Llation and return to rest within a handful of cycles. Nonetheless, if the pulse is big enough, the network will display sustained oscillation. Normally, the sustained oscillation will be either spindle or delta wave depending on the parameter setting with the network. This indicates that there exit a steady equilibrium point corresponding for the resting state in addition to a stable limit cycle corresponding to spindle or spikeandwave oscillation. Fig. shows the phase flows of spindle and spikeandwave oscillations in the twodimensiol subspace. The spindle oscillation is obtained from a second simulation with all the parameters corresponding for the handle condition. The spikeandwave 
oscillation is obtained with the identical set of parameters except that the conductance of GABAA receptors in cerebral cortex is set to become. The phase flows in Fig. B and Fig. D demonstrate the limit cycles corresponding to spindle and SW oscillations, respectively. To demonstrate the transition from spindle to 
spikeandwave, we use the conductance of GABAA receptors in cerebral cortex, gGABAA(INPY ), because the control parameter, within a second simulation. PubMed ID:http://jpet.aspetjournals.org/content/154/1/64 At each and every time step of :ms, the conductance is decreased by :{ mS. As a result, the control parameter undergoes stepwise linear decay from an SF-837 biological activity initial value of :mS at time s to ONE one.MedChemExpress Pulchinenoside C orgFor a given activity of the network, the underlying parameter combitions form a complex parameter set in a highdimensiol parameter space, where each point in the parameter set of SW oscillations can be considered as a specific pathological instance, which corresponds to a particular individual suffering from epilepsy. As a result, the integrative view of mechanisms underlying epileptic seizures has direct implications on the optimal treatments of epilepsies. To discuss the implication on optimal therapeutic treatments, in this section, we first use simulation to show trajectory activities modified by drug intervention, then introduce the doseresponse relationship, define a drug optimization problem, and filly alyze results from the optimization. Trajectory activities modified by drug intervention. In this section, we show trajectory activities modified by drug intervention. We perform second simulations to demonstrate that the spikeandwave oscillation (seizure) could be switched back to normal spindle oscillation by modifying different network parameters with time gradually to mimic the effects of different drugs. Initially, the network is set to be oscillating in SW mode with gP :mScm and all the other parameters corresponding to the control condition. When a drug is applied, we assume all the target sypsesion channels in the network will be proportiolly affected. First, we use the conductances of all the GABAA receptor channels as the target parameters to reflect the effect of GABAA agonists. In the simulation, all the target parameters linearly scale up at each time step from an initial value of xGABAA at time s to xGABAA at time s, where xGABAA represents the target parameter values in the control condition. As shown in Fig. A and Fig. B, due to the increase of GABAA mediated inhibition, the mode of the network is transited from SW back to spindle at about s. Second, we demonstrate the effect of AMPA antagonists with all the conductances of AMPA receptor channels as the target parameters. In the simulation, all the target parameters linearly scale down at each time step from an initial value of xAMPA at time s to :xAMPA at time s, where xAMPA represents the.Llation and return to rest in a couple of cycles. Nevertheless, if the pulse is substantial enough, the network will show sustained oscillation. Normally, the sustained oscillation will be either spindle or delta wave according to the parameter setting of the network. This indicates that there exit a steady equilibrium point corresponding to the resting state in addition to a steady limit cycle corresponding to spindle or spikeandwave oscillation. Fig. shows the phase flows of spindle and spikeandwave oscillations in the twodimensiol subspace. The spindle oscillation is obtained from a second simulation using the parameters corresponding towards the control situation. The spikeandwave oscillation is obtained together with the identical set of parameters except that the conductance of GABAA receptors in cerebral cortex is set to be. The phase flows in Fig. B and Fig. D demonstrate the limit cycles corresponding to spindle and SW oscillations, respectively. To demonstrate the transition from spindle to spikeandwave, we make use of the conductance of GABAA receptors in cerebral cortex, gGABAA(INPY ), because the manage parameter, within a second simulation. PubMed ID:http://jpet.aspetjournals.org/content/154/1/64 At each time step of :ms, the conductance is decreased by :{ mS. As a result, the control parameter undergoes stepwise linear decay from an initial value of :mS at time s to ONE one.orgFor a given activity of the network, the underlying parameter combitions form a complex parameter set in a highdimensiol parameter space, where each point in the parameter set of SW oscillations can be considered as a specific pathological instance, which corresponds to a particular individual suffering from epilepsy. As a result, the integrative view of mechanisms underlying epileptic seizures has direct implications on the optimal treatments of epilepsies. To discuss the implication on optimal therapeutic treatments, in this section, we first use simulation to show trajectory activities modified by drug intervention, then introduce the doseresponse relationship, define a drug optimization problem, and filly alyze results from the optimization. Trajectory activities modified by drug intervention. In this section, we show trajectory activities modified by drug intervention. We perform second simulations to demonstrate that the spikeandwave oscillation (seizure) could be switched back to normal spindle oscillation by modifying different network parameters with time gradually to mimic the effects of different drugs. Initially, the network is set to be oscillating in SW mode with gP :mScm and all the other parameters corresponding to the control condition. When a drug is applied, we assume all the target sypsesion channels in the network will be proportiolly affected. First, we use the conductances of all the GABAA receptor channels as the target parameters to reflect the effect of GABAA agonists. In the simulation, all the target parameters linearly scale up at each time step from an initial value of xGABAA at time s to xGABAA at time s, where xGABAA represents the target parameter values in the control condition. As shown in Fig. A and Fig. B, due to the increase of GABAA mediated inhibition, the mode of the network is transited from SW back to spindle at about s. Second, we demonstrate the effect of AMPA antagonists with all the conductances of AMPA receptor channels as the target parameters. In the simulation, all the target parameters linearly scale down at each time step from an initial value of xAMPA at time s to :xAMPA at time s, where xAMPA represents the.