| Recently a large number of studies on the photo-transduction mechanism in Drosophila compound eye have been done to reveal how visual signals are processed and encoded. Drosophila compound eye has a large visual angle and depth of field, making the eye very sensitive to moving objects. Partly due to this, the compound eye has long been one of the important objects in bionics research.The visual system of Drosophila is composed of a compound eye, the optic lobe, and some fiber pathways. Each compound eye is composed of～750 small eyes (called ommatidia) with columnar structure. Each ommatidium contains 20 cells, including corneal cells, crystalline cone cells, pigment cells, and eight light-sensitive photoreceptors (referred to as R1-R8) in the central area. These photoreceptors have axons to go and connect to the optic lobe through the optic hole on the bottom of compound eye. Optic lobes include lamina, medulla, lobula plate and lobula. When photons are absorbed by different photoreceptors in neighboring ommatidia, the visual information in different photoreceptors is integrated into one cartridge in the lamina.The eight photoreceptors are arranged in a circle. R1-R6 are in the periphery, and R7 and R8 are in the center. Each photoreceptor has a specific structure called rhabdomere. A rhabdomere consists of 30000 to 50000 microvilli and can respond to photon stimuli. Thus, the membrane of a photoreceptor is divided into the light-sensitive part (rhabdomere) that is responsible for light perception and the light insensitive part (cell body). When a photon is captured by a microvillus, rhodopsin (R) is converted into the active state of the photopigment, metarhodopsin (M). This photo transduction leads to the activation of heterotrimeric G-protein (Gα) by promoting the conversion of guanosine diphosphate (GDP) to guanosine triphosphate (GTP).In turn, GTP leads to activation of phospholipase Cβ (PLCβ), which hydrolyzes the minor phospholipid, phosphatidylinositol 4,5-bisphosphate (PIP) into the soluble inositol 1,4,5-trisphosphate (InsP) and the membrane-bound diacylglycerol (DAG). Subsequently, two classes of light-sensitive channels, TRP that is highly permeable to Ca2+ and TRPL that is a non-selective cation channel, open by a still unknown mechanism. The currents produced by TRP/TPRL channels then provide a stimulus to the light insensitive cell body membrane, activating the ion channels on cell body membrane. By these mechanisms, Drosophila photoreceptors convert optical signals to electrical signals, which are further processed by optic lobes and finally transmitted to the central brain. This pathway makes Drosophila see objects.The conversion of optical signals to electrical signals can be decomposed into four modules:(i) Random photon absorption model, which accounts for the fact that the number of photons absorbed by each microvillus varies across the rhabdomere. The randomness of photon capture is based on Poisson statistics.(ii) Model for the phototransduction cascade in a single microvillus, which produce a series of quantum bumps.(iii) Integration of quantum bumps from 30,000 microvilli into the light-induced current (LIC). (iv) The signals of the macroscopic LIC then drive the last processing stage on the photo-insensitive cell body membrane with voltage-gated ion channels. The first three steps happen in the microvilli, the last one on cell body, and together they convert light signals into electrical signals.As early as 1991, Hardie at University of Cambridge investigated light induced currents in Drosophila photoreceptors. He suggested that there are positive and negative feedbacks mediated by Ca2+ ions, which enter the cell during the light response. His studies showed that Ca2+ plays a key role in photoreceptor function. In 2008, a model with ordinary differential equations was built by Alain Pumir for the description of phototransduction cascade. Alain Pumir used Hill function to describe the nonlinearity of the positive and negative feedbacks mediated by Ca2+ ions. In the following year, Zhuoyi Song at University of Sheffield developed a more detailed biophysical model for Drosophila photoreceptor, which describes both photo-sensitive and photo-insensitive membranes. The photo-sensitive part of the model consists of linear and nonlinear differential equations that describe biochemical reactions involved in the phototransduction cascade. On the other hand, the photo-insensitive membrane is represented by an electrical circuit model based on Hodgkin-Huxley formalism of ionic activities.In all the related studies, few examined the three steps from photon transduction to membrane potential, probably because considerable details about ion channels on the membrane of cell body remain unclear. While Zhuoyi Song’s model handled both photo-sensitive and photo-insensitive membranes of the photoreceptor, details on whether and how he used the Hodgkin-Huxley equations to describe ionic channels were very limited. Moreover, an explicit link between the photo-sensitive and photo-insensitive parts is absent. Upon previous works, we have developed a new biophysical model for light transduction in Drosophila photoreceptor, which combines activities in the microvilli and on the membrane of cell body. To our knowledge, this is one of the few models that cover photoreceptor’s response to light in microvilli and on cell body. While this succinct model is far from all-inclusive, it can reasonably reproduce the key features of phototransduction at the subcellular and cellular levels. The generation of experimentally observed changes of membrane potential suggests that the absence of some ion channels with relatively minor roles on the cell membrane does not ominously impair the validity and usefulness of this model.The model was developed aiming further to examine how multiple cells encode light signals via gap junction and neural superposition, and further, to examine proposed