| BACKGROUNDOver a long period of time to study biological systems relies mainly on experiments, and even now experiment is still the most important method. However, when biological researches go deeper, especially targeting some quantitative properties at the micro levels, to rely solely on experimental methods is not enough. The rise of computer simulation technology and mathematical modeling have made biological researches enter a new era, allowing researchers to use mathematical models to study biological systems. To apply mathematical modeling to biosystems not only greatly saves the cost of research, but also makes biological studies at the micro-level more feasible.The study of vertebrate and invertebrate visual system has a long history, and has already reached a certain understanding at the macro and micro levels. Due to its regular structural pattern, Drosophila compound eye has been often used as an ideal model for the study of invertebrate visual systems. Drosophila compound eye is composed of about 750 identical hexagonal ommatidia arranged in particular pattern. Different from vertebrate monocular, compound eyes can receive light signals better and have larger visual range, but their resolution is lower. A Drosophila eye is consisted of a’lamina’(ommatidia) and four visual signal processing layers, including lamina, medulla, lobula and lobula plate. Photons are received, and transduced into electrical signals, in the microvillus of the photoreceptors in the ommatidia within lamina. After an electric signal is generated from a light signal, a chain of reactions further amplify the signal through ion channels and transmit it to the synapse of photoreceptor cells. The synaptic release of neurotransmitters, through the synaptic cleft, passes the signal to the unipolar lamina layer neurons (L1, L2), followed by the transmission of the signal from the lamina layer to the neurons the neuron medulla layer, and finally, to the lobula and lobula plate layers for final processing by the brain.The conversion from optical signals to chemical and electric signals is known as light transmission chain and is modulated by a phosphoinositide. The basic processes are as follows:after absorption of photons by the microvillus of the photoreceptor cells, the ground state of rhodopsin (R) is converted into active state metarrhodopsin (M*); M* in turn activates G protein in the cell membrane to generate G*; G* further activates PLC. PLC then hydrolyzes PIP2 to generate IP3 and DAG, the latter is involved in the activation of the two calcium-dependent channels, TRP and TRP1. After the calcium channels open, calcium ions begin to flow into the microvillus and generate ion current (known as photo-induced current). Photo-induced current can activate various ion channels on the cell membrane, producing ion currents and depolarizing transmembrane voltage.Depolarized membrane voltage at the synapse of photoreceptor cell leads to the activation of calcium channels on the plasma membrane of the area and the release of histamine as the neurotransmitter that stimulates the histamine-dependent chloride channels within the postsynaptic monopolar neurons, causing monopolar neurons excited. This process finishes the signal transmission between the photoreceptor cells and the monopolar neurons.Currently, the basic structure of the Drosophila compound eye, as well as the mechanism of optical signal processing, has been largely understood. Most of the important molecules involved in this process are already identified. These allow establishment of a quantitative model to describe details and dynamics of the chain of actions.OBJECTIVES AND SIGNIFICANCEAs a common model used for studying invertebrates visual system, Drosophila compound eye, with its basic structure and the phototransduction mechanism has been well understood. Since experimental methods, usually adopted by researchers, have some limitations, it is hard for studies to go deeper into the micro levels. It is especially so for studies of the nervous system. Fly visual system finally passes signals to the brain for a final processing and for receiving feedbacks; it is difficult to study the signal transmission and feedback system via experiments.This thesis has the following three purposes:1. To identify the mechanism for a model to examine the concentration of intracellular calcium regulation.2. To build a model describing histamine release, aiming to reveal the roles of calcium ions from different sources in promoting histamine release.3. To examine histamine inhibition by calcium ion in the model.By building a model describing the calcium ion and histamine release on photoreceptor synapse, we expect to reveal the roles of intracellular calcium ions from various sources in histamine release, and to reveal the major role of histamine inhibition by calcium influx through cacophony. Our study shows that the entire process of optical signal transduction in Drosophila photoreceptor can studied using mathematical models. As a neurotransmitter between photoreceptor and lamina neurons, histamine laid the foundation for the histamine-dependent activation of chloride channels on lamina neurons (L1, L2) and for the feedback of L1, L2 neurons to photoreceptor.METHODSThe methods contain the following five aspects:Simplify the system:Many molecules are involved in the process of visual signal transduction, to make the model reasonably simplified we just selected the key molecules. The simplified model consists of the following components:(1) depolarized membrane voltage firstly caused the voltage-gated calcium channels on plasma membrane open, leading to the calcium influx and the generation of IP3. (2) IP3 is then immediately transferred into the endoplasmic reticulum membrane (ER), where it binds to its receptor, IP3R, promoting calcium release into the cytoplasm from the endoplasmic reticulum. (3) When the endoplasmic reticulum calcium concentration is below a certain threshold, the calcium influx factor (CIF) on endoplasmic reticulum membrane spreads quickly to the plasma membrane; CIF then activates the SOC (store-operated calcium channel) on plasma membrane and calcium influx through these channels. Meanwhile, the intracellular calcium flows into endoplasmic reticulum through SERCA on endoplasmic reticulum membrane and out to extracellular space via PMC A on plasma membrane. (4) Finally, calcium ions, released from endoplasmic reticulum and from the influx through membrane channels, work together to induce the histamine release on plasma membrane.Describing nonlinearity:Many molecular interactions cannot be mathema-tically described linearly, such as the dependence of histamine release on calcium ions. In equations of the model we use Hill functions to describe non-linear relationship between molecular interactions.Numerical solution:MATLAB provides convenient functions for numerically solve differential equations. In addition to using built-in functions such as ode23, ode45, we also use MATLAB to implement the Range Kutta algorithm with variable time-steps.Parameter estimation:For mathematical modeling parameter estimation is very critical aspect that directly affects the quality of a model. For biological models, the parameters should match the physiological characteristics of biological systems, and should be based on biological experimental data. We estimate and adjust parameters in the model to enable the model be able to simulate the expected results. To evaluate the impact of a parameter or variable on the overall system, we also compare variable responses of the model under different conditions.System simulation:Using MATLAB software to compile and simulate the model, observation the dynamic characteristics of each variable in system. By comparing the variable response characteristics under different conditions reveal the role of a parameter or variable in the overall system, such as by comparing the calcium concentration dynamic changes in cases of presence or absence of the endoplasmic reticulum calcium release, it can be obtained that the endoplasmic reticulum calcium release is also involved in promoting the release of histamine.RESULTSBy modeling and simulation this study produces the following results; together they reveal that the calcium from different sources work together to promote the release of histamine.1. Calcium ions in photoreceptor synapse induce the release of histamine on the plasma membrane. The main sources of intracellular calcium are the calcium influx through cacophony, the calcium release of endoplasmic reticulum and the calcium influx through SOC. All of them are responsible for histamine release.2. The histamines released into the synaptic cleft inhibit calcium influx, and the inhibitory effect may be mainly on the inhibition of cacophony calcium influx.3. The various calcium sources promote endoplasmic reticulum calcium release, and endoplasmic reticulum calcium release further induced calcium influx through the SOC. |
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