In Silico Laboratory Experiments Using Statistical Model Checking: A New Model of the Palytoxin-Induced Pump Channel as Case Study.

Studying biological systems is a difficult but important task. Traditional methods include laboratory experimentation and computer simulations. However, often researchers need to explore important but potentially rare events that are not easily observed or simulated. We use UPPAAL-SMC, a formal verification tool to support a methodology that allows us to model biological systems, specify events and conditions that we want to analyze, and to explore system executions using controlled simulations. We also describe an efficient way to reproduce laboratory experiments in silico. Unlike traditional simulations, we are able to guide the experiment to explore special events and conditions by expressing these conditions in temporal logic formulas. We have applied this methodology to create a more detailed model of Palytoxin-induced Na +/K + pump channels than was previously possible. Moreover, we have reproduced experimental protocols and their associated electrophysiological recordings, which has not been done in previous works. As a consequence, we have been able to propose a new diprotomeric model for the PTX-pump complex and study its behaviour. The use of our methodology has enabled us to reduce the effort and time to perform this research. It can be used to model and analyze other complex biological systems, potentially increasing the productivity of such studies.

Effects of A1 receptor agonist/antagonist on spontaneous seizures in pilocarpine-induced epileptic rats.

Adenosine is an endogenous anticonvulsant that activates pre- and postsynaptic adenosine A1 receptors. A1 receptor agonists increase the latency for the development of seizures and status epilepticus following pilocarpine administration. Although hippocampal adenosine is increased in the chronic phase of the pilocarpine model, it is not known whether the modulation of A1 receptors may influence the frequency of spontaneous recurrent seizures (SRS). Here, we tested the hypothesis that the A1 receptor agonist RPia ([R]-N-phenylisopropyladenosine) and the A1 antagonist DPCPX (8-Cyclopentyl-1,3-dipropylxanthine) administered to chronic pilocarpine epileptic rats would respectively decrease and increase the frequency of SRS and hippocampal excitability. Four months after Pilo-induced SE, chronic epileptic rats were video-monitored for the recording of SRS before (basal) and after a 2-week treatment with RPia (25µg/kg) or DPCPX (50µg/kg). Following sacrifice, brain slices were studied with electrophysiology. We found that rats given RPia had a 93% nonsignificant reduction in the frequency of seizures compared with their own pretreatment baseline. In contrast, the administration of DPCPX resulted in an 87% significant increase in seizure rate. Nontreated epileptic rats had a similar frequency of seizures along the study. Corroborating our behavioral data, in vitro recordings showed that slices from animals previously given DPCPX had a shorter latency to develop epileptiform activity, longer and higher DC shifts, and higher spike amplitude compared with slices from nontreated Pilo controls. In contrast, smaller spike amplitude was recorded in slices from animals given RPia. In summary, the administration of A1 agonists reduced hippocampal excitability but not the frequency of spontaneous recurrent seizures in chronic epileptic rats, whereas A1 receptor antagonists increased both.

Furthering our understanding of SUDEP: the role of animal models.

Sudden and unexpected death in epilepsy (SUDEP) is the most common type of death among patients with epilepsy. Here, we address the importance of the experimental models in search of the mechanisms underlying SUDEP. Most studies have investigated the cardiovascular responses in animal models of epilepsy. However, there are few proposed SUDEP models in literature. Hypoventilation, apnea, respiratory distress, pulmonary hypertension, autonomic dysregulation and arrhythmia are common findings in epilepsy models. Impairments on adenosinergic and serotonergic systems, brainstem spreading depolarization, seizure-activation of neural substrates related to cardiorespiratory control, altered autonomic control, and mutations on sodium and potassium channels are hypothesis suggested. Overall, current research highlights the evident multifactorial nature of SUDEP, which involves acute and chronic aspects ranging from systemic to molecular alterations. Thus, we are convinced that elucidation and prevention of SUDEP can be achieved only through the interaction between basic and clinical science.

Role of adenosine in the antiepileptic effects of deep brain stimulation.

Despite the effectiveness of anterior thalamic nucleus (AN) deep brain stimulation (DBS) for the treatment of epilepsy, mechanisms responsible for the antiepileptic effects of this therapy remain elusive. As adenosine modulates neuronal excitability and seizure activity in animal models, we hypothesized that this nucleoside could be one of the substrates involved in the effects of AN DBS. We applied 5 days of stimulation to rats rendered chronically epileptic by pilocarpine injections and recorded epileptiform activity in hippocampal slices. We found that slices from animals given DBS had reduced hippocampal excitability and were less susceptible to develop ictal activity. In live animals, AN DBS significantly increased adenosine levels in the hippocampus as measured by microdialysis. The reduced excitability of DBS in vitro was completely abolished in animals pre-treated with A1 receptor antagonists and was strongly potentiated by A1 receptor agonists. We conclude that some of the antiepileptic effects of DBS may be mediated by adenosine.

Effects of anterior thalamic nucleus deep brain stimulation in chronic epileptic rats.

Deep brain stimulation (DBS) has been investigated for the treatment of epilepsy. In rodents, an increase in the latency for the development of seizures and status epilepticus (SE) has been reported in different animal models but the consequences of delivering stimulation to chronic epileptic animals have not been extensively addressed. We study the effects of anterior thalamic nucleus (AN) stimulation at different current intensities in rats rendered epileptic following pilocarpine (Pilo) administration. Four months after Pilo-induced SE, chronic epileptic rats were bilaterally implanted with AN electrodes or had sham-surgery. Stimulation was delivered for 6 h/day, 5 days/week at 130 Hz, 90 µsec. and either 100 µA or 500 µA. The frequency of spontaneous recurrent seizures in animals receiving stimulation was compared to that recorded in the preoperative period and in rats given sham treatment. To investigate the effects of DBS on hippocampal excitability, brain slices from animals receiving AN DBS or sham surgery were studied with electrophysiology. We found that rats treated with AN DBS at 100 µA had a 52% non-significant reduction in the frequency of seizures as compared to sham-treated controls and 61% less seizures than at baseline. Animals given DBS at 500 µA had 5.1 times more seizures than controls and a 2.8 fold increase in seizure rate as compared to preoperative values. In non-stimulated controls, the average frequency of seizures before and after surgery remained unaltered. In vitro recordings have shown that slices from animals previously given DBS at 100 µA had a longer latency for the development of epileptiform activity, shorter and smaller DC shifts, and a smaller spike amplitude compared to non-stimulated controls. In contrast, a higher spike amplitude was recorded in slices from animals given AN DBS at 500 µA.

Palytoxin and the sodium/potassium pump--phosphorylation and potassium interaction.

We proposed a reaction model for investigating interactions between K+ and the palytoxin-sodium-potassium (PTX-Na+/K+) pump complex under conditions where enzyme phosphorylation may occur. The model is composed of (i) the Albers-Post model for Na+/K+-ATPase, describing Na+ and K+ pumping; (ii) the reaction model proposed for Na+/K+-ATPase interactions with its ligands (Na+, K+, ATP, ADP and P) and with PTX. A mathematical model derived for representing the reactions was used to simulate experimental studies of the PTX-induced current, in different concentrations for the pump ligands. The simulations allow interpretation of the simultaneous action of Na+/K+-ATPase phosphorylation and K+ on the PTX-induced channels. The results suggest that(i) phosphorylation increases the PTX toxic effect, increasing its affinity and reducing the K+occlusion rate, and (ii) K+ causes channel blockage, increases the toxin dissociation rate and impedes the induced channel phosphorylation, implying reduction of the PTX toxic effect.