theoretical models of motion detection. Using this model, we have tried to reach a better understanding of the phototransduction mechanism in Drosophila photoreceptor.Firstly, we analyzed the exchange of molecules and currents between the microvilli and cell body. When the photoreceptor is in a resting state, the absorption of a photon in a microvillus triggers a serious of biochemical reactions that finally open the TRP and TRPL channels. Opened TRP and TRPL channels cause a positive feedback of Ca2+ influx into the microvillus. On the one hand, the increased Ca2+ in the microvillus causes its diffusion into the cell body; on the other hand the TRP and TRPL currents stimulate cell body to depolarize membrane potential. Quantum bump is the averaged current generated by each TRP channel, and the sum of all bumps is LIC. LIC stimulates cell body membrane to depolarize membrane potential. Via voltage-dependent gating mechanisms, LIC activates more voltage-gated ion channels on the membrane of cell body. It is notable that Ca2+ influx during a quantum bump causes a 1000-fold transient increase of internal concentration of Ca2+ in a microvillus, which drives a sequential positive and negative feedbacks determining the shape and size of the quantum bump. The threshold for positive feedback is lower than that for negative feedback, so that initial elevation of Ca2+ facilitates opening of more TRP channels and increases the rate of Ca2+ influx. At higher Ca2+ levels, negative feedback drives rapid closing of TRP channels and shut-off of the PLCβ activity, thereby terminating the response.After building the model of phototransduction cascade in microvilli, we selected the main ion currents on cell body membrane upon reported experimental studies to build a simplified model of cell body electrical activities. For instance, it is reported that the light-activated channels are also permeable to Mg2+, with a permeability ratio to Ca2+ of Pca:PMg=5:1,so Mg2+ currents are neglected here. The final cell body model contains four ion currents, which are Ca2+ current, Na+ current, K+ current, and a leakage current. The voltage-gated K+ current is used to represent all K+ currents that repolarize the cell body’s membrane potential. The voltage-gated Na+ and Ca2+ currents depolarize membrane potential.Since Ca2+ is particularly important in both microvilli and cell body, we analyzed the Ca dynamics before building the model. In the microvilli, Ca2+ is computed with four terms:diffuse to the cell body, influx from extra-microvilli space, buffered by calcium buffers, and efflux to extra-microvilli space. As in the microvilli model, Ca2+ in the cell body is also computed with four terms:diffuse from microvilli, influx from extra-cell body space, buffered by some molecules in cell body, and efflux to extra-cell body space by transportations such as Na+/Ca2+ exchanger.Upon integrating the microvilli and cell body model, we obtained a computational model for the whole Drosophila photoreceptor. The model includes 32 equations and 65 parameters. How to set these parameters is a well-recognized difficult issue. We determined these parameters mainly by two methods. One was to analyze the experimental findings, and the other was to use the constraints among related factors. For instance, the external Ca2+ concentration is 103 to 104 order more than the internal Ca2+ concentration in microvilli. After setting initial ranges of parameters, we made considerable effort to adjust parameters to make the model robust and generate outcomes consistent with experimental data. The ordinary differential equations are solved using the fourth-order Runge-Kutta method with adaptive time step in matlab platform.After setting parameters, we examined the validity of the model by making some simulations. Firstly, we simulated the changes of quantum bump and membrane voltage over time upon different light stimulation. The membrane voltage depends on two factors:the quantum bump and the number of microvilli that absorbs the photon, and we assumed that the latter is a constant so as to focus only on the former’s influence on membrane voltage. We found that quantum bump and membrane voltage increase, with the increase of light intensity. Then we simulated the calcium concentration in microvilli and cell body, with results agreeing largely with what were observed in biological experiments. Thirdly, we examined the threshold value of extra-microvilli calcium concentration, which was 0.1 mM, whose changes can positively or negatively regulate the quantum bump. Fourthly, we study the influence of intra-microvilli calcium concentration on quantum bump, the amplitude of quantum bump became smaller as the calcium concentration became larger. Lastly, we plotted all the variables over time.A photoreceptor with microvilli not only transduces light signals into electrical signals, but also, via gap junctions between their axons in the cartridges in the lamina, influences the membrane potential of neighboring photoreceptors, making light signals encoded by electrical activities of a population of cells. Thus, a promising approach to studying the mechanism of Drosophila compound eye is to build model for multiple photoreceptors connected via gap junctions. Simulating photoreceptors’ responses to light in a two or three dimension space will help us get more knowledge about the function of Drosophila compound eye.Traditional experimental studies focus merely on measuring what are observed, lacking means to quantify potential mechanisms. We build a biologically reasonable mathematical model to quantitatively examine experimental observations. This model, which shows considerable reliability and robustness, reveals how calcium plays an important role in the photo transduction process. Our modeling and simulations results provide new information for the understanding of photo-transduction mechanism in Drosophila compound eye. |
PDF Full Text Request