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Drosophila melanogaster is one of the most widely studied organisms in the world, yet its electrophysiology has yet to be documented in detail. My simulations will model components of the motor circuitry of Drosophila, addressing this gap in information. Parameters for Hodgkin-Huxley type differential equations were derived from voltage-clamp data of previously characterized ionic membrane currents from these neurons. These parameters and the equations were written into computer code. A specialized program called XPP read this code and simulated the spiking activity of the neuron. Once this model neuron has been fully constructed with multiple currents, we will be able to study how motor neurons work and generate the crawling behavior through computational experiments. Such a model will likely be useful in a variety of future experiments involving Drosophila. As work on the model neuron continues, it will be tested against voltage clamp and current clamp recordings to ensure a realistic model.
There is a long history of measuring crawling in Drosophila larvae but little is known about the mechanisms that control the crawling. Locomotion is a process that is controlled by an output of the central nervous system. A cluster of neurons have been identified in the third instar larvae CNS of Drosophila that controls locomotion [1]. This model neuron will further our understanding of coordinated nervous system function.
The balance of currents in a cell directs the firing properties of the neuron. The Drosophila motor neuron has many membrane currents including sodium, potassium, and calcium channels [3]. These membranes are expressed in terms of equivalent circuits. Equation 1 describes the current of a sodium channel. G stands for the maximal conductance (mS/cm2), m and h represent the 3 activation and 1 inactivation gates probability of being open or closed [2]. (V-ENa) is the sodium driving force, while ENa is the equilibrium potential for sodium[2]. Equations 2 and 3 are first-order differential equations describing the activation gates (m) and the inactivation gate (h) [2]. The first voltage-dependent variable is the steady-state activation and inactivation curve. The second variable is the corresponding time constant. To construct a model of the neuron we reproduced voltage-clamp data from the literature in order to calculate steady-state and time constant graphs. In order to obtain the parameters for these graphs, a MATLAB optimization program was utilized. Once parameters and equations were obtained, XPP (neural simulation program) can replicate the spiking activity of a neuron according to the input code. The complete model neuron with all known membrane currents can then be tested under simulated current clamp conditions and hand-tuned to reproduce current clamp data obtained from collaborators.
Figure 1 (picoamperes vs. milliseconds)
This figure illustrates the best fit that MATLAB could produce for the available sodium current voltage-clamp data. The parameters for the Boltzmann and Gaussian functions that produce this numerical fit are shown in table 1.
Table 1
The parameters in Table 1 are used to calculate the voltage-dependent functions, equations 4 and 5.
Figure 2[2]
Steady-state activation and inactivation functions and voltage-dependent time constants in an example Hodgkin-Huxley Model
Figure 3
This is an example of the output from XPP using the values derived from Figure 2. This figure shows an influx of sodium into the cell causing a spike in membrane voltage. The flow of potassium out of the cell returns the cell to a lower voltage. A leak current normalizes the voltage to the resting value.
Building a model of the Drosophila larval crawl motor neuron entails many aspects. The MATLAB optimization program was limited in finding an accurate fit. Reliance on published data results in possible voltage-clamp errors during data collection. However, once data is obtained for all known currents existing in the motor neuron, an accurate model can be built. The accuracy can be tested against existing current-clamp data to see if similar results are produced. Our collaborators have many interests in the research. A model neuron would help address what causes the delays in responses of different types of motor neurons in the fly larva and be useful for studies of the after-hyperpolarization caused by ion pumps in motor neurons. In addition, it could be used determine the contribution of different Na channel splice variants to spiking.
This material is based upon work supported by the Howard Hughes Medical Institute under Grant No.52005873. We would also like to thank our collaborators at the Griffiths Lab at Brandies University and the Baines Lab at University of Oxford.
-Choi JC, Park D, Griffith LC (2004) Electrophysiological and morphological characterization of identified motor neurons in the Drosophila third instar larva central nervous system, J Neurophysiol 91(5):2353-2365.
-Izhikevich, E.M. (2007). Dynamical systems in neuroscience. MIT Press.
-Saitu M, Wu C-F (1991) Expression of ion channels and mutational effects in giant Drosophila neurons differentiated from cell division-arrested embryonic neuroblasts, J Neurosci11(7): 2135-2150
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