data and/or purely theoretical assumptions The biological or mathematical models created can be either simple or complex multilayered and may be used in interpreting experimental data or probing the predicted behavior of complex.
The human physiology has a well developed and coordinated system of doing the same process within a time scale of few milliseconds with the help of the release of neurotransmitter Ach. The endothelial cells contain a Go protein-coupled receptor (GPCR) that binds this Ach and activates its associated effectors Phospholipase C which has one of its associated secondary messenger as inositol trisphosphate (IP3). IP3 mediates the opening of the IP3 gated Ca2+ channels in the endoplasmic reticulum with subsequent rise of the cytosolic Ca2+ concentration which forms a complex with Calmodulin. This Ca2+/calmodulin further activate the isoenzyme eNOS (endothelial NO Synthase) which then converts L-Arginine (Arg) and Oxygen (O2) to citruline and nitric oxide. The diffusion of NO through the non-striated smooth muscle cells found within the walls of blood vessels causes contraction of muscle fibers resulting in a more relaxed state of conformation leading to relaxation of the muscle cells i.e. vasodilatation [6-10] [ Fig. 1].  Therapeutically nitroglycerin has been widely used for treating intense chest pain of angina as it is known to slowly decomposes in the body to Nitric Oxide (NO), thereby being able to mimic the natural pathway of vasodilatation [6,7].
In the present work, acetylcholine induced vasodilatation of the smooth muscle cell that surrounds the blood vessels which feed the heart muscle itself [3-5, 8] has been studied using an insilico approach.

MATERIAL AND METHODS
Signaling events are initiated on the plane of the membrane which is further propagated through the volumes of the cytosol and multiple intracellular compartments dictated in terms of the cellular pathway [11]. Spatial, mathematical modeling and simulation in these situations is an important component to understand the behavior of signaling of the cell and further decode the information of the physiological working of the cell. Web-based VCell modeling environment was used in the present study to build a spatial model for modeling Ach induced arterial smooth muscle relaxation.
Virtual Cell is a web based application in which compartmental topology, geometry, molecular characteristics, and relevant interaction parameters can be used defined. The VCell then automatically forms a corresponding mathematical system of ordinary and/or partial differential equations from the given biological description.
The following workflow was used to address the various parameters that are involved in the process of model building:

(i) Physiology Building and Defining the chemical and physiological input parameter of the model:
In the navigation tree, physiology icon was selected and it was used to specify structure diagram in the main workspace i.e. to add compartments and membranes in the model being generated. The compartments and membranes were then populated with molecular species and thereafter reactions or fluxes were then created in the reaction diagram tab [ Fig. 2] or the table view [ Fig. 3]. The reaction kinetic tab for the initial reacting species was selected to mass action and the expression was given as (Kf.Ach-Kr.Ach_GPCR) with the units (molecules/µm2s). The rate constant for forward reaction (Kf) was chosen as 10.0 µm2s and reverse rate constant (Kr) as 0.1 µm2s [13]. Other reacting species were also studied under the condition of mass action. (ii) Simulation studies and geometry definition: Virtual Cell was then used to create the simulation models using its graphical user interface. After building the physiological model its various components were mapped to the geometric domains of cell structures given in VCell [Fig. 4]. The input parameters of the model were specified and the mathematical description of the model was automatically generated by the software in the form of differential equations, which were accessed using the menu tab of MathModels. The geometry was defined with the line tool and was followed by specifying the initial concentration of Ach as 10 µm as reported by Taylor et al. [13] [ Fig. 5], thus completing the steps of structure mapping.

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ILNS Volume 52 Once structure mapping was completed, a model to study the time-dependent action of neurotransmitter Ach for 1 second on the endothelial cell at time intervals of every 0.05 seconds was generated.

RESULTS AND DISCUSSION
A time simulated spatial model can be used as an exceptional tool for testing and developing new hypotheses and interpret their results. Another benefit of the time simulated spatial modeling is that it can help to extract quantitative information from the dynamic behavior of the cell [1, 14].
Virtual cell is a novel platform to emulates real life process and perform virtual experiments that. In the present work, VCell was used to construct and study the time dependent variation in the concentration of various species of molecules (namely Ach, GPCR, phospholipase C and NO) that are involved in Ach induced vasodilatation of endothelial muscle cells [8][9]12].
The initial concentration of Ach was taken as 10.0 µM [13] and the reaction model used was mass action kinetic type reaction, to study time dependent changes in the concentration of Ach on a single endothelial muscle cells, as VCell studies a single cell at a time. In the entire muscle segment having large number of cells, the secreted 10.0 µM concentration of Ach would have an exponential effect.
Acetylcholine that was secreted in the cells exterior binds to the GPCR present on the cell membrane resulting in the decrease in concentration on Ach [ Fig. 6A] and increase in Ach bound to GPCR [ Fig. 6B] and Table 1.

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The difference of slopes of the time plot was due to the fact that the concentration of ACh in the cellular exterior changes slowly [ Fig.6A] as compared to the binding of the ACh to the GPCR receptor [ Fig.6B] which was given for only one cell in the VCell model. # ACh bound to GPCR on one cell studied in the model generated using VCell Binding of Ach to GPCR initiates the signal transduction and its downstream effect is the activation of the membrane component Phospholipase C, which starts a chain of reaction in the cytoplasm of the endothelial cell ultimately leading to the production NO. Nitric oxide has a very short half life of around 2 to 20 seconds [12,[15][16] and it quickly diffuses through the endothelial cells adhering to Fick's law of diffusion, into the neighboring smooth muscle cells where it triggers the actual muscle relaxation [7][8][9]. The change in concentration of NO in the extracellular medium was seen in Fig. 7A while in Fig.7B the increase in concentration of NO in a single cell as it enters into it, was observed.

ILNS Volume 52
In the present work, a biological model was generated to study the spatial distribution and time-dependant change in concentration of the various species reported to be involved in vasodilatation [8][9]12] using VCell. The model generated for Ach induced vasodilatation helps us to understand the time-dependence of the secretion of Ach, the process of vasodilatation and regulation of contractibility of the blood vessel supplying the cardiac muscles. Such models can greatly help us in understanding biological systems using a systems biology approach [17].

CONCLUSION
Therefore from the results we have been able to ellucidate the time-dependance of various biochemical parameters involved in Ach induced vasoilation and their spacial distribution in different compartments of arterial smooth muscle cells.   International Letters of Natural Sciences Vol. 52