Channel Model of Second Messenger Mediated Transformation of Gaba Induced Currents

Hermissenda crassicornis exhibits Pavlovian conditioning in response to repeated presentations of paired light and turbulence stimuli. The behavioral changes are correlated with a change in electrical properties of the B photoreceptor cell. In response to turbulence, the hair cell releases GABA onto the terminal branches of the B cell. After repeated stimulation of the B cell using a light flash paired with GABA, the net GABA induced currents change from inhibitory to excitatory. To investigate the mechanisms underlying the change in GABA induced currents from net inhibitory to net excitatory, channel models of the GABA induced currents are developed. The similarity of measured and modeled currents supports the hypothesis that the transformation of GABA currents depends on second messenger mediated events such as phosphorylation. INTRODUCTION Classical conditioning of Hermissenda crassicornis with paired light and turbulence causes behavioral changes characteristic of classical conditioning in mammals. The behavioral changes are correlated with a decrease in potassium channel conductance of the B photoreceptor cell [1], the site of convergence of the light evoked neural signal and the turbulence evoked neural signal. A model of the voltage dependent and light induced currents has been developed [3,7]. To develop a complete model of the biophysics of the B cell, in order to investigate the role of various currents and current interactions in producing such aspects of classical conditioning as stimulus specificity and ISI, a model of the turbulence induced currents is required. In response to turbulence, the hair cell releases GABA onto the terminal branches of GABA RA œ GABA R A œ GABA RA GABA RB œ GABA R B the B cell. After repeated stimulation of the B cell using a light flash paired with GABA, the net GABA induced currents change from inhibitory to excitatory [2]. The GABA induced currents, measured under voltage clamp, are composed of an outward chloride current, and a biphasic potassium current whose temporal characteristics are suggestive of an early outward ionotropic current and a late, apparent inward, metabotropic current. After repeated pairings, the magnitude of both the chloride current and the early outward potassium current are much reduced, and the late inward potassium current is enhanced. Elevation of intracellular calcium concentration in response to GABA stimulation is prolonged following paired stimulation, suggesting that calcium mediated second messengers are involved in the transformation. To investigate the mechanisms underlying the change in GABA induced currents from net inhibitory to net excitatory, channel models of the GABA induced currents are developed. METHODS The Hodgkin-Huxley formalism was used to develop models of three GABA induced currents: (1) a GABA chloride current, (2) a GABA ionotropic potassium current, A B and (3) a GABA metabotropic potassium current. B A three state kinetic model describes the GABA chloride current [6]: A where R is the unbound state, GABA-R is the bound and conducting state, and A A * GABA-R is the bound and inactive state. The rate constants are voltage dependent. A The decreased affinity of the receptor for GABA, presumably by calcium activated phosphorylation of the receptor, is modeled as a decrease in the rate constants and . A two state kinetic model describes the GABA ionotropic K current: B where R is the unbound state, and GABA-R is the bound and conducting state. The B B * rate constants are voltage dependent, and the solution of the first order differential equation that describes the kinetic model shows that the steady state value and time constant depend on GABA concentration. The decreased affinity of the receptor for GABA, presumably by calcium activated phosphorylation of the receptor, is modeled as a decrease in the rate constant . M(t) Aexp (t t0) 2 2)2 hss 1 M(t) The later inward GABA metabotropic potassium current is actually the reduction of B an outward potassium current below its steady state value, caused by calcium or a calcium activated second messenger. This mechanism is similar to the previously described calcium mediated reduction in steady state potassium current in the B cell soma [1, 7]. Thus, the metabotropic potassium current is described with a two-state kinetic model whose rate constants are dependent on the concentration of calcium dependent second messenger. Second messenger concentration increases consequent to the release of calcium from intracellular stores caused by GABA binding to the metabotropic receptor. Rather than attempting to model the entire chemical cascade, whose details are unknown, the second messenger concentration is modeled as a Gaussian: where t is the time at which the second messenger concentration peaks, A is the peak o value, and ) controls the rate of increase and decrease. Steady state inactivation is a function of the second messenger concentration: The steady state value and time constant of inactivation, as well as steady state activation, are voltage dependent. The effect of paired stimulation on the metabotropic GABA potassium current is modeled as an increase in the parameters A, t , and ) in o the equation for second messenger concentration. This change in second messenger concentration is based on the measurements showing a prolonged elevation of intracellular calcium concentration, consequent to paired stimulation [2, 4]. The biochemical rate equations are described with differential equations which were programmed in GENESIS [9] and solved numerically. Results of computer simulations under voltage clamp and current clamp conditions were compared to the biophysically measured currents and voltage responses, respectively. In the simulations, GABA concentration is modeled as a step increase and then a linear decrease. RESULTS The total GABA current is equal to the sum of ionotropic and metabotropic potassium B currents. Figure 1 shows the similarity between the measured and modeled GABA induced potassium currents. Figure 1a illustrates the measured GABA induced potassium current for voltage clamp of -90, -70, -50 and -30 mV from Alkon et al.[2]. Figure 1b illustrates the modeled GABA induced potassium current under the